TSTP Solution File: SEU219+2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU219+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:08:24 EDT 2022
% Result : Theorem 3.31s 3.71s
% Output : CNFRefutation 16.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 279
% Syntax : Number of formulae : 6245 (2507 unt; 111 typ; 0 def)
% Number of atoms : 60328 (21617 equ; 0 cnn)
% Maximal formula atoms : 15 ( 9 avg)
% Number of connectives : 136140 (23071 ~;23842 |; 820 &;87973 @)
% ( 140 <=>; 294 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 217 ( 217 >; 0 *; 0 +; 0 <<)
% Number of symbols : 114 ( 111 usr; 12 con; 0-5 aty)
% Number of variables : 19756 ( 0 ^19714 !; 42 ?;19756 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_are_equipotent,type,
are_equipotent: $i > $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_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_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_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_powerset,type,
powerset: $i > $i ).
thf(tp_proper_subset,type,
proper_subset: $i > $i > $o ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_composition,type,
relation_composition: $i > $i > $i ).
thf(tp_relation_dom,type,
relation_dom: $i > $i ).
thf(tp_relation_dom_restriction,type,
relation_dom_restriction: $i > $i > $i ).
thf(tp_relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
thf(tp_relation_field,type,
relation_field: $i > $i ).
thf(tp_relation_image,type,
relation_image: $i > $i > $i ).
thf(tp_relation_inverse,type,
relation_inverse: $i > $i ).
thf(tp_relation_inverse_image,type,
relation_inverse_image: $i > $i > $i ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_relation_rng_restriction,type,
relation_rng_restriction: $i > $i > $i ).
thf(tp_sK10_SY395,type,
sK10_SY395: $i > $i > $i > $i ).
thf(tp_sK11_C,type,
sK11_C: $i > $i > $i ).
thf(tp_sK12_SY396,type,
sK12_SY396: $i > $i > $i ).
thf(tp_sK13_D,type,
sK13_D: $i > $i > $i > $i ).
thf(tp_sK14_D,type,
sK14_D: $i > $i > $i > $i ).
thf(tp_sK15_C,type,
sK15_C: $i > $i > $i ).
thf(tp_sK16_SY398,type,
sK16_SY398: $i > $i > $i ).
thf(tp_sK17_D,type,
sK17_D: $i > $i > $i > $i ).
thf(tp_sK18_C,type,
sK18_C: $i > $i > $i ).
thf(tp_sK19_C,type,
sK19_C: $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_SY399,type,
sK20_SY399: $i > $i > $i ).
thf(tp_sK21_E,type,
sK21_E: $i > $i > $i > $i > $i ).
thf(tp_sK22_SY400,type,
sK22_SY400: $i > $i > $i > $i > $i ).
thf(tp_sK23_D,type,
sK23_D: $i > $i > $i > $i ).
thf(tp_sK24_SY403,type,
sK24_SY403: $i > $i > $i > $i ).
thf(tp_sK25_SY405,type,
sK25_SY405: $i > $i > $i > $i ).
thf(tp_sK26_D,type,
sK26_D: $i > $i > $i > $i ).
thf(tp_sK27_D,type,
sK27_D: $i > $i > $i > $i ).
thf(tp_sK28_C,type,
sK28_C: $i > $i > $i ).
thf(tp_sK29_B,type,
sK29_B: $i > $i ).
thf(tp_sK2_B,type,
sK2_B: $i > $i ).
thf(tp_sK30_C,type,
sK30_C: $i > $i > $i ).
thf(tp_sK31_D,type,
sK31_D: $i > $i > $i > $i ).
thf(tp_sK32_C,type,
sK32_C: $i > $i > $i ).
thf(tp_sK33_SY406,type,
sK33_SY406: $i > $i > $i ).
thf(tp_sK34_E,type,
sK34_E: $i > $i > $i > $i > $i ).
thf(tp_sK35_D,type,
sK35_D: $i > $i > $i > $i ).
thf(tp_sK36_SY409,type,
sK36_SY409: $i > $i > $i > $i ).
thf(tp_sK37_E,type,
sK37_E: $i > $i > $i > $i > $i ).
thf(tp_sK38_D,type,
sK38_D: $i > $i > $i > $i ).
thf(tp_sK39_SY411,type,
sK39_SY411: $i > $i > $i > $i ).
thf(tp_sK3_SY386,type,
sK3_SY386: $i > $i > $i ).
thf(tp_sK40_D,type,
sK40_D: $i > $i > $i > $i ).
thf(tp_sK41_SY412,type,
sK41_SY412: $i > $i > $i > $i ).
thf(tp_sK42_D,type,
sK42_D: $i > $i > $i > $i ).
thf(tp_sK43_SY413,type,
sK43_SY413: $i > $i > $i > $i ).
thf(tp_sK44_C,type,
sK44_C: $i > $i > $i ).
thf(tp_sK45_SY414,type,
sK45_SY414: $i > $i > $i ).
thf(tp_sK46_B,type,
sK46_B: $i > $i ).
thf(tp_sK47_SY415,type,
sK47_SY415: $i > $i ).
thf(tp_sK48_C,type,
sK48_C: $i > $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_C,type,
sK50_C: $i > $i > $i ).
thf(tp_sK51_D,type,
sK51_D: $i > $i > $i > $i ).
thf(tp_sK52_D,type,
sK52_D: $i > $i > $i > $i ).
thf(tp_sK53_A,type,
sK53_A: $i ).
thf(tp_sK54_A,type,
sK54_A: $i ).
thf(tp_sK55_A,type,
sK55_A: $i ).
thf(tp_sK56_A,type,
sK56_A: $i ).
thf(tp_sK57_A,type,
sK57_A: $i ).
thf(tp_sK58_A,type,
sK58_A: $i ).
thf(tp_sK59_D,type,
sK59_D: $i > $i > $i > $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_sK60_C,type,
sK60_C: $i > $i > $i ).
thf(tp_sK61_SY417,type,
sK61_SY417: $i > $i > $i ).
thf(tp_sK62_D,type,
sK62_D: $i > $i > $i > $i ).
thf(tp_sK63_C,type,
sK63_C: $i > $i > $i ).
thf(tp_sK64_SY419,type,
sK64_SY419: $i > $i > $i ).
thf(tp_sK65_C,type,
sK65_C: $i > $i > $i ).
thf(tp_sK66_SY420,type,
sK66_SY420: $i > $i > $i ).
thf(tp_sK67_C,type,
sK67_C: $i > $i > $i ).
thf(tp_sK68_SY421,type,
sK68_SY421: $i > $i > $i ).
thf(tp_sK69_B,type,
sK69_B: $i > $i ).
thf(tp_sK6_A,type,
sK6_A: $i ).
thf(tp_sK70_C,type,
sK70_C: $i > $i > $i ).
thf(tp_sK71_SY424,type,
sK71_SY424: $i > $i > $i ).
thf(tp_sK7_F,type,
sK7_F: $i > $i > $i > $i > $i > $i ).
thf(tp_sK8_D,type,
sK8_D: $i > $i > $i > $i ).
thf(tp_sK9_SY391,type,
sK9_SY391: $i > $i > $i > $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(tp_set_meet,type,
set_meet: $i > $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subset_complement,type,
subset_complement: $i > $i > $i ).
thf(tp_subset_difference,type,
subset_difference: $i > $i > $i > $i ).
thf(tp_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(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 )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(4,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(7,axiom,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(9,axiom,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(10,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(11,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(12,axiom,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(14,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] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(20,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(21,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(22,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(24,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(25,axiom,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(26,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(28,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(29,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(32,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(36,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(37,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(38,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(39,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(40,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(41,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(42,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(44,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(45,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(46,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(47,axiom,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(48,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(49,axiom,
! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
thf(50,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(51,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(52,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(53,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(54,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(55,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(56,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_inverse @ A ) )
& ( relation @ ( relation_inverse @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc11_relat_1) ).
thf(57,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(61,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(63,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(66,axiom,
! [A: $i] : ( relation @ ( identity_relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(68,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(71,axiom,
! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(81,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(89,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(90,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(92,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(93,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(94,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(95,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(98,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(99,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(100,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(102,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(103,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(104,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(105,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(106,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(107,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(108,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(109,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(110,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(111,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(112,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(113,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(114,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(115,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(116,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(117,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(118,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(119,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(120,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(121,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(122,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(123,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(124,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(126,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(127,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(128,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(130,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(133,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(134,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(135,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(136,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(138,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(139,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(140,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(141,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(143,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(144,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(145,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(146,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(149,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(150,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(151,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(152,axiom,
! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(153,axiom,
( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).
thf(154,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(156,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(158,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(159,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(162,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(163,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(165,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(166,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(167,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(168,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(170,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(171,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(172,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(173,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(174,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(175,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(176,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(177,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(178,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(179,axiom,
! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(180,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(181,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(182,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(183,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(184,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(185,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(186,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(187,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(188,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(189,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(190,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(191,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(192,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(193,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(195,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(196,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(197,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(198,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(199,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(200,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(201,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(202,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(203,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(204,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(205,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(206,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(207,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(209,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(210,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(211,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(212,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(213,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(214,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(215,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(216,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(218,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(220,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(221,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(222,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(225,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(226,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(229,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(230,axiom,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(231,conjecture,
! [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(232,negated_conjecture,
( ( ! [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 ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[231]) ).
thf(233,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 ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[232]) ).
thf(234,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(235,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(236,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(237,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(238,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(239,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(240,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(241,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(242,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(243,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(244,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(245,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(246,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(247,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(248,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(249,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(250,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(251,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(252,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(253,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(254,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(255,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(256,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(257,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(258,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(259,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(260,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)],[92]) ).
thf(261,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(262,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)],[94]) ).
thf(263,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)],[99]) ).
thf(264,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)],[100]) ).
thf(265,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)],[103]) ).
thf(266,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)],[104]) ).
thf(267,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(268,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)],[106]) ).
thf(269,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)],[107]) ).
thf(270,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)],[108]) ).
thf(271,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)],[109]) ).
thf(272,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)],[110]) ).
thf(273,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(274,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(275,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(276,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)],[115]) ).
thf(277,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)],[117]) ).
thf(278,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)],[118]) ).
thf(279,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)],[119]) ).
thf(280,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)],[120]) ).
thf(281,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(282,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)],[122]) ).
thf(283,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(284,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(285,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(286,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_dom_restriction @ B @ A )
= ( relation_composition @ ( identity_relation @ A ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(287,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(288,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)],[138]) ).
thf(289,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)],[139]) ).
thf(290,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(291,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)],[144]) ).
thf(292,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(293,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(294,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(295,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(296,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)],[158]) ).
thf(297,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(298,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(299,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(300,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(301,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(302,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)],[172]) ).
thf(303,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(304,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(305,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)],[175]) ).
thf(306,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(307,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(308,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(309,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ A )
=> ( ( apply @ ( identity_relation @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(310,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)],[181]) ).
thf(311,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)],[182]) ).
thf(312,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)],[183]) ).
thf(313,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)],[184]) ).
thf(314,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(315,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(316,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)],[187]) ).
thf(317,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)],[189]) ).
thf(318,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)],[190]) ).
thf(319,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)],[192]) ).
thf(320,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(321,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)],[196]) ).
thf(322,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(323,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)],[199]) ).
thf(324,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)],[201]) ).
thf(325,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)],[206]) ).
thf(326,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(327,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)],[210]) ).
thf(328,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)],[212]) ).
thf(329,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)],[218]) ).
thf(330,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)],[220]) ).
thf(331,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(332,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(333,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(334,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(335,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(336,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(337,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(338,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(339,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(340,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(341,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(342,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(343,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(344,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)],[36]) ).
thf(345,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(346,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(347,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(348,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(349,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(350,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)],[45]) ).
thf(351,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(352,plain,
( ( ! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(353,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(354,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)],[54]) ).
thf(355,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_inverse @ A ) )
& ( relation @ ( relation_inverse @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(356,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)],[57]) ).
thf(357,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(358,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(359,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(360,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(361,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(362,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( function_inverse @ A ) )
& ( function @ ( function_inverse @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(363,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( ( function_inverse @ A )
= ( relation_inverse @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(364,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(365,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)],[98]) ).
thf(366,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)],[102]) ).
thf(367,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)],[111]) ).
thf(368,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)],[116]) ).
thf(369,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(370,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(371,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(372,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(373,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)],[136]) ).
thf(374,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(375,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)],[141]) ).
thf(376,plain,
( ( ! [A: $i] :
( ( ( relation_dom @ ( identity_relation @ A ) )
= A )
& ( ( relation_rng @ ( identity_relation @ A ) )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(377,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_dom @ A )
= empty_set )
<=> ( ( relation_rng @ A )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(378,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
=> ( A = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(379,plain,
( ( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(380,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)],[156]) ).
thf(381,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)],[162]) ).
thf(382,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)],[165]) ).
thf(383,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)],[167]) ).
thf(384,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)],[168]) ).
thf(385,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)],[178]) ).
thf(386,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)],[188]) ).
thf(387,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(388,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)],[193]) ).
thf(389,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)],[198]) ).
thf(390,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(391,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)],[202]) ).
thf(392,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(393,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)],[204]) ).
thf(394,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(395,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)],[207]) ).
thf(396,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)],[211]) ).
thf(397,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(398,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(399,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(400,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)],[216]) ).
thf(401,plain,
( ( ( ( relation @ sK1_A )
& ( function @ sK1_A ) )
=> ( ( one_to_one @ sK1_A )
=> ( ( ( relation_rng @ sK1_A )
= ( relation_dom @ ( function_inverse @ sK1_A ) ) )
& ( ( relation_dom @ sK1_A )
= ( relation_rng @ ( function_inverse @ sK1_A ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[233]) ).
thf(402,plain,
( ( relation @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[401]) ).
thf(403,plain,
( ( function @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[401]) ).
thf(404,plain,
( ( one_to_one @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[401]) ).
thf(405,plain,
( ( ( ( relation_rng @ sK1_A )
= ( relation_dom @ ( function_inverse @ sK1_A ) ) )
& ( ( relation_dom @ sK1_A )
= ( relation_rng @ ( function_inverse @ sK1_A ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[401]) ).
thf(406,plain,
( ( ( relation_rng @ sK1_A )
= ( relation_dom @ ( function_inverse @ sK1_A ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[405]) ).
thf(407,plain,
( ( ( relation_dom @ sK1_A )
= ( relation_rng @ ( function_inverse @ sK1_A ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[405]) ).
thf(408,plain,
( ( ( ( relation_rng @ sK1_A )
!= ( relation_dom @ ( function_inverse @ sK1_A ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[406]) ).
thf(409,plain,
( ( ( ( relation_dom @ sK1_A )
!= ( relation_rng @ ( function_inverse @ sK1_A ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[407]) ).
thf(410,plain,
( ( ! [A: $i] :
( ! [SY384: $i] :
( ~ ( subset @ SY384 @ ( sK2_B @ A ) )
| ( are_equipotent @ SY384 @ ( sK2_B @ A ) )
| ( in @ SY384 @ ( sK2_B @ A ) ) )
& ! [SY385: $i] :
( ( ! [SY390: $i] :
( ~ ( subset @ SY390 @ SY385 )
| ( in @ SY390 @ ( sK3_SY386 @ SY385 @ A ) ) )
& ( in @ ( sK3_SY386 @ SY385 @ A ) @ ( sK2_B @ A ) ) )
| ~ ( in @ SY385 @ ( sK2_B @ A ) ) )
& ! [SY388: $i,SY389: $i] :
( ~ ( in @ SY388 @ ( sK2_B @ A ) )
| ~ ( subset @ SY389 @ SY388 )
| ( in @ SY389 @ ( sK2_B @ A ) ) )
& ( in @ A @ ( sK2_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[234]) ).
thf(411,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[235]) ).
thf(412,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[236]) ).
thf(413,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[237]) ).
thf(414,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)],[240]) ).
thf(415,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[241]) ).
thf(416,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[243]) ).
thf(417,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[245]) ).
thf(418,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[246]) ).
thf(419,plain,
( ( empty @ sK6_A )
= $true ),
inference(extcnf_combined,[status(esa)],[247]) ).
thf(420,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[248]) ).
thf(421,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[249]) ).
thf(422,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[250]) ).
thf(423,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[251]) ).
thf(424,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[253]) ).
thf(425,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)],[259]) ).
thf(426,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ! [SY394: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ C @ B @ A ) @ SY394 ) @ A )
| ~ ( in @ ( ordered_pair @ SY394 @ ( sK9_SY391 @ C @ B @ A ) ) @ B ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ C @ B @ A ) @ ( sK9_SY391 @ C @ B @ A ) ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK8_D @ C @ B @ A ) @ ( sK10_SY395 @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK10_SY395 @ C @ B @ A ) @ ( sK9_SY391 @ C @ B @ A ) ) @ B ) )
| ( in @ ( ordered_pair @ ( sK8_D @ C @ B @ A ) @ ( sK9_SY391 @ 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 @ ( sK7_F @ E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK7_F @ E @ D @ C @ B @ A ) @ E ) @ B ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[260]) ).
thf(427,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)],[261]) ).
thf(428,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK11_C @ B @ A ) @ ( sK12_SY396 @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ B @ A ) @ ( sK11_C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( sK11_C @ B @ A ) @ ( sK12_SY396 @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK12_SY396 @ B @ A ) @ ( sK11_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)],[262]) ).
thf(429,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK13_D @ C @ B @ A ) @ A )
| ( in @ ( sK13_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK13_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK13_D @ C @ B @ A ) @ A )
| ( in @ ( sK13_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK13_D @ C @ B @ A ) @ B )
| ( in @ ( sK13_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)],[263]) ).
thf(430,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY397: $i] :
( ~ ( in @ ( sK15_C @ B @ A ) @ SY397 )
| ~ ( in @ SY397 @ A ) )
| ~ ( in @ ( sK15_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK15_C @ B @ A ) @ ( sK16_SY398 @ B @ A ) )
& ( in @ ( sK16_SY398 @ B @ A ) @ A ) )
| ( in @ ( sK15_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 @ ( sK14_D @ C @ B @ A ) )
& ( in @ ( sK14_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[264]) ).
thf(431,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)],[265]) ).
thf(432,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK17_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK17_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK17_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK17_D @ C @ B @ A ) @ A )
| ( in @ ( sK17_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK17_D @ C @ B @ A ) @ B )
| ( in @ ( sK17_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)],[266]) ).
thf(433,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK18_C @ B @ A ) @ A )
& ~ ( in @ ( sK18_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)],[267]) ).
thf(434,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( in @ ( ordered_pair @ ( sK19_C @ B @ A ) @ ( sK20_SY399 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK19_C @ B @ A ) @ ( sK20_SY399 @ 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)],[268]) ).
thf(435,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY401: $i,SY402: $i] :
( ~ ( in @ SY401 @ A )
| ~ ( in @ SY402 @ B )
| ( ( sK23_D @ C @ B @ A )
!= ( ordered_pair @ SY401 @ SY402 ) ) )
| ~ ( in @ ( sK23_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK24_SY403 @ C @ B @ A ) @ A )
& ( in @ ( sK25_SY405 @ C @ B @ A ) @ B )
& ( ( sK23_D @ C @ B @ A )
= ( ordered_pair @ ( sK24_SY403 @ C @ B @ A ) @ ( sK25_SY405 @ C @ B @ A ) ) ) )
| ( in @ ( sK23_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 @ ( sK21_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK22_SY400 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK21_E @ D @ C @ B @ A ) @ ( sK22_SY400 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[269]) ).
thf(436,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK26_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK26_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK26_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK26_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK26_D @ C @ B @ A ) @ C )
| ( in @ ( sK26_D @ C @ B @ A ) @ A )
| ( in @ ( sK26_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)],[270]) ).
thf(437,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK27_D @ C @ B @ A ) @ C )
| ( ( sK27_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK27_D @ C @ B @ A ) @ C )
| ( ( sK27_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK27_D @ C @ B @ A ) @ C )
| ( ( sK27_D @ C @ B @ A )
= A )
| ( ( sK27_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)],[271]) ).
thf(438,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)],[272]) ).
thf(439,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK28_C @ B @ A ) @ B )
| ~ ( subset @ ( sK28_C @ B @ A ) @ A ) )
& ( ( in @ ( sK28_C @ B @ A ) @ B )
| ( subset @ ( sK28_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)],[273]) ).
thf(440,plain,
( ( ! [A: $i] :
( ( in @ ( sK29_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[274]) ).
thf(441,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK30_C @ B @ A )
!= A )
| ~ ( in @ ( sK30_C @ B @ A ) @ B ) )
& ( ( ( sK30_C @ B @ A )
= A )
| ( in @ ( sK30_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)],[275]) ).
thf(442,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( ( ( ( in @ ( sK33_SY406 @ B @ A ) @ A )
& ~ ( in @ ( sK32_C @ B @ A ) @ ( sK33_SY406 @ B @ A ) ) )
| ~ ( in @ ( sK32_C @ B @ A ) @ B ) )
& ( ! [SY407: $i] :
( ~ ( in @ SY407 @ A )
| ( in @ ( sK32_C @ B @ A ) @ SY407 ) )
| ( in @ ( sK32_C @ B @ A ) @ B ) ) )
| ( B
= ( set_meet @ A ) ) ) )
& ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( ! [C: $i] :
( ( ( in @ ( sK31_D @ C @ B @ A ) @ A )
& ~ ( in @ C @ ( sK31_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)],[276]) ).
thf(443,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY408: $i] :
( ~ ( in @ ( ordered_pair @ ( sK35_D @ C @ B @ A ) @ SY408 ) @ A )
| ~ ( in @ SY408 @ B ) )
| ~ ( in @ ( sK35_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK35_D @ C @ B @ A ) @ ( sK36_SY409 @ C @ B @ A ) ) @ A )
& ( in @ ( sK36_SY409 @ C @ B @ A ) @ B ) )
| ( in @ ( sK35_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 @ ( sK34_E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( sK34_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[277]) ).
thf(444,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY410: $i] :
( ~ ( in @ ( ordered_pair @ SY410 @ ( sK38_D @ C @ B @ A ) ) @ A )
| ~ ( in @ SY410 @ B ) )
| ~ ( in @ ( sK38_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK39_SY411 @ C @ B @ A ) @ ( sK38_D @ C @ B @ A ) ) @ A )
& ( in @ ( sK39_SY411 @ C @ B @ A ) @ B ) )
| ( in @ ( sK38_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 @ ( sK37_E @ D @ C @ B @ A ) @ D ) @ A )
& ( in @ ( sK37_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[278]) ).
thf(445,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK41_SY412 @ C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ C @ B @ A ) @ ( sK41_SY412 @ C @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ C @ B @ A ) @ ( sK41_SY412 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK41_SY412 @ C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK40_D @ C @ B @ A ) @ ( sK41_SY412 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK40_D @ C @ B @ A ) @ ( sK41_SY412 @ C @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK40_D @ C @ B @ A ) @ ( sK41_SY412 @ 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)],[279]) ).
thf(446,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK42_D @ C @ B @ A ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ C @ B @ A ) @ ( sK43_SY413 @ C @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ C @ B @ A ) @ ( sK43_SY413 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK42_D @ C @ B @ A ) @ B )
| ( in @ ( ordered_pair @ ( sK42_D @ C @ B @ A ) @ ( sK43_SY413 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK42_D @ C @ B @ A ) @ ( sK43_SY413 @ C @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK42_D @ C @ B @ A ) @ ( sK43_SY413 @ 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)],[280]) ).
thf(447,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)],[281]) ).
thf(448,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( ( ( sK44_C @ B @ A )
!= ( sK45_SY414 @ B @ A ) )
| ~ ( in @ ( sK44_C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ B @ A ) @ ( sK45_SY414 @ B @ A ) ) @ B ) )
& ( ( ( sK44_C @ B @ A )
= ( sK45_SY414 @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK44_C @ B @ A ) @ ( sK45_SY414 @ B @ A ) ) @ B ) )
& ( ( in @ ( sK44_C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK44_C @ B @ A ) @ ( sK45_SY414 @ 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)],[282]) ).
thf(449,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[285]) ).
thf(450,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( relation_dom_restriction @ B @ A )
= ( relation_composition @ ( identity_relation @ A ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[286]) ).
thf(451,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[287]) ).
thf(452,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)],[288]) ).
thf(453,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)],[289]) ).
thf(454,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)],[291]) ).
thf(455,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[292]) ).
thf(456,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[293]) ).
thf(457,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[294]) ).
thf(458,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK46_B @ A ) @ ( sK47_SY415 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[295]) ).
thf(459,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK48_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)],[296]) ).
thf(460,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[298]) ).
thf(461,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[299]) ).
thf(462,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[301]) ).
thf(463,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK49_C @ B @ A ) @ A )
& ( in @ ( sK49_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)],[302]) ).
thf(464,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)],[303]) ).
thf(465,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)],[305]) ).
thf(466,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)],[306]) ).
thf(467,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)],[307]) ).
thf(468,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ A )
| ( ( apply @ ( identity_relation @ A ) @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[309]) ).
thf(469,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ( in @ ( sK50_C @ B @ A ) @ A )
& ( ( apply @ B @ ( sK50_C @ B @ A ) )
!= ( sK50_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)],[310]) ).
thf(470,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)],[311]) ).
thf(471,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)],[312]) ).
thf(472,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)],[313]) ).
thf(473,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[315]) ).
thf(474,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)],[316]) ).
thf(475,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)],[317]) ).
thf(476,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)],[318]) ).
thf(477,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)],[319]) ).
thf(478,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[320]) ).
thf(479,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)],[321]) ).
thf(480,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)],[323]) ).
thf(481,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 @ ( sK51_D @ C @ B @ A ) @ ( relation_rng @ C ) )
& ( in @ ( ordered_pair @ A @ ( sK51_D @ C @ B @ A ) ) @ C )
& ( in @ ( sK51_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[324]) ).
thf(482,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 @ ( sK52_D @ C @ B @ A ) @ ( relation_dom @ C ) )
& ( in @ ( ordered_pair @ ( sK52_D @ C @ B @ A ) @ A ) @ C )
& ( in @ ( sK52_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[325]) ).
thf(483,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[326]) ).
thf(484,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)],[327]) ).
thf(485,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)],[328]) ).
thf(486,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)],[329]) ).
thf(487,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)],[330]) ).
thf(488,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[331]) ).
thf(489,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)],[332]) ).
thf(490,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)],[333]) ).
thf(491,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)],[334]) ).
thf(492,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[335]) ).
thf(493,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(extcnf_combined,[status(esa)],[336]) ).
thf(494,plain,
( ( ( relation @ sK53_A )
& ( relation_empty_yielding @ sK53_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[337]) ).
thf(495,plain,
( ( ( function @ sK54_A )
& ( relation @ sK54_A )
& ( one_to_one @ sK54_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[338]) ).
thf(496,plain,
( ( ~ ( empty @ sK55_A )
& ( relation @ sK55_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[339]) ).
thf(497,plain,
( ( ( empty @ sK56_A )
& ( relation @ sK56_A )
& ( function @ sK56_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[340]) ).
thf(498,plain,
( ( ( empty @ sK57_A )
& ( relation @ sK57_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[341]) ).
thf(499,plain,
( ( ( function @ sK58_A )
& ( relation @ sK58_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[342]) ).
thf(500,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[343]) ).
thf(501,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)],[344]) ).
thf(502,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[345]) ).
thf(503,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[346]) ).
thf(504,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[347]) ).
thf(505,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[348]) ).
thf(506,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)],[350]) ).
thf(507,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[351]) ).
thf(508,plain,
( ( ! [A: $i] : ( function @ ( identity_relation @ A ) )
& ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[352]) ).
thf(509,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[353]) ).
thf(510,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)],[354]) ).
thf(511,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_inverse @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[355]) ).
thf(512,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)],[356]) ).
thf(513,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[357]) ).
thf(514,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[358]) ).
thf(515,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[360]) ).
thf(516,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[361]) ).
thf(517,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)],[362]) ).
thf(518,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ( function_inverse @ A )
= ( relation_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[363]) ).
thf(519,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[364]) ).
thf(520,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY416: $i] :
~ ( in @ ( ordered_pair @ SY416 @ ( sK60_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK60_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK61_SY417 @ B @ A ) @ ( sK60_C @ B @ A ) ) @ A )
| ( in @ ( sK60_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 @ ( sK59_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[365]) ).
thf(521,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY418: $i] :
~ ( in @ ( ordered_pair @ ( sK63_C @ B @ A ) @ SY418 ) @ A )
| ~ ( in @ ( sK63_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK63_C @ B @ A ) @ ( sK64_SY419 @ B @ A ) ) @ A )
| ( in @ ( sK63_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 @ ( sK62_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[366]) ).
thf(522,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK65_C @ B @ A ) @ ( sK66_SY420 @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ B @ A ) @ ( sK66_SY420 @ B @ A ) ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK65_C @ B @ A ) @ ( sK66_SY420 @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK65_C @ B @ A ) @ ( sK66_SY420 @ 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)],[367]) ).
thf(523,plain,
( ( ! [A: $i] :
( ( ! [SY422: $i,SY423: $i] :
( ( sK69_B @ A )
!= ( ordered_pair @ SY422 @ SY423 ) )
& ( in @ ( sK69_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK67_C @ B @ A ) @ ( sK68_SY421 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[368]) ).
thf(524,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)],[369]) ).
thf(525,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[370]) ).
thf(526,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[371]) ).
thf(527,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[372]) ).
thf(528,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)],[373]) ).
thf(529,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[374]) ).
thf(530,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)],[375]) ).
thf(531,plain,
( ( ! [A: $i] :
( ( relation_dom @ ( identity_relation @ A ) )
= A )
& ! [A: $i] :
( ( relation_rng @ ( identity_relation @ A ) )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[376]) ).
thf(532,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)],[377]) ).
thf(533,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)],[378]) ).
thf(534,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ! [B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ( ( ( sK71_SY424 @ B @ A )
= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ( ( sK70_C @ B @ A )
= ( apply @ A @ ( sK71_SY424 @ B @ A ) ) ) )
& ( ( ( sK71_SY424 @ B @ A )
= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ( in @ ( sK71_SY424 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( ( sK71_SY424 @ B @ A )
= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ( ( sK71_SY424 @ B @ A )
!= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ~ ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) ) )
& ( ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) )
| ( ( sK70_C @ B @ A )
= ( apply @ A @ ( sK71_SY424 @ B @ A ) ) ) )
& ( ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) )
| ( in @ ( sK71_SY424 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) )
| ( ( sK71_SY424 @ B @ A )
!= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ~ ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) ) )
& ( ( ( sK70_C @ B @ A )
!= ( apply @ A @ ( sK71_SY424 @ B @ A ) ) )
| ~ ( in @ ( sK71_SY424 @ B @ A ) @ ( relation_dom @ A ) )
| ( ( sK70_C @ B @ A )
= ( apply @ A @ ( sK71_SY424 @ B @ A ) ) ) )
& ( ( ( sK70_C @ B @ A )
!= ( apply @ A @ ( sK71_SY424 @ B @ A ) ) )
| ~ ( in @ ( sK71_SY424 @ B @ A ) @ ( relation_dom @ A ) )
| ( in @ ( sK71_SY424 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( ( sK70_C @ B @ A )
!= ( apply @ A @ ( sK71_SY424 @ B @ A ) ) )
| ~ ( in @ ( sK71_SY424 @ B @ A ) @ ( relation_dom @ A ) )
| ( ( sK71_SY424 @ B @ A )
!= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ~ ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) ) ) )
| ( ( relation_dom @ B )
!= ( relation_rng @ A ) )
| ( B
= ( function_inverse @ A ) ) )
& ! [B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( B
!= ( function_inverse @ A ) )
| ( ! [C: $i,D: $i] :
( ( D
!= ( apply @ B @ C ) )
| ~ ( in @ C @ ( relation_rng @ A ) )
| ( C
= ( apply @ A @ D ) ) )
& ! [C: $i,D: $i] :
( ( D
!= ( apply @ B @ C ) )
| ~ ( in @ C @ ( relation_rng @ A ) )
| ( in @ D @ ( relation_dom @ A ) ) )
& ! [C: $i,D: $i] :
( ( C
!= ( apply @ A @ D ) )
| ~ ( in @ D @ ( relation_dom @ A ) )
| ( D
= ( apply @ B @ C ) ) )
& ! [C: $i] :
( ! [D: $i] :
( ( C
!= ( apply @ A @ D ) )
| ~ ( in @ D @ ( relation_dom @ A ) ) )
| ( in @ C @ ( relation_rng @ A ) ) ) ) )
& ! [B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( B
!= ( function_inverse @ A ) )
| ( ( relation_dom @ B )
= ( relation_rng @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[380]) ).
thf(535,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)],[381]) ).
thf(536,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)],[382]) ).
thf(537,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)],[383]) ).
thf(538,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)],[384]) ).
thf(539,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)],[385]) ).
thf(540,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)],[386]) ).
thf(541,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[387]) ).
thf(542,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)],[388]) ).
thf(543,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)],[389]) ).
thf(544,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[390]) ).
thf(545,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)],[391]) ).
thf(546,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[392]) ).
thf(547,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)],[393]) ).
thf(548,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[394]) ).
thf(549,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)],[395]) ).
thf(550,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)],[396]) ).
thf(551,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[397]) ).
thf(552,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[398]) ).
thf(553,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[399]) ).
thf(554,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)],[400]) ).
thf(555,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)],[554]) ).
thf(556,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[553]) ).
thf(557,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[552]) ).
thf(558,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[551]) ).
thf(559,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)],[550]) ).
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(copy,[status(thm)],[549]) ).
thf(561,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[548]) ).
thf(562,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)],[547]) ).
thf(563,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[546]) ).
thf(564,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)],[545]) ).
thf(565,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[544]) ).
thf(566,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)],[543]) ).
thf(567,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)],[542]) ).
thf(568,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[541]) ).
thf(569,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)],[540]) ).
thf(570,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)],[539]) ).
thf(571,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[538]) ).
thf(572,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[537]) ).
thf(573,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)],[536]) ).
thf(574,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)],[535]) ).
thf(575,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ! [B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ( ( ( sK71_SY424 @ B @ A )
= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ( ( sK70_C @ B @ A )
= ( apply @ A @ ( sK71_SY424 @ B @ A ) ) ) )
& ( ( ( sK71_SY424 @ B @ A )
= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ( in @ ( sK71_SY424 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( ( sK71_SY424 @ B @ A )
= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ( ( sK71_SY424 @ B @ A )
!= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ~ ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) ) )
& ( ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) )
| ( ( sK70_C @ B @ A )
= ( apply @ A @ ( sK71_SY424 @ B @ A ) ) ) )
& ( ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) )
| ( in @ ( sK71_SY424 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) )
| ( ( sK71_SY424 @ B @ A )
!= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ~ ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) ) )
& ( ( ( sK70_C @ B @ A )
!= ( apply @ A @ ( sK71_SY424 @ B @ A ) ) )
| ~ ( in @ ( sK71_SY424 @ B @ A ) @ ( relation_dom @ A ) )
| ( ( sK70_C @ B @ A )
= ( apply @ A @ ( sK71_SY424 @ B @ A ) ) ) )
& ( ( ( sK70_C @ B @ A )
!= ( apply @ A @ ( sK71_SY424 @ B @ A ) ) )
| ~ ( in @ ( sK71_SY424 @ B @ A ) @ ( relation_dom @ A ) )
| ( in @ ( sK71_SY424 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( ( sK70_C @ B @ A )
!= ( apply @ A @ ( sK71_SY424 @ B @ A ) ) )
| ~ ( in @ ( sK71_SY424 @ B @ A ) @ ( relation_dom @ A ) )
| ( ( sK71_SY424 @ B @ A )
!= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ~ ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) ) ) )
| ( ( relation_dom @ B )
!= ( relation_rng @ A ) )
| ( B
= ( function_inverse @ A ) ) )
& ! [B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( B
!= ( function_inverse @ A ) )
| ( ! [C: $i,D: $i] :
( ( D
!= ( apply @ B @ C ) )
| ~ ( in @ C @ ( relation_rng @ A ) )
| ( C
= ( apply @ A @ D ) ) )
& ! [C: $i,D: $i] :
( ( D
!= ( apply @ B @ C ) )
| ~ ( in @ C @ ( relation_rng @ A ) )
| ( in @ D @ ( relation_dom @ A ) ) )
& ! [C: $i,D: $i] :
( ( C
!= ( apply @ A @ D ) )
| ~ ( in @ D @ ( relation_dom @ A ) )
| ( D
= ( apply @ B @ C ) ) )
& ! [C: $i] :
( ! [D: $i] :
( ( C
!= ( apply @ A @ D ) )
| ~ ( in @ D @ ( relation_dom @ A ) ) )
| ( in @ C @ ( relation_rng @ A ) ) ) ) )
& ! [B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( B
!= ( function_inverse @ A ) )
| ( ( relation_dom @ B )
= ( relation_rng @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[534]) ).
thf(576,plain,
( ( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(577,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)],[533]) ).
thf(578,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)],[532]) ).
thf(579,plain,
( ( ! [A: $i] :
( ( relation_dom @ ( identity_relation @ A ) )
= A )
& ! [A: $i] :
( ( relation_rng @ ( identity_relation @ A ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[531]) ).
thf(580,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)],[530]) ).
thf(581,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[529]) ).
thf(582,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)],[528]) ).
thf(583,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[527]) ).
thf(584,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[526]) ).
thf(585,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[525]) ).
thf(586,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)],[524]) ).
thf(587,plain,
( ( ! [A: $i] :
( ( ! [SY422: $i,SY423: $i] :
( ( sK69_B @ A )
!= ( ordered_pair @ SY422 @ SY423 ) )
& ( in @ ( sK69_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK67_C @ B @ A ) @ ( sK68_SY421 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[523]) ).
thf(588,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK65_C @ B @ A ) @ ( sK66_SY420 @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ B @ A ) @ ( sK66_SY420 @ B @ A ) ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK65_C @ B @ A ) @ ( sK66_SY420 @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK65_C @ B @ A ) @ ( sK66_SY420 @ 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)],[522]) ).
thf(589,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY418: $i] :
~ ( in @ ( ordered_pair @ ( sK63_C @ B @ A ) @ SY418 ) @ A )
| ~ ( in @ ( sK63_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK63_C @ B @ A ) @ ( sK64_SY419 @ B @ A ) ) @ A )
| ( in @ ( sK63_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 @ ( sK62_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[521]) ).
thf(590,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY416: $i] :
~ ( in @ ( ordered_pair @ SY416 @ ( sK60_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK60_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK61_SY417 @ B @ A ) @ ( sK60_C @ B @ A ) ) @ A )
| ( in @ ( sK60_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 @ ( sK59_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[520]) ).
thf(591,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[519]) ).
thf(592,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ( function_inverse @ A )
= ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[518]) ).
thf(593,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)],[517]) ).
thf(594,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[516]) ).
thf(595,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[515]) ).
thf(596,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(597,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[514]) ).
thf(598,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[513]) ).
thf(599,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)],[512]) ).
thf(600,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_inverse @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[511]) ).
thf(601,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)],[510]) ).
thf(602,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[509]) ).
thf(603,plain,
( ( ! [A: $i] : ( function @ ( identity_relation @ A ) )
& ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[508]) ).
thf(604,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[507]) ).
thf(605,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)],[506]) ).
thf(606,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[349]) ).
thf(607,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[505]) ).
thf(608,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[504]) ).
thf(609,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[503]) ).
thf(610,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[502]) ).
thf(611,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)],[501]) ).
thf(612,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[500]) ).
thf(613,plain,
( ( ( function @ sK58_A )
& ( relation @ sK58_A ) )
= $true ),
inference(copy,[status(thm)],[499]) ).
thf(614,plain,
( ( ( empty @ sK57_A )
& ( relation @ sK57_A ) )
= $true ),
inference(copy,[status(thm)],[498]) ).
thf(615,plain,
( ( ( empty @ sK56_A )
& ( relation @ sK56_A )
& ( function @ sK56_A ) )
= $true ),
inference(copy,[status(thm)],[497]) ).
thf(616,plain,
( ( ~ ( empty @ sK55_A )
& ( relation @ sK55_A ) )
= $true ),
inference(copy,[status(thm)],[496]) ).
thf(617,plain,
( ( ( function @ sK54_A )
& ( relation @ sK54_A )
& ( one_to_one @ sK54_A ) )
= $true ),
inference(copy,[status(thm)],[495]) ).
thf(618,plain,
( ( ( relation @ sK53_A )
& ( relation_empty_yielding @ sK53_A ) )
= $true ),
inference(copy,[status(thm)],[494]) ).
thf(619,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[493]) ).
thf(620,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[492]) ).
thf(621,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)],[491]) ).
thf(622,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)],[490]) ).
thf(623,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)],[489]) ).
thf(624,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[488]) ).
thf(625,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)],[487]) ).
thf(626,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)],[486]) ).
thf(627,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)],[485]) ).
thf(628,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)],[484]) ).
thf(629,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[483]) ).
thf(630,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 @ ( sK52_D @ C @ B @ A ) @ ( relation_dom @ C ) )
& ( in @ ( ordered_pair @ ( sK52_D @ C @ B @ A ) @ A ) @ C )
& ( in @ ( sK52_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[482]) ).
thf(631,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ! [D: $i] :
( ~ ( in @ D @ ( relation_rng @ C ) )
| ~ ( in @ ( ordered_pair @ A @ D ) @ C )
| ~ ( in @ D @ B ) )
| ( in @ A @ ( relation_inverse_image @ C @ B ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_inverse_image @ C @ B ) )
| ( ( in @ ( sK51_D @ C @ B @ A ) @ ( relation_rng @ C ) )
& ( in @ ( ordered_pair @ A @ ( sK51_D @ C @ B @ A ) ) @ C )
& ( in @ ( sK51_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[481]) ).
thf(632,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)],[480]) ).
thf(633,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[322]) ).
thf(634,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[479]) ).
thf(635,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[478]) ).
thf(636,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)],[477]) ).
thf(637,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)],[476]) ).
thf(638,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)],[475]) ).
thf(639,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[474]) ).
thf(640,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[473]) ).
thf(641,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[314]) ).
thf(642,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)],[472]) ).
thf(643,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[471]) ).
thf(644,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)],[470]) ).
thf(645,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ( in @ ( sK50_C @ B @ A ) @ A )
& ( ( apply @ B @ ( sK50_C @ B @ A ) )
!= ( sK50_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)],[469]) ).
thf(646,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ A )
| ( ( apply @ ( identity_relation @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[468]) ).
thf(647,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[308]) ).
thf(648,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)],[467]) ).
thf(649,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)],[466]) ).
thf(650,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)],[465]) ).
thf(651,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[304]) ).
thf(652,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)],[464]) ).
thf(653,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK49_C @ B @ A ) @ A )
& ( in @ ( sK49_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[463]) ).
thf(654,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[462]) ).
thf(655,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[300]) ).
thf(656,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[461]) ).
thf(657,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[460]) ).
thf(658,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[297]) ).
thf(659,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK48_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)],[459]) ).
thf(660,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK46_B @ A ) @ ( sK47_SY415 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[458]) ).
thf(661,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[457]) ).
thf(662,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[456]) ).
thf(663,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[455]) ).
thf(664,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)],[454]) ).
thf(665,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[290]) ).
thf(666,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)],[453]) ).
thf(667,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[452]) ).
thf(668,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[451]) ).
thf(669,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( relation_dom_restriction @ B @ A )
= ( relation_composition @ ( identity_relation @ A ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[450]) ).
thf(670,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[449]) ).
thf(671,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[284]) ).
thf(672,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[283]) ).
thf(673,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( ( ( sK44_C @ B @ A )
!= ( sK45_SY414 @ B @ A ) )
| ~ ( in @ ( sK44_C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ B @ A ) @ ( sK45_SY414 @ B @ A ) ) @ B ) )
& ( ( ( sK44_C @ B @ A )
= ( sK45_SY414 @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK44_C @ B @ A ) @ ( sK45_SY414 @ B @ A ) ) @ B ) )
& ( ( in @ ( sK44_C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK44_C @ B @ A ) @ ( sK45_SY414 @ 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)],[448]) ).
thf(674,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)],[447]) ).
thf(675,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK42_D @ C @ B @ A ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ C @ B @ A ) @ ( sK43_SY413 @ C @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ C @ B @ A ) @ ( sK43_SY413 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK42_D @ C @ B @ A ) @ B )
| ( in @ ( ordered_pair @ ( sK42_D @ C @ B @ A ) @ ( sK43_SY413 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK42_D @ C @ B @ A ) @ ( sK43_SY413 @ C @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK42_D @ C @ B @ A ) @ ( sK43_SY413 @ 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)],[446]) ).
thf(676,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK41_SY412 @ C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ C @ B @ A ) @ ( sK41_SY412 @ C @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ C @ B @ A ) @ ( sK41_SY412 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK41_SY412 @ C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK40_D @ C @ B @ A ) @ ( sK41_SY412 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK40_D @ C @ B @ A ) @ ( sK41_SY412 @ C @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK40_D @ C @ B @ A ) @ ( sK41_SY412 @ 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)],[445]) ).
thf(677,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY410: $i] :
( ~ ( in @ ( ordered_pair @ SY410 @ ( sK38_D @ C @ B @ A ) ) @ A )
| ~ ( in @ SY410 @ B ) )
| ~ ( in @ ( sK38_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK39_SY411 @ C @ B @ A ) @ ( sK38_D @ C @ B @ A ) ) @ A )
& ( in @ ( sK39_SY411 @ C @ B @ A ) @ B ) )
| ( in @ ( sK38_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 @ ( sK37_E @ D @ C @ B @ A ) @ D ) @ A )
& ( in @ ( sK37_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[444]) ).
thf(678,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY408: $i] :
( ~ ( in @ ( ordered_pair @ ( sK35_D @ C @ B @ A ) @ SY408 ) @ A )
| ~ ( in @ SY408 @ B ) )
| ~ ( in @ ( sK35_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK35_D @ C @ B @ A ) @ ( sK36_SY409 @ C @ B @ A ) ) @ A )
& ( in @ ( sK36_SY409 @ C @ B @ A ) @ B ) )
| ( in @ ( sK35_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 @ ( sK34_E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( sK34_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[443]) ).
thf(679,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( ( ( ( in @ ( sK33_SY406 @ B @ A ) @ A )
& ~ ( in @ ( sK32_C @ B @ A ) @ ( sK33_SY406 @ B @ A ) ) )
| ~ ( in @ ( sK32_C @ B @ A ) @ B ) )
& ( ! [SY407: $i] :
( ~ ( in @ SY407 @ A )
| ( in @ ( sK32_C @ B @ A ) @ SY407 ) )
| ( in @ ( sK32_C @ B @ A ) @ B ) ) )
| ( B
= ( set_meet @ A ) ) ) )
& ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( ! [C: $i] :
( ( ( in @ ( sK31_D @ C @ B @ A ) @ A )
& ~ ( in @ C @ ( sK31_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)],[442]) ).
thf(680,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK30_C @ B @ A )
!= A )
| ~ ( in @ ( sK30_C @ B @ A ) @ B ) )
& ( ( ( sK30_C @ B @ A )
= A )
| ( in @ ( sK30_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)],[441]) ).
thf(681,plain,
( ( ! [A: $i] :
( ( in @ ( sK29_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[440]) ).
thf(682,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK28_C @ B @ A ) @ B )
| ~ ( subset @ ( sK28_C @ B @ A ) @ A ) )
& ( ( in @ ( sK28_C @ B @ A ) @ B )
| ( subset @ ( sK28_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)],[439]) ).
thf(683,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)],[438]) ).
thf(684,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK27_D @ C @ B @ A ) @ C )
| ( ( sK27_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK27_D @ C @ B @ A ) @ C )
| ( ( sK27_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK27_D @ C @ B @ A ) @ C )
| ( ( sK27_D @ C @ B @ A )
= A )
| ( ( sK27_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)],[437]) ).
thf(685,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK26_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK26_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK26_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK26_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK26_D @ C @ B @ A ) @ C )
| ( in @ ( sK26_D @ C @ B @ A ) @ A )
| ( in @ ( sK26_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)],[436]) ).
thf(686,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY401: $i,SY402: $i] :
( ~ ( in @ SY401 @ A )
| ~ ( in @ SY402 @ B )
| ( ( sK23_D @ C @ B @ A )
!= ( ordered_pair @ SY401 @ SY402 ) ) )
| ~ ( in @ ( sK23_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK24_SY403 @ C @ B @ A ) @ A )
& ( in @ ( sK25_SY405 @ C @ B @ A ) @ B )
& ( ( sK23_D @ C @ B @ A )
= ( ordered_pair @ ( sK24_SY403 @ C @ B @ A ) @ ( sK25_SY405 @ C @ B @ A ) ) ) )
| ( in @ ( sK23_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 @ ( sK21_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK22_SY400 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK21_E @ D @ C @ B @ A ) @ ( sK22_SY400 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(687,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( in @ ( ordered_pair @ ( sK19_C @ B @ A ) @ ( sK20_SY399 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK19_C @ B @ A ) @ ( sK20_SY399 @ 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)],[434]) ).
thf(688,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK18_C @ B @ A ) @ A )
& ~ ( in @ ( sK18_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)],[433]) ).
thf(689,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK17_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK17_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK17_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK17_D @ C @ B @ A ) @ A )
| ( in @ ( sK17_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK17_D @ C @ B @ A ) @ B )
| ( in @ ( sK17_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)],[432]) ).
thf(690,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)],[431]) ).
thf(691,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY397: $i] :
( ~ ( in @ ( sK15_C @ B @ A ) @ SY397 )
| ~ ( in @ SY397 @ A ) )
| ~ ( in @ ( sK15_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK15_C @ B @ A ) @ ( sK16_SY398 @ B @ A ) )
& ( in @ ( sK16_SY398 @ B @ A ) @ A ) )
| ( in @ ( sK15_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 @ ( sK14_D @ C @ B @ A ) )
& ( in @ ( sK14_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[430]) ).
thf(692,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK13_D @ C @ B @ A ) @ A )
| ( in @ ( sK13_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK13_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK13_D @ C @ B @ A ) @ A )
| ( in @ ( sK13_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK13_D @ C @ B @ A ) @ B )
| ( in @ ( sK13_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)],[429]) ).
thf(693,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK11_C @ B @ A ) @ ( sK12_SY396 @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ B @ A ) @ ( sK11_C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( sK11_C @ B @ A ) @ ( sK12_SY396 @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK12_SY396 @ B @ A ) @ ( sK11_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)],[428]) ).
thf(694,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)],[427]) ).
thf(695,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ! [SY394: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ C @ B @ A ) @ SY394 ) @ A )
| ~ ( in @ ( ordered_pair @ SY394 @ ( sK9_SY391 @ C @ B @ A ) ) @ B ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ C @ B @ A ) @ ( sK9_SY391 @ C @ B @ A ) ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK8_D @ C @ B @ A ) @ ( sK10_SY395 @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK10_SY395 @ C @ B @ A ) @ ( sK9_SY391 @ C @ B @ A ) ) @ B ) )
| ( in @ ( ordered_pair @ ( sK8_D @ C @ B @ A ) @ ( sK9_SY391 @ 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 @ ( sK7_F @ E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK7_F @ E @ D @ C @ B @ A ) @ E ) @ B ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(696,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)],[425]) ).
thf(697,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[258]) ).
thf(698,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[257]) ).
thf(699,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[256]) ).
thf(700,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[255]) ).
thf(701,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[254]) ).
thf(702,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[424]) ).
thf(703,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[252]) ).
thf(704,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(705,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(706,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(707,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(708,plain,
( ( empty @ sK6_A )
= $true ),
inference(copy,[status(thm)],[419]) ).
thf(709,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(copy,[status(thm)],[418]) ).
thf(710,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(711,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[244]) ).
thf(712,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(713,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(714,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(715,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)],[414]) ).
thf(716,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[239]) ).
thf(717,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(718,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(719,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(720,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(721,plain,
( ( ! [A: $i] :
( ! [SY384: $i] :
( ~ ( subset @ SY384 @ ( sK2_B @ A ) )
| ( are_equipotent @ SY384 @ ( sK2_B @ A ) )
| ( in @ SY384 @ ( sK2_B @ A ) ) )
& ! [SY385: $i] :
( ( ! [SY390: $i] :
( ~ ( subset @ SY390 @ SY385 )
| ( in @ SY390 @ ( sK3_SY386 @ SY385 @ A ) ) )
& ( in @ ( sK3_SY386 @ SY385 @ A ) @ ( sK2_B @ A ) ) )
| ~ ( in @ SY385 @ ( sK2_B @ A ) ) )
& ! [SY388: $i,SY389: $i] :
( ~ ( in @ SY388 @ ( sK2_B @ A ) )
| ~ ( subset @ SY389 @ SY388 )
| ( in @ SY389 @ ( sK2_B @ A ) ) )
& ( in @ A @ ( sK2_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(722,plain,
( ( one_to_one @ sK1_A )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(723,plain,
( ( function @ sK1_A )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(724,plain,
( ( relation @ sK1_A )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(725,plain,
( ( ( ( relation_rng @ sK1_A )
!= ( relation_dom @ ( function_inverse @ sK1_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(726,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)],[621]) ).
thf(727,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)],[652]) ).
thf(728,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY406 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ ( sK33_SY406 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK31_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)],[679]) ).
thf(729,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK48_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)],[659]) ).
thf(730,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)],[601]) ).
thf(731,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)],[648]) ).
thf(732,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)],[611]) ).
thf(733,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 @ ( sK52_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX2 ) )
| ~ ( in @ ( ordered_pair @ ( sK52_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) @ SX2 ) )
| ~ ( in @ ( sK52_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[630]) ).
thf(734,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)],[674]) ).
thf(735,plain,
( ( ~ ( ~ ( relation @ sK53_A )
| ~ ( relation_empty_yielding @ sK53_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[618]) ).
thf(736,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK13_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK13_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK13_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK13_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK13_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( in @ ( sK13_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK13_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)],[692]) ).
thf(737,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)],[683]) ).
thf(738,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[606]) ).
thf(739,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ ( sK41_SY412 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SX2 @ SX1 @ SX0 ) @ ( sK41_SY412 @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SX2 @ SX1 @ SX0 ) @ ( sK41_SY412 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK41_SY412 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK40_D @ SX2 @ SX1 @ SX0 ) @ ( sK41_SY412 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SX2 @ SX1 @ SX0 ) @ ( sK41_SY412 @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK40_D @ SX2 @ SX1 @ SX0 ) @ ( sK41_SY412 @ 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)],[676]) ).
thf(740,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK27_D @ SX2 @ SX1 @ SX0 )
!= SX0 ) )
| ~ ( ~ ( in @ ( sK27_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK27_D @ SX2 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ( ( in @ ( sK27_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK27_D @ SX2 @ SX1 @ SX0 )
= SX0 )
| ( ( sK27_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)],[684]) ).
thf(741,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK28_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK28_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)],[682]) ).
thf(742,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)],[694]) ).
thf(743,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ ( sK63_C @ SX1 @ SX0 ) @ SX2 ) @ SX0 )
| ~ ( in @ ( sK63_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_C @ SX1 @ SX0 ) @ ( sK64_SY419 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK63_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 @ ( sK62_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[589]) ).
thf(744,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ ( sK35_D @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ~ ( in @ ( sK35_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SX2 @ SX1 @ SX0 ) @ ( sK36_SY409 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK36_SY409 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( in @ ( sK35_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 @ ( sK34_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK34_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[678]) ).
thf(745,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ ( sK38_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ~ ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SX2 @ SX1 @ SX0 ) @ ( sK38_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK39_SY411 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( in @ ( sK38_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 @ ( sK37_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ ( sK37_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[677]) ).
thf(746,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 @ ( sK51_D @ SX2 @ SX1 @ SX0 ) @ ( relation_rng @ SX2 ) )
| ~ ( in @ ( ordered_pair @ SX0 @ ( sK51_D @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( in @ ( sK51_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[631]) ).
thf(747,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)],[636]) ).
thf(748,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ ( sK42_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SX2 @ SX1 @ SX0 ) @ ( sK43_SY413 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SX2 @ SX1 @ SX0 ) @ ( sK43_SY413 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK42_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK42_D @ SX2 @ SX1 @ SX0 ) @ ( sK43_SY413 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SX2 @ SX1 @ SX0 ) @ ( sK43_SY413 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK42_D @ SX2 @ SX1 @ SX0 ) @ ( sK43_SY413 @ 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)],[675]) ).
thf(749,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)],[599]) ).
thf(750,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SX1 @ SX0 ) @ ( sK12_SY396 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SX1 @ SX0 ) @ ( sK11_C @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_C @ SX1 @ SX0 ) @ ( sK12_SY396 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK12_SY396 @ SX1 @ SX0 ) @ ( sK11_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)],[693]) ).
thf(751,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ SX2 @ ( sK60_C @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK60_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK61_SY417 @ SX1 @ SX0 ) @ ( sK60_C @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK60_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 @ ( sK59_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[590]) ).
thf(752,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)],[715]) ).
thf(753,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)],[666]) ).
thf(754,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ ( sK9_SY391 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ ( sK9_SY391 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ ( sK10_SY395 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SX2 @ SX1 @ SX0 ) @ ( sK9_SY391 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ ( sK9_SY391 @ 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 @ ( sK7_F @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX4 ) @ SX1 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[695]) ).
thf(755,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)],[626]) ).
thf(756,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)],[577]) ).
thf(757,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX1 @ ( sK2_B @ SX0 ) )
| ( are_equipotent @ SX1 @ ( sK2_B @ SX0 ) )
| ( in @ SX1 @ ( sK2_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK3_SY386 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK3_SY386 @ SX1 @ SX0 ) @ ( sK2_B @ SX0 ) ) )
| ~ ( in @ SX1 @ ( sK2_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK2_B @ SX0 ) )
| ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK2_B @ SX0 ) ) )
| ~ ( in @ SX0 @ ( sK2_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[721]) ).
thf(758,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)],[593]) ).
thf(759,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[600]) ).
thf(760,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK69_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK69_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK67_C @ SX1 @ SX0 ) @ ( sK68_SY421 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[587]) ).
thf(761,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)],[569]) ).
thf(762,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)],[555]) ).
thf(763,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ sK56_A )
| ~ ( relation @ sK56_A ) )
| ~ ( function @ sK56_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[615]) ).
thf(764,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)],[650]) ).
thf(765,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( relation_dom @ ( identity_relation @ SX0 ) )
= SX0 )
| ~ ! [SX0: $i] :
( ( relation_rng @ ( identity_relation @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[579]) ).
thf(766,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)],[664]) ).
thf(767,plain,
( ( ~ ( ~ ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) )
| ~ ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[603]) ).
thf(768,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SX1 @ SX0 ) @ ( sK20_SY399 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( in @ ( ordered_pair @ ( sK19_C @ SX1 @ SX0 ) @ ( sK20_SY399 @ 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)],[687]) ).
thf(769,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK30_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK30_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK30_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK30_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)],[680]) ).
thf(770,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)],[567]) ).
thf(771,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)],[586]) ).
thf(772,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[697]) ).
thf(773,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SX1 @ SX0 )
= ( apply @ SX1 @ ( sK70_C @ SX1 @ SX0 ) ) )
| ( ( sK70_C @ SX1 @ SX0 )
= ( apply @ SX0 @ ( sK71_SY424 @ SX1 @ SX0 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SX1 @ SX0 )
= ( apply @ SX1 @ ( sK70_C @ SX1 @ SX0 ) ) )
| ( in @ ( sK71_SY424 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SX1 @ SX0 )
= ( apply @ SX1 @ ( sK70_C @ SX1 @ SX0 ) ) )
| ( ( sK71_SY424 @ SX1 @ SX0 )
!= ( apply @ SX1 @ ( sK70_C @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK70_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) )
| ( ( sK70_C @ SX1 @ SX0 )
= ( apply @ SX0 @ ( sK71_SY424 @ SX1 @ SX0 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) )
| ( in @ ( sK71_SY424 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) )
| ( ( sK71_SY424 @ SX1 @ SX0 )
!= ( apply @ SX1 @ ( sK70_C @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK70_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK71_SY424 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK71_SY424 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ( ( sK70_C @ SX1 @ SX0 )
= ( apply @ SX0 @ ( sK71_SY424 @ SX1 @ SX0 ) ) ) )
| ~ ( ( ( sK70_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK71_SY424 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK71_SY424 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ( in @ ( sK71_SY424 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) ) )
| ~ ( ( ( sK70_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK71_SY424 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK71_SY424 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ( ( sK71_SY424 @ SX1 @ SX0 )
!= ( apply @ SX1 @ ( sK70_C @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK70_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) ) ) ) )
| ( ( relation_dom @ SX1 )
!= ( relation_rng @ SX0 ) )
| ( SX1
= ( function_inverse @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( function_inverse @ SX0 ) )
| ~ ( ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX3
!= ( apply @ SX1 @ SX2 ) )
| ~ ( in @ SX2 @ ( relation_rng @ SX0 ) )
| ( SX2
= ( apply @ SX0 @ SX3 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( SX3
!= ( apply @ SX1 @ SX2 ) )
| ~ ( in @ SX2 @ ( relation_rng @ SX0 ) )
| ( in @ SX3 @ ( relation_dom @ SX0 ) ) ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX2
!= ( apply @ SX0 @ SX3 ) )
| ~ ( in @ SX3 @ ( relation_dom @ SX0 ) )
| ( SX3
= ( apply @ SX1 @ SX2 ) ) )
| ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ( SX2
!= ( apply @ SX0 @ SX3 ) )
| ~ ( in @ SX3 @ ( relation_dom @ SX0 ) ) )
| ( in @ SX2 @ ( relation_rng @ SX0 ) ) ) ) ) )
| ~ ! [SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( function_inverse @ SX0 ) )
| ( ( relation_dom @ SX1 )
= ( relation_rng @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[575]) ).
thf(774,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[609]) ).
thf(775,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)],[696]) ).
thf(776,plain,
( ( ~ ( ~ ~ ( empty @ sK55_A )
| ~ ( relation @ sK55_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[616]) ).
thf(777,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK18_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK18_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)],[688]) ).
thf(778,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK49_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK49_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)],[653]) ).
thf(779,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)],[625]) ).
thf(780,plain,
( ( ~ ( ( ( relation_dom @ empty_set )
!= empty_set )
| ( ( relation_rng @ empty_set )
!= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[576]) ).
thf(781,plain,
( ( ~ ( ~ ( empty @ sK57_A )
| ~ ( relation @ sK57_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[614]) ).
thf(782,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)],[644]) ).
thf(783,plain,
( ( ~ ( ~ ( function @ sK58_A )
| ~ ( relation @ sK58_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[613]) ).
thf(784,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)],[690]) ).
thf(785,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)],[570]) ).
thf(786,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)],[649]) ).
thf(787,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( in @ ( sK29_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[681]) ).
thf(788,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK26_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ~ ( in @ ( sK26_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK26_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ( ( in @ ( sK26_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( in @ ( sK26_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK26_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)],[685]) ).
thf(789,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[610]) ).
thf(790,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)],[642]) ).
thf(791,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)],[578]) ).
thf(792,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)],[623]) ).
thf(793,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK17_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK17_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK17_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK17_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK17_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ( in @ ( sK17_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK17_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)],[689]) ).
thf(794,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)],[605]) ).
thf(795,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK44_C @ SX1 @ SX0 )
!= ( sK45_SY414 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY414 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK44_C @ SX1 @ SX0 )
= ( sK45_SY414 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY414 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY414 @ 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)],[673]) ).
thf(796,plain,
( ( ~ ( ~ ~ ( ~ ( function @ sK54_A )
| ~ ( relation @ sK54_A ) )
| ~ ( one_to_one @ sK54_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[617]) ).
thf(797,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)],[580]) ).
thf(798,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK50_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK50_C @ SX1 @ SX0 ) )
!= ( sK50_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)],[645]) ).
thf(799,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i,SX4: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX4 @ SX1 )
| ( ( sK23_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ SX3 @ SX4 ) ) )
| ~ ( in @ ( sK23_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY403 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK25_SY405 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( sK23_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ ( sK24_SY403 @ SX2 @ SX1 @ SX0 ) @ ( sK25_SY405 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( in @ ( sK23_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 @ ( sK21_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK22_SY400 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( SX3
!= ( ordered_pair @ ( sK21_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK22_SY400 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[686]) ).
thf(800,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)],[627]) ).
thf(801,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ ( sK16_SY398 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK16_SY398 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK15_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 @ ( sK14_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK14_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[691]) ).
thf(802,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)],[622]) ).
thf(803,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY420 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY420 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY420 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY420 @ 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)],[588]) ).
thf(804,plain,
! [SV1: $i] :
( ( ! [SY425: $i] :
( ~ ( relation @ SY425 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV1 @ SY425 ) ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(805,plain,
! [SV2: $i] :
( ( ! [SY426: $i] :
( ~ ( relation @ SY426 )
| ( subset @ ( relation_rng_restriction @ SV2 @ SY426 ) @ SY426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(806,plain,
! [SV3: $i] :
( ( ! [SY427: $i] :
( ~ ( relation @ SY427 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV3 @ SY427 ) ) @ ( relation_rng @ SY427 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(807,plain,
! [SV4: $i] :
( ( ! [SY428: $i] :
( ~ ( relation @ SY428 )
| ( ( relation_rng @ ( relation_rng_restriction @ SV4 @ SY428 ) )
= ( set_intersection2 @ ( relation_rng @ SY428 ) @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(808,plain,
! [SV5: $i] :
( ( ! [SY429: $i,SY430: $i] :
( ~ ( relation @ SY430 )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV5 @ SY430 ) @ SY429 )
= ( relation_rng_restriction @ SV5 @ ( relation_dom_restriction @ SY430 @ SY429 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(809,plain,
! [SV6: $i] :
( ( ! [SY431: $i] :
( ~ ( relation @ SY431 )
| ( subset @ ( relation_image @ SY431 @ SV6 ) @ ( relation_rng @ SY431 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(810,plain,
! [SV7: $i] :
( ( ! [SY432: $i] :
( ~ ( relation @ SY432 )
| ( ( relation_image @ SY432 @ SV7 )
= ( relation_image @ SY432 @ ( set_intersection2 @ ( relation_dom @ SY432 ) @ SV7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(811,plain,
! [SV8: $i] :
( ( ~ ( relation @ SV8 )
| ( ( relation_image @ SV8 @ ( relation_dom @ SV8 ) )
= ( relation_rng @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(812,plain,
! [SV9: $i] :
( ( ~ ( relation @ SV9 )
| ! [SY433: $i] :
( ~ ( relation @ SY433 )
| ( ( relation_rng @ ( relation_composition @ SV9 @ SY433 ) )
= ( relation_image @ SY433 @ ( relation_rng @ SV9 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(813,plain,
! [SV10: $i] :
( ( ! [SY434: $i] :
( ~ ( relation @ SY434 )
| ( subset @ ( relation_inverse_image @ SY434 @ SV10 ) @ ( relation_dom @ SY434 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(814,plain,
! [SV11: $i] :
( ( ! [SY435: $i,SY436: $i] :
( ~ ( relation @ SY436 )
| ~ ( subset @ SV11 @ SY435 )
| ( subset @ ( relation_inverse_image @ SY436 @ SV11 ) @ ( relation_inverse_image @ SY436 @ SY435 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(815,plain,
! [SV12: $i] :
( ( ~ ( relation @ SV12 )
| ( subset @ SV12 @ ( cartesian_product2 @ ( relation_dom @ SV12 ) @ ( relation_rng @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(816,plain,
! [SV13: $i] :
( ( ~ ( relation @ SV13 )
| ! [SY437: $i] :
( ~ ( relation @ SY437 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV13 @ SY437 ) ) @ ( relation_dom @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(817,plain,
! [SV14: $i] :
( ( ~ ( relation @ SV14 )
| ! [SY438: $i] :
( ~ ( relation @ SY438 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV14 @ SY438 ) ) @ ( relation_rng @ SY438 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(818,plain,
! [SV15: $i] :
( ( ~ ( relation @ SV15 )
| ! [SY439: $i] :
( ~ ( relation @ SY439 )
| ~ ( subset @ ( relation_rng @ SV15 ) @ ( relation_dom @ SY439 ) )
| ( ( relation_dom @ ( relation_composition @ SV15 @ SY439 ) )
= ( relation_dom @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(819,plain,
! [SV16: $i] :
( ( ~ ( relation @ SV16 )
| ! [SY440: $i] :
( ~ ( relation @ SY440 )
| ~ ( subset @ ( relation_dom @ SV16 ) @ ( relation_rng @ SY440 ) )
| ( ( relation_rng @ ( relation_composition @ SY440 @ SV16 ) )
= ( relation_rng @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(820,plain,
! [SV17: $i] :
( ( ! [SY441: $i] :
( ~ ( relation @ SY441 )
| ( subset @ ( relation_dom_restriction @ SY441 @ SV17 ) @ SY441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(821,plain,
! [SV18: $i] :
( ( ! [SY442: $i] :
( ~ ( relation @ SY442 )
| ( ( relation_dom @ ( relation_dom_restriction @ SY442 @ SV18 ) )
= ( set_intersection2 @ ( relation_dom @ SY442 ) @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(822,plain,
! [SV19: $i] :
( ( ! [SY443: $i] :
( ~ ( relation @ SY443 )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ SY443 @ SV19 ) ) @ ( relation_rng @ SY443 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(823,plain,
! [SV20: $i] :
( ( ~ ( empty @ SV20 )
| ( function @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(824,plain,
! [SV21: $i] :
( ( ~ ( empty @ SV21 )
| ( relation @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(825,plain,
! [SV22: $i] :
( ( ~ ( relation @ SV22 )
| ( ( relation_field @ SV22 )
= ( set_union2 @ ( relation_dom @ SV22 ) @ ( relation_rng @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(826,plain,
! [SV23: $i] :
( ( ~ ( function @ SV23 )
| ~ ( relation @ SV23 )
| ~ ( one_to_one @ SV23 )
| ( ( function_inverse @ SV23 )
= ( relation_inverse @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(827,plain,
! [SV24: $i] :
( ( ~ ( relation @ SV24 )
| ( relation @ ( relation_inverse @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(828,plain,
! [SV25: $i] :
( ( ! [SY444: $i] :
( ~ ( relation @ SV25 )
| ~ ( relation @ SY444 )
| ( relation @ ( relation_composition @ SV25 @ SY444 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(829,plain,
! [SV26: $i] :
( ( relation @ ( identity_relation @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(830,plain,
! [SV27: $i] :
( ( ~ ( relation @ SV27 )
| ! [SY445: $i] : ( relation @ ( relation_dom_restriction @ SV27 @ SY445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(831,plain,
! [SV28: $i] :
( ( ! [SY446: $i] :
( ~ ( relation @ SY446 )
| ( relation @ ( relation_rng_restriction @ SV28 @ SY446 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(832,plain,
! [SV29: $i] :
( ( ! [SY447: $i] :
( ~ ( relation @ SV29 )
| ~ ( relation @ SY447 )
| ( relation @ ( set_intersection2 @ SV29 @ SY447 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(833,plain,
! [SV30: $i] :
( ( ! [SY448: $i] :
( ~ ( relation @ SV30 )
| ~ ( relation @ SY448 )
| ( relation @ ( set_union2 @ SV30 @ SY448 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(834,plain,
! [SV31: $i] :
( ( ( empty @ SV31 )
| ~ ( relation @ SV31 )
| ~ ( empty @ ( relation_dom @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(835,plain,
! [SV32: $i] :
( ( ( empty @ SV32 )
| ~ ( relation @ SV32 )
| ~ ( empty @ ( relation_rng @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(836,plain,
! [SV33: $i] :
( ( ~ ( relation @ SV33 )
| ( ( relation_inverse @ ( relation_inverse @ SV33 ) )
= SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(837,plain,
! [SV34: $i] :
( ( ( ( singleton @ SV34 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(838,plain,
! [SV35: $i] :
( ( ! [SY449: $i] :
( ~ ( in @ SV35 @ SY449 )
| ( ( set_union2 @ ( singleton @ SV35 ) @ SY449 )
= SY449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(839,plain,
! [SV36: $i] :
( ( ! [SY450: $i] :
( ~ ( in @ SV36 @ SY450 )
| ( subset @ SV36 @ ( union @ SY450 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(840,plain,
! [SV37: $i] :
( ( ! [SY451: $i,SY452: $i,SY453: $i] :
( ~ ( subset @ SV37 @ SY451 )
| ~ ( subset @ SY452 @ SY453 )
| ( subset @ ( cartesian_product2 @ SV37 @ SY452 ) @ ( cartesian_product2 @ SY451 @ SY453 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(841,plain,
! [SV38: $i] :
( ( ! [SY454: $i] :
( ~ ( subset @ SV38 @ SY454 )
| ( ( set_union2 @ SV38 @ SY454 )
= SY454 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(842,plain,
! [SV39: $i] :
( ( ! [SY455: $i] :
( ~ ( relation @ SY455 )
| ( SV39 = empty_set )
| ~ ( subset @ SV39 @ ( relation_rng @ SY455 ) )
| ( ( relation_inverse_image @ SY455 @ SV39 )
!= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(843,plain,
! [SV40: $i] :
( ( ! [SY456: $i] : ( subset @ ( set_intersection2 @ SV40 @ SY456 ) @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(844,plain,
! [SV41: $i] :
( ( ! [SY457: $i,SY458: $i] :
( ~ ( subset @ SV41 @ SY457 )
| ~ ( subset @ SV41 @ SY458 )
| ( subset @ SV41 @ ( set_intersection2 @ SY457 @ SY458 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(845,plain,
! [SV42: $i] :
( ( ! [SY459: $i,SY460: $i] :
( ~ ( subset @ SV42 @ SY459 )
| ~ ( subset @ SY459 @ SY460 )
| ( subset @ SV42 @ SY460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(846,plain,
! [SV43: $i] :
( ( ! [SY461: $i] :
( ~ ( function @ SY461 )
| ~ ( relation @ SY461 )
| ! [SY462: $i] :
( ~ ( function @ SY462 )
| ~ ( relation @ SY462 )
| ~ ( in @ SV43 @ ( relation_dom @ ( relation_composition @ SY462 @ SY461 ) ) )
| ( ( apply @ ( relation_composition @ SY462 @ SY461 ) @ SV43 )
= ( apply @ SY461 @ ( apply @ SY462 @ SV43 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(847,plain,
! [SV44: $i] :
( ( ! [SY463: $i] :
( ~ ( function @ SY463 )
| ~ ( relation @ SY463 )
| ! [SY464: $i] :
( ~ ( function @ SY464 )
| ~ ( relation @ SY464 )
| ~ ( in @ SV44 @ ( relation_dom @ SY463 ) )
| ( ( apply @ ( relation_composition @ SY463 @ SY464 ) @ SV44 )
= ( apply @ SY464 @ ( apply @ SY463 @ SV44 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(848,plain,
! [SV45: $i] :
( ( ! [SY465: $i] :
( ~ ( subset @ SV45 @ SY465 )
| ! [SY466: $i] : ( subset @ ( set_intersection2 @ SV45 @ SY466 ) @ ( set_intersection2 @ SY465 @ SY466 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(849,plain,
! [SV46: $i] :
( ( ! [SY467: $i] :
( ~ ( subset @ SV46 @ SY467 )
| ( ( set_intersection2 @ SV46 @ SY467 )
= SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(850,plain,
! [SV47: $i] :
( ( subset @ empty_set @ SV47 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(851,plain,
! [SV48: $i] :
( ( ! [SY468: $i] :
( ~ ( subset @ SV48 @ SY468 )
| ! [SY469: $i] : ( subset @ ( set_difference @ SV48 @ SY469 ) @ ( set_difference @ SY468 @ SY469 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(852,plain,
! [SV49: $i] :
( ( ! [SY470: $i] :
( ~ ( in @ SY470 @ SV49 )
| ( ( apply @ ( identity_relation @ SV49 ) @ SY470 )
= SY470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(853,plain,
! [SV50: $i] :
( ( ! [SY471: $i] : ( subset @ ( set_difference @ SV50 @ SY471 ) @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(854,plain,
! [SV51: $i] :
( ( ! [SY472: $i] :
( ( set_union2 @ SV51 @ ( set_difference @ SY472 @ SV51 ) )
= ( set_union2 @ SV51 @ SY472 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(855,plain,
! [SV52: $i] :
( ( ~ ( subset @ SV52 @ empty_set )
| ( SV52 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(856,plain,
! [SV53: $i] :
( ( ! [SY473: $i] :
( ( set_difference @ ( set_union2 @ SV53 @ SY473 ) @ SY473 )
= ( set_difference @ SV53 @ SY473 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(857,plain,
! [SV54: $i] :
( ( ! [SY474: $i] :
( ~ ( subset @ SV54 @ SY474 )
| ( SY474
= ( set_union2 @ SV54 @ ( set_difference @ SY474 @ SV54 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(858,plain,
! [SV55: $i] :
( ( ! [SY475: $i] :
( ~ ( in @ SV55 @ SY475 )
| ( ( set_union2 @ ( singleton @ SV55 ) @ SY475 )
= SY475 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(859,plain,
! [SV56: $i] :
( ( ! [SY476: $i] :
( ( set_difference @ SV56 @ ( set_difference @ SV56 @ SY476 ) )
= ( set_intersection2 @ SV56 @ SY476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(860,plain,
! [SV57: $i] :
( ( ~ ( relation @ SV57 )
| ( in @ ( ordered_pair @ ( sK46_B @ SV57 ) @ ( sK47_SY415 @ SV57 ) ) @ SV57 )
| ( SV57 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(861,plain,
! [SV58: $i] :
( ( ! [SY477: $i] :
( ~ ( proper_subset @ SY477 @ SV58 )
| ~ ( subset @ SV58 @ SY477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(862,plain,
! [SV59: $i] :
( ( ! [SY478: $i,SY479: $i] :
( ~ ( disjoint @ SY478 @ SY479 )
| ~ ( subset @ SV59 @ SY478 )
| ( disjoint @ SV59 @ SY479 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(863,plain,
! [SV60: $i] :
( ( ! [SY480: $i] :
( ~ ( subset @ ( singleton @ SV60 ) @ ( singleton @ SY480 ) )
| ( SV60 = SY480 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(864,plain,
! [SV61: $i] :
( ( ! [SY481: $i] : ( subset @ SV61 @ ( set_union2 @ SV61 @ SY481 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(865,plain,
! [SV62: $i] :
( ( ! [SY482: $i,SY483: $i] :
( ~ ( subset @ SV62 @ SY482 )
| ~ ( subset @ SY483 @ SY482 )
| ( subset @ ( set_union2 @ SV62 @ SY483 ) @ SY482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(866,plain,
! [SV63: $i] :
( ( ! [SY484: $i] :
( ~ ( in @ SV63 @ SY484 )
| ( subset @ SV63 @ ( union @ SY484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(867,plain,
! [SV64: $i] :
( ( ! [SY485: $i] :
( ~ ( relation @ SY485 )
| ( ( relation_dom_restriction @ SY485 @ SV64 )
= ( relation_composition @ ( identity_relation @ SV64 ) @ SY485 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(868,plain,
! [SV65: $i] :
( ( ! [SY486: $i] :
( ~ ( in @ SV65 @ SY486 )
| ~ ( in @ SY486 @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(869,plain,
! [SV66: $i] :
( ( ! [SY487: $i] :
( ( set_union2 @ SV66 @ SY487 )
= ( set_union2 @ SY487 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(870,plain,
! [SV67: $i] :
( ( ! [SY488: $i] :
( ( set_intersection2 @ SV67 @ SY488 )
= ( set_intersection2 @ SY488 @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(871,plain,
! [SV68: $i] :
( ( ~ ( empty @ ( powerset @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(872,plain,
! [SV69: $i] :
( ( ! [SY489: $i] :
~ ( empty @ ( ordered_pair @ SV69 @ SY489 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(873,plain,
! [SV70: $i] :
( ( ~ ( empty @ ( singleton @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(874,plain,
! [SV71: $i] :
( ( ( empty @ SV71 )
| ! [SY490: $i] :
~ ( empty @ ( set_union2 @ SV71 @ SY490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(875,plain,
! [SV72: $i] :
( ( ! [SY491: $i] :
~ ( empty @ ( unordered_pair @ SV72 @ SY491 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(876,plain,
! [SV73: $i] :
( ( ( empty @ SV73 )
| ! [SY492: $i] :
~ ( empty @ ( set_union2 @ SY492 @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(877,plain,
! [SV74: $i] :
( ( ! [SY493: $i] :
( ( empty @ SV74 )
| ( empty @ SY493 )
| ~ ( empty @ ( cartesian_product2 @ SV74 @ SY493 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(878,plain,
! [SV75: $i] :
( ( ( set_union2 @ SV75 @ SV75 )
= SV75 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(879,plain,
! [SV76: $i] :
( ( ( set_intersection2 @ SV76 @ SV76 )
= SV76 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(880,plain,
( ( empty @ sK5_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[709]) ).
thf(881,plain,
! [SV77: $i] :
( ( subset @ SV77 @ SV77 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(882,plain,
! [SV78: $i] :
( ( ( set_union2 @ SV78 @ empty_set )
= SV78 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(883,plain,
! [SV79: $i] :
( ( ! [SY494: $i] :
( ~ ( in @ SV79 @ SY494 )
| ( element @ SV79 @ SY494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(884,plain,
! [SV80: $i] :
( ( ( set_intersection2 @ SV80 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(885,plain,
! [SV81: $i] :
( ( ! [SY495: $i] :
( ~ ( element @ SV81 @ SY495 )
| ( empty @ SY495 )
| ( in @ SV81 @ SY495 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(886,plain,
! [SV82: $i] :
( ( ( set_difference @ SV82 @ empty_set )
= SV82 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(887,plain,
! [SV83: $i] :
( ( ( set_difference @ empty_set @ SV83 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(888,plain,
! [SV84: $i] :
( ( ~ ( empty @ SV84 )
| ( SV84 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(889,plain,
! [SV85: $i] :
( ( ! [SY496: $i] :
( ~ ( empty @ SY496 )
| ~ ( in @ SV85 @ SY496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(890,plain,
! [SV86: $i] :
( ( ! [SY497: $i] :
( ( SV86 = SY497 )
| ~ ( empty @ SV86 )
| ~ ( empty @ SY497 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(891,plain,
( ( ( relation_rng @ sK1_A )
= ( relation_dom @ ( function_inverse @ sK1_A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[725]) ).
thf(892,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)],[726]) ).
thf(893,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)],[727]) ).
thf(894,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY406 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ ( sK33_SY406 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK31_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)],[728]) ).
thf(895,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK48_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)],[729]) ).
thf(896,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)],[730]) ).
thf(897,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)],[731]) ).
thf(898,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)],[732]) ).
thf(899,plain,
! [SV87: $i] :
( ( ~ ( ~ ! [SY498: $i,SY499: $i] :
( ~ ( relation @ SY499 )
| ! [SY500: $i] :
( ~ ( in @ SY500 @ ( relation_dom @ SY499 ) )
| ~ ( in @ ( ordered_pair @ SY500 @ SV87 ) @ SY499 )
| ~ ( in @ SY500 @ SY498 ) )
| ( in @ SV87 @ ( relation_image @ SY499 @ SY498 ) ) )
| ~ ! [SY501: $i,SY502: $i] :
( ~ ( relation @ SY502 )
| ~ ( in @ SV87 @ ( relation_image @ SY502 @ SY501 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK52_D @ SY502 @ SY501 @ SV87 ) @ ( relation_dom @ SY502 ) )
| ~ ( in @ ( ordered_pair @ ( sK52_D @ SY502 @ SY501 @ SV87 ) @ SV87 ) @ SY502 ) )
| ~ ( in @ ( sK52_D @ SY502 @ SY501 @ SV87 ) @ SY501 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(900,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)],[734]) ).
thf(901,plain,
( ( ~ ( relation @ sK53_A )
| ~ ( relation_empty_yielding @ sK53_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[735]) ).
thf(902,plain,
! [SV88: $i] :
( ( ~ ( ~ ! [SY503: $i,SY504: $i] :
( ~ ( ~ ( ~ ( in @ ( sK13_D @ SY504 @ SY503 @ SV88 ) @ SV88 )
| ( in @ ( sK13_D @ SY504 @ SY503 @ SV88 ) @ SY503 )
| ~ ( in @ ( sK13_D @ SY504 @ SY503 @ SV88 ) @ SY504 ) )
| ~ ~ ( ~ ( ( in @ ( sK13_D @ SY504 @ SY503 @ SV88 ) @ SV88 )
| ( in @ ( sK13_D @ SY504 @ SY503 @ SV88 ) @ SY504 ) )
| ~ ( ~ ( in @ ( sK13_D @ SY504 @ SY503 @ SV88 ) @ SY503 )
| ( in @ ( sK13_D @ SY504 @ SY503 @ SV88 ) @ SY504 ) ) ) )
| ( SY504
= ( set_difference @ SV88 @ SY503 ) ) )
| ~ ! [SY505: $i,SY506: $i] :
( ( SY506
!= ( set_difference @ SV88 @ SY505 ) )
| ~ ( ~ ! [SY507: $i] :
( ~ ( in @ SY507 @ SV88 )
| ( in @ SY507 @ SY505 )
| ( in @ SY507 @ SY506 ) )
| ~ ~ ( ~ ! [SY508: $i] :
( ~ ( in @ SY508 @ SY506 )
| ( in @ SY508 @ SV88 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY506 )
| ~ ( in @ SX3 @ SY505 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(903,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)],[737]) ).
thf(904,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[738]) ).
thf(905,plain,
! [SV89: $i] :
( ( ! [SY510: $i] :
( ~ ( relation @ SY510 )
| ~ ( ~ ! [SY511: $i] :
( ~ ( relation @ SY511 )
| ~ ( ~ ( ~ ( in @ ( sK41_SY412 @ SY511 @ SY510 @ SV89 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY511 @ SY510 @ SV89 ) @ ( sK41_SY412 @ SY511 @ SY510 @ SV89 ) ) @ SY510 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY511 @ SY510 @ SV89 ) @ ( sK41_SY412 @ SY511 @ SY510 @ SV89 ) ) @ SY511 ) )
| ~ ~ ( ~ ( ( in @ ( sK41_SY412 @ SY511 @ SY510 @ SV89 ) @ SV89 )
| ( in @ ( ordered_pair @ ( sK40_D @ SY511 @ SY510 @ SV89 ) @ ( sK41_SY412 @ SY511 @ SY510 @ SV89 ) ) @ SY511 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SY511 @ SY510 @ SV89 ) @ ( sK41_SY412 @ SY511 @ SY510 @ SV89 ) ) @ SY510 )
| ( in @ ( ordered_pair @ ( sK40_D @ SY511 @ SY510 @ SV89 ) @ ( sK41_SY412 @ SY511 @ SY510 @ SV89 ) ) @ SY511 ) ) ) )
| ( SY511
= ( relation_rng_restriction @ SV89 @ SY510 ) ) )
| ~ ! [SY512: $i] :
( ~ ( relation @ SY512 )
| ( SY512
!= ( relation_rng_restriction @ SV89 @ SY510 ) )
| ~ ( ~ ! [SY513: $i,SY514: $i] :
( ~ ( in @ SY514 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY513 @ SY514 ) @ SY510 )
| ( in @ ( ordered_pair @ SY513 @ SY514 ) @ SY512 ) )
| ~ ~ ( ~ ! [SY515: $i,SY516: $i] :
( ~ ( in @ ( ordered_pair @ SY515 @ SY516 ) @ SY512 )
| ( in @ SY516 @ SV89 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY512 )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY510 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(906,plain,
! [SV90: $i] :
( ( ~ ( ~ ! [SY519: $i,SY520: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY520 @ SY519 @ SV90 ) @ SY520 )
| ( ( sK27_D @ SY520 @ SY519 @ SV90 )
!= SV90 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY520 @ SY519 @ SV90 ) @ SY520 )
| ( ( sK27_D @ SY520 @ SY519 @ SV90 )
!= SY519 ) ) )
| ~ ( ( in @ ( sK27_D @ SY520 @ SY519 @ SV90 ) @ SY520 )
| ( ( sK27_D @ SY520 @ SY519 @ SV90 )
= SV90 )
| ( ( sK27_D @ SY520 @ SY519 @ SV90 )
= SY519 ) ) )
| ( SY520
= ( unordered_pair @ SV90 @ SY519 ) ) )
| ~ ! [SY521: $i,SY522: $i] :
( ( SY522
!= ( unordered_pair @ SV90 @ SY521 ) )
| ~ ( ~ ! [SY523: $i] :
( ~ ( in @ SY523 @ SY522 )
| ( SY523 = SV90 )
| ( SY523 = SY521 ) )
| ~ ~ ( ~ ! [SY524: $i] :
( ( SY524 != SV90 )
| ( in @ SY524 @ SY522 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY521 )
| ( in @ SX3 @ SY522 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(907,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK28_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK28_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)],[741]) ).
thf(908,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)],[742]) ).
thf(909,plain,
! [SV91: $i] :
( ( ~ ( relation @ SV91 )
| ~ ( ~ ! [SY526: $i] :
( ~ ( ~ ( ! [SY527: $i] :
~ ( in @ ( ordered_pair @ ( sK63_C @ SY526 @ SV91 ) @ SY527 ) @ SV91 )
| ~ ( in @ ( sK63_C @ SY526 @ SV91 ) @ SY526 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_C @ SY526 @ SV91 ) @ ( sK64_SY419 @ SY526 @ SV91 ) ) @ SV91 )
| ( in @ ( sK63_C @ SY526 @ SV91 ) @ SY526 ) ) )
| ( SY526
= ( relation_dom @ SV91 ) ) )
| ~ ! [SY528: $i] :
( ( SY528
!= ( relation_dom @ SV91 ) )
| ~ ( ~ ! [SY529: $i] :
( ! [SY530: $i] :
~ ( in @ ( ordered_pair @ SY529 @ SY530 ) @ SV91 )
| ( in @ SY529 @ SY528 ) )
| ~ ! [SY531: $i] :
( ~ ( in @ SY531 @ SY528 )
| ( in @ ( ordered_pair @ SY531 @ ( sK62_D @ SY531 @ SY528 @ SV91 ) ) @ SV91 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(910,plain,
! [SV92: $i] :
( ( ~ ( relation @ SV92 )
| ~ ( ~ ! [SY532: $i,SY533: $i] :
( ~ ( ~ ( ! [SY534: $i] :
( ~ ( in @ ( ordered_pair @ ( sK35_D @ SY533 @ SY532 @ SV92 ) @ SY534 ) @ SV92 )
| ~ ( in @ SY534 @ SY532 ) )
| ~ ( in @ ( sK35_D @ SY533 @ SY532 @ SV92 ) @ SY533 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SY533 @ SY532 @ SV92 ) @ ( sK36_SY409 @ SY533 @ SY532 @ SV92 ) ) @ SV92 )
| ~ ( in @ ( sK36_SY409 @ SY533 @ SY532 @ SV92 ) @ SY532 ) )
| ( in @ ( sK35_D @ SY533 @ SY532 @ SV92 ) @ SY533 ) ) )
| ( SY533
= ( relation_inverse_image @ SV92 @ SY532 ) ) )
| ~ ! [SY535: $i,SY536: $i] :
( ( SY536
!= ( relation_inverse_image @ SV92 @ SY535 ) )
| ~ ( ~ ! [SY537: $i] :
( ! [SY538: $i] :
( ~ ( in @ ( ordered_pair @ SY537 @ SY538 ) @ SV92 )
| ~ ( in @ SY538 @ SY535 ) )
| ( in @ SY537 @ SY536 ) )
| ~ ! [SY539: $i] :
( ~ ( in @ SY539 @ SY536 )
| ~ ( ~ ( in @ ( ordered_pair @ SY539 @ ( sK34_E @ SY539 @ SY536 @ SY535 @ SV92 ) ) @ SV92 )
| ~ ( in @ ( sK34_E @ SY539 @ SY536 @ SY535 @ SV92 ) @ SY535 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(911,plain,
! [SV93: $i] :
( ( ~ ( relation @ SV93 )
| ~ ( ~ ! [SY540: $i,SY541: $i] :
( ~ ( ~ ( ! [SY542: $i] :
( ~ ( in @ ( ordered_pair @ SY542 @ ( sK38_D @ SY541 @ SY540 @ SV93 ) ) @ SV93 )
| ~ ( in @ SY542 @ SY540 ) )
| ~ ( in @ ( sK38_D @ SY541 @ SY540 @ SV93 ) @ SY541 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SY541 @ SY540 @ SV93 ) @ ( sK38_D @ SY541 @ SY540 @ SV93 ) ) @ SV93 )
| ~ ( in @ ( sK39_SY411 @ SY541 @ SY540 @ SV93 ) @ SY540 ) )
| ( in @ ( sK38_D @ SY541 @ SY540 @ SV93 ) @ SY541 ) ) )
| ( SY541
= ( relation_image @ SV93 @ SY540 ) ) )
| ~ ! [SY543: $i,SY544: $i] :
( ( SY544
!= ( relation_image @ SV93 @ SY543 ) )
| ~ ( ~ ! [SY545: $i] :
( ! [SY546: $i] :
( ~ ( in @ ( ordered_pair @ SY546 @ SY545 ) @ SV93 )
| ~ ( in @ SY546 @ SY543 ) )
| ( in @ SY545 @ SY544 ) )
| ~ ! [SY547: $i] :
( ~ ( in @ SY547 @ SY544 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SY547 @ SY544 @ SY543 @ SV93 ) @ SY547 ) @ SV93 )
| ~ ( in @ ( sK37_E @ SY547 @ SY544 @ SY543 @ SV93 ) @ SY543 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(912,plain,
! [SV94: $i] :
( ( ~ ( ~ ! [SY548: $i,SY549: $i] :
( ~ ( relation @ SY549 )
| ! [SY550: $i] :
( ~ ( in @ SY550 @ ( relation_rng @ SY549 ) )
| ~ ( in @ ( ordered_pair @ SV94 @ SY550 ) @ SY549 )
| ~ ( in @ SY550 @ SY548 ) )
| ( in @ SV94 @ ( relation_inverse_image @ SY549 @ SY548 ) ) )
| ~ ! [SY551: $i,SY552: $i] :
( ~ ( relation @ SY552 )
| ~ ( in @ SV94 @ ( relation_inverse_image @ SY552 @ SY551 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK51_D @ SY552 @ SY551 @ SV94 ) @ ( relation_rng @ SY552 ) )
| ~ ( in @ ( ordered_pair @ SV94 @ ( sK51_D @ SY552 @ SY551 @ SV94 ) ) @ SY552 ) )
| ~ ( in @ ( sK51_D @ SY552 @ SY551 @ SV94 ) @ SY551 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(913,plain,
! [SV95: $i] :
( ( ! [SY553: $i] :
( ~ ( function @ SY553 )
| ~ ( relation @ SY553 )
| ~ ( ~ ! [SY554: $i] :
( ~ ( function @ SY554 )
| ~ ( relation @ SY554 )
| ~ ( in @ SV95 @ ( relation_dom @ SY554 ) )
| ~ ( in @ ( apply @ SY554 @ SV95 ) @ ( relation_dom @ SY553 ) )
| ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY554 @ SY553 ) ) ) )
| ~ ~ ( ~ ! [SY555: $i] :
( ~ ( function @ SY555 )
| ~ ( relation @ SY555 )
| ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY555 @ SY553 ) ) )
| ( in @ SV95 @ ( relation_dom @ SY555 ) ) )
| ~ ! [SY556: $i] :
( ~ ( function @ SY556 )
| ~ ( relation @ SY556 )
| ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY556 @ SY553 ) ) )
| ( in @ ( apply @ SY556 @ SV95 ) @ ( relation_dom @ SY553 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(914,plain,
! [SV96: $i] :
( ( ~ ( relation @ SV96 )
| ~ ( ~ ! [SY557: $i,SY558: $i] :
( ~ ( relation @ SY558 )
| ~ ( ~ ( ~ ( in @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ SY557 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ ( sK43_SY413 @ SY558 @ SY557 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ ( sK43_SY413 @ SY558 @ SY557 @ SV96 ) ) @ SY558 ) )
| ~ ~ ( ~ ( ( in @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ SY557 )
| ( in @ ( ordered_pair @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ ( sK43_SY413 @ SY558 @ SY557 @ SV96 ) ) @ SY558 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ ( sK43_SY413 @ SY558 @ SY557 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ ( sK43_SY413 @ SY558 @ SY557 @ SV96 ) ) @ SY558 ) ) ) )
| ( SY558
= ( relation_dom_restriction @ SV96 @ SY557 ) ) )
| ~ ! [SY559: $i,SY560: $i] :
( ~ ( relation @ SY560 )
| ( SY560
!= ( relation_dom_restriction @ SV96 @ SY559 ) )
| ~ ( ~ ! [SY561: $i,SY562: $i] :
( ~ ( in @ SY561 @ SY559 )
| ~ ( in @ ( ordered_pair @ SY561 @ SY562 ) @ SV96 )
| ( in @ ( ordered_pair @ SY561 @ SY562 ) @ SY560 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY560 )
| ( in @ SX3 @ SY559 ) )
| ~ ! [SY565: $i,SY566: $i] :
( ~ ( in @ ( ordered_pair @ SY565 @ SY566 ) @ SY560 )
| ( in @ ( ordered_pair @ SY565 @ SY566 ) @ SV96 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(915,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)],[749]) ).
thf(916,plain,
! [SV97: $i] :
( ( ~ ( relation @ SV97 )
| ~ ( ~ ! [SY567: $i] :
( ~ ( relation @ SY567 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SY567 @ SV97 ) @ ( sK12_SY396 @ SY567 @ SV97 ) ) @ SY567 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SY567 @ SV97 ) @ ( sK11_C @ SY567 @ SV97 ) ) @ SV97 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_C @ SY567 @ SV97 ) @ ( sK12_SY396 @ SY567 @ SV97 ) ) @ SY567 )
| ( in @ ( ordered_pair @ ( sK12_SY396 @ SY567 @ SV97 ) @ ( sK11_C @ SY567 @ SV97 ) ) @ SV97 ) ) )
| ( SY567
= ( relation_inverse @ SV97 ) ) )
| ~ ! [SY568: $i] :
( ~ ( relation @ SY568 )
| ( SY568
!= ( relation_inverse @ SV97 ) )
| ~ ( ~ ! [SY569: $i,SY570: $i] :
( ~ ( in @ ( ordered_pair @ SY569 @ SY570 ) @ SY568 )
| ( in @ ( ordered_pair @ SY570 @ SY569 ) @ SV97 ) )
| ~ ! [SY571: $i,SY572: $i] :
( ~ ( in @ ( ordered_pair @ SY572 @ SY571 ) @ SV97 )
| ( in @ ( ordered_pair @ SY571 @ SY572 ) @ SY568 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(917,plain,
! [SV98: $i] :
( ( ~ ( relation @ SV98 )
| ~ ( ~ ! [SY573: $i] :
( ~ ( ~ ( ! [SY574: $i] :
~ ( in @ ( ordered_pair @ SY574 @ ( sK60_C @ SY573 @ SV98 ) ) @ SV98 )
| ~ ( in @ ( sK60_C @ SY573 @ SV98 ) @ SY573 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK61_SY417 @ SY573 @ SV98 ) @ ( sK60_C @ SY573 @ SV98 ) ) @ SV98 )
| ( in @ ( sK60_C @ SY573 @ SV98 ) @ SY573 ) ) )
| ( SY573
= ( relation_rng @ SV98 ) ) )
| ~ ! [SY575: $i] :
( ( SY575
!= ( relation_rng @ SV98 ) )
| ~ ( ~ ! [SY576: $i] :
( ! [SY577: $i] :
~ ( in @ ( ordered_pair @ SY577 @ SY576 ) @ SV98 )
| ( in @ SY576 @ SY575 ) )
| ~ ! [SY578: $i] :
( ~ ( in @ SY578 @ SY575 )
| ( in @ ( ordered_pair @ ( sK59_D @ SY578 @ SY575 @ SV98 ) @ SY578 ) @ SV98 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(918,plain,
! [SV99: $i] :
( ( ! [SY579: $i] :
( ~ ( ~ ( ~ ( in @ ( sK4_C @ SY579 @ SV99 ) @ SV99 )
| ~ ( in @ ( sK4_C @ SY579 @ SV99 ) @ SY579 ) )
| ~ ( ( in @ ( sK4_C @ SY579 @ SV99 ) @ SV99 )
| ( in @ ( sK4_C @ SY579 @ SV99 ) @ SY579 ) ) )
| ( SV99 = SY579 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(919,plain,
! [SV100: $i] :
( ( ~ ( ~ ! [SY580: $i,SY581: $i] :
( ~ ( function @ SY581 )
| ~ ( relation @ SY581 )
| ( SY580
!= ( apply @ SY581 @ SV100 ) )
| ~ ( in @ SV100 @ ( relation_dom @ SY581 ) )
| ( in @ ( ordered_pair @ SV100 @ SY580 ) @ SY581 ) )
| ~ ~ ( ~ ! [SY582: $i,SY583: $i] :
( ~ ( function @ SY583 )
| ~ ( relation @ SY583 )
| ~ ( in @ ( ordered_pair @ SV100 @ SY582 ) @ SY583 )
| ( SY582
= ( apply @ SY583 @ SV100 ) ) )
| ~ ! [SY584: $i,SY585: $i] :
( ~ ( function @ SY585 )
| ~ ( relation @ SY585 )
| ~ ( in @ ( ordered_pair @ SV100 @ SY584 ) @ SY585 )
| ( in @ SV100 @ ( relation_dom @ SY585 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(920,plain,
! [SV101: $i] :
( ( ~ ( relation @ SV101 )
| ! [SY586: $i] :
( ~ ( relation @ SY586 )
| ~ ( ~ ! [SY587: $i] :
( ~ ( relation @ SY587 )
| ~ ( ~ ( ! [SY588: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY587 @ SY586 @ SV101 ) @ SY588 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY588 @ ( sK9_SY391 @ SY587 @ SY586 @ SV101 ) ) @ SY586 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SY587 @ SY586 @ SV101 ) @ ( sK9_SY391 @ SY587 @ SY586 @ SV101 ) ) @ SY587 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY587 @ SY586 @ SV101 ) @ ( sK10_SY395 @ SY587 @ SY586 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SY587 @ SY586 @ SV101 ) @ ( sK9_SY391 @ SY587 @ SY586 @ SV101 ) ) @ SY586 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SY587 @ SY586 @ SV101 ) @ ( sK9_SY391 @ SY587 @ SY586 @ SV101 ) ) @ SY587 ) ) )
| ( SY587
= ( relation_composition @ SV101 @ SY586 ) ) )
| ~ ! [SY589: $i] :
( ~ ( relation @ SY589 )
| ( SY589
!= ( relation_composition @ SV101 @ SY586 ) )
| ~ ( ~ ! [SY590: $i,SY591: $i] :
( ! [SY592: $i] :
( ~ ( in @ ( ordered_pair @ SY590 @ SY592 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY592 @ SY591 ) @ SY586 ) )
| ( in @ ( ordered_pair @ SY590 @ SY591 ) @ SY589 ) )
| ~ ! [SY593: $i,SY594: $i] :
( ~ ( in @ ( ordered_pair @ SY593 @ SY594 ) @ SY589 )
| ~ ( ~ ( in @ ( ordered_pair @ SY593 @ ( sK7_F @ SY594 @ SY593 @ SY589 @ SY586 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY594 @ SY593 @ SY589 @ SY586 @ SV101 ) @ SY594 ) @ SY586 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(921,plain,
! [SV102: $i] :
( ( ! [SY595: $i] :
~ ( ~ ! [SY596: $i,SY597: $i] :
( ~ ( in @ SV102 @ SY596 )
| ~ ( in @ SY595 @ SY597 )
| ( in @ ( ordered_pair @ SV102 @ SY595 ) @ ( cartesian_product2 @ SY596 @ SY597 ) ) )
| ~ ~ ( ~ ! [SY598: $i] :
( ! [SY599: $i] :
~ ( in @ ( ordered_pair @ SV102 @ SY595 ) @ ( cartesian_product2 @ SY598 @ SY599 ) )
| ( in @ SV102 @ SY598 ) )
| ~ ! [SY600: $i,SY601: $i] :
( ~ ( in @ ( ordered_pair @ SV102 @ SY595 ) @ ( cartesian_product2 @ SY600 @ SY601 ) )
| ( in @ SY595 @ SY601 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(922,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)],[756]) ).
thf(923,plain,
! [SV103: $i] :
( ( ~ ( ~ ! [SY602: $i] :
( ~ ( subset @ SY602 @ ( sK2_B @ SV103 ) )
| ( are_equipotent @ SY602 @ ( sK2_B @ SV103 ) )
| ( in @ SY602 @ ( sK2_B @ SV103 ) ) )
| ~ ~ ( ~ ! [SY603: $i] :
( ~ ( ~ ! [SY604: $i] :
( ~ ( subset @ SY604 @ SY603 )
| ( in @ SY604 @ ( sK3_SY386 @ SY603 @ SV103 ) ) )
| ~ ( in @ ( sK3_SY386 @ SY603 @ SV103 ) @ ( sK2_B @ SV103 ) ) )
| ~ ( in @ SY603 @ ( sK2_B @ SV103 ) ) )
| ~ ~ ( ~ ! [SY605: $i,SY606: $i] :
( ~ ( in @ SY605 @ ( sK2_B @ SV103 ) )
| ~ ( subset @ SY606 @ SY605 )
| ( in @ SY606 @ ( sK2_B @ SV103 ) ) )
| ~ ( in @ SV103 @ ( sK2_B @ SV103 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(924,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)],[758]) ).
thf(925,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[759]) ).
thf(926,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK69_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK69_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK67_C @ SX1 @ SX0 ) @ ( sK68_SY421 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[760]) ).
thf(927,plain,
! [SV104: $i] :
( ( ~ ( relation @ SV104 )
| ~ ( ~ ! [SY607: $i] :
( ~ ( relation @ SY607 )
| ~ ( subset @ SV104 @ SY607 )
| ( subset @ ( relation_dom @ SV104 ) @ ( relation_dom @ SY607 ) ) )
| ~ ! [SY608: $i] :
( ~ ( relation @ SY608 )
| ~ ( subset @ SV104 @ SY608 )
| ( subset @ ( relation_rng @ SV104 ) @ ( relation_rng @ SY608 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(928,plain,
! [SV105: $i] :
( ( ~ ( ~ ! [SY609: $i,SY610: $i] :
( ~ ( relation @ SY610 )
| ~ ( in @ SV105 @ SY609 )
| ~ ( in @ SV105 @ ( relation_rng @ SY610 ) )
| ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SY609 @ SY610 ) ) ) )
| ~ ~ ( ~ ! [SY611: $i,SY612: $i] :
( ~ ( relation @ SY612 )
| ~ ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SY611 @ SY612 ) ) )
| ( in @ SV105 @ SY611 ) )
| ~ ! [SY613: $i,SY614: $i] :
( ~ ( relation @ SY614 )
| ~ ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SY613 @ SY614 ) ) )
| ( in @ SV105 @ ( relation_rng @ SY614 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(929,plain,
( ( ~ ~ ( ~ ( empty @ sK56_A )
| ~ ( relation @ sK56_A ) )
| ~ ( function @ sK56_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(930,plain,
! [SV106: $i] :
( ( ~ ( ~ ! [SY615: $i,SY616: $i] :
( ~ ( in @ SV106 @ SY616 )
| ~ ( in @ SY615 @ SY616 )
| ( subset @ ( unordered_pair @ SV106 @ SY615 ) @ SY616 ) )
| ~ ~ ( ~ ! [SY617: $i,SY618: $i] :
( ~ ( subset @ ( unordered_pair @ SV106 @ SY617 ) @ SY618 )
| ( in @ SV106 @ SY618 ) )
| ~ ! [SY619: $i,SY620: $i] :
( ~ ( subset @ ( unordered_pair @ SV106 @ SY619 ) @ SY620 )
| ( in @ SY619 @ SY620 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(931,plain,
( ( ~ ! [SX0: $i] :
( ( relation_dom @ ( identity_relation @ SX0 ) )
= SX0 )
| ~ ! [SX0: $i] :
( ( relation_rng @ ( identity_relation @ SX0 ) )
= SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[765]) ).
thf(932,plain,
! [SV107: $i] :
( ( ! [SY621: $i] :
~ ( ~ ! [SY622: $i,SY623: $i] :
( ~ ( relation @ SY623 )
| ~ ( in @ SV107 @ SY622 )
| ~ ( in @ ( ordered_pair @ SV107 @ SY621 ) @ SY623 )
| ( in @ ( ordered_pair @ SV107 @ SY621 ) @ ( relation_composition @ ( identity_relation @ SY622 ) @ SY623 ) ) )
| ~ ~ ( ~ ! [SY624: $i,SY625: $i] :
( ~ ( relation @ SY625 )
| ~ ( in @ ( ordered_pair @ SV107 @ SY621 ) @ ( relation_composition @ ( identity_relation @ SY624 ) @ SY625 ) )
| ( in @ SV107 @ SY624 ) )
| ~ ! [SY626: $i,SY627: $i] :
( ~ ( relation @ SY627 )
| ~ ( in @ ( ordered_pair @ SV107 @ SY621 ) @ ( relation_composition @ ( identity_relation @ SY626 ) @ SY627 ) )
| ( in @ ( ordered_pair @ SV107 @ SY621 ) @ SY627 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(933,plain,
( ( ~ ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) )
| ~ ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[767]) ).
thf(934,plain,
! [SV108: $i] :
( ( ~ ( relation @ SV108 )
| ~ ( ~ ! [SY628: $i] :
( ~ ( relation @ SY628 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SY628 @ SV108 ) @ ( sK20_SY399 @ SY628 @ SV108 ) ) @ SV108 )
| ~ ~ ( in @ ( ordered_pair @ ( sK19_C @ SY628 @ SV108 ) @ ( sK20_SY399 @ SY628 @ SV108 ) ) @ SY628 ) )
| ( subset @ SV108 @ SY628 ) )
| ~ ! [SY629: $i] :
( ~ ( relation @ SY629 )
| ~ ( subset @ SV108 @ SY629 )
| ! [SY630: $i,SY631: $i] :
( ~ ( in @ ( ordered_pair @ SY630 @ SY631 ) @ SV108 )
| ( in @ ( ordered_pair @ SY630 @ SY631 ) @ SY629 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(935,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK30_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK30_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK30_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK30_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)],[769]) ).
thf(936,plain,
! [SV109: $i] :
( ( ~ ( ~ ! [SY632: $i,SY633: $i] :
( ~ ( relation @ SY633 )
| ~ ( in @ ( ordered_pair @ SV109 @ SY632 ) @ SY633 )
| ( in @ SV109 @ ( relation_dom @ SY633 ) ) )
| ~ ! [SY634: $i,SY635: $i] :
( ~ ( relation @ SY635 )
| ~ ( in @ ( ordered_pair @ SV109 @ SY634 ) @ SY635 )
| ( in @ SY634 @ ( relation_rng @ SY635 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(937,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)],[771]) ).
thf(938,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[772]) ).
thf(939,plain,
! [SV110: $i] :
( ( ~ ( function @ SV110 )
| ~ ( relation @ SV110 )
| ~ ( one_to_one @ SV110 )
| ~ ( ~ ! [SY636: $i] :
( ~ ( function @ SY636 )
| ~ ( relation @ SY636 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SY636 @ SV110 )
= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ( ( sK70_C @ SY636 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY636 @ SV110 )
= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY636 @ SV110 )
= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ( ( sK71_SY424 @ SY636 @ SV110 )
!= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK70_C @ SY636 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK71_SY424 @ SY636 @ SV110 )
!= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY636 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK70_C @ SY636 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SY636 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SY636 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK71_SY424 @ SY636 @ SV110 )
!= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ( ( relation_dom @ SY636 )
!= ( relation_rng @ SV110 ) )
| ( SY636
= ( function_inverse @ SV110 ) ) )
| ~ ~ ( ~ ! [SY637: $i] :
( ~ ( function @ SY637 )
| ~ ( relation @ SY637 )
| ( SY637
!= ( function_inverse @ SV110 ) )
| ~ ( ~ ~ ( ~ ! [SY638: $i,SY639: $i] :
( ( SY639
!= ( apply @ SY637 @ SY638 ) )
| ~ ( in @ SY638 @ ( relation_rng @ SV110 ) )
| ( SY638
= ( apply @ SV110 @ SY639 ) ) )
| ~ ! [SY640: $i,SY641: $i] :
( ( SY641
!= ( apply @ SY637 @ SY640 ) )
| ~ ( in @ SY640 @ ( relation_rng @ SV110 ) )
| ( in @ SY641 @ ( relation_dom @ SV110 ) ) ) )
| ~ ~ ( ~ ! [SY642: $i,SY643: $i] :
( ( SY642
!= ( apply @ SV110 @ SY643 ) )
| ~ ( in @ SY643 @ ( relation_dom @ SV110 ) )
| ( SY643
= ( apply @ SY637 @ SY642 ) ) )
| ~ ! [SY644: $i] :
( ! [SY645: $i] :
( ( SY644
!= ( apply @ SV110 @ SY645 ) )
| ~ ( in @ SY645 @ ( relation_dom @ SV110 ) ) )
| ( in @ SY644 @ ( relation_rng @ SV110 ) ) ) ) ) )
| ~ ! [SY646: $i] :
( ~ ( function @ SY646 )
| ~ ( relation @ SY646 )
| ( SY646
!= ( function_inverse @ SV110 ) )
| ( ( relation_dom @ SY646 )
= ( relation_rng @ SV110 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(940,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[774]) ).
thf(941,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)],[775]) ).
thf(942,plain,
( ( ~ ~ ( empty @ sK55_A )
| ~ ( relation @ sK55_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[776]) ).
thf(943,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK18_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK18_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)],[777]) ).
thf(944,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK49_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK49_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)],[778]) ).
thf(945,plain,
! [SV111: $i] :
( ( ! [SY647: $i] :
~ ( ~ ! [SY648: $i,SY649: $i] :
( ~ ( in @ SV111 @ SY648 )
| ~ ( in @ SY647 @ SY649 )
| ( in @ ( ordered_pair @ SV111 @ SY647 ) @ ( cartesian_product2 @ SY648 @ SY649 ) ) )
| ~ ~ ( ~ ! [SY650: $i] :
( ! [SY651: $i] :
~ ( in @ ( ordered_pair @ SV111 @ SY647 ) @ ( cartesian_product2 @ SY650 @ SY651 ) )
| ( in @ SV111 @ SY650 ) )
| ~ ! [SY652: $i,SY653: $i] :
( ~ ( in @ ( ordered_pair @ SV111 @ SY647 ) @ ( cartesian_product2 @ SY652 @ SY653 ) )
| ( in @ SY647 @ SY653 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(946,plain,
( ( ( ( relation_dom @ empty_set )
!= empty_set )
| ( ( relation_rng @ empty_set )
!= empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[780]) ).
thf(947,plain,
( ( ~ ( empty @ sK57_A )
| ~ ( relation @ sK57_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[781]) ).
thf(948,plain,
! [SV112: $i] :
( ( ! [SY654: $i] :
~ ( ~ ! [SY655: $i] :
( ! [SY656: $i] :
( ( ordered_pair @ SV112 @ SY654 )
!= ( ordered_pair @ SY655 @ SY656 ) )
| ( SV112 = SY655 ) )
| ~ ! [SY657: $i,SY658: $i] :
( ( ( ordered_pair @ SV112 @ SY654 )
!= ( ordered_pair @ SY657 @ SY658 ) )
| ( SY654 = SY658 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(949,plain,
( ( ~ ( function @ sK58_A )
| ~ ( relation @ sK58_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[783]) ).
thf(950,plain,
! [SV113: $i] :
( ( ~ ( function @ SV113 )
| ~ ( relation @ SV113 )
| ~ ( ~ ~ ( ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ ( relation_dom @ SV113 ) )
| ! [SY660: $i] :
( ( SY660
!= ( apply @ SV113 @ SY659 ) )
| ( in @ ( ordered_pair @ SY659 @ SY660 ) @ SV113 ) ) )
| ~ ! [SY661: $i] :
( ~ ( in @ SY661 @ ( relation_dom @ SV113 ) )
| ! [SY662: $i] :
( ~ ( in @ ( ordered_pair @ SY661 @ SY662 ) @ SV113 )
| ( SY662
= ( apply @ SV113 @ SY661 ) ) ) ) )
| ~ ~ ( ~ ! [SY663: $i] :
( ( in @ SY663 @ ( relation_dom @ SV113 ) )
| ! [SY664: $i] :
( ( SY664
!= ( apply @ SV113 @ SY663 ) )
| ( SY664 = empty_set ) ) )
| ~ ! [SY665: $i] :
( ( in @ SY665 @ ( relation_dom @ SV113 ) )
| ! [SY666: $i] :
( ( SY666 != empty_set )
| ( SY666
= ( apply @ SV113 @ SY665 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(951,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[785]) ).
thf(952,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)],[786]) ).
thf(953,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK29_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[787]) ).
thf(954,plain,
! [SV114: $i] :
( ( ~ ( ~ ! [SY667: $i,SY668: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY668 @ SY667 @ SV114 ) @ SY668 )
| ~ ( in @ ( sK26_D @ SY668 @ SY667 @ SV114 ) @ SV114 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY668 @ SY667 @ SV114 ) @ SY668 )
| ~ ( in @ ( sK26_D @ SY668 @ SY667 @ SV114 ) @ SY667 ) ) )
| ~ ( ( in @ ( sK26_D @ SY668 @ SY667 @ SV114 ) @ SY668 )
| ( in @ ( sK26_D @ SY668 @ SY667 @ SV114 ) @ SV114 )
| ( in @ ( sK26_D @ SY668 @ SY667 @ SV114 ) @ SY667 ) ) )
| ( SY668
= ( set_union2 @ SV114 @ SY667 ) ) )
| ~ ! [SY669: $i,SY670: $i] :
( ( SY670
!= ( set_union2 @ SV114 @ SY669 ) )
| ~ ( ~ ! [SY671: $i] :
( ~ ( in @ SY671 @ SY670 )
| ( in @ SY671 @ SV114 )
| ( in @ SY671 @ SY669 ) )
| ~ ~ ( ~ ! [SY672: $i] :
( ~ ( in @ SY672 @ SV114 )
| ( in @ SY672 @ SY670 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY669 )
| ( in @ SX3 @ SY670 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(955,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[789]) ).
thf(956,plain,
! [SV115: $i] :
( ( ~ ( ~ ! [SY674: $i,SY675: $i] :
( ~ ( relation @ SY675 )
| ~ ( in @ ( ordered_pair @ SV115 @ SY674 ) @ SY675 )
| ( in @ SV115 @ ( relation_field @ SY675 ) ) )
| ~ ! [SY676: $i,SY677: $i] :
( ~ ( relation @ SY677 )
| ~ ( in @ ( ordered_pair @ SV115 @ SY676 ) @ SY677 )
| ( in @ SY676 @ ( relation_field @ SY677 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(957,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)],[791]) ).
thf(958,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)],[792]) ).
thf(959,plain,
! [SV116: $i] :
( ( ~ ( ~ ! [SY678: $i,SY679: $i] :
( ~ ( ~ ( ~ ( in @ ( sK17_D @ SY679 @ SY678 @ SV116 ) @ SV116 )
| ~ ( in @ ( sK17_D @ SY679 @ SY678 @ SV116 ) @ SY678 )
| ~ ( in @ ( sK17_D @ SY679 @ SY678 @ SV116 ) @ SY679 ) )
| ~ ~ ( ~ ( ( in @ ( sK17_D @ SY679 @ SY678 @ SV116 ) @ SV116 )
| ( in @ ( sK17_D @ SY679 @ SY678 @ SV116 ) @ SY679 ) )
| ~ ( ( in @ ( sK17_D @ SY679 @ SY678 @ SV116 ) @ SY678 )
| ( in @ ( sK17_D @ SY679 @ SY678 @ SV116 ) @ SY679 ) ) ) )
| ( SY679
= ( set_intersection2 @ SV116 @ SY678 ) ) )
| ~ ! [SY680: $i,SY681: $i] :
( ( SY681
!= ( set_intersection2 @ SV116 @ SY680 ) )
| ~ ( ~ ! [SY682: $i] :
( ~ ( in @ SY682 @ SV116 )
| ~ ( in @ SY682 @ SY680 )
| ( in @ SY682 @ SY681 ) )
| ~ ~ ( ~ ! [SY683: $i] :
( ~ ( in @ SY683 @ SY681 )
| ( in @ SY683 @ SV116 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY681 )
| ( in @ SX3 @ SY680 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(960,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)],[794]) ).
thf(961,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK44_C @ SX1 @ SX0 )
!= ( sK45_SY414 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY414 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK44_C @ SX1 @ SX0 )
= ( sK45_SY414 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY414 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY414 @ 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)],[795]) ).
thf(962,plain,
( ( ~ ~ ( ~ ( function @ sK54_A )
| ~ ( relation @ sK54_A ) )
| ~ ( one_to_one @ sK54_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[796]) ).
thf(963,plain,
! [SV117: $i] :
( ( ~ ( ~ ! [SY685: $i,SY686: $i] :
( ~ ( relation @ SY686 )
| ~ ( in @ SV117 @ SY685 )
| ~ ( in @ SV117 @ ( relation_dom @ SY686 ) )
| ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SY686 @ SY685 ) ) ) )
| ~ ~ ( ~ ! [SY687: $i,SY688: $i] :
( ~ ( relation @ SY688 )
| ~ ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SY688 @ SY687 ) ) )
| ( in @ SV117 @ SY687 ) )
| ~ ! [SY689: $i,SY690: $i] :
( ~ ( relation @ SY690 )
| ~ ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SY690 @ SY689 ) ) )
| ( in @ SV117 @ ( relation_dom @ SY690 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(964,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK50_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK50_C @ SX1 @ SX0 ) )
!= ( sK50_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)],[798]) ).
thf(965,plain,
! [SV118: $i] :
( ( ~ ( ~ ! [SY691: $i,SY692: $i] :
( ~ ( ~ ( ! [SY693: $i,SY694: $i] :
( ~ ( in @ SY693 @ SV118 )
| ~ ( in @ SY694 @ SY691 )
| ( ( sK23_D @ SY692 @ SY691 @ SV118 )
!= ( ordered_pair @ SY693 @ SY694 ) ) )
| ~ ( in @ ( sK23_D @ SY692 @ SY691 @ SV118 ) @ SY692 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY403 @ SY692 @ SY691 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK25_SY405 @ SY692 @ SY691 @ SV118 ) @ SY691 ) )
| ( ( sK23_D @ SY692 @ SY691 @ SV118 )
!= ( ordered_pair @ ( sK24_SY403 @ SY692 @ SY691 @ SV118 ) @ ( sK25_SY405 @ SY692 @ SY691 @ SV118 ) ) ) )
| ( in @ ( sK23_D @ SY692 @ SY691 @ SV118 ) @ SY692 ) ) )
| ( SY692
= ( cartesian_product2 @ SV118 @ SY691 ) ) )
| ~ ! [SY695: $i,SY696: $i] :
( ( SY696
!= ( cartesian_product2 @ SV118 @ SY695 ) )
| ~ ( ~ ! [SY697: $i] :
( ! [SY698: $i,SY699: $i] :
( ~ ( in @ SY698 @ SV118 )
| ~ ( in @ SY699 @ SY695 )
| ( SY697
!= ( ordered_pair @ SY698 @ SY699 ) ) )
| ( in @ SY697 @ SY696 ) )
| ~ ! [SY700: $i] :
( ~ ( in @ SY700 @ SY696 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY700 @ SY696 @ SY695 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK22_SY400 @ SY700 @ SY696 @ SY695 @ SV118 ) @ SY695 ) )
| ( SY700
!= ( ordered_pair @ ( sK21_E @ SY700 @ SY696 @ SY695 @ SV118 ) @ ( sK22_SY400 @ SY700 @ SY696 @ SY695 @ SV118 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(966,plain,
! [SV119: $i] :
( ( ~ ( ~ ! [SY701: $i] :
( ~ ( subset @ SV119 @ SY701 )
| ! [SY702: $i] : ( subset @ ( cartesian_product2 @ SV119 @ SY702 ) @ ( cartesian_product2 @ SY701 @ SY702 ) ) )
| ~ ! [SY703: $i] :
( ~ ( subset @ SV119 @ SY703 )
| ! [SY704: $i] : ( subset @ ( cartesian_product2 @ SY704 @ SV119 ) @ ( cartesian_product2 @ SY704 @ SY703 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(967,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ ( sK16_SY398 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK16_SY398 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK15_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 @ ( sK14_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK14_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[801]) ).
thf(968,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)],[802]) ).
thf(969,plain,
! [SV120: $i] :
( ( ~ ( relation @ SV120 )
| ~ ( ~ ! [SY705: $i] :
( ~ ( relation @ SY705 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SY705 @ SV120 ) @ ( sK66_SY420 @ SY705 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SY705 @ SV120 ) @ ( sK66_SY420 @ SY705 @ SV120 ) ) @ SY705 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_C @ SY705 @ SV120 ) @ ( sK66_SY420 @ SY705 @ SV120 ) ) @ SV120 )
| ( in @ ( ordered_pair @ ( sK65_C @ SY705 @ SV120 ) @ ( sK66_SY420 @ SY705 @ SV120 ) ) @ SY705 ) ) )
| ( SV120 = SY705 ) )
| ~ ! [SY706: $i] :
( ~ ( relation @ SY706 )
| ( SV120 != SY706 )
| ~ ( ~ ! [SY707: $i,SY708: $i] :
( ~ ( in @ ( ordered_pair @ SY707 @ SY708 ) @ SV120 )
| ( in @ ( ordered_pair @ SY707 @ SY708 ) @ SY706 ) )
| ~ ! [SY709: $i,SY710: $i] :
( ~ ( in @ ( ordered_pair @ SY709 @ SY710 ) @ SY706 )
| ( in @ ( ordered_pair @ SY709 @ SY710 ) @ SV120 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(970,plain,
! [SV1: $i,SV121: $i] :
( ( ~ ( relation @ SV121 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV1 @ SV121 ) ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(971,plain,
! [SV2: $i,SV122: $i] :
( ( ~ ( relation @ SV122 )
| ( subset @ ( relation_rng_restriction @ SV2 @ SV122 ) @ SV122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(972,plain,
! [SV3: $i,SV123: $i] :
( ( ~ ( relation @ SV123 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV3 @ SV123 ) ) @ ( relation_rng @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(973,plain,
! [SV4: $i,SV124: $i] :
( ( ~ ( relation @ SV124 )
| ( ( relation_rng @ ( relation_rng_restriction @ SV4 @ SV124 ) )
= ( set_intersection2 @ ( relation_rng @ SV124 ) @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(974,plain,
! [SV125: $i,SV5: $i] :
( ( ! [SY711: $i] :
( ~ ( relation @ SY711 )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV5 @ SY711 ) @ SV125 )
= ( relation_rng_restriction @ SV5 @ ( relation_dom_restriction @ SY711 @ SV125 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(975,plain,
! [SV6: $i,SV126: $i] :
( ( ~ ( relation @ SV126 )
| ( subset @ ( relation_image @ SV126 @ SV6 ) @ ( relation_rng @ SV126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(976,plain,
! [SV7: $i,SV127: $i] :
( ( ~ ( relation @ SV127 )
| ( ( relation_image @ SV127 @ SV7 )
= ( relation_image @ SV127 @ ( set_intersection2 @ ( relation_dom @ SV127 ) @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(977,plain,
! [SV8: $i] :
( ( ( ~ ( relation @ SV8 ) )
= $true )
| ( ( ( relation_image @ SV8 @ ( relation_dom @ SV8 ) )
= ( relation_rng @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[811]) ).
thf(978,plain,
! [SV9: $i] :
( ( ( ~ ( relation @ SV9 ) )
= $true )
| ( ( ! [SY433: $i] :
( ~ ( relation @ SY433 )
| ( ( relation_rng @ ( relation_composition @ SV9 @ SY433 ) )
= ( relation_image @ SY433 @ ( relation_rng @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[812]) ).
thf(979,plain,
! [SV10: $i,SV128: $i] :
( ( ~ ( relation @ SV128 )
| ( subset @ ( relation_inverse_image @ SV128 @ SV10 ) @ ( relation_dom @ SV128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(980,plain,
! [SV129: $i,SV11: $i] :
( ( ! [SY712: $i] :
( ~ ( relation @ SY712 )
| ~ ( subset @ SV11 @ SV129 )
| ( subset @ ( relation_inverse_image @ SY712 @ SV11 ) @ ( relation_inverse_image @ SY712 @ SV129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(981,plain,
! [SV12: $i] :
( ( ( ~ ( relation @ SV12 ) )
= $true )
| ( ( subset @ SV12 @ ( cartesian_product2 @ ( relation_dom @ SV12 ) @ ( relation_rng @ SV12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[815]) ).
thf(982,plain,
! [SV13: $i] :
( ( ( ~ ( relation @ SV13 ) )
= $true )
| ( ( ! [SY437: $i] :
( ~ ( relation @ SY437 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV13 @ SY437 ) ) @ ( relation_dom @ SV13 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[816]) ).
thf(983,plain,
! [SV14: $i] :
( ( ( ~ ( relation @ SV14 ) )
= $true )
| ( ( ! [SY438: $i] :
( ~ ( relation @ SY438 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV14 @ SY438 ) ) @ ( relation_rng @ SY438 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[817]) ).
thf(984,plain,
! [SV15: $i] :
( ( ( ~ ( relation @ SV15 ) )
= $true )
| ( ( ! [SY439: $i] :
( ~ ( relation @ SY439 )
| ~ ( subset @ ( relation_rng @ SV15 ) @ ( relation_dom @ SY439 ) )
| ( ( relation_dom @ ( relation_composition @ SV15 @ SY439 ) )
= ( relation_dom @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[818]) ).
thf(985,plain,
! [SV16: $i] :
( ( ( ~ ( relation @ SV16 ) )
= $true )
| ( ( ! [SY440: $i] :
( ~ ( relation @ SY440 )
| ~ ( subset @ ( relation_dom @ SV16 ) @ ( relation_rng @ SY440 ) )
| ( ( relation_rng @ ( relation_composition @ SY440 @ SV16 ) )
= ( relation_rng @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[819]) ).
thf(986,plain,
! [SV17: $i,SV130: $i] :
( ( ~ ( relation @ SV130 )
| ( subset @ ( relation_dom_restriction @ SV130 @ SV17 ) @ SV130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(987,plain,
! [SV18: $i,SV131: $i] :
( ( ~ ( relation @ SV131 )
| ( ( relation_dom @ ( relation_dom_restriction @ SV131 @ SV18 ) )
= ( set_intersection2 @ ( relation_dom @ SV131 ) @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(988,plain,
! [SV19: $i,SV132: $i] :
( ( ~ ( relation @ SV132 )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV132 @ SV19 ) ) @ ( relation_rng @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(989,plain,
! [SV20: $i] :
( ( ( ~ ( empty @ SV20 ) )
= $true )
| ( ( function @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[823]) ).
thf(990,plain,
! [SV21: $i] :
( ( ( ~ ( empty @ SV21 ) )
= $true )
| ( ( relation @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[824]) ).
thf(991,plain,
! [SV22: $i] :
( ( ( ~ ( relation @ SV22 ) )
= $true )
| ( ( ( relation_field @ SV22 )
= ( set_union2 @ ( relation_dom @ SV22 ) @ ( relation_rng @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[825]) ).
thf(992,plain,
! [SV23: $i] :
( ( ( ~ ( function @ SV23 )
| ~ ( relation @ SV23 ) )
= $true )
| ( ( ~ ( one_to_one @ SV23 )
| ( ( function_inverse @ SV23 )
= ( relation_inverse @ SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[826]) ).
thf(993,plain,
! [SV24: $i] :
( ( ( ~ ( relation @ SV24 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[827]) ).
thf(994,plain,
! [SV133: $i,SV25: $i] :
( ( ~ ( relation @ SV25 )
| ~ ( relation @ SV133 )
| ( relation @ ( relation_composition @ SV25 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(995,plain,
! [SV27: $i] :
( ( ( ~ ( relation @ SV27 ) )
= $true )
| ( ( ! [SY445: $i] : ( relation @ ( relation_dom_restriction @ SV27 @ SY445 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[830]) ).
thf(996,plain,
! [SV28: $i,SV134: $i] :
( ( ~ ( relation @ SV134 )
| ( relation @ ( relation_rng_restriction @ SV28 @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(997,plain,
! [SV135: $i,SV29: $i] :
( ( ~ ( relation @ SV29 )
| ~ ( relation @ SV135 )
| ( relation @ ( set_intersection2 @ SV29 @ SV135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(998,plain,
! [SV136: $i,SV30: $i] :
( ( ~ ( relation @ SV30 )
| ~ ( relation @ SV136 )
| ( relation @ ( set_union2 @ SV30 @ SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(999,plain,
! [SV31: $i] :
( ( ( ( empty @ SV31 )
| ~ ( relation @ SV31 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV31 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[834]) ).
thf(1000,plain,
! [SV32: $i] :
( ( ( ( empty @ SV32 )
| ~ ( relation @ SV32 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV32 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[835]) ).
thf(1001,plain,
! [SV33: $i] :
( ( ( ~ ( relation @ SV33 ) )
= $true )
| ( ( ( relation_inverse @ ( relation_inverse @ SV33 ) )
= SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[836]) ).
thf(1002,plain,
! [SV34: $i] :
( ( ( singleton @ SV34 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[837]) ).
thf(1003,plain,
! [SV137: $i,SV35: $i] :
( ( ~ ( in @ SV35 @ SV137 )
| ( ( set_union2 @ ( singleton @ SV35 ) @ SV137 )
= SV137 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(1004,plain,
! [SV138: $i,SV36: $i] :
( ( ~ ( in @ SV36 @ SV138 )
| ( subset @ SV36 @ ( union @ SV138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(1005,plain,
! [SV139: $i,SV37: $i] :
( ( ! [SY713: $i,SY714: $i] :
( ~ ( subset @ SV37 @ SV139 )
| ~ ( subset @ SY713 @ SY714 )
| ( subset @ ( cartesian_product2 @ SV37 @ SY713 ) @ ( cartesian_product2 @ SV139 @ SY714 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(1006,plain,
! [SV140: $i,SV38: $i] :
( ( ~ ( subset @ SV38 @ SV140 )
| ( ( set_union2 @ SV38 @ SV140 )
= SV140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(1007,plain,
! [SV39: $i,SV141: $i] :
( ( ~ ( relation @ SV141 )
| ( SV39 = empty_set )
| ~ ( subset @ SV39 @ ( relation_rng @ SV141 ) )
| ( ( relation_inverse_image @ SV141 @ SV39 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(1008,plain,
! [SV142: $i,SV40: $i] :
( ( subset @ ( set_intersection2 @ SV40 @ SV142 ) @ SV40 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(1009,plain,
! [SV143: $i,SV41: $i] :
( ( ! [SY715: $i] :
( ~ ( subset @ SV41 @ SV143 )
| ~ ( subset @ SV41 @ SY715 )
| ( subset @ SV41 @ ( set_intersection2 @ SV143 @ SY715 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(1010,plain,
! [SV144: $i,SV42: $i] :
( ( ! [SY716: $i] :
( ~ ( subset @ SV42 @ SV144 )
| ~ ( subset @ SV144 @ SY716 )
| ( subset @ SV42 @ SY716 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(1011,plain,
! [SV43: $i,SV145: $i] :
( ( ~ ( function @ SV145 )
| ~ ( relation @ SV145 )
| ! [SY717: $i] :
( ~ ( function @ SY717 )
| ~ ( relation @ SY717 )
| ~ ( in @ SV43 @ ( relation_dom @ ( relation_composition @ SY717 @ SV145 ) ) )
| ( ( apply @ ( relation_composition @ SY717 @ SV145 ) @ SV43 )
= ( apply @ SV145 @ ( apply @ SY717 @ SV43 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(1012,plain,
! [SV44: $i,SV146: $i] :
( ( ~ ( function @ SV146 )
| ~ ( relation @ SV146 )
| ! [SY718: $i] :
( ~ ( function @ SY718 )
| ~ ( relation @ SY718 )
| ~ ( in @ SV44 @ ( relation_dom @ SV146 ) )
| ( ( apply @ ( relation_composition @ SV146 @ SY718 ) @ SV44 )
= ( apply @ SY718 @ ( apply @ SV146 @ SV44 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(1013,plain,
! [SV147: $i,SV45: $i] :
( ( ~ ( subset @ SV45 @ SV147 )
| ! [SY719: $i] : ( subset @ ( set_intersection2 @ SV45 @ SY719 ) @ ( set_intersection2 @ SV147 @ SY719 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(1014,plain,
! [SV148: $i,SV46: $i] :
( ( ~ ( subset @ SV46 @ SV148 )
| ( ( set_intersection2 @ SV46 @ SV148 )
= SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(1015,plain,
! [SV149: $i,SV48: $i] :
( ( ~ ( subset @ SV48 @ SV149 )
| ! [SY720: $i] : ( subset @ ( set_difference @ SV48 @ SY720 ) @ ( set_difference @ SV149 @ SY720 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(1016,plain,
! [SV49: $i,SV150: $i] :
( ( ~ ( in @ SV150 @ SV49 )
| ( ( apply @ ( identity_relation @ SV49 ) @ SV150 )
= SV150 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(1017,plain,
! [SV151: $i,SV50: $i] :
( ( subset @ ( set_difference @ SV50 @ SV151 ) @ SV50 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(1018,plain,
! [SV152: $i,SV51: $i] :
( ( ( set_union2 @ SV51 @ ( set_difference @ SV152 @ SV51 ) )
= ( set_union2 @ SV51 @ SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(1019,plain,
! [SV52: $i] :
( ( ( ~ ( subset @ SV52 @ empty_set ) )
= $true )
| ( ( SV52 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[855]) ).
thf(1020,plain,
! [SV153: $i,SV53: $i] :
( ( ( set_difference @ ( set_union2 @ SV53 @ SV153 ) @ SV153 )
= ( set_difference @ SV53 @ SV153 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(1021,plain,
! [SV154: $i,SV54: $i] :
( ( ~ ( subset @ SV54 @ SV154 )
| ( SV154
= ( set_union2 @ SV54 @ ( set_difference @ SV154 @ SV54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(1022,plain,
! [SV155: $i,SV55: $i] :
( ( ~ ( in @ SV55 @ SV155 )
| ( ( set_union2 @ ( singleton @ SV55 ) @ SV155 )
= SV155 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(1023,plain,
! [SV156: $i,SV56: $i] :
( ( ( set_difference @ SV56 @ ( set_difference @ SV56 @ SV156 ) )
= ( set_intersection2 @ SV56 @ SV156 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(1024,plain,
! [SV57: $i] :
( ( ( ~ ( relation @ SV57 ) )
= $true )
| ( ( ( in @ ( ordered_pair @ ( sK46_B @ SV57 ) @ ( sK47_SY415 @ SV57 ) ) @ SV57 )
| ( SV57 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[860]) ).
thf(1025,plain,
! [SV58: $i,SV157: $i] :
( ( ~ ( proper_subset @ SV157 @ SV58 )
| ~ ( subset @ SV58 @ SV157 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(1026,plain,
! [SV59: $i,SV158: $i] :
( ( ! [SY721: $i] :
( ~ ( disjoint @ SV158 @ SY721 )
| ~ ( subset @ SV59 @ SV158 )
| ( disjoint @ SV59 @ SY721 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(1027,plain,
! [SV159: $i,SV60: $i] :
( ( ~ ( subset @ ( singleton @ SV60 ) @ ( singleton @ SV159 ) )
| ( SV60 = SV159 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[863]) ).
thf(1028,plain,
! [SV160: $i,SV61: $i] :
( ( subset @ SV61 @ ( set_union2 @ SV61 @ SV160 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(1029,plain,
! [SV161: $i,SV62: $i] :
( ( ! [SY722: $i] :
( ~ ( subset @ SV62 @ SV161 )
| ~ ( subset @ SY722 @ SV161 )
| ( subset @ ( set_union2 @ SV62 @ SY722 ) @ SV161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(1030,plain,
! [SV162: $i,SV63: $i] :
( ( ~ ( in @ SV63 @ SV162 )
| ( subset @ SV63 @ ( union @ SV162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(1031,plain,
! [SV64: $i,SV163: $i] :
( ( ~ ( relation @ SV163 )
| ( ( relation_dom_restriction @ SV163 @ SV64 )
= ( relation_composition @ ( identity_relation @ SV64 ) @ SV163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(1032,plain,
! [SV164: $i,SV65: $i] :
( ( ~ ( in @ SV65 @ SV164 )
| ~ ( in @ SV164 @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(1033,plain,
! [SV165: $i,SV66: $i] :
( ( ( set_union2 @ SV66 @ SV165 )
= ( set_union2 @ SV165 @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(1034,plain,
! [SV166: $i,SV67: $i] :
( ( ( set_intersection2 @ SV67 @ SV166 )
= ( set_intersection2 @ SV166 @ SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[870]) ).
thf(1035,plain,
! [SV68: $i] :
( ( empty @ ( powerset @ SV68 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[871]) ).
thf(1036,plain,
! [SV167: $i,SV69: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV69 @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(1037,plain,
! [SV70: $i] :
( ( empty @ ( singleton @ SV70 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[873]) ).
thf(1038,plain,
! [SV71: $i] :
( ( ( empty @ SV71 )
= $true )
| ( ( ! [SY490: $i] :
~ ( empty @ ( set_union2 @ SV71 @ SY490 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[874]) ).
thf(1039,plain,
! [SV168: $i,SV72: $i] :
( ( ~ ( empty @ ( unordered_pair @ SV72 @ SV168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(1040,plain,
! [SV73: $i] :
( ( ( empty @ SV73 )
= $true )
| ( ( ! [SY492: $i] :
~ ( empty @ ( set_union2 @ SY492 @ SV73 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[876]) ).
thf(1041,plain,
! [SV169: $i,SV74: $i] :
( ( ( empty @ SV74 )
| ( empty @ SV169 )
| ~ ( empty @ ( cartesian_product2 @ SV74 @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[877]) ).
thf(1042,plain,
! [SV170: $i,SV79: $i] :
( ( ~ ( in @ SV79 @ SV170 )
| ( element @ SV79 @ SV170 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(1043,plain,
! [SV171: $i,SV81: $i] :
( ( ~ ( element @ SV81 @ SV171 )
| ( empty @ SV171 )
| ( in @ SV81 @ SV171 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[885]) ).
thf(1044,plain,
! [SV84: $i] :
( ( ( ~ ( empty @ SV84 ) )
= $true )
| ( ( SV84 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[888]) ).
thf(1045,plain,
! [SV85: $i,SV172: $i] :
( ( ~ ( empty @ SV172 )
| ~ ( in @ SV85 @ SV172 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(1046,plain,
! [SV173: $i,SV86: $i] :
( ( ( SV86 = SV173 )
| ~ ( empty @ SV86 )
| ~ ( empty @ SV173 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(1047,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[892]) ).
thf(1048,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[892]) ).
thf(1049,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[893]) ).
thf(1050,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)],[893]) ).
thf(1051,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY406 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ ( sK33_SY406 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK31_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)],[894]) ).
thf(1052,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)],[894]) ).
thf(1053,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK48_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[895]) ).
thf(1054,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[895]) ).
thf(1055,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)],[896]) ).
thf(1056,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)],[896]) ).
thf(1057,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[897]) ).
thf(1058,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[897]) ).
thf(1059,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[898]) ).
thf(1060,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[898]) ).
thf(1061,plain,
! [SV87: $i] :
( ( ~ ! [SY498: $i,SY499: $i] :
( ~ ( relation @ SY499 )
| ! [SY500: $i] :
( ~ ( in @ SY500 @ ( relation_dom @ SY499 ) )
| ~ ( in @ ( ordered_pair @ SY500 @ SV87 ) @ SY499 )
| ~ ( in @ SY500 @ SY498 ) )
| ( in @ SV87 @ ( relation_image @ SY499 @ SY498 ) ) )
| ~ ! [SY501: $i,SY502: $i] :
( ~ ( relation @ SY502 )
| ~ ( in @ SV87 @ ( relation_image @ SY502 @ SY501 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK52_D @ SY502 @ SY501 @ SV87 ) @ ( relation_dom @ SY502 ) )
| ~ ( in @ ( ordered_pair @ ( sK52_D @ SY502 @ SY501 @ SV87 ) @ SV87 ) @ SY502 ) )
| ~ ( in @ ( sK52_D @ SY502 @ SY501 @ SV87 ) @ SY501 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[899]) ).
thf(1062,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[900]) ).
thf(1063,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)],[900]) ).
thf(1064,plain,
( ( ~ ( relation @ sK53_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[901]) ).
thf(1065,plain,
( ( ~ ( relation_empty_yielding @ sK53_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[901]) ).
thf(1066,plain,
! [SV88: $i] :
( ( ~ ! [SY503: $i,SY504: $i] :
( ~ ( ~ ( ~ ( in @ ( sK13_D @ SY504 @ SY503 @ SV88 ) @ SV88 )
| ( in @ ( sK13_D @ SY504 @ SY503 @ SV88 ) @ SY503 )
| ~ ( in @ ( sK13_D @ SY504 @ SY503 @ SV88 ) @ SY504 ) )
| ~ ~ ( ~ ( ( in @ ( sK13_D @ SY504 @ SY503 @ SV88 ) @ SV88 )
| ( in @ ( sK13_D @ SY504 @ SY503 @ SV88 ) @ SY504 ) )
| ~ ( ~ ( in @ ( sK13_D @ SY504 @ SY503 @ SV88 ) @ SY503 )
| ( in @ ( sK13_D @ SY504 @ SY503 @ SV88 ) @ SY504 ) ) ) )
| ( SY504
= ( set_difference @ SV88 @ SY503 ) ) )
| ~ ! [SY505: $i,SY506: $i] :
( ( SY506
!= ( set_difference @ SV88 @ SY505 ) )
| ~ ( ~ ! [SY507: $i] :
( ~ ( in @ SY507 @ SV88 )
| ( in @ SY507 @ SY505 )
| ( in @ SY507 @ SY506 ) )
| ~ ~ ( ~ ! [SY508: $i] :
( ~ ( in @ SY508 @ SY506 )
| ( in @ SY508 @ SV88 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY506 )
| ~ ( in @ SX3 @ SY505 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(1067,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)],[903]) ).
thf(1068,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)],[903]) ).
thf(1069,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[904]) ).
thf(1070,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[904]) ).
thf(1071,plain,
! [SV89: $i,SV174: $i] :
( ( ~ ( relation @ SV174 )
| ~ ( ~ ! [SY723: $i] :
( ~ ( relation @ SY723 )
| ~ ( ~ ( ~ ( in @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY723 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) ) @ SV174 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY723 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) ) @ SY723 ) )
| ~ ~ ( ~ ( ( in @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) @ SV89 )
| ( in @ ( ordered_pair @ ( sK40_D @ SY723 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) ) @ SY723 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SY723 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) ) @ SV174 )
| ( in @ ( ordered_pair @ ( sK40_D @ SY723 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) ) @ SY723 ) ) ) )
| ( SY723
= ( relation_rng_restriction @ SV89 @ SV174 ) ) )
| ~ ! [SY724: $i] :
( ~ ( relation @ SY724 )
| ( SY724
!= ( relation_rng_restriction @ SV89 @ SV174 ) )
| ~ ( ~ ! [SY725: $i,SY726: $i] :
( ~ ( in @ SY726 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY725 @ SY726 ) @ SV174 )
| ( in @ ( ordered_pair @ SY725 @ SY726 ) @ SY724 ) )
| ~ ~ ( ~ ! [SY515: $i,SY516: $i] :
( ~ ( in @ ( ordered_pair @ SY515 @ SY516 ) @ SY724 )
| ( in @ SY516 @ SV89 ) )
| ~ ! [SY729: $i,SY730: $i] :
( ~ ( in @ ( ordered_pair @ SY729 @ SY730 ) @ SY724 )
| ( in @ ( ordered_pair @ SY729 @ SY730 ) @ SV174 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(1072,plain,
! [SV90: $i] :
( ( ~ ! [SY519: $i,SY520: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY520 @ SY519 @ SV90 ) @ SY520 )
| ( ( sK27_D @ SY520 @ SY519 @ SV90 )
!= SV90 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY520 @ SY519 @ SV90 ) @ SY520 )
| ( ( sK27_D @ SY520 @ SY519 @ SV90 )
!= SY519 ) ) )
| ~ ( ( in @ ( sK27_D @ SY520 @ SY519 @ SV90 ) @ SY520 )
| ( ( sK27_D @ SY520 @ SY519 @ SV90 )
= SV90 )
| ( ( sK27_D @ SY520 @ SY519 @ SV90 )
= SY519 ) ) )
| ( SY520
= ( unordered_pair @ SV90 @ SY519 ) ) )
| ~ ! [SY521: $i,SY522: $i] :
( ( SY522
!= ( unordered_pair @ SV90 @ SY521 ) )
| ~ ( ~ ! [SY523: $i] :
( ~ ( in @ SY523 @ SY522 )
| ( SY523 = SV90 )
| ( SY523 = SY521 ) )
| ~ ~ ( ~ ! [SY524: $i] :
( ( SY524 != SV90 )
| ( in @ SY524 @ SY522 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY521 )
| ( in @ SX3 @ SY522 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[906]) ).
thf(1073,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK28_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK28_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[907]) ).
thf(1074,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)],[907]) ).
thf(1075,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[908]) ).
thf(1076,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[908]) ).
thf(1077,plain,
! [SV91: $i] :
( ( ( ~ ( relation @ SV91 ) )
= $true )
| ( ( ~ ( ~ ! [SY526: $i] :
( ~ ( ~ ( ! [SY527: $i] :
~ ( in @ ( ordered_pair @ ( sK63_C @ SY526 @ SV91 ) @ SY527 ) @ SV91 )
| ~ ( in @ ( sK63_C @ SY526 @ SV91 ) @ SY526 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_C @ SY526 @ SV91 ) @ ( sK64_SY419 @ SY526 @ SV91 ) ) @ SV91 )
| ( in @ ( sK63_C @ SY526 @ SV91 ) @ SY526 ) ) )
| ( SY526
= ( relation_dom @ SV91 ) ) )
| ~ ! [SY528: $i] :
( ( SY528
!= ( relation_dom @ SV91 ) )
| ~ ( ~ ! [SY529: $i] :
( ! [SY530: $i] :
~ ( in @ ( ordered_pair @ SY529 @ SY530 ) @ SV91 )
| ( in @ SY529 @ SY528 ) )
| ~ ! [SY531: $i] :
( ~ ( in @ SY531 @ SY528 )
| ( in @ ( ordered_pair @ SY531 @ ( sK62_D @ SY531 @ SY528 @ SV91 ) ) @ SV91 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[909]) ).
thf(1078,plain,
! [SV92: $i] :
( ( ( ~ ( relation @ SV92 ) )
= $true )
| ( ( ~ ( ~ ! [SY532: $i,SY533: $i] :
( ~ ( ~ ( ! [SY534: $i] :
( ~ ( in @ ( ordered_pair @ ( sK35_D @ SY533 @ SY532 @ SV92 ) @ SY534 ) @ SV92 )
| ~ ( in @ SY534 @ SY532 ) )
| ~ ( in @ ( sK35_D @ SY533 @ SY532 @ SV92 ) @ SY533 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SY533 @ SY532 @ SV92 ) @ ( sK36_SY409 @ SY533 @ SY532 @ SV92 ) ) @ SV92 )
| ~ ( in @ ( sK36_SY409 @ SY533 @ SY532 @ SV92 ) @ SY532 ) )
| ( in @ ( sK35_D @ SY533 @ SY532 @ SV92 ) @ SY533 ) ) )
| ( SY533
= ( relation_inverse_image @ SV92 @ SY532 ) ) )
| ~ ! [SY535: $i,SY536: $i] :
( ( SY536
!= ( relation_inverse_image @ SV92 @ SY535 ) )
| ~ ( ~ ! [SY537: $i] :
( ! [SY538: $i] :
( ~ ( in @ ( ordered_pair @ SY537 @ SY538 ) @ SV92 )
| ~ ( in @ SY538 @ SY535 ) )
| ( in @ SY537 @ SY536 ) )
| ~ ! [SY539: $i] :
( ~ ( in @ SY539 @ SY536 )
| ~ ( ~ ( in @ ( ordered_pair @ SY539 @ ( sK34_E @ SY539 @ SY536 @ SY535 @ SV92 ) ) @ SV92 )
| ~ ( in @ ( sK34_E @ SY539 @ SY536 @ SY535 @ SV92 ) @ SY535 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[910]) ).
thf(1079,plain,
! [SV93: $i] :
( ( ( ~ ( relation @ SV93 ) )
= $true )
| ( ( ~ ( ~ ! [SY540: $i,SY541: $i] :
( ~ ( ~ ( ! [SY542: $i] :
( ~ ( in @ ( ordered_pair @ SY542 @ ( sK38_D @ SY541 @ SY540 @ SV93 ) ) @ SV93 )
| ~ ( in @ SY542 @ SY540 ) )
| ~ ( in @ ( sK38_D @ SY541 @ SY540 @ SV93 ) @ SY541 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SY541 @ SY540 @ SV93 ) @ ( sK38_D @ SY541 @ SY540 @ SV93 ) ) @ SV93 )
| ~ ( in @ ( sK39_SY411 @ SY541 @ SY540 @ SV93 ) @ SY540 ) )
| ( in @ ( sK38_D @ SY541 @ SY540 @ SV93 ) @ SY541 ) ) )
| ( SY541
= ( relation_image @ SV93 @ SY540 ) ) )
| ~ ! [SY543: $i,SY544: $i] :
( ( SY544
!= ( relation_image @ SV93 @ SY543 ) )
| ~ ( ~ ! [SY545: $i] :
( ! [SY546: $i] :
( ~ ( in @ ( ordered_pair @ SY546 @ SY545 ) @ SV93 )
| ~ ( in @ SY546 @ SY543 ) )
| ( in @ SY545 @ SY544 ) )
| ~ ! [SY547: $i] :
( ~ ( in @ SY547 @ SY544 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SY547 @ SY544 @ SY543 @ SV93 ) @ SY547 ) @ SV93 )
| ~ ( in @ ( sK37_E @ SY547 @ SY544 @ SY543 @ SV93 ) @ SY543 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[911]) ).
thf(1080,plain,
! [SV94: $i] :
( ( ~ ! [SY548: $i,SY549: $i] :
( ~ ( relation @ SY549 )
| ! [SY550: $i] :
( ~ ( in @ SY550 @ ( relation_rng @ SY549 ) )
| ~ ( in @ ( ordered_pair @ SV94 @ SY550 ) @ SY549 )
| ~ ( in @ SY550 @ SY548 ) )
| ( in @ SV94 @ ( relation_inverse_image @ SY549 @ SY548 ) ) )
| ~ ! [SY551: $i,SY552: $i] :
( ~ ( relation @ SY552 )
| ~ ( in @ SV94 @ ( relation_inverse_image @ SY552 @ SY551 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK51_D @ SY552 @ SY551 @ SV94 ) @ ( relation_rng @ SY552 ) )
| ~ ( in @ ( ordered_pair @ SV94 @ ( sK51_D @ SY552 @ SY551 @ SV94 ) ) @ SY552 ) )
| ~ ( in @ ( sK51_D @ SY552 @ SY551 @ SV94 ) @ SY551 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[912]) ).
thf(1081,plain,
! [SV95: $i,SV175: $i] :
( ( ~ ( function @ SV175 )
| ~ ( relation @ SV175 )
| ~ ( ~ ! [SY731: $i] :
( ~ ( function @ SY731 )
| ~ ( relation @ SY731 )
| ~ ( in @ SV95 @ ( relation_dom @ SY731 ) )
| ~ ( in @ ( apply @ SY731 @ SV95 ) @ ( relation_dom @ SV175 ) )
| ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY731 @ SV175 ) ) ) )
| ~ ~ ( ~ ! [SY732: $i] :
( ~ ( function @ SY732 )
| ~ ( relation @ SY732 )
| ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY732 @ SV175 ) ) )
| ( in @ SV95 @ ( relation_dom @ SY732 ) ) )
| ~ ! [SY733: $i] :
( ~ ( function @ SY733 )
| ~ ( relation @ SY733 )
| ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY733 @ SV175 ) ) )
| ( in @ ( apply @ SY733 @ SV95 ) @ ( relation_dom @ SV175 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(1082,plain,
! [SV96: $i] :
( ( ( ~ ( relation @ SV96 ) )
= $true )
| ( ( ~ ( ~ ! [SY557: $i,SY558: $i] :
( ~ ( relation @ SY558 )
| ~ ( ~ ( ~ ( in @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ SY557 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ ( sK43_SY413 @ SY558 @ SY557 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ ( sK43_SY413 @ SY558 @ SY557 @ SV96 ) ) @ SY558 ) )
| ~ ~ ( ~ ( ( in @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ SY557 )
| ( in @ ( ordered_pair @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ ( sK43_SY413 @ SY558 @ SY557 @ SV96 ) ) @ SY558 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ ( sK43_SY413 @ SY558 @ SY557 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ ( sK43_SY413 @ SY558 @ SY557 @ SV96 ) ) @ SY558 ) ) ) )
| ( SY558
= ( relation_dom_restriction @ SV96 @ SY557 ) ) )
| ~ ! [SY559: $i,SY560: $i] :
( ~ ( relation @ SY560 )
| ( SY560
!= ( relation_dom_restriction @ SV96 @ SY559 ) )
| ~ ( ~ ! [SY561: $i,SY562: $i] :
( ~ ( in @ SY561 @ SY559 )
| ~ ( in @ ( ordered_pair @ SY561 @ SY562 ) @ SV96 )
| ( in @ ( ordered_pair @ SY561 @ SY562 ) @ SY560 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY560 )
| ( in @ SX3 @ SY559 ) )
| ~ ! [SY565: $i,SY566: $i] :
( ~ ( in @ ( ordered_pair @ SY565 @ SY566 ) @ SY560 )
| ( in @ ( ordered_pair @ SY565 @ SY566 ) @ SV96 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[914]) ).
thf(1083,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[915]) ).
thf(1084,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[915]) ).
thf(1085,plain,
! [SV97: $i] :
( ( ( ~ ( relation @ SV97 ) )
= $true )
| ( ( ~ ( ~ ! [SY567: $i] :
( ~ ( relation @ SY567 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SY567 @ SV97 ) @ ( sK12_SY396 @ SY567 @ SV97 ) ) @ SY567 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SY567 @ SV97 ) @ ( sK11_C @ SY567 @ SV97 ) ) @ SV97 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_C @ SY567 @ SV97 ) @ ( sK12_SY396 @ SY567 @ SV97 ) ) @ SY567 )
| ( in @ ( ordered_pair @ ( sK12_SY396 @ SY567 @ SV97 ) @ ( sK11_C @ SY567 @ SV97 ) ) @ SV97 ) ) )
| ( SY567
= ( relation_inverse @ SV97 ) ) )
| ~ ! [SY568: $i] :
( ~ ( relation @ SY568 )
| ( SY568
!= ( relation_inverse @ SV97 ) )
| ~ ( ~ ! [SY569: $i,SY570: $i] :
( ~ ( in @ ( ordered_pair @ SY569 @ SY570 ) @ SY568 )
| ( in @ ( ordered_pair @ SY570 @ SY569 ) @ SV97 ) )
| ~ ! [SY571: $i,SY572: $i] :
( ~ ( in @ ( ordered_pair @ SY572 @ SY571 ) @ SV97 )
| ( in @ ( ordered_pair @ SY571 @ SY572 ) @ SY568 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[916]) ).
thf(1086,plain,
! [SV98: $i] :
( ( ( ~ ( relation @ SV98 ) )
= $true )
| ( ( ~ ( ~ ! [SY573: $i] :
( ~ ( ~ ( ! [SY574: $i] :
~ ( in @ ( ordered_pair @ SY574 @ ( sK60_C @ SY573 @ SV98 ) ) @ SV98 )
| ~ ( in @ ( sK60_C @ SY573 @ SV98 ) @ SY573 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK61_SY417 @ SY573 @ SV98 ) @ ( sK60_C @ SY573 @ SV98 ) ) @ SV98 )
| ( in @ ( sK60_C @ SY573 @ SV98 ) @ SY573 ) ) )
| ( SY573
= ( relation_rng @ SV98 ) ) )
| ~ ! [SY575: $i] :
( ( SY575
!= ( relation_rng @ SV98 ) )
| ~ ( ~ ! [SY576: $i] :
( ! [SY577: $i] :
~ ( in @ ( ordered_pair @ SY577 @ SY576 ) @ SV98 )
| ( in @ SY576 @ SY575 ) )
| ~ ! [SY578: $i] :
( ~ ( in @ SY578 @ SY575 )
| ( in @ ( ordered_pair @ ( sK59_D @ SY578 @ SY575 @ SV98 ) @ SY578 ) @ SV98 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[917]) ).
thf(1087,plain,
! [SV99: $i,SV176: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK4_C @ SV176 @ SV99 ) @ SV99 )
| ~ ( in @ ( sK4_C @ SV176 @ SV99 ) @ SV176 ) )
| ~ ( ( in @ ( sK4_C @ SV176 @ SV99 ) @ SV99 )
| ( in @ ( sK4_C @ SV176 @ SV99 ) @ SV176 ) ) )
| ( SV99 = SV176 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(1088,plain,
! [SV100: $i] :
( ( ~ ! [SY580: $i,SY581: $i] :
( ~ ( function @ SY581 )
| ~ ( relation @ SY581 )
| ( SY580
!= ( apply @ SY581 @ SV100 ) )
| ~ ( in @ SV100 @ ( relation_dom @ SY581 ) )
| ( in @ ( ordered_pair @ SV100 @ SY580 ) @ SY581 ) )
| ~ ~ ( ~ ! [SY582: $i,SY583: $i] :
( ~ ( function @ SY583 )
| ~ ( relation @ SY583 )
| ~ ( in @ ( ordered_pair @ SV100 @ SY582 ) @ SY583 )
| ( SY582
= ( apply @ SY583 @ SV100 ) ) )
| ~ ! [SY584: $i,SY585: $i] :
( ~ ( function @ SY585 )
| ~ ( relation @ SY585 )
| ~ ( in @ ( ordered_pair @ SV100 @ SY584 ) @ SY585 )
| ( in @ SV100 @ ( relation_dom @ SY585 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[919]) ).
thf(1089,plain,
! [SV101: $i] :
( ( ( ~ ( relation @ SV101 ) )
= $true )
| ( ( ! [SY586: $i] :
( ~ ( relation @ SY586 )
| ~ ( ~ ! [SY587: $i] :
( ~ ( relation @ SY587 )
| ~ ( ~ ( ! [SY588: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY587 @ SY586 @ SV101 ) @ SY588 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY588 @ ( sK9_SY391 @ SY587 @ SY586 @ SV101 ) ) @ SY586 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SY587 @ SY586 @ SV101 ) @ ( sK9_SY391 @ SY587 @ SY586 @ SV101 ) ) @ SY587 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY587 @ SY586 @ SV101 ) @ ( sK10_SY395 @ SY587 @ SY586 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SY587 @ SY586 @ SV101 ) @ ( sK9_SY391 @ SY587 @ SY586 @ SV101 ) ) @ SY586 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SY587 @ SY586 @ SV101 ) @ ( sK9_SY391 @ SY587 @ SY586 @ SV101 ) ) @ SY587 ) ) )
| ( SY587
= ( relation_composition @ SV101 @ SY586 ) ) )
| ~ ! [SY589: $i] :
( ~ ( relation @ SY589 )
| ( SY589
!= ( relation_composition @ SV101 @ SY586 ) )
| ~ ( ~ ! [SY590: $i,SY591: $i] :
( ! [SY592: $i] :
( ~ ( in @ ( ordered_pair @ SY590 @ SY592 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY592 @ SY591 ) @ SY586 ) )
| ( in @ ( ordered_pair @ SY590 @ SY591 ) @ SY589 ) )
| ~ ! [SY593: $i,SY594: $i] :
( ~ ( in @ ( ordered_pair @ SY593 @ SY594 ) @ SY589 )
| ~ ( ~ ( in @ ( ordered_pair @ SY593 @ ( sK7_F @ SY594 @ SY593 @ SY589 @ SY586 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY594 @ SY593 @ SY589 @ SY586 @ SV101 ) @ SY594 ) @ SY586 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[920]) ).
thf(1090,plain,
! [SV177: $i,SV102: $i] :
( ( ~ ( ~ ! [SY734: $i,SY735: $i] :
( ~ ( in @ SV102 @ SY734 )
| ~ ( in @ SV177 @ SY735 )
| ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SY734 @ SY735 ) ) )
| ~ ~ ( ~ ! [SY736: $i] :
( ! [SY737: $i] :
~ ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SY736 @ SY737 ) )
| ( in @ SV102 @ SY736 ) )
| ~ ! [SY738: $i,SY739: $i] :
( ~ ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SY738 @ SY739 ) )
| ( in @ SV177 @ SY739 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1091,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[922]) ).
thf(1092,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[922]) ).
thf(1093,plain,
! [SV103: $i] :
( ( ~ ! [SY602: $i] :
( ~ ( subset @ SY602 @ ( sK2_B @ SV103 ) )
| ( are_equipotent @ SY602 @ ( sK2_B @ SV103 ) )
| ( in @ SY602 @ ( sK2_B @ SV103 ) ) )
| ~ ~ ( ~ ! [SY603: $i] :
( ~ ( ~ ! [SY604: $i] :
( ~ ( subset @ SY604 @ SY603 )
| ( in @ SY604 @ ( sK3_SY386 @ SY603 @ SV103 ) ) )
| ~ ( in @ ( sK3_SY386 @ SY603 @ SV103 ) @ ( sK2_B @ SV103 ) ) )
| ~ ( in @ SY603 @ ( sK2_B @ SV103 ) ) )
| ~ ~ ( ~ ! [SY605: $i,SY606: $i] :
( ~ ( in @ SY605 @ ( sK2_B @ SV103 ) )
| ~ ( subset @ SY606 @ SY605 )
| ( in @ SY606 @ ( sK2_B @ SV103 ) ) )
| ~ ( in @ SV103 @ ( sK2_B @ SV103 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[923]) ).
thf(1094,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( function @ ( function_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[924]) ).
thf(1095,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( relation @ ( function_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[924]) ).
thf(1096,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[925]) ).
thf(1097,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[925]) ).
thf(1098,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK69_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK69_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[926]) ).
thf(1099,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK67_C @ SX1 @ SX0 ) @ ( sK68_SY421 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[926]) ).
thf(1100,plain,
! [SV104: $i] :
( ( ( ~ ( relation @ SV104 ) )
= $true )
| ( ( ~ ( ~ ! [SY607: $i] :
( ~ ( relation @ SY607 )
| ~ ( subset @ SV104 @ SY607 )
| ( subset @ ( relation_dom @ SV104 ) @ ( relation_dom @ SY607 ) ) )
| ~ ! [SY608: $i] :
( ~ ( relation @ SY608 )
| ~ ( subset @ SV104 @ SY608 )
| ( subset @ ( relation_rng @ SV104 ) @ ( relation_rng @ SY608 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[927]) ).
thf(1101,plain,
! [SV105: $i] :
( ( ~ ! [SY609: $i,SY610: $i] :
( ~ ( relation @ SY610 )
| ~ ( in @ SV105 @ SY609 )
| ~ ( in @ SV105 @ ( relation_rng @ SY610 ) )
| ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SY609 @ SY610 ) ) ) )
| ~ ~ ( ~ ! [SY611: $i,SY612: $i] :
( ~ ( relation @ SY612 )
| ~ ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SY611 @ SY612 ) ) )
| ( in @ SV105 @ SY611 ) )
| ~ ! [SY613: $i,SY614: $i] :
( ~ ( relation @ SY614 )
| ~ ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SY613 @ SY614 ) ) )
| ( in @ SV105 @ ( relation_rng @ SY614 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[928]) ).
thf(1102,plain,
( ( ~ ~ ( ~ ( empty @ sK56_A )
| ~ ( relation @ sK56_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[929]) ).
thf(1103,plain,
( ( ~ ( function @ sK56_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[929]) ).
thf(1104,plain,
! [SV106: $i] :
( ( ~ ! [SY615: $i,SY616: $i] :
( ~ ( in @ SV106 @ SY616 )
| ~ ( in @ SY615 @ SY616 )
| ( subset @ ( unordered_pair @ SV106 @ SY615 ) @ SY616 ) )
| ~ ~ ( ~ ! [SY617: $i,SY618: $i] :
( ~ ( subset @ ( unordered_pair @ SV106 @ SY617 ) @ SY618 )
| ( in @ SV106 @ SY618 ) )
| ~ ! [SY619: $i,SY620: $i] :
( ~ ( subset @ ( unordered_pair @ SV106 @ SY619 ) @ SY620 )
| ( in @ SY619 @ SY620 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[930]) ).
thf(1105,plain,
( ( ~ ! [SX0: $i] :
( ( relation_dom @ ( identity_relation @ SX0 ) )
= SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[931]) ).
thf(1106,plain,
( ( ~ ! [SX0: $i] :
( ( relation_rng @ ( identity_relation @ SX0 ) )
= SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[931]) ).
thf(1107,plain,
! [SV178: $i,SV107: $i] :
( ( ~ ( ~ ! [SY740: $i,SY741: $i] :
( ~ ( relation @ SY741 )
| ~ ( in @ SV107 @ SY740 )
| ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ SY741 )
| ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SY740 ) @ SY741 ) ) )
| ~ ~ ( ~ ! [SY742: $i,SY743: $i] :
( ~ ( relation @ SY743 )
| ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SY742 ) @ SY743 ) )
| ( in @ SV107 @ SY742 ) )
| ~ ! [SY744: $i,SY745: $i] :
( ~ ( relation @ SY745 )
| ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SY744 ) @ SY745 ) )
| ( in @ ( ordered_pair @ SV107 @ SV178 ) @ SY745 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1108,plain,
( ( ~ ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[933]) ).
thf(1109,plain,
( ( ~ ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[933]) ).
thf(1110,plain,
! [SV108: $i] :
( ( ( ~ ( relation @ SV108 ) )
= $true )
| ( ( ~ ( ~ ! [SY628: $i] :
( ~ ( relation @ SY628 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SY628 @ SV108 ) @ ( sK20_SY399 @ SY628 @ SV108 ) ) @ SV108 )
| ~ ~ ( in @ ( ordered_pair @ ( sK19_C @ SY628 @ SV108 ) @ ( sK20_SY399 @ SY628 @ SV108 ) ) @ SY628 ) )
| ( subset @ SV108 @ SY628 ) )
| ~ ! [SY629: $i] :
( ~ ( relation @ SY629 )
| ~ ( subset @ SV108 @ SY629 )
| ! [SY630: $i,SY631: $i] :
( ~ ( in @ ( ordered_pair @ SY630 @ SY631 ) @ SV108 )
| ( in @ ( ordered_pair @ SY630 @ SY631 ) @ SY629 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[934]) ).
thf(1111,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK30_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK30_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK30_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK30_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[935]) ).
thf(1112,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)],[935]) ).
thf(1113,plain,
! [SV109: $i] :
( ( ~ ! [SY632: $i,SY633: $i] :
( ~ ( relation @ SY633 )
| ~ ( in @ ( ordered_pair @ SV109 @ SY632 ) @ SY633 )
| ( in @ SV109 @ ( relation_dom @ SY633 ) ) )
| ~ ! [SY634: $i,SY635: $i] :
( ~ ( relation @ SY635 )
| ~ ( in @ ( ordered_pair @ SV109 @ SY634 ) @ SY635 )
| ( in @ SY634 @ ( relation_rng @ SY635 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[936]) ).
thf(1114,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)],[937]) ).
thf(1115,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[937]) ).
thf(1116,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[938]) ).
thf(1117,plain,
( ( ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[938]) ).
thf(1118,plain,
! [SV110: $i] :
( ( ( ~ ( function @ SV110 )
| ~ ( relation @ SV110 ) )
= $true )
| ( ( ~ ( one_to_one @ SV110 )
| ~ ( ~ ! [SY636: $i] :
( ~ ( function @ SY636 )
| ~ ( relation @ SY636 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SY636 @ SV110 )
= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ( ( sK70_C @ SY636 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY636 @ SV110 )
= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY636 @ SV110 )
= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ( ( sK71_SY424 @ SY636 @ SV110 )
!= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK70_C @ SY636 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK71_SY424 @ SY636 @ SV110 )
!= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY636 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK70_C @ SY636 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SY636 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SY636 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK71_SY424 @ SY636 @ SV110 )
!= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ( ( relation_dom @ SY636 )
!= ( relation_rng @ SV110 ) )
| ( SY636
= ( function_inverse @ SV110 ) ) )
| ~ ~ ( ~ ! [SY637: $i] :
( ~ ( function @ SY637 )
| ~ ( relation @ SY637 )
| ( SY637
!= ( function_inverse @ SV110 ) )
| ~ ( ~ ~ ( ~ ! [SY638: $i,SY639: $i] :
( ( SY639
!= ( apply @ SY637 @ SY638 ) )
| ~ ( in @ SY638 @ ( relation_rng @ SV110 ) )
| ( SY638
= ( apply @ SV110 @ SY639 ) ) )
| ~ ! [SY640: $i,SY641: $i] :
( ( SY641
!= ( apply @ SY637 @ SY640 ) )
| ~ ( in @ SY640 @ ( relation_rng @ SV110 ) )
| ( in @ SY641 @ ( relation_dom @ SV110 ) ) ) )
| ~ ~ ( ~ ! [SY642: $i,SY643: $i] :
( ( SY642
!= ( apply @ SV110 @ SY643 ) )
| ~ ( in @ SY643 @ ( relation_dom @ SV110 ) )
| ( SY643
= ( apply @ SY637 @ SY642 ) ) )
| ~ ! [SY644: $i] :
( ! [SY645: $i] :
( ( SY644
!= ( apply @ SV110 @ SY645 ) )
| ~ ( in @ SY645 @ ( relation_dom @ SV110 ) ) )
| ( in @ SY644 @ ( relation_rng @ SV110 ) ) ) ) ) )
| ~ ! [SY646: $i] :
( ~ ( function @ SY646 )
| ~ ( relation @ SY646 )
| ( SY646
!= ( function_inverse @ SV110 ) )
| ( ( relation_dom @ SY646 )
= ( relation_rng @ SV110 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[939]) ).
thf(1119,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[940]) ).
thf(1120,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[940]) ).
thf(1121,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[941]) ).
thf(1122,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)],[941]) ).
thf(1123,plain,
( ( ~ ~ ( empty @ sK55_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[942]) ).
thf(1124,plain,
( ( ~ ( relation @ sK55_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[942]) ).
thf(1125,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK18_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK18_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[943]) ).
thf(1126,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[943]) ).
thf(1127,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK49_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK49_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[944]) ).
thf(1128,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[944]) ).
thf(1129,plain,
! [SV179: $i,SV111: $i] :
( ( ~ ( ~ ! [SY746: $i,SY747: $i] :
( ~ ( in @ SV111 @ SY746 )
| ~ ( in @ SV179 @ SY747 )
| ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SY746 @ SY747 ) ) )
| ~ ~ ( ~ ! [SY748: $i] :
( ! [SY749: $i] :
~ ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SY748 @ SY749 ) )
| ( in @ SV111 @ SY748 ) )
| ~ ! [SY750: $i,SY751: $i] :
( ~ ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SY750 @ SY751 ) )
| ( in @ SV179 @ SY751 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1130,plain,
( ( ( ( relation_dom @ empty_set )
!= empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[946]) ).
thf(1131,plain,
( ( ( ( relation_rng @ empty_set )
!= empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[946]) ).
thf(1132,plain,
( ( ~ ( empty @ sK57_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[947]) ).
thf(1133,plain,
( ( ~ ( relation @ sK57_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[947]) ).
thf(1134,plain,
! [SV180: $i,SV112: $i] :
( ( ~ ( ~ ! [SY752: $i] :
( ! [SY753: $i] :
( ( ordered_pair @ SV112 @ SV180 )
!= ( ordered_pair @ SY752 @ SY753 ) )
| ( SV112 = SY752 ) )
| ~ ! [SY754: $i,SY755: $i] :
( ( ( ordered_pair @ SV112 @ SV180 )
!= ( ordered_pair @ SY754 @ SY755 ) )
| ( SV180 = SY755 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1135,plain,
( ( ~ ( function @ sK58_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[949]) ).
thf(1136,plain,
( ( ~ ( relation @ sK58_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[949]) ).
thf(1137,plain,
! [SV113: $i] :
( ( ( ~ ( function @ SV113 )
| ~ ( relation @ SV113 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ ( relation_dom @ SV113 ) )
| ! [SY660: $i] :
( ( SY660
!= ( apply @ SV113 @ SY659 ) )
| ( in @ ( ordered_pair @ SY659 @ SY660 ) @ SV113 ) ) )
| ~ ! [SY661: $i] :
( ~ ( in @ SY661 @ ( relation_dom @ SV113 ) )
| ! [SY662: $i] :
( ~ ( in @ ( ordered_pair @ SY661 @ SY662 ) @ SV113 )
| ( SY662
= ( apply @ SV113 @ SY661 ) ) ) ) )
| ~ ~ ( ~ ! [SY663: $i] :
( ( in @ SY663 @ ( relation_dom @ SV113 ) )
| ! [SY664: $i] :
( ( SY664
!= ( apply @ SV113 @ SY663 ) )
| ( SY664 = empty_set ) ) )
| ~ ! [SY665: $i] :
( ( in @ SY665 @ ( relation_dom @ SV113 ) )
| ! [SY666: $i] :
( ( SY666 != empty_set )
| ( SY666
= ( apply @ SV113 @ SY665 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[950]) ).
thf(1138,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[951]) ).
thf(1139,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[951]) ).
thf(1140,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[952]) ).
thf(1141,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[952]) ).
thf(1142,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK29_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[953]) ).
thf(1143,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[953]) ).
thf(1144,plain,
! [SV114: $i] :
( ( ~ ! [SY667: $i,SY668: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY668 @ SY667 @ SV114 ) @ SY668 )
| ~ ( in @ ( sK26_D @ SY668 @ SY667 @ SV114 ) @ SV114 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY668 @ SY667 @ SV114 ) @ SY668 )
| ~ ( in @ ( sK26_D @ SY668 @ SY667 @ SV114 ) @ SY667 ) ) )
| ~ ( ( in @ ( sK26_D @ SY668 @ SY667 @ SV114 ) @ SY668 )
| ( in @ ( sK26_D @ SY668 @ SY667 @ SV114 ) @ SV114 )
| ( in @ ( sK26_D @ SY668 @ SY667 @ SV114 ) @ SY667 ) ) )
| ( SY668
= ( set_union2 @ SV114 @ SY667 ) ) )
| ~ ! [SY669: $i,SY670: $i] :
( ( SY670
!= ( set_union2 @ SV114 @ SY669 ) )
| ~ ( ~ ! [SY671: $i] :
( ~ ( in @ SY671 @ SY670 )
| ( in @ SY671 @ SV114 )
| ( in @ SY671 @ SY669 ) )
| ~ ~ ( ~ ! [SY672: $i] :
( ~ ( in @ SY672 @ SV114 )
| ( in @ SY672 @ SY670 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY669 )
| ( in @ SX3 @ SY670 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[954]) ).
thf(1145,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[955]) ).
thf(1146,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[955]) ).
thf(1147,plain,
! [SV115: $i] :
( ( ~ ! [SY674: $i,SY675: $i] :
( ~ ( relation @ SY675 )
| ~ ( in @ ( ordered_pair @ SV115 @ SY674 ) @ SY675 )
| ( in @ SV115 @ ( relation_field @ SY675 ) ) )
| ~ ! [SY676: $i,SY677: $i] :
( ~ ( relation @ SY677 )
| ~ ( in @ ( ordered_pair @ SV115 @ SY676 ) @ SY677 )
| ( in @ SY676 @ ( relation_field @ SY677 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[956]) ).
thf(1148,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( ( relation_rng @ SX0 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[957]) ).
thf(1149,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( ( relation_dom @ SX0 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[957]) ).
thf(1150,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[958]) ).
thf(1151,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)],[958]) ).
thf(1152,plain,
! [SV116: $i] :
( ( ~ ! [SY678: $i,SY679: $i] :
( ~ ( ~ ( ~ ( in @ ( sK17_D @ SY679 @ SY678 @ SV116 ) @ SV116 )
| ~ ( in @ ( sK17_D @ SY679 @ SY678 @ SV116 ) @ SY678 )
| ~ ( in @ ( sK17_D @ SY679 @ SY678 @ SV116 ) @ SY679 ) )
| ~ ~ ( ~ ( ( in @ ( sK17_D @ SY679 @ SY678 @ SV116 ) @ SV116 )
| ( in @ ( sK17_D @ SY679 @ SY678 @ SV116 ) @ SY679 ) )
| ~ ( ( in @ ( sK17_D @ SY679 @ SY678 @ SV116 ) @ SY678 )
| ( in @ ( sK17_D @ SY679 @ SY678 @ SV116 ) @ SY679 ) ) ) )
| ( SY679
= ( set_intersection2 @ SV116 @ SY678 ) ) )
| ~ ! [SY680: $i,SY681: $i] :
( ( SY681
!= ( set_intersection2 @ SV116 @ SY680 ) )
| ~ ( ~ ! [SY682: $i] :
( ~ ( in @ SY682 @ SV116 )
| ~ ( in @ SY682 @ SY680 )
| ( in @ SY682 @ SY681 ) )
| ~ ~ ( ~ ! [SY683: $i] :
( ~ ( in @ SY683 @ SY681 )
| ( in @ SY683 @ SV116 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY681 )
| ( in @ SX3 @ SY680 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[959]) ).
thf(1153,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( function @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[960]) ).
thf(1154,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[960]) ).
thf(1155,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK44_C @ SX1 @ SX0 )
!= ( sK45_SY414 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY414 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK44_C @ SX1 @ SX0 )
= ( sK45_SY414 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY414 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY414 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[961]) ).
thf(1156,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)],[961]) ).
thf(1157,plain,
( ( ~ ~ ( ~ ( function @ sK54_A )
| ~ ( relation @ sK54_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[962]) ).
thf(1158,plain,
( ( ~ ( one_to_one @ sK54_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[962]) ).
thf(1159,plain,
! [SV117: $i] :
( ( ~ ! [SY685: $i,SY686: $i] :
( ~ ( relation @ SY686 )
| ~ ( in @ SV117 @ SY685 )
| ~ ( in @ SV117 @ ( relation_dom @ SY686 ) )
| ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SY686 @ SY685 ) ) ) )
| ~ ~ ( ~ ! [SY687: $i,SY688: $i] :
( ~ ( relation @ SY688 )
| ~ ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SY688 @ SY687 ) ) )
| ( in @ SV117 @ SY687 ) )
| ~ ! [SY689: $i,SY690: $i] :
( ~ ( relation @ SY690 )
| ~ ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SY690 @ SY689 ) ) )
| ( in @ SV117 @ ( relation_dom @ SY690 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[963]) ).
thf(1160,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK50_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK50_C @ SX1 @ SX0 ) )
!= ( sK50_C @ SX1 @ SX0 ) ) ) )
| ( ( relation_dom @ SX1 )
!= SX0 )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[964]) ).
thf(1161,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)],[964]) ).
thf(1162,plain,
! [SV118: $i] :
( ( ~ ! [SY691: $i,SY692: $i] :
( ~ ( ~ ( ! [SY693: $i,SY694: $i] :
( ~ ( in @ SY693 @ SV118 )
| ~ ( in @ SY694 @ SY691 )
| ( ( sK23_D @ SY692 @ SY691 @ SV118 )
!= ( ordered_pair @ SY693 @ SY694 ) ) )
| ~ ( in @ ( sK23_D @ SY692 @ SY691 @ SV118 ) @ SY692 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY403 @ SY692 @ SY691 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK25_SY405 @ SY692 @ SY691 @ SV118 ) @ SY691 ) )
| ( ( sK23_D @ SY692 @ SY691 @ SV118 )
!= ( ordered_pair @ ( sK24_SY403 @ SY692 @ SY691 @ SV118 ) @ ( sK25_SY405 @ SY692 @ SY691 @ SV118 ) ) ) )
| ( in @ ( sK23_D @ SY692 @ SY691 @ SV118 ) @ SY692 ) ) )
| ( SY692
= ( cartesian_product2 @ SV118 @ SY691 ) ) )
| ~ ! [SY695: $i,SY696: $i] :
( ( SY696
!= ( cartesian_product2 @ SV118 @ SY695 ) )
| ~ ( ~ ! [SY697: $i] :
( ! [SY698: $i,SY699: $i] :
( ~ ( in @ SY698 @ SV118 )
| ~ ( in @ SY699 @ SY695 )
| ( SY697
!= ( ordered_pair @ SY698 @ SY699 ) ) )
| ( in @ SY697 @ SY696 ) )
| ~ ! [SY700: $i] :
( ~ ( in @ SY700 @ SY696 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY700 @ SY696 @ SY695 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK22_SY400 @ SY700 @ SY696 @ SY695 @ SV118 ) @ SY695 ) )
| ( SY700
!= ( ordered_pair @ ( sK21_E @ SY700 @ SY696 @ SY695 @ SV118 ) @ ( sK22_SY400 @ SY700 @ SY696 @ SY695 @ SV118 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[965]) ).
thf(1163,plain,
! [SV119: $i] :
( ( ~ ! [SY701: $i] :
( ~ ( subset @ SV119 @ SY701 )
| ! [SY702: $i] : ( subset @ ( cartesian_product2 @ SV119 @ SY702 ) @ ( cartesian_product2 @ SY701 @ SY702 ) ) )
| ~ ! [SY703: $i] :
( ~ ( subset @ SV119 @ SY703 )
| ! [SY704: $i] : ( subset @ ( cartesian_product2 @ SY704 @ SV119 ) @ ( cartesian_product2 @ SY704 @ SY703 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(1164,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ ( sK16_SY398 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK16_SY398 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK15_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[967]) ).
thf(1165,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 @ ( sK14_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK14_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[967]) ).
thf(1166,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[968]) ).
thf(1167,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[968]) ).
thf(1168,plain,
! [SV120: $i] :
( ( ( ~ ( relation @ SV120 ) )
= $true )
| ( ( ~ ( ~ ! [SY705: $i] :
( ~ ( relation @ SY705 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SY705 @ SV120 ) @ ( sK66_SY420 @ SY705 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SY705 @ SV120 ) @ ( sK66_SY420 @ SY705 @ SV120 ) ) @ SY705 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_C @ SY705 @ SV120 ) @ ( sK66_SY420 @ SY705 @ SV120 ) ) @ SV120 )
| ( in @ ( ordered_pair @ ( sK65_C @ SY705 @ SV120 ) @ ( sK66_SY420 @ SY705 @ SV120 ) ) @ SY705 ) ) )
| ( SV120 = SY705 ) )
| ~ ! [SY706: $i] :
( ~ ( relation @ SY706 )
| ( SV120 != SY706 )
| ~ ( ~ ! [SY707: $i,SY708: $i] :
( ~ ( in @ ( ordered_pair @ SY707 @ SY708 ) @ SV120 )
| ( in @ ( ordered_pair @ SY707 @ SY708 ) @ SY706 ) )
| ~ ! [SY709: $i,SY710: $i] :
( ~ ( in @ ( ordered_pair @ SY709 @ SY710 ) @ SY706 )
| ( in @ ( ordered_pair @ SY709 @ SY710 ) @ SV120 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[969]) ).
thf(1169,plain,
! [SV1: $i,SV121: $i] :
( ( ( ~ ( relation @ SV121 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV1 @ SV121 ) ) @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[970]) ).
thf(1170,plain,
! [SV2: $i,SV122: $i] :
( ( ( ~ ( relation @ SV122 ) )
= $true )
| ( ( subset @ ( relation_rng_restriction @ SV2 @ SV122 ) @ SV122 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[971]) ).
thf(1171,plain,
! [SV3: $i,SV123: $i] :
( ( ( ~ ( relation @ SV123 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV3 @ SV123 ) ) @ ( relation_rng @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[972]) ).
thf(1172,plain,
! [SV4: $i,SV124: $i] :
( ( ( ~ ( relation @ SV124 ) )
= $true )
| ( ( ( relation_rng @ ( relation_rng_restriction @ SV4 @ SV124 ) )
= ( set_intersection2 @ ( relation_rng @ SV124 ) @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[973]) ).
thf(1173,plain,
! [SV125: $i,SV5: $i,SV181: $i] :
( ( ~ ( relation @ SV181 )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV5 @ SV181 ) @ SV125 )
= ( relation_rng_restriction @ SV5 @ ( relation_dom_restriction @ SV181 @ SV125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1174,plain,
! [SV6: $i,SV126: $i] :
( ( ( ~ ( relation @ SV126 ) )
= $true )
| ( ( subset @ ( relation_image @ SV126 @ SV6 ) @ ( relation_rng @ SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[975]) ).
thf(1175,plain,
! [SV7: $i,SV127: $i] :
( ( ( ~ ( relation @ SV127 ) )
= $true )
| ( ( ( relation_image @ SV127 @ SV7 )
= ( relation_image @ SV127 @ ( set_intersection2 @ ( relation_dom @ SV127 ) @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[976]) ).
thf(1176,plain,
! [SV8: $i] :
( ( ( relation @ SV8 )
= $false )
| ( ( ( relation_image @ SV8 @ ( relation_dom @ SV8 ) )
= ( relation_rng @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[977]) ).
thf(1177,plain,
! [SV9: $i] :
( ( ( relation @ SV9 )
= $false )
| ( ( ! [SY433: $i] :
( ~ ( relation @ SY433 )
| ( ( relation_rng @ ( relation_composition @ SV9 @ SY433 ) )
= ( relation_image @ SY433 @ ( relation_rng @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[978]) ).
thf(1178,plain,
! [SV10: $i,SV128: $i] :
( ( ( ~ ( relation @ SV128 ) )
= $true )
| ( ( subset @ ( relation_inverse_image @ SV128 @ SV10 ) @ ( relation_dom @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[979]) ).
thf(1179,plain,
! [SV129: $i,SV11: $i,SV182: $i] :
( ( ~ ( relation @ SV182 )
| ~ ( subset @ SV11 @ SV129 )
| ( subset @ ( relation_inverse_image @ SV182 @ SV11 ) @ ( relation_inverse_image @ SV182 @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1180,plain,
! [SV12: $i] :
( ( ( relation @ SV12 )
= $false )
| ( ( subset @ SV12 @ ( cartesian_product2 @ ( relation_dom @ SV12 ) @ ( relation_rng @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[981]) ).
thf(1181,plain,
! [SV13: $i] :
( ( ( relation @ SV13 )
= $false )
| ( ( ! [SY437: $i] :
( ~ ( relation @ SY437 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV13 @ SY437 ) ) @ ( relation_dom @ SV13 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1182,plain,
! [SV14: $i] :
( ( ( relation @ SV14 )
= $false )
| ( ( ! [SY438: $i] :
( ~ ( relation @ SY438 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV14 @ SY438 ) ) @ ( relation_rng @ SY438 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[983]) ).
thf(1183,plain,
! [SV15: $i] :
( ( ( relation @ SV15 )
= $false )
| ( ( ! [SY439: $i] :
( ~ ( relation @ SY439 )
| ~ ( subset @ ( relation_rng @ SV15 ) @ ( relation_dom @ SY439 ) )
| ( ( relation_dom @ ( relation_composition @ SV15 @ SY439 ) )
= ( relation_dom @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[984]) ).
thf(1184,plain,
! [SV16: $i] :
( ( ( relation @ SV16 )
= $false )
| ( ( ! [SY440: $i] :
( ~ ( relation @ SY440 )
| ~ ( subset @ ( relation_dom @ SV16 ) @ ( relation_rng @ SY440 ) )
| ( ( relation_rng @ ( relation_composition @ SY440 @ SV16 ) )
= ( relation_rng @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[985]) ).
thf(1185,plain,
! [SV17: $i,SV130: $i] :
( ( ( ~ ( relation @ SV130 ) )
= $true )
| ( ( subset @ ( relation_dom_restriction @ SV130 @ SV17 ) @ SV130 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[986]) ).
thf(1186,plain,
! [SV18: $i,SV131: $i] :
( ( ( ~ ( relation @ SV131 ) )
= $true )
| ( ( ( relation_dom @ ( relation_dom_restriction @ SV131 @ SV18 ) )
= ( set_intersection2 @ ( relation_dom @ SV131 ) @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[987]) ).
thf(1187,plain,
! [SV19: $i,SV132: $i] :
( ( ( ~ ( relation @ SV132 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV132 @ SV19 ) ) @ ( relation_rng @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[988]) ).
thf(1188,plain,
! [SV20: $i] :
( ( ( empty @ SV20 )
= $false )
| ( ( function @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(1189,plain,
! [SV21: $i] :
( ( ( empty @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[990]) ).
thf(1190,plain,
! [SV22: $i] :
( ( ( relation @ SV22 )
= $false )
| ( ( ( relation_field @ SV22 )
= ( set_union2 @ ( relation_dom @ SV22 ) @ ( relation_rng @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[991]) ).
thf(1191,plain,
! [SV23: $i] :
( ( ( ~ ( function @ SV23 ) )
= $true )
| ( ( ~ ( relation @ SV23 ) )
= $true )
| ( ( ~ ( one_to_one @ SV23 )
| ( ( function_inverse @ SV23 )
= ( relation_inverse @ SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[992]) ).
thf(1192,plain,
! [SV24: $i] :
( ( ( relation @ SV24 )
= $false )
| ( ( relation @ ( relation_inverse @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[993]) ).
thf(1193,plain,
! [SV133: $i,SV25: $i] :
( ( ( ~ ( relation @ SV25 )
| ~ ( relation @ SV133 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV25 @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[994]) ).
thf(1194,plain,
! [SV27: $i] :
( ( ( relation @ SV27 )
= $false )
| ( ( ! [SY445: $i] : ( relation @ ( relation_dom_restriction @ SV27 @ SY445 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[995]) ).
thf(1195,plain,
! [SV28: $i,SV134: $i] :
( ( ( ~ ( relation @ SV134 ) )
= $true )
| ( ( relation @ ( relation_rng_restriction @ SV28 @ SV134 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[996]) ).
thf(1196,plain,
! [SV135: $i,SV29: $i] :
( ( ( ~ ( relation @ SV29 )
| ~ ( relation @ SV135 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV29 @ SV135 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[997]) ).
thf(1197,plain,
! [SV136: $i,SV30: $i] :
( ( ( ~ ( relation @ SV30 )
| ~ ( relation @ SV136 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV30 @ SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[998]) ).
thf(1198,plain,
! [SV31: $i] :
( ( ( empty @ SV31 )
= $true )
| ( ( ~ ( relation @ SV31 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV31 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[999]) ).
thf(1199,plain,
! [SV32: $i] :
( ( ( empty @ SV32 )
= $true )
| ( ( ~ ( relation @ SV32 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV32 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1000]) ).
thf(1200,plain,
! [SV33: $i] :
( ( ( relation @ SV33 )
= $false )
| ( ( ( relation_inverse @ ( relation_inverse @ SV33 ) )
= SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1001]) ).
thf(1201,plain,
! [SV137: $i,SV35: $i] :
( ( ( ~ ( in @ SV35 @ SV137 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV35 ) @ SV137 )
= SV137 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1003]) ).
thf(1202,plain,
! [SV138: $i,SV36: $i] :
( ( ( ~ ( in @ SV36 @ SV138 ) )
= $true )
| ( ( subset @ SV36 @ ( union @ SV138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1004]) ).
thf(1203,plain,
! [SV183: $i,SV139: $i,SV37: $i] :
( ( ! [SY756: $i] :
( ~ ( subset @ SV37 @ SV139 )
| ~ ( subset @ SV183 @ SY756 )
| ( subset @ ( cartesian_product2 @ SV37 @ SV183 ) @ ( cartesian_product2 @ SV139 @ SY756 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1204,plain,
! [SV140: $i,SV38: $i] :
( ( ( ~ ( subset @ SV38 @ SV140 ) )
= $true )
| ( ( ( set_union2 @ SV38 @ SV140 )
= SV140 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1006]) ).
thf(1205,plain,
! [SV39: $i,SV141: $i] :
( ( ( ~ ( relation @ SV141 ) )
= $true )
| ( ( ( SV39 = empty_set )
| ~ ( subset @ SV39 @ ( relation_rng @ SV141 ) )
| ( ( relation_inverse_image @ SV141 @ SV39 )
!= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1007]) ).
thf(1206,plain,
! [SV184: $i,SV143: $i,SV41: $i] :
( ( ~ ( subset @ SV41 @ SV143 )
| ~ ( subset @ SV41 @ SV184 )
| ( subset @ SV41 @ ( set_intersection2 @ SV143 @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1207,plain,
! [SV185: $i,SV144: $i,SV42: $i] :
( ( ~ ( subset @ SV42 @ SV144 )
| ~ ( subset @ SV144 @ SV185 )
| ( subset @ SV42 @ SV185 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1208,plain,
! [SV43: $i,SV145: $i] :
( ( ( ~ ( function @ SV145 )
| ~ ( relation @ SV145 ) )
= $true )
| ( ( ! [SY717: $i] :
( ~ ( function @ SY717 )
| ~ ( relation @ SY717 )
| ~ ( in @ SV43 @ ( relation_dom @ ( relation_composition @ SY717 @ SV145 ) ) )
| ( ( apply @ ( relation_composition @ SY717 @ SV145 ) @ SV43 )
= ( apply @ SV145 @ ( apply @ SY717 @ SV43 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1011]) ).
thf(1209,plain,
! [SV44: $i,SV146: $i] :
( ( ( ~ ( function @ SV146 )
| ~ ( relation @ SV146 ) )
= $true )
| ( ( ! [SY718: $i] :
( ~ ( function @ SY718 )
| ~ ( relation @ SY718 )
| ~ ( in @ SV44 @ ( relation_dom @ SV146 ) )
| ( ( apply @ ( relation_composition @ SV146 @ SY718 ) @ SV44 )
= ( apply @ SY718 @ ( apply @ SV146 @ SV44 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1012]) ).
thf(1210,plain,
! [SV147: $i,SV45: $i] :
( ( ( ~ ( subset @ SV45 @ SV147 ) )
= $true )
| ( ( ! [SY719: $i] : ( subset @ ( set_intersection2 @ SV45 @ SY719 ) @ ( set_intersection2 @ SV147 @ SY719 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1013]) ).
thf(1211,plain,
! [SV148: $i,SV46: $i] :
( ( ( ~ ( subset @ SV46 @ SV148 ) )
= $true )
| ( ( ( set_intersection2 @ SV46 @ SV148 )
= SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1014]) ).
thf(1212,plain,
! [SV149: $i,SV48: $i] :
( ( ( ~ ( subset @ SV48 @ SV149 ) )
= $true )
| ( ( ! [SY720: $i] : ( subset @ ( set_difference @ SV48 @ SY720 ) @ ( set_difference @ SV149 @ SY720 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1015]) ).
thf(1213,plain,
! [SV49: $i,SV150: $i] :
( ( ( ~ ( in @ SV150 @ SV49 ) )
= $true )
| ( ( ( apply @ ( identity_relation @ SV49 ) @ SV150 )
= SV150 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1016]) ).
thf(1214,plain,
! [SV52: $i] :
( ( ( subset @ SV52 @ empty_set )
= $false )
| ( ( SV52 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1019]) ).
thf(1215,plain,
! [SV154: $i,SV54: $i] :
( ( ( ~ ( subset @ SV54 @ SV154 ) )
= $true )
| ( ( SV154
= ( set_union2 @ SV54 @ ( set_difference @ SV154 @ SV54 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1021]) ).
thf(1216,plain,
! [SV155: $i,SV55: $i] :
( ( ( ~ ( in @ SV55 @ SV155 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV55 ) @ SV155 )
= SV155 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1022]) ).
thf(1217,plain,
! [SV57: $i] :
( ( ( relation @ SV57 )
= $false )
| ( ( ( in @ ( ordered_pair @ ( sK46_B @ SV57 ) @ ( sK47_SY415 @ SV57 ) ) @ SV57 )
| ( SV57 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1024]) ).
thf(1218,plain,
! [SV58: $i,SV157: $i] :
( ( ( ~ ( proper_subset @ SV157 @ SV58 ) )
= $true )
| ( ( ~ ( subset @ SV58 @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1025]) ).
thf(1219,plain,
! [SV59: $i,SV186: $i,SV158: $i] :
( ( ~ ( disjoint @ SV158 @ SV186 )
| ~ ( subset @ SV59 @ SV158 )
| ( disjoint @ SV59 @ SV186 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1220,plain,
! [SV159: $i,SV60: $i] :
( ( ( ~ ( subset @ ( singleton @ SV60 ) @ ( singleton @ SV159 ) ) )
= $true )
| ( ( SV60 = SV159 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1027]) ).
thf(1221,plain,
! [SV187: $i,SV161: $i,SV62: $i] :
( ( ~ ( subset @ SV62 @ SV161 )
| ~ ( subset @ SV187 @ SV161 )
| ( subset @ ( set_union2 @ SV62 @ SV187 ) @ SV161 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1222,plain,
! [SV162: $i,SV63: $i] :
( ( ( ~ ( in @ SV63 @ SV162 ) )
= $true )
| ( ( subset @ SV63 @ ( union @ SV162 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1030]) ).
thf(1223,plain,
! [SV64: $i,SV163: $i] :
( ( ( ~ ( relation @ SV163 ) )
= $true )
| ( ( ( relation_dom_restriction @ SV163 @ SV64 )
= ( relation_composition @ ( identity_relation @ SV64 ) @ SV163 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1031]) ).
thf(1224,plain,
! [SV164: $i,SV65: $i] :
( ( ( ~ ( in @ SV65 @ SV164 ) )
= $true )
| ( ( ~ ( in @ SV164 @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1032]) ).
thf(1225,plain,
! [SV167: $i,SV69: $i] :
( ( empty @ ( ordered_pair @ SV69 @ SV167 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1036]) ).
thf(1226,plain,
! [SV188: $i,SV71: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV71 @ SV188 ) ) )
= $true )
| ( ( empty @ SV71 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1227,plain,
! [SV168: $i,SV72: $i] :
( ( empty @ ( unordered_pair @ SV72 @ SV168 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1039]) ).
thf(1228,plain,
! [SV73: $i,SV189: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV189 @ SV73 ) ) )
= $true )
| ( ( empty @ SV73 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1229,plain,
! [SV169: $i,SV74: $i] :
( ( ( ( empty @ SV74 )
| ( empty @ SV169 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV74 @ SV169 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1041]) ).
thf(1230,plain,
! [SV170: $i,SV79: $i] :
( ( ( ~ ( in @ SV79 @ SV170 ) )
= $true )
| ( ( element @ SV79 @ SV170 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1042]) ).
thf(1231,plain,
! [SV171: $i,SV81: $i] :
( ( ( ~ ( element @ SV81 @ SV171 ) )
= $true )
| ( ( ( empty @ SV171 )
| ( in @ SV81 @ SV171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1043]) ).
thf(1232,plain,
! [SV84: $i] :
( ( ( empty @ SV84 )
= $false )
| ( ( SV84 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1044]) ).
thf(1233,plain,
! [SV85: $i,SV172: $i] :
( ( ( ~ ( empty @ SV172 ) )
= $true )
| ( ( ~ ( in @ SV85 @ SV172 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1045]) ).
thf(1234,plain,
! [SV173: $i,SV86: $i] :
( ( ( ( SV86 = SV173 )
| ~ ( empty @ SV86 ) )
= $true )
| ( ( ~ ( empty @ SV173 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1046]) ).
thf(1235,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1047]) ).
thf(1236,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1048]) ).
thf(1237,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1049]) ).
thf(1238,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)],[1050]) ).
thf(1239,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY406 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ ( sK33_SY406 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK31_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)],[1051]) ).
thf(1240,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)],[1052]) ).
thf(1241,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK48_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1053]) ).
thf(1242,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1054]) ).
thf(1243,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)],[1055]) ).
thf(1244,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)],[1056]) ).
thf(1245,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1057]) ).
thf(1246,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1058]) ).
thf(1247,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1059]) ).
thf(1248,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1060]) ).
thf(1249,plain,
! [SV87: $i] :
( ( ~ ! [SY498: $i,SY499: $i] :
( ~ ( relation @ SY499 )
| ! [SY500: $i] :
( ~ ( in @ SY500 @ ( relation_dom @ SY499 ) )
| ~ ( in @ ( ordered_pair @ SY500 @ SV87 ) @ SY499 )
| ~ ( in @ SY500 @ SY498 ) )
| ( in @ SV87 @ ( relation_image @ SY499 @ SY498 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1061]) ).
thf(1250,plain,
! [SV87: $i] :
( ( ~ ! [SY501: $i,SY502: $i] :
( ~ ( relation @ SY502 )
| ~ ( in @ SV87 @ ( relation_image @ SY502 @ SY501 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK52_D @ SY502 @ SY501 @ SV87 ) @ ( relation_dom @ SY502 ) )
| ~ ( in @ ( ordered_pair @ ( sK52_D @ SY502 @ SY501 @ SV87 ) @ SV87 ) @ SY502 ) )
| ~ ( in @ ( sK52_D @ SY502 @ SY501 @ SV87 ) @ SY501 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1061]) ).
thf(1251,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1062]) ).
thf(1252,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)],[1063]) ).
thf(1253,plain,
( ( relation @ sK53_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1064]) ).
thf(1254,plain,
( ( relation_empty_yielding @ sK53_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1065]) ).
thf(1255,plain,
! [SV88: $i] :
( ( ~ ! [SY503: $i,SY504: $i] :
( ~ ( ~ ( ~ ( in @ ( sK13_D @ SY504 @ SY503 @ SV88 ) @ SV88 )
| ( in @ ( sK13_D @ SY504 @ SY503 @ SV88 ) @ SY503 )
| ~ ( in @ ( sK13_D @ SY504 @ SY503 @ SV88 ) @ SY504 ) )
| ~ ~ ( ~ ( ( in @ ( sK13_D @ SY504 @ SY503 @ SV88 ) @ SV88 )
| ( in @ ( sK13_D @ SY504 @ SY503 @ SV88 ) @ SY504 ) )
| ~ ( ~ ( in @ ( sK13_D @ SY504 @ SY503 @ SV88 ) @ SY503 )
| ( in @ ( sK13_D @ SY504 @ SY503 @ SV88 ) @ SY504 ) ) ) )
| ( SY504
= ( set_difference @ SV88 @ SY503 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1066]) ).
thf(1256,plain,
! [SV88: $i] :
( ( ~ ! [SY505: $i,SY506: $i] :
( ( SY506
!= ( set_difference @ SV88 @ SY505 ) )
| ~ ( ~ ! [SY507: $i] :
( ~ ( in @ SY507 @ SV88 )
| ( in @ SY507 @ SY505 )
| ( in @ SY507 @ SY506 ) )
| ~ ~ ( ~ ! [SY508: $i] :
( ~ ( in @ SY508 @ SY506 )
| ( in @ SY508 @ SV88 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY506 )
| ~ ( in @ SX3 @ SY505 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1066]) ).
thf(1257,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)],[1067]) ).
thf(1258,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)],[1068]) ).
thf(1259,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1069]) ).
thf(1260,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1070]) ).
thf(1261,plain,
! [SV89: $i,SV174: $i] :
( ( ( ~ ( relation @ SV174 ) )
= $true )
| ( ( ~ ( ~ ! [SY723: $i] :
( ~ ( relation @ SY723 )
| ~ ( ~ ( ~ ( in @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY723 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) ) @ SV174 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY723 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) ) @ SY723 ) )
| ~ ~ ( ~ ( ( in @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) @ SV89 )
| ( in @ ( ordered_pair @ ( sK40_D @ SY723 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) ) @ SY723 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SY723 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) ) @ SV174 )
| ( in @ ( ordered_pair @ ( sK40_D @ SY723 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) ) @ SY723 ) ) ) )
| ( SY723
= ( relation_rng_restriction @ SV89 @ SV174 ) ) )
| ~ ! [SY724: $i] :
( ~ ( relation @ SY724 )
| ( SY724
!= ( relation_rng_restriction @ SV89 @ SV174 ) )
| ~ ( ~ ! [SY725: $i,SY726: $i] :
( ~ ( in @ SY726 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY725 @ SY726 ) @ SV174 )
| ( in @ ( ordered_pair @ SY725 @ SY726 ) @ SY724 ) )
| ~ ~ ( ~ ! [SY515: $i,SY516: $i] :
( ~ ( in @ ( ordered_pair @ SY515 @ SY516 ) @ SY724 )
| ( in @ SY516 @ SV89 ) )
| ~ ! [SY729: $i,SY730: $i] :
( ~ ( in @ ( ordered_pair @ SY729 @ SY730 ) @ SY724 )
| ( in @ ( ordered_pair @ SY729 @ SY730 ) @ SV174 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1071]) ).
thf(1262,plain,
! [SV90: $i] :
( ( ~ ! [SY519: $i,SY520: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY520 @ SY519 @ SV90 ) @ SY520 )
| ( ( sK27_D @ SY520 @ SY519 @ SV90 )
!= SV90 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY520 @ SY519 @ SV90 ) @ SY520 )
| ( ( sK27_D @ SY520 @ SY519 @ SV90 )
!= SY519 ) ) )
| ~ ( ( in @ ( sK27_D @ SY520 @ SY519 @ SV90 ) @ SY520 )
| ( ( sK27_D @ SY520 @ SY519 @ SV90 )
= SV90 )
| ( ( sK27_D @ SY520 @ SY519 @ SV90 )
= SY519 ) ) )
| ( SY520
= ( unordered_pair @ SV90 @ SY519 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1072]) ).
thf(1263,plain,
! [SV90: $i] :
( ( ~ ! [SY521: $i,SY522: $i] :
( ( SY522
!= ( unordered_pair @ SV90 @ SY521 ) )
| ~ ( ~ ! [SY523: $i] :
( ~ ( in @ SY523 @ SY522 )
| ( SY523 = SV90 )
| ( SY523 = SY521 ) )
| ~ ~ ( ~ ! [SY524: $i] :
( ( SY524 != SV90 )
| ( in @ SY524 @ SY522 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY521 )
| ( in @ SX3 @ SY522 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1072]) ).
thf(1264,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK28_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK28_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1073]) ).
thf(1265,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)],[1074]) ).
thf(1266,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1075]) ).
thf(1267,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1076]) ).
thf(1268,plain,
! [SV91: $i] :
( ( ( relation @ SV91 )
= $false )
| ( ( ~ ( ~ ! [SY526: $i] :
( ~ ( ~ ( ! [SY527: $i] :
~ ( in @ ( ordered_pair @ ( sK63_C @ SY526 @ SV91 ) @ SY527 ) @ SV91 )
| ~ ( in @ ( sK63_C @ SY526 @ SV91 ) @ SY526 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_C @ SY526 @ SV91 ) @ ( sK64_SY419 @ SY526 @ SV91 ) ) @ SV91 )
| ( in @ ( sK63_C @ SY526 @ SV91 ) @ SY526 ) ) )
| ( SY526
= ( relation_dom @ SV91 ) ) )
| ~ ! [SY528: $i] :
( ( SY528
!= ( relation_dom @ SV91 ) )
| ~ ( ~ ! [SY529: $i] :
( ! [SY530: $i] :
~ ( in @ ( ordered_pair @ SY529 @ SY530 ) @ SV91 )
| ( in @ SY529 @ SY528 ) )
| ~ ! [SY531: $i] :
( ~ ( in @ SY531 @ SY528 )
| ( in @ ( ordered_pair @ SY531 @ ( sK62_D @ SY531 @ SY528 @ SV91 ) ) @ SV91 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1077]) ).
thf(1269,plain,
! [SV92: $i] :
( ( ( relation @ SV92 )
= $false )
| ( ( ~ ( ~ ! [SY532: $i,SY533: $i] :
( ~ ( ~ ( ! [SY534: $i] :
( ~ ( in @ ( ordered_pair @ ( sK35_D @ SY533 @ SY532 @ SV92 ) @ SY534 ) @ SV92 )
| ~ ( in @ SY534 @ SY532 ) )
| ~ ( in @ ( sK35_D @ SY533 @ SY532 @ SV92 ) @ SY533 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SY533 @ SY532 @ SV92 ) @ ( sK36_SY409 @ SY533 @ SY532 @ SV92 ) ) @ SV92 )
| ~ ( in @ ( sK36_SY409 @ SY533 @ SY532 @ SV92 ) @ SY532 ) )
| ( in @ ( sK35_D @ SY533 @ SY532 @ SV92 ) @ SY533 ) ) )
| ( SY533
= ( relation_inverse_image @ SV92 @ SY532 ) ) )
| ~ ! [SY535: $i,SY536: $i] :
( ( SY536
!= ( relation_inverse_image @ SV92 @ SY535 ) )
| ~ ( ~ ! [SY537: $i] :
( ! [SY538: $i] :
( ~ ( in @ ( ordered_pair @ SY537 @ SY538 ) @ SV92 )
| ~ ( in @ SY538 @ SY535 ) )
| ( in @ SY537 @ SY536 ) )
| ~ ! [SY539: $i] :
( ~ ( in @ SY539 @ SY536 )
| ~ ( ~ ( in @ ( ordered_pair @ SY539 @ ( sK34_E @ SY539 @ SY536 @ SY535 @ SV92 ) ) @ SV92 )
| ~ ( in @ ( sK34_E @ SY539 @ SY536 @ SY535 @ SV92 ) @ SY535 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1078]) ).
thf(1270,plain,
! [SV93: $i] :
( ( ( relation @ SV93 )
= $false )
| ( ( ~ ( ~ ! [SY540: $i,SY541: $i] :
( ~ ( ~ ( ! [SY542: $i] :
( ~ ( in @ ( ordered_pair @ SY542 @ ( sK38_D @ SY541 @ SY540 @ SV93 ) ) @ SV93 )
| ~ ( in @ SY542 @ SY540 ) )
| ~ ( in @ ( sK38_D @ SY541 @ SY540 @ SV93 ) @ SY541 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SY541 @ SY540 @ SV93 ) @ ( sK38_D @ SY541 @ SY540 @ SV93 ) ) @ SV93 )
| ~ ( in @ ( sK39_SY411 @ SY541 @ SY540 @ SV93 ) @ SY540 ) )
| ( in @ ( sK38_D @ SY541 @ SY540 @ SV93 ) @ SY541 ) ) )
| ( SY541
= ( relation_image @ SV93 @ SY540 ) ) )
| ~ ! [SY543: $i,SY544: $i] :
( ( SY544
!= ( relation_image @ SV93 @ SY543 ) )
| ~ ( ~ ! [SY545: $i] :
( ! [SY546: $i] :
( ~ ( in @ ( ordered_pair @ SY546 @ SY545 ) @ SV93 )
| ~ ( in @ SY546 @ SY543 ) )
| ( in @ SY545 @ SY544 ) )
| ~ ! [SY547: $i] :
( ~ ( in @ SY547 @ SY544 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SY547 @ SY544 @ SY543 @ SV93 ) @ SY547 ) @ SV93 )
| ~ ( in @ ( sK37_E @ SY547 @ SY544 @ SY543 @ SV93 ) @ SY543 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1079]) ).
thf(1271,plain,
! [SV94: $i] :
( ( ~ ! [SY548: $i,SY549: $i] :
( ~ ( relation @ SY549 )
| ! [SY550: $i] :
( ~ ( in @ SY550 @ ( relation_rng @ SY549 ) )
| ~ ( in @ ( ordered_pair @ SV94 @ SY550 ) @ SY549 )
| ~ ( in @ SY550 @ SY548 ) )
| ( in @ SV94 @ ( relation_inverse_image @ SY549 @ SY548 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1080]) ).
thf(1272,plain,
! [SV94: $i] :
( ( ~ ! [SY551: $i,SY552: $i] :
( ~ ( relation @ SY552 )
| ~ ( in @ SV94 @ ( relation_inverse_image @ SY552 @ SY551 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK51_D @ SY552 @ SY551 @ SV94 ) @ ( relation_rng @ SY552 ) )
| ~ ( in @ ( ordered_pair @ SV94 @ ( sK51_D @ SY552 @ SY551 @ SV94 ) ) @ SY552 ) )
| ~ ( in @ ( sK51_D @ SY552 @ SY551 @ SV94 ) @ SY551 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1080]) ).
thf(1273,plain,
! [SV95: $i,SV175: $i] :
( ( ( ~ ( function @ SV175 )
| ~ ( relation @ SV175 ) )
= $true )
| ( ( ~ ( ~ ! [SY731: $i] :
( ~ ( function @ SY731 )
| ~ ( relation @ SY731 )
| ~ ( in @ SV95 @ ( relation_dom @ SY731 ) )
| ~ ( in @ ( apply @ SY731 @ SV95 ) @ ( relation_dom @ SV175 ) )
| ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY731 @ SV175 ) ) ) )
| ~ ~ ( ~ ! [SY732: $i] :
( ~ ( function @ SY732 )
| ~ ( relation @ SY732 )
| ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY732 @ SV175 ) ) )
| ( in @ SV95 @ ( relation_dom @ SY732 ) ) )
| ~ ! [SY733: $i] :
( ~ ( function @ SY733 )
| ~ ( relation @ SY733 )
| ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY733 @ SV175 ) ) )
| ( in @ ( apply @ SY733 @ SV95 ) @ ( relation_dom @ SV175 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1081]) ).
thf(1274,plain,
! [SV96: $i] :
( ( ( relation @ SV96 )
= $false )
| ( ( ~ ( ~ ! [SY557: $i,SY558: $i] :
( ~ ( relation @ SY558 )
| ~ ( ~ ( ~ ( in @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ SY557 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ ( sK43_SY413 @ SY558 @ SY557 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ ( sK43_SY413 @ SY558 @ SY557 @ SV96 ) ) @ SY558 ) )
| ~ ~ ( ~ ( ( in @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ SY557 )
| ( in @ ( ordered_pair @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ ( sK43_SY413 @ SY558 @ SY557 @ SV96 ) ) @ SY558 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ ( sK43_SY413 @ SY558 @ SY557 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ ( sK43_SY413 @ SY558 @ SY557 @ SV96 ) ) @ SY558 ) ) ) )
| ( SY558
= ( relation_dom_restriction @ SV96 @ SY557 ) ) )
| ~ ! [SY559: $i,SY560: $i] :
( ~ ( relation @ SY560 )
| ( SY560
!= ( relation_dom_restriction @ SV96 @ SY559 ) )
| ~ ( ~ ! [SY561: $i,SY562: $i] :
( ~ ( in @ SY561 @ SY559 )
| ~ ( in @ ( ordered_pair @ SY561 @ SY562 ) @ SV96 )
| ( in @ ( ordered_pair @ SY561 @ SY562 ) @ SY560 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY560 )
| ( in @ SX3 @ SY559 ) )
| ~ ! [SY565: $i,SY566: $i] :
( ~ ( in @ ( ordered_pair @ SY565 @ SY566 ) @ SY560 )
| ( in @ ( ordered_pair @ SY565 @ SY566 ) @ SV96 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1082]) ).
thf(1275,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1083]) ).
thf(1276,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1084]) ).
thf(1277,plain,
! [SV97: $i] :
( ( ( relation @ SV97 )
= $false )
| ( ( ~ ( ~ ! [SY567: $i] :
( ~ ( relation @ SY567 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SY567 @ SV97 ) @ ( sK12_SY396 @ SY567 @ SV97 ) ) @ SY567 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SY567 @ SV97 ) @ ( sK11_C @ SY567 @ SV97 ) ) @ SV97 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_C @ SY567 @ SV97 ) @ ( sK12_SY396 @ SY567 @ SV97 ) ) @ SY567 )
| ( in @ ( ordered_pair @ ( sK12_SY396 @ SY567 @ SV97 ) @ ( sK11_C @ SY567 @ SV97 ) ) @ SV97 ) ) )
| ( SY567
= ( relation_inverse @ SV97 ) ) )
| ~ ! [SY568: $i] :
( ~ ( relation @ SY568 )
| ( SY568
!= ( relation_inverse @ SV97 ) )
| ~ ( ~ ! [SY569: $i,SY570: $i] :
( ~ ( in @ ( ordered_pair @ SY569 @ SY570 ) @ SY568 )
| ( in @ ( ordered_pair @ SY570 @ SY569 ) @ SV97 ) )
| ~ ! [SY571: $i,SY572: $i] :
( ~ ( in @ ( ordered_pair @ SY572 @ SY571 ) @ SV97 )
| ( in @ ( ordered_pair @ SY571 @ SY572 ) @ SY568 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1085]) ).
thf(1278,plain,
! [SV98: $i] :
( ( ( relation @ SV98 )
= $false )
| ( ( ~ ( ~ ! [SY573: $i] :
( ~ ( ~ ( ! [SY574: $i] :
~ ( in @ ( ordered_pair @ SY574 @ ( sK60_C @ SY573 @ SV98 ) ) @ SV98 )
| ~ ( in @ ( sK60_C @ SY573 @ SV98 ) @ SY573 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK61_SY417 @ SY573 @ SV98 ) @ ( sK60_C @ SY573 @ SV98 ) ) @ SV98 )
| ( in @ ( sK60_C @ SY573 @ SV98 ) @ SY573 ) ) )
| ( SY573
= ( relation_rng @ SV98 ) ) )
| ~ ! [SY575: $i] :
( ( SY575
!= ( relation_rng @ SV98 ) )
| ~ ( ~ ! [SY576: $i] :
( ! [SY577: $i] :
~ ( in @ ( ordered_pair @ SY577 @ SY576 ) @ SV98 )
| ( in @ SY576 @ SY575 ) )
| ~ ! [SY578: $i] :
( ~ ( in @ SY578 @ SY575 )
| ( in @ ( ordered_pair @ ( sK59_D @ SY578 @ SY575 @ SV98 ) @ SY578 ) @ SV98 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1086]) ).
thf(1279,plain,
! [SV99: $i,SV176: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK4_C @ SV176 @ SV99 ) @ SV99 )
| ~ ( in @ ( sK4_C @ SV176 @ SV99 ) @ SV176 ) )
| ~ ( ( in @ ( sK4_C @ SV176 @ SV99 ) @ SV99 )
| ( in @ ( sK4_C @ SV176 @ SV99 ) @ SV176 ) ) ) )
= $true )
| ( ( SV99 = SV176 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1087]) ).
thf(1280,plain,
! [SV100: $i] :
( ( ~ ! [SY580: $i,SY581: $i] :
( ~ ( function @ SY581 )
| ~ ( relation @ SY581 )
| ( SY580
!= ( apply @ SY581 @ SV100 ) )
| ~ ( in @ SV100 @ ( relation_dom @ SY581 ) )
| ( in @ ( ordered_pair @ SV100 @ SY580 ) @ SY581 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1088]) ).
thf(1281,plain,
! [SV100: $i] :
( ( ~ ~ ( ~ ! [SY582: $i,SY583: $i] :
( ~ ( function @ SY583 )
| ~ ( relation @ SY583 )
| ~ ( in @ ( ordered_pair @ SV100 @ SY582 ) @ SY583 )
| ( SY582
= ( apply @ SY583 @ SV100 ) ) )
| ~ ! [SY584: $i,SY585: $i] :
( ~ ( function @ SY585 )
| ~ ( relation @ SY585 )
| ~ ( in @ ( ordered_pair @ SV100 @ SY584 ) @ SY585 )
| ( in @ SV100 @ ( relation_dom @ SY585 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1088]) ).
thf(1282,plain,
! [SV101: $i] :
( ( ( relation @ SV101 )
= $false )
| ( ( ! [SY586: $i] :
( ~ ( relation @ SY586 )
| ~ ( ~ ! [SY587: $i] :
( ~ ( relation @ SY587 )
| ~ ( ~ ( ! [SY588: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY587 @ SY586 @ SV101 ) @ SY588 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY588 @ ( sK9_SY391 @ SY587 @ SY586 @ SV101 ) ) @ SY586 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SY587 @ SY586 @ SV101 ) @ ( sK9_SY391 @ SY587 @ SY586 @ SV101 ) ) @ SY587 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY587 @ SY586 @ SV101 ) @ ( sK10_SY395 @ SY587 @ SY586 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SY587 @ SY586 @ SV101 ) @ ( sK9_SY391 @ SY587 @ SY586 @ SV101 ) ) @ SY586 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SY587 @ SY586 @ SV101 ) @ ( sK9_SY391 @ SY587 @ SY586 @ SV101 ) ) @ SY587 ) ) )
| ( SY587
= ( relation_composition @ SV101 @ SY586 ) ) )
| ~ ! [SY589: $i] :
( ~ ( relation @ SY589 )
| ( SY589
!= ( relation_composition @ SV101 @ SY586 ) )
| ~ ( ~ ! [SY590: $i,SY591: $i] :
( ! [SY592: $i] :
( ~ ( in @ ( ordered_pair @ SY590 @ SY592 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY592 @ SY591 ) @ SY586 ) )
| ( in @ ( ordered_pair @ SY590 @ SY591 ) @ SY589 ) )
| ~ ! [SY593: $i,SY594: $i] :
( ~ ( in @ ( ordered_pair @ SY593 @ SY594 ) @ SY589 )
| ~ ( ~ ( in @ ( ordered_pair @ SY593 @ ( sK7_F @ SY594 @ SY593 @ SY589 @ SY586 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY594 @ SY593 @ SY589 @ SY586 @ SV101 ) @ SY594 ) @ SY586 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1089]) ).
thf(1283,plain,
! [SV177: $i,SV102: $i] :
( ( ~ ! [SY734: $i,SY735: $i] :
( ~ ( in @ SV102 @ SY734 )
| ~ ( in @ SV177 @ SY735 )
| ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SY734 @ SY735 ) ) )
| ~ ~ ( ~ ! [SY736: $i] :
( ! [SY737: $i] :
~ ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SY736 @ SY737 ) )
| ( in @ SV102 @ SY736 ) )
| ~ ! [SY738: $i,SY739: $i] :
( ~ ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SY738 @ SY739 ) )
| ( in @ SV177 @ SY739 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1090]) ).
thf(1284,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1091]) ).
thf(1285,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1092]) ).
thf(1286,plain,
! [SV103: $i] :
( ( ~ ! [SY602: $i] :
( ~ ( subset @ SY602 @ ( sK2_B @ SV103 ) )
| ( are_equipotent @ SY602 @ ( sK2_B @ SV103 ) )
| ( in @ SY602 @ ( sK2_B @ SV103 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1093]) ).
thf(1287,plain,
! [SV103: $i] :
( ( ~ ~ ( ~ ! [SY603: $i] :
( ~ ( ~ ! [SY604: $i] :
( ~ ( subset @ SY604 @ SY603 )
| ( in @ SY604 @ ( sK3_SY386 @ SY603 @ SV103 ) ) )
| ~ ( in @ ( sK3_SY386 @ SY603 @ SV103 ) @ ( sK2_B @ SV103 ) ) )
| ~ ( in @ SY603 @ ( sK2_B @ SV103 ) ) )
| ~ ~ ( ~ ! [SY605: $i,SY606: $i] :
( ~ ( in @ SY605 @ ( sK2_B @ SV103 ) )
| ~ ( subset @ SY606 @ SY605 )
| ( in @ SY606 @ ( sK2_B @ SV103 ) ) )
| ~ ( in @ SV103 @ ( sK2_B @ SV103 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1093]) ).
thf(1288,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( function @ ( function_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1094]) ).
thf(1289,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( relation @ ( function_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1095]) ).
thf(1290,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1096]) ).
thf(1291,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1097]) ).
thf(1292,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK69_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK69_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1098]) ).
thf(1293,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK67_C @ SX1 @ SX0 ) @ ( sK68_SY421 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1099]) ).
thf(1294,plain,
! [SV104: $i] :
( ( ( relation @ SV104 )
= $false )
| ( ( ~ ( ~ ! [SY607: $i] :
( ~ ( relation @ SY607 )
| ~ ( subset @ SV104 @ SY607 )
| ( subset @ ( relation_dom @ SV104 ) @ ( relation_dom @ SY607 ) ) )
| ~ ! [SY608: $i] :
( ~ ( relation @ SY608 )
| ~ ( subset @ SV104 @ SY608 )
| ( subset @ ( relation_rng @ SV104 ) @ ( relation_rng @ SY608 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1100]) ).
thf(1295,plain,
! [SV105: $i] :
( ( ~ ! [SY609: $i,SY610: $i] :
( ~ ( relation @ SY610 )
| ~ ( in @ SV105 @ SY609 )
| ~ ( in @ SV105 @ ( relation_rng @ SY610 ) )
| ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SY609 @ SY610 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1101]) ).
thf(1296,plain,
! [SV105: $i] :
( ( ~ ~ ( ~ ! [SY611: $i,SY612: $i] :
( ~ ( relation @ SY612 )
| ~ ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SY611 @ SY612 ) ) )
| ( in @ SV105 @ SY611 ) )
| ~ ! [SY613: $i,SY614: $i] :
( ~ ( relation @ SY614 )
| ~ ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SY613 @ SY614 ) ) )
| ( in @ SV105 @ ( relation_rng @ SY614 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1101]) ).
thf(1297,plain,
( ( ~ ( ~ ( empty @ sK56_A )
| ~ ( relation @ sK56_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1102]) ).
thf(1298,plain,
( ( function @ sK56_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1103]) ).
thf(1299,plain,
! [SV106: $i] :
( ( ~ ! [SY615: $i,SY616: $i] :
( ~ ( in @ SV106 @ SY616 )
| ~ ( in @ SY615 @ SY616 )
| ( subset @ ( unordered_pair @ SV106 @ SY615 ) @ SY616 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1104]) ).
thf(1300,plain,
! [SV106: $i] :
( ( ~ ~ ( ~ ! [SY617: $i,SY618: $i] :
( ~ ( subset @ ( unordered_pair @ SV106 @ SY617 ) @ SY618 )
| ( in @ SV106 @ SY618 ) )
| ~ ! [SY619: $i,SY620: $i] :
( ~ ( subset @ ( unordered_pair @ SV106 @ SY619 ) @ SY620 )
| ( in @ SY619 @ SY620 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1104]) ).
thf(1301,plain,
( ( ! [SX0: $i] :
( ( relation_dom @ ( identity_relation @ SX0 ) )
= SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1105]) ).
thf(1302,plain,
( ( ! [SX0: $i] :
( ( relation_rng @ ( identity_relation @ SX0 ) )
= SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1106]) ).
thf(1303,plain,
! [SV178: $i,SV107: $i] :
( ( ~ ! [SY740: $i,SY741: $i] :
( ~ ( relation @ SY741 )
| ~ ( in @ SV107 @ SY740 )
| ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ SY741 )
| ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SY740 ) @ SY741 ) ) )
| ~ ~ ( ~ ! [SY742: $i,SY743: $i] :
( ~ ( relation @ SY743 )
| ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SY742 ) @ SY743 ) )
| ( in @ SV107 @ SY742 ) )
| ~ ! [SY744: $i,SY745: $i] :
( ~ ( relation @ SY745 )
| ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SY744 ) @ SY745 ) )
| ( in @ ( ordered_pair @ SV107 @ SV178 ) @ SY745 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1107]) ).
thf(1304,plain,
( ( ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1108]) ).
thf(1305,plain,
( ( ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1109]) ).
thf(1306,plain,
! [SV108: $i] :
( ( ( relation @ SV108 )
= $false )
| ( ( ~ ( ~ ! [SY628: $i] :
( ~ ( relation @ SY628 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SY628 @ SV108 ) @ ( sK20_SY399 @ SY628 @ SV108 ) ) @ SV108 )
| ~ ~ ( in @ ( ordered_pair @ ( sK19_C @ SY628 @ SV108 ) @ ( sK20_SY399 @ SY628 @ SV108 ) ) @ SY628 ) )
| ( subset @ SV108 @ SY628 ) )
| ~ ! [SY629: $i] :
( ~ ( relation @ SY629 )
| ~ ( subset @ SV108 @ SY629 )
| ! [SY630: $i,SY631: $i] :
( ~ ( in @ ( ordered_pair @ SY630 @ SY631 ) @ SV108 )
| ( in @ ( ordered_pair @ SY630 @ SY631 ) @ SY629 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1110]) ).
thf(1307,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK30_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK30_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK30_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK30_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1111]) ).
thf(1308,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)],[1112]) ).
thf(1309,plain,
! [SV109: $i] :
( ( ~ ! [SY632: $i,SY633: $i] :
( ~ ( relation @ SY633 )
| ~ ( in @ ( ordered_pair @ SV109 @ SY632 ) @ SY633 )
| ( in @ SV109 @ ( relation_dom @ SY633 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1113]) ).
thf(1310,plain,
! [SV109: $i] :
( ( ~ ! [SY634: $i,SY635: $i] :
( ~ ( relation @ SY635 )
| ~ ( in @ ( ordered_pair @ SV109 @ SY634 ) @ SY635 )
| ( in @ SY634 @ ( relation_rng @ SY635 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1113]) ).
thf(1311,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)],[1114]) ).
thf(1312,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1115]) ).
thf(1313,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1116]) ).
thf(1314,plain,
( ( relation_empty_yielding @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1117]) ).
thf(1315,plain,
! [SV110: $i] :
( ( ( ~ ( function @ SV110 ) )
= $true )
| ( ( ~ ( relation @ SV110 ) )
= $true )
| ( ( ~ ( one_to_one @ SV110 )
| ~ ( ~ ! [SY636: $i] :
( ~ ( function @ SY636 )
| ~ ( relation @ SY636 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SY636 @ SV110 )
= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ( ( sK70_C @ SY636 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY636 @ SV110 )
= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY636 @ SV110 )
= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ( ( sK71_SY424 @ SY636 @ SV110 )
!= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK70_C @ SY636 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK71_SY424 @ SY636 @ SV110 )
!= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY636 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK70_C @ SY636 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SY636 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SY636 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK71_SY424 @ SY636 @ SV110 )
!= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ( ( relation_dom @ SY636 )
!= ( relation_rng @ SV110 ) )
| ( SY636
= ( function_inverse @ SV110 ) ) )
| ~ ~ ( ~ ! [SY637: $i] :
( ~ ( function @ SY637 )
| ~ ( relation @ SY637 )
| ( SY637
!= ( function_inverse @ SV110 ) )
| ~ ( ~ ~ ( ~ ! [SY638: $i,SY639: $i] :
( ( SY639
!= ( apply @ SY637 @ SY638 ) )
| ~ ( in @ SY638 @ ( relation_rng @ SV110 ) )
| ( SY638
= ( apply @ SV110 @ SY639 ) ) )
| ~ ! [SY640: $i,SY641: $i] :
( ( SY641
!= ( apply @ SY637 @ SY640 ) )
| ~ ( in @ SY640 @ ( relation_rng @ SV110 ) )
| ( in @ SY641 @ ( relation_dom @ SV110 ) ) ) )
| ~ ~ ( ~ ! [SY642: $i,SY643: $i] :
( ( SY642
!= ( apply @ SV110 @ SY643 ) )
| ~ ( in @ SY643 @ ( relation_dom @ SV110 ) )
| ( SY643
= ( apply @ SY637 @ SY642 ) ) )
| ~ ! [SY644: $i] :
( ! [SY645: $i] :
( ( SY644
!= ( apply @ SV110 @ SY645 ) )
| ~ ( in @ SY645 @ ( relation_dom @ SV110 ) ) )
| ( in @ SY644 @ ( relation_rng @ SV110 ) ) ) ) ) )
| ~ ! [SY646: $i] :
( ~ ( function @ SY646 )
| ~ ( relation @ SY646 )
| ( SY646
!= ( function_inverse @ SV110 ) )
| ( ( relation_dom @ SY646 )
= ( relation_rng @ SV110 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1118]) ).
thf(1316,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1119]) ).
thf(1317,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1120]) ).
thf(1318,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1121]) ).
thf(1319,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)],[1122]) ).
thf(1320,plain,
( ( ~ ( empty @ sK55_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1123]) ).
thf(1321,plain,
( ( relation @ sK55_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1124]) ).
thf(1322,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK18_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK18_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1125]) ).
thf(1323,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1126]) ).
thf(1324,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK49_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK49_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1127]) ).
thf(1325,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1128]) ).
thf(1326,plain,
! [SV179: $i,SV111: $i] :
( ( ~ ! [SY746: $i,SY747: $i] :
( ~ ( in @ SV111 @ SY746 )
| ~ ( in @ SV179 @ SY747 )
| ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SY746 @ SY747 ) ) )
| ~ ~ ( ~ ! [SY748: $i] :
( ! [SY749: $i] :
~ ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SY748 @ SY749 ) )
| ( in @ SV111 @ SY748 ) )
| ~ ! [SY750: $i,SY751: $i] :
( ~ ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SY750 @ SY751 ) )
| ( in @ SV179 @ SY751 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1129]) ).
thf(1327,plain,
( ( ( relation_dom @ empty_set )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1130]) ).
thf(1328,plain,
( ( ( relation_rng @ empty_set )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1131]) ).
thf(1329,plain,
( ( empty @ sK57_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1132]) ).
thf(1330,plain,
( ( relation @ sK57_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1133]) ).
thf(1331,plain,
! [SV180: $i,SV112: $i] :
( ( ~ ! [SY752: $i] :
( ! [SY753: $i] :
( ( ordered_pair @ SV112 @ SV180 )
!= ( ordered_pair @ SY752 @ SY753 ) )
| ( SV112 = SY752 ) )
| ~ ! [SY754: $i,SY755: $i] :
( ( ( ordered_pair @ SV112 @ SV180 )
!= ( ordered_pair @ SY754 @ SY755 ) )
| ( SV180 = SY755 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1134]) ).
thf(1332,plain,
( ( function @ sK58_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1135]) ).
thf(1333,plain,
( ( relation @ sK58_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1136]) ).
thf(1334,plain,
! [SV113: $i] :
( ( ( ~ ( function @ SV113 ) )
= $true )
| ( ( ~ ( relation @ SV113 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ ( relation_dom @ SV113 ) )
| ! [SY660: $i] :
( ( SY660
!= ( apply @ SV113 @ SY659 ) )
| ( in @ ( ordered_pair @ SY659 @ SY660 ) @ SV113 ) ) )
| ~ ! [SY661: $i] :
( ~ ( in @ SY661 @ ( relation_dom @ SV113 ) )
| ! [SY662: $i] :
( ~ ( in @ ( ordered_pair @ SY661 @ SY662 ) @ SV113 )
| ( SY662
= ( apply @ SV113 @ SY661 ) ) ) ) )
| ~ ~ ( ~ ! [SY663: $i] :
( ( in @ SY663 @ ( relation_dom @ SV113 ) )
| ! [SY664: $i] :
( ( SY664
!= ( apply @ SV113 @ SY663 ) )
| ( SY664 = empty_set ) ) )
| ~ ! [SY665: $i] :
( ( in @ SY665 @ ( relation_dom @ SV113 ) )
| ! [SY666: $i] :
( ( SY666 != empty_set )
| ( SY666
= ( apply @ SV113 @ SY665 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1137]) ).
thf(1335,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1138]) ).
thf(1336,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1139]) ).
thf(1337,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1140]) ).
thf(1338,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1141]) ).
thf(1339,plain,
( ( ! [SX0: $i] :
( ( in @ ( sK29_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1142]) ).
thf(1340,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1143]) ).
thf(1341,plain,
! [SV114: $i] :
( ( ~ ! [SY667: $i,SY668: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY668 @ SY667 @ SV114 ) @ SY668 )
| ~ ( in @ ( sK26_D @ SY668 @ SY667 @ SV114 ) @ SV114 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY668 @ SY667 @ SV114 ) @ SY668 )
| ~ ( in @ ( sK26_D @ SY668 @ SY667 @ SV114 ) @ SY667 ) ) )
| ~ ( ( in @ ( sK26_D @ SY668 @ SY667 @ SV114 ) @ SY668 )
| ( in @ ( sK26_D @ SY668 @ SY667 @ SV114 ) @ SV114 )
| ( in @ ( sK26_D @ SY668 @ SY667 @ SV114 ) @ SY667 ) ) )
| ( SY668
= ( set_union2 @ SV114 @ SY667 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1144]) ).
thf(1342,plain,
! [SV114: $i] :
( ( ~ ! [SY669: $i,SY670: $i] :
( ( SY670
!= ( set_union2 @ SV114 @ SY669 ) )
| ~ ( ~ ! [SY671: $i] :
( ~ ( in @ SY671 @ SY670 )
| ( in @ SY671 @ SV114 )
| ( in @ SY671 @ SY669 ) )
| ~ ~ ( ~ ! [SY672: $i] :
( ~ ( in @ SY672 @ SV114 )
| ( in @ SY672 @ SY670 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY669 )
| ( in @ SX3 @ SY670 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1144]) ).
thf(1343,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1145]) ).
thf(1344,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1146]) ).
thf(1345,plain,
! [SV115: $i] :
( ( ~ ! [SY674: $i,SY675: $i] :
( ~ ( relation @ SY675 )
| ~ ( in @ ( ordered_pair @ SV115 @ SY674 ) @ SY675 )
| ( in @ SV115 @ ( relation_field @ SY675 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1147]) ).
thf(1346,plain,
! [SV115: $i] :
( ( ~ ! [SY676: $i,SY677: $i] :
( ~ ( relation @ SY677 )
| ~ ( in @ ( ordered_pair @ SV115 @ SY676 ) @ SY677 )
| ( in @ SY676 @ ( relation_field @ SY677 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1147]) ).
thf(1347,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( ( relation_rng @ SX0 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1148]) ).
thf(1348,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( ( relation_dom @ SX0 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1149]) ).
thf(1349,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1150]) ).
thf(1350,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)],[1151]) ).
thf(1351,plain,
! [SV116: $i] :
( ( ~ ! [SY678: $i,SY679: $i] :
( ~ ( ~ ( ~ ( in @ ( sK17_D @ SY679 @ SY678 @ SV116 ) @ SV116 )
| ~ ( in @ ( sK17_D @ SY679 @ SY678 @ SV116 ) @ SY678 )
| ~ ( in @ ( sK17_D @ SY679 @ SY678 @ SV116 ) @ SY679 ) )
| ~ ~ ( ~ ( ( in @ ( sK17_D @ SY679 @ SY678 @ SV116 ) @ SV116 )
| ( in @ ( sK17_D @ SY679 @ SY678 @ SV116 ) @ SY679 ) )
| ~ ( ( in @ ( sK17_D @ SY679 @ SY678 @ SV116 ) @ SY678 )
| ( in @ ( sK17_D @ SY679 @ SY678 @ SV116 ) @ SY679 ) ) ) )
| ( SY679
= ( set_intersection2 @ SV116 @ SY678 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1152]) ).
thf(1352,plain,
! [SV116: $i] :
( ( ~ ! [SY680: $i,SY681: $i] :
( ( SY681
!= ( set_intersection2 @ SV116 @ SY680 ) )
| ~ ( ~ ! [SY682: $i] :
( ~ ( in @ SY682 @ SV116 )
| ~ ( in @ SY682 @ SY680 )
| ( in @ SY682 @ SY681 ) )
| ~ ~ ( ~ ! [SY683: $i] :
( ~ ( in @ SY683 @ SY681 )
| ( in @ SY683 @ SV116 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY681 )
| ( in @ SX3 @ SY680 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1152]) ).
thf(1353,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( function @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1153]) ).
thf(1354,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1154]) ).
thf(1355,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK44_C @ SX1 @ SX0 )
!= ( sK45_SY414 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY414 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK44_C @ SX1 @ SX0 )
= ( sK45_SY414 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY414 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY414 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1155]) ).
thf(1356,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)],[1156]) ).
thf(1357,plain,
( ( ~ ( ~ ( function @ sK54_A )
| ~ ( relation @ sK54_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1157]) ).
thf(1358,plain,
( ( one_to_one @ sK54_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1158]) ).
thf(1359,plain,
! [SV117: $i] :
( ( ~ ! [SY685: $i,SY686: $i] :
( ~ ( relation @ SY686 )
| ~ ( in @ SV117 @ SY685 )
| ~ ( in @ SV117 @ ( relation_dom @ SY686 ) )
| ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SY686 @ SY685 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1159]) ).
thf(1360,plain,
! [SV117: $i] :
( ( ~ ~ ( ~ ! [SY687: $i,SY688: $i] :
( ~ ( relation @ SY688 )
| ~ ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SY688 @ SY687 ) ) )
| ( in @ SV117 @ SY687 ) )
| ~ ! [SY689: $i,SY690: $i] :
( ~ ( relation @ SY690 )
| ~ ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SY690 @ SY689 ) ) )
| ( in @ SV117 @ ( relation_dom @ SY690 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1159]) ).
thf(1361,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK50_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK50_C @ SX1 @ SX0 ) )
!= ( sK50_C @ SX1 @ SX0 ) ) ) )
| ( ( relation_dom @ SX1 )
!= SX0 )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1160]) ).
thf(1362,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)],[1161]) ).
thf(1363,plain,
! [SV118: $i] :
( ( ~ ! [SY691: $i,SY692: $i] :
( ~ ( ~ ( ! [SY693: $i,SY694: $i] :
( ~ ( in @ SY693 @ SV118 )
| ~ ( in @ SY694 @ SY691 )
| ( ( sK23_D @ SY692 @ SY691 @ SV118 )
!= ( ordered_pair @ SY693 @ SY694 ) ) )
| ~ ( in @ ( sK23_D @ SY692 @ SY691 @ SV118 ) @ SY692 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY403 @ SY692 @ SY691 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK25_SY405 @ SY692 @ SY691 @ SV118 ) @ SY691 ) )
| ( ( sK23_D @ SY692 @ SY691 @ SV118 )
!= ( ordered_pair @ ( sK24_SY403 @ SY692 @ SY691 @ SV118 ) @ ( sK25_SY405 @ SY692 @ SY691 @ SV118 ) ) ) )
| ( in @ ( sK23_D @ SY692 @ SY691 @ SV118 ) @ SY692 ) ) )
| ( SY692
= ( cartesian_product2 @ SV118 @ SY691 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1162]) ).
thf(1364,plain,
! [SV118: $i] :
( ( ~ ! [SY695: $i,SY696: $i] :
( ( SY696
!= ( cartesian_product2 @ SV118 @ SY695 ) )
| ~ ( ~ ! [SY697: $i] :
( ! [SY698: $i,SY699: $i] :
( ~ ( in @ SY698 @ SV118 )
| ~ ( in @ SY699 @ SY695 )
| ( SY697
!= ( ordered_pair @ SY698 @ SY699 ) ) )
| ( in @ SY697 @ SY696 ) )
| ~ ! [SY700: $i] :
( ~ ( in @ SY700 @ SY696 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY700 @ SY696 @ SY695 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK22_SY400 @ SY700 @ SY696 @ SY695 @ SV118 ) @ SY695 ) )
| ( SY700
!= ( ordered_pair @ ( sK21_E @ SY700 @ SY696 @ SY695 @ SV118 ) @ ( sK22_SY400 @ SY700 @ SY696 @ SY695 @ SV118 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1162]) ).
thf(1365,plain,
! [SV119: $i] :
( ( ~ ! [SY701: $i] :
( ~ ( subset @ SV119 @ SY701 )
| ! [SY702: $i] : ( subset @ ( cartesian_product2 @ SV119 @ SY702 ) @ ( cartesian_product2 @ SY701 @ SY702 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1163]) ).
thf(1366,plain,
! [SV119: $i] :
( ( ~ ! [SY703: $i] :
( ~ ( subset @ SV119 @ SY703 )
| ! [SY704: $i] : ( subset @ ( cartesian_product2 @ SY704 @ SV119 ) @ ( cartesian_product2 @ SY704 @ SY703 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1163]) ).
thf(1367,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ ( sK16_SY398 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK16_SY398 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK15_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1164]) ).
thf(1368,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 @ ( sK14_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK14_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1165]) ).
thf(1369,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1166]) ).
thf(1370,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1167]) ).
thf(1371,plain,
! [SV120: $i] :
( ( ( relation @ SV120 )
= $false )
| ( ( ~ ( ~ ! [SY705: $i] :
( ~ ( relation @ SY705 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SY705 @ SV120 ) @ ( sK66_SY420 @ SY705 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SY705 @ SV120 ) @ ( sK66_SY420 @ SY705 @ SV120 ) ) @ SY705 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_C @ SY705 @ SV120 ) @ ( sK66_SY420 @ SY705 @ SV120 ) ) @ SV120 )
| ( in @ ( ordered_pair @ ( sK65_C @ SY705 @ SV120 ) @ ( sK66_SY420 @ SY705 @ SV120 ) ) @ SY705 ) ) )
| ( SV120 = SY705 ) )
| ~ ! [SY706: $i] :
( ~ ( relation @ SY706 )
| ( SV120 != SY706 )
| ~ ( ~ ! [SY707: $i,SY708: $i] :
( ~ ( in @ ( ordered_pair @ SY707 @ SY708 ) @ SV120 )
| ( in @ ( ordered_pair @ SY707 @ SY708 ) @ SY706 ) )
| ~ ! [SY709: $i,SY710: $i] :
( ~ ( in @ ( ordered_pair @ SY709 @ SY710 ) @ SY706 )
| ( in @ ( ordered_pair @ SY709 @ SY710 ) @ SV120 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1168]) ).
thf(1372,plain,
! [SV1: $i,SV121: $i] :
( ( ( relation @ SV121 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV1 @ SV121 ) ) @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1169]) ).
thf(1373,plain,
! [SV2: $i,SV122: $i] :
( ( ( relation @ SV122 )
= $false )
| ( ( subset @ ( relation_rng_restriction @ SV2 @ SV122 ) @ SV122 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1170]) ).
thf(1374,plain,
! [SV3: $i,SV123: $i] :
( ( ( relation @ SV123 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV3 @ SV123 ) ) @ ( relation_rng @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1171]) ).
thf(1375,plain,
! [SV4: $i,SV124: $i] :
( ( ( relation @ SV124 )
= $false )
| ( ( ( relation_rng @ ( relation_rng_restriction @ SV4 @ SV124 ) )
= ( set_intersection2 @ ( relation_rng @ SV124 ) @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1172]) ).
thf(1376,plain,
! [SV125: $i,SV5: $i,SV181: $i] :
( ( ( ~ ( relation @ SV181 ) )
= $true )
| ( ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV5 @ SV181 ) @ SV125 )
= ( relation_rng_restriction @ SV5 @ ( relation_dom_restriction @ SV181 @ SV125 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1173]) ).
thf(1377,plain,
! [SV6: $i,SV126: $i] :
( ( ( relation @ SV126 )
= $false )
| ( ( subset @ ( relation_image @ SV126 @ SV6 ) @ ( relation_rng @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1174]) ).
thf(1378,plain,
! [SV7: $i,SV127: $i] :
( ( ( relation @ SV127 )
= $false )
| ( ( ( relation_image @ SV127 @ SV7 )
= ( relation_image @ SV127 @ ( set_intersection2 @ ( relation_dom @ SV127 ) @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1379,plain,
! [SV9: $i,SV190: $i] :
( ( ( ~ ( relation @ SV190 )
| ( ( relation_rng @ ( relation_composition @ SV9 @ SV190 ) )
= ( relation_image @ SV190 @ ( relation_rng @ SV9 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1177]) ).
thf(1380,plain,
! [SV10: $i,SV128: $i] :
( ( ( relation @ SV128 )
= $false )
| ( ( subset @ ( relation_inverse_image @ SV128 @ SV10 ) @ ( relation_dom @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1178]) ).
thf(1381,plain,
! [SV129: $i,SV11: $i,SV182: $i] :
( ( ( ~ ( relation @ SV182 ) )
= $true )
| ( ( ~ ( subset @ SV11 @ SV129 )
| ( subset @ ( relation_inverse_image @ SV182 @ SV11 ) @ ( relation_inverse_image @ SV182 @ SV129 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1179]) ).
thf(1382,plain,
! [SV13: $i,SV191: $i] :
( ( ( ~ ( relation @ SV191 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV13 @ SV191 ) ) @ ( relation_dom @ SV13 ) ) )
= $true )
| ( ( relation @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1383,plain,
! [SV14: $i,SV192: $i] :
( ( ( ~ ( relation @ SV192 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV14 @ SV192 ) ) @ ( relation_rng @ SV192 ) ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1384,plain,
! [SV15: $i,SV193: $i] :
( ( ( ~ ( relation @ SV193 )
| ~ ( subset @ ( relation_rng @ SV15 ) @ ( relation_dom @ SV193 ) )
| ( ( relation_dom @ ( relation_composition @ SV15 @ SV193 ) )
= ( relation_dom @ SV15 ) ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1183]) ).
thf(1385,plain,
! [SV16: $i,SV194: $i] :
( ( ( ~ ( relation @ SV194 )
| ~ ( subset @ ( relation_dom @ SV16 ) @ ( relation_rng @ SV194 ) )
| ( ( relation_rng @ ( relation_composition @ SV194 @ SV16 ) )
= ( relation_rng @ SV16 ) ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1386,plain,
! [SV17: $i,SV130: $i] :
( ( ( relation @ SV130 )
= $false )
| ( ( subset @ ( relation_dom_restriction @ SV130 @ SV17 ) @ SV130 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1185]) ).
thf(1387,plain,
! [SV18: $i,SV131: $i] :
( ( ( relation @ SV131 )
= $false )
| ( ( ( relation_dom @ ( relation_dom_restriction @ SV131 @ SV18 ) )
= ( set_intersection2 @ ( relation_dom @ SV131 ) @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1186]) ).
thf(1388,plain,
! [SV19: $i,SV132: $i] :
( ( ( relation @ SV132 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV132 @ SV19 ) ) @ ( relation_rng @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1187]) ).
thf(1389,plain,
! [SV23: $i] :
( ( ( function @ SV23 )
= $false )
| ( ( ~ ( relation @ SV23 ) )
= $true )
| ( ( ~ ( one_to_one @ SV23 )
| ( ( function_inverse @ SV23 )
= ( relation_inverse @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1191]) ).
thf(1390,plain,
! [SV133: $i,SV25: $i] :
( ( ( ~ ( relation @ SV25 ) )
= $true )
| ( ( ~ ( relation @ SV133 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV25 @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1193]) ).
thf(1391,plain,
! [SV195: $i,SV27: $i] :
( ( ( relation @ ( relation_dom_restriction @ SV27 @ SV195 ) )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1392,plain,
! [SV28: $i,SV134: $i] :
( ( ( relation @ SV134 )
= $false )
| ( ( relation @ ( relation_rng_restriction @ SV28 @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1195]) ).
thf(1393,plain,
! [SV135: $i,SV29: $i] :
( ( ( ~ ( relation @ SV29 ) )
= $true )
| ( ( ~ ( relation @ SV135 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV29 @ SV135 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1196]) ).
thf(1394,plain,
! [SV136: $i,SV30: $i] :
( ( ( ~ ( relation @ SV30 ) )
= $true )
| ( ( ~ ( relation @ SV136 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV30 @ SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1197]) ).
thf(1395,plain,
! [SV31: $i] :
( ( ( relation @ SV31 )
= $false )
| ( ( empty @ SV31 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV31 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1198]) ).
thf(1396,plain,
! [SV32: $i] :
( ( ( relation @ SV32 )
= $false )
| ( ( empty @ SV32 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1199]) ).
thf(1397,plain,
! [SV137: $i,SV35: $i] :
( ( ( in @ SV35 @ SV137 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV35 ) @ SV137 )
= SV137 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1201]) ).
thf(1398,plain,
! [SV138: $i,SV36: $i] :
( ( ( in @ SV36 @ SV138 )
= $false )
| ( ( subset @ SV36 @ ( union @ SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1202]) ).
thf(1399,plain,
! [SV196: $i,SV183: $i,SV139: $i,SV37: $i] :
( ( ~ ( subset @ SV37 @ SV139 )
| ~ ( subset @ SV183 @ SV196 )
| ( subset @ ( cartesian_product2 @ SV37 @ SV183 ) @ ( cartesian_product2 @ SV139 @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1400,plain,
! [SV140: $i,SV38: $i] :
( ( ( subset @ SV38 @ SV140 )
= $false )
| ( ( ( set_union2 @ SV38 @ SV140 )
= SV140 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1204]) ).
thf(1401,plain,
! [SV39: $i,SV141: $i] :
( ( ( relation @ SV141 )
= $false )
| ( ( ( SV39 = empty_set )
| ~ ( subset @ SV39 @ ( relation_rng @ SV141 ) )
| ( ( relation_inverse_image @ SV141 @ SV39 )
!= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1205]) ).
thf(1402,plain,
! [SV184: $i,SV143: $i,SV41: $i] :
( ( ( ~ ( subset @ SV41 @ SV143 )
| ~ ( subset @ SV41 @ SV184 ) )
= $true )
| ( ( subset @ SV41 @ ( set_intersection2 @ SV143 @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1206]) ).
thf(1403,plain,
! [SV185: $i,SV144: $i,SV42: $i] :
( ( ( ~ ( subset @ SV42 @ SV144 )
| ~ ( subset @ SV144 @ SV185 ) )
= $true )
| ( ( subset @ SV42 @ SV185 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1207]) ).
thf(1404,plain,
! [SV43: $i,SV145: $i] :
( ( ( ~ ( function @ SV145 ) )
= $true )
| ( ( ~ ( relation @ SV145 ) )
= $true )
| ( ( ! [SY717: $i] :
( ~ ( function @ SY717 )
| ~ ( relation @ SY717 )
| ~ ( in @ SV43 @ ( relation_dom @ ( relation_composition @ SY717 @ SV145 ) ) )
| ( ( apply @ ( relation_composition @ SY717 @ SV145 ) @ SV43 )
= ( apply @ SV145 @ ( apply @ SY717 @ SV43 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1208]) ).
thf(1405,plain,
! [SV44: $i,SV146: $i] :
( ( ( ~ ( function @ SV146 ) )
= $true )
| ( ( ~ ( relation @ SV146 ) )
= $true )
| ( ( ! [SY718: $i] :
( ~ ( function @ SY718 )
| ~ ( relation @ SY718 )
| ~ ( in @ SV44 @ ( relation_dom @ SV146 ) )
| ( ( apply @ ( relation_composition @ SV146 @ SY718 ) @ SV44 )
= ( apply @ SY718 @ ( apply @ SV146 @ SV44 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1209]) ).
thf(1406,plain,
! [SV147: $i,SV45: $i] :
( ( ( subset @ SV45 @ SV147 )
= $false )
| ( ( ! [SY719: $i] : ( subset @ ( set_intersection2 @ SV45 @ SY719 ) @ ( set_intersection2 @ SV147 @ SY719 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1210]) ).
thf(1407,plain,
! [SV148: $i,SV46: $i] :
( ( ( subset @ SV46 @ SV148 )
= $false )
| ( ( ( set_intersection2 @ SV46 @ SV148 )
= SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1211]) ).
thf(1408,plain,
! [SV149: $i,SV48: $i] :
( ( ( subset @ SV48 @ SV149 )
= $false )
| ( ( ! [SY720: $i] : ( subset @ ( set_difference @ SV48 @ SY720 ) @ ( set_difference @ SV149 @ SY720 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1212]) ).
thf(1409,plain,
! [SV49: $i,SV150: $i] :
( ( ( in @ SV150 @ SV49 )
= $false )
| ( ( ( apply @ ( identity_relation @ SV49 ) @ SV150 )
= SV150 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1213]) ).
thf(1410,plain,
! [SV154: $i,SV54: $i] :
( ( ( subset @ SV54 @ SV154 )
= $false )
| ( ( SV154
= ( set_union2 @ SV54 @ ( set_difference @ SV154 @ SV54 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1215]) ).
thf(1411,plain,
! [SV155: $i,SV55: $i] :
( ( ( in @ SV55 @ SV155 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV55 ) @ SV155 )
= SV155 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1412,plain,
! [SV57: $i] :
( ( ( in @ ( ordered_pair @ ( sK46_B @ SV57 ) @ ( sK47_SY415 @ SV57 ) ) @ SV57 )
= $true )
| ( ( SV57 = empty_set )
= $true )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1217]) ).
thf(1413,plain,
! [SV58: $i,SV157: $i] :
( ( ( proper_subset @ SV157 @ SV58 )
= $false )
| ( ( ~ ( subset @ SV58 @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1218]) ).
thf(1414,plain,
! [SV59: $i,SV186: $i,SV158: $i] :
( ( ( ~ ( disjoint @ SV158 @ SV186 )
| ~ ( subset @ SV59 @ SV158 ) )
= $true )
| ( ( disjoint @ SV59 @ SV186 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1219]) ).
thf(1415,plain,
! [SV159: $i,SV60: $i] :
( ( ( subset @ ( singleton @ SV60 ) @ ( singleton @ SV159 ) )
= $false )
| ( ( SV60 = SV159 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1220]) ).
thf(1416,plain,
! [SV187: $i,SV161: $i,SV62: $i] :
( ( ( ~ ( subset @ SV62 @ SV161 )
| ~ ( subset @ SV187 @ SV161 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV62 @ SV187 ) @ SV161 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1221]) ).
thf(1417,plain,
! [SV162: $i,SV63: $i] :
( ( ( in @ SV63 @ SV162 )
= $false )
| ( ( subset @ SV63 @ ( union @ SV162 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1222]) ).
thf(1418,plain,
! [SV64: $i,SV163: $i] :
( ( ( relation @ SV163 )
= $false )
| ( ( ( relation_dom_restriction @ SV163 @ SV64 )
= ( relation_composition @ ( identity_relation @ SV64 ) @ SV163 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1223]) ).
thf(1419,plain,
! [SV164: $i,SV65: $i] :
( ( ( in @ SV65 @ SV164 )
= $false )
| ( ( ~ ( in @ SV164 @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1224]) ).
thf(1420,plain,
! [SV188: $i,SV71: $i] :
( ( ( empty @ ( set_union2 @ SV71 @ SV188 ) )
= $false )
| ( ( empty @ SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1226]) ).
thf(1421,plain,
! [SV73: $i,SV189: $i] :
( ( ( empty @ ( set_union2 @ SV189 @ SV73 ) )
= $false )
| ( ( empty @ SV73 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1228]) ).
thf(1422,plain,
! [SV169: $i,SV74: $i] :
( ( ( empty @ SV74 )
= $true )
| ( ( empty @ SV169 )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV74 @ SV169 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1229]) ).
thf(1423,plain,
! [SV170: $i,SV79: $i] :
( ( ( in @ SV79 @ SV170 )
= $false )
| ( ( element @ SV79 @ SV170 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1230]) ).
thf(1424,plain,
! [SV171: $i,SV81: $i] :
( ( ( element @ SV81 @ SV171 )
= $false )
| ( ( ( empty @ SV171 )
| ( in @ SV81 @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1231]) ).
thf(1425,plain,
! [SV85: $i,SV172: $i] :
( ( ( empty @ SV172 )
= $false )
| ( ( ~ ( in @ SV85 @ SV172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1233]) ).
thf(1426,plain,
! [SV173: $i,SV86: $i] :
( ( ( SV86 = SV173 )
= $true )
| ( ( ~ ( empty @ SV86 ) )
= $true )
| ( ( ~ ( empty @ SV173 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1234]) ).
thf(1427,plain,
! [SV197: $i] :
( ( ! [SY757: $i] :
( ~ ( in @ SV197 @ SY757 )
| ( subset @ ( singleton @ SV197 ) @ SY757 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1428,plain,
! [SV198: $i] :
( ( ! [SY758: $i] :
( ~ ( subset @ ( singleton @ SV198 ) @ SY758 )
| ( in @ SV198 @ SY758 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1236]) ).
thf(1429,plain,
! [SV199: $i] :
( ( ! [SY759: $i] :
( ~ ( subset @ SV199 @ ( singleton @ SY759 ) )
| ( SV199 = empty_set )
| ( SV199
= ( singleton @ SY759 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1237]) ).
thf(1430,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)],[1238]) ).
thf(1431,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY406 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ ( sK33_SY406 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK31_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)],[1239]) ).
thf(1432,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)],[1240]) ).
thf(1433,plain,
! [SV200: $i] :
( ( ! [SY760: $i] :
( ( disjoint @ SV200 @ SY760 )
| ( in @ ( sK48_C @ SY760 @ SV200 ) @ ( set_intersection2 @ SV200 @ SY760 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1434,plain,
! [SV201: $i] :
( ( ! [SY761: $i] :
( ! [SY762: $i] :
~ ( in @ SY762 @ ( set_intersection2 @ SV201 @ SY761 ) )
| ~ ( disjoint @ SV201 @ SY761 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1242]) ).
thf(1435,plain,
! [SV202: $i] :
( ( ! [SY763: $i] :
( ~ ( function @ SV202 )
| ~ ( relation @ SV202 )
| ~ ( relation @ SY763 )
| ~ ( function @ SY763 )
| ( function @ ( relation_composition @ SV202 @ SY763 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1243]) ).
thf(1436,plain,
! [SV203: $i] :
( ( ! [SY764: $i] :
( ~ ( function @ SV203 )
| ~ ( relation @ SV203 )
| ~ ( relation @ SY764 )
| ~ ( function @ SY764 )
| ( relation @ ( relation_composition @ SV203 @ SY764 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1244]) ).
thf(1437,plain,
! [SV204: $i] :
( ( ! [SY765: $i] :
( ( ( set_difference @ SV204 @ SY765 )
!= empty_set )
| ( subset @ SV204 @ SY765 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(1438,plain,
! [SV205: $i] :
( ( ! [SY766: $i] :
( ~ ( subset @ SV205 @ SY766 )
| ( ( set_difference @ SV205 @ SY766 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1439,plain,
! [SV206: $i] :
( ( ! [SY767: $i] :
( ~ ( empty @ SV206 )
| ~ ( relation @ SY767 )
| ( empty @ ( relation_composition @ SV206 @ SY767 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1440,plain,
! [SV207: $i] :
( ( ! [SY768: $i] :
( ~ ( empty @ SV207 )
| ~ ( relation @ SY768 )
| ( relation @ ( relation_composition @ SV207 @ SY768 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1441,plain,
! [SV87: $i] :
( ( ! [SY498: $i,SY499: $i] :
( ~ ( relation @ SY499 )
| ! [SY500: $i] :
( ~ ( in @ SY500 @ ( relation_dom @ SY499 ) )
| ~ ( in @ ( ordered_pair @ SY500 @ SV87 ) @ SY499 )
| ~ ( in @ SY500 @ SY498 ) )
| ( in @ SV87 @ ( relation_image @ SY499 @ SY498 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1249]) ).
thf(1442,plain,
! [SV87: $i] :
( ( ! [SY501: $i,SY502: $i] :
( ~ ( relation @ SY502 )
| ~ ( in @ SV87 @ ( relation_image @ SY502 @ SY501 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK52_D @ SY502 @ SY501 @ SV87 ) @ ( relation_dom @ SY502 ) )
| ~ ( in @ ( ordered_pair @ ( sK52_D @ SY502 @ SY501 @ SV87 ) @ SV87 ) @ SY502 ) )
| ~ ( in @ ( sK52_D @ SY502 @ SY501 @ SV87 ) @ SY501 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1250]) ).
thf(1443,plain,
! [SV208: $i] :
( ( ! [SY769: $i] :
( ~ ( subset @ SV208 @ SY769 )
| ~ ( subset @ SY769 @ SV208 )
| ( SV208 = SY769 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1444,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)],[1252]) ).
thf(1445,plain,
! [SV88: $i] :
( ( ! [SY503: $i,SY504: $i] :
( ~ ( ~ ( ~ ( in @ ( sK13_D @ SY504 @ SY503 @ SV88 ) @ SV88 )
| ( in @ ( sK13_D @ SY504 @ SY503 @ SV88 ) @ SY503 )
| ~ ( in @ ( sK13_D @ SY504 @ SY503 @ SV88 ) @ SY504 ) )
| ~ ~ ( ~ ( ( in @ ( sK13_D @ SY504 @ SY503 @ SV88 ) @ SV88 )
| ( in @ ( sK13_D @ SY504 @ SY503 @ SV88 ) @ SY504 ) )
| ~ ( ~ ( in @ ( sK13_D @ SY504 @ SY503 @ SV88 ) @ SY503 )
| ( in @ ( sK13_D @ SY504 @ SY503 @ SV88 ) @ SY504 ) ) ) )
| ( SY504
= ( set_difference @ SV88 @ SY503 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1255]) ).
thf(1446,plain,
! [SV88: $i] :
( ( ! [SY505: $i,SY506: $i] :
( ( SY506
!= ( set_difference @ SV88 @ SY505 ) )
| ~ ( ~ ! [SY507: $i] :
( ~ ( in @ SY507 @ SV88 )
| ( in @ SY507 @ SY505 )
| ( in @ SY507 @ SY506 ) )
| ~ ~ ( ~ ! [SY508: $i] :
( ~ ( in @ SY508 @ SY506 )
| ( in @ SY508 @ SV88 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY506 )
| ~ ( in @ SX3 @ SY505 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1256]) ).
thf(1447,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)],[1257]) ).
thf(1448,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)],[1258]) ).
thf(1449,plain,
! [SV89: $i,SV174: $i] :
( ( ( relation @ SV174 )
= $false )
| ( ( ~ ( ~ ! [SY723: $i] :
( ~ ( relation @ SY723 )
| ~ ( ~ ( ~ ( in @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY723 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) ) @ SV174 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY723 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) ) @ SY723 ) )
| ~ ~ ( ~ ( ( in @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) @ SV89 )
| ( in @ ( ordered_pair @ ( sK40_D @ SY723 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) ) @ SY723 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SY723 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) ) @ SV174 )
| ( in @ ( ordered_pair @ ( sK40_D @ SY723 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) ) @ SY723 ) ) ) )
| ( SY723
= ( relation_rng_restriction @ SV89 @ SV174 ) ) )
| ~ ! [SY724: $i] :
( ~ ( relation @ SY724 )
| ( SY724
!= ( relation_rng_restriction @ SV89 @ SV174 ) )
| ~ ( ~ ! [SY725: $i,SY726: $i] :
( ~ ( in @ SY726 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY725 @ SY726 ) @ SV174 )
| ( in @ ( ordered_pair @ SY725 @ SY726 ) @ SY724 ) )
| ~ ~ ( ~ ! [SY515: $i,SY516: $i] :
( ~ ( in @ ( ordered_pair @ SY515 @ SY516 ) @ SY724 )
| ( in @ SY516 @ SV89 ) )
| ~ ! [SY729: $i,SY730: $i] :
( ~ ( in @ ( ordered_pair @ SY729 @ SY730 ) @ SY724 )
| ( in @ ( ordered_pair @ SY729 @ SY730 ) @ SV174 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1261]) ).
thf(1450,plain,
! [SV90: $i] :
( ( ! [SY519: $i,SY520: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY520 @ SY519 @ SV90 ) @ SY520 )
| ( ( sK27_D @ SY520 @ SY519 @ SV90 )
!= SV90 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY520 @ SY519 @ SV90 ) @ SY520 )
| ( ( sK27_D @ SY520 @ SY519 @ SV90 )
!= SY519 ) ) )
| ~ ( ( in @ ( sK27_D @ SY520 @ SY519 @ SV90 ) @ SY520 )
| ( ( sK27_D @ SY520 @ SY519 @ SV90 )
= SV90 )
| ( ( sK27_D @ SY520 @ SY519 @ SV90 )
= SY519 ) ) )
| ( SY520
= ( unordered_pair @ SV90 @ SY519 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1262]) ).
thf(1451,plain,
! [SV90: $i] :
( ( ! [SY521: $i,SY522: $i] :
( ( SY522
!= ( unordered_pair @ SV90 @ SY521 ) )
| ~ ( ~ ! [SY523: $i] :
( ~ ( in @ SY523 @ SY522 )
| ( SY523 = SV90 )
| ( SY523 = SY521 ) )
| ~ ~ ( ~ ! [SY524: $i] :
( ( SY524 != SV90 )
| ( in @ SY524 @ SY522 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY521 )
| ( in @ SX3 @ SY522 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1263]) ).
thf(1452,plain,
! [SV209: $i] :
( ( ! [SY770: $i] :
( ~ ( ~ ( ~ ( in @ ( sK28_C @ SY770 @ SV209 ) @ SY770 )
| ~ ( subset @ ( sK28_C @ SY770 @ SV209 ) @ SV209 ) )
| ~ ( ( in @ ( sK28_C @ SY770 @ SV209 ) @ SY770 )
| ( subset @ ( sK28_C @ SY770 @ SV209 ) @ SV209 ) ) )
| ( SY770
= ( powerset @ SV209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1264]) ).
thf(1453,plain,
! [SV210: $i] :
( ( ! [SY771: $i] :
( ( SY771
!= ( powerset @ SV210 ) )
| ~ ( ~ ! [SY772: $i] :
( ~ ( in @ SY772 @ SY771 )
| ( subset @ SY772 @ SV210 ) )
| ~ ! [SY773: $i] :
( ~ ( subset @ SY773 @ SV210 )
| ( in @ SY773 @ SY771 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1454,plain,
! [SV211: $i] :
( ( ! [SY774: $i] :
( ( ( set_intersection2 @ SV211 @ SY774 )
!= empty_set )
| ( disjoint @ SV211 @ SY774 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1455,plain,
! [SV212: $i] :
( ( ! [SY775: $i] :
( ~ ( disjoint @ SV212 @ SY775 )
| ( ( set_intersection2 @ SV212 @ SY775 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1456,plain,
! [SV91: $i] :
( ( ( ~ ! [SY526: $i] :
( ~ ( ~ ( ! [SY527: $i] :
~ ( in @ ( ordered_pair @ ( sK63_C @ SY526 @ SV91 ) @ SY527 ) @ SV91 )
| ~ ( in @ ( sK63_C @ SY526 @ SV91 ) @ SY526 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_C @ SY526 @ SV91 ) @ ( sK64_SY419 @ SY526 @ SV91 ) ) @ SV91 )
| ( in @ ( sK63_C @ SY526 @ SV91 ) @ SY526 ) ) )
| ( SY526
= ( relation_dom @ SV91 ) ) )
| ~ ! [SY528: $i] :
( ( SY528
!= ( relation_dom @ SV91 ) )
| ~ ( ~ ! [SY529: $i] :
( ! [SY530: $i] :
~ ( in @ ( ordered_pair @ SY529 @ SY530 ) @ SV91 )
| ( in @ SY529 @ SY528 ) )
| ~ ! [SY531: $i] :
( ~ ( in @ SY531 @ SY528 )
| ( in @ ( ordered_pair @ SY531 @ ( sK62_D @ SY531 @ SY528 @ SV91 ) ) @ SV91 ) ) ) ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1268]) ).
thf(1457,plain,
! [SV92: $i] :
( ( ( ~ ! [SY532: $i,SY533: $i] :
( ~ ( ~ ( ! [SY534: $i] :
( ~ ( in @ ( ordered_pair @ ( sK35_D @ SY533 @ SY532 @ SV92 ) @ SY534 ) @ SV92 )
| ~ ( in @ SY534 @ SY532 ) )
| ~ ( in @ ( sK35_D @ SY533 @ SY532 @ SV92 ) @ SY533 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SY533 @ SY532 @ SV92 ) @ ( sK36_SY409 @ SY533 @ SY532 @ SV92 ) ) @ SV92 )
| ~ ( in @ ( sK36_SY409 @ SY533 @ SY532 @ SV92 ) @ SY532 ) )
| ( in @ ( sK35_D @ SY533 @ SY532 @ SV92 ) @ SY533 ) ) )
| ( SY533
= ( relation_inverse_image @ SV92 @ SY532 ) ) )
| ~ ! [SY535: $i,SY536: $i] :
( ( SY536
!= ( relation_inverse_image @ SV92 @ SY535 ) )
| ~ ( ~ ! [SY537: $i] :
( ! [SY538: $i] :
( ~ ( in @ ( ordered_pair @ SY537 @ SY538 ) @ SV92 )
| ~ ( in @ SY538 @ SY535 ) )
| ( in @ SY537 @ SY536 ) )
| ~ ! [SY539: $i] :
( ~ ( in @ SY539 @ SY536 )
| ~ ( ~ ( in @ ( ordered_pair @ SY539 @ ( sK34_E @ SY539 @ SY536 @ SY535 @ SV92 ) ) @ SV92 )
| ~ ( in @ ( sK34_E @ SY539 @ SY536 @ SY535 @ SV92 ) @ SY535 ) ) ) ) ) )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1269]) ).
thf(1458,plain,
! [SV93: $i] :
( ( ( ~ ! [SY540: $i,SY541: $i] :
( ~ ( ~ ( ! [SY542: $i] :
( ~ ( in @ ( ordered_pair @ SY542 @ ( sK38_D @ SY541 @ SY540 @ SV93 ) ) @ SV93 )
| ~ ( in @ SY542 @ SY540 ) )
| ~ ( in @ ( sK38_D @ SY541 @ SY540 @ SV93 ) @ SY541 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SY541 @ SY540 @ SV93 ) @ ( sK38_D @ SY541 @ SY540 @ SV93 ) ) @ SV93 )
| ~ ( in @ ( sK39_SY411 @ SY541 @ SY540 @ SV93 ) @ SY540 ) )
| ( in @ ( sK38_D @ SY541 @ SY540 @ SV93 ) @ SY541 ) ) )
| ( SY541
= ( relation_image @ SV93 @ SY540 ) ) )
| ~ ! [SY543: $i,SY544: $i] :
( ( SY544
!= ( relation_image @ SV93 @ SY543 ) )
| ~ ( ~ ! [SY545: $i] :
( ! [SY546: $i] :
( ~ ( in @ ( ordered_pair @ SY546 @ SY545 ) @ SV93 )
| ~ ( in @ SY546 @ SY543 ) )
| ( in @ SY545 @ SY544 ) )
| ~ ! [SY547: $i] :
( ~ ( in @ SY547 @ SY544 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SY547 @ SY544 @ SY543 @ SV93 ) @ SY547 ) @ SV93 )
| ~ ( in @ ( sK37_E @ SY547 @ SY544 @ SY543 @ SV93 ) @ SY543 ) ) ) ) ) )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1270]) ).
thf(1459,plain,
! [SV94: $i] :
( ( ! [SY548: $i,SY549: $i] :
( ~ ( relation @ SY549 )
| ! [SY550: $i] :
( ~ ( in @ SY550 @ ( relation_rng @ SY549 ) )
| ~ ( in @ ( ordered_pair @ SV94 @ SY550 ) @ SY549 )
| ~ ( in @ SY550 @ SY548 ) )
| ( in @ SV94 @ ( relation_inverse_image @ SY549 @ SY548 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1271]) ).
thf(1460,plain,
! [SV94: $i] :
( ( ! [SY551: $i,SY552: $i] :
( ~ ( relation @ SY552 )
| ~ ( in @ SV94 @ ( relation_inverse_image @ SY552 @ SY551 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK51_D @ SY552 @ SY551 @ SV94 ) @ ( relation_rng @ SY552 ) )
| ~ ( in @ ( ordered_pair @ SV94 @ ( sK51_D @ SY552 @ SY551 @ SV94 ) ) @ SY552 ) )
| ~ ( in @ ( sK51_D @ SY552 @ SY551 @ SV94 ) @ SY551 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1272]) ).
thf(1461,plain,
! [SV95: $i,SV175: $i] :
( ( ( ~ ( function @ SV175 ) )
= $true )
| ( ( ~ ( relation @ SV175 ) )
= $true )
| ( ( ~ ( ~ ! [SY731: $i] :
( ~ ( function @ SY731 )
| ~ ( relation @ SY731 )
| ~ ( in @ SV95 @ ( relation_dom @ SY731 ) )
| ~ ( in @ ( apply @ SY731 @ SV95 ) @ ( relation_dom @ SV175 ) )
| ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY731 @ SV175 ) ) ) )
| ~ ~ ( ~ ! [SY732: $i] :
( ~ ( function @ SY732 )
| ~ ( relation @ SY732 )
| ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY732 @ SV175 ) ) )
| ( in @ SV95 @ ( relation_dom @ SY732 ) ) )
| ~ ! [SY733: $i] :
( ~ ( function @ SY733 )
| ~ ( relation @ SY733 )
| ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY733 @ SV175 ) ) )
| ( in @ ( apply @ SY733 @ SV95 ) @ ( relation_dom @ SV175 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1273]) ).
thf(1462,plain,
! [SV96: $i] :
( ( ( ~ ! [SY557: $i,SY558: $i] :
( ~ ( relation @ SY558 )
| ~ ( ~ ( ~ ( in @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ SY557 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ ( sK43_SY413 @ SY558 @ SY557 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ ( sK43_SY413 @ SY558 @ SY557 @ SV96 ) ) @ SY558 ) )
| ~ ~ ( ~ ( ( in @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ SY557 )
| ( in @ ( ordered_pair @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ ( sK43_SY413 @ SY558 @ SY557 @ SV96 ) ) @ SY558 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ ( sK43_SY413 @ SY558 @ SY557 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ ( sK43_SY413 @ SY558 @ SY557 @ SV96 ) ) @ SY558 ) ) ) )
| ( SY558
= ( relation_dom_restriction @ SV96 @ SY557 ) ) )
| ~ ! [SY559: $i,SY560: $i] :
( ~ ( relation @ SY560 )
| ( SY560
!= ( relation_dom_restriction @ SV96 @ SY559 ) )
| ~ ( ~ ! [SY561: $i,SY562: $i] :
( ~ ( in @ SY561 @ SY559 )
| ~ ( in @ ( ordered_pair @ SY561 @ SY562 ) @ SV96 )
| ( in @ ( ordered_pair @ SY561 @ SY562 ) @ SY560 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY560 )
| ( in @ SX3 @ SY559 ) )
| ~ ! [SY565: $i,SY566: $i] :
( ~ ( in @ ( ordered_pair @ SY565 @ SY566 ) @ SY560 )
| ( in @ ( ordered_pair @ SY565 @ SY566 ) @ SV96 ) ) ) ) ) )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1274]) ).
thf(1463,plain,
! [SV213: $i] :
( ( ! [SY776: $i] :
( ~ ( empty @ SV213 )
| ~ ( relation @ SY776 )
| ( empty @ ( relation_composition @ SY776 @ SV213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1275]) ).
thf(1464,plain,
! [SV214: $i] :
( ( ! [SY777: $i] :
( ~ ( empty @ SV214 )
| ~ ( relation @ SY777 )
| ( relation @ ( relation_composition @ SY777 @ SV214 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1276]) ).
thf(1465,plain,
! [SV97: $i] :
( ( ( ~ ! [SY567: $i] :
( ~ ( relation @ SY567 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SY567 @ SV97 ) @ ( sK12_SY396 @ SY567 @ SV97 ) ) @ SY567 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SY567 @ SV97 ) @ ( sK11_C @ SY567 @ SV97 ) ) @ SV97 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_C @ SY567 @ SV97 ) @ ( sK12_SY396 @ SY567 @ SV97 ) ) @ SY567 )
| ( in @ ( ordered_pair @ ( sK12_SY396 @ SY567 @ SV97 ) @ ( sK11_C @ SY567 @ SV97 ) ) @ SV97 ) ) )
| ( SY567
= ( relation_inverse @ SV97 ) ) )
| ~ ! [SY568: $i] :
( ~ ( relation @ SY568 )
| ( SY568
!= ( relation_inverse @ SV97 ) )
| ~ ( ~ ! [SY569: $i,SY570: $i] :
( ~ ( in @ ( ordered_pair @ SY569 @ SY570 ) @ SY568 )
| ( in @ ( ordered_pair @ SY570 @ SY569 ) @ SV97 ) )
| ~ ! [SY571: $i,SY572: $i] :
( ~ ( in @ ( ordered_pair @ SY572 @ SY571 ) @ SV97 )
| ( in @ ( ordered_pair @ SY571 @ SY572 ) @ SY568 ) ) ) ) )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1277]) ).
thf(1466,plain,
! [SV98: $i] :
( ( ( ~ ! [SY573: $i] :
( ~ ( ~ ( ! [SY574: $i] :
~ ( in @ ( ordered_pair @ SY574 @ ( sK60_C @ SY573 @ SV98 ) ) @ SV98 )
| ~ ( in @ ( sK60_C @ SY573 @ SV98 ) @ SY573 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK61_SY417 @ SY573 @ SV98 ) @ ( sK60_C @ SY573 @ SV98 ) ) @ SV98 )
| ( in @ ( sK60_C @ SY573 @ SV98 ) @ SY573 ) ) )
| ( SY573
= ( relation_rng @ SV98 ) ) )
| ~ ! [SY575: $i] :
( ( SY575
!= ( relation_rng @ SV98 ) )
| ~ ( ~ ! [SY576: $i] :
( ! [SY577: $i] :
~ ( in @ ( ordered_pair @ SY577 @ SY576 ) @ SV98 )
| ( in @ SY576 @ SY575 ) )
| ~ ! [SY578: $i] :
( ~ ( in @ SY578 @ SY575 )
| ( in @ ( ordered_pair @ ( sK59_D @ SY578 @ SY575 @ SV98 ) @ SY578 ) @ SV98 ) ) ) ) )
= $false )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1278]) ).
thf(1467,plain,
! [SV99: $i,SV176: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_C @ SV176 @ SV99 ) @ SV99 )
| ~ ( in @ ( sK4_C @ SV176 @ SV99 ) @ SV176 ) )
| ~ ( ( in @ ( sK4_C @ SV176 @ SV99 ) @ SV99 )
| ( in @ ( sK4_C @ SV176 @ SV99 ) @ SV176 ) ) )
= $false )
| ( ( SV99 = SV176 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1279]) ).
thf(1468,plain,
! [SV100: $i] :
( ( ! [SY580: $i,SY581: $i] :
( ~ ( function @ SY581 )
| ~ ( relation @ SY581 )
| ( SY580
!= ( apply @ SY581 @ SV100 ) )
| ~ ( in @ SV100 @ ( relation_dom @ SY581 ) )
| ( in @ ( ordered_pair @ SV100 @ SY580 ) @ SY581 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1280]) ).
thf(1469,plain,
! [SV100: $i] :
( ( ~ ( ~ ! [SY582: $i,SY583: $i] :
( ~ ( function @ SY583 )
| ~ ( relation @ SY583 )
| ~ ( in @ ( ordered_pair @ SV100 @ SY582 ) @ SY583 )
| ( SY582
= ( apply @ SY583 @ SV100 ) ) )
| ~ ! [SY584: $i,SY585: $i] :
( ~ ( function @ SY585 )
| ~ ( relation @ SY585 )
| ~ ( in @ ( ordered_pair @ SV100 @ SY584 ) @ SY585 )
| ( in @ SV100 @ ( relation_dom @ SY585 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1281]) ).
thf(1470,plain,
! [SV101: $i,SV215: $i] :
( ( ( ~ ( relation @ SV215 )
| ~ ( ~ ! [SY778: $i] :
( ~ ( relation @ SY778 )
| ~ ( ~ ( ! [SY779: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY778 @ SV215 @ SV101 ) @ SY779 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY779 @ ( sK9_SY391 @ SY778 @ SV215 @ SV101 ) ) @ SV215 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SY778 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SY778 @ SV215 @ SV101 ) ) @ SY778 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY778 @ SV215 @ SV101 ) @ ( sK10_SY395 @ SY778 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SY778 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SY778 @ SV215 @ SV101 ) ) @ SV215 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SY778 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SY778 @ SV215 @ SV101 ) ) @ SY778 ) ) )
| ( SY778
= ( relation_composition @ SV101 @ SV215 ) ) )
| ~ ! [SY780: $i] :
( ~ ( relation @ SY780 )
| ( SY780
!= ( relation_composition @ SV101 @ SV215 ) )
| ~ ( ~ ! [SY781: $i,SY782: $i] :
( ! [SY783: $i] :
( ~ ( in @ ( ordered_pair @ SY781 @ SY783 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY783 @ SY782 ) @ SV215 ) )
| ( in @ ( ordered_pair @ SY781 @ SY782 ) @ SY780 ) )
| ~ ! [SY784: $i,SY785: $i] :
( ~ ( in @ ( ordered_pair @ SY784 @ SY785 ) @ SY780 )
| ~ ( ~ ( in @ ( ordered_pair @ SY784 @ ( sK7_F @ SY785 @ SY784 @ SY780 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY785 @ SY784 @ SY780 @ SV215 @ SV101 ) @ SY785 ) @ SV215 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1471,plain,
! [SV177: $i,SV102: $i] :
( ( ~ ! [SY734: $i,SY735: $i] :
( ~ ( in @ SV102 @ SY734 )
| ~ ( in @ SV177 @ SY735 )
| ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SY734 @ SY735 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1283]) ).
thf(1472,plain,
! [SV177: $i,SV102: $i] :
( ( ~ ~ ( ~ ! [SY736: $i] :
( ! [SY737: $i] :
~ ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SY736 @ SY737 ) )
| ( in @ SV102 @ SY736 ) )
| ~ ! [SY738: $i,SY739: $i] :
( ~ ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SY738 @ SY739 ) )
| ( in @ SV177 @ SY739 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1283]) ).
thf(1473,plain,
! [SV216: $i] :
( ( ~ ( relation @ SV216 )
| ( ( relation_dom @ SV216 )
!= empty_set )
| ( SV216 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1474,plain,
! [SV217: $i] :
( ( ~ ( relation @ SV217 )
| ( ( relation_rng @ SV217 )
!= empty_set )
| ( SV217 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1285]) ).
thf(1475,plain,
! [SV103: $i] :
( ( ! [SY602: $i] :
( ~ ( subset @ SY602 @ ( sK2_B @ SV103 ) )
| ( are_equipotent @ SY602 @ ( sK2_B @ SV103 ) )
| ( in @ SY602 @ ( sK2_B @ SV103 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1286]) ).
thf(1476,plain,
! [SV103: $i] :
( ( ~ ( ~ ! [SY603: $i] :
( ~ ( ~ ! [SY604: $i] :
( ~ ( subset @ SY604 @ SY603 )
| ( in @ SY604 @ ( sK3_SY386 @ SY603 @ SV103 ) ) )
| ~ ( in @ ( sK3_SY386 @ SY603 @ SV103 ) @ ( sK2_B @ SV103 ) ) )
| ~ ( in @ SY603 @ ( sK2_B @ SV103 ) ) )
| ~ ~ ( ~ ! [SY605: $i,SY606: $i] :
( ~ ( in @ SY605 @ ( sK2_B @ SV103 ) )
| ~ ( subset @ SY606 @ SY605 )
| ( in @ SY606 @ ( sK2_B @ SV103 ) ) )
| ~ ( in @ SV103 @ ( sK2_B @ SV103 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1287]) ).
thf(1477,plain,
! [SV218: $i] :
( ( ~ ( function @ SV218 )
| ~ ( relation @ SV218 )
| ( function @ ( function_inverse @ SV218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1478,plain,
! [SV219: $i] :
( ( ~ ( function @ SV219 )
| ~ ( relation @ SV219 )
| ( relation @ ( function_inverse @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1479,plain,
! [SV220: $i] :
( ( ~ ( empty @ SV220 )
| ( empty @ ( relation_inverse @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1290]) ).
thf(1480,plain,
! [SV221: $i] :
( ( ~ ( empty @ SV221 )
| ( relation @ ( relation_inverse @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1291]) ).
thf(1481,plain,
! [SV222: $i] :
( ( ~ ( ~ ! [SY786: $i,SY787: $i] :
( ( sK69_B @ SV222 )
!= ( ordered_pair @ SY786 @ SY787 ) )
| ~ ( in @ ( sK69_B @ SV222 ) @ SV222 ) )
| ( relation @ SV222 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1292]) ).
thf(1482,plain,
! [SV223: $i] :
( ( ~ ( relation @ SV223 )
| ! [SY788: $i] :
( ( SY788
= ( ordered_pair @ ( sK67_C @ SY788 @ SV223 ) @ ( sK68_SY421 @ SY788 @ SV223 ) ) )
| ~ ( in @ SY788 @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1483,plain,
! [SV104: $i] :
( ( ( ~ ! [SY607: $i] :
( ~ ( relation @ SY607 )
| ~ ( subset @ SV104 @ SY607 )
| ( subset @ ( relation_dom @ SV104 ) @ ( relation_dom @ SY607 ) ) )
| ~ ! [SY608: $i] :
( ~ ( relation @ SY608 )
| ~ ( subset @ SV104 @ SY608 )
| ( subset @ ( relation_rng @ SV104 ) @ ( relation_rng @ SY608 ) ) ) )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1294]) ).
thf(1484,plain,
! [SV105: $i] :
( ( ! [SY609: $i,SY610: $i] :
( ~ ( relation @ SY610 )
| ~ ( in @ SV105 @ SY609 )
| ~ ( in @ SV105 @ ( relation_rng @ SY610 ) )
| ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SY609 @ SY610 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1295]) ).
thf(1485,plain,
! [SV105: $i] :
( ( ~ ( ~ ! [SY611: $i,SY612: $i] :
( ~ ( relation @ SY612 )
| ~ ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SY611 @ SY612 ) ) )
| ( in @ SV105 @ SY611 ) )
| ~ ! [SY613: $i,SY614: $i] :
( ~ ( relation @ SY614 )
| ~ ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SY613 @ SY614 ) ) )
| ( in @ SV105 @ ( relation_rng @ SY614 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1296]) ).
thf(1486,plain,
( ( ~ ( empty @ sK56_A )
| ~ ( relation @ sK56_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1297]) ).
thf(1487,plain,
! [SV106: $i] :
( ( ! [SY615: $i,SY616: $i] :
( ~ ( in @ SV106 @ SY616 )
| ~ ( in @ SY615 @ SY616 )
| ( subset @ ( unordered_pair @ SV106 @ SY615 ) @ SY616 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1299]) ).
thf(1488,plain,
! [SV106: $i] :
( ( ~ ( ~ ! [SY617: $i,SY618: $i] :
( ~ ( subset @ ( unordered_pair @ SV106 @ SY617 ) @ SY618 )
| ( in @ SV106 @ SY618 ) )
| ~ ! [SY619: $i,SY620: $i] :
( ~ ( subset @ ( unordered_pair @ SV106 @ SY619 ) @ SY620 )
| ( in @ SY619 @ SY620 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1300]) ).
thf(1489,plain,
! [SV224: $i] :
( ( ( relation_dom @ ( identity_relation @ SV224 ) )
= SV224 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1490,plain,
! [SV225: $i] :
( ( ( relation_rng @ ( identity_relation @ SV225 ) )
= SV225 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1302]) ).
thf(1491,plain,
! [SV178: $i,SV107: $i] :
( ( ~ ! [SY740: $i,SY741: $i] :
( ~ ( relation @ SY741 )
| ~ ( in @ SV107 @ SY740 )
| ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ SY741 )
| ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SY740 ) @ SY741 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1303]) ).
thf(1492,plain,
! [SV178: $i,SV107: $i] :
( ( ~ ~ ( ~ ! [SY742: $i,SY743: $i] :
( ~ ( relation @ SY743 )
| ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SY742 ) @ SY743 ) )
| ( in @ SV107 @ SY742 ) )
| ~ ! [SY744: $i,SY745: $i] :
( ~ ( relation @ SY745 )
| ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SY744 ) @ SY745 ) )
| ( in @ ( ordered_pair @ SV107 @ SV178 ) @ SY745 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1303]) ).
thf(1493,plain,
! [SV226: $i] :
( ( function @ ( identity_relation @ SV226 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1304]) ).
thf(1494,plain,
! [SV227: $i] :
( ( relation @ ( identity_relation @ SV227 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1305]) ).
thf(1495,plain,
! [SV108: $i] :
( ( ( ~ ! [SY628: $i] :
( ~ ( relation @ SY628 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SY628 @ SV108 ) @ ( sK20_SY399 @ SY628 @ SV108 ) ) @ SV108 )
| ~ ~ ( in @ ( ordered_pair @ ( sK19_C @ SY628 @ SV108 ) @ ( sK20_SY399 @ SY628 @ SV108 ) ) @ SY628 ) )
| ( subset @ SV108 @ SY628 ) )
| ~ ! [SY629: $i] :
( ~ ( relation @ SY629 )
| ~ ( subset @ SV108 @ SY629 )
| ! [SY630: $i,SY631: $i] :
( ~ ( in @ ( ordered_pair @ SY630 @ SY631 ) @ SV108 )
| ( in @ ( ordered_pair @ SY630 @ SY631 ) @ SY629 ) ) ) )
= $false )
| ( ( relation @ SV108 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1306]) ).
thf(1496,plain,
! [SV228: $i] :
( ( ! [SY789: $i] :
( ~ ( ~ ( ( ( sK30_C @ SY789 @ SV228 )
!= SV228 )
| ~ ( in @ ( sK30_C @ SY789 @ SV228 ) @ SY789 ) )
| ~ ( ( ( sK30_C @ SY789 @ SV228 )
= SV228 )
| ( in @ ( sK30_C @ SY789 @ SV228 ) @ SY789 ) ) )
| ( SY789
= ( singleton @ SV228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1497,plain,
! [SV229: $i] :
( ( ! [SY790: $i] :
( ( SY790
!= ( singleton @ SV229 ) )
| ~ ( ~ ! [SY791: $i] :
( ( SY791 != SV229 )
| ( in @ SY791 @ SY790 ) )
| ~ ! [SY792: $i] :
( ~ ( in @ SY792 @ SY790 )
| ( SY792 = SV229 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1308]) ).
thf(1498,plain,
! [SV109: $i] :
( ( ! [SY632: $i,SY633: $i] :
( ~ ( relation @ SY633 )
| ~ ( in @ ( ordered_pair @ SV109 @ SY632 ) @ SY633 )
| ( in @ SV109 @ ( relation_dom @ SY633 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1309]) ).
thf(1499,plain,
! [SV109: $i] :
( ( ! [SY634: $i,SY635: $i] :
( ~ ( relation @ SY635 )
| ~ ( in @ ( ordered_pair @ SV109 @ SY634 ) @ SY635 )
| ( in @ SY634 @ ( relation_rng @ SY635 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1310]) ).
thf(1500,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)],[1311]) ).
thf(1501,plain,
! [SV230: $i] :
( ( ~ ( empty @ SV230 )
| ~ ( relation @ SV230 )
| ~ ( function @ SV230 )
| ( one_to_one @ SV230 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1312]) ).
thf(1502,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1313]) ).
thf(1503,plain,
! [SV110: $i] :
( ( ( function @ SV110 )
= $false )
| ( ( ~ ( relation @ SV110 ) )
= $true )
| ( ( ~ ( one_to_one @ SV110 )
| ~ ( ~ ! [SY636: $i] :
( ~ ( function @ SY636 )
| ~ ( relation @ SY636 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SY636 @ SV110 )
= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ( ( sK70_C @ SY636 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY636 @ SV110 )
= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY636 @ SV110 )
= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ( ( sK71_SY424 @ SY636 @ SV110 )
!= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK70_C @ SY636 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK71_SY424 @ SY636 @ SV110 )
!= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY636 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK70_C @ SY636 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SY636 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SY636 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK71_SY424 @ SY636 @ SV110 )
!= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ( ( relation_dom @ SY636 )
!= ( relation_rng @ SV110 ) )
| ( SY636
= ( function_inverse @ SV110 ) ) )
| ~ ~ ( ~ ! [SY637: $i] :
( ~ ( function @ SY637 )
| ~ ( relation @ SY637 )
| ( SY637
!= ( function_inverse @ SV110 ) )
| ~ ( ~ ~ ( ~ ! [SY638: $i,SY639: $i] :
( ( SY639
!= ( apply @ SY637 @ SY638 ) )
| ~ ( in @ SY638 @ ( relation_rng @ SV110 ) )
| ( SY638
= ( apply @ SV110 @ SY639 ) ) )
| ~ ! [SY640: $i,SY641: $i] :
( ( SY641
!= ( apply @ SY637 @ SY640 ) )
| ~ ( in @ SY640 @ ( relation_rng @ SV110 ) )
| ( in @ SY641 @ ( relation_dom @ SV110 ) ) ) )
| ~ ~ ( ~ ! [SY642: $i,SY643: $i] :
( ( SY642
!= ( apply @ SV110 @ SY643 ) )
| ~ ( in @ SY643 @ ( relation_dom @ SV110 ) )
| ( SY643
= ( apply @ SY637 @ SY642 ) ) )
| ~ ! [SY644: $i] :
( ! [SY645: $i] :
( ( SY644
!= ( apply @ SV110 @ SY645 ) )
| ~ ( in @ SY645 @ ( relation_dom @ SV110 ) ) )
| ( in @ SY644 @ ( relation_rng @ SV110 ) ) ) ) ) )
| ~ ! [SY646: $i] :
( ~ ( function @ SY646 )
| ~ ( relation @ SY646 )
| ( SY646
!= ( function_inverse @ SV110 ) )
| ( ( relation_dom @ SY646 )
= ( relation_rng @ SV110 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1315]) ).
thf(1504,plain,
! [SV231: $i] :
( ( ~ ( empty @ SV231 )
| ( empty @ ( relation_dom @ SV231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1505,plain,
! [SV232: $i] :
( ( ~ ( empty @ SV232 )
| ( relation @ ( relation_dom @ SV232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1317]) ).
thf(1506,plain,
! [SV233: $i] :
( ( ! [SY793: $i] :
( ( SV233 = SY793 )
| ~ ( subset @ SV233 @ SY793 )
| ( proper_subset @ SV233 @ SY793 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1318]) ).
thf(1507,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)],[1319]) ).
thf(1508,plain,
( ( empty @ sK55_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1320]) ).
thf(1509,plain,
! [SV234: $i] :
( ( ! [SY794: $i] :
( ~ ( ~ ( in @ ( sK18_C @ SY794 @ SV234 ) @ SV234 )
| ~ ~ ( in @ ( sK18_C @ SY794 @ SV234 ) @ SY794 ) )
| ( subset @ SV234 @ SY794 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1510,plain,
! [SV235: $i] :
( ( ! [SY795: $i] :
( ~ ( subset @ SV235 @ SY795 )
| ! [SY796: $i] :
( ~ ( in @ SY796 @ SV235 )
| ( in @ SY796 @ SY795 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1323]) ).
thf(1511,plain,
! [SV236: $i] :
( ( ! [SY797: $i] :
( ( disjoint @ SV236 @ SY797 )
| ~ ( ~ ( in @ ( sK49_C @ SY797 @ SV236 ) @ SV236 )
| ~ ( in @ ( sK49_C @ SY797 @ SV236 ) @ SY797 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1512,plain,
! [SV237: $i] :
( ( ! [SY798: $i] :
( ! [SY799: $i] :
( ~ ( in @ SY799 @ SV237 )
| ~ ( in @ SY799 @ SY798 ) )
| ~ ( disjoint @ SV237 @ SY798 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1513,plain,
! [SV179: $i,SV111: $i] :
( ( ~ ! [SY746: $i,SY747: $i] :
( ~ ( in @ SV111 @ SY746 )
| ~ ( in @ SV179 @ SY747 )
| ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SY746 @ SY747 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1326]) ).
thf(1514,plain,
! [SV179: $i,SV111: $i] :
( ( ~ ~ ( ~ ! [SY748: $i] :
( ! [SY749: $i] :
~ ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SY748 @ SY749 ) )
| ( in @ SV111 @ SY748 ) )
| ~ ! [SY750: $i,SY751: $i] :
( ~ ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SY750 @ SY751 ) )
| ( in @ SV179 @ SY751 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1326]) ).
thf(1515,plain,
! [SV180: $i,SV112: $i] :
( ( ~ ! [SY752: $i] :
( ! [SY753: $i] :
( ( ordered_pair @ SV112 @ SV180 )
!= ( ordered_pair @ SY752 @ SY753 ) )
| ( SV112 = SY752 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1331]) ).
thf(1516,plain,
! [SV180: $i,SV112: $i] :
( ( ~ ! [SY754: $i,SY755: $i] :
( ( ( ordered_pair @ SV112 @ SV180 )
!= ( ordered_pair @ SY754 @ SY755 ) )
| ( SV180 = SY755 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1331]) ).
thf(1517,plain,
! [SV113: $i] :
( ( ( function @ SV113 )
= $false )
| ( ( ~ ( relation @ SV113 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ ( relation_dom @ SV113 ) )
| ! [SY660: $i] :
( ( SY660
!= ( apply @ SV113 @ SY659 ) )
| ( in @ ( ordered_pair @ SY659 @ SY660 ) @ SV113 ) ) )
| ~ ! [SY661: $i] :
( ~ ( in @ SY661 @ ( relation_dom @ SV113 ) )
| ! [SY662: $i] :
( ~ ( in @ ( ordered_pair @ SY661 @ SY662 ) @ SV113 )
| ( SY662
= ( apply @ SV113 @ SY661 ) ) ) ) )
| ~ ~ ( ~ ! [SY663: $i] :
( ( in @ SY663 @ ( relation_dom @ SV113 ) )
| ! [SY664: $i] :
( ( SY664
!= ( apply @ SV113 @ SY663 ) )
| ( SY664 = empty_set ) ) )
| ~ ! [SY665: $i] :
( ( in @ SY665 @ ( relation_dom @ SV113 ) )
| ! [SY666: $i] :
( ( SY666 != empty_set )
| ( SY666
= ( apply @ SV113 @ SY665 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1334]) ).
thf(1518,plain,
! [SV238: $i] :
( ( ~ ( relation @ SV238 )
| ( ( relation_rng @ SV238 )
= ( relation_dom @ ( relation_inverse @ SV238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1335]) ).
thf(1519,plain,
! [SV239: $i] :
( ( ~ ( relation @ SV239 )
| ( ( relation_dom @ SV239 )
= ( relation_rng @ ( relation_inverse @ SV239 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1336]) ).
thf(1520,plain,
! [SV240: $i] :
( ( ! [SY800: $i] :
( ~ ( in @ SV240 @ SY800 )
| ( subset @ ( singleton @ SV240 ) @ SY800 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1337]) ).
thf(1521,plain,
! [SV241: $i] :
( ( ! [SY801: $i] :
( ~ ( subset @ ( singleton @ SV241 ) @ SY801 )
| ( in @ SV241 @ SY801 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1338]) ).
thf(1522,plain,
! [SV242: $i] :
( ( ( in @ ( sK29_B @ SV242 ) @ SV242 )
| ( SV242 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1339]) ).
thf(1523,plain,
! [SV243: $i] :
( ( ( SV243 != empty_set )
| ! [SY802: $i] :
~ ( in @ SY802 @ SV243 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1524,plain,
! [SV114: $i] :
( ( ! [SY667: $i,SY668: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY668 @ SY667 @ SV114 ) @ SY668 )
| ~ ( in @ ( sK26_D @ SY668 @ SY667 @ SV114 ) @ SV114 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY668 @ SY667 @ SV114 ) @ SY668 )
| ~ ( in @ ( sK26_D @ SY668 @ SY667 @ SV114 ) @ SY667 ) ) )
| ~ ( ( in @ ( sK26_D @ SY668 @ SY667 @ SV114 ) @ SY668 )
| ( in @ ( sK26_D @ SY668 @ SY667 @ SV114 ) @ SV114 )
| ( in @ ( sK26_D @ SY668 @ SY667 @ SV114 ) @ SY667 ) ) )
| ( SY668
= ( set_union2 @ SV114 @ SY667 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1341]) ).
thf(1525,plain,
! [SV114: $i] :
( ( ! [SY669: $i,SY670: $i] :
( ( SY670
!= ( set_union2 @ SV114 @ SY669 ) )
| ~ ( ~ ! [SY671: $i] :
( ~ ( in @ SY671 @ SY670 )
| ( in @ SY671 @ SV114 )
| ( in @ SY671 @ SY669 ) )
| ~ ~ ( ~ ! [SY672: $i] :
( ~ ( in @ SY672 @ SV114 )
| ( in @ SY672 @ SY670 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY669 )
| ( in @ SX3 @ SY670 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1342]) ).
thf(1526,plain,
! [SV244: $i] :
( ( ~ ( empty @ SV244 )
| ( empty @ ( relation_rng @ SV244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1343]) ).
thf(1527,plain,
! [SV245: $i] :
( ( ~ ( empty @ SV245 )
| ( relation @ ( relation_rng @ SV245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1344]) ).
thf(1528,plain,
! [SV115: $i] :
( ( ! [SY674: $i,SY675: $i] :
( ~ ( relation @ SY675 )
| ~ ( in @ ( ordered_pair @ SV115 @ SY674 ) @ SY675 )
| ( in @ SV115 @ ( relation_field @ SY675 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1345]) ).
thf(1529,plain,
! [SV115: $i] :
( ( ! [SY676: $i,SY677: $i] :
( ~ ( relation @ SY677 )
| ~ ( in @ ( ordered_pair @ SV115 @ SY676 ) @ SY677 )
| ( in @ SY676 @ ( relation_field @ SY677 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1346]) ).
thf(1530,plain,
! [SV246: $i] :
( ( ~ ( relation @ SV246 )
| ( ( relation_dom @ SV246 )
!= empty_set )
| ( ( relation_rng @ SV246 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1347]) ).
thf(1531,plain,
! [SV247: $i] :
( ( ~ ( relation @ SV247 )
| ( ( relation_rng @ SV247 )
!= empty_set )
| ( ( relation_dom @ SV247 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1348]) ).
thf(1532,plain,
! [SV248: $i] :
( ( ! [SY803: $i] :
( ~ ( subset @ SV248 @ ( singleton @ SY803 ) )
| ( SV248 = empty_set )
| ( SV248
= ( singleton @ SY803 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1349]) ).
thf(1533,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)],[1350]) ).
thf(1534,plain,
! [SV116: $i] :
( ( ! [SY678: $i,SY679: $i] :
( ~ ( ~ ( ~ ( in @ ( sK17_D @ SY679 @ SY678 @ SV116 ) @ SV116 )
| ~ ( in @ ( sK17_D @ SY679 @ SY678 @ SV116 ) @ SY678 )
| ~ ( in @ ( sK17_D @ SY679 @ SY678 @ SV116 ) @ SY679 ) )
| ~ ~ ( ~ ( ( in @ ( sK17_D @ SY679 @ SY678 @ SV116 ) @ SV116 )
| ( in @ ( sK17_D @ SY679 @ SY678 @ SV116 ) @ SY679 ) )
| ~ ( ( in @ ( sK17_D @ SY679 @ SY678 @ SV116 ) @ SY678 )
| ( in @ ( sK17_D @ SY679 @ SY678 @ SV116 ) @ SY679 ) ) ) )
| ( SY679
= ( set_intersection2 @ SV116 @ SY678 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1351]) ).
thf(1535,plain,
! [SV116: $i] :
( ( ! [SY680: $i,SY681: $i] :
( ( SY681
!= ( set_intersection2 @ SV116 @ SY680 ) )
| ~ ( ~ ! [SY682: $i] :
( ~ ( in @ SY682 @ SV116 )
| ~ ( in @ SY682 @ SY680 )
| ( in @ SY682 @ SY681 ) )
| ~ ~ ( ~ ! [SY683: $i] :
( ~ ( in @ SY683 @ SY681 )
| ( in @ SY683 @ SV116 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY681 )
| ( in @ SX3 @ SY680 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1352]) ).
thf(1536,plain,
! [SV249: $i] :
( ( ~ ( function @ SV249 )
| ~ ( relation @ SV249 )
| ~ ( one_to_one @ SV249 )
| ( function @ ( relation_inverse @ SV249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1353]) ).
thf(1537,plain,
! [SV250: $i] :
( ( ~ ( function @ SV250 )
| ~ ( relation @ SV250 )
| ~ ( one_to_one @ SV250 )
| ( relation @ ( relation_inverse @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1354]) ).
thf(1538,plain,
! [SV251: $i] :
( ( ! [SY804: $i] :
( ~ ( relation @ SY804 )
| ~ ( ~ ( ( ( sK44_C @ SY804 @ SV251 )
!= ( sK45_SY414 @ SY804 @ SV251 ) )
| ~ ( in @ ( sK44_C @ SY804 @ SV251 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SY804 @ SV251 ) @ ( sK45_SY414 @ SY804 @ SV251 ) ) @ SY804 ) )
| ~ ~ ( ~ ( ( ( sK44_C @ SY804 @ SV251 )
= ( sK45_SY414 @ SY804 @ SV251 ) )
| ( in @ ( ordered_pair @ ( sK44_C @ SY804 @ SV251 ) @ ( sK45_SY414 @ SY804 @ SV251 ) ) @ SY804 ) )
| ~ ( ( in @ ( sK44_C @ SY804 @ SV251 ) @ SV251 )
| ( in @ ( ordered_pair @ ( sK44_C @ SY804 @ SV251 ) @ ( sK45_SY414 @ SY804 @ SV251 ) ) @ SY804 ) ) ) )
| ( SY804
= ( identity_relation @ SV251 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1355]) ).
thf(1539,plain,
! [SV252: $i] :
( ( ! [SY805: $i] :
( ~ ( relation @ SY805 )
| ( SY805
!= ( identity_relation @ SV252 ) )
| ~ ( ~ ! [SY806: $i,SY807: $i] :
( ( SY806 != SY807 )
| ~ ( in @ SY806 @ SV252 )
| ( in @ ( ordered_pair @ SY806 @ SY807 ) @ SY805 ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SY805 )
| ( SX2 = SX3 ) )
| ~ ! [SY810: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SY810 @ SX3 ) @ SY805 )
| ( in @ SY810 @ SV252 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1356]) ).
thf(1540,plain,
( ( ~ ( function @ sK54_A )
| ~ ( relation @ sK54_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1357]) ).
thf(1541,plain,
! [SV117: $i] :
( ( ! [SY685: $i,SY686: $i] :
( ~ ( relation @ SY686 )
| ~ ( in @ SV117 @ SY685 )
| ~ ( in @ SV117 @ ( relation_dom @ SY686 ) )
| ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SY686 @ SY685 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1359]) ).
thf(1542,plain,
! [SV117: $i] :
( ( ~ ( ~ ! [SY687: $i,SY688: $i] :
( ~ ( relation @ SY688 )
| ~ ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SY688 @ SY687 ) ) )
| ( in @ SV117 @ SY687 ) )
| ~ ! [SY689: $i,SY690: $i] :
( ~ ( relation @ SY690 )
| ~ ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SY690 @ SY689 ) ) )
| ( in @ SV117 @ ( relation_dom @ SY690 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1360]) ).
thf(1543,plain,
! [SV253: $i] :
( ( ! [SY812: $i] :
( ~ ( function @ SY812 )
| ~ ( relation @ SY812 )
| ~ ( ~ ( in @ ( sK50_C @ SY812 @ SV253 ) @ SV253 )
| ~ ( ( ( apply @ SY812 @ ( sK50_C @ SY812 @ SV253 ) )
!= ( sK50_C @ SY812 @ SV253 ) ) ) )
| ( ( relation_dom @ SY812 )
!= SV253 )
| ( SY812
= ( identity_relation @ SV253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1361]) ).
thf(1544,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)],[1362]) ).
thf(1545,plain,
! [SV118: $i] :
( ( ! [SY691: $i,SY692: $i] :
( ~ ( ~ ( ! [SY693: $i,SY694: $i] :
( ~ ( in @ SY693 @ SV118 )
| ~ ( in @ SY694 @ SY691 )
| ( ( sK23_D @ SY692 @ SY691 @ SV118 )
!= ( ordered_pair @ SY693 @ SY694 ) ) )
| ~ ( in @ ( sK23_D @ SY692 @ SY691 @ SV118 ) @ SY692 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY403 @ SY692 @ SY691 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK25_SY405 @ SY692 @ SY691 @ SV118 ) @ SY691 ) )
| ( ( sK23_D @ SY692 @ SY691 @ SV118 )
!= ( ordered_pair @ ( sK24_SY403 @ SY692 @ SY691 @ SV118 ) @ ( sK25_SY405 @ SY692 @ SY691 @ SV118 ) ) ) )
| ( in @ ( sK23_D @ SY692 @ SY691 @ SV118 ) @ SY692 ) ) )
| ( SY692
= ( cartesian_product2 @ SV118 @ SY691 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1363]) ).
thf(1546,plain,
! [SV118: $i] :
( ( ! [SY695: $i,SY696: $i] :
( ( SY696
!= ( cartesian_product2 @ SV118 @ SY695 ) )
| ~ ( ~ ! [SY697: $i] :
( ! [SY698: $i,SY699: $i] :
( ~ ( in @ SY698 @ SV118 )
| ~ ( in @ SY699 @ SY695 )
| ( SY697
!= ( ordered_pair @ SY698 @ SY699 ) ) )
| ( in @ SY697 @ SY696 ) )
| ~ ! [SY700: $i] :
( ~ ( in @ SY700 @ SY696 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY700 @ SY696 @ SY695 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK22_SY400 @ SY700 @ SY696 @ SY695 @ SV118 ) @ SY695 ) )
| ( SY700
!= ( ordered_pair @ ( sK21_E @ SY700 @ SY696 @ SY695 @ SV118 ) @ ( sK22_SY400 @ SY700 @ SY696 @ SY695 @ SV118 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1364]) ).
thf(1547,plain,
! [SV119: $i] :
( ( ! [SY701: $i] :
( ~ ( subset @ SV119 @ SY701 )
| ! [SY702: $i] : ( subset @ ( cartesian_product2 @ SV119 @ SY702 ) @ ( cartesian_product2 @ SY701 @ SY702 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1365]) ).
thf(1548,plain,
! [SV119: $i] :
( ( ! [SY703: $i] :
( ~ ( subset @ SV119 @ SY703 )
| ! [SY704: $i] : ( subset @ ( cartesian_product2 @ SY704 @ SV119 ) @ ( cartesian_product2 @ SY704 @ SY703 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1366]) ).
thf(1549,plain,
! [SV254: $i] :
( ( ! [SY813: $i] :
( ~ ( ~ ( ! [SY814: $i] :
( ~ ( in @ ( sK15_C @ SY813 @ SV254 ) @ SY814 )
| ~ ( in @ SY814 @ SV254 ) )
| ~ ( in @ ( sK15_C @ SY813 @ SV254 ) @ SY813 ) )
| ~ ( ~ ( ~ ( in @ ( sK15_C @ SY813 @ SV254 ) @ ( sK16_SY398 @ SY813 @ SV254 ) )
| ~ ( in @ ( sK16_SY398 @ SY813 @ SV254 ) @ SV254 ) )
| ( in @ ( sK15_C @ SY813 @ SV254 ) @ SY813 ) ) )
| ( SY813
= ( union @ SV254 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1367]) ).
thf(1550,plain,
! [SV255: $i] :
( ( ! [SY815: $i] :
( ( SY815
!= ( union @ SV255 ) )
| ~ ( ~ ! [SY816: $i] :
( ! [SY817: $i] :
( ~ ( in @ SY816 @ SY817 )
| ~ ( in @ SY817 @ SV255 ) )
| ( in @ SY816 @ SY815 ) )
| ~ ! [SY818: $i] :
( ~ ( in @ SY818 @ SY815 )
| ~ ( ~ ( in @ SY818 @ ( sK14_D @ SY818 @ SY815 @ SV255 ) )
| ~ ( in @ ( sK14_D @ SY818 @ SY815 @ SV255 ) @ SV255 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1368]) ).
thf(1551,plain,
! [SV256: $i] :
( ( ! [SY819: $i] :
( ( ( set_difference @ SV256 @ SY819 )
!= empty_set )
| ( subset @ SV256 @ SY819 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1369]) ).
thf(1552,plain,
! [SV257: $i] :
( ( ! [SY820: $i] :
( ~ ( subset @ SV257 @ SY820 )
| ( ( set_difference @ SV257 @ SY820 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1553,plain,
! [SV120: $i] :
( ( ( ~ ! [SY705: $i] :
( ~ ( relation @ SY705 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SY705 @ SV120 ) @ ( sK66_SY420 @ SY705 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SY705 @ SV120 ) @ ( sK66_SY420 @ SY705 @ SV120 ) ) @ SY705 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_C @ SY705 @ SV120 ) @ ( sK66_SY420 @ SY705 @ SV120 ) ) @ SV120 )
| ( in @ ( ordered_pair @ ( sK65_C @ SY705 @ SV120 ) @ ( sK66_SY420 @ SY705 @ SV120 ) ) @ SY705 ) ) )
| ( SV120 = SY705 ) )
| ~ ! [SY706: $i] :
( ~ ( relation @ SY706 )
| ( SV120 != SY706 )
| ~ ( ~ ! [SY707: $i,SY708: $i] :
( ~ ( in @ ( ordered_pair @ SY707 @ SY708 ) @ SV120 )
| ( in @ ( ordered_pair @ SY707 @ SY708 ) @ SY706 ) )
| ~ ! [SY709: $i,SY710: $i] :
( ~ ( in @ ( ordered_pair @ SY709 @ SY710 ) @ SY706 )
| ( in @ ( ordered_pair @ SY709 @ SY710 ) @ SV120 ) ) ) ) )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1371]) ).
thf(1554,plain,
! [SV125: $i,SV5: $i,SV181: $i] :
( ( ( relation @ SV181 )
= $false )
| ( ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV5 @ SV181 ) @ SV125 )
= ( relation_rng_restriction @ SV5 @ ( relation_dom_restriction @ SV181 @ SV125 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1376]) ).
thf(1555,plain,
! [SV9: $i,SV190: $i] :
( ( ( ~ ( relation @ SV190 ) )
= $true )
| ( ( ( relation_rng @ ( relation_composition @ SV9 @ SV190 ) )
= ( relation_image @ SV190 @ ( relation_rng @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1379]) ).
thf(1556,plain,
! [SV129: $i,SV11: $i,SV182: $i] :
( ( ( relation @ SV182 )
= $false )
| ( ( ~ ( subset @ SV11 @ SV129 )
| ( subset @ ( relation_inverse_image @ SV182 @ SV11 ) @ ( relation_inverse_image @ SV182 @ SV129 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1381]) ).
thf(1557,plain,
! [SV13: $i,SV191: $i] :
( ( ( ~ ( relation @ SV191 ) )
= $true )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV13 @ SV191 ) ) @ ( relation_dom @ SV13 ) )
= $true )
| ( ( relation @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1382]) ).
thf(1558,plain,
! [SV14: $i,SV192: $i] :
( ( ( ~ ( relation @ SV192 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV14 @ SV192 ) ) @ ( relation_rng @ SV192 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1383]) ).
thf(1559,plain,
! [SV15: $i,SV193: $i] :
( ( ( ~ ( relation @ SV193 ) )
= $true )
| ( ( ~ ( subset @ ( relation_rng @ SV15 ) @ ( relation_dom @ SV193 ) )
| ( ( relation_dom @ ( relation_composition @ SV15 @ SV193 ) )
= ( relation_dom @ SV15 ) ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1384]) ).
thf(1560,plain,
! [SV16: $i,SV194: $i] :
( ( ( ~ ( relation @ SV194 ) )
= $true )
| ( ( ~ ( subset @ ( relation_dom @ SV16 ) @ ( relation_rng @ SV194 ) )
| ( ( relation_rng @ ( relation_composition @ SV194 @ SV16 ) )
= ( relation_rng @ SV16 ) ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1385]) ).
thf(1561,plain,
! [SV23: $i] :
( ( ( relation @ SV23 )
= $false )
| ( ( function @ SV23 )
= $false )
| ( ( ~ ( one_to_one @ SV23 )
| ( ( function_inverse @ SV23 )
= ( relation_inverse @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1389]) ).
thf(1562,plain,
! [SV133: $i,SV25: $i] :
( ( ( relation @ SV25 )
= $false )
| ( ( ~ ( relation @ SV133 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV25 @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1390]) ).
thf(1563,plain,
! [SV135: $i,SV29: $i] :
( ( ( relation @ SV29 )
= $false )
| ( ( ~ ( relation @ SV135 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV29 @ SV135 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1393]) ).
thf(1564,plain,
! [SV136: $i,SV30: $i] :
( ( ( relation @ SV30 )
= $false )
| ( ( ~ ( relation @ SV136 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV30 @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1394]) ).
thf(1565,plain,
! [SV31: $i] :
( ( ( empty @ ( relation_dom @ SV31 ) )
= $false )
| ( ( empty @ SV31 )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1395]) ).
thf(1566,plain,
! [SV32: $i] :
( ( ( empty @ ( relation_rng @ SV32 ) )
= $false )
| ( ( empty @ SV32 )
= $true )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1396]) ).
thf(1567,plain,
! [SV196: $i,SV183: $i,SV139: $i,SV37: $i] :
( ( ( ~ ( subset @ SV37 @ SV139 )
| ~ ( subset @ SV183 @ SV196 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV37 @ SV183 ) @ ( cartesian_product2 @ SV139 @ SV196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1399]) ).
thf(1568,plain,
! [SV141: $i,SV39: $i] :
( ( ( ( SV39 = empty_set )
| ~ ( subset @ SV39 @ ( relation_rng @ SV141 ) ) )
= $true )
| ( ( ( ( relation_inverse_image @ SV141 @ SV39 )
!= empty_set ) )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1401]) ).
thf(1569,plain,
! [SV184: $i,SV143: $i,SV41: $i] :
( ( ( ~ ( subset @ SV41 @ SV143 ) )
= $true )
| ( ( ~ ( subset @ SV41 @ SV184 ) )
= $true )
| ( ( subset @ SV41 @ ( set_intersection2 @ SV143 @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1402]) ).
thf(1570,plain,
! [SV185: $i,SV144: $i,SV42: $i] :
( ( ( ~ ( subset @ SV42 @ SV144 ) )
= $true )
| ( ( ~ ( subset @ SV144 @ SV185 ) )
= $true )
| ( ( subset @ SV42 @ SV185 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1403]) ).
thf(1571,plain,
! [SV43: $i,SV145: $i] :
( ( ( function @ SV145 )
= $false )
| ( ( ~ ( relation @ SV145 ) )
= $true )
| ( ( ! [SY717: $i] :
( ~ ( function @ SY717 )
| ~ ( relation @ SY717 )
| ~ ( in @ SV43 @ ( relation_dom @ ( relation_composition @ SY717 @ SV145 ) ) )
| ( ( apply @ ( relation_composition @ SY717 @ SV145 ) @ SV43 )
= ( apply @ SV145 @ ( apply @ SY717 @ SV43 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1404]) ).
thf(1572,plain,
! [SV44: $i,SV146: $i] :
( ( ( function @ SV146 )
= $false )
| ( ( ~ ( relation @ SV146 ) )
= $true )
| ( ( ! [SY718: $i] :
( ~ ( function @ SY718 )
| ~ ( relation @ SY718 )
| ~ ( in @ SV44 @ ( relation_dom @ SV146 ) )
| ( ( apply @ ( relation_composition @ SV146 @ SY718 ) @ SV44 )
= ( apply @ SY718 @ ( apply @ SV146 @ SV44 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1405]) ).
thf(1573,plain,
! [SV147: $i,SV258: $i,SV45: $i] :
( ( ( subset @ ( set_intersection2 @ SV45 @ SV258 ) @ ( set_intersection2 @ SV147 @ SV258 ) )
= $true )
| ( ( subset @ SV45 @ SV147 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1406]) ).
thf(1574,plain,
! [SV149: $i,SV259: $i,SV48: $i] :
( ( ( subset @ ( set_difference @ SV48 @ SV259 ) @ ( set_difference @ SV149 @ SV259 ) )
= $true )
| ( ( subset @ SV48 @ SV149 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1408]) ).
thf(1575,plain,
! [SV157: $i,SV58: $i] :
( ( ( subset @ SV58 @ SV157 )
= $false )
| ( ( proper_subset @ SV157 @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1413]) ).
thf(1576,plain,
! [SV59: $i,SV186: $i,SV158: $i] :
( ( ( ~ ( disjoint @ SV158 @ SV186 ) )
= $true )
| ( ( ~ ( subset @ SV59 @ SV158 ) )
= $true )
| ( ( disjoint @ SV59 @ SV186 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1414]) ).
thf(1577,plain,
! [SV187: $i,SV161: $i,SV62: $i] :
( ( ( ~ ( subset @ SV62 @ SV161 ) )
= $true )
| ( ( ~ ( subset @ SV187 @ SV161 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV62 @ SV187 ) @ SV161 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1416]) ).
thf(1578,plain,
! [SV65: $i,SV164: $i] :
( ( ( in @ SV164 @ SV65 )
= $false )
| ( ( in @ SV65 @ SV164 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1419]) ).
thf(1579,plain,
! [SV169: $i,SV74: $i] :
( ( ( empty @ ( cartesian_product2 @ SV74 @ SV169 ) )
= $false )
| ( ( empty @ SV169 )
= $true )
| ( ( empty @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1422]) ).
thf(1580,plain,
! [SV81: $i,SV171: $i] :
( ( ( empty @ SV171 )
= $true )
| ( ( in @ SV81 @ SV171 )
= $true )
| ( ( element @ SV81 @ SV171 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1424]) ).
thf(1581,plain,
! [SV172: $i,SV85: $i] :
( ( ( in @ SV85 @ SV172 )
= $false )
| ( ( empty @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1425]) ).
thf(1582,plain,
! [SV173: $i,SV86: $i] :
( ( ( empty @ SV86 )
= $false )
| ( ( SV86 = SV173 )
= $true )
| ( ( ~ ( empty @ SV173 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1426]) ).
thf(1583,plain,
! [SV260: $i,SV197: $i] :
( ( ~ ( in @ SV197 @ SV260 )
| ( subset @ ( singleton @ SV197 ) @ SV260 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1427]) ).
thf(1584,plain,
! [SV261: $i,SV198: $i] :
( ( ~ ( subset @ ( singleton @ SV198 ) @ SV261 )
| ( in @ SV198 @ SV261 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1428]) ).
thf(1585,plain,
! [SV262: $i,SV199: $i] :
( ( ~ ( subset @ SV199 @ ( singleton @ SV262 ) )
| ( SV199 = empty_set )
| ( SV199
= ( singleton @ SV262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1429]) ).
thf(1586,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1430]) ).
thf(1587,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1430]) ).
thf(1588,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY406 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ ( sK33_SY406 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1431]) ).
thf(1589,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK31_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)],[1431]) ).
thf(1590,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1432]) ).
thf(1591,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1432]) ).
thf(1592,plain,
! [SV263: $i,SV200: $i] :
( ( ( disjoint @ SV200 @ SV263 )
| ( in @ ( sK48_C @ SV263 @ SV200 ) @ ( set_intersection2 @ SV200 @ SV263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1433]) ).
thf(1593,plain,
! [SV264: $i,SV201: $i] :
( ( ! [SY821: $i] :
~ ( in @ SY821 @ ( set_intersection2 @ SV201 @ SV264 ) )
| ~ ( disjoint @ SV201 @ SV264 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1434]) ).
thf(1594,plain,
! [SV265: $i,SV202: $i] :
( ( ~ ( function @ SV202 )
| ~ ( relation @ SV202 )
| ~ ( relation @ SV265 )
| ~ ( function @ SV265 )
| ( function @ ( relation_composition @ SV202 @ SV265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1435]) ).
thf(1595,plain,
! [SV266: $i,SV203: $i] :
( ( ~ ( function @ SV203 )
| ~ ( relation @ SV203 )
| ~ ( relation @ SV266 )
| ~ ( function @ SV266 )
| ( relation @ ( relation_composition @ SV203 @ SV266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1436]) ).
thf(1596,plain,
! [SV267: $i,SV204: $i] :
( ( ( ( set_difference @ SV204 @ SV267 )
!= empty_set )
| ( subset @ SV204 @ SV267 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1437]) ).
thf(1597,plain,
! [SV268: $i,SV205: $i] :
( ( ~ ( subset @ SV205 @ SV268 )
| ( ( set_difference @ SV205 @ SV268 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(1598,plain,
! [SV269: $i,SV206: $i] :
( ( ~ ( empty @ SV206 )
| ~ ( relation @ SV269 )
| ( empty @ ( relation_composition @ SV206 @ SV269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1439]) ).
thf(1599,plain,
! [SV270: $i,SV207: $i] :
( ( ~ ( empty @ SV207 )
| ~ ( relation @ SV270 )
| ( relation @ ( relation_composition @ SV207 @ SV270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1440]) ).
thf(1600,plain,
! [SV271: $i,SV87: $i] :
( ( ! [SY822: $i] :
( ~ ( relation @ SY822 )
| ! [SY823: $i] :
( ~ ( in @ SY823 @ ( relation_dom @ SY822 ) )
| ~ ( in @ ( ordered_pair @ SY823 @ SV87 ) @ SY822 )
| ~ ( in @ SY823 @ SV271 ) )
| ( in @ SV87 @ ( relation_image @ SY822 @ SV271 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1441]) ).
thf(1601,plain,
! [SV272: $i,SV87: $i] :
( ( ! [SY824: $i] :
( ~ ( relation @ SY824 )
| ~ ( in @ SV87 @ ( relation_image @ SY824 @ SV272 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK52_D @ SY824 @ SV272 @ SV87 ) @ ( relation_dom @ SY824 ) )
| ~ ( in @ ( ordered_pair @ ( sK52_D @ SY824 @ SV272 @ SV87 ) @ SV87 ) @ SY824 ) )
| ~ ( in @ ( sK52_D @ SY824 @ SV272 @ SV87 ) @ SV272 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1602,plain,
! [SV273: $i,SV208: $i] :
( ( ~ ( subset @ SV208 @ SV273 )
| ~ ( subset @ SV273 @ SV208 )
| ( SV208 = SV273 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1443]) ).
thf(1603,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1444]) ).
thf(1604,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1444]) ).
thf(1605,plain,
! [SV88: $i,SV274: $i] :
( ( ! [SY825: $i] :
( ~ ( ~ ( ~ ( in @ ( sK13_D @ SY825 @ SV274 @ SV88 ) @ SV88 )
| ( in @ ( sK13_D @ SY825 @ SV274 @ SV88 ) @ SV274 )
| ~ ( in @ ( sK13_D @ SY825 @ SV274 @ SV88 ) @ SY825 ) )
| ~ ~ ( ~ ( ( in @ ( sK13_D @ SY825 @ SV274 @ SV88 ) @ SV88 )
| ( in @ ( sK13_D @ SY825 @ SV274 @ SV88 ) @ SY825 ) )
| ~ ( ~ ( in @ ( sK13_D @ SY825 @ SV274 @ SV88 ) @ SV274 )
| ( in @ ( sK13_D @ SY825 @ SV274 @ SV88 ) @ SY825 ) ) ) )
| ( SY825
= ( set_difference @ SV88 @ SV274 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1445]) ).
thf(1606,plain,
! [SV275: $i,SV88: $i] :
( ( ! [SY826: $i] :
( ( SY826
!= ( set_difference @ SV88 @ SV275 ) )
| ~ ( ~ ! [SY827: $i] :
( ~ ( in @ SY827 @ SV88 )
| ( in @ SY827 @ SV275 )
| ( in @ SY827 @ SY826 ) )
| ~ ~ ( ~ ! [SY508: $i] :
( ~ ( in @ SY508 @ SY826 )
| ( in @ SY508 @ SV88 ) )
| ~ ! [SY829: $i] :
( ~ ( in @ SY829 @ SY826 )
| ~ ( in @ SY829 @ SV275 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(1607,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1447]) ).
thf(1608,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1447]) ).
thf(1609,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1448]) ).
thf(1610,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1448]) ).
thf(1611,plain,
! [SV89: $i,SV174: $i] :
( ( ( ~ ! [SY723: $i] :
( ~ ( relation @ SY723 )
| ~ ( ~ ( ~ ( in @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY723 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) ) @ SV174 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY723 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) ) @ SY723 ) )
| ~ ~ ( ~ ( ( in @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) @ SV89 )
| ( in @ ( ordered_pair @ ( sK40_D @ SY723 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) ) @ SY723 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SY723 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) ) @ SV174 )
| ( in @ ( ordered_pair @ ( sK40_D @ SY723 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) ) @ SY723 ) ) ) )
| ( SY723
= ( relation_rng_restriction @ SV89 @ SV174 ) ) )
| ~ ! [SY724: $i] :
( ~ ( relation @ SY724 )
| ( SY724
!= ( relation_rng_restriction @ SV89 @ SV174 ) )
| ~ ( ~ ! [SY725: $i,SY726: $i] :
( ~ ( in @ SY726 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY725 @ SY726 ) @ SV174 )
| ( in @ ( ordered_pair @ SY725 @ SY726 ) @ SY724 ) )
| ~ ~ ( ~ ! [SY515: $i,SY516: $i] :
( ~ ( in @ ( ordered_pair @ SY515 @ SY516 ) @ SY724 )
| ( in @ SY516 @ SV89 ) )
| ~ ! [SY729: $i,SY730: $i] :
( ~ ( in @ ( ordered_pair @ SY729 @ SY730 ) @ SY724 )
| ( in @ ( ordered_pair @ SY729 @ SY730 ) @ SV174 ) ) ) ) ) )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1449]) ).
thf(1612,plain,
! [SV90: $i,SV276: $i] :
( ( ! [SY830: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY830 @ SV276 @ SV90 ) @ SY830 )
| ( ( sK27_D @ SY830 @ SV276 @ SV90 )
!= SV90 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY830 @ SV276 @ SV90 ) @ SY830 )
| ( ( sK27_D @ SY830 @ SV276 @ SV90 )
!= SV276 ) ) )
| ~ ( ( in @ ( sK27_D @ SY830 @ SV276 @ SV90 ) @ SY830 )
| ( ( sK27_D @ SY830 @ SV276 @ SV90 )
= SV90 )
| ( ( sK27_D @ SY830 @ SV276 @ SV90 )
= SV276 ) ) )
| ( SY830
= ( unordered_pair @ SV90 @ SV276 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1450]) ).
thf(1613,plain,
! [SV277: $i,SV90: $i] :
( ( ! [SY831: $i] :
( ( SY831
!= ( unordered_pair @ SV90 @ SV277 ) )
| ~ ( ~ ! [SY832: $i] :
( ~ ( in @ SY832 @ SY831 )
| ( SY832 = SV90 )
| ( SY832 = SV277 ) )
| ~ ~ ( ~ ! [SY524: $i] :
( ( SY524 != SV90 )
| ( in @ SY524 @ SY831 ) )
| ~ ! [SY834: $i] :
( ( SY834 != SV277 )
| ( in @ SY834 @ SY831 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1451]) ).
thf(1614,plain,
! [SV209: $i,SV278: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK28_C @ SV278 @ SV209 ) @ SV278 )
| ~ ( subset @ ( sK28_C @ SV278 @ SV209 ) @ SV209 ) )
| ~ ( ( in @ ( sK28_C @ SV278 @ SV209 ) @ SV278 )
| ( subset @ ( sK28_C @ SV278 @ SV209 ) @ SV209 ) ) )
| ( SV278
= ( powerset @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(1615,plain,
! [SV210: $i,SV279: $i] :
( ( ( SV279
!= ( powerset @ SV210 ) )
| ~ ( ~ ! [SY835: $i] :
( ~ ( in @ SY835 @ SV279 )
| ( subset @ SY835 @ SV210 ) )
| ~ ! [SY836: $i] :
( ~ ( subset @ SY836 @ SV210 )
| ( in @ SY836 @ SV279 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(1616,plain,
! [SV280: $i,SV211: $i] :
( ( ( ( set_intersection2 @ SV211 @ SV280 )
!= empty_set )
| ( disjoint @ SV211 @ SV280 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1454]) ).
thf(1617,plain,
! [SV281: $i,SV212: $i] :
( ( ~ ( disjoint @ SV212 @ SV281 )
| ( ( set_intersection2 @ SV212 @ SV281 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1455]) ).
thf(1618,plain,
! [SV91: $i] :
( ( ( ~ ! [SY526: $i] :
( ~ ( ~ ( ! [SY527: $i] :
~ ( in @ ( ordered_pair @ ( sK63_C @ SY526 @ SV91 ) @ SY527 ) @ SV91 )
| ~ ( in @ ( sK63_C @ SY526 @ SV91 ) @ SY526 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_C @ SY526 @ SV91 ) @ ( sK64_SY419 @ SY526 @ SV91 ) ) @ SV91 )
| ( in @ ( sK63_C @ SY526 @ SV91 ) @ SY526 ) ) )
| ( SY526
= ( relation_dom @ SV91 ) ) ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1456]) ).
thf(1619,plain,
! [SV91: $i] :
( ( ( ~ ! [SY528: $i] :
( ( SY528
!= ( relation_dom @ SV91 ) )
| ~ ( ~ ! [SY529: $i] :
( ! [SY530: $i] :
~ ( in @ ( ordered_pair @ SY529 @ SY530 ) @ SV91 )
| ( in @ SY529 @ SY528 ) )
| ~ ! [SY531: $i] :
( ~ ( in @ SY531 @ SY528 )
| ( in @ ( ordered_pair @ SY531 @ ( sK62_D @ SY531 @ SY528 @ SV91 ) ) @ SV91 ) ) ) ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1456]) ).
thf(1620,plain,
! [SV92: $i] :
( ( ( ~ ! [SY532: $i,SY533: $i] :
( ~ ( ~ ( ! [SY534: $i] :
( ~ ( in @ ( ordered_pair @ ( sK35_D @ SY533 @ SY532 @ SV92 ) @ SY534 ) @ SV92 )
| ~ ( in @ SY534 @ SY532 ) )
| ~ ( in @ ( sK35_D @ SY533 @ SY532 @ SV92 ) @ SY533 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SY533 @ SY532 @ SV92 ) @ ( sK36_SY409 @ SY533 @ SY532 @ SV92 ) ) @ SV92 )
| ~ ( in @ ( sK36_SY409 @ SY533 @ SY532 @ SV92 ) @ SY532 ) )
| ( in @ ( sK35_D @ SY533 @ SY532 @ SV92 ) @ SY533 ) ) )
| ( SY533
= ( relation_inverse_image @ SV92 @ SY532 ) ) ) )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1457]) ).
thf(1621,plain,
! [SV92: $i] :
( ( ( ~ ! [SY535: $i,SY536: $i] :
( ( SY536
!= ( relation_inverse_image @ SV92 @ SY535 ) )
| ~ ( ~ ! [SY537: $i] :
( ! [SY538: $i] :
( ~ ( in @ ( ordered_pair @ SY537 @ SY538 ) @ SV92 )
| ~ ( in @ SY538 @ SY535 ) )
| ( in @ SY537 @ SY536 ) )
| ~ ! [SY539: $i] :
( ~ ( in @ SY539 @ SY536 )
| ~ ( ~ ( in @ ( ordered_pair @ SY539 @ ( sK34_E @ SY539 @ SY536 @ SY535 @ SV92 ) ) @ SV92 )
| ~ ( in @ ( sK34_E @ SY539 @ SY536 @ SY535 @ SV92 ) @ SY535 ) ) ) ) ) )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1457]) ).
thf(1622,plain,
! [SV93: $i] :
( ( ( ~ ! [SY540: $i,SY541: $i] :
( ~ ( ~ ( ! [SY542: $i] :
( ~ ( in @ ( ordered_pair @ SY542 @ ( sK38_D @ SY541 @ SY540 @ SV93 ) ) @ SV93 )
| ~ ( in @ SY542 @ SY540 ) )
| ~ ( in @ ( sK38_D @ SY541 @ SY540 @ SV93 ) @ SY541 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SY541 @ SY540 @ SV93 ) @ ( sK38_D @ SY541 @ SY540 @ SV93 ) ) @ SV93 )
| ~ ( in @ ( sK39_SY411 @ SY541 @ SY540 @ SV93 ) @ SY540 ) )
| ( in @ ( sK38_D @ SY541 @ SY540 @ SV93 ) @ SY541 ) ) )
| ( SY541
= ( relation_image @ SV93 @ SY540 ) ) ) )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1458]) ).
thf(1623,plain,
! [SV93: $i] :
( ( ( ~ ! [SY543: $i,SY544: $i] :
( ( SY544
!= ( relation_image @ SV93 @ SY543 ) )
| ~ ( ~ ! [SY545: $i] :
( ! [SY546: $i] :
( ~ ( in @ ( ordered_pair @ SY546 @ SY545 ) @ SV93 )
| ~ ( in @ SY546 @ SY543 ) )
| ( in @ SY545 @ SY544 ) )
| ~ ! [SY547: $i] :
( ~ ( in @ SY547 @ SY544 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SY547 @ SY544 @ SY543 @ SV93 ) @ SY547 ) @ SV93 )
| ~ ( in @ ( sK37_E @ SY547 @ SY544 @ SY543 @ SV93 ) @ SY543 ) ) ) ) ) )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1458]) ).
thf(1624,plain,
! [SV282: $i,SV94: $i] :
( ( ! [SY837: $i] :
( ~ ( relation @ SY837 )
| ! [SY838: $i] :
( ~ ( in @ SY838 @ ( relation_rng @ SY837 ) )
| ~ ( in @ ( ordered_pair @ SV94 @ SY838 ) @ SY837 )
| ~ ( in @ SY838 @ SV282 ) )
| ( in @ SV94 @ ( relation_inverse_image @ SY837 @ SV282 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(1625,plain,
! [SV283: $i,SV94: $i] :
( ( ! [SY839: $i] :
( ~ ( relation @ SY839 )
| ~ ( in @ SV94 @ ( relation_inverse_image @ SY839 @ SV283 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK51_D @ SY839 @ SV283 @ SV94 ) @ ( relation_rng @ SY839 ) )
| ~ ( in @ ( ordered_pair @ SV94 @ ( sK51_D @ SY839 @ SV283 @ SV94 ) ) @ SY839 ) )
| ~ ( in @ ( sK51_D @ SY839 @ SV283 @ SV94 ) @ SV283 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(1626,plain,
! [SV95: $i,SV175: $i] :
( ( ( function @ SV175 )
= $false )
| ( ( ~ ( relation @ SV175 ) )
= $true )
| ( ( ~ ( ~ ! [SY731: $i] :
( ~ ( function @ SY731 )
| ~ ( relation @ SY731 )
| ~ ( in @ SV95 @ ( relation_dom @ SY731 ) )
| ~ ( in @ ( apply @ SY731 @ SV95 ) @ ( relation_dom @ SV175 ) )
| ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY731 @ SV175 ) ) ) )
| ~ ~ ( ~ ! [SY732: $i] :
( ~ ( function @ SY732 )
| ~ ( relation @ SY732 )
| ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY732 @ SV175 ) ) )
| ( in @ SV95 @ ( relation_dom @ SY732 ) ) )
| ~ ! [SY733: $i] :
( ~ ( function @ SY733 )
| ~ ( relation @ SY733 )
| ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY733 @ SV175 ) ) )
| ( in @ ( apply @ SY733 @ SV95 ) @ ( relation_dom @ SV175 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1461]) ).
thf(1627,plain,
! [SV96: $i] :
( ( ( ~ ! [SY557: $i,SY558: $i] :
( ~ ( relation @ SY558 )
| ~ ( ~ ( ~ ( in @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ SY557 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ ( sK43_SY413 @ SY558 @ SY557 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ ( sK43_SY413 @ SY558 @ SY557 @ SV96 ) ) @ SY558 ) )
| ~ ~ ( ~ ( ( in @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ SY557 )
| ( in @ ( ordered_pair @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ ( sK43_SY413 @ SY558 @ SY557 @ SV96 ) ) @ SY558 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ ( sK43_SY413 @ SY558 @ SY557 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ ( sK43_SY413 @ SY558 @ SY557 @ SV96 ) ) @ SY558 ) ) ) )
| ( SY558
= ( relation_dom_restriction @ SV96 @ SY557 ) ) ) )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1462]) ).
thf(1628,plain,
! [SV96: $i] :
( ( ( ~ ! [SY559: $i,SY560: $i] :
( ~ ( relation @ SY560 )
| ( SY560
!= ( relation_dom_restriction @ SV96 @ SY559 ) )
| ~ ( ~ ! [SY561: $i,SY562: $i] :
( ~ ( in @ SY561 @ SY559 )
| ~ ( in @ ( ordered_pair @ SY561 @ SY562 ) @ SV96 )
| ( in @ ( ordered_pair @ SY561 @ SY562 ) @ SY560 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY560 )
| ( in @ SX3 @ SY559 ) )
| ~ ! [SY565: $i,SY566: $i] :
( ~ ( in @ ( ordered_pair @ SY565 @ SY566 ) @ SY560 )
| ( in @ ( ordered_pair @ SY565 @ SY566 ) @ SV96 ) ) ) ) ) )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1462]) ).
thf(1629,plain,
! [SV284: $i,SV213: $i] :
( ( ~ ( empty @ SV213 )
| ~ ( relation @ SV284 )
| ( empty @ ( relation_composition @ SV284 @ SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(1630,plain,
! [SV285: $i,SV214: $i] :
( ( ~ ( empty @ SV214 )
| ~ ( relation @ SV285 )
| ( relation @ ( relation_composition @ SV285 @ SV214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1464]) ).
thf(1631,plain,
! [SV97: $i] :
( ( ( ~ ! [SY567: $i] :
( ~ ( relation @ SY567 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SY567 @ SV97 ) @ ( sK12_SY396 @ SY567 @ SV97 ) ) @ SY567 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SY567 @ SV97 ) @ ( sK11_C @ SY567 @ SV97 ) ) @ SV97 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_C @ SY567 @ SV97 ) @ ( sK12_SY396 @ SY567 @ SV97 ) ) @ SY567 )
| ( in @ ( ordered_pair @ ( sK12_SY396 @ SY567 @ SV97 ) @ ( sK11_C @ SY567 @ SV97 ) ) @ SV97 ) ) )
| ( SY567
= ( relation_inverse @ SV97 ) ) ) )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1465]) ).
thf(1632,plain,
! [SV97: $i] :
( ( ( ~ ! [SY568: $i] :
( ~ ( relation @ SY568 )
| ( SY568
!= ( relation_inverse @ SV97 ) )
| ~ ( ~ ! [SY569: $i,SY570: $i] :
( ~ ( in @ ( ordered_pair @ SY569 @ SY570 ) @ SY568 )
| ( in @ ( ordered_pair @ SY570 @ SY569 ) @ SV97 ) )
| ~ ! [SY571: $i,SY572: $i] :
( ~ ( in @ ( ordered_pair @ SY572 @ SY571 ) @ SV97 )
| ( in @ ( ordered_pair @ SY571 @ SY572 ) @ SY568 ) ) ) ) )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1465]) ).
thf(1633,plain,
! [SV98: $i] :
( ( ( ~ ! [SY573: $i] :
( ~ ( ~ ( ! [SY574: $i] :
~ ( in @ ( ordered_pair @ SY574 @ ( sK60_C @ SY573 @ SV98 ) ) @ SV98 )
| ~ ( in @ ( sK60_C @ SY573 @ SV98 ) @ SY573 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK61_SY417 @ SY573 @ SV98 ) @ ( sK60_C @ SY573 @ SV98 ) ) @ SV98 )
| ( in @ ( sK60_C @ SY573 @ SV98 ) @ SY573 ) ) )
| ( SY573
= ( relation_rng @ SV98 ) ) ) )
= $false )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1466]) ).
thf(1634,plain,
! [SV98: $i] :
( ( ( ~ ! [SY575: $i] :
( ( SY575
!= ( relation_rng @ SV98 ) )
| ~ ( ~ ! [SY576: $i] :
( ! [SY577: $i] :
~ ( in @ ( ordered_pair @ SY577 @ SY576 ) @ SV98 )
| ( in @ SY576 @ SY575 ) )
| ~ ! [SY578: $i] :
( ~ ( in @ SY578 @ SY575 )
| ( in @ ( ordered_pair @ ( sK59_D @ SY578 @ SY575 @ SV98 ) @ SY578 ) @ SV98 ) ) ) ) )
= $false )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1466]) ).
thf(1635,plain,
! [SV99: $i,SV176: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_C @ SV176 @ SV99 ) @ SV99 )
| ~ ( in @ ( sK4_C @ SV176 @ SV99 ) @ SV176 ) ) )
= $false )
| ( ( SV99 = SV176 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1467]) ).
thf(1636,plain,
! [SV99: $i,SV176: $i] :
( ( ( ~ ( ( in @ ( sK4_C @ SV176 @ SV99 ) @ SV99 )
| ( in @ ( sK4_C @ SV176 @ SV99 ) @ SV176 ) ) )
= $false )
| ( ( SV99 = SV176 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1467]) ).
thf(1637,plain,
! [SV100: $i,SV286: $i] :
( ( ! [SY840: $i] :
( ~ ( function @ SY840 )
| ~ ( relation @ SY840 )
| ( SV286
!= ( apply @ SY840 @ SV100 ) )
| ~ ( in @ SV100 @ ( relation_dom @ SY840 ) )
| ( in @ ( ordered_pair @ SV100 @ SV286 ) @ SY840 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1468]) ).
thf(1638,plain,
! [SV100: $i] :
( ( ~ ! [SY582: $i,SY583: $i] :
( ~ ( function @ SY583 )
| ~ ( relation @ SY583 )
| ~ ( in @ ( ordered_pair @ SV100 @ SY582 ) @ SY583 )
| ( SY582
= ( apply @ SY583 @ SV100 ) ) )
| ~ ! [SY584: $i,SY585: $i] :
( ~ ( function @ SY585 )
| ~ ( relation @ SY585 )
| ~ ( in @ ( ordered_pair @ SV100 @ SY584 ) @ SY585 )
| ( in @ SV100 @ ( relation_dom @ SY585 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1469]) ).
thf(1639,plain,
! [SV101: $i,SV215: $i] :
( ( ( ~ ( relation @ SV215 ) )
= $true )
| ( ( ~ ( ~ ! [SY778: $i] :
( ~ ( relation @ SY778 )
| ~ ( ~ ( ! [SY779: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY778 @ SV215 @ SV101 ) @ SY779 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY779 @ ( sK9_SY391 @ SY778 @ SV215 @ SV101 ) ) @ SV215 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SY778 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SY778 @ SV215 @ SV101 ) ) @ SY778 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY778 @ SV215 @ SV101 ) @ ( sK10_SY395 @ SY778 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SY778 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SY778 @ SV215 @ SV101 ) ) @ SV215 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SY778 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SY778 @ SV215 @ SV101 ) ) @ SY778 ) ) )
| ( SY778
= ( relation_composition @ SV101 @ SV215 ) ) )
| ~ ! [SY780: $i] :
( ~ ( relation @ SY780 )
| ( SY780
!= ( relation_composition @ SV101 @ SV215 ) )
| ~ ( ~ ! [SY781: $i,SY782: $i] :
( ! [SY783: $i] :
( ~ ( in @ ( ordered_pair @ SY781 @ SY783 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY783 @ SY782 ) @ SV215 ) )
| ( in @ ( ordered_pair @ SY781 @ SY782 ) @ SY780 ) )
| ~ ! [SY784: $i,SY785: $i] :
( ~ ( in @ ( ordered_pair @ SY784 @ SY785 ) @ SY780 )
| ~ ( ~ ( in @ ( ordered_pair @ SY784 @ ( sK7_F @ SY785 @ SY784 @ SY780 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY785 @ SY784 @ SY780 @ SV215 @ SV101 ) @ SY785 ) @ SV215 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1470]) ).
thf(1640,plain,
! [SV177: $i,SV102: $i] :
( ( ! [SY734: $i,SY735: $i] :
( ~ ( in @ SV102 @ SY734 )
| ~ ( in @ SV177 @ SY735 )
| ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SY734 @ SY735 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1471]) ).
thf(1641,plain,
! [SV177: $i,SV102: $i] :
( ( ~ ( ~ ! [SY736: $i] :
( ! [SY737: $i] :
~ ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SY736 @ SY737 ) )
| ( in @ SV102 @ SY736 ) )
| ~ ! [SY738: $i,SY739: $i] :
( ~ ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SY738 @ SY739 ) )
| ( in @ SV177 @ SY739 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1472]) ).
thf(1642,plain,
! [SV216: $i] :
( ( ( ~ ( relation @ SV216 ) )
= $true )
| ( ( ( ( relation_dom @ SV216 )
!= empty_set )
| ( SV216 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1473]) ).
thf(1643,plain,
! [SV217: $i] :
( ( ( ~ ( relation @ SV217 ) )
= $true )
| ( ( ( ( relation_rng @ SV217 )
!= empty_set )
| ( SV217 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1474]) ).
thf(1644,plain,
! [SV103: $i,SV287: $i] :
( ( ~ ( subset @ SV287 @ ( sK2_B @ SV103 ) )
| ( are_equipotent @ SV287 @ ( sK2_B @ SV103 ) )
| ( in @ SV287 @ ( sK2_B @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1475]) ).
thf(1645,plain,
! [SV103: $i] :
( ( ~ ! [SY603: $i] :
( ~ ( ~ ! [SY604: $i] :
( ~ ( subset @ SY604 @ SY603 )
| ( in @ SY604 @ ( sK3_SY386 @ SY603 @ SV103 ) ) )
| ~ ( in @ ( sK3_SY386 @ SY603 @ SV103 ) @ ( sK2_B @ SV103 ) ) )
| ~ ( in @ SY603 @ ( sK2_B @ SV103 ) ) )
| ~ ~ ( ~ ! [SY605: $i,SY606: $i] :
( ~ ( in @ SY605 @ ( sK2_B @ SV103 ) )
| ~ ( subset @ SY606 @ SY605 )
| ( in @ SY606 @ ( sK2_B @ SV103 ) ) )
| ~ ( in @ SV103 @ ( sK2_B @ SV103 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1476]) ).
thf(1646,plain,
! [SV218: $i] :
( ( ( ~ ( function @ SV218 )
| ~ ( relation @ SV218 ) )
= $true )
| ( ( function @ ( function_inverse @ SV218 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1477]) ).
thf(1647,plain,
! [SV219: $i] :
( ( ( ~ ( function @ SV219 )
| ~ ( relation @ SV219 ) )
= $true )
| ( ( relation @ ( function_inverse @ SV219 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1478]) ).
thf(1648,plain,
! [SV220: $i] :
( ( ( ~ ( empty @ SV220 ) )
= $true )
| ( ( empty @ ( relation_inverse @ SV220 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1479]) ).
thf(1649,plain,
! [SV221: $i] :
( ( ( ~ ( empty @ SV221 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV221 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1480]) ).
thf(1650,plain,
! [SV222: $i] :
( ( ( ~ ( ~ ! [SY786: $i,SY787: $i] :
( ( sK69_B @ SV222 )
!= ( ordered_pair @ SY786 @ SY787 ) )
| ~ ( in @ ( sK69_B @ SV222 ) @ SV222 ) ) )
= $true )
| ( ( relation @ SV222 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1481]) ).
thf(1651,plain,
! [SV223: $i] :
( ( ( ~ ( relation @ SV223 ) )
= $true )
| ( ( ! [SY788: $i] :
( ( SY788
= ( ordered_pair @ ( sK67_C @ SY788 @ SV223 ) @ ( sK68_SY421 @ SY788 @ SV223 ) ) )
| ~ ( in @ SY788 @ SV223 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1482]) ).
thf(1652,plain,
! [SV104: $i] :
( ( ( ~ ! [SY607: $i] :
( ~ ( relation @ SY607 )
| ~ ( subset @ SV104 @ SY607 )
| ( subset @ ( relation_dom @ SV104 ) @ ( relation_dom @ SY607 ) ) ) )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1483]) ).
thf(1653,plain,
! [SV104: $i] :
( ( ( ~ ! [SY608: $i] :
( ~ ( relation @ SY608 )
| ~ ( subset @ SV104 @ SY608 )
| ( subset @ ( relation_rng @ SV104 ) @ ( relation_rng @ SY608 ) ) ) )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1483]) ).
thf(1654,plain,
! [SV288: $i,SV105: $i] :
( ( ! [SY841: $i] :
( ~ ( relation @ SY841 )
| ~ ( in @ SV105 @ SV288 )
| ~ ( in @ SV105 @ ( relation_rng @ SY841 ) )
| ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SV288 @ SY841 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1484]) ).
thf(1655,plain,
! [SV105: $i] :
( ( ~ ! [SY611: $i,SY612: $i] :
( ~ ( relation @ SY612 )
| ~ ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SY611 @ SY612 ) ) )
| ( in @ SV105 @ SY611 ) )
| ~ ! [SY613: $i,SY614: $i] :
( ~ ( relation @ SY614 )
| ~ ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SY613 @ SY614 ) ) )
| ( in @ SV105 @ ( relation_rng @ SY614 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1485]) ).
thf(1656,plain,
( ( ~ ( empty @ sK56_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1486]) ).
thf(1657,plain,
( ( ~ ( relation @ sK56_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1486]) ).
thf(1658,plain,
! [SV289: $i,SV106: $i] :
( ( ! [SY842: $i] :
( ~ ( in @ SV106 @ SY842 )
| ~ ( in @ SV289 @ SY842 )
| ( subset @ ( unordered_pair @ SV106 @ SV289 ) @ SY842 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1487]) ).
thf(1659,plain,
! [SV106: $i] :
( ( ~ ! [SY617: $i,SY618: $i] :
( ~ ( subset @ ( unordered_pair @ SV106 @ SY617 ) @ SY618 )
| ( in @ SV106 @ SY618 ) )
| ~ ! [SY619: $i,SY620: $i] :
( ~ ( subset @ ( unordered_pair @ SV106 @ SY619 ) @ SY620 )
| ( in @ SY619 @ SY620 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1488]) ).
thf(1660,plain,
! [SV178: $i,SV107: $i] :
( ( ! [SY740: $i,SY741: $i] :
( ~ ( relation @ SY741 )
| ~ ( in @ SV107 @ SY740 )
| ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ SY741 )
| ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SY740 ) @ SY741 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1491]) ).
thf(1661,plain,
! [SV178: $i,SV107: $i] :
( ( ~ ( ~ ! [SY742: $i,SY743: $i] :
( ~ ( relation @ SY743 )
| ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SY742 ) @ SY743 ) )
| ( in @ SV107 @ SY742 ) )
| ~ ! [SY744: $i,SY745: $i] :
( ~ ( relation @ SY745 )
| ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SY744 ) @ SY745 ) )
| ( in @ ( ordered_pair @ SV107 @ SV178 ) @ SY745 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1492]) ).
thf(1662,plain,
! [SV108: $i] :
( ( ( ~ ! [SY628: $i] :
( ~ ( relation @ SY628 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SY628 @ SV108 ) @ ( sK20_SY399 @ SY628 @ SV108 ) ) @ SV108 )
| ~ ~ ( in @ ( ordered_pair @ ( sK19_C @ SY628 @ SV108 ) @ ( sK20_SY399 @ SY628 @ SV108 ) ) @ SY628 ) )
| ( subset @ SV108 @ SY628 ) ) )
= $false )
| ( ( relation @ SV108 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1495]) ).
thf(1663,plain,
! [SV108: $i] :
( ( ( ~ ! [SY629: $i] :
( ~ ( relation @ SY629 )
| ~ ( subset @ SV108 @ SY629 )
| ! [SY630: $i,SY631: $i] :
( ~ ( in @ ( ordered_pair @ SY630 @ SY631 ) @ SV108 )
| ( in @ ( ordered_pair @ SY630 @ SY631 ) @ SY629 ) ) ) )
= $false )
| ( ( relation @ SV108 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1495]) ).
thf(1664,plain,
! [SV228: $i,SV290: $i] :
( ( ~ ( ~ ( ( ( sK30_C @ SV290 @ SV228 )
!= SV228 )
| ~ ( in @ ( sK30_C @ SV290 @ SV228 ) @ SV290 ) )
| ~ ( ( ( sK30_C @ SV290 @ SV228 )
= SV228 )
| ( in @ ( sK30_C @ SV290 @ SV228 ) @ SV290 ) ) )
| ( SV290
= ( singleton @ SV228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1496]) ).
thf(1665,plain,
! [SV229: $i,SV291: $i] :
( ( ( SV291
!= ( singleton @ SV229 ) )
| ~ ( ~ ! [SY843: $i] :
( ( SY843 != SV229 )
| ( in @ SY843 @ SV291 ) )
| ~ ! [SY844: $i] :
( ~ ( in @ SY844 @ SV291 )
| ( SY844 = SV229 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1497]) ).
thf(1666,plain,
! [SV292: $i,SV109: $i] :
( ( ! [SY845: $i] :
( ~ ( relation @ SY845 )
| ~ ( in @ ( ordered_pair @ SV109 @ SV292 ) @ SY845 )
| ( in @ SV109 @ ( relation_dom @ SY845 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1498]) ).
thf(1667,plain,
! [SV293: $i,SV109: $i] :
( ( ! [SY846: $i] :
( ~ ( relation @ SY846 )
| ~ ( in @ ( ordered_pair @ SV109 @ SV293 ) @ SY846 )
| ( in @ SV293 @ ( relation_rng @ SY846 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1499]) ).
thf(1668,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1500]) ).
thf(1669,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1500]) ).
thf(1670,plain,
! [SV230: $i] :
( ( ( ~ ( empty @ SV230 )
| ~ ( relation @ SV230 )
| ~ ( function @ SV230 ) )
= $true )
| ( ( one_to_one @ SV230 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1501]) ).
thf(1671,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1502]) ).
thf(1672,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1502]) ).
thf(1673,plain,
! [SV110: $i] :
( ( ( relation @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( ~ ( one_to_one @ SV110 )
| ~ ( ~ ! [SY636: $i] :
( ~ ( function @ SY636 )
| ~ ( relation @ SY636 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SY636 @ SV110 )
= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ( ( sK70_C @ SY636 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY636 @ SV110 )
= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY636 @ SV110 )
= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ( ( sK71_SY424 @ SY636 @ SV110 )
!= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK70_C @ SY636 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK71_SY424 @ SY636 @ SV110 )
!= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY636 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK70_C @ SY636 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SY636 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SY636 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK71_SY424 @ SY636 @ SV110 )
!= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ( ( relation_dom @ SY636 )
!= ( relation_rng @ SV110 ) )
| ( SY636
= ( function_inverse @ SV110 ) ) )
| ~ ~ ( ~ ! [SY637: $i] :
( ~ ( function @ SY637 )
| ~ ( relation @ SY637 )
| ( SY637
!= ( function_inverse @ SV110 ) )
| ~ ( ~ ~ ( ~ ! [SY638: $i,SY639: $i] :
( ( SY639
!= ( apply @ SY637 @ SY638 ) )
| ~ ( in @ SY638 @ ( relation_rng @ SV110 ) )
| ( SY638
= ( apply @ SV110 @ SY639 ) ) )
| ~ ! [SY640: $i,SY641: $i] :
( ( SY641
!= ( apply @ SY637 @ SY640 ) )
| ~ ( in @ SY640 @ ( relation_rng @ SV110 ) )
| ( in @ SY641 @ ( relation_dom @ SV110 ) ) ) )
| ~ ~ ( ~ ! [SY642: $i,SY643: $i] :
( ( SY642
!= ( apply @ SV110 @ SY643 ) )
| ~ ( in @ SY643 @ ( relation_dom @ SV110 ) )
| ( SY643
= ( apply @ SY637 @ SY642 ) ) )
| ~ ! [SY644: $i] :
( ! [SY645: $i] :
( ( SY644
!= ( apply @ SV110 @ SY645 ) )
| ~ ( in @ SY645 @ ( relation_dom @ SV110 ) ) )
| ( in @ SY644 @ ( relation_rng @ SV110 ) ) ) ) ) )
| ~ ! [SY646: $i] :
( ~ ( function @ SY646 )
| ~ ( relation @ SY646 )
| ( SY646
!= ( function_inverse @ SV110 ) )
| ( ( relation_dom @ SY646 )
= ( relation_rng @ SV110 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1503]) ).
thf(1674,plain,
! [SV231: $i] :
( ( ( ~ ( empty @ SV231 ) )
= $true )
| ( ( empty @ ( relation_dom @ SV231 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1504]) ).
thf(1675,plain,
! [SV232: $i] :
( ( ( ~ ( empty @ SV232 ) )
= $true )
| ( ( relation @ ( relation_dom @ SV232 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1505]) ).
thf(1676,plain,
! [SV294: $i,SV233: $i] :
( ( ( SV233 = SV294 )
| ~ ( subset @ SV233 @ SV294 )
| ( proper_subset @ SV233 @ SV294 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(1677,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1507]) ).
thf(1678,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1507]) ).
thf(1679,plain,
! [SV234: $i,SV295: $i] :
( ( ~ ( ~ ( in @ ( sK18_C @ SV295 @ SV234 ) @ SV234 )
| ~ ~ ( in @ ( sK18_C @ SV295 @ SV234 ) @ SV295 ) )
| ( subset @ SV234 @ SV295 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1509]) ).
thf(1680,plain,
! [SV296: $i,SV235: $i] :
( ( ~ ( subset @ SV235 @ SV296 )
| ! [SY847: $i] :
( ~ ( in @ SY847 @ SV235 )
| ( in @ SY847 @ SV296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1510]) ).
thf(1681,plain,
! [SV297: $i,SV236: $i] :
( ( ( disjoint @ SV236 @ SV297 )
| ~ ( ~ ( in @ ( sK49_C @ SV297 @ SV236 ) @ SV236 )
| ~ ( in @ ( sK49_C @ SV297 @ SV236 ) @ SV297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1511]) ).
thf(1682,plain,
! [SV298: $i,SV237: $i] :
( ( ! [SY848: $i] :
( ~ ( in @ SY848 @ SV237 )
| ~ ( in @ SY848 @ SV298 ) )
| ~ ( disjoint @ SV237 @ SV298 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1512]) ).
thf(1683,plain,
! [SV179: $i,SV111: $i] :
( ( ! [SY746: $i,SY747: $i] :
( ~ ( in @ SV111 @ SY746 )
| ~ ( in @ SV179 @ SY747 )
| ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SY746 @ SY747 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1513]) ).
thf(1684,plain,
! [SV179: $i,SV111: $i] :
( ( ~ ( ~ ! [SY748: $i] :
( ! [SY749: $i] :
~ ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SY748 @ SY749 ) )
| ( in @ SV111 @ SY748 ) )
| ~ ! [SY750: $i,SY751: $i] :
( ~ ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SY750 @ SY751 ) )
| ( in @ SV179 @ SY751 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1514]) ).
thf(1685,plain,
! [SV180: $i,SV112: $i] :
( ( ! [SY752: $i] :
( ! [SY753: $i] :
( ( ordered_pair @ SV112 @ SV180 )
!= ( ordered_pair @ SY752 @ SY753 ) )
| ( SV112 = SY752 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1515]) ).
thf(1686,plain,
! [SV180: $i,SV112: $i] :
( ( ! [SY754: $i,SY755: $i] :
( ( ( ordered_pair @ SV112 @ SV180 )
!= ( ordered_pair @ SY754 @ SY755 ) )
| ( SV180 = SY755 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1516]) ).
thf(1687,plain,
! [SV113: $i] :
( ( ( relation @ SV113 )
= $false )
| ( ( function @ SV113 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ ( relation_dom @ SV113 ) )
| ! [SY660: $i] :
( ( SY660
!= ( apply @ SV113 @ SY659 ) )
| ( in @ ( ordered_pair @ SY659 @ SY660 ) @ SV113 ) ) )
| ~ ! [SY661: $i] :
( ~ ( in @ SY661 @ ( relation_dom @ SV113 ) )
| ! [SY662: $i] :
( ~ ( in @ ( ordered_pair @ SY661 @ SY662 ) @ SV113 )
| ( SY662
= ( apply @ SV113 @ SY661 ) ) ) ) )
| ~ ~ ( ~ ! [SY663: $i] :
( ( in @ SY663 @ ( relation_dom @ SV113 ) )
| ! [SY664: $i] :
( ( SY664
!= ( apply @ SV113 @ SY663 ) )
| ( SY664 = empty_set ) ) )
| ~ ! [SY665: $i] :
( ( in @ SY665 @ ( relation_dom @ SV113 ) )
| ! [SY666: $i] :
( ( SY666 != empty_set )
| ( SY666
= ( apply @ SV113 @ SY665 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1517]) ).
thf(1688,plain,
! [SV238: $i] :
( ( ( ~ ( relation @ SV238 ) )
= $true )
| ( ( ( relation_rng @ SV238 )
= ( relation_dom @ ( relation_inverse @ SV238 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1518]) ).
thf(1689,plain,
! [SV239: $i] :
( ( ( ~ ( relation @ SV239 ) )
= $true )
| ( ( ( relation_dom @ SV239 )
= ( relation_rng @ ( relation_inverse @ SV239 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1519]) ).
thf(1690,plain,
! [SV299: $i,SV240: $i] :
( ( ~ ( in @ SV240 @ SV299 )
| ( subset @ ( singleton @ SV240 ) @ SV299 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(1691,plain,
! [SV300: $i,SV241: $i] :
( ( ~ ( subset @ ( singleton @ SV241 ) @ SV300 )
| ( in @ SV241 @ SV300 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1521]) ).
thf(1692,plain,
! [SV242: $i] :
( ( ( in @ ( sK29_B @ SV242 ) @ SV242 )
= $true )
| ( ( SV242 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1522]) ).
thf(1693,plain,
! [SV243: $i] :
( ( ( ( SV243 != empty_set ) )
= $true )
| ( ( ! [SY802: $i] :
~ ( in @ SY802 @ SV243 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1523]) ).
thf(1694,plain,
! [SV114: $i,SV301: $i] :
( ( ! [SY849: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY849 @ SV301 @ SV114 ) @ SY849 )
| ~ ( in @ ( sK26_D @ SY849 @ SV301 @ SV114 ) @ SV114 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY849 @ SV301 @ SV114 ) @ SY849 )
| ~ ( in @ ( sK26_D @ SY849 @ SV301 @ SV114 ) @ SV301 ) ) )
| ~ ( ( in @ ( sK26_D @ SY849 @ SV301 @ SV114 ) @ SY849 )
| ( in @ ( sK26_D @ SY849 @ SV301 @ SV114 ) @ SV114 )
| ( in @ ( sK26_D @ SY849 @ SV301 @ SV114 ) @ SV301 ) ) )
| ( SY849
= ( set_union2 @ SV114 @ SV301 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1524]) ).
thf(1695,plain,
! [SV302: $i,SV114: $i] :
( ( ! [SY850: $i] :
( ( SY850
!= ( set_union2 @ SV114 @ SV302 ) )
| ~ ( ~ ! [SY851: $i] :
( ~ ( in @ SY851 @ SY850 )
| ( in @ SY851 @ SV114 )
| ( in @ SY851 @ SV302 ) )
| ~ ~ ( ~ ! [SY672: $i] :
( ~ ( in @ SY672 @ SV114 )
| ( in @ SY672 @ SY850 ) )
| ~ ! [SY853: $i] :
( ~ ( in @ SY853 @ SV302 )
| ( in @ SY853 @ SY850 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1525]) ).
thf(1696,plain,
! [SV244: $i] :
( ( ( ~ ( empty @ SV244 ) )
= $true )
| ( ( empty @ ( relation_rng @ SV244 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1526]) ).
thf(1697,plain,
! [SV245: $i] :
( ( ( ~ ( empty @ SV245 ) )
= $true )
| ( ( relation @ ( relation_rng @ SV245 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1527]) ).
thf(1698,plain,
! [SV303: $i,SV115: $i] :
( ( ! [SY854: $i] :
( ~ ( relation @ SY854 )
| ~ ( in @ ( ordered_pair @ SV115 @ SV303 ) @ SY854 )
| ( in @ SV115 @ ( relation_field @ SY854 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(1699,plain,
! [SV304: $i,SV115: $i] :
( ( ! [SY855: $i] :
( ~ ( relation @ SY855 )
| ~ ( in @ ( ordered_pair @ SV115 @ SV304 ) @ SY855 )
| ( in @ SV304 @ ( relation_field @ SY855 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(1700,plain,
! [SV246: $i] :
( ( ( ~ ( relation @ SV246 ) )
= $true )
| ( ( ( ( relation_dom @ SV246 )
!= empty_set )
| ( ( relation_rng @ SV246 )
= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1530]) ).
thf(1701,plain,
! [SV247: $i] :
( ( ( ~ ( relation @ SV247 ) )
= $true )
| ( ( ( ( relation_rng @ SV247 )
!= empty_set )
| ( ( relation_dom @ SV247 )
= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1531]) ).
thf(1702,plain,
! [SV305: $i,SV248: $i] :
( ( ~ ( subset @ SV248 @ ( singleton @ SV305 ) )
| ( SV248 = empty_set )
| ( SV248
= ( singleton @ SV305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(1703,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1533]) ).
thf(1704,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1533]) ).
thf(1705,plain,
! [SV116: $i,SV306: $i] :
( ( ! [SY856: $i] :
( ~ ( ~ ( ~ ( in @ ( sK17_D @ SY856 @ SV306 @ SV116 ) @ SV116 )
| ~ ( in @ ( sK17_D @ SY856 @ SV306 @ SV116 ) @ SV306 )
| ~ ( in @ ( sK17_D @ SY856 @ SV306 @ SV116 ) @ SY856 ) )
| ~ ~ ( ~ ( ( in @ ( sK17_D @ SY856 @ SV306 @ SV116 ) @ SV116 )
| ( in @ ( sK17_D @ SY856 @ SV306 @ SV116 ) @ SY856 ) )
| ~ ( ( in @ ( sK17_D @ SY856 @ SV306 @ SV116 ) @ SV306 )
| ( in @ ( sK17_D @ SY856 @ SV306 @ SV116 ) @ SY856 ) ) ) )
| ( SY856
= ( set_intersection2 @ SV116 @ SV306 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(1706,plain,
! [SV307: $i,SV116: $i] :
( ( ! [SY857: $i] :
( ( SY857
!= ( set_intersection2 @ SV116 @ SV307 ) )
| ~ ( ~ ! [SY858: $i] :
( ~ ( in @ SY858 @ SV116 )
| ~ ( in @ SY858 @ SV307 )
| ( in @ SY858 @ SY857 ) )
| ~ ~ ( ~ ! [SY683: $i] :
( ~ ( in @ SY683 @ SY857 )
| ( in @ SY683 @ SV116 ) )
| ~ ! [SY860: $i] :
( ~ ( in @ SY860 @ SY857 )
| ( in @ SY860 @ SV307 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1535]) ).
thf(1707,plain,
! [SV249: $i] :
( ( ( ~ ( function @ SV249 )
| ~ ( relation @ SV249 )
| ~ ( one_to_one @ SV249 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV249 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1536]) ).
thf(1708,plain,
! [SV250: $i] :
( ( ( ~ ( function @ SV250 )
| ~ ( relation @ SV250 )
| ~ ( one_to_one @ SV250 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1537]) ).
thf(1709,plain,
! [SV251: $i,SV308: $i] :
( ( ~ ( relation @ SV308 )
| ~ ( ~ ( ( ( sK44_C @ SV308 @ SV251 )
!= ( sK45_SY414 @ SV308 @ SV251 ) )
| ~ ( in @ ( sK44_C @ SV308 @ SV251 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 ) )
| ~ ~ ( ~ ( ( ( sK44_C @ SV308 @ SV251 )
= ( sK45_SY414 @ SV308 @ SV251 ) )
| ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 ) )
| ~ ( ( in @ ( sK44_C @ SV308 @ SV251 ) @ SV251 )
| ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 ) ) ) )
| ( SV308
= ( identity_relation @ SV251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1538]) ).
thf(1710,plain,
! [SV252: $i,SV309: $i] :
( ( ~ ( relation @ SV309 )
| ( SV309
!= ( identity_relation @ SV252 ) )
| ~ ( ~ ! [SY861: $i,SY862: $i] :
( ( SY861 != SY862 )
| ~ ( in @ SY861 @ SV252 )
| ( in @ ( ordered_pair @ SY861 @ SY862 ) @ SV309 ) )
| ~ ~ ( ~ ! [SY863: $i,SY864: $i] :
( ~ ( in @ ( ordered_pair @ SY863 @ SY864 ) @ SV309 )
| ( SY863 = SY864 ) )
| ~ ! [SY865: $i] :
( ! [SY866: $i] :
~ ( in @ ( ordered_pair @ SY865 @ SY866 ) @ SV309 )
| ( in @ SY865 @ SV252 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1539]) ).
thf(1711,plain,
( ( ~ ( function @ sK54_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1540]) ).
thf(1712,plain,
( ( ~ ( relation @ sK54_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1540]) ).
thf(1713,plain,
! [SV310: $i,SV117: $i] :
( ( ! [SY867: $i] :
( ~ ( relation @ SY867 )
| ~ ( in @ SV117 @ SV310 )
| ~ ( in @ SV117 @ ( relation_dom @ SY867 ) )
| ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SY867 @ SV310 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1541]) ).
thf(1714,plain,
! [SV117: $i] :
( ( ~ ! [SY687: $i,SY688: $i] :
( ~ ( relation @ SY688 )
| ~ ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SY688 @ SY687 ) ) )
| ( in @ SV117 @ SY687 ) )
| ~ ! [SY689: $i,SY690: $i] :
( ~ ( relation @ SY690 )
| ~ ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SY690 @ SY689 ) ) )
| ( in @ SV117 @ ( relation_dom @ SY690 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1542]) ).
thf(1715,plain,
! [SV253: $i,SV311: $i] :
( ( ~ ( function @ SV311 )
| ~ ( relation @ SV311 )
| ~ ( ~ ( in @ ( sK50_C @ SV311 @ SV253 ) @ SV253 )
| ~ ( ( ( apply @ SV311 @ ( sK50_C @ SV311 @ SV253 ) )
!= ( sK50_C @ SV311 @ SV253 ) ) ) )
| ( ( relation_dom @ SV311 )
!= SV253 )
| ( SV311
= ( identity_relation @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1543]) ).
thf(1716,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)],[1544]) ).
thf(1717,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1544]) ).
thf(1718,plain,
! [SV312: $i,SV118: $i] :
( ( ! [SY868: $i] :
( ~ ( ~ ( ! [SY869: $i,SY870: $i] :
( ~ ( in @ SY869 @ SV118 )
| ~ ( in @ SY870 @ SV312 )
| ( ( sK23_D @ SY868 @ SV312 @ SV118 )
!= ( ordered_pair @ SY869 @ SY870 ) ) )
| ~ ( in @ ( sK23_D @ SY868 @ SV312 @ SV118 ) @ SY868 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY403 @ SY868 @ SV312 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK25_SY405 @ SY868 @ SV312 @ SV118 ) @ SV312 ) )
| ( ( sK23_D @ SY868 @ SV312 @ SV118 )
!= ( ordered_pair @ ( sK24_SY403 @ SY868 @ SV312 @ SV118 ) @ ( sK25_SY405 @ SY868 @ SV312 @ SV118 ) ) ) )
| ( in @ ( sK23_D @ SY868 @ SV312 @ SV118 ) @ SY868 ) ) )
| ( SY868
= ( cartesian_product2 @ SV118 @ SV312 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(1719,plain,
! [SV313: $i,SV118: $i] :
( ( ! [SY871: $i] :
( ( SY871
!= ( cartesian_product2 @ SV118 @ SV313 ) )
| ~ ( ~ ! [SY872: $i] :
( ! [SY873: $i,SY874: $i] :
( ~ ( in @ SY873 @ SV118 )
| ~ ( in @ SY874 @ SV313 )
| ( SY872
!= ( ordered_pair @ SY873 @ SY874 ) ) )
| ( in @ SY872 @ SY871 ) )
| ~ ! [SY875: $i] :
( ~ ( in @ SY875 @ SY871 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY875 @ SY871 @ SV313 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK22_SY400 @ SY875 @ SY871 @ SV313 @ SV118 ) @ SV313 ) )
| ( SY875
!= ( ordered_pair @ ( sK21_E @ SY875 @ SY871 @ SV313 @ SV118 ) @ ( sK22_SY400 @ SY875 @ SY871 @ SV313 @ SV118 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1546]) ).
thf(1720,plain,
! [SV314: $i,SV119: $i] :
( ( ~ ( subset @ SV119 @ SV314 )
| ! [SY876: $i] : ( subset @ ( cartesian_product2 @ SV119 @ SY876 ) @ ( cartesian_product2 @ SV314 @ SY876 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1547]) ).
thf(1721,plain,
! [SV315: $i,SV119: $i] :
( ( ~ ( subset @ SV119 @ SV315 )
| ! [SY877: $i] : ( subset @ ( cartesian_product2 @ SY877 @ SV119 ) @ ( cartesian_product2 @ SY877 @ SV315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1548]) ).
thf(1722,plain,
! [SV254: $i,SV316: $i] :
( ( ~ ( ~ ( ! [SY878: $i] :
( ~ ( in @ ( sK15_C @ SV316 @ SV254 ) @ SY878 )
| ~ ( in @ SY878 @ SV254 ) )
| ~ ( in @ ( sK15_C @ SV316 @ SV254 ) @ SV316 ) )
| ~ ( ~ ( ~ ( in @ ( sK15_C @ SV316 @ SV254 ) @ ( sK16_SY398 @ SV316 @ SV254 ) )
| ~ ( in @ ( sK16_SY398 @ SV316 @ SV254 ) @ SV254 ) )
| ( in @ ( sK15_C @ SV316 @ SV254 ) @ SV316 ) ) )
| ( SV316
= ( union @ SV254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1549]) ).
thf(1723,plain,
! [SV255: $i,SV317: $i] :
( ( ( SV317
!= ( union @ SV255 ) )
| ~ ( ~ ! [SY879: $i] :
( ! [SY817: $i] :
( ~ ( in @ SY879 @ SY817 )
| ~ ( in @ SY817 @ SV255 ) )
| ( in @ SY879 @ SV317 ) )
| ~ ! [SY881: $i] :
( ~ ( in @ SY881 @ SV317 )
| ~ ( ~ ( in @ SY881 @ ( sK14_D @ SY881 @ SV317 @ SV255 ) )
| ~ ( in @ ( sK14_D @ SY881 @ SV317 @ SV255 ) @ SV255 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1550]) ).
thf(1724,plain,
! [SV318: $i,SV256: $i] :
( ( ( ( set_difference @ SV256 @ SV318 )
!= empty_set )
| ( subset @ SV256 @ SV318 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(1725,plain,
! [SV319: $i,SV257: $i] :
( ( ~ ( subset @ SV257 @ SV319 )
| ( ( set_difference @ SV257 @ SV319 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1552]) ).
thf(1726,plain,
! [SV120: $i] :
( ( ( ~ ! [SY705: $i] :
( ~ ( relation @ SY705 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SY705 @ SV120 ) @ ( sK66_SY420 @ SY705 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SY705 @ SV120 ) @ ( sK66_SY420 @ SY705 @ SV120 ) ) @ SY705 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_C @ SY705 @ SV120 ) @ ( sK66_SY420 @ SY705 @ SV120 ) ) @ SV120 )
| ( in @ ( ordered_pair @ ( sK65_C @ SY705 @ SV120 ) @ ( sK66_SY420 @ SY705 @ SV120 ) ) @ SY705 ) ) )
| ( SV120 = SY705 ) ) )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1553]) ).
thf(1727,plain,
! [SV120: $i] :
( ( ( ~ ! [SY706: $i] :
( ~ ( relation @ SY706 )
| ( SV120 != SY706 )
| ~ ( ~ ! [SY707: $i,SY708: $i] :
( ~ ( in @ ( ordered_pair @ SY707 @ SY708 ) @ SV120 )
| ( in @ ( ordered_pair @ SY707 @ SY708 ) @ SY706 ) )
| ~ ! [SY709: $i,SY710: $i] :
( ~ ( in @ ( ordered_pair @ SY709 @ SY710 ) @ SY706 )
| ( in @ ( ordered_pair @ SY709 @ SY710 ) @ SV120 ) ) ) ) )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1553]) ).
thf(1728,plain,
! [SV9: $i,SV190: $i] :
( ( ( relation @ SV190 )
= $false )
| ( ( ( relation_rng @ ( relation_composition @ SV9 @ SV190 ) )
= ( relation_image @ SV190 @ ( relation_rng @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1555]) ).
thf(1729,plain,
! [SV182: $i,SV129: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ SV129 ) )
= $true )
| ( ( subset @ ( relation_inverse_image @ SV182 @ SV11 ) @ ( relation_inverse_image @ SV182 @ SV129 ) )
= $true )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1556]) ).
thf(1730,plain,
! [SV13: $i,SV191: $i] :
( ( ( relation @ SV191 )
= $false )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV13 @ SV191 ) ) @ ( relation_dom @ SV13 ) )
= $true )
| ( ( relation @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1557]) ).
thf(1731,plain,
! [SV14: $i,SV192: $i] :
( ( ( relation @ SV192 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV14 @ SV192 ) ) @ ( relation_rng @ SV192 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1558]) ).
thf(1732,plain,
! [SV15: $i,SV193: $i] :
( ( ( relation @ SV193 )
= $false )
| ( ( ~ ( subset @ ( relation_rng @ SV15 ) @ ( relation_dom @ SV193 ) )
| ( ( relation_dom @ ( relation_composition @ SV15 @ SV193 ) )
= ( relation_dom @ SV15 ) ) )
= $true )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1559]) ).
thf(1733,plain,
! [SV16: $i,SV194: $i] :
( ( ( relation @ SV194 )
= $false )
| ( ( ~ ( subset @ ( relation_dom @ SV16 ) @ ( relation_rng @ SV194 ) )
| ( ( relation_rng @ ( relation_composition @ SV194 @ SV16 ) )
= ( relation_rng @ SV16 ) ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1560]) ).
thf(1734,plain,
! [SV23: $i] :
( ( ( ~ ( one_to_one @ SV23 ) )
= $true )
| ( ( ( function_inverse @ SV23 )
= ( relation_inverse @ SV23 ) )
= $true )
| ( ( function @ SV23 )
= $false )
| ( ( relation @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1561]) ).
thf(1735,plain,
! [SV25: $i,SV133: $i] :
( ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV25 )
= $false )
| ( ( relation @ ( relation_composition @ SV25 @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1562]) ).
thf(1736,plain,
! [SV29: $i,SV135: $i] :
( ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV29 )
= $false )
| ( ( relation @ ( set_intersection2 @ SV29 @ SV135 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1563]) ).
thf(1737,plain,
! [SV30: $i,SV136: $i] :
( ( ( relation @ SV136 )
= $false )
| ( ( relation @ SV30 )
= $false )
| ( ( relation @ ( set_union2 @ SV30 @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1564]) ).
thf(1738,plain,
! [SV196: $i,SV183: $i,SV139: $i,SV37: $i] :
( ( ( ~ ( subset @ SV37 @ SV139 ) )
= $true )
| ( ( ~ ( subset @ SV183 @ SV196 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV37 @ SV183 ) @ ( cartesian_product2 @ SV139 @ SV196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1567]) ).
thf(1739,plain,
! [SV141: $i,SV39: $i] :
( ( ( SV39 = empty_set )
= $true )
| ( ( ~ ( subset @ SV39 @ ( relation_rng @ SV141 ) ) )
= $true )
| ( ( ( ( relation_inverse_image @ SV141 @ SV39 )
!= empty_set ) )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1568]) ).
thf(1740,plain,
! [SV184: $i,SV143: $i,SV41: $i] :
( ( ( subset @ SV41 @ SV143 )
= $false )
| ( ( ~ ( subset @ SV41 @ SV184 ) )
= $true )
| ( ( subset @ SV41 @ ( set_intersection2 @ SV143 @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1569]) ).
thf(1741,plain,
! [SV185: $i,SV144: $i,SV42: $i] :
( ( ( subset @ SV42 @ SV144 )
= $false )
| ( ( ~ ( subset @ SV144 @ SV185 ) )
= $true )
| ( ( subset @ SV42 @ SV185 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1570]) ).
thf(1742,plain,
! [SV43: $i,SV145: $i] :
( ( ( relation @ SV145 )
= $false )
| ( ( function @ SV145 )
= $false )
| ( ( ! [SY717: $i] :
( ~ ( function @ SY717 )
| ~ ( relation @ SY717 )
| ~ ( in @ SV43 @ ( relation_dom @ ( relation_composition @ SY717 @ SV145 ) ) )
| ( ( apply @ ( relation_composition @ SY717 @ SV145 ) @ SV43 )
= ( apply @ SV145 @ ( apply @ SY717 @ SV43 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1571]) ).
thf(1743,plain,
! [SV44: $i,SV146: $i] :
( ( ( relation @ SV146 )
= $false )
| ( ( function @ SV146 )
= $false )
| ( ( ! [SY718: $i] :
( ~ ( function @ SY718 )
| ~ ( relation @ SY718 )
| ~ ( in @ SV44 @ ( relation_dom @ SV146 ) )
| ( ( apply @ ( relation_composition @ SV146 @ SY718 ) @ SV44 )
= ( apply @ SY718 @ ( apply @ SV146 @ SV44 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1572]) ).
thf(1744,plain,
! [SV59: $i,SV186: $i,SV158: $i] :
( ( ( disjoint @ SV158 @ SV186 )
= $false )
| ( ( ~ ( subset @ SV59 @ SV158 ) )
= $true )
| ( ( disjoint @ SV59 @ SV186 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1576]) ).
thf(1745,plain,
! [SV187: $i,SV161: $i,SV62: $i] :
( ( ( subset @ SV62 @ SV161 )
= $false )
| ( ( ~ ( subset @ SV187 @ SV161 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV62 @ SV187 ) @ SV161 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1577]) ).
thf(1746,plain,
! [SV86: $i,SV173: $i] :
( ( ( empty @ SV173 )
= $false )
| ( ( SV86 = SV173 )
= $true )
| ( ( empty @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1582]) ).
thf(1747,plain,
! [SV260: $i,SV197: $i] :
( ( ( ~ ( in @ SV197 @ SV260 ) )
= $true )
| ( ( subset @ ( singleton @ SV197 ) @ SV260 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1583]) ).
thf(1748,plain,
! [SV261: $i,SV198: $i] :
( ( ( ~ ( subset @ ( singleton @ SV198 ) @ SV261 ) )
= $true )
| ( ( in @ SV198 @ SV261 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1584]) ).
thf(1749,plain,
! [SV262: $i,SV199: $i] :
( ( ( ~ ( subset @ SV199 @ ( singleton @ SV262 ) ) )
= $true )
| ( ( ( SV199 = empty_set )
| ( SV199
= ( singleton @ SV262 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1585]) ).
thf(1750,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1586]) ).
thf(1751,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1587]) ).
thf(1752,plain,
( ( ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY406 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ ( sK33_SY406 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1588]) ).
thf(1753,plain,
( ( ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK31_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)],[1589]) ).
thf(1754,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1590]) ).
thf(1755,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1591]) ).
thf(1756,plain,
! [SV263: $i,SV200: $i] :
( ( ( disjoint @ SV200 @ SV263 )
= $true )
| ( ( in @ ( sK48_C @ SV263 @ SV200 ) @ ( set_intersection2 @ SV200 @ SV263 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1592]) ).
thf(1757,plain,
! [SV264: $i,SV201: $i] :
( ( ( ! [SY821: $i] :
~ ( in @ SY821 @ ( set_intersection2 @ SV201 @ SV264 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV201 @ SV264 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1593]) ).
thf(1758,plain,
! [SV265: $i,SV202: $i] :
( ( ( ~ ( function @ SV202 )
| ~ ( relation @ SV202 )
| ~ ( relation @ SV265 )
| ~ ( function @ SV265 ) )
= $true )
| ( ( function @ ( relation_composition @ SV202 @ SV265 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1594]) ).
thf(1759,plain,
! [SV266: $i,SV203: $i] :
( ( ( ~ ( function @ SV203 )
| ~ ( relation @ SV203 )
| ~ ( relation @ SV266 )
| ~ ( function @ SV266 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV203 @ SV266 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1595]) ).
thf(1760,plain,
! [SV267: $i,SV204: $i] :
( ( ( ( ( set_difference @ SV204 @ SV267 )
!= empty_set ) )
= $true )
| ( ( subset @ SV204 @ SV267 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1596]) ).
thf(1761,plain,
! [SV268: $i,SV205: $i] :
( ( ( ~ ( subset @ SV205 @ SV268 ) )
= $true )
| ( ( ( set_difference @ SV205 @ SV268 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1597]) ).
thf(1762,plain,
! [SV269: $i,SV206: $i] :
( ( ( ~ ( empty @ SV206 )
| ~ ( relation @ SV269 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV206 @ SV269 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1598]) ).
thf(1763,plain,
! [SV270: $i,SV207: $i] :
( ( ( ~ ( empty @ SV207 )
| ~ ( relation @ SV270 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV207 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1599]) ).
thf(1764,plain,
! [SV271: $i,SV87: $i,SV320: $i] :
( ( ~ ( relation @ SV320 )
| ! [SY882: $i] :
( ~ ( in @ SY882 @ ( relation_dom @ SV320 ) )
| ~ ( in @ ( ordered_pair @ SY882 @ SV87 ) @ SV320 )
| ~ ( in @ SY882 @ SV271 ) )
| ( in @ SV87 @ ( relation_image @ SV320 @ SV271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1600]) ).
thf(1765,plain,
! [SV272: $i,SV87: $i,SV321: $i] :
( ( ~ ( relation @ SV321 )
| ~ ( in @ SV87 @ ( relation_image @ SV321 @ SV272 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK52_D @ SV321 @ SV272 @ SV87 ) @ ( relation_dom @ SV321 ) )
| ~ ( in @ ( ordered_pair @ ( sK52_D @ SV321 @ SV272 @ SV87 ) @ SV87 ) @ SV321 ) )
| ~ ( in @ ( sK52_D @ SV321 @ SV272 @ SV87 ) @ SV272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1601]) ).
thf(1766,plain,
! [SV273: $i,SV208: $i] :
( ( ( ~ ( subset @ SV208 @ SV273 )
| ~ ( subset @ SV273 @ SV208 ) )
= $true )
| ( ( SV208 = SV273 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1602]) ).
thf(1767,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1603]) ).
thf(1768,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1604]) ).
thf(1769,plain,
! [SV88: $i,SV274: $i,SV322: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV88 )
| ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV274 )
| ~ ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV322 ) )
| ~ ~ ( ~ ( ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV88 )
| ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV322 ) )
| ~ ( ~ ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV274 )
| ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV322 ) ) ) )
| ( SV322
= ( set_difference @ SV88 @ SV274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1605]) ).
thf(1770,plain,
! [SV275: $i,SV88: $i,SV323: $i] :
( ( ( SV323
!= ( set_difference @ SV88 @ SV275 ) )
| ~ ( ~ ! [SY883: $i] :
( ~ ( in @ SY883 @ SV88 )
| ( in @ SY883 @ SV275 )
| ( in @ SY883 @ SV323 ) )
| ~ ~ ( ~ ! [SY884: $i] :
( ~ ( in @ SY884 @ SV323 )
| ( in @ SY884 @ SV88 ) )
| ~ ! [SY885: $i] :
( ~ ( in @ SY885 @ SV323 )
| ~ ( in @ SY885 @ SV275 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1606]) ).
thf(1771,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1607]) ).
thf(1772,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1608]) ).
thf(1773,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1609]) ).
thf(1774,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1610]) ).
thf(1775,plain,
! [SV89: $i,SV174: $i] :
( ( ( ~ ! [SY723: $i] :
( ~ ( relation @ SY723 )
| ~ ( ~ ( ~ ( in @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY723 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) ) @ SV174 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY723 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) ) @ SY723 ) )
| ~ ~ ( ~ ( ( in @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) @ SV89 )
| ( in @ ( ordered_pair @ ( sK40_D @ SY723 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) ) @ SY723 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SY723 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) ) @ SV174 )
| ( in @ ( ordered_pair @ ( sK40_D @ SY723 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) ) @ SY723 ) ) ) )
| ( SY723
= ( relation_rng_restriction @ SV89 @ SV174 ) ) ) )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1611]) ).
thf(1776,plain,
! [SV174: $i,SV89: $i] :
( ( ( ~ ! [SY724: $i] :
( ~ ( relation @ SY724 )
| ( SY724
!= ( relation_rng_restriction @ SV89 @ SV174 ) )
| ~ ( ~ ! [SY725: $i,SY726: $i] :
( ~ ( in @ SY726 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY725 @ SY726 ) @ SV174 )
| ( in @ ( ordered_pair @ SY725 @ SY726 ) @ SY724 ) )
| ~ ~ ( ~ ! [SY515: $i,SY516: $i] :
( ~ ( in @ ( ordered_pair @ SY515 @ SY516 ) @ SY724 )
| ( in @ SY516 @ SV89 ) )
| ~ ! [SY729: $i,SY730: $i] :
( ~ ( in @ ( ordered_pair @ SY729 @ SY730 ) @ SY724 )
| ( in @ ( ordered_pair @ SY729 @ SY730 ) @ SV174 ) ) ) ) ) )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1611]) ).
thf(1777,plain,
! [SV90: $i,SV276: $i,SV324: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SV324 @ SV276 @ SV90 ) @ SV324 )
| ( ( sK27_D @ SV324 @ SV276 @ SV90 )
!= SV90 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV324 @ SV276 @ SV90 ) @ SV324 )
| ( ( sK27_D @ SV324 @ SV276 @ SV90 )
!= SV276 ) ) )
| ~ ( ( in @ ( sK27_D @ SV324 @ SV276 @ SV90 ) @ SV324 )
| ( ( sK27_D @ SV324 @ SV276 @ SV90 )
= SV90 )
| ( ( sK27_D @ SV324 @ SV276 @ SV90 )
= SV276 ) ) )
| ( SV324
= ( unordered_pair @ SV90 @ SV276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(1778,plain,
! [SV277: $i,SV90: $i,SV325: $i] :
( ( ( SV325
!= ( unordered_pair @ SV90 @ SV277 ) )
| ~ ( ~ ! [SY886: $i] :
( ~ ( in @ SY886 @ SV325 )
| ( SY886 = SV90 )
| ( SY886 = SV277 ) )
| ~ ~ ( ~ ! [SY887: $i] :
( ( SY887 != SV90 )
| ( in @ SY887 @ SV325 ) )
| ~ ! [SY888: $i] :
( ( SY888 != SV277 )
| ( in @ SY888 @ SV325 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(1779,plain,
! [SV209: $i,SV278: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK28_C @ SV278 @ SV209 ) @ SV278 )
| ~ ( subset @ ( sK28_C @ SV278 @ SV209 ) @ SV209 ) )
| ~ ( ( in @ ( sK28_C @ SV278 @ SV209 ) @ SV278 )
| ( subset @ ( sK28_C @ SV278 @ SV209 ) @ SV209 ) ) ) )
= $true )
| ( ( SV278
= ( powerset @ SV209 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1614]) ).
thf(1780,plain,
! [SV210: $i,SV279: $i] :
( ( ( ( SV279
!= ( powerset @ SV210 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY835: $i] :
( ~ ( in @ SY835 @ SV279 )
| ( subset @ SY835 @ SV210 ) )
| ~ ! [SY836: $i] :
( ~ ( subset @ SY836 @ SV210 )
| ( in @ SY836 @ SV279 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1615]) ).
thf(1781,plain,
! [SV280: $i,SV211: $i] :
( ( ( ( ( set_intersection2 @ SV211 @ SV280 )
!= empty_set ) )
= $true )
| ( ( disjoint @ SV211 @ SV280 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1616]) ).
thf(1782,plain,
! [SV281: $i,SV212: $i] :
( ( ( ~ ( disjoint @ SV212 @ SV281 ) )
= $true )
| ( ( ( set_intersection2 @ SV212 @ SV281 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1617]) ).
thf(1783,plain,
! [SV91: $i] :
( ( ( ! [SY526: $i] :
( ~ ( ~ ( ! [SY527: $i] :
~ ( in @ ( ordered_pair @ ( sK63_C @ SY526 @ SV91 ) @ SY527 ) @ SV91 )
| ~ ( in @ ( sK63_C @ SY526 @ SV91 ) @ SY526 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_C @ SY526 @ SV91 ) @ ( sK64_SY419 @ SY526 @ SV91 ) ) @ SV91 )
| ( in @ ( sK63_C @ SY526 @ SV91 ) @ SY526 ) ) )
| ( SY526
= ( relation_dom @ SV91 ) ) ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1618]) ).
thf(1784,plain,
! [SV91: $i] :
( ( ( ! [SY528: $i] :
( ( SY528
!= ( relation_dom @ SV91 ) )
| ~ ( ~ ! [SY529: $i] :
( ! [SY530: $i] :
~ ( in @ ( ordered_pair @ SY529 @ SY530 ) @ SV91 )
| ( in @ SY529 @ SY528 ) )
| ~ ! [SY531: $i] :
( ~ ( in @ SY531 @ SY528 )
| ( in @ ( ordered_pair @ SY531 @ ( sK62_D @ SY531 @ SY528 @ SV91 ) ) @ SV91 ) ) ) ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1619]) ).
thf(1785,plain,
! [SV92: $i] :
( ( ( ! [SY532: $i,SY533: $i] :
( ~ ( ~ ( ! [SY534: $i] :
( ~ ( in @ ( ordered_pair @ ( sK35_D @ SY533 @ SY532 @ SV92 ) @ SY534 ) @ SV92 )
| ~ ( in @ SY534 @ SY532 ) )
| ~ ( in @ ( sK35_D @ SY533 @ SY532 @ SV92 ) @ SY533 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SY533 @ SY532 @ SV92 ) @ ( sK36_SY409 @ SY533 @ SY532 @ SV92 ) ) @ SV92 )
| ~ ( in @ ( sK36_SY409 @ SY533 @ SY532 @ SV92 ) @ SY532 ) )
| ( in @ ( sK35_D @ SY533 @ SY532 @ SV92 ) @ SY533 ) ) )
| ( SY533
= ( relation_inverse_image @ SV92 @ SY532 ) ) ) )
= $true )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1620]) ).
thf(1786,plain,
! [SV92: $i] :
( ( ( ! [SY535: $i,SY536: $i] :
( ( SY536
!= ( relation_inverse_image @ SV92 @ SY535 ) )
| ~ ( ~ ! [SY537: $i] :
( ! [SY538: $i] :
( ~ ( in @ ( ordered_pair @ SY537 @ SY538 ) @ SV92 )
| ~ ( in @ SY538 @ SY535 ) )
| ( in @ SY537 @ SY536 ) )
| ~ ! [SY539: $i] :
( ~ ( in @ SY539 @ SY536 )
| ~ ( ~ ( in @ ( ordered_pair @ SY539 @ ( sK34_E @ SY539 @ SY536 @ SY535 @ SV92 ) ) @ SV92 )
| ~ ( in @ ( sK34_E @ SY539 @ SY536 @ SY535 @ SV92 ) @ SY535 ) ) ) ) ) )
= $true )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1621]) ).
thf(1787,plain,
! [SV93: $i] :
( ( ( ! [SY540: $i,SY541: $i] :
( ~ ( ~ ( ! [SY542: $i] :
( ~ ( in @ ( ordered_pair @ SY542 @ ( sK38_D @ SY541 @ SY540 @ SV93 ) ) @ SV93 )
| ~ ( in @ SY542 @ SY540 ) )
| ~ ( in @ ( sK38_D @ SY541 @ SY540 @ SV93 ) @ SY541 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SY541 @ SY540 @ SV93 ) @ ( sK38_D @ SY541 @ SY540 @ SV93 ) ) @ SV93 )
| ~ ( in @ ( sK39_SY411 @ SY541 @ SY540 @ SV93 ) @ SY540 ) )
| ( in @ ( sK38_D @ SY541 @ SY540 @ SV93 ) @ SY541 ) ) )
| ( SY541
= ( relation_image @ SV93 @ SY540 ) ) ) )
= $true )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1622]) ).
thf(1788,plain,
! [SV93: $i] :
( ( ( ! [SY543: $i,SY544: $i] :
( ( SY544
!= ( relation_image @ SV93 @ SY543 ) )
| ~ ( ~ ! [SY545: $i] :
( ! [SY546: $i] :
( ~ ( in @ ( ordered_pair @ SY546 @ SY545 ) @ SV93 )
| ~ ( in @ SY546 @ SY543 ) )
| ( in @ SY545 @ SY544 ) )
| ~ ! [SY547: $i] :
( ~ ( in @ SY547 @ SY544 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SY547 @ SY544 @ SY543 @ SV93 ) @ SY547 ) @ SV93 )
| ~ ( in @ ( sK37_E @ SY547 @ SY544 @ SY543 @ SV93 ) @ SY543 ) ) ) ) ) )
= $true )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1623]) ).
thf(1789,plain,
! [SV282: $i,SV94: $i,SV326: $i] :
( ( ~ ( relation @ SV326 )
| ! [SY889: $i] :
( ~ ( in @ SY889 @ ( relation_rng @ SV326 ) )
| ~ ( in @ ( ordered_pair @ SV94 @ SY889 ) @ SV326 )
| ~ ( in @ SY889 @ SV282 ) )
| ( in @ SV94 @ ( relation_inverse_image @ SV326 @ SV282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1624]) ).
thf(1790,plain,
! [SV283: $i,SV94: $i,SV327: $i] :
( ( ~ ( relation @ SV327 )
| ~ ( in @ SV94 @ ( relation_inverse_image @ SV327 @ SV283 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK51_D @ SV327 @ SV283 @ SV94 ) @ ( relation_rng @ SV327 ) )
| ~ ( in @ ( ordered_pair @ SV94 @ ( sK51_D @ SV327 @ SV283 @ SV94 ) ) @ SV327 ) )
| ~ ( in @ ( sK51_D @ SV327 @ SV283 @ SV94 ) @ SV283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1625]) ).
thf(1791,plain,
! [SV95: $i,SV175: $i] :
( ( ( relation @ SV175 )
= $false )
| ( ( function @ SV175 )
= $false )
| ( ( ~ ( ~ ! [SY731: $i] :
( ~ ( function @ SY731 )
| ~ ( relation @ SY731 )
| ~ ( in @ SV95 @ ( relation_dom @ SY731 ) )
| ~ ( in @ ( apply @ SY731 @ SV95 ) @ ( relation_dom @ SV175 ) )
| ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY731 @ SV175 ) ) ) )
| ~ ~ ( ~ ! [SY732: $i] :
( ~ ( function @ SY732 )
| ~ ( relation @ SY732 )
| ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY732 @ SV175 ) ) )
| ( in @ SV95 @ ( relation_dom @ SY732 ) ) )
| ~ ! [SY733: $i] :
( ~ ( function @ SY733 )
| ~ ( relation @ SY733 )
| ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY733 @ SV175 ) ) )
| ( in @ ( apply @ SY733 @ SV95 ) @ ( relation_dom @ SV175 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1626]) ).
thf(1792,plain,
! [SV96: $i] :
( ( ( ! [SY557: $i,SY558: $i] :
( ~ ( relation @ SY558 )
| ~ ( ~ ( ~ ( in @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ SY557 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ ( sK43_SY413 @ SY558 @ SY557 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ ( sK43_SY413 @ SY558 @ SY557 @ SV96 ) ) @ SY558 ) )
| ~ ~ ( ~ ( ( in @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ SY557 )
| ( in @ ( ordered_pair @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ ( sK43_SY413 @ SY558 @ SY557 @ SV96 ) ) @ SY558 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ ( sK43_SY413 @ SY558 @ SY557 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK42_D @ SY558 @ SY557 @ SV96 ) @ ( sK43_SY413 @ SY558 @ SY557 @ SV96 ) ) @ SY558 ) ) ) )
| ( SY558
= ( relation_dom_restriction @ SV96 @ SY557 ) ) ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1627]) ).
thf(1793,plain,
! [SV96: $i] :
( ( ( ! [SY559: $i,SY560: $i] :
( ~ ( relation @ SY560 )
| ( SY560
!= ( relation_dom_restriction @ SV96 @ SY559 ) )
| ~ ( ~ ! [SY561: $i,SY562: $i] :
( ~ ( in @ SY561 @ SY559 )
| ~ ( in @ ( ordered_pair @ SY561 @ SY562 ) @ SV96 )
| ( in @ ( ordered_pair @ SY561 @ SY562 ) @ SY560 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY560 )
| ( in @ SX3 @ SY559 ) )
| ~ ! [SY565: $i,SY566: $i] :
( ~ ( in @ ( ordered_pair @ SY565 @ SY566 ) @ SY560 )
| ( in @ ( ordered_pair @ SY565 @ SY566 ) @ SV96 ) ) ) ) ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1628]) ).
thf(1794,plain,
! [SV284: $i,SV213: $i] :
( ( ( ~ ( empty @ SV213 )
| ~ ( relation @ SV284 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV284 @ SV213 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1629]) ).
thf(1795,plain,
! [SV285: $i,SV214: $i] :
( ( ( ~ ( empty @ SV214 )
| ~ ( relation @ SV285 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV285 @ SV214 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1630]) ).
thf(1796,plain,
! [SV97: $i] :
( ( ( ! [SY567: $i] :
( ~ ( relation @ SY567 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SY567 @ SV97 ) @ ( sK12_SY396 @ SY567 @ SV97 ) ) @ SY567 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SY567 @ SV97 ) @ ( sK11_C @ SY567 @ SV97 ) ) @ SV97 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_C @ SY567 @ SV97 ) @ ( sK12_SY396 @ SY567 @ SV97 ) ) @ SY567 )
| ( in @ ( ordered_pair @ ( sK12_SY396 @ SY567 @ SV97 ) @ ( sK11_C @ SY567 @ SV97 ) ) @ SV97 ) ) )
| ( SY567
= ( relation_inverse @ SV97 ) ) ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1631]) ).
thf(1797,plain,
! [SV97: $i] :
( ( ( ! [SY568: $i] :
( ~ ( relation @ SY568 )
| ( SY568
!= ( relation_inverse @ SV97 ) )
| ~ ( ~ ! [SY569: $i,SY570: $i] :
( ~ ( in @ ( ordered_pair @ SY569 @ SY570 ) @ SY568 )
| ( in @ ( ordered_pair @ SY570 @ SY569 ) @ SV97 ) )
| ~ ! [SY571: $i,SY572: $i] :
( ~ ( in @ ( ordered_pair @ SY572 @ SY571 ) @ SV97 )
| ( in @ ( ordered_pair @ SY571 @ SY572 ) @ SY568 ) ) ) ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1632]) ).
thf(1798,plain,
! [SV98: $i] :
( ( ( ! [SY573: $i] :
( ~ ( ~ ( ! [SY574: $i] :
~ ( in @ ( ordered_pair @ SY574 @ ( sK60_C @ SY573 @ SV98 ) ) @ SV98 )
| ~ ( in @ ( sK60_C @ SY573 @ SV98 ) @ SY573 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK61_SY417 @ SY573 @ SV98 ) @ ( sK60_C @ SY573 @ SV98 ) ) @ SV98 )
| ( in @ ( sK60_C @ SY573 @ SV98 ) @ SY573 ) ) )
| ( SY573
= ( relation_rng @ SV98 ) ) ) )
= $true )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1633]) ).
thf(1799,plain,
! [SV98: $i] :
( ( ( ! [SY575: $i] :
( ( SY575
!= ( relation_rng @ SV98 ) )
| ~ ( ~ ! [SY576: $i] :
( ! [SY577: $i] :
~ ( in @ ( ordered_pair @ SY577 @ SY576 ) @ SV98 )
| ( in @ SY576 @ SY575 ) )
| ~ ! [SY578: $i] :
( ~ ( in @ SY578 @ SY575 )
| ( in @ ( ordered_pair @ ( sK59_D @ SY578 @ SY575 @ SV98 ) @ SY578 ) @ SV98 ) ) ) ) )
= $true )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1634]) ).
thf(1800,plain,
! [SV99: $i,SV176: $i] :
( ( ( ~ ( in @ ( sK4_C @ SV176 @ SV99 ) @ SV99 )
| ~ ( in @ ( sK4_C @ SV176 @ SV99 ) @ SV176 ) )
= $true )
| ( ( SV99 = SV176 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1635]) ).
thf(1801,plain,
! [SV99: $i,SV176: $i] :
( ( ( ( in @ ( sK4_C @ SV176 @ SV99 ) @ SV99 )
| ( in @ ( sK4_C @ SV176 @ SV99 ) @ SV176 ) )
= $true )
| ( ( SV99 = SV176 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1636]) ).
thf(1802,plain,
! [SV100: $i,SV286: $i,SV328: $i] :
( ( ~ ( function @ SV328 )
| ~ ( relation @ SV328 )
| ( SV286
!= ( apply @ SV328 @ SV100 ) )
| ~ ( in @ SV100 @ ( relation_dom @ SV328 ) )
| ( in @ ( ordered_pair @ SV100 @ SV286 ) @ SV328 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(1803,plain,
! [SV100: $i] :
( ( ~ ! [SY582: $i,SY583: $i] :
( ~ ( function @ SY583 )
| ~ ( relation @ SY583 )
| ~ ( in @ ( ordered_pair @ SV100 @ SY582 ) @ SY583 )
| ( SY582
= ( apply @ SY583 @ SV100 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1638]) ).
thf(1804,plain,
! [SV100: $i] :
( ( ~ ! [SY584: $i,SY585: $i] :
( ~ ( function @ SY585 )
| ~ ( relation @ SY585 )
| ~ ( in @ ( ordered_pair @ SV100 @ SY584 ) @ SY585 )
| ( in @ SV100 @ ( relation_dom @ SY585 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1638]) ).
thf(1805,plain,
! [SV101: $i,SV215: $i] :
( ( ( relation @ SV215 )
= $false )
| ( ( ~ ( ~ ! [SY778: $i] :
( ~ ( relation @ SY778 )
| ~ ( ~ ( ! [SY779: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY778 @ SV215 @ SV101 ) @ SY779 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY779 @ ( sK9_SY391 @ SY778 @ SV215 @ SV101 ) ) @ SV215 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SY778 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SY778 @ SV215 @ SV101 ) ) @ SY778 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY778 @ SV215 @ SV101 ) @ ( sK10_SY395 @ SY778 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SY778 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SY778 @ SV215 @ SV101 ) ) @ SV215 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SY778 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SY778 @ SV215 @ SV101 ) ) @ SY778 ) ) )
| ( SY778
= ( relation_composition @ SV101 @ SV215 ) ) )
| ~ ! [SY780: $i] :
( ~ ( relation @ SY780 )
| ( SY780
!= ( relation_composition @ SV101 @ SV215 ) )
| ~ ( ~ ! [SY781: $i,SY782: $i] :
( ! [SY783: $i] :
( ~ ( in @ ( ordered_pair @ SY781 @ SY783 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY783 @ SY782 ) @ SV215 ) )
| ( in @ ( ordered_pair @ SY781 @ SY782 ) @ SY780 ) )
| ~ ! [SY784: $i,SY785: $i] :
( ~ ( in @ ( ordered_pair @ SY784 @ SY785 ) @ SY780 )
| ~ ( ~ ( in @ ( ordered_pair @ SY784 @ ( sK7_F @ SY785 @ SY784 @ SY780 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY785 @ SY784 @ SY780 @ SV215 @ SV101 ) @ SY785 ) @ SV215 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1639]) ).
thf(1806,plain,
! [SV177: $i,SV329: $i,SV102: $i] :
( ( ! [SY890: $i] :
( ~ ( in @ SV102 @ SV329 )
| ~ ( in @ SV177 @ SY890 )
| ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SV329 @ SY890 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(1807,plain,
! [SV177: $i,SV102: $i] :
( ( ~ ! [SY736: $i] :
( ! [SY737: $i] :
~ ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SY736 @ SY737 ) )
| ( in @ SV102 @ SY736 ) )
| ~ ! [SY738: $i,SY739: $i] :
( ~ ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SY738 @ SY739 ) )
| ( in @ SV177 @ SY739 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1641]) ).
thf(1808,plain,
! [SV216: $i] :
( ( ( relation @ SV216 )
= $false )
| ( ( ( ( relation_dom @ SV216 )
!= empty_set )
| ( SV216 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1642]) ).
thf(1809,plain,
! [SV217: $i] :
( ( ( relation @ SV217 )
= $false )
| ( ( ( ( relation_rng @ SV217 )
!= empty_set )
| ( SV217 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1643]) ).
thf(1810,plain,
! [SV103: $i,SV287: $i] :
( ( ( ~ ( subset @ SV287 @ ( sK2_B @ SV103 ) )
| ( are_equipotent @ SV287 @ ( sK2_B @ SV103 ) ) )
= $true )
| ( ( in @ SV287 @ ( sK2_B @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1644]) ).
thf(1811,plain,
! [SV103: $i] :
( ( ~ ! [SY603: $i] :
( ~ ( ~ ! [SY604: $i] :
( ~ ( subset @ SY604 @ SY603 )
| ( in @ SY604 @ ( sK3_SY386 @ SY603 @ SV103 ) ) )
| ~ ( in @ ( sK3_SY386 @ SY603 @ SV103 ) @ ( sK2_B @ SV103 ) ) )
| ~ ( in @ SY603 @ ( sK2_B @ SV103 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1645]) ).
thf(1812,plain,
! [SV103: $i] :
( ( ~ ~ ( ~ ! [SY605: $i,SY606: $i] :
( ~ ( in @ SY605 @ ( sK2_B @ SV103 ) )
| ~ ( subset @ SY606 @ SY605 )
| ( in @ SY606 @ ( sK2_B @ SV103 ) ) )
| ~ ( in @ SV103 @ ( sK2_B @ SV103 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1645]) ).
thf(1813,plain,
! [SV218: $i] :
( ( ( ~ ( function @ SV218 ) )
= $true )
| ( ( ~ ( relation @ SV218 ) )
= $true )
| ( ( function @ ( function_inverse @ SV218 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1646]) ).
thf(1814,plain,
! [SV219: $i] :
( ( ( ~ ( function @ SV219 ) )
= $true )
| ( ( ~ ( relation @ SV219 ) )
= $true )
| ( ( relation @ ( function_inverse @ SV219 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1647]) ).
thf(1815,plain,
! [SV220: $i] :
( ( ( empty @ SV220 )
= $false )
| ( ( empty @ ( relation_inverse @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1648]) ).
thf(1816,plain,
! [SV221: $i] :
( ( ( empty @ SV221 )
= $false )
| ( ( relation @ ( relation_inverse @ SV221 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1649]) ).
thf(1817,plain,
! [SV222: $i] :
( ( ( ~ ! [SY786: $i,SY787: $i] :
( ( sK69_B @ SV222 )
!= ( ordered_pair @ SY786 @ SY787 ) )
| ~ ( in @ ( sK69_B @ SV222 ) @ SV222 ) )
= $false )
| ( ( relation @ SV222 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1650]) ).
thf(1818,plain,
! [SV223: $i] :
( ( ( relation @ SV223 )
= $false )
| ( ( ! [SY788: $i] :
( ( SY788
= ( ordered_pair @ ( sK67_C @ SY788 @ SV223 ) @ ( sK68_SY421 @ SY788 @ SV223 ) ) )
| ~ ( in @ SY788 @ SV223 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1651]) ).
thf(1819,plain,
! [SV104: $i] :
( ( ( ! [SY607: $i] :
( ~ ( relation @ SY607 )
| ~ ( subset @ SV104 @ SY607 )
| ( subset @ ( relation_dom @ SV104 ) @ ( relation_dom @ SY607 ) ) ) )
= $true )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1652]) ).
thf(1820,plain,
! [SV104: $i] :
( ( ( ! [SY608: $i] :
( ~ ( relation @ SY608 )
| ~ ( subset @ SV104 @ SY608 )
| ( subset @ ( relation_rng @ SV104 ) @ ( relation_rng @ SY608 ) ) ) )
= $true )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1653]) ).
thf(1821,plain,
! [SV288: $i,SV105: $i,SV330: $i] :
( ( ~ ( relation @ SV330 )
| ~ ( in @ SV105 @ SV288 )
| ~ ( in @ SV105 @ ( relation_rng @ SV330 ) )
| ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SV288 @ SV330 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(1822,plain,
! [SV105: $i] :
( ( ~ ! [SY611: $i,SY612: $i] :
( ~ ( relation @ SY612 )
| ~ ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SY611 @ SY612 ) ) )
| ( in @ SV105 @ SY611 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1655]) ).
thf(1823,plain,
! [SV105: $i] :
( ( ~ ! [SY613: $i,SY614: $i] :
( ~ ( relation @ SY614 )
| ~ ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SY613 @ SY614 ) ) )
| ( in @ SV105 @ ( relation_rng @ SY614 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1655]) ).
thf(1824,plain,
( ( empty @ sK56_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1656]) ).
thf(1825,plain,
( ( relation @ sK56_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1657]) ).
thf(1826,plain,
! [SV289: $i,SV331: $i,SV106: $i] :
( ( ~ ( in @ SV106 @ SV331 )
| ~ ( in @ SV289 @ SV331 )
| ( subset @ ( unordered_pair @ SV106 @ SV289 ) @ SV331 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1658]) ).
thf(1827,plain,
! [SV106: $i] :
( ( ~ ! [SY617: $i,SY618: $i] :
( ~ ( subset @ ( unordered_pair @ SV106 @ SY617 ) @ SY618 )
| ( in @ SV106 @ SY618 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1659]) ).
thf(1828,plain,
! [SV106: $i] :
( ( ~ ! [SY619: $i,SY620: $i] :
( ~ ( subset @ ( unordered_pair @ SV106 @ SY619 ) @ SY620 )
| ( in @ SY619 @ SY620 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1659]) ).
thf(1829,plain,
! [SV178: $i,SV332: $i,SV107: $i] :
( ( ! [SY891: $i] :
( ~ ( relation @ SY891 )
| ~ ( in @ SV107 @ SV332 )
| ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ SY891 )
| ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SV332 ) @ SY891 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1660]) ).
thf(1830,plain,
! [SV178: $i,SV107: $i] :
( ( ~ ! [SY742: $i,SY743: $i] :
( ~ ( relation @ SY743 )
| ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SY742 ) @ SY743 ) )
| ( in @ SV107 @ SY742 ) )
| ~ ! [SY744: $i,SY745: $i] :
( ~ ( relation @ SY745 )
| ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SY744 ) @ SY745 ) )
| ( in @ ( ordered_pair @ SV107 @ SV178 ) @ SY745 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1661]) ).
thf(1831,plain,
! [SV108: $i] :
( ( ( ! [SY628: $i] :
( ~ ( relation @ SY628 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SY628 @ SV108 ) @ ( sK20_SY399 @ SY628 @ SV108 ) ) @ SV108 )
| ~ ~ ( in @ ( ordered_pair @ ( sK19_C @ SY628 @ SV108 ) @ ( sK20_SY399 @ SY628 @ SV108 ) ) @ SY628 ) )
| ( subset @ SV108 @ SY628 ) ) )
= $true )
| ( ( relation @ SV108 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1662]) ).
thf(1832,plain,
! [SV108: $i] :
( ( ( ! [SY629: $i] :
( ~ ( relation @ SY629 )
| ~ ( subset @ SV108 @ SY629 )
| ! [SY630: $i,SY631: $i] :
( ~ ( in @ ( ordered_pair @ SY630 @ SY631 ) @ SV108 )
| ( in @ ( ordered_pair @ SY630 @ SY631 ) @ SY629 ) ) ) )
= $true )
| ( ( relation @ SV108 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1663]) ).
thf(1833,plain,
! [SV228: $i,SV290: $i] :
( ( ( ~ ( ~ ( ( ( sK30_C @ SV290 @ SV228 )
!= SV228 )
| ~ ( in @ ( sK30_C @ SV290 @ SV228 ) @ SV290 ) )
| ~ ( ( ( sK30_C @ SV290 @ SV228 )
= SV228 )
| ( in @ ( sK30_C @ SV290 @ SV228 ) @ SV290 ) ) ) )
= $true )
| ( ( SV290
= ( singleton @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1664]) ).
thf(1834,plain,
! [SV229: $i,SV291: $i] :
( ( ( ( SV291
!= ( singleton @ SV229 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY843: $i] :
( ( SY843 != SV229 )
| ( in @ SY843 @ SV291 ) )
| ~ ! [SY844: $i] :
( ~ ( in @ SY844 @ SV291 )
| ( SY844 = SV229 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1665]) ).
thf(1835,plain,
! [SV292: $i,SV109: $i,SV333: $i] :
( ( ~ ( relation @ SV333 )
| ~ ( in @ ( ordered_pair @ SV109 @ SV292 ) @ SV333 )
| ( in @ SV109 @ ( relation_dom @ SV333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1666]) ).
thf(1836,plain,
! [SV293: $i,SV109: $i,SV334: $i] :
( ( ~ ( relation @ SV334 )
| ~ ( in @ ( ordered_pair @ SV109 @ SV293 ) @ SV334 )
| ( in @ SV293 @ ( relation_rng @ SV334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1667]) ).
thf(1837,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1668]) ).
thf(1838,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1669]) ).
thf(1839,plain,
! [SV230: $i] :
( ( ( ~ ( empty @ SV230 )
| ~ ( relation @ SV230 ) )
= $true )
| ( ( ~ ( function @ SV230 ) )
= $true )
| ( ( one_to_one @ SV230 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1670]) ).
thf(1840,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1671]) ).
thf(1841,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1672]) ).
thf(1842,plain,
! [SV110: $i] :
( ( ( ~ ( one_to_one @ SV110 ) )
= $true )
| ( ( ~ ( ~ ! [SY636: $i] :
( ~ ( function @ SY636 )
| ~ ( relation @ SY636 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SY636 @ SV110 )
= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ( ( sK70_C @ SY636 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY636 @ SV110 )
= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY636 @ SV110 )
= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ( ( sK71_SY424 @ SY636 @ SV110 )
!= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK70_C @ SY636 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK71_SY424 @ SY636 @ SV110 )
!= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY636 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK70_C @ SY636 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SY636 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SY636 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK71_SY424 @ SY636 @ SV110 )
!= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ( ( relation_dom @ SY636 )
!= ( relation_rng @ SV110 ) )
| ( SY636
= ( function_inverse @ SV110 ) ) )
| ~ ~ ( ~ ! [SY637: $i] :
( ~ ( function @ SY637 )
| ~ ( relation @ SY637 )
| ( SY637
!= ( function_inverse @ SV110 ) )
| ~ ( ~ ~ ( ~ ! [SY638: $i,SY639: $i] :
( ( SY639
!= ( apply @ SY637 @ SY638 ) )
| ~ ( in @ SY638 @ ( relation_rng @ SV110 ) )
| ( SY638
= ( apply @ SV110 @ SY639 ) ) )
| ~ ! [SY640: $i,SY641: $i] :
( ( SY641
!= ( apply @ SY637 @ SY640 ) )
| ~ ( in @ SY640 @ ( relation_rng @ SV110 ) )
| ( in @ SY641 @ ( relation_dom @ SV110 ) ) ) )
| ~ ~ ( ~ ! [SY642: $i,SY643: $i] :
( ( SY642
!= ( apply @ SV110 @ SY643 ) )
| ~ ( in @ SY643 @ ( relation_dom @ SV110 ) )
| ( SY643
= ( apply @ SY637 @ SY642 ) ) )
| ~ ! [SY644: $i] :
( ! [SY645: $i] :
( ( SY644
!= ( apply @ SV110 @ SY645 ) )
| ~ ( in @ SY645 @ ( relation_dom @ SV110 ) ) )
| ( in @ SY644 @ ( relation_rng @ SV110 ) ) ) ) ) )
| ~ ! [SY646: $i] :
( ~ ( function @ SY646 )
| ~ ( relation @ SY646 )
| ( SY646
!= ( function_inverse @ SV110 ) )
| ( ( relation_dom @ SY646 )
= ( relation_rng @ SV110 ) ) ) ) ) )
= $true )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1673]) ).
thf(1843,plain,
! [SV231: $i] :
( ( ( empty @ SV231 )
= $false )
| ( ( empty @ ( relation_dom @ SV231 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1674]) ).
thf(1844,plain,
! [SV232: $i] :
( ( ( empty @ SV232 )
= $false )
| ( ( relation @ ( relation_dom @ SV232 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1675]) ).
thf(1845,plain,
! [SV294: $i,SV233: $i] :
( ( ( ( SV233 = SV294 )
| ~ ( subset @ SV233 @ SV294 ) )
= $true )
| ( ( proper_subset @ SV233 @ SV294 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1676]) ).
thf(1846,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1677]) ).
thf(1847,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1678]) ).
thf(1848,plain,
! [SV234: $i,SV295: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_C @ SV295 @ SV234 ) @ SV234 )
| ~ ~ ( in @ ( sK18_C @ SV295 @ SV234 ) @ SV295 ) ) )
= $true )
| ( ( subset @ SV234 @ SV295 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1679]) ).
thf(1849,plain,
! [SV296: $i,SV235: $i] :
( ( ( ~ ( subset @ SV235 @ SV296 ) )
= $true )
| ( ( ! [SY847: $i] :
( ~ ( in @ SY847 @ SV235 )
| ( in @ SY847 @ SV296 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1680]) ).
thf(1850,plain,
! [SV297: $i,SV236: $i] :
( ( ( disjoint @ SV236 @ SV297 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK49_C @ SV297 @ SV236 ) @ SV236 )
| ~ ( in @ ( sK49_C @ SV297 @ SV236 ) @ SV297 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1681]) ).
thf(1851,plain,
! [SV298: $i,SV237: $i] :
( ( ( ! [SY848: $i] :
( ~ ( in @ SY848 @ SV237 )
| ~ ( in @ SY848 @ SV298 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV237 @ SV298 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1682]) ).
thf(1852,plain,
! [SV179: $i,SV335: $i,SV111: $i] :
( ( ! [SY892: $i] :
( ~ ( in @ SV111 @ SV335 )
| ~ ( in @ SV179 @ SY892 )
| ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SV335 @ SY892 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1683]) ).
thf(1853,plain,
! [SV179: $i,SV111: $i] :
( ( ~ ! [SY748: $i] :
( ! [SY749: $i] :
~ ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SY748 @ SY749 ) )
| ( in @ SV111 @ SY748 ) )
| ~ ! [SY750: $i,SY751: $i] :
( ~ ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SY750 @ SY751 ) )
| ( in @ SV179 @ SY751 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1684]) ).
thf(1854,plain,
! [SV336: $i,SV180: $i,SV112: $i] :
( ( ! [SY893: $i] :
( ( ordered_pair @ SV112 @ SV180 )
!= ( ordered_pair @ SV336 @ SY893 ) )
| ( SV112 = SV336 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1685]) ).
thf(1855,plain,
! [SV337: $i,SV180: $i,SV112: $i] :
( ( ! [SY894: $i] :
( ( ( ordered_pair @ SV112 @ SV180 )
!= ( ordered_pair @ SV337 @ SY894 ) )
| ( SV180 = SY894 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1686]) ).
thf(1856,plain,
! [SV113: $i] :
( ( ( ~ ~ ( ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ ( relation_dom @ SV113 ) )
| ! [SY660: $i] :
( ( SY660
!= ( apply @ SV113 @ SY659 ) )
| ( in @ ( ordered_pair @ SY659 @ SY660 ) @ SV113 ) ) )
| ~ ! [SY661: $i] :
( ~ ( in @ SY661 @ ( relation_dom @ SV113 ) )
| ! [SY662: $i] :
( ~ ( in @ ( ordered_pair @ SY661 @ SY662 ) @ SV113 )
| ( SY662
= ( apply @ SV113 @ SY661 ) ) ) ) )
| ~ ~ ( ~ ! [SY663: $i] :
( ( in @ SY663 @ ( relation_dom @ SV113 ) )
| ! [SY664: $i] :
( ( SY664
!= ( apply @ SV113 @ SY663 ) )
| ( SY664 = empty_set ) ) )
| ~ ! [SY665: $i] :
( ( in @ SY665 @ ( relation_dom @ SV113 ) )
| ! [SY666: $i] :
( ( SY666 != empty_set )
| ( SY666
= ( apply @ SV113 @ SY665 ) ) ) ) ) )
= $false )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1687]) ).
thf(1857,plain,
! [SV238: $i] :
( ( ( relation @ SV238 )
= $false )
| ( ( ( relation_rng @ SV238 )
= ( relation_dom @ ( relation_inverse @ SV238 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1688]) ).
thf(1858,plain,
! [SV239: $i] :
( ( ( relation @ SV239 )
= $false )
| ( ( ( relation_dom @ SV239 )
= ( relation_rng @ ( relation_inverse @ SV239 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1689]) ).
thf(1859,plain,
! [SV299: $i,SV240: $i] :
( ( ( ~ ( in @ SV240 @ SV299 ) )
= $true )
| ( ( subset @ ( singleton @ SV240 ) @ SV299 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1690]) ).
thf(1860,plain,
! [SV300: $i,SV241: $i] :
( ( ( ~ ( subset @ ( singleton @ SV241 ) @ SV300 ) )
= $true )
| ( ( in @ SV241 @ SV300 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1691]) ).
thf(1861,plain,
! [SV243: $i] :
( ( ( SV243 = empty_set )
= $false )
| ( ( ! [SY802: $i] :
~ ( in @ SY802 @ SV243 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1693]) ).
thf(1862,plain,
! [SV114: $i,SV301: $i,SV338: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV338 )
| ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV114 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV338 )
| ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV301 ) ) )
| ~ ( ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV338 )
| ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV114 )
| ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV301 ) ) )
| ( SV338
= ( set_union2 @ SV114 @ SV301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1694]) ).
thf(1863,plain,
! [SV302: $i,SV114: $i,SV339: $i] :
( ( ( SV339
!= ( set_union2 @ SV114 @ SV302 ) )
| ~ ( ~ ! [SY895: $i] :
( ~ ( in @ SY895 @ SV339 )
| ( in @ SY895 @ SV114 )
| ( in @ SY895 @ SV302 ) )
| ~ ~ ( ~ ! [SY896: $i] :
( ~ ( in @ SY896 @ SV114 )
| ( in @ SY896 @ SV339 ) )
| ~ ! [SY897: $i] :
( ~ ( in @ SY897 @ SV302 )
| ( in @ SY897 @ SV339 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1695]) ).
thf(1864,plain,
! [SV244: $i] :
( ( ( empty @ SV244 )
= $false )
| ( ( empty @ ( relation_rng @ SV244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1696]) ).
thf(1865,plain,
! [SV245: $i] :
( ( ( empty @ SV245 )
= $false )
| ( ( relation @ ( relation_rng @ SV245 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1697]) ).
thf(1866,plain,
! [SV303: $i,SV115: $i,SV340: $i] :
( ( ~ ( relation @ SV340 )
| ~ ( in @ ( ordered_pair @ SV115 @ SV303 ) @ SV340 )
| ( in @ SV115 @ ( relation_field @ SV340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1698]) ).
thf(1867,plain,
! [SV304: $i,SV115: $i,SV341: $i] :
( ( ~ ( relation @ SV341 )
| ~ ( in @ ( ordered_pair @ SV115 @ SV304 ) @ SV341 )
| ( in @ SV304 @ ( relation_field @ SV341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1699]) ).
thf(1868,plain,
! [SV246: $i] :
( ( ( relation @ SV246 )
= $false )
| ( ( ( ( relation_dom @ SV246 )
!= empty_set )
| ( ( relation_rng @ SV246 )
= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1700]) ).
thf(1869,plain,
! [SV247: $i] :
( ( ( relation @ SV247 )
= $false )
| ( ( ( ( relation_rng @ SV247 )
!= empty_set )
| ( ( relation_dom @ SV247 )
= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1701]) ).
thf(1870,plain,
! [SV305: $i,SV248: $i] :
( ( ( ~ ( subset @ SV248 @ ( singleton @ SV305 ) ) )
= $true )
| ( ( ( SV248 = empty_set )
| ( SV248
= ( singleton @ SV305 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1702]) ).
thf(1871,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1703]) ).
thf(1872,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1704]) ).
thf(1873,plain,
! [SV116: $i,SV306: $i,SV342: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV116 )
| ~ ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV306 )
| ~ ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV342 ) )
| ~ ~ ( ~ ( ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV116 )
| ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV342 ) )
| ~ ( ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV306 )
| ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV342 ) ) ) )
| ( SV342
= ( set_intersection2 @ SV116 @ SV306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1705]) ).
thf(1874,plain,
! [SV307: $i,SV116: $i,SV343: $i] :
( ( ( SV343
!= ( set_intersection2 @ SV116 @ SV307 ) )
| ~ ( ~ ! [SY898: $i] :
( ~ ( in @ SY898 @ SV116 )
| ~ ( in @ SY898 @ SV307 )
| ( in @ SY898 @ SV343 ) )
| ~ ~ ( ~ ! [SY899: $i] :
( ~ ( in @ SY899 @ SV343 )
| ( in @ SY899 @ SV116 ) )
| ~ ! [SY900: $i] :
( ~ ( in @ SY900 @ SV343 )
| ( in @ SY900 @ SV307 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1706]) ).
thf(1875,plain,
! [SV249: $i] :
( ( ( ~ ( function @ SV249 )
| ~ ( relation @ SV249 ) )
= $true )
| ( ( ~ ( one_to_one @ SV249 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV249 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1707]) ).
thf(1876,plain,
! [SV250: $i] :
( ( ( ~ ( function @ SV250 )
| ~ ( relation @ SV250 ) )
= $true )
| ( ( ~ ( one_to_one @ SV250 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1708]) ).
thf(1877,plain,
! [SV251: $i,SV308: $i] :
( ( ( ~ ( relation @ SV308 ) )
= $true )
| ( ( ~ ( ~ ( ( ( sK44_C @ SV308 @ SV251 )
!= ( sK45_SY414 @ SV308 @ SV251 ) )
| ~ ( in @ ( sK44_C @ SV308 @ SV251 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 ) )
| ~ ~ ( ~ ( ( ( sK44_C @ SV308 @ SV251 )
= ( sK45_SY414 @ SV308 @ SV251 ) )
| ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 ) )
| ~ ( ( in @ ( sK44_C @ SV308 @ SV251 ) @ SV251 )
| ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 ) ) ) )
| ( SV308
= ( identity_relation @ SV251 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1709]) ).
thf(1878,plain,
! [SV252: $i,SV309: $i] :
( ( ( ~ ( relation @ SV309 ) )
= $true )
| ( ( ( SV309
!= ( identity_relation @ SV252 ) )
| ~ ( ~ ! [SY861: $i,SY862: $i] :
( ( SY861 != SY862 )
| ~ ( in @ SY861 @ SV252 )
| ( in @ ( ordered_pair @ SY861 @ SY862 ) @ SV309 ) )
| ~ ~ ( ~ ! [SY863: $i,SY864: $i] :
( ~ ( in @ ( ordered_pair @ SY863 @ SY864 ) @ SV309 )
| ( SY863 = SY864 ) )
| ~ ! [SY865: $i] :
( ! [SY866: $i] :
~ ( in @ ( ordered_pair @ SY865 @ SY866 ) @ SV309 )
| ( in @ SY865 @ SV252 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1710]) ).
thf(1879,plain,
( ( function @ sK54_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1711]) ).
thf(1880,plain,
( ( relation @ sK54_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1712]) ).
thf(1881,plain,
! [SV310: $i,SV117: $i,SV344: $i] :
( ( ~ ( relation @ SV344 )
| ~ ( in @ SV117 @ SV310 )
| ~ ( in @ SV117 @ ( relation_dom @ SV344 ) )
| ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SV344 @ SV310 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1713]) ).
thf(1882,plain,
! [SV117: $i] :
( ( ~ ! [SY687: $i,SY688: $i] :
( ~ ( relation @ SY688 )
| ~ ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SY688 @ SY687 ) ) )
| ( in @ SV117 @ SY687 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1714]) ).
thf(1883,plain,
! [SV117: $i] :
( ( ~ ! [SY689: $i,SY690: $i] :
( ~ ( relation @ SY690 )
| ~ ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SY690 @ SY689 ) ) )
| ( in @ SV117 @ ( relation_dom @ SY690 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1714]) ).
thf(1884,plain,
! [SV253: $i,SV311: $i] :
( ( ( ~ ( function @ SV311 )
| ~ ( relation @ SV311 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK50_C @ SV311 @ SV253 ) @ SV253 )
| ~ ( ( ( apply @ SV311 @ ( sK50_C @ SV311 @ SV253 ) )
!= ( sK50_C @ SV311 @ SV253 ) ) ) )
| ( ( relation_dom @ SV311 )
!= SV253 )
| ( SV311
= ( identity_relation @ SV253 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1715]) ).
thf(1885,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)],[1716]) ).
thf(1886,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1717]) ).
thf(1887,plain,
! [SV345: $i,SV312: $i,SV118: $i] :
( ( ~ ( ~ ( ! [SY901: $i,SY902: $i] :
( ~ ( in @ SY901 @ SV118 )
| ~ ( in @ SY902 @ SV312 )
| ( ( sK23_D @ SV345 @ SV312 @ SV118 )
!= ( ordered_pair @ SY901 @ SY902 ) ) )
| ~ ( in @ ( sK23_D @ SV345 @ SV312 @ SV118 ) @ SV345 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY403 @ SV345 @ SV312 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK25_SY405 @ SV345 @ SV312 @ SV118 ) @ SV312 ) )
| ( ( sK23_D @ SV345 @ SV312 @ SV118 )
!= ( ordered_pair @ ( sK24_SY403 @ SV345 @ SV312 @ SV118 ) @ ( sK25_SY405 @ SV345 @ SV312 @ SV118 ) ) ) )
| ( in @ ( sK23_D @ SV345 @ SV312 @ SV118 ) @ SV345 ) ) )
| ( SV345
= ( cartesian_product2 @ SV118 @ SV312 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1718]) ).
thf(1888,plain,
! [SV313: $i,SV118: $i,SV346: $i] :
( ( ( SV346
!= ( cartesian_product2 @ SV118 @ SV313 ) )
| ~ ( ~ ! [SY903: $i] :
( ! [SY873: $i,SY874: $i] :
( ~ ( in @ SY873 @ SV118 )
| ~ ( in @ SY874 @ SV313 )
| ( SY903
!= ( ordered_pair @ SY873 @ SY874 ) ) )
| ( in @ SY903 @ SV346 ) )
| ~ ! [SY906: $i] :
( ~ ( in @ SY906 @ SV346 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY906 @ SV346 @ SV313 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK22_SY400 @ SY906 @ SV346 @ SV313 @ SV118 ) @ SV313 ) )
| ( SY906
!= ( ordered_pair @ ( sK21_E @ SY906 @ SV346 @ SV313 @ SV118 ) @ ( sK22_SY400 @ SY906 @ SV346 @ SV313 @ SV118 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1719]) ).
thf(1889,plain,
! [SV314: $i,SV119: $i] :
( ( ( ~ ( subset @ SV119 @ SV314 ) )
= $true )
| ( ( ! [SY876: $i] : ( subset @ ( cartesian_product2 @ SV119 @ SY876 ) @ ( cartesian_product2 @ SV314 @ SY876 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1720]) ).
thf(1890,plain,
! [SV315: $i,SV119: $i] :
( ( ( ~ ( subset @ SV119 @ SV315 ) )
= $true )
| ( ( ! [SY877: $i] : ( subset @ ( cartesian_product2 @ SY877 @ SV119 ) @ ( cartesian_product2 @ SY877 @ SV315 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1721]) ).
thf(1891,plain,
! [SV254: $i,SV316: $i] :
( ( ( ~ ( ~ ( ! [SY878: $i] :
( ~ ( in @ ( sK15_C @ SV316 @ SV254 ) @ SY878 )
| ~ ( in @ SY878 @ SV254 ) )
| ~ ( in @ ( sK15_C @ SV316 @ SV254 ) @ SV316 ) )
| ~ ( ~ ( ~ ( in @ ( sK15_C @ SV316 @ SV254 ) @ ( sK16_SY398 @ SV316 @ SV254 ) )
| ~ ( in @ ( sK16_SY398 @ SV316 @ SV254 ) @ SV254 ) )
| ( in @ ( sK15_C @ SV316 @ SV254 ) @ SV316 ) ) ) )
= $true )
| ( ( SV316
= ( union @ SV254 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1722]) ).
thf(1892,plain,
! [SV255: $i,SV317: $i] :
( ( ( ( SV317
!= ( union @ SV255 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY879: $i] :
( ! [SY817: $i] :
( ~ ( in @ SY879 @ SY817 )
| ~ ( in @ SY817 @ SV255 ) )
| ( in @ SY879 @ SV317 ) )
| ~ ! [SY881: $i] :
( ~ ( in @ SY881 @ SV317 )
| ~ ( ~ ( in @ SY881 @ ( sK14_D @ SY881 @ SV317 @ SV255 ) )
| ~ ( in @ ( sK14_D @ SY881 @ SV317 @ SV255 ) @ SV255 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1723]) ).
thf(1893,plain,
! [SV318: $i,SV256: $i] :
( ( ( ( ( set_difference @ SV256 @ SV318 )
!= empty_set ) )
= $true )
| ( ( subset @ SV256 @ SV318 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1724]) ).
thf(1894,plain,
! [SV319: $i,SV257: $i] :
( ( ( ~ ( subset @ SV257 @ SV319 ) )
= $true )
| ( ( ( set_difference @ SV257 @ SV319 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1725]) ).
thf(1895,plain,
! [SV120: $i] :
( ( ( ! [SY705: $i] :
( ~ ( relation @ SY705 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SY705 @ SV120 ) @ ( sK66_SY420 @ SY705 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SY705 @ SV120 ) @ ( sK66_SY420 @ SY705 @ SV120 ) ) @ SY705 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_C @ SY705 @ SV120 ) @ ( sK66_SY420 @ SY705 @ SV120 ) ) @ SV120 )
| ( in @ ( ordered_pair @ ( sK65_C @ SY705 @ SV120 ) @ ( sK66_SY420 @ SY705 @ SV120 ) ) @ SY705 ) ) )
| ( SV120 = SY705 ) ) )
= $true )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1726]) ).
thf(1896,plain,
! [SV120: $i] :
( ( ( ! [SY706: $i] :
( ~ ( relation @ SY706 )
| ( SV120 != SY706 )
| ~ ( ~ ! [SY707: $i,SY708: $i] :
( ~ ( in @ ( ordered_pair @ SY707 @ SY708 ) @ SV120 )
| ( in @ ( ordered_pair @ SY707 @ SY708 ) @ SY706 ) )
| ~ ! [SY709: $i,SY710: $i] :
( ~ ( in @ ( ordered_pair @ SY709 @ SY710 ) @ SY706 )
| ( in @ ( ordered_pair @ SY709 @ SY710 ) @ SV120 ) ) ) ) )
= $true )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1727]) ).
thf(1897,plain,
! [SV182: $i,SV129: $i,SV11: $i] :
( ( ( subset @ SV11 @ SV129 )
= $false )
| ( ( subset @ ( relation_inverse_image @ SV182 @ SV11 ) @ ( relation_inverse_image @ SV182 @ SV129 ) )
= $true )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1729]) ).
thf(1898,plain,
! [SV193: $i,SV15: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV15 ) @ ( relation_dom @ SV193 ) ) )
= $true )
| ( ( ( relation_dom @ ( relation_composition @ SV15 @ SV193 ) )
= ( relation_dom @ SV15 ) )
= $true )
| ( ( relation @ SV193 )
= $false )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1732]) ).
thf(1899,plain,
! [SV194: $i,SV16: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV16 ) @ ( relation_rng @ SV194 ) ) )
= $true )
| ( ( ( relation_rng @ ( relation_composition @ SV194 @ SV16 ) )
= ( relation_rng @ SV16 ) )
= $true )
| ( ( relation @ SV194 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1733]) ).
thf(1900,plain,
! [SV23: $i] :
( ( ( one_to_one @ SV23 )
= $false )
| ( ( ( function_inverse @ SV23 )
= ( relation_inverse @ SV23 ) )
= $true )
| ( ( function @ SV23 )
= $false )
| ( ( relation @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1734]) ).
thf(1901,plain,
! [SV196: $i,SV183: $i,SV139: $i,SV37: $i] :
( ( ( subset @ SV37 @ SV139 )
= $false )
| ( ( ~ ( subset @ SV183 @ SV196 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV37 @ SV183 ) @ ( cartesian_product2 @ SV139 @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1738]) ).
thf(1902,plain,
! [SV141: $i,SV39: $i] :
( ( ( subset @ SV39 @ ( relation_rng @ SV141 ) )
= $false )
| ( ( SV39 = empty_set )
= $true )
| ( ( ( ( relation_inverse_image @ SV141 @ SV39 )
!= empty_set ) )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1739]) ).
thf(1903,plain,
! [SV143: $i,SV184: $i,SV41: $i] :
( ( ( subset @ SV41 @ SV184 )
= $false )
| ( ( subset @ SV41 @ SV143 )
= $false )
| ( ( subset @ SV41 @ ( set_intersection2 @ SV143 @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1740]) ).
thf(1904,plain,
! [SV42: $i,SV185: $i,SV144: $i] :
( ( ( subset @ SV144 @ SV185 )
= $false )
| ( ( subset @ SV42 @ SV144 )
= $false )
| ( ( subset @ SV42 @ SV185 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1741]) ).
thf(1905,plain,
! [SV145: $i,SV43: $i,SV347: $i] :
( ( ( ~ ( function @ SV347 )
| ~ ( relation @ SV347 )
| ~ ( in @ SV43 @ ( relation_dom @ ( relation_composition @ SV347 @ SV145 ) ) )
| ( ( apply @ ( relation_composition @ SV347 @ SV145 ) @ SV43 )
= ( apply @ SV145 @ ( apply @ SV347 @ SV43 ) ) ) )
= $true )
| ( ( function @ SV145 )
= $false )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1742]) ).
thf(1906,plain,
! [SV146: $i,SV44: $i,SV348: $i] :
( ( ( ~ ( function @ SV348 )
| ~ ( relation @ SV348 )
| ~ ( in @ SV44 @ ( relation_dom @ SV146 ) )
| ( ( apply @ ( relation_composition @ SV146 @ SV348 ) @ SV44 )
= ( apply @ SV348 @ ( apply @ SV146 @ SV44 ) ) ) )
= $true )
| ( ( function @ SV146 )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1743]) ).
thf(1907,plain,
! [SV186: $i,SV158: $i,SV59: $i] :
( ( ( subset @ SV59 @ SV158 )
= $false )
| ( ( disjoint @ SV158 @ SV186 )
= $false )
| ( ( disjoint @ SV59 @ SV186 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1744]) ).
thf(1908,plain,
! [SV62: $i,SV161: $i,SV187: $i] :
( ( ( subset @ SV187 @ SV161 )
= $false )
| ( ( subset @ SV62 @ SV161 )
= $false )
| ( ( subset @ ( set_union2 @ SV62 @ SV187 ) @ SV161 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1745]) ).
thf(1909,plain,
! [SV260: $i,SV197: $i] :
( ( ( in @ SV197 @ SV260 )
= $false )
| ( ( subset @ ( singleton @ SV197 ) @ SV260 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1747]) ).
thf(1910,plain,
! [SV261: $i,SV198: $i] :
( ( ( subset @ ( singleton @ SV198 ) @ SV261 )
= $false )
| ( ( in @ SV198 @ SV261 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1748]) ).
thf(1911,plain,
! [SV262: $i,SV199: $i] :
( ( ( subset @ SV199 @ ( singleton @ SV262 ) )
= $false )
| ( ( ( SV199 = empty_set )
| ( SV199
= ( singleton @ SV262 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1749]) ).
thf(1912,plain,
! [SV349: $i] :
( ( ( SV349 != empty_set )
| ! [SY907: $i] : ( subset @ SV349 @ ( singleton @ SY907 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1750]) ).
thf(1913,plain,
! [SV350: $i] :
( ( ! [SY908: $i] :
( ( SV350
!= ( singleton @ SY908 ) )
| ( subset @ SV350 @ ( singleton @ SY908 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1751]) ).
thf(1914,plain,
! [SV351: $i] :
( ( ( SV351 = empty_set )
| ! [SY909: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY406 @ SY909 @ SV351 ) @ SV351 )
| ~ ~ ( in @ ( sK32_C @ SY909 @ SV351 ) @ ( sK33_SY406 @ SY909 @ SV351 ) ) )
| ~ ( in @ ( sK32_C @ SY909 @ SV351 ) @ SY909 ) )
| ~ ( ! [SY910: $i] :
( ~ ( in @ SY910 @ SV351 )
| ( in @ ( sK32_C @ SY909 @ SV351 ) @ SY910 ) )
| ( in @ ( sK32_C @ SY909 @ SV351 ) @ SY909 ) ) )
| ( SY909
= ( set_meet @ SV351 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(1915,plain,
! [SV352: $i] :
( ( ( SV352 = empty_set )
| ! [SY911: $i] :
( ( SY911
!= ( set_meet @ SV352 ) )
| ~ ( ~ ! [SY912: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY912 @ SY911 @ SV352 ) @ SV352 )
| ~ ~ ( in @ SY912 @ ( sK31_D @ SY912 @ SY911 @ SV352 ) ) )
| ( in @ SY912 @ SY911 ) )
| ~ ! [SY913: $i] :
( ~ ( in @ SY913 @ SY911 )
| ! [SY914: $i] :
( ~ ( in @ SY914 @ SV352 )
| ( in @ SY913 @ SY914 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1753]) ).
thf(1916,plain,
! [SV353: $i] :
( ( ( SV353 != empty_set )
| ! [SY915: $i] :
( ( SY915
!= ( set_meet @ SV353 ) )
| ( SY915 = empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1754]) ).
thf(1917,plain,
! [SV354: $i] :
( ( ( SV354 != empty_set )
| ! [SY916: $i] :
( ( SY916 != empty_set )
| ( SY916
= ( set_meet @ SV354 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1755]) ).
thf(1918,plain,
! [SV264: $i,SV201: $i,SV355: $i] :
( ( ( ~ ( in @ SV355 @ ( set_intersection2 @ SV201 @ SV264 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV201 @ SV264 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1757]) ).
thf(1919,plain,
! [SV265: $i,SV202: $i] :
( ( ( ~ ( function @ SV202 )
| ~ ( relation @ SV202 )
| ~ ( relation @ SV265 ) )
= $true )
| ( ( ~ ( function @ SV265 ) )
= $true )
| ( ( function @ ( relation_composition @ SV202 @ SV265 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1758]) ).
thf(1920,plain,
! [SV266: $i,SV203: $i] :
( ( ( ~ ( function @ SV203 )
| ~ ( relation @ SV203 )
| ~ ( relation @ SV266 ) )
= $true )
| ( ( ~ ( function @ SV266 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV203 @ SV266 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1759]) ).
thf(1921,plain,
! [SV267: $i,SV204: $i] :
( ( ( ( set_difference @ SV204 @ SV267 )
= empty_set )
= $false )
| ( ( subset @ SV204 @ SV267 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1760]) ).
thf(1922,plain,
! [SV268: $i,SV205: $i] :
( ( ( subset @ SV205 @ SV268 )
= $false )
| ( ( ( set_difference @ SV205 @ SV268 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1761]) ).
thf(1923,plain,
! [SV269: $i,SV206: $i] :
( ( ( ~ ( empty @ SV206 ) )
= $true )
| ( ( ~ ( relation @ SV269 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV206 @ SV269 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1762]) ).
thf(1924,plain,
! [SV270: $i,SV207: $i] :
( ( ( ~ ( empty @ SV207 ) )
= $true )
| ( ( ~ ( relation @ SV270 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV207 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1763]) ).
thf(1925,plain,
! [SV271: $i,SV87: $i,SV320: $i] :
( ( ( ~ ( relation @ SV320 ) )
= $true )
| ( ( ! [SY882: $i] :
( ~ ( in @ SY882 @ ( relation_dom @ SV320 ) )
| ~ ( in @ ( ordered_pair @ SY882 @ SV87 ) @ SV320 )
| ~ ( in @ SY882 @ SV271 ) )
| ( in @ SV87 @ ( relation_image @ SV320 @ SV271 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1764]) ).
thf(1926,plain,
! [SV272: $i,SV87: $i,SV321: $i] :
( ( ( ~ ( relation @ SV321 ) )
= $true )
| ( ( ~ ( in @ SV87 @ ( relation_image @ SV321 @ SV272 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK52_D @ SV321 @ SV272 @ SV87 ) @ ( relation_dom @ SV321 ) )
| ~ ( in @ ( ordered_pair @ ( sK52_D @ SV321 @ SV272 @ SV87 ) @ SV87 ) @ SV321 ) )
| ~ ( in @ ( sK52_D @ SV321 @ SV272 @ SV87 ) @ SV272 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1765]) ).
thf(1927,plain,
! [SV273: $i,SV208: $i] :
( ( ( ~ ( subset @ SV208 @ SV273 ) )
= $true )
| ( ( ~ ( subset @ SV273 @ SV208 ) )
= $true )
| ( ( SV208 = SV273 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1766]) ).
thf(1928,plain,
! [SV356: $i] :
( ( ! [SY917: $i] :
( ( SV356 != SY917 )
| ( subset @ SV356 @ SY917 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1767]) ).
thf(1929,plain,
! [SV357: $i] :
( ( ! [SY918: $i] :
( ( SV357 != SY918 )
| ( subset @ SY918 @ SV357 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1768]) ).
thf(1930,plain,
! [SV88: $i,SV274: $i,SV322: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV88 )
| ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV274 )
| ~ ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV322 ) )
| ~ ~ ( ~ ( ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV88 )
| ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV322 ) )
| ~ ( ~ ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV274 )
| ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV322 ) ) ) ) )
= $true )
| ( ( SV322
= ( set_difference @ SV88 @ SV274 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1769]) ).
thf(1931,plain,
! [SV275: $i,SV88: $i,SV323: $i] :
( ( ( ( SV323
!= ( set_difference @ SV88 @ SV275 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY883: $i] :
( ~ ( in @ SY883 @ SV88 )
| ( in @ SY883 @ SV275 )
| ( in @ SY883 @ SV323 ) )
| ~ ~ ( ~ ! [SY884: $i] :
( ~ ( in @ SY884 @ SV323 )
| ( in @ SY884 @ SV88 ) )
| ~ ! [SY885: $i] :
( ~ ( in @ SY885 @ SV323 )
| ~ ( in @ SY885 @ SV275 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1770]) ).
thf(1932,plain,
! [SV358: $i] :
( ( ( empty @ SV358 )
| ! [SY919: $i] :
( ~ ( element @ SY919 @ SV358 )
| ( in @ SY919 @ SV358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1771]) ).
thf(1933,plain,
! [SV359: $i] :
( ( ( empty @ SV359 )
| ! [SY920: $i] :
( ~ ( in @ SY920 @ SV359 )
| ( element @ SY920 @ SV359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1772]) ).
thf(1934,plain,
! [SV360: $i] :
( ( ~ ( empty @ SV360 )
| ! [SY921: $i] :
( ~ ( element @ SY921 @ SV360 )
| ( empty @ SY921 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1773]) ).
thf(1935,plain,
! [SV361: $i] :
( ( ~ ( empty @ SV361 )
| ! [SY922: $i] :
( ~ ( empty @ SY922 )
| ( element @ SY922 @ SV361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1774]) ).
thf(1936,plain,
! [SV89: $i,SV174: $i] :
( ( ( ! [SY723: $i] :
( ~ ( relation @ SY723 )
| ~ ( ~ ( ~ ( in @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY723 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) ) @ SV174 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY723 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) ) @ SY723 ) )
| ~ ~ ( ~ ( ( in @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) @ SV89 )
| ( in @ ( ordered_pair @ ( sK40_D @ SY723 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) ) @ SY723 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SY723 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) ) @ SV174 )
| ( in @ ( ordered_pair @ ( sK40_D @ SY723 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SY723 @ SV174 @ SV89 ) ) @ SY723 ) ) ) )
| ( SY723
= ( relation_rng_restriction @ SV89 @ SV174 ) ) ) )
= $true )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1775]) ).
thf(1937,plain,
! [SV174: $i,SV89: $i] :
( ( ( ! [SY724: $i] :
( ~ ( relation @ SY724 )
| ( SY724
!= ( relation_rng_restriction @ SV89 @ SV174 ) )
| ~ ( ~ ! [SY725: $i,SY726: $i] :
( ~ ( in @ SY726 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY725 @ SY726 ) @ SV174 )
| ( in @ ( ordered_pair @ SY725 @ SY726 ) @ SY724 ) )
| ~ ~ ( ~ ! [SY515: $i,SY516: $i] :
( ~ ( in @ ( ordered_pair @ SY515 @ SY516 ) @ SY724 )
| ( in @ SY516 @ SV89 ) )
| ~ ! [SY729: $i,SY730: $i] :
( ~ ( in @ ( ordered_pair @ SY729 @ SY730 ) @ SY724 )
| ( in @ ( ordered_pair @ SY729 @ SY730 ) @ SV174 ) ) ) ) ) )
= $true )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1776]) ).
thf(1938,plain,
! [SV90: $i,SV276: $i,SV324: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SV324 @ SV276 @ SV90 ) @ SV324 )
| ( ( sK27_D @ SV324 @ SV276 @ SV90 )
!= SV90 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV324 @ SV276 @ SV90 ) @ SV324 )
| ( ( sK27_D @ SV324 @ SV276 @ SV90 )
!= SV276 ) ) )
| ~ ( ( in @ ( sK27_D @ SV324 @ SV276 @ SV90 ) @ SV324 )
| ( ( sK27_D @ SV324 @ SV276 @ SV90 )
= SV90 )
| ( ( sK27_D @ SV324 @ SV276 @ SV90 )
= SV276 ) ) ) )
= $true )
| ( ( SV324
= ( unordered_pair @ SV90 @ SV276 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1777]) ).
thf(1939,plain,
! [SV277: $i,SV90: $i,SV325: $i] :
( ( ( ( SV325
!= ( unordered_pair @ SV90 @ SV277 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY886: $i] :
( ~ ( in @ SY886 @ SV325 )
| ( SY886 = SV90 )
| ( SY886 = SV277 ) )
| ~ ~ ( ~ ! [SY887: $i] :
( ( SY887 != SV90 )
| ( in @ SY887 @ SV325 ) )
| ~ ! [SY888: $i] :
( ( SY888 != SV277 )
| ( in @ SY888 @ SV325 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1778]) ).
thf(1940,plain,
! [SV209: $i,SV278: $i] :
( ( ( ~ ( ~ ( in @ ( sK28_C @ SV278 @ SV209 ) @ SV278 )
| ~ ( subset @ ( sK28_C @ SV278 @ SV209 ) @ SV209 ) )
| ~ ( ( in @ ( sK28_C @ SV278 @ SV209 ) @ SV278 )
| ( subset @ ( sK28_C @ SV278 @ SV209 ) @ SV209 ) ) )
= $false )
| ( ( SV278
= ( powerset @ SV209 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1779]) ).
thf(1941,plain,
! [SV210: $i,SV279: $i] :
( ( ( SV279
= ( powerset @ SV210 ) )
= $false )
| ( ( ~ ( ~ ! [SY835: $i] :
( ~ ( in @ SY835 @ SV279 )
| ( subset @ SY835 @ SV210 ) )
| ~ ! [SY836: $i] :
( ~ ( subset @ SY836 @ SV210 )
| ( in @ SY836 @ SV279 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1780]) ).
thf(1942,plain,
! [SV280: $i,SV211: $i] :
( ( ( ( set_intersection2 @ SV211 @ SV280 )
= empty_set )
= $false )
| ( ( disjoint @ SV211 @ SV280 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1781]) ).
thf(1943,plain,
! [SV281: $i,SV212: $i] :
( ( ( disjoint @ SV212 @ SV281 )
= $false )
| ( ( ( set_intersection2 @ SV212 @ SV281 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1782]) ).
thf(1944,plain,
! [SV91: $i,SV362: $i] :
( ( ( ~ ( ~ ( ! [SY923: $i] :
~ ( in @ ( ordered_pair @ ( sK63_C @ SV362 @ SV91 ) @ SY923 ) @ SV91 )
| ~ ( in @ ( sK63_C @ SV362 @ SV91 ) @ SV362 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_C @ SV362 @ SV91 ) @ ( sK64_SY419 @ SV362 @ SV91 ) ) @ SV91 )
| ( in @ ( sK63_C @ SV362 @ SV91 ) @ SV362 ) ) )
| ( SV362
= ( relation_dom @ SV91 ) ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1783]) ).
thf(1945,plain,
! [SV91: $i,SV363: $i] :
( ( ( ( SV363
!= ( relation_dom @ SV91 ) )
| ~ ( ~ ! [SY924: $i] :
( ! [SY530: $i] :
~ ( in @ ( ordered_pair @ SY924 @ SY530 ) @ SV91 )
| ( in @ SY924 @ SV363 ) )
| ~ ! [SY926: $i] :
( ~ ( in @ SY926 @ SV363 )
| ( in @ ( ordered_pair @ SY926 @ ( sK62_D @ SY926 @ SV363 @ SV91 ) ) @ SV91 ) ) ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1784]) ).
thf(1946,plain,
! [SV92: $i,SV364: $i] :
( ( ( ! [SY927: $i] :
( ~ ( ~ ( ! [SY928: $i] :
( ~ ( in @ ( ordered_pair @ ( sK35_D @ SY927 @ SV364 @ SV92 ) @ SY928 ) @ SV92 )
| ~ ( in @ SY928 @ SV364 ) )
| ~ ( in @ ( sK35_D @ SY927 @ SV364 @ SV92 ) @ SY927 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SY927 @ SV364 @ SV92 ) @ ( sK36_SY409 @ SY927 @ SV364 @ SV92 ) ) @ SV92 )
| ~ ( in @ ( sK36_SY409 @ SY927 @ SV364 @ SV92 ) @ SV364 ) )
| ( in @ ( sK35_D @ SY927 @ SV364 @ SV92 ) @ SY927 ) ) )
| ( SY927
= ( relation_inverse_image @ SV92 @ SV364 ) ) ) )
= $true )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1785]) ).
thf(1947,plain,
! [SV365: $i,SV92: $i] :
( ( ( ! [SY929: $i] :
( ( SY929
!= ( relation_inverse_image @ SV92 @ SV365 ) )
| ~ ( ~ ! [SY930: $i] :
( ! [SY931: $i] :
( ~ ( in @ ( ordered_pair @ SY930 @ SY931 ) @ SV92 )
| ~ ( in @ SY931 @ SV365 ) )
| ( in @ SY930 @ SY929 ) )
| ~ ! [SY932: $i] :
( ~ ( in @ SY932 @ SY929 )
| ~ ( ~ ( in @ ( ordered_pair @ SY932 @ ( sK34_E @ SY932 @ SY929 @ SV365 @ SV92 ) ) @ SV92 )
| ~ ( in @ ( sK34_E @ SY932 @ SY929 @ SV365 @ SV92 ) @ SV365 ) ) ) ) ) )
= $true )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1786]) ).
thf(1948,plain,
! [SV93: $i,SV366: $i] :
( ( ( ! [SY933: $i] :
( ~ ( ~ ( ! [SY934: $i] :
( ~ ( in @ ( ordered_pair @ SY934 @ ( sK38_D @ SY933 @ SV366 @ SV93 ) ) @ SV93 )
| ~ ( in @ SY934 @ SV366 ) )
| ~ ( in @ ( sK38_D @ SY933 @ SV366 @ SV93 ) @ SY933 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SY933 @ SV366 @ SV93 ) @ ( sK38_D @ SY933 @ SV366 @ SV93 ) ) @ SV93 )
| ~ ( in @ ( sK39_SY411 @ SY933 @ SV366 @ SV93 ) @ SV366 ) )
| ( in @ ( sK38_D @ SY933 @ SV366 @ SV93 ) @ SY933 ) ) )
| ( SY933
= ( relation_image @ SV93 @ SV366 ) ) ) )
= $true )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1787]) ).
thf(1949,plain,
! [SV367: $i,SV93: $i] :
( ( ( ! [SY935: $i] :
( ( SY935
!= ( relation_image @ SV93 @ SV367 ) )
| ~ ( ~ ! [SY936: $i] :
( ! [SY937: $i] :
( ~ ( in @ ( ordered_pair @ SY937 @ SY936 ) @ SV93 )
| ~ ( in @ SY937 @ SV367 ) )
| ( in @ SY936 @ SY935 ) )
| ~ ! [SY938: $i] :
( ~ ( in @ SY938 @ SY935 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SY938 @ SY935 @ SV367 @ SV93 ) @ SY938 ) @ SV93 )
| ~ ( in @ ( sK37_E @ SY938 @ SY935 @ SV367 @ SV93 ) @ SV367 ) ) ) ) ) )
= $true )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1788]) ).
thf(1950,plain,
! [SV282: $i,SV94: $i,SV326: $i] :
( ( ( ~ ( relation @ SV326 ) )
= $true )
| ( ( ! [SY889: $i] :
( ~ ( in @ SY889 @ ( relation_rng @ SV326 ) )
| ~ ( in @ ( ordered_pair @ SV94 @ SY889 ) @ SV326 )
| ~ ( in @ SY889 @ SV282 ) )
| ( in @ SV94 @ ( relation_inverse_image @ SV326 @ SV282 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1789]) ).
thf(1951,plain,
! [SV283: $i,SV94: $i,SV327: $i] :
( ( ( ~ ( relation @ SV327 ) )
= $true )
| ( ( ~ ( in @ SV94 @ ( relation_inverse_image @ SV327 @ SV283 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK51_D @ SV327 @ SV283 @ SV94 ) @ ( relation_rng @ SV327 ) )
| ~ ( in @ ( ordered_pair @ SV94 @ ( sK51_D @ SV327 @ SV283 @ SV94 ) ) @ SV327 ) )
| ~ ( in @ ( sK51_D @ SV327 @ SV283 @ SV94 ) @ SV283 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1790]) ).
thf(1952,plain,
! [SV175: $i,SV95: $i] :
( ( ( ~ ! [SY731: $i] :
( ~ ( function @ SY731 )
| ~ ( relation @ SY731 )
| ~ ( in @ SV95 @ ( relation_dom @ SY731 ) )
| ~ ( in @ ( apply @ SY731 @ SV95 ) @ ( relation_dom @ SV175 ) )
| ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY731 @ SV175 ) ) ) )
| ~ ~ ( ~ ! [SY732: $i] :
( ~ ( function @ SY732 )
| ~ ( relation @ SY732 )
| ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY732 @ SV175 ) ) )
| ( in @ SV95 @ ( relation_dom @ SY732 ) ) )
| ~ ! [SY733: $i] :
( ~ ( function @ SY733 )
| ~ ( relation @ SY733 )
| ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY733 @ SV175 ) ) )
| ( in @ ( apply @ SY733 @ SV95 ) @ ( relation_dom @ SV175 ) ) ) ) )
= $false )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1791]) ).
thf(1953,plain,
! [SV96: $i,SV368: $i] :
( ( ( ! [SY939: $i] :
( ~ ( relation @ SY939 )
| ~ ( ~ ( ~ ( in @ ( sK42_D @ SY939 @ SV368 @ SV96 ) @ SV368 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SY939 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SY939 @ SV368 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SY939 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SY939 @ SV368 @ SV96 ) ) @ SY939 ) )
| ~ ~ ( ~ ( ( in @ ( sK42_D @ SY939 @ SV368 @ SV96 ) @ SV368 )
| ( in @ ( ordered_pair @ ( sK42_D @ SY939 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SY939 @ SV368 @ SV96 ) ) @ SY939 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SY939 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SY939 @ SV368 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK42_D @ SY939 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SY939 @ SV368 @ SV96 ) ) @ SY939 ) ) ) )
| ( SY939
= ( relation_dom_restriction @ SV96 @ SV368 ) ) ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1792]) ).
thf(1954,plain,
! [SV369: $i,SV96: $i] :
( ( ( ! [SY940: $i] :
( ~ ( relation @ SY940 )
| ( SY940
!= ( relation_dom_restriction @ SV96 @ SV369 ) )
| ~ ( ~ ! [SY941: $i,SY942: $i] :
( ~ ( in @ SY941 @ SV369 )
| ~ ( in @ ( ordered_pair @ SY941 @ SY942 ) @ SV96 )
| ( in @ ( ordered_pair @ SY941 @ SY942 ) @ SY940 ) )
| ~ ~ ( ~ ! [SY943: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SY943 @ SX4 ) @ SY940 )
| ( in @ SY943 @ SV369 ) )
| ~ ! [SY565: $i,SY566: $i] :
( ~ ( in @ ( ordered_pair @ SY565 @ SY566 ) @ SY940 )
| ( in @ ( ordered_pair @ SY565 @ SY566 ) @ SV96 ) ) ) ) ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1793]) ).
thf(1955,plain,
! [SV284: $i,SV213: $i] :
( ( ( ~ ( empty @ SV213 ) )
= $true )
| ( ( ~ ( relation @ SV284 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV284 @ SV213 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1794]) ).
thf(1956,plain,
! [SV285: $i,SV214: $i] :
( ( ( ~ ( empty @ SV214 ) )
= $true )
| ( ( ~ ( relation @ SV285 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV285 @ SV214 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1795]) ).
thf(1957,plain,
! [SV97: $i,SV370: $i] :
( ( ( ~ ( relation @ SV370 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SV370 @ SV97 ) @ ( sK12_SY396 @ SV370 @ SV97 ) ) @ SV370 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SV370 @ SV97 ) @ ( sK11_C @ SV370 @ SV97 ) ) @ SV97 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_C @ SV370 @ SV97 ) @ ( sK12_SY396 @ SV370 @ SV97 ) ) @ SV370 )
| ( in @ ( ordered_pair @ ( sK12_SY396 @ SV370 @ SV97 ) @ ( sK11_C @ SV370 @ SV97 ) ) @ SV97 ) ) )
| ( SV370
= ( relation_inverse @ SV97 ) ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1796]) ).
thf(1958,plain,
! [SV97: $i,SV371: $i] :
( ( ( ~ ( relation @ SV371 )
| ( SV371
!= ( relation_inverse @ SV97 ) )
| ~ ( ~ ! [SY947: $i,SY948: $i] :
( ~ ( in @ ( ordered_pair @ SY947 @ SY948 ) @ SV371 )
| ( in @ ( ordered_pair @ SY948 @ SY947 ) @ SV97 ) )
| ~ ! [SY949: $i,SY950: $i] :
( ~ ( in @ ( ordered_pair @ SY950 @ SY949 ) @ SV97 )
| ( in @ ( ordered_pair @ SY949 @ SY950 ) @ SV371 ) ) ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1797]) ).
thf(1959,plain,
! [SV98: $i,SV372: $i] :
( ( ( ~ ( ~ ( ! [SY951: $i] :
~ ( in @ ( ordered_pair @ SY951 @ ( sK60_C @ SV372 @ SV98 ) ) @ SV98 )
| ~ ( in @ ( sK60_C @ SV372 @ SV98 ) @ SV372 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK61_SY417 @ SV372 @ SV98 ) @ ( sK60_C @ SV372 @ SV98 ) ) @ SV98 )
| ( in @ ( sK60_C @ SV372 @ SV98 ) @ SV372 ) ) )
| ( SV372
= ( relation_rng @ SV98 ) ) )
= $true )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1798]) ).
thf(1960,plain,
! [SV98: $i,SV373: $i] :
( ( ( ( SV373
!= ( relation_rng @ SV98 ) )
| ~ ( ~ ! [SY952: $i] :
( ! [SY577: $i] :
~ ( in @ ( ordered_pair @ SY577 @ SY952 ) @ SV98 )
| ( in @ SY952 @ SV373 ) )
| ~ ! [SY954: $i] :
( ~ ( in @ SY954 @ SV373 )
| ( in @ ( ordered_pair @ ( sK59_D @ SY954 @ SV373 @ SV98 ) @ SY954 ) @ SV98 ) ) ) )
= $true )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1799]) ).
thf(1961,plain,
! [SV99: $i,SV176: $i] :
( ( ( ~ ( in @ ( sK4_C @ SV176 @ SV99 ) @ SV99 ) )
= $true )
| ( ( ~ ( in @ ( sK4_C @ SV176 @ SV99 ) @ SV176 ) )
= $true )
| ( ( SV99 = SV176 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1800]) ).
thf(1962,plain,
! [SV99: $i,SV176: $i] :
( ( ( in @ ( sK4_C @ SV176 @ SV99 ) @ SV99 )
= $true )
| ( ( in @ ( sK4_C @ SV176 @ SV99 ) @ SV176 )
= $true )
| ( ( SV99 = SV176 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1801]) ).
thf(1963,plain,
! [SV100: $i,SV286: $i,SV328: $i] :
( ( ( ~ ( function @ SV328 )
| ~ ( relation @ SV328 ) )
= $true )
| ( ( ( SV286
!= ( apply @ SV328 @ SV100 ) )
| ~ ( in @ SV100 @ ( relation_dom @ SV328 ) )
| ( in @ ( ordered_pair @ SV100 @ SV286 ) @ SV328 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1802]) ).
thf(1964,plain,
! [SV100: $i] :
( ( ! [SY582: $i,SY583: $i] :
( ~ ( function @ SY583 )
| ~ ( relation @ SY583 )
| ~ ( in @ ( ordered_pair @ SV100 @ SY582 ) @ SY583 )
| ( SY582
= ( apply @ SY583 @ SV100 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1803]) ).
thf(1965,plain,
! [SV100: $i] :
( ( ! [SY584: $i,SY585: $i] :
( ~ ( function @ SY585 )
| ~ ( relation @ SY585 )
| ~ ( in @ ( ordered_pair @ SV100 @ SY584 ) @ SY585 )
| ( in @ SV100 @ ( relation_dom @ SY585 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1804]) ).
thf(1966,plain,
! [SV101: $i,SV215: $i] :
( ( ( ~ ! [SY778: $i] :
( ~ ( relation @ SY778 )
| ~ ( ~ ( ! [SY779: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY778 @ SV215 @ SV101 ) @ SY779 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY779 @ ( sK9_SY391 @ SY778 @ SV215 @ SV101 ) ) @ SV215 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SY778 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SY778 @ SV215 @ SV101 ) ) @ SY778 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY778 @ SV215 @ SV101 ) @ ( sK10_SY395 @ SY778 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SY778 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SY778 @ SV215 @ SV101 ) ) @ SV215 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SY778 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SY778 @ SV215 @ SV101 ) ) @ SY778 ) ) )
| ( SY778
= ( relation_composition @ SV101 @ SV215 ) ) )
| ~ ! [SY780: $i] :
( ~ ( relation @ SY780 )
| ( SY780
!= ( relation_composition @ SV101 @ SV215 ) )
| ~ ( ~ ! [SY781: $i,SY782: $i] :
( ! [SY783: $i] :
( ~ ( in @ ( ordered_pair @ SY781 @ SY783 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY783 @ SY782 ) @ SV215 ) )
| ( in @ ( ordered_pair @ SY781 @ SY782 ) @ SY780 ) )
| ~ ! [SY784: $i,SY785: $i] :
( ~ ( in @ ( ordered_pair @ SY784 @ SY785 ) @ SY780 )
| ~ ( ~ ( in @ ( ordered_pair @ SY784 @ ( sK7_F @ SY785 @ SY784 @ SY780 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY785 @ SY784 @ SY780 @ SV215 @ SV101 ) @ SY785 ) @ SV215 ) ) ) ) ) )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1805]) ).
thf(1967,plain,
! [SV374: $i,SV177: $i,SV329: $i,SV102: $i] :
( ( ~ ( in @ SV102 @ SV329 )
| ~ ( in @ SV177 @ SV374 )
| ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SV329 @ SV374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1806]) ).
thf(1968,plain,
! [SV177: $i,SV102: $i] :
( ( ~ ! [SY736: $i] :
( ! [SY737: $i] :
~ ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SY736 @ SY737 ) )
| ( in @ SV102 @ SY736 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1807]) ).
thf(1969,plain,
! [SV177: $i,SV102: $i] :
( ( ~ ! [SY738: $i,SY739: $i] :
( ~ ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SY738 @ SY739 ) )
| ( in @ SV177 @ SY739 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1807]) ).
thf(1970,plain,
! [SV216: $i] :
( ( ( ( ( relation_dom @ SV216 )
!= empty_set ) )
= $true )
| ( ( SV216 = empty_set )
= $true )
| ( ( relation @ SV216 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1808]) ).
thf(1971,plain,
! [SV217: $i] :
( ( ( ( ( relation_rng @ SV217 )
!= empty_set ) )
= $true )
| ( ( SV217 = empty_set )
= $true )
| ( ( relation @ SV217 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1809]) ).
thf(1972,plain,
! [SV103: $i,SV287: $i] :
( ( ( ~ ( subset @ SV287 @ ( sK2_B @ SV103 ) ) )
= $true )
| ( ( are_equipotent @ SV287 @ ( sK2_B @ SV103 ) )
= $true )
| ( ( in @ SV287 @ ( sK2_B @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1810]) ).
thf(1973,plain,
! [SV103: $i] :
( ( ! [SY603: $i] :
( ~ ( ~ ! [SY604: $i] :
( ~ ( subset @ SY604 @ SY603 )
| ( in @ SY604 @ ( sK3_SY386 @ SY603 @ SV103 ) ) )
| ~ ( in @ ( sK3_SY386 @ SY603 @ SV103 ) @ ( sK2_B @ SV103 ) ) )
| ~ ( in @ SY603 @ ( sK2_B @ SV103 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1811]) ).
thf(1974,plain,
! [SV103: $i] :
( ( ~ ( ~ ! [SY605: $i,SY606: $i] :
( ~ ( in @ SY605 @ ( sK2_B @ SV103 ) )
| ~ ( subset @ SY606 @ SY605 )
| ( in @ SY606 @ ( sK2_B @ SV103 ) ) )
| ~ ( in @ SV103 @ ( sK2_B @ SV103 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1812]) ).
thf(1975,plain,
! [SV218: $i] :
( ( ( function @ SV218 )
= $false )
| ( ( ~ ( relation @ SV218 ) )
= $true )
| ( ( function @ ( function_inverse @ SV218 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1813]) ).
thf(1976,plain,
! [SV219: $i] :
( ( ( function @ SV219 )
= $false )
| ( ( ~ ( relation @ SV219 ) )
= $true )
| ( ( relation @ ( function_inverse @ SV219 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1814]) ).
thf(1977,plain,
! [SV222: $i] :
( ( ( ~ ! [SY786: $i,SY787: $i] :
( ( sK69_B @ SV222 )
!= ( ordered_pair @ SY786 @ SY787 ) ) )
= $false )
| ( ( relation @ SV222 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1817]) ).
thf(1978,plain,
! [SV222: $i] :
( ( ( ~ ( in @ ( sK69_B @ SV222 ) @ SV222 ) )
= $false )
| ( ( relation @ SV222 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1817]) ).
thf(1979,plain,
! [SV223: $i,SV375: $i] :
( ( ( ( SV375
= ( ordered_pair @ ( sK67_C @ SV375 @ SV223 ) @ ( sK68_SY421 @ SV375 @ SV223 ) ) )
| ~ ( in @ SV375 @ SV223 ) )
= $true )
| ( ( relation @ SV223 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1818]) ).
thf(1980,plain,
! [SV104: $i,SV376: $i] :
( ( ( ~ ( relation @ SV376 )
| ~ ( subset @ SV104 @ SV376 )
| ( subset @ ( relation_dom @ SV104 ) @ ( relation_dom @ SV376 ) ) )
= $true )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1819]) ).
thf(1981,plain,
! [SV104: $i,SV377: $i] :
( ( ( ~ ( relation @ SV377 )
| ~ ( subset @ SV104 @ SV377 )
| ( subset @ ( relation_rng @ SV104 ) @ ( relation_rng @ SV377 ) ) )
= $true )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1820]) ).
thf(1982,plain,
! [SV288: $i,SV105: $i,SV330: $i] :
( ( ( ~ ( relation @ SV330 ) )
= $true )
| ( ( ~ ( in @ SV105 @ SV288 )
| ~ ( in @ SV105 @ ( relation_rng @ SV330 ) )
| ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SV288 @ SV330 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1821]) ).
thf(1983,plain,
! [SV105: $i] :
( ( ! [SY611: $i,SY612: $i] :
( ~ ( relation @ SY612 )
| ~ ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SY611 @ SY612 ) ) )
| ( in @ SV105 @ SY611 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1822]) ).
thf(1984,plain,
! [SV105: $i] :
( ( ! [SY613: $i,SY614: $i] :
( ~ ( relation @ SY614 )
| ~ ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SY613 @ SY614 ) ) )
| ( in @ SV105 @ ( relation_rng @ SY614 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1823]) ).
thf(1985,plain,
! [SV289: $i,SV331: $i,SV106: $i] :
( ( ( ~ ( in @ SV106 @ SV331 )
| ~ ( in @ SV289 @ SV331 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV106 @ SV289 ) @ SV331 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1826]) ).
thf(1986,plain,
! [SV106: $i] :
( ( ! [SY617: $i,SY618: $i] :
( ~ ( subset @ ( unordered_pair @ SV106 @ SY617 ) @ SY618 )
| ( in @ SV106 @ SY618 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1827]) ).
thf(1987,plain,
! [SV106: $i] :
( ( ! [SY619: $i,SY620: $i] :
( ~ ( subset @ ( unordered_pair @ SV106 @ SY619 ) @ SY620 )
| ( in @ SY619 @ SY620 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1828]) ).
thf(1988,plain,
! [SV178: $i,SV332: $i,SV107: $i,SV378: $i] :
( ( ~ ( relation @ SV378 )
| ~ ( in @ SV107 @ SV332 )
| ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ SV378 )
| ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SV332 ) @ SV378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(1989,plain,
! [SV178: $i,SV107: $i] :
( ( ~ ! [SY742: $i,SY743: $i] :
( ~ ( relation @ SY743 )
| ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SY742 ) @ SY743 ) )
| ( in @ SV107 @ SY742 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1830]) ).
thf(1990,plain,
! [SV178: $i,SV107: $i] :
( ( ~ ! [SY744: $i,SY745: $i] :
( ~ ( relation @ SY745 )
| ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SY744 ) @ SY745 ) )
| ( in @ ( ordered_pair @ SV107 @ SV178 ) @ SY745 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1830]) ).
thf(1991,plain,
! [SV108: $i,SV379: $i] :
( ( ( ~ ( relation @ SV379 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV379 @ SV108 ) @ ( sK20_SY399 @ SV379 @ SV108 ) ) @ SV108 )
| ~ ~ ( in @ ( ordered_pair @ ( sK19_C @ SV379 @ SV108 ) @ ( sK20_SY399 @ SV379 @ SV108 ) ) @ SV379 ) )
| ( subset @ SV108 @ SV379 ) )
= $true )
| ( ( relation @ SV108 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1831]) ).
thf(1992,plain,
! [SV108: $i,SV380: $i] :
( ( ( ~ ( relation @ SV380 )
| ~ ( subset @ SV108 @ SV380 )
| ! [SY955: $i,SY956: $i] :
( ~ ( in @ ( ordered_pair @ SY955 @ SY956 ) @ SV108 )
| ( in @ ( ordered_pair @ SY955 @ SY956 ) @ SV380 ) ) )
= $true )
| ( ( relation @ SV108 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1832]) ).
thf(1993,plain,
! [SV228: $i,SV290: $i] :
( ( ( ~ ( ( ( sK30_C @ SV290 @ SV228 )
!= SV228 )
| ~ ( in @ ( sK30_C @ SV290 @ SV228 ) @ SV290 ) )
| ~ ( ( ( sK30_C @ SV290 @ SV228 )
= SV228 )
| ( in @ ( sK30_C @ SV290 @ SV228 ) @ SV290 ) ) )
= $false )
| ( ( SV290
= ( singleton @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1833]) ).
thf(1994,plain,
! [SV229: $i,SV291: $i] :
( ( ( SV291
= ( singleton @ SV229 ) )
= $false )
| ( ( ~ ( ~ ! [SY843: $i] :
( ( SY843 != SV229 )
| ( in @ SY843 @ SV291 ) )
| ~ ! [SY844: $i] :
( ~ ( in @ SY844 @ SV291 )
| ( SY844 = SV229 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1834]) ).
thf(1995,plain,
! [SV292: $i,SV109: $i,SV333: $i] :
( ( ( ~ ( relation @ SV333 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV109 @ SV292 ) @ SV333 )
| ( in @ SV109 @ ( relation_dom @ SV333 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1835]) ).
thf(1996,plain,
! [SV293: $i,SV109: $i,SV334: $i] :
( ( ( ~ ( relation @ SV334 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV109 @ SV293 ) @ SV334 )
| ( in @ SV293 @ ( relation_rng @ SV334 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1836]) ).
thf(1997,plain,
! [SV381: $i] :
( ( ~ ( empty @ SV381 )
| ~ ( relation @ SV381 )
| ~ ( function @ SV381 )
| ( function @ SV381 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1837]) ).
thf(1998,plain,
! [SV382: $i] :
( ( ~ ( empty @ SV382 )
| ~ ( relation @ SV382 )
| ~ ( function @ SV382 )
| ( relation @ SV382 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1838]) ).
thf(1999,plain,
! [SV230: $i] :
( ( ( ~ ( empty @ SV230 ) )
= $true )
| ( ( ~ ( relation @ SV230 ) )
= $true )
| ( ( ~ ( function @ SV230 ) )
= $true )
| ( ( one_to_one @ SV230 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1839]) ).
thf(2000,plain,
! [SV110: $i] :
( ( ( one_to_one @ SV110 )
= $false )
| ( ( ~ ( ~ ! [SY636: $i] :
( ~ ( function @ SY636 )
| ~ ( relation @ SY636 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SY636 @ SV110 )
= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ( ( sK70_C @ SY636 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY636 @ SV110 )
= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY636 @ SV110 )
= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ( ( sK71_SY424 @ SY636 @ SV110 )
!= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK70_C @ SY636 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK71_SY424 @ SY636 @ SV110 )
!= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY636 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK70_C @ SY636 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SY636 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SY636 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK71_SY424 @ SY636 @ SV110 )
!= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ( ( relation_dom @ SY636 )
!= ( relation_rng @ SV110 ) )
| ( SY636
= ( function_inverse @ SV110 ) ) )
| ~ ~ ( ~ ! [SY637: $i] :
( ~ ( function @ SY637 )
| ~ ( relation @ SY637 )
| ( SY637
!= ( function_inverse @ SV110 ) )
| ~ ( ~ ~ ( ~ ! [SY638: $i,SY639: $i] :
( ( SY639
!= ( apply @ SY637 @ SY638 ) )
| ~ ( in @ SY638 @ ( relation_rng @ SV110 ) )
| ( SY638
= ( apply @ SV110 @ SY639 ) ) )
| ~ ! [SY640: $i,SY641: $i] :
( ( SY641
!= ( apply @ SY637 @ SY640 ) )
| ~ ( in @ SY640 @ ( relation_rng @ SV110 ) )
| ( in @ SY641 @ ( relation_dom @ SV110 ) ) ) )
| ~ ~ ( ~ ! [SY642: $i,SY643: $i] :
( ( SY642
!= ( apply @ SV110 @ SY643 ) )
| ~ ( in @ SY643 @ ( relation_dom @ SV110 ) )
| ( SY643
= ( apply @ SY637 @ SY642 ) ) )
| ~ ! [SY644: $i] :
( ! [SY645: $i] :
( ( SY644
!= ( apply @ SV110 @ SY645 ) )
| ~ ( in @ SY645 @ ( relation_dom @ SV110 ) ) )
| ( in @ SY644 @ ( relation_rng @ SV110 ) ) ) ) ) )
| ~ ! [SY646: $i] :
( ~ ( function @ SY646 )
| ~ ( relation @ SY646 )
| ( SY646
!= ( function_inverse @ SV110 ) )
| ( ( relation_dom @ SY646 )
= ( relation_rng @ SV110 ) ) ) ) ) )
= $true )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1842]) ).
thf(2001,plain,
! [SV294: $i,SV233: $i] :
( ( ( SV233 = SV294 )
= $true )
| ( ( ~ ( subset @ SV233 @ SV294 ) )
= $true )
| ( ( proper_subset @ SV233 @ SV294 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1845]) ).
thf(2002,plain,
! [SV383: $i] :
( ( ! [SY957: $i] :
( ~ ( proper_subset @ SV383 @ SY957 )
| ( SV383 != SY957 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1846]) ).
thf(2003,plain,
! [SV384: $i] :
( ( ! [SY958: $i] :
( ~ ( proper_subset @ SV384 @ SY958 )
| ( subset @ SV384 @ SY958 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1847]) ).
thf(2004,plain,
! [SV234: $i,SV295: $i] :
( ( ( ~ ( in @ ( sK18_C @ SV295 @ SV234 ) @ SV234 )
| ~ ~ ( in @ ( sK18_C @ SV295 @ SV234 ) @ SV295 ) )
= $false )
| ( ( subset @ SV234 @ SV295 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1848]) ).
thf(2005,plain,
! [SV296: $i,SV235: $i] :
( ( ( subset @ SV235 @ SV296 )
= $false )
| ( ( ! [SY847: $i] :
( ~ ( in @ SY847 @ SV235 )
| ( in @ SY847 @ SV296 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1849]) ).
thf(2006,plain,
! [SV236: $i,SV297: $i] :
( ( ( ~ ( in @ ( sK49_C @ SV297 @ SV236 ) @ SV236 )
| ~ ( in @ ( sK49_C @ SV297 @ SV236 ) @ SV297 ) )
= $false )
| ( ( disjoint @ SV236 @ SV297 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1850]) ).
thf(2007,plain,
! [SV298: $i,SV237: $i,SV385: $i] :
( ( ( ~ ( in @ SV385 @ SV237 )
| ~ ( in @ SV385 @ SV298 ) )
= $true )
| ( ( ~ ( disjoint @ SV237 @ SV298 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1851]) ).
thf(2008,plain,
! [SV386: $i,SV179: $i,SV335: $i,SV111: $i] :
( ( ~ ( in @ SV111 @ SV335 )
| ~ ( in @ SV179 @ SV386 )
| ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SV335 @ SV386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1852]) ).
thf(2009,plain,
! [SV179: $i,SV111: $i] :
( ( ~ ! [SY748: $i] :
( ! [SY749: $i] :
~ ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SY748 @ SY749 ) )
| ( in @ SV111 @ SY748 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1853]) ).
thf(2010,plain,
! [SV179: $i,SV111: $i] :
( ( ~ ! [SY750: $i,SY751: $i] :
( ~ ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SY750 @ SY751 ) )
| ( in @ SV179 @ SY751 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1853]) ).
thf(2011,plain,
! [SV336: $i,SV180: $i,SV112: $i] :
( ( ( ! [SY893: $i] :
( ( ordered_pair @ SV112 @ SV180 )
!= ( ordered_pair @ SV336 @ SY893 ) ) )
= $true )
| ( ( SV112 = SV336 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1854]) ).
thf(2012,plain,
! [SV387: $i,SV337: $i,SV180: $i,SV112: $i] :
( ( ( ( ordered_pair @ SV112 @ SV180 )
!= ( ordered_pair @ SV337 @ SV387 ) )
| ( SV180 = SV387 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1855]) ).
thf(2013,plain,
! [SV113: $i] :
( ( ( ~ ~ ( ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ ( relation_dom @ SV113 ) )
| ! [SY660: $i] :
( ( SY660
!= ( apply @ SV113 @ SY659 ) )
| ( in @ ( ordered_pair @ SY659 @ SY660 ) @ SV113 ) ) )
| ~ ! [SY661: $i] :
( ~ ( in @ SY661 @ ( relation_dom @ SV113 ) )
| ! [SY662: $i] :
( ~ ( in @ ( ordered_pair @ SY661 @ SY662 ) @ SV113 )
| ( SY662
= ( apply @ SV113 @ SY661 ) ) ) ) ) )
= $false )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1856]) ).
thf(2014,plain,
! [SV113: $i] :
( ( ( ~ ~ ( ~ ! [SY663: $i] :
( ( in @ SY663 @ ( relation_dom @ SV113 ) )
| ! [SY664: $i] :
( ( SY664
!= ( apply @ SV113 @ SY663 ) )
| ( SY664 = empty_set ) ) )
| ~ ! [SY665: $i] :
( ( in @ SY665 @ ( relation_dom @ SV113 ) )
| ! [SY666: $i] :
( ( SY666 != empty_set )
| ( SY666
= ( apply @ SV113 @ SY665 ) ) ) ) ) )
= $false )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1856]) ).
thf(2015,plain,
! [SV299: $i,SV240: $i] :
( ( ( in @ SV240 @ SV299 )
= $false )
| ( ( subset @ ( singleton @ SV240 ) @ SV299 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1859]) ).
thf(2016,plain,
! [SV300: $i,SV241: $i] :
( ( ( subset @ ( singleton @ SV241 ) @ SV300 )
= $false )
| ( ( in @ SV241 @ SV300 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1860]) ).
thf(2017,plain,
! [SV243: $i,SV388: $i] :
( ( ( ~ ( in @ SV388 @ SV243 ) )
= $true )
| ( ( SV243 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1861]) ).
thf(2018,plain,
! [SV114: $i,SV301: $i,SV338: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV338 )
| ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV114 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV338 )
| ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV301 ) ) )
| ~ ( ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV338 )
| ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV114 )
| ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV301 ) ) ) )
= $true )
| ( ( SV338
= ( set_union2 @ SV114 @ SV301 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1862]) ).
thf(2019,plain,
! [SV302: $i,SV114: $i,SV339: $i] :
( ( ( ( SV339
!= ( set_union2 @ SV114 @ SV302 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY895: $i] :
( ~ ( in @ SY895 @ SV339 )
| ( in @ SY895 @ SV114 )
| ( in @ SY895 @ SV302 ) )
| ~ ~ ( ~ ! [SY896: $i] :
( ~ ( in @ SY896 @ SV114 )
| ( in @ SY896 @ SV339 ) )
| ~ ! [SY897: $i] :
( ~ ( in @ SY897 @ SV302 )
| ( in @ SY897 @ SV339 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1863]) ).
thf(2020,plain,
! [SV303: $i,SV115: $i,SV340: $i] :
( ( ( ~ ( relation @ SV340 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV115 @ SV303 ) @ SV340 )
| ( in @ SV115 @ ( relation_field @ SV340 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1866]) ).
thf(2021,plain,
! [SV304: $i,SV115: $i,SV341: $i] :
( ( ( ~ ( relation @ SV341 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV115 @ SV304 ) @ SV341 )
| ( in @ SV304 @ ( relation_field @ SV341 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1867]) ).
thf(2022,plain,
! [SV246: $i] :
( ( ( ( ( relation_dom @ SV246 )
!= empty_set ) )
= $true )
| ( ( ( relation_rng @ SV246 )
= empty_set )
= $true )
| ( ( relation @ SV246 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1868]) ).
thf(2023,plain,
! [SV247: $i] :
( ( ( ( ( relation_rng @ SV247 )
!= empty_set ) )
= $true )
| ( ( ( relation_dom @ SV247 )
= empty_set )
= $true )
| ( ( relation @ SV247 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1869]) ).
thf(2024,plain,
! [SV305: $i,SV248: $i] :
( ( ( subset @ SV248 @ ( singleton @ SV305 ) )
= $false )
| ( ( ( SV248 = empty_set )
| ( SV248
= ( singleton @ SV305 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1870]) ).
thf(2025,plain,
! [SV389: $i] :
( ( ( SV389 != empty_set )
| ! [SY959: $i] : ( subset @ SV389 @ ( singleton @ SY959 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1871]) ).
thf(2026,plain,
! [SV390: $i] :
( ( ! [SY960: $i] :
( ( SV390
!= ( singleton @ SY960 ) )
| ( subset @ SV390 @ ( singleton @ SY960 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1872]) ).
thf(2027,plain,
! [SV116: $i,SV306: $i,SV342: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV116 )
| ~ ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV306 )
| ~ ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV342 ) )
| ~ ~ ( ~ ( ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV116 )
| ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV342 ) )
| ~ ( ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV306 )
| ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV342 ) ) ) ) )
= $true )
| ( ( SV342
= ( set_intersection2 @ SV116 @ SV306 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1873]) ).
thf(2028,plain,
! [SV307: $i,SV116: $i,SV343: $i] :
( ( ( ( SV343
!= ( set_intersection2 @ SV116 @ SV307 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY898: $i] :
( ~ ( in @ SY898 @ SV116 )
| ~ ( in @ SY898 @ SV307 )
| ( in @ SY898 @ SV343 ) )
| ~ ~ ( ~ ! [SY899: $i] :
( ~ ( in @ SY899 @ SV343 )
| ( in @ SY899 @ SV116 ) )
| ~ ! [SY900: $i] :
( ~ ( in @ SY900 @ SV343 )
| ( in @ SY900 @ SV307 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1874]) ).
thf(2029,plain,
! [SV249: $i] :
( ( ( ~ ( function @ SV249 ) )
= $true )
| ( ( ~ ( relation @ SV249 ) )
= $true )
| ( ( ~ ( one_to_one @ SV249 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV249 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1875]) ).
thf(2030,plain,
! [SV250: $i] :
( ( ( ~ ( function @ SV250 ) )
= $true )
| ( ( ~ ( relation @ SV250 ) )
= $true )
| ( ( ~ ( one_to_one @ SV250 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1876]) ).
thf(2031,plain,
! [SV251: $i,SV308: $i] :
( ( ( relation @ SV308 )
= $false )
| ( ( ~ ( ~ ( ( ( sK44_C @ SV308 @ SV251 )
!= ( sK45_SY414 @ SV308 @ SV251 ) )
| ~ ( in @ ( sK44_C @ SV308 @ SV251 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 ) )
| ~ ~ ( ~ ( ( ( sK44_C @ SV308 @ SV251 )
= ( sK45_SY414 @ SV308 @ SV251 ) )
| ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 ) )
| ~ ( ( in @ ( sK44_C @ SV308 @ SV251 ) @ SV251 )
| ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 ) ) ) )
| ( SV308
= ( identity_relation @ SV251 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1877]) ).
thf(2032,plain,
! [SV252: $i,SV309: $i] :
( ( ( relation @ SV309 )
= $false )
| ( ( ( SV309
!= ( identity_relation @ SV252 ) )
| ~ ( ~ ! [SY861: $i,SY862: $i] :
( ( SY861 != SY862 )
| ~ ( in @ SY861 @ SV252 )
| ( in @ ( ordered_pair @ SY861 @ SY862 ) @ SV309 ) )
| ~ ~ ( ~ ! [SY863: $i,SY864: $i] :
( ~ ( in @ ( ordered_pair @ SY863 @ SY864 ) @ SV309 )
| ( SY863 = SY864 ) )
| ~ ! [SY865: $i] :
( ! [SY866: $i] :
~ ( in @ ( ordered_pair @ SY865 @ SY866 ) @ SV309 )
| ( in @ SY865 @ SV252 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1878]) ).
thf(2033,plain,
! [SV310: $i,SV117: $i,SV344: $i] :
( ( ( ~ ( relation @ SV344 ) )
= $true )
| ( ( ~ ( in @ SV117 @ SV310 )
| ~ ( in @ SV117 @ ( relation_dom @ SV344 ) )
| ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SV344 @ SV310 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1881]) ).
thf(2034,plain,
! [SV117: $i] :
( ( ! [SY687: $i,SY688: $i] :
( ~ ( relation @ SY688 )
| ~ ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SY688 @ SY687 ) ) )
| ( in @ SV117 @ SY687 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1882]) ).
thf(2035,plain,
! [SV117: $i] :
( ( ! [SY689: $i,SY690: $i] :
( ~ ( relation @ SY690 )
| ~ ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SY690 @ SY689 ) ) )
| ( in @ SV117 @ ( relation_dom @ SY690 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1883]) ).
thf(2036,plain,
! [SV253: $i,SV311: $i] :
( ( ( ~ ( function @ SV311 ) )
= $true )
| ( ( ~ ( relation @ SV311 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK50_C @ SV311 @ SV253 ) @ SV253 )
| ~ ( ( ( apply @ SV311 @ ( sK50_C @ SV311 @ SV253 ) )
!= ( sK50_C @ SV311 @ SV253 ) ) ) )
| ( ( relation_dom @ SV311 )
!= SV253 )
| ( SV311
= ( identity_relation @ SV253 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1884]) ).
thf(2037,plain,
! [SV391: $i] :
( ( ! [SY961: $i] :
( ~ ( function @ SY961 )
| ~ ( relation @ SY961 )
| ( SY961
!= ( identity_relation @ SV391 ) )
| ! [SY962: $i] :
( ~ ( in @ SY962 @ SV391 )
| ( ( apply @ SY961 @ SY962 )
= SY962 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(2038,plain,
! [SV392: $i] :
( ( ! [SY963: $i] :
( ~ ( function @ SY963 )
| ~ ( relation @ SY963 )
| ( SY963
!= ( identity_relation @ SV392 ) )
| ( ( relation_dom @ SY963 )
= SV392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1886]) ).
thf(2039,plain,
! [SV345: $i,SV312: $i,SV118: $i] :
( ( ( ~ ( ~ ( ! [SY901: $i,SY902: $i] :
( ~ ( in @ SY901 @ SV118 )
| ~ ( in @ SY902 @ SV312 )
| ( ( sK23_D @ SV345 @ SV312 @ SV118 )
!= ( ordered_pair @ SY901 @ SY902 ) ) )
| ~ ( in @ ( sK23_D @ SV345 @ SV312 @ SV118 ) @ SV345 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY403 @ SV345 @ SV312 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK25_SY405 @ SV345 @ SV312 @ SV118 ) @ SV312 ) )
| ( ( sK23_D @ SV345 @ SV312 @ SV118 )
!= ( ordered_pair @ ( sK24_SY403 @ SV345 @ SV312 @ SV118 ) @ ( sK25_SY405 @ SV345 @ SV312 @ SV118 ) ) ) )
| ( in @ ( sK23_D @ SV345 @ SV312 @ SV118 ) @ SV345 ) ) ) )
= $true )
| ( ( SV345
= ( cartesian_product2 @ SV118 @ SV312 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1887]) ).
thf(2040,plain,
! [SV313: $i,SV118: $i,SV346: $i] :
( ( ( ( SV346
!= ( cartesian_product2 @ SV118 @ SV313 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY903: $i] :
( ! [SY873: $i,SY874: $i] :
( ~ ( in @ SY873 @ SV118 )
| ~ ( in @ SY874 @ SV313 )
| ( SY903
!= ( ordered_pair @ SY873 @ SY874 ) ) )
| ( in @ SY903 @ SV346 ) )
| ~ ! [SY906: $i] :
( ~ ( in @ SY906 @ SV346 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY906 @ SV346 @ SV313 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK22_SY400 @ SY906 @ SV346 @ SV313 @ SV118 ) @ SV313 ) )
| ( SY906
!= ( ordered_pair @ ( sK21_E @ SY906 @ SV346 @ SV313 @ SV118 ) @ ( sK22_SY400 @ SY906 @ SV346 @ SV313 @ SV118 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1888]) ).
thf(2041,plain,
! [SV314: $i,SV119: $i] :
( ( ( subset @ SV119 @ SV314 )
= $false )
| ( ( ! [SY876: $i] : ( subset @ ( cartesian_product2 @ SV119 @ SY876 ) @ ( cartesian_product2 @ SV314 @ SY876 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1889]) ).
thf(2042,plain,
! [SV315: $i,SV119: $i] :
( ( ( subset @ SV119 @ SV315 )
= $false )
| ( ( ! [SY877: $i] : ( subset @ ( cartesian_product2 @ SY877 @ SV119 ) @ ( cartesian_product2 @ SY877 @ SV315 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1890]) ).
thf(2043,plain,
! [SV254: $i,SV316: $i] :
( ( ( ~ ( ! [SY878: $i] :
( ~ ( in @ ( sK15_C @ SV316 @ SV254 ) @ SY878 )
| ~ ( in @ SY878 @ SV254 ) )
| ~ ( in @ ( sK15_C @ SV316 @ SV254 ) @ SV316 ) )
| ~ ( ~ ( ~ ( in @ ( sK15_C @ SV316 @ SV254 ) @ ( sK16_SY398 @ SV316 @ SV254 ) )
| ~ ( in @ ( sK16_SY398 @ SV316 @ SV254 ) @ SV254 ) )
| ( in @ ( sK15_C @ SV316 @ SV254 ) @ SV316 ) ) )
= $false )
| ( ( SV316
= ( union @ SV254 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1891]) ).
thf(2044,plain,
! [SV255: $i,SV317: $i] :
( ( ( SV317
= ( union @ SV255 ) )
= $false )
| ( ( ~ ( ~ ! [SY879: $i] :
( ! [SY817: $i] :
( ~ ( in @ SY879 @ SY817 )
| ~ ( in @ SY817 @ SV255 ) )
| ( in @ SY879 @ SV317 ) )
| ~ ! [SY881: $i] :
( ~ ( in @ SY881 @ SV317 )
| ~ ( ~ ( in @ SY881 @ ( sK14_D @ SY881 @ SV317 @ SV255 ) )
| ~ ( in @ ( sK14_D @ SY881 @ SV317 @ SV255 ) @ SV255 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1892]) ).
thf(2045,plain,
! [SV318: $i,SV256: $i] :
( ( ( ( set_difference @ SV256 @ SV318 )
= empty_set )
= $false )
| ( ( subset @ SV256 @ SV318 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1893]) ).
thf(2046,plain,
! [SV319: $i,SV257: $i] :
( ( ( subset @ SV257 @ SV319 )
= $false )
| ( ( ( set_difference @ SV257 @ SV319 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1894]) ).
thf(2047,plain,
! [SV120: $i,SV393: $i] :
( ( ( ~ ( relation @ SV393 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV393 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV120 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV393 ) ) )
| ( SV120 = SV393 ) )
= $true )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1895]) ).
thf(2048,plain,
! [SV120: $i,SV394: $i] :
( ( ( ~ ( relation @ SV394 )
| ( SV120 != SV394 )
| ~ ( ~ ! [SY964: $i,SY965: $i] :
( ~ ( in @ ( ordered_pair @ SY964 @ SY965 ) @ SV120 )
| ( in @ ( ordered_pair @ SY964 @ SY965 ) @ SV394 ) )
| ~ ! [SY966: $i,SY967: $i] :
( ~ ( in @ ( ordered_pair @ SY966 @ SY967 ) @ SV394 )
| ( in @ ( ordered_pair @ SY966 @ SY967 ) @ SV120 ) ) ) )
= $true )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1896]) ).
thf(2049,plain,
! [SV193: $i,SV15: $i] :
( ( ( subset @ ( relation_rng @ SV15 ) @ ( relation_dom @ SV193 ) )
= $false )
| ( ( ( relation_dom @ ( relation_composition @ SV15 @ SV193 ) )
= ( relation_dom @ SV15 ) )
= $true )
| ( ( relation @ SV193 )
= $false )
| ( ( relation @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1898]) ).
thf(2050,plain,
! [SV194: $i,SV16: $i] :
( ( ( subset @ ( relation_dom @ SV16 ) @ ( relation_rng @ SV194 ) )
= $false )
| ( ( ( relation_rng @ ( relation_composition @ SV194 @ SV16 ) )
= ( relation_rng @ SV16 ) )
= $true )
| ( ( relation @ SV194 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1899]) ).
thf(2051,plain,
! [SV139: $i,SV37: $i,SV196: $i,SV183: $i] :
( ( ( subset @ SV183 @ SV196 )
= $false )
| ( ( subset @ SV37 @ SV139 )
= $false )
| ( ( subset @ ( cartesian_product2 @ SV37 @ SV183 ) @ ( cartesian_product2 @ SV139 @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1901]) ).
thf(2052,plain,
! [SV39: $i,SV141: $i] :
( ( ( ( relation_inverse_image @ SV141 @ SV39 )
= empty_set )
= $false )
| ( ( SV39 = empty_set )
= $true )
| ( ( subset @ SV39 @ ( relation_rng @ SV141 ) )
= $false )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1902]) ).
thf(2053,plain,
! [SV145: $i,SV43: $i,SV347: $i] :
( ( ( ~ ( function @ SV347 )
| ~ ( relation @ SV347 ) )
= $true )
| ( ( ~ ( in @ SV43 @ ( relation_dom @ ( relation_composition @ SV347 @ SV145 ) ) )
| ( ( apply @ ( relation_composition @ SV347 @ SV145 ) @ SV43 )
= ( apply @ SV145 @ ( apply @ SV347 @ SV43 ) ) ) )
= $true )
| ( ( function @ SV145 )
= $false )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1905]) ).
thf(2054,plain,
! [SV146: $i,SV44: $i,SV348: $i] :
( ( ( ~ ( function @ SV348 )
| ~ ( relation @ SV348 ) )
= $true )
| ( ( ~ ( in @ SV44 @ ( relation_dom @ SV146 ) )
| ( ( apply @ ( relation_composition @ SV146 @ SV348 ) @ SV44 )
= ( apply @ SV348 @ ( apply @ SV146 @ SV44 ) ) ) )
= $true )
| ( ( function @ SV146 )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1906]) ).
thf(2055,plain,
! [SV262: $i,SV199: $i] :
( ( ( SV199 = empty_set )
= $true )
| ( ( SV199
= ( singleton @ SV262 ) )
= $true )
| ( ( subset @ SV199 @ ( singleton @ SV262 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1911]) ).
thf(2056,plain,
! [SV349: $i] :
( ( ( ( SV349 != empty_set ) )
= $true )
| ( ( ! [SY907: $i] : ( subset @ SV349 @ ( singleton @ SY907 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1912]) ).
thf(2057,plain,
! [SV395: $i,SV350: $i] :
( ( ( SV350
!= ( singleton @ SV395 ) )
| ( subset @ SV350 @ ( singleton @ SV395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(2058,plain,
! [SV351: $i] :
( ( ( SV351 = empty_set )
= $true )
| ( ( ! [SY909: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY406 @ SY909 @ SV351 ) @ SV351 )
| ~ ~ ( in @ ( sK32_C @ SY909 @ SV351 ) @ ( sK33_SY406 @ SY909 @ SV351 ) ) )
| ~ ( in @ ( sK32_C @ SY909 @ SV351 ) @ SY909 ) )
| ~ ( ! [SY910: $i] :
( ~ ( in @ SY910 @ SV351 )
| ( in @ ( sK32_C @ SY909 @ SV351 ) @ SY910 ) )
| ( in @ ( sK32_C @ SY909 @ SV351 ) @ SY909 ) ) )
| ( SY909
= ( set_meet @ SV351 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1914]) ).
thf(2059,plain,
! [SV352: $i] :
( ( ( SV352 = empty_set )
= $true )
| ( ( ! [SY911: $i] :
( ( SY911
!= ( set_meet @ SV352 ) )
| ~ ( ~ ! [SY912: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY912 @ SY911 @ SV352 ) @ SV352 )
| ~ ~ ( in @ SY912 @ ( sK31_D @ SY912 @ SY911 @ SV352 ) ) )
| ( in @ SY912 @ SY911 ) )
| ~ ! [SY913: $i] :
( ~ ( in @ SY913 @ SY911 )
| ! [SY914: $i] :
( ~ ( in @ SY914 @ SV352 )
| ( in @ SY913 @ SY914 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1915]) ).
thf(2060,plain,
! [SV353: $i] :
( ( ( ( SV353 != empty_set ) )
= $true )
| ( ( ! [SY915: $i] :
( ( SY915
!= ( set_meet @ SV353 ) )
| ( SY915 = empty_set ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1916]) ).
thf(2061,plain,
! [SV354: $i] :
( ( ( ( SV354 != empty_set ) )
= $true )
| ( ( ! [SY916: $i] :
( ( SY916 != empty_set )
| ( SY916
= ( set_meet @ SV354 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1917]) ).
thf(2062,plain,
! [SV264: $i,SV201: $i,SV355: $i] :
( ( ( in @ SV355 @ ( set_intersection2 @ SV201 @ SV264 ) )
= $false )
| ( ( ~ ( disjoint @ SV201 @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1918]) ).
thf(2063,plain,
! [SV265: $i,SV202: $i] :
( ( ( ~ ( function @ SV202 )
| ~ ( relation @ SV202 ) )
= $true )
| ( ( ~ ( relation @ SV265 ) )
= $true )
| ( ( ~ ( function @ SV265 ) )
= $true )
| ( ( function @ ( relation_composition @ SV202 @ SV265 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1919]) ).
thf(2064,plain,
! [SV266: $i,SV203: $i] :
( ( ( ~ ( function @ SV203 )
| ~ ( relation @ SV203 ) )
= $true )
| ( ( ~ ( relation @ SV266 ) )
= $true )
| ( ( ~ ( function @ SV266 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV203 @ SV266 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1920]) ).
thf(2065,plain,
! [SV269: $i,SV206: $i] :
( ( ( empty @ SV206 )
= $false )
| ( ( ~ ( relation @ SV269 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV206 @ SV269 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1923]) ).
thf(2066,plain,
! [SV270: $i,SV207: $i] :
( ( ( empty @ SV207 )
= $false )
| ( ( ~ ( relation @ SV270 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV207 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1924]) ).
thf(2067,plain,
! [SV271: $i,SV87: $i,SV320: $i] :
( ( ( relation @ SV320 )
= $false )
| ( ( ! [SY882: $i] :
( ~ ( in @ SY882 @ ( relation_dom @ SV320 ) )
| ~ ( in @ ( ordered_pair @ SY882 @ SV87 ) @ SV320 )
| ~ ( in @ SY882 @ SV271 ) )
| ( in @ SV87 @ ( relation_image @ SV320 @ SV271 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1925]) ).
thf(2068,plain,
! [SV272: $i,SV87: $i,SV321: $i] :
( ( ( relation @ SV321 )
= $false )
| ( ( ~ ( in @ SV87 @ ( relation_image @ SV321 @ SV272 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK52_D @ SV321 @ SV272 @ SV87 ) @ ( relation_dom @ SV321 ) )
| ~ ( in @ ( ordered_pair @ ( sK52_D @ SV321 @ SV272 @ SV87 ) @ SV87 ) @ SV321 ) )
| ~ ( in @ ( sK52_D @ SV321 @ SV272 @ SV87 ) @ SV272 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1926]) ).
thf(2069,plain,
! [SV273: $i,SV208: $i] :
( ( ( subset @ SV208 @ SV273 )
= $false )
| ( ( ~ ( subset @ SV273 @ SV208 ) )
= $true )
| ( ( SV208 = SV273 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1927]) ).
thf(2070,plain,
! [SV396: $i,SV356: $i] :
( ( ( SV356 != SV396 )
| ( subset @ SV356 @ SV396 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1928]) ).
thf(2071,plain,
! [SV397: $i,SV357: $i] :
( ( ( SV357 != SV397 )
| ( subset @ SV397 @ SV357 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1929]) ).
thf(2072,plain,
! [SV88: $i,SV274: $i,SV322: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV88 )
| ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV274 )
| ~ ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV322 ) )
| ~ ~ ( ~ ( ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV88 )
| ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV322 ) )
| ~ ( ~ ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV274 )
| ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV322 ) ) ) )
= $false )
| ( ( SV322
= ( set_difference @ SV88 @ SV274 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1930]) ).
thf(2073,plain,
! [SV275: $i,SV88: $i,SV323: $i] :
( ( ( SV323
= ( set_difference @ SV88 @ SV275 ) )
= $false )
| ( ( ~ ( ~ ! [SY883: $i] :
( ~ ( in @ SY883 @ SV88 )
| ( in @ SY883 @ SV275 )
| ( in @ SY883 @ SV323 ) )
| ~ ~ ( ~ ! [SY884: $i] :
( ~ ( in @ SY884 @ SV323 )
| ( in @ SY884 @ SV88 ) )
| ~ ! [SY885: $i] :
( ~ ( in @ SY885 @ SV323 )
| ~ ( in @ SY885 @ SV275 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1931]) ).
thf(2074,plain,
! [SV358: $i] :
( ( ( empty @ SV358 )
= $true )
| ( ( ! [SY919: $i] :
( ~ ( element @ SY919 @ SV358 )
| ( in @ SY919 @ SV358 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1932]) ).
thf(2075,plain,
! [SV359: $i] :
( ( ( empty @ SV359 )
= $true )
| ( ( ! [SY920: $i] :
( ~ ( in @ SY920 @ SV359 )
| ( element @ SY920 @ SV359 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1933]) ).
thf(2076,plain,
! [SV360: $i] :
( ( ( ~ ( empty @ SV360 ) )
= $true )
| ( ( ! [SY921: $i] :
( ~ ( element @ SY921 @ SV360 )
| ( empty @ SY921 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1934]) ).
thf(2077,plain,
! [SV361: $i] :
( ( ( ~ ( empty @ SV361 ) )
= $true )
| ( ( ! [SY922: $i] :
( ~ ( empty @ SY922 )
| ( element @ SY922 @ SV361 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1935]) ).
thf(2078,plain,
! [SV89: $i,SV174: $i,SV398: $i] :
( ( ( ~ ( relation @ SV398 )
| ~ ( ~ ( ~ ( in @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV174 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 ) )
| ~ ~ ( ~ ( ( in @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) @ SV89 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV174 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 ) ) ) )
| ( SV398
= ( relation_rng_restriction @ SV89 @ SV174 ) ) )
= $true )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1936]) ).
thf(2079,plain,
! [SV174: $i,SV89: $i,SV399: $i] :
( ( ( ~ ( relation @ SV399 )
| ( SV399
!= ( relation_rng_restriction @ SV89 @ SV174 ) )
| ~ ( ~ ! [SY968: $i,SY969: $i] :
( ~ ( in @ SY969 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY968 @ SY969 ) @ SV174 )
| ( in @ ( ordered_pair @ SY968 @ SY969 ) @ SV399 ) )
| ~ ~ ( ~ ! [SY970: $i,SY971: $i] :
( ~ ( in @ ( ordered_pair @ SY970 @ SY971 ) @ SV399 )
| ( in @ SY971 @ SV89 ) )
| ~ ! [SY972: $i,SY973: $i] :
( ~ ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV399 )
| ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV174 ) ) ) ) )
= $true )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1937]) ).
thf(2080,plain,
! [SV90: $i,SV276: $i,SV324: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SV324 @ SV276 @ SV90 ) @ SV324 )
| ( ( sK27_D @ SV324 @ SV276 @ SV90 )
!= SV90 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV324 @ SV276 @ SV90 ) @ SV324 )
| ( ( sK27_D @ SV324 @ SV276 @ SV90 )
!= SV276 ) ) )
| ~ ( ( in @ ( sK27_D @ SV324 @ SV276 @ SV90 ) @ SV324 )
| ( ( sK27_D @ SV324 @ SV276 @ SV90 )
= SV90 )
| ( ( sK27_D @ SV324 @ SV276 @ SV90 )
= SV276 ) ) )
= $false )
| ( ( SV324
= ( unordered_pair @ SV90 @ SV276 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1938]) ).
thf(2081,plain,
! [SV277: $i,SV90: $i,SV325: $i] :
( ( ( SV325
= ( unordered_pair @ SV90 @ SV277 ) )
= $false )
| ( ( ~ ( ~ ! [SY886: $i] :
( ~ ( in @ SY886 @ SV325 )
| ( SY886 = SV90 )
| ( SY886 = SV277 ) )
| ~ ~ ( ~ ! [SY887: $i] :
( ( SY887 != SV90 )
| ( in @ SY887 @ SV325 ) )
| ~ ! [SY888: $i] :
( ( SY888 != SV277 )
| ( in @ SY888 @ SV325 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1939]) ).
thf(2082,plain,
! [SV209: $i,SV278: $i] :
( ( ( ~ ( ~ ( in @ ( sK28_C @ SV278 @ SV209 ) @ SV278 )
| ~ ( subset @ ( sK28_C @ SV278 @ SV209 ) @ SV209 ) ) )
= $false )
| ( ( SV278
= ( powerset @ SV209 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1940]) ).
thf(2083,plain,
! [SV209: $i,SV278: $i] :
( ( ( ~ ( ( in @ ( sK28_C @ SV278 @ SV209 ) @ SV278 )
| ( subset @ ( sK28_C @ SV278 @ SV209 ) @ SV209 ) ) )
= $false )
| ( ( SV278
= ( powerset @ SV209 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1940]) ).
thf(2084,plain,
! [SV210: $i,SV279: $i] :
( ( ( ~ ! [SY835: $i] :
( ~ ( in @ SY835 @ SV279 )
| ( subset @ SY835 @ SV210 ) )
| ~ ! [SY836: $i] :
( ~ ( subset @ SY836 @ SV210 )
| ( in @ SY836 @ SV279 ) ) )
= $false )
| ( ( SV279
= ( powerset @ SV210 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1941]) ).
thf(2085,plain,
! [SV91: $i,SV362: $i] :
( ( ( ~ ( ~ ( ! [SY923: $i] :
~ ( in @ ( ordered_pair @ ( sK63_C @ SV362 @ SV91 ) @ SY923 ) @ SV91 )
| ~ ( in @ ( sK63_C @ SV362 @ SV91 ) @ SV362 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_C @ SV362 @ SV91 ) @ ( sK64_SY419 @ SV362 @ SV91 ) ) @ SV91 )
| ( in @ ( sK63_C @ SV362 @ SV91 ) @ SV362 ) ) ) )
= $true )
| ( ( SV362
= ( relation_dom @ SV91 ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1944]) ).
thf(2086,plain,
! [SV91: $i,SV363: $i] :
( ( ( ( SV363
!= ( relation_dom @ SV91 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY924: $i] :
( ! [SY530: $i] :
~ ( in @ ( ordered_pair @ SY924 @ SY530 ) @ SV91 )
| ( in @ SY924 @ SV363 ) )
| ~ ! [SY926: $i] :
( ~ ( in @ SY926 @ SV363 )
| ( in @ ( ordered_pair @ SY926 @ ( sK62_D @ SY926 @ SV363 @ SV91 ) ) @ SV91 ) ) ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1945]) ).
thf(2087,plain,
! [SV92: $i,SV364: $i,SV400: $i] :
( ( ( ~ ( ~ ( ! [SY974: $i] :
( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SY974 ) @ SV92 )
| ~ ( in @ SY974 @ SV364 ) )
| ~ ( in @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SV400 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ ( sK36_SY409 @ SV400 @ SV364 @ SV92 ) ) @ SV92 )
| ~ ( in @ ( sK36_SY409 @ SV400 @ SV364 @ SV92 ) @ SV364 ) )
| ( in @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SV400 ) ) )
| ( SV400
= ( relation_inverse_image @ SV92 @ SV364 ) ) )
= $true )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1946]) ).
thf(2088,plain,
! [SV365: $i,SV92: $i,SV401: $i] :
( ( ( ( SV401
!= ( relation_inverse_image @ SV92 @ SV365 ) )
| ~ ( ~ ! [SY975: $i] :
( ! [SY931: $i] :
( ~ ( in @ ( ordered_pair @ SY975 @ SY931 ) @ SV92 )
| ~ ( in @ SY931 @ SV365 ) )
| ( in @ SY975 @ SV401 ) )
| ~ ! [SY977: $i] :
( ~ ( in @ SY977 @ SV401 )
| ~ ( ~ ( in @ ( ordered_pair @ SY977 @ ( sK34_E @ SY977 @ SV401 @ SV365 @ SV92 ) ) @ SV92 )
| ~ ( in @ ( sK34_E @ SY977 @ SV401 @ SV365 @ SV92 ) @ SV365 ) ) ) ) )
= $true )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1947]) ).
thf(2089,plain,
! [SV93: $i,SV366: $i,SV402: $i] :
( ( ( ~ ( ~ ( ! [SY978: $i] :
( ~ ( in @ ( ordered_pair @ SY978 @ ( sK38_D @ SV402 @ SV366 @ SV93 ) ) @ SV93 )
| ~ ( in @ SY978 @ SV366 ) )
| ~ ( in @ ( sK38_D @ SV402 @ SV366 @ SV93 ) @ SV402 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SV402 @ SV366 @ SV93 ) @ ( sK38_D @ SV402 @ SV366 @ SV93 ) ) @ SV93 )
| ~ ( in @ ( sK39_SY411 @ SV402 @ SV366 @ SV93 ) @ SV366 ) )
| ( in @ ( sK38_D @ SV402 @ SV366 @ SV93 ) @ SV402 ) ) )
| ( SV402
= ( relation_image @ SV93 @ SV366 ) ) )
= $true )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1948]) ).
thf(2090,plain,
! [SV367: $i,SV93: $i,SV403: $i] :
( ( ( ( SV403
!= ( relation_image @ SV93 @ SV367 ) )
| ~ ( ~ ! [SY979: $i] :
( ! [SY937: $i] :
( ~ ( in @ ( ordered_pair @ SY937 @ SY979 ) @ SV93 )
| ~ ( in @ SY937 @ SV367 ) )
| ( in @ SY979 @ SV403 ) )
| ~ ! [SY981: $i] :
( ~ ( in @ SY981 @ SV403 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SY981 @ SV403 @ SV367 @ SV93 ) @ SY981 ) @ SV93 )
| ~ ( in @ ( sK37_E @ SY981 @ SV403 @ SV367 @ SV93 ) @ SV367 ) ) ) ) )
= $true )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1949]) ).
thf(2091,plain,
! [SV282: $i,SV94: $i,SV326: $i] :
( ( ( relation @ SV326 )
= $false )
| ( ( ! [SY889: $i] :
( ~ ( in @ SY889 @ ( relation_rng @ SV326 ) )
| ~ ( in @ ( ordered_pair @ SV94 @ SY889 ) @ SV326 )
| ~ ( in @ SY889 @ SV282 ) )
| ( in @ SV94 @ ( relation_inverse_image @ SV326 @ SV282 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1950]) ).
thf(2092,plain,
! [SV283: $i,SV94: $i,SV327: $i] :
( ( ( relation @ SV327 )
= $false )
| ( ( ~ ( in @ SV94 @ ( relation_inverse_image @ SV327 @ SV283 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK51_D @ SV327 @ SV283 @ SV94 ) @ ( relation_rng @ SV327 ) )
| ~ ( in @ ( ordered_pair @ SV94 @ ( sK51_D @ SV327 @ SV283 @ SV94 ) ) @ SV327 ) )
| ~ ( in @ ( sK51_D @ SV327 @ SV283 @ SV94 ) @ SV283 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1951]) ).
thf(2093,plain,
! [SV175: $i,SV95: $i] :
( ( ( ~ ! [SY731: $i] :
( ~ ( function @ SY731 )
| ~ ( relation @ SY731 )
| ~ ( in @ SV95 @ ( relation_dom @ SY731 ) )
| ~ ( in @ ( apply @ SY731 @ SV95 ) @ ( relation_dom @ SV175 ) )
| ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY731 @ SV175 ) ) ) ) )
= $false )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1952]) ).
thf(2094,plain,
! [SV175: $i,SV95: $i] :
( ( ( ~ ~ ( ~ ! [SY732: $i] :
( ~ ( function @ SY732 )
| ~ ( relation @ SY732 )
| ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY732 @ SV175 ) ) )
| ( in @ SV95 @ ( relation_dom @ SY732 ) ) )
| ~ ! [SY733: $i] :
( ~ ( function @ SY733 )
| ~ ( relation @ SY733 )
| ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY733 @ SV175 ) ) )
| ( in @ ( apply @ SY733 @ SV95 ) @ ( relation_dom @ SV175 ) ) ) ) )
= $false )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1952]) ).
thf(2095,plain,
! [SV96: $i,SV368: $i,SV404: $i] :
( ( ( ~ ( relation @ SV404 )
| ~ ( ~ ( ~ ( in @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ SV368 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 ) )
| ~ ~ ( ~ ( ( in @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ SV368 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 ) ) ) )
| ( SV404
= ( relation_dom_restriction @ SV96 @ SV368 ) ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1953]) ).
thf(2096,plain,
! [SV369: $i,SV96: $i,SV405: $i] :
( ( ( ~ ( relation @ SV405 )
| ( SV405
!= ( relation_dom_restriction @ SV96 @ SV369 ) )
| ~ ( ~ ! [SY982: $i,SY983: $i] :
( ~ ( in @ SY982 @ SV369 )
| ~ ( in @ ( ordered_pair @ SY982 @ SY983 ) @ SV96 )
| ( in @ ( ordered_pair @ SY982 @ SY983 ) @ SV405 ) )
| ~ ~ ( ~ ! [SY984: $i] :
( ! [SY985: $i] :
~ ( in @ ( ordered_pair @ SY984 @ SY985 ) @ SV405 )
| ( in @ SY984 @ SV369 ) )
| ~ ! [SY986: $i,SY987: $i] :
( ~ ( in @ ( ordered_pair @ SY986 @ SY987 ) @ SV405 )
| ( in @ ( ordered_pair @ SY986 @ SY987 ) @ SV96 ) ) ) ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(2097,plain,
! [SV284: $i,SV213: $i] :
( ( ( empty @ SV213 )
= $false )
| ( ( ~ ( relation @ SV284 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV284 @ SV213 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1955]) ).
thf(2098,plain,
! [SV285: $i,SV214: $i] :
( ( ( empty @ SV214 )
= $false )
| ( ( ~ ( relation @ SV285 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV285 @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1956]) ).
thf(2099,plain,
! [SV97: $i,SV370: $i] :
( ( ( ~ ( relation @ SV370 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SV370 @ SV97 ) @ ( sK12_SY396 @ SV370 @ SV97 ) ) @ SV370 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SV370 @ SV97 ) @ ( sK11_C @ SV370 @ SV97 ) ) @ SV97 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_C @ SV370 @ SV97 ) @ ( sK12_SY396 @ SV370 @ SV97 ) ) @ SV370 )
| ( in @ ( ordered_pair @ ( sK12_SY396 @ SV370 @ SV97 ) @ ( sK11_C @ SV370 @ SV97 ) ) @ SV97 ) ) )
| ( SV370
= ( relation_inverse @ SV97 ) ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1957]) ).
thf(2100,plain,
! [SV97: $i,SV371: $i] :
( ( ( ~ ( relation @ SV371 ) )
= $true )
| ( ( ( SV371
!= ( relation_inverse @ SV97 ) )
| ~ ( ~ ! [SY947: $i,SY948: $i] :
( ~ ( in @ ( ordered_pair @ SY947 @ SY948 ) @ SV371 )
| ( in @ ( ordered_pair @ SY948 @ SY947 ) @ SV97 ) )
| ~ ! [SY949: $i,SY950: $i] :
( ~ ( in @ ( ordered_pair @ SY950 @ SY949 ) @ SV97 )
| ( in @ ( ordered_pair @ SY949 @ SY950 ) @ SV371 ) ) ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1958]) ).
thf(2101,plain,
! [SV98: $i,SV372: $i] :
( ( ( ~ ( ~ ( ! [SY951: $i] :
~ ( in @ ( ordered_pair @ SY951 @ ( sK60_C @ SV372 @ SV98 ) ) @ SV98 )
| ~ ( in @ ( sK60_C @ SV372 @ SV98 ) @ SV372 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK61_SY417 @ SV372 @ SV98 ) @ ( sK60_C @ SV372 @ SV98 ) ) @ SV98 )
| ( in @ ( sK60_C @ SV372 @ SV98 ) @ SV372 ) ) ) )
= $true )
| ( ( SV372
= ( relation_rng @ SV98 ) )
= $true )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1959]) ).
thf(2102,plain,
! [SV98: $i,SV373: $i] :
( ( ( ( SV373
!= ( relation_rng @ SV98 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY952: $i] :
( ! [SY577: $i] :
~ ( in @ ( ordered_pair @ SY577 @ SY952 ) @ SV98 )
| ( in @ SY952 @ SV373 ) )
| ~ ! [SY954: $i] :
( ~ ( in @ SY954 @ SV373 )
| ( in @ ( ordered_pair @ ( sK59_D @ SY954 @ SV373 @ SV98 ) @ SY954 ) @ SV98 ) ) ) )
= $true )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1960]) ).
thf(2103,plain,
! [SV99: $i,SV176: $i] :
( ( ( in @ ( sK4_C @ SV176 @ SV99 ) @ SV99 )
= $false )
| ( ( ~ ( in @ ( sK4_C @ SV176 @ SV99 ) @ SV176 ) )
= $true )
| ( ( SV99 = SV176 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1961]) ).
thf(2104,plain,
! [SV100: $i,SV286: $i,SV328: $i] :
( ( ( ~ ( function @ SV328 ) )
= $true )
| ( ( ~ ( relation @ SV328 ) )
= $true )
| ( ( ( SV286
!= ( apply @ SV328 @ SV100 ) )
| ~ ( in @ SV100 @ ( relation_dom @ SV328 ) )
| ( in @ ( ordered_pair @ SV100 @ SV286 ) @ SV328 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1963]) ).
thf(2105,plain,
! [SV406: $i,SV100: $i] :
( ( ! [SY988: $i] :
( ~ ( function @ SY988 )
| ~ ( relation @ SY988 )
| ~ ( in @ ( ordered_pair @ SV100 @ SV406 ) @ SY988 )
| ( SV406
= ( apply @ SY988 @ SV100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1964]) ).
thf(2106,plain,
! [SV407: $i,SV100: $i] :
( ( ! [SY989: $i] :
( ~ ( function @ SY989 )
| ~ ( relation @ SY989 )
| ~ ( in @ ( ordered_pair @ SV100 @ SV407 ) @ SY989 )
| ( in @ SV100 @ ( relation_dom @ SY989 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1965]) ).
thf(2107,plain,
! [SV101: $i,SV215: $i] :
( ( ( ~ ! [SY778: $i] :
( ~ ( relation @ SY778 )
| ~ ( ~ ( ! [SY779: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY778 @ SV215 @ SV101 ) @ SY779 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY779 @ ( sK9_SY391 @ SY778 @ SV215 @ SV101 ) ) @ SV215 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SY778 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SY778 @ SV215 @ SV101 ) ) @ SY778 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY778 @ SV215 @ SV101 ) @ ( sK10_SY395 @ SY778 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SY778 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SY778 @ SV215 @ SV101 ) ) @ SV215 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SY778 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SY778 @ SV215 @ SV101 ) ) @ SY778 ) ) )
| ( SY778
= ( relation_composition @ SV101 @ SV215 ) ) ) )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1966]) ).
thf(2108,plain,
! [SV215: $i,SV101: $i] :
( ( ( ~ ! [SY780: $i] :
( ~ ( relation @ SY780 )
| ( SY780
!= ( relation_composition @ SV101 @ SV215 ) )
| ~ ( ~ ! [SY781: $i,SY782: $i] :
( ! [SY783: $i] :
( ~ ( in @ ( ordered_pair @ SY781 @ SY783 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY783 @ SY782 ) @ SV215 ) )
| ( in @ ( ordered_pair @ SY781 @ SY782 ) @ SY780 ) )
| ~ ! [SY784: $i,SY785: $i] :
( ~ ( in @ ( ordered_pair @ SY784 @ SY785 ) @ SY780 )
| ~ ( ~ ( in @ ( ordered_pair @ SY784 @ ( sK7_F @ SY785 @ SY784 @ SY780 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY785 @ SY784 @ SY780 @ SV215 @ SV101 ) @ SY785 ) @ SV215 ) ) ) ) ) )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1966]) ).
thf(2109,plain,
! [SV374: $i,SV177: $i,SV329: $i,SV102: $i] :
( ( ( ~ ( in @ SV102 @ SV329 )
| ~ ( in @ SV177 @ SV374 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SV329 @ SV374 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1967]) ).
thf(2110,plain,
! [SV177: $i,SV102: $i] :
( ( ! [SY736: $i] :
( ! [SY737: $i] :
~ ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SY736 @ SY737 ) )
| ( in @ SV102 @ SY736 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1968]) ).
thf(2111,plain,
! [SV177: $i,SV102: $i] :
( ( ! [SY738: $i,SY739: $i] :
( ~ ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SY738 @ SY739 ) )
| ( in @ SV177 @ SY739 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1969]) ).
thf(2112,plain,
! [SV216: $i] :
( ( ( ( relation_dom @ SV216 )
= empty_set )
= $false )
| ( ( SV216 = empty_set )
= $true )
| ( ( relation @ SV216 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1970]) ).
thf(2113,plain,
! [SV217: $i] :
( ( ( ( relation_rng @ SV217 )
= empty_set )
= $false )
| ( ( SV217 = empty_set )
= $true )
| ( ( relation @ SV217 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1971]) ).
thf(2114,plain,
! [SV103: $i,SV287: $i] :
( ( ( subset @ SV287 @ ( sK2_B @ SV103 ) )
= $false )
| ( ( are_equipotent @ SV287 @ ( sK2_B @ SV103 ) )
= $true )
| ( ( in @ SV287 @ ( sK2_B @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1972]) ).
thf(2115,plain,
! [SV103: $i,SV408: $i] :
( ( ~ ( ~ ! [SY990: $i] :
( ~ ( subset @ SY990 @ SV408 )
| ( in @ SY990 @ ( sK3_SY386 @ SV408 @ SV103 ) ) )
| ~ ( in @ ( sK3_SY386 @ SV408 @ SV103 ) @ ( sK2_B @ SV103 ) ) )
| ~ ( in @ SV408 @ ( sK2_B @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1973]) ).
thf(2116,plain,
! [SV103: $i] :
( ( ~ ! [SY605: $i,SY606: $i] :
( ~ ( in @ SY605 @ ( sK2_B @ SV103 ) )
| ~ ( subset @ SY606 @ SY605 )
| ( in @ SY606 @ ( sK2_B @ SV103 ) ) )
| ~ ( in @ SV103 @ ( sK2_B @ SV103 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1974]) ).
thf(2117,plain,
! [SV218: $i] :
( ( ( relation @ SV218 )
= $false )
| ( ( function @ SV218 )
= $false )
| ( ( function @ ( function_inverse @ SV218 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1975]) ).
thf(2118,plain,
! [SV219: $i] :
( ( ( relation @ SV219 )
= $false )
| ( ( function @ SV219 )
= $false )
| ( ( relation @ ( function_inverse @ SV219 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1976]) ).
thf(2119,plain,
! [SV222: $i] :
( ( ( ! [SY786: $i,SY787: $i] :
( ( sK69_B @ SV222 )
!= ( ordered_pair @ SY786 @ SY787 ) ) )
= $true )
| ( ( relation @ SV222 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1977]) ).
thf(2120,plain,
! [SV222: $i] :
( ( ( in @ ( sK69_B @ SV222 ) @ SV222 )
= $true )
| ( ( relation @ SV222 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1978]) ).
thf(2121,plain,
! [SV223: $i,SV375: $i] :
( ( ( SV375
= ( ordered_pair @ ( sK67_C @ SV375 @ SV223 ) @ ( sK68_SY421 @ SV375 @ SV223 ) ) )
= $true )
| ( ( ~ ( in @ SV375 @ SV223 ) )
= $true )
| ( ( relation @ SV223 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1979]) ).
thf(2122,plain,
! [SV104: $i,SV376: $i] :
( ( ( ~ ( relation @ SV376 ) )
= $true )
| ( ( ~ ( subset @ SV104 @ SV376 )
| ( subset @ ( relation_dom @ SV104 ) @ ( relation_dom @ SV376 ) ) )
= $true )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1980]) ).
thf(2123,plain,
! [SV104: $i,SV377: $i] :
( ( ( ~ ( relation @ SV377 ) )
= $true )
| ( ( ~ ( subset @ SV104 @ SV377 )
| ( subset @ ( relation_rng @ SV104 ) @ ( relation_rng @ SV377 ) ) )
= $true )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1981]) ).
thf(2124,plain,
! [SV288: $i,SV105: $i,SV330: $i] :
( ( ( relation @ SV330 )
= $false )
| ( ( ~ ( in @ SV105 @ SV288 )
| ~ ( in @ SV105 @ ( relation_rng @ SV330 ) )
| ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SV288 @ SV330 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1982]) ).
thf(2125,plain,
! [SV409: $i,SV105: $i] :
( ( ! [SY991: $i] :
( ~ ( relation @ SY991 )
| ~ ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SV409 @ SY991 ) ) )
| ( in @ SV105 @ SV409 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2126,plain,
! [SV410: $i,SV105: $i] :
( ( ! [SY992: $i] :
( ~ ( relation @ SY992 )
| ~ ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SV410 @ SY992 ) ) )
| ( in @ SV105 @ ( relation_rng @ SY992 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1984]) ).
thf(2127,plain,
! [SV289: $i,SV331: $i,SV106: $i] :
( ( ( ~ ( in @ SV106 @ SV331 ) )
= $true )
| ( ( ~ ( in @ SV289 @ SV331 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV106 @ SV289 ) @ SV331 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1985]) ).
thf(2128,plain,
! [SV411: $i,SV106: $i] :
( ( ! [SY993: $i] :
( ~ ( subset @ ( unordered_pair @ SV106 @ SV411 ) @ SY993 )
| ( in @ SV106 @ SY993 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1986]) ).
thf(2129,plain,
! [SV412: $i,SV106: $i] :
( ( ! [SY994: $i] :
( ~ ( subset @ ( unordered_pair @ SV106 @ SV412 ) @ SY994 )
| ( in @ SV412 @ SY994 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1987]) ).
thf(2130,plain,
! [SV178: $i,SV332: $i,SV107: $i,SV378: $i] :
( ( ( ~ ( relation @ SV378 ) )
= $true )
| ( ( ~ ( in @ SV107 @ SV332 )
| ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ SV378 )
| ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SV332 ) @ SV378 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1988]) ).
thf(2131,plain,
! [SV178: $i,SV107: $i] :
( ( ! [SY742: $i,SY743: $i] :
( ~ ( relation @ SY743 )
| ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SY742 ) @ SY743 ) )
| ( in @ SV107 @ SY742 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1989]) ).
thf(2132,plain,
! [SV178: $i,SV107: $i] :
( ( ! [SY744: $i,SY745: $i] :
( ~ ( relation @ SY745 )
| ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SY744 ) @ SY745 ) )
| ( in @ ( ordered_pair @ SV107 @ SV178 ) @ SY745 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1990]) ).
thf(2133,plain,
! [SV108: $i,SV379: $i] :
( ( ( ~ ( relation @ SV379 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV379 @ SV108 ) @ ( sK20_SY399 @ SV379 @ SV108 ) ) @ SV108 )
| ~ ~ ( in @ ( ordered_pair @ ( sK19_C @ SV379 @ SV108 ) @ ( sK20_SY399 @ SV379 @ SV108 ) ) @ SV379 ) )
| ( subset @ SV108 @ SV379 ) )
= $true )
| ( ( relation @ SV108 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1991]) ).
thf(2134,plain,
! [SV108: $i,SV380: $i] :
( ( ( ~ ( relation @ SV380 ) )
= $true )
| ( ( ~ ( subset @ SV108 @ SV380 )
| ! [SY955: $i,SY956: $i] :
( ~ ( in @ ( ordered_pair @ SY955 @ SY956 ) @ SV108 )
| ( in @ ( ordered_pair @ SY955 @ SY956 ) @ SV380 ) ) )
= $true )
| ( ( relation @ SV108 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1992]) ).
thf(2135,plain,
! [SV228: $i,SV290: $i] :
( ( ( ~ ( ( ( sK30_C @ SV290 @ SV228 )
!= SV228 )
| ~ ( in @ ( sK30_C @ SV290 @ SV228 ) @ SV290 ) ) )
= $false )
| ( ( SV290
= ( singleton @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1993]) ).
thf(2136,plain,
! [SV228: $i,SV290: $i] :
( ( ( ~ ( ( ( sK30_C @ SV290 @ SV228 )
= SV228 )
| ( in @ ( sK30_C @ SV290 @ SV228 ) @ SV290 ) ) )
= $false )
| ( ( SV290
= ( singleton @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1993]) ).
thf(2137,plain,
! [SV291: $i,SV229: $i] :
( ( ( ~ ! [SY843: $i] :
( ( SY843 != SV229 )
| ( in @ SY843 @ SV291 ) )
| ~ ! [SY844: $i] :
( ~ ( in @ SY844 @ SV291 )
| ( SY844 = SV229 ) ) )
= $false )
| ( ( SV291
= ( singleton @ SV229 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1994]) ).
thf(2138,plain,
! [SV292: $i,SV109: $i,SV333: $i] :
( ( ( relation @ SV333 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV109 @ SV292 ) @ SV333 )
| ( in @ SV109 @ ( relation_dom @ SV333 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1995]) ).
thf(2139,plain,
! [SV293: $i,SV109: $i,SV334: $i] :
( ( ( relation @ SV334 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV109 @ SV293 ) @ SV334 )
| ( in @ SV293 @ ( relation_rng @ SV334 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1996]) ).
thf(2140,plain,
! [SV381: $i] :
( ( ( ~ ( empty @ SV381 )
| ~ ( relation @ SV381 )
| ~ ( function @ SV381 ) )
= $true )
| ( ( function @ SV381 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1997]) ).
thf(2141,plain,
! [SV382: $i] :
( ( ( ~ ( empty @ SV382 )
| ~ ( relation @ SV382 )
| ~ ( function @ SV382 ) )
= $true )
| ( ( relation @ SV382 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1998]) ).
thf(2142,plain,
! [SV230: $i] :
( ( ( empty @ SV230 )
= $false )
| ( ( ~ ( relation @ SV230 ) )
= $true )
| ( ( ~ ( function @ SV230 ) )
= $true )
| ( ( one_to_one @ SV230 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1999]) ).
thf(2143,plain,
! [SV110: $i] :
( ( ( ~ ! [SY636: $i] :
( ~ ( function @ SY636 )
| ~ ( relation @ SY636 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SY636 @ SV110 )
= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ( ( sK70_C @ SY636 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY636 @ SV110 )
= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY636 @ SV110 )
= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ( ( sK71_SY424 @ SY636 @ SV110 )
!= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK70_C @ SY636 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK71_SY424 @ SY636 @ SV110 )
!= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY636 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK70_C @ SY636 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SY636 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SY636 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK71_SY424 @ SY636 @ SV110 )
!= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ( ( relation_dom @ SY636 )
!= ( relation_rng @ SV110 ) )
| ( SY636
= ( function_inverse @ SV110 ) ) )
| ~ ~ ( ~ ! [SY637: $i] :
( ~ ( function @ SY637 )
| ~ ( relation @ SY637 )
| ( SY637
!= ( function_inverse @ SV110 ) )
| ~ ( ~ ~ ( ~ ! [SY638: $i,SY639: $i] :
( ( SY639
!= ( apply @ SY637 @ SY638 ) )
| ~ ( in @ SY638 @ ( relation_rng @ SV110 ) )
| ( SY638
= ( apply @ SV110 @ SY639 ) ) )
| ~ ! [SY640: $i,SY641: $i] :
( ( SY641
!= ( apply @ SY637 @ SY640 ) )
| ~ ( in @ SY640 @ ( relation_rng @ SV110 ) )
| ( in @ SY641 @ ( relation_dom @ SV110 ) ) ) )
| ~ ~ ( ~ ! [SY642: $i,SY643: $i] :
( ( SY642
!= ( apply @ SV110 @ SY643 ) )
| ~ ( in @ SY643 @ ( relation_dom @ SV110 ) )
| ( SY643
= ( apply @ SY637 @ SY642 ) ) )
| ~ ! [SY644: $i] :
( ! [SY645: $i] :
( ( SY644
!= ( apply @ SV110 @ SY645 ) )
| ~ ( in @ SY645 @ ( relation_dom @ SV110 ) ) )
| ( in @ SY644 @ ( relation_rng @ SV110 ) ) ) ) ) )
| ~ ! [SY646: $i] :
( ~ ( function @ SY646 )
| ~ ( relation @ SY646 )
| ( SY646
!= ( function_inverse @ SV110 ) )
| ( ( relation_dom @ SY646 )
= ( relation_rng @ SV110 ) ) ) ) )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2000]) ).
thf(2144,plain,
! [SV294: $i,SV233: $i] :
( ( ( subset @ SV233 @ SV294 )
= $false )
| ( ( SV233 = SV294 )
= $true )
| ( ( proper_subset @ SV233 @ SV294 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2001]) ).
thf(2145,plain,
! [SV413: $i,SV383: $i] :
( ( ~ ( proper_subset @ SV383 @ SV413 )
| ( SV383 != SV413 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2002]) ).
thf(2146,plain,
! [SV414: $i,SV384: $i] :
( ( ~ ( proper_subset @ SV384 @ SV414 )
| ( subset @ SV384 @ SV414 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2003]) ).
thf(2147,plain,
! [SV234: $i,SV295: $i] :
( ( ( ~ ( in @ ( sK18_C @ SV295 @ SV234 ) @ SV234 ) )
= $false )
| ( ( subset @ SV234 @ SV295 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2004]) ).
thf(2148,plain,
! [SV234: $i,SV295: $i] :
( ( ( ~ ~ ( in @ ( sK18_C @ SV295 @ SV234 ) @ SV295 ) )
= $false )
| ( ( subset @ SV234 @ SV295 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2004]) ).
thf(2149,plain,
! [SV296: $i,SV235: $i,SV415: $i] :
( ( ( ~ ( in @ SV415 @ SV235 )
| ( in @ SV415 @ SV296 ) )
= $true )
| ( ( subset @ SV235 @ SV296 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2005]) ).
thf(2150,plain,
! [SV236: $i,SV297: $i] :
( ( ( ~ ( in @ ( sK49_C @ SV297 @ SV236 ) @ SV236 ) )
= $false )
| ( ( disjoint @ SV236 @ SV297 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2006]) ).
thf(2151,plain,
! [SV236: $i,SV297: $i] :
( ( ( ~ ( in @ ( sK49_C @ SV297 @ SV236 ) @ SV297 ) )
= $false )
| ( ( disjoint @ SV236 @ SV297 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2006]) ).
thf(2152,plain,
! [SV298: $i,SV237: $i,SV385: $i] :
( ( ( ~ ( in @ SV385 @ SV237 ) )
= $true )
| ( ( ~ ( in @ SV385 @ SV298 ) )
= $true )
| ( ( ~ ( disjoint @ SV237 @ SV298 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2007]) ).
thf(2153,plain,
! [SV386: $i,SV179: $i,SV335: $i,SV111: $i] :
( ( ( ~ ( in @ SV111 @ SV335 )
| ~ ( in @ SV179 @ SV386 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SV335 @ SV386 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2008]) ).
thf(2154,plain,
! [SV179: $i,SV111: $i] :
( ( ! [SY748: $i] :
( ! [SY749: $i] :
~ ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SY748 @ SY749 ) )
| ( in @ SV111 @ SY748 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2009]) ).
thf(2155,plain,
! [SV179: $i,SV111: $i] :
( ( ! [SY750: $i,SY751: $i] :
( ~ ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SY750 @ SY751 ) )
| ( in @ SV179 @ SY751 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2010]) ).
thf(2156,plain,
! [SV416: $i,SV336: $i,SV180: $i,SV112: $i] :
( ( ( ( ( ordered_pair @ SV112 @ SV180 )
!= ( ordered_pair @ SV336 @ SV416 ) ) )
= $true )
| ( ( SV112 = SV336 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2011]) ).
thf(2157,plain,
! [SV387: $i,SV337: $i,SV180: $i,SV112: $i] :
( ( ( ( ( ordered_pair @ SV112 @ SV180 )
!= ( ordered_pair @ SV337 @ SV387 ) ) )
= $true )
| ( ( SV180 = SV387 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2012]) ).
thf(2158,plain,
! [SV113: $i] :
( ( ( ~ ( ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ ( relation_dom @ SV113 ) )
| ! [SY660: $i] :
( ( SY660
!= ( apply @ SV113 @ SY659 ) )
| ( in @ ( ordered_pair @ SY659 @ SY660 ) @ SV113 ) ) )
| ~ ! [SY661: $i] :
( ~ ( in @ SY661 @ ( relation_dom @ SV113 ) )
| ! [SY662: $i] :
( ~ ( in @ ( ordered_pair @ SY661 @ SY662 ) @ SV113 )
| ( SY662
= ( apply @ SV113 @ SY661 ) ) ) ) ) )
= $true )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2013]) ).
thf(2159,plain,
! [SV113: $i] :
( ( ( ~ ( ~ ! [SY663: $i] :
( ( in @ SY663 @ ( relation_dom @ SV113 ) )
| ! [SY664: $i] :
( ( SY664
!= ( apply @ SV113 @ SY663 ) )
| ( SY664 = empty_set ) ) )
| ~ ! [SY665: $i] :
( ( in @ SY665 @ ( relation_dom @ SV113 ) )
| ! [SY666: $i] :
( ( SY666 != empty_set )
| ( SY666
= ( apply @ SV113 @ SY665 ) ) ) ) ) )
= $true )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2014]) ).
thf(2160,plain,
! [SV243: $i,SV388: $i] :
( ( ( in @ SV388 @ SV243 )
= $false )
| ( ( SV243 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2017]) ).
thf(2161,plain,
! [SV114: $i,SV301: $i,SV338: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV338 )
| ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV114 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV338 )
| ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV301 ) ) )
| ~ ( ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV338 )
| ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV114 )
| ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV301 ) ) )
= $false )
| ( ( SV338
= ( set_union2 @ SV114 @ SV301 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2018]) ).
thf(2162,plain,
! [SV302: $i,SV114: $i,SV339: $i] :
( ( ( SV339
= ( set_union2 @ SV114 @ SV302 ) )
= $false )
| ( ( ~ ( ~ ! [SY895: $i] :
( ~ ( in @ SY895 @ SV339 )
| ( in @ SY895 @ SV114 )
| ( in @ SY895 @ SV302 ) )
| ~ ~ ( ~ ! [SY896: $i] :
( ~ ( in @ SY896 @ SV114 )
| ( in @ SY896 @ SV339 ) )
| ~ ! [SY897: $i] :
( ~ ( in @ SY897 @ SV302 )
| ( in @ SY897 @ SV339 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2019]) ).
thf(2163,plain,
! [SV303: $i,SV115: $i,SV340: $i] :
( ( ( relation @ SV340 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV115 @ SV303 ) @ SV340 )
| ( in @ SV115 @ ( relation_field @ SV340 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2020]) ).
thf(2164,plain,
! [SV304: $i,SV115: $i,SV341: $i] :
( ( ( relation @ SV341 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV115 @ SV304 ) @ SV341 )
| ( in @ SV304 @ ( relation_field @ SV341 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2021]) ).
thf(2165,plain,
! [SV246: $i] :
( ( ( ( relation_dom @ SV246 )
= empty_set )
= $false )
| ( ( ( relation_rng @ SV246 )
= empty_set )
= $true )
| ( ( relation @ SV246 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2022]) ).
thf(2166,plain,
! [SV247: $i] :
( ( ( ( relation_rng @ SV247 )
= empty_set )
= $false )
| ( ( ( relation_dom @ SV247 )
= empty_set )
= $true )
| ( ( relation @ SV247 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2023]) ).
thf(2167,plain,
! [SV305: $i,SV248: $i] :
( ( ( SV248 = empty_set )
= $true )
| ( ( SV248
= ( singleton @ SV305 ) )
= $true )
| ( ( subset @ SV248 @ ( singleton @ SV305 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2024]) ).
thf(2168,plain,
! [SV389: $i] :
( ( ( ( SV389 != empty_set ) )
= $true )
| ( ( ! [SY959: $i] : ( subset @ SV389 @ ( singleton @ SY959 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2025]) ).
thf(2169,plain,
! [SV417: $i,SV390: $i] :
( ( ( SV390
!= ( singleton @ SV417 ) )
| ( subset @ SV390 @ ( singleton @ SV417 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2026]) ).
thf(2170,plain,
! [SV116: $i,SV306: $i,SV342: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV116 )
| ~ ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV306 )
| ~ ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV342 ) )
| ~ ~ ( ~ ( ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV116 )
| ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV342 ) )
| ~ ( ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV306 )
| ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV342 ) ) ) )
= $false )
| ( ( SV342
= ( set_intersection2 @ SV116 @ SV306 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2027]) ).
thf(2171,plain,
! [SV307: $i,SV116: $i,SV343: $i] :
( ( ( SV343
= ( set_intersection2 @ SV116 @ SV307 ) )
= $false )
| ( ( ~ ( ~ ! [SY898: $i] :
( ~ ( in @ SY898 @ SV116 )
| ~ ( in @ SY898 @ SV307 )
| ( in @ SY898 @ SV343 ) )
| ~ ~ ( ~ ! [SY899: $i] :
( ~ ( in @ SY899 @ SV343 )
| ( in @ SY899 @ SV116 ) )
| ~ ! [SY900: $i] :
( ~ ( in @ SY900 @ SV343 )
| ( in @ SY900 @ SV307 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2028]) ).
thf(2172,plain,
! [SV249: $i] :
( ( ( function @ SV249 )
= $false )
| ( ( ~ ( relation @ SV249 ) )
= $true )
| ( ( ~ ( one_to_one @ SV249 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2029]) ).
thf(2173,plain,
! [SV250: $i] :
( ( ( function @ SV250 )
= $false )
| ( ( ~ ( relation @ SV250 ) )
= $true )
| ( ( ~ ( one_to_one @ SV250 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2030]) ).
thf(2174,plain,
! [SV251: $i,SV308: $i] :
( ( ( ~ ( ~ ( ( ( sK44_C @ SV308 @ SV251 )
!= ( sK45_SY414 @ SV308 @ SV251 ) )
| ~ ( in @ ( sK44_C @ SV308 @ SV251 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 ) )
| ~ ~ ( ~ ( ( ( sK44_C @ SV308 @ SV251 )
= ( sK45_SY414 @ SV308 @ SV251 ) )
| ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 ) )
| ~ ( ( in @ ( sK44_C @ SV308 @ SV251 ) @ SV251 )
| ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 ) ) ) ) )
= $true )
| ( ( SV308
= ( identity_relation @ SV251 ) )
= $true )
| ( ( relation @ SV308 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2031]) ).
thf(2175,plain,
! [SV252: $i,SV309: $i] :
( ( ( ( SV309
!= ( identity_relation @ SV252 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY861: $i,SY862: $i] :
( ( SY861 != SY862 )
| ~ ( in @ SY861 @ SV252 )
| ( in @ ( ordered_pair @ SY861 @ SY862 ) @ SV309 ) )
| ~ ~ ( ~ ! [SY863: $i,SY864: $i] :
( ~ ( in @ ( ordered_pair @ SY863 @ SY864 ) @ SV309 )
| ( SY863 = SY864 ) )
| ~ ! [SY865: $i] :
( ! [SY866: $i] :
~ ( in @ ( ordered_pair @ SY865 @ SY866 ) @ SV309 )
| ( in @ SY865 @ SV252 ) ) ) ) )
= $true )
| ( ( relation @ SV309 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2032]) ).
thf(2176,plain,
! [SV310: $i,SV117: $i,SV344: $i] :
( ( ( relation @ SV344 )
= $false )
| ( ( ~ ( in @ SV117 @ SV310 )
| ~ ( in @ SV117 @ ( relation_dom @ SV344 ) )
| ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SV344 @ SV310 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2033]) ).
thf(2177,plain,
! [SV418: $i,SV117: $i] :
( ( ! [SY995: $i] :
( ~ ( relation @ SY995 )
| ~ ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SY995 @ SV418 ) ) )
| ( in @ SV117 @ SV418 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2034]) ).
thf(2178,plain,
! [SV419: $i,SV117: $i] :
( ( ! [SY996: $i] :
( ~ ( relation @ SY996 )
| ~ ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SY996 @ SV419 ) ) )
| ( in @ SV117 @ ( relation_dom @ SY996 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2179,plain,
! [SV253: $i,SV311: $i] :
( ( ( function @ SV311 )
= $false )
| ( ( ~ ( relation @ SV311 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK50_C @ SV311 @ SV253 ) @ SV253 )
| ~ ( ( ( apply @ SV311 @ ( sK50_C @ SV311 @ SV253 ) )
!= ( sK50_C @ SV311 @ SV253 ) ) ) )
| ( ( relation_dom @ SV311 )
!= SV253 )
| ( SV311
= ( identity_relation @ SV253 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2036]) ).
thf(2180,plain,
! [SV391: $i,SV420: $i] :
( ( ~ ( function @ SV420 )
| ~ ( relation @ SV420 )
| ( SV420
!= ( identity_relation @ SV391 ) )
| ! [SY997: $i] :
( ~ ( in @ SY997 @ SV391 )
| ( ( apply @ SV420 @ SY997 )
= SY997 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2037]) ).
thf(2181,plain,
! [SV392: $i,SV421: $i] :
( ( ~ ( function @ SV421 )
| ~ ( relation @ SV421 )
| ( SV421
!= ( identity_relation @ SV392 ) )
| ( ( relation_dom @ SV421 )
= SV392 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2038]) ).
thf(2182,plain,
! [SV345: $i,SV312: $i,SV118: $i] :
( ( ( ~ ( ! [SY901: $i,SY902: $i] :
( ~ ( in @ SY901 @ SV118 )
| ~ ( in @ SY902 @ SV312 )
| ( ( sK23_D @ SV345 @ SV312 @ SV118 )
!= ( ordered_pair @ SY901 @ SY902 ) ) )
| ~ ( in @ ( sK23_D @ SV345 @ SV312 @ SV118 ) @ SV345 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY403 @ SV345 @ SV312 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK25_SY405 @ SV345 @ SV312 @ SV118 ) @ SV312 ) )
| ( ( sK23_D @ SV345 @ SV312 @ SV118 )
!= ( ordered_pair @ ( sK24_SY403 @ SV345 @ SV312 @ SV118 ) @ ( sK25_SY405 @ SV345 @ SV312 @ SV118 ) ) ) )
| ( in @ ( sK23_D @ SV345 @ SV312 @ SV118 ) @ SV345 ) ) )
= $false )
| ( ( SV345
= ( cartesian_product2 @ SV118 @ SV312 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2039]) ).
thf(2183,plain,
! [SV313: $i,SV118: $i,SV346: $i] :
( ( ( SV346
= ( cartesian_product2 @ SV118 @ SV313 ) )
= $false )
| ( ( ~ ( ~ ! [SY903: $i] :
( ! [SY873: $i,SY874: $i] :
( ~ ( in @ SY873 @ SV118 )
| ~ ( in @ SY874 @ SV313 )
| ( SY903
!= ( ordered_pair @ SY873 @ SY874 ) ) )
| ( in @ SY903 @ SV346 ) )
| ~ ! [SY906: $i] :
( ~ ( in @ SY906 @ SV346 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY906 @ SV346 @ SV313 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK22_SY400 @ SY906 @ SV346 @ SV313 @ SV118 ) @ SV313 ) )
| ( SY906
!= ( ordered_pair @ ( sK21_E @ SY906 @ SV346 @ SV313 @ SV118 ) @ ( sK22_SY400 @ SY906 @ SV346 @ SV313 @ SV118 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2040]) ).
thf(2184,plain,
! [SV314: $i,SV422: $i,SV119: $i] :
( ( ( subset @ ( cartesian_product2 @ SV119 @ SV422 ) @ ( cartesian_product2 @ SV314 @ SV422 ) )
= $true )
| ( ( subset @ SV119 @ SV314 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2041]) ).
thf(2185,plain,
! [SV315: $i,SV119: $i,SV423: $i] :
( ( ( subset @ ( cartesian_product2 @ SV423 @ SV119 ) @ ( cartesian_product2 @ SV423 @ SV315 ) )
= $true )
| ( ( subset @ SV119 @ SV315 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2042]) ).
thf(2186,plain,
! [SV254: $i,SV316: $i] :
( ( ( ~ ( ! [SY878: $i] :
( ~ ( in @ ( sK15_C @ SV316 @ SV254 ) @ SY878 )
| ~ ( in @ SY878 @ SV254 ) )
| ~ ( in @ ( sK15_C @ SV316 @ SV254 ) @ SV316 ) ) )
= $false )
| ( ( SV316
= ( union @ SV254 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2043]) ).
thf(2187,plain,
! [SV254: $i,SV316: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK15_C @ SV316 @ SV254 ) @ ( sK16_SY398 @ SV316 @ SV254 ) )
| ~ ( in @ ( sK16_SY398 @ SV316 @ SV254 ) @ SV254 ) )
| ( in @ ( sK15_C @ SV316 @ SV254 ) @ SV316 ) ) )
= $false )
| ( ( SV316
= ( union @ SV254 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2043]) ).
thf(2188,plain,
! [SV317: $i,SV255: $i] :
( ( ( ~ ! [SY879: $i] :
( ! [SY817: $i] :
( ~ ( in @ SY879 @ SY817 )
| ~ ( in @ SY817 @ SV255 ) )
| ( in @ SY879 @ SV317 ) )
| ~ ! [SY881: $i] :
( ~ ( in @ SY881 @ SV317 )
| ~ ( ~ ( in @ SY881 @ ( sK14_D @ SY881 @ SV317 @ SV255 ) )
| ~ ( in @ ( sK14_D @ SY881 @ SV317 @ SV255 ) @ SV255 ) ) ) )
= $false )
| ( ( SV317
= ( union @ SV255 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2044]) ).
thf(2189,plain,
! [SV120: $i,SV393: $i] :
( ( ( ~ ( relation @ SV393 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV393 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV120 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV393 ) ) )
| ( SV120 = SV393 ) )
= $true )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2047]) ).
thf(2190,plain,
! [SV120: $i,SV394: $i] :
( ( ( ~ ( relation @ SV394 ) )
= $true )
| ( ( ( SV120 != SV394 )
| ~ ( ~ ! [SY964: $i,SY965: $i] :
( ~ ( in @ ( ordered_pair @ SY964 @ SY965 ) @ SV120 )
| ( in @ ( ordered_pair @ SY964 @ SY965 ) @ SV394 ) )
| ~ ! [SY966: $i,SY967: $i] :
( ~ ( in @ ( ordered_pair @ SY966 @ SY967 ) @ SV394 )
| ( in @ ( ordered_pair @ SY966 @ SY967 ) @ SV120 ) ) ) )
= $true )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2048]) ).
thf(2191,plain,
! [SV145: $i,SV43: $i,SV347: $i] :
( ( ( ~ ( function @ SV347 ) )
= $true )
| ( ( ~ ( relation @ SV347 ) )
= $true )
| ( ( ~ ( in @ SV43 @ ( relation_dom @ ( relation_composition @ SV347 @ SV145 ) ) )
| ( ( apply @ ( relation_composition @ SV347 @ SV145 ) @ SV43 )
= ( apply @ SV145 @ ( apply @ SV347 @ SV43 ) ) ) )
= $true )
| ( ( function @ SV145 )
= $false )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2053]) ).
thf(2192,plain,
! [SV146: $i,SV44: $i,SV348: $i] :
( ( ( ~ ( function @ SV348 ) )
= $true )
| ( ( ~ ( relation @ SV348 ) )
= $true )
| ( ( ~ ( in @ SV44 @ ( relation_dom @ SV146 ) )
| ( ( apply @ ( relation_composition @ SV146 @ SV348 ) @ SV44 )
= ( apply @ SV348 @ ( apply @ SV146 @ SV44 ) ) ) )
= $true )
| ( ( function @ SV146 )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2054]) ).
thf(2193,plain,
! [SV349: $i] :
( ( ( SV349 = empty_set )
= $false )
| ( ( ! [SY907: $i] : ( subset @ SV349 @ ( singleton @ SY907 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2056]) ).
thf(2194,plain,
! [SV395: $i,SV350: $i] :
( ( ( ( SV350
!= ( singleton @ SV395 ) ) )
= $true )
| ( ( subset @ SV350 @ ( singleton @ SV395 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2057]) ).
thf(2195,plain,
! [SV351: $i,SV424: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY406 @ SV424 @ SV351 ) @ SV351 )
| ~ ~ ( in @ ( sK32_C @ SV424 @ SV351 ) @ ( sK33_SY406 @ SV424 @ SV351 ) ) )
| ~ ( in @ ( sK32_C @ SV424 @ SV351 ) @ SV424 ) )
| ~ ( ! [SY998: $i] :
( ~ ( in @ SY998 @ SV351 )
| ( in @ ( sK32_C @ SV424 @ SV351 ) @ SY998 ) )
| ( in @ ( sK32_C @ SV424 @ SV351 ) @ SV424 ) ) )
| ( SV424
= ( set_meet @ SV351 ) ) )
= $true )
| ( ( SV351 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2058]) ).
thf(2196,plain,
! [SV352: $i,SV425: $i] :
( ( ( ( SV425
!= ( set_meet @ SV352 ) )
| ~ ( ~ ! [SY999: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY999 @ SV425 @ SV352 ) @ SV352 )
| ~ ~ ( in @ SY999 @ ( sK31_D @ SY999 @ SV425 @ SV352 ) ) )
| ( in @ SY999 @ SV425 ) )
| ~ ! [SY1000: $i] :
( ~ ( in @ SY1000 @ SV425 )
| ! [SY914: $i] :
( ~ ( in @ SY914 @ SV352 )
| ( in @ SY1000 @ SY914 ) ) ) ) )
= $true )
| ( ( SV352 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2059]) ).
thf(2197,plain,
! [SV353: $i] :
( ( ( SV353 = empty_set )
= $false )
| ( ( ! [SY915: $i] :
( ( SY915
!= ( set_meet @ SV353 ) )
| ( SY915 = empty_set ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2060]) ).
thf(2198,plain,
! [SV354: $i] :
( ( ( SV354 = empty_set )
= $false )
| ( ( ! [SY916: $i] :
( ( SY916 != empty_set )
| ( SY916
= ( set_meet @ SV354 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2061]) ).
thf(2199,plain,
! [SV355: $i,SV264: $i,SV201: $i] :
( ( ( disjoint @ SV201 @ SV264 )
= $false )
| ( ( in @ SV355 @ ( set_intersection2 @ SV201 @ SV264 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2062]) ).
thf(2200,plain,
! [SV265: $i,SV202: $i] :
( ( ( ~ ( function @ SV202 ) )
= $true )
| ( ( ~ ( relation @ SV202 ) )
= $true )
| ( ( ~ ( relation @ SV265 ) )
= $true )
| ( ( ~ ( function @ SV265 ) )
= $true )
| ( ( function @ ( relation_composition @ SV202 @ SV265 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2063]) ).
thf(2201,plain,
! [SV266: $i,SV203: $i] :
( ( ( ~ ( function @ SV203 ) )
= $true )
| ( ( ~ ( relation @ SV203 ) )
= $true )
| ( ( ~ ( relation @ SV266 ) )
= $true )
| ( ( ~ ( function @ SV266 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV203 @ SV266 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2064]) ).
thf(2202,plain,
! [SV206: $i,SV269: $i] :
( ( ( relation @ SV269 )
= $false )
| ( ( empty @ SV206 )
= $false )
| ( ( empty @ ( relation_composition @ SV206 @ SV269 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2065]) ).
thf(2203,plain,
! [SV207: $i,SV270: $i] :
( ( ( relation @ SV270 )
= $false )
| ( ( empty @ SV207 )
= $false )
| ( ( relation @ ( relation_composition @ SV207 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2066]) ).
thf(2204,plain,
! [SV271: $i,SV87: $i,SV320: $i] :
( ( ( ! [SY882: $i] :
( ~ ( in @ SY882 @ ( relation_dom @ SV320 ) )
| ~ ( in @ ( ordered_pair @ SY882 @ SV87 ) @ SV320 )
| ~ ( in @ SY882 @ SV271 ) ) )
= $true )
| ( ( in @ SV87 @ ( relation_image @ SV320 @ SV271 ) )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2067]) ).
thf(2205,plain,
! [SV272: $i,SV321: $i,SV87: $i] :
( ( ( ~ ( in @ SV87 @ ( relation_image @ SV321 @ SV272 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK52_D @ SV321 @ SV272 @ SV87 ) @ ( relation_dom @ SV321 ) )
| ~ ( in @ ( ordered_pair @ ( sK52_D @ SV321 @ SV272 @ SV87 ) @ SV87 ) @ SV321 ) )
| ~ ( in @ ( sK52_D @ SV321 @ SV272 @ SV87 ) @ SV272 ) ) )
= $true )
| ( ( relation @ SV321 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2068]) ).
thf(2206,plain,
! [SV208: $i,SV273: $i] :
( ( ( subset @ SV273 @ SV208 )
= $false )
| ( ( subset @ SV208 @ SV273 )
= $false )
| ( ( SV208 = SV273 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2069]) ).
thf(2207,plain,
! [SV396: $i,SV356: $i] :
( ( ( ( SV356 != SV396 ) )
= $true )
| ( ( subset @ SV356 @ SV396 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2070]) ).
thf(2208,plain,
! [SV397: $i,SV357: $i] :
( ( ( ( SV357 != SV397 ) )
= $true )
| ( ( subset @ SV397 @ SV357 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2071]) ).
thf(2209,plain,
! [SV88: $i,SV274: $i,SV322: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV88 )
| ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV274 )
| ~ ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV322 ) ) )
= $false )
| ( ( SV322
= ( set_difference @ SV88 @ SV274 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2072]) ).
thf(2210,plain,
! [SV88: $i,SV274: $i,SV322: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV88 )
| ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV322 ) )
| ~ ( ~ ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV274 )
| ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV322 ) ) ) )
= $false )
| ( ( SV322
= ( set_difference @ SV88 @ SV274 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2072]) ).
thf(2211,plain,
! [SV323: $i,SV275: $i,SV88: $i] :
( ( ( ~ ! [SY883: $i] :
( ~ ( in @ SY883 @ SV88 )
| ( in @ SY883 @ SV275 )
| ( in @ SY883 @ SV323 ) )
| ~ ~ ( ~ ! [SY884: $i] :
( ~ ( in @ SY884 @ SV323 )
| ( in @ SY884 @ SV88 ) )
| ~ ! [SY885: $i] :
( ~ ( in @ SY885 @ SV323 )
| ~ ( in @ SY885 @ SV275 ) ) ) )
= $false )
| ( ( SV323
= ( set_difference @ SV88 @ SV275 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2073]) ).
thf(2212,plain,
! [SV358: $i,SV426: $i] :
( ( ( ~ ( element @ SV426 @ SV358 )
| ( in @ SV426 @ SV358 ) )
= $true )
| ( ( empty @ SV358 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2074]) ).
thf(2213,plain,
! [SV359: $i,SV427: $i] :
( ( ( ~ ( in @ SV427 @ SV359 )
| ( element @ SV427 @ SV359 ) )
= $true )
| ( ( empty @ SV359 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2214,plain,
! [SV360: $i] :
( ( ( empty @ SV360 )
= $false )
| ( ( ! [SY921: $i] :
( ~ ( element @ SY921 @ SV360 )
| ( empty @ SY921 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2076]) ).
thf(2215,plain,
! [SV361: $i] :
( ( ( empty @ SV361 )
= $false )
| ( ( ! [SY922: $i] :
( ~ ( empty @ SY922 )
| ( element @ SY922 @ SV361 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2077]) ).
thf(2216,plain,
! [SV89: $i,SV174: $i,SV398: $i] :
( ( ( ~ ( relation @ SV398 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV174 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 ) )
| ~ ~ ( ~ ( ( in @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) @ SV89 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV174 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 ) ) ) )
| ( SV398
= ( relation_rng_restriction @ SV89 @ SV174 ) ) )
= $true )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2078]) ).
thf(2217,plain,
! [SV174: $i,SV89: $i,SV399: $i] :
( ( ( ~ ( relation @ SV399 ) )
= $true )
| ( ( ( SV399
!= ( relation_rng_restriction @ SV89 @ SV174 ) )
| ~ ( ~ ! [SY968: $i,SY969: $i] :
( ~ ( in @ SY969 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY968 @ SY969 ) @ SV174 )
| ( in @ ( ordered_pair @ SY968 @ SY969 ) @ SV399 ) )
| ~ ~ ( ~ ! [SY970: $i,SY971: $i] :
( ~ ( in @ ( ordered_pair @ SY970 @ SY971 ) @ SV399 )
| ( in @ SY971 @ SV89 ) )
| ~ ! [SY972: $i,SY973: $i] :
( ~ ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV399 )
| ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV174 ) ) ) ) )
= $true )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2079]) ).
thf(2218,plain,
! [SV90: $i,SV276: $i,SV324: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SV324 @ SV276 @ SV90 ) @ SV324 )
| ( ( sK27_D @ SV324 @ SV276 @ SV90 )
!= SV90 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV324 @ SV276 @ SV90 ) @ SV324 )
| ( ( sK27_D @ SV324 @ SV276 @ SV90 )
!= SV276 ) ) ) )
= $false )
| ( ( SV324
= ( unordered_pair @ SV90 @ SV276 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2080]) ).
thf(2219,plain,
! [SV90: $i,SV276: $i,SV324: $i] :
( ( ( ~ ( ( in @ ( sK27_D @ SV324 @ SV276 @ SV90 ) @ SV324 )
| ( ( sK27_D @ SV324 @ SV276 @ SV90 )
= SV90 )
| ( ( sK27_D @ SV324 @ SV276 @ SV90 )
= SV276 ) ) )
= $false )
| ( ( SV324
= ( unordered_pair @ SV90 @ SV276 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2080]) ).
thf(2220,plain,
! [SV277: $i,SV90: $i,SV325: $i] :
( ( ( ~ ! [SY886: $i] :
( ~ ( in @ SY886 @ SV325 )
| ( SY886 = SV90 )
| ( SY886 = SV277 ) )
| ~ ~ ( ~ ! [SY887: $i] :
( ( SY887 != SV90 )
| ( in @ SY887 @ SV325 ) )
| ~ ! [SY888: $i] :
( ( SY888 != SV277 )
| ( in @ SY888 @ SV325 ) ) ) )
= $false )
| ( ( SV325
= ( unordered_pair @ SV90 @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2081]) ).
thf(2221,plain,
! [SV209: $i,SV278: $i] :
( ( ( ~ ( in @ ( sK28_C @ SV278 @ SV209 ) @ SV278 )
| ~ ( subset @ ( sK28_C @ SV278 @ SV209 ) @ SV209 ) )
= $true )
| ( ( SV278
= ( powerset @ SV209 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2082]) ).
thf(2222,plain,
! [SV209: $i,SV278: $i] :
( ( ( ( in @ ( sK28_C @ SV278 @ SV209 ) @ SV278 )
| ( subset @ ( sK28_C @ SV278 @ SV209 ) @ SV209 ) )
= $true )
| ( ( SV278
= ( powerset @ SV209 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2083]) ).
thf(2223,plain,
! [SV210: $i,SV279: $i] :
( ( ( ~ ! [SY835: $i] :
( ~ ( in @ SY835 @ SV279 )
| ( subset @ SY835 @ SV210 ) ) )
= $false )
| ( ( SV279
= ( powerset @ SV210 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2084]) ).
thf(2224,plain,
! [SV279: $i,SV210: $i] :
( ( ( ~ ! [SY836: $i] :
( ~ ( subset @ SY836 @ SV210 )
| ( in @ SY836 @ SV279 ) ) )
= $false )
| ( ( SV279
= ( powerset @ SV210 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2084]) ).
thf(2225,plain,
! [SV91: $i,SV362: $i] :
( ( ( ~ ( ! [SY923: $i] :
~ ( in @ ( ordered_pair @ ( sK63_C @ SV362 @ SV91 ) @ SY923 ) @ SV91 )
| ~ ( in @ ( sK63_C @ SV362 @ SV91 ) @ SV362 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_C @ SV362 @ SV91 ) @ ( sK64_SY419 @ SV362 @ SV91 ) ) @ SV91 )
| ( in @ ( sK63_C @ SV362 @ SV91 ) @ SV362 ) ) )
= $false )
| ( ( SV362
= ( relation_dom @ SV91 ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2085]) ).
thf(2226,plain,
! [SV91: $i,SV363: $i] :
( ( ( SV363
= ( relation_dom @ SV91 ) )
= $false )
| ( ( ~ ( ~ ! [SY924: $i] :
( ! [SY530: $i] :
~ ( in @ ( ordered_pair @ SY924 @ SY530 ) @ SV91 )
| ( in @ SY924 @ SV363 ) )
| ~ ! [SY926: $i] :
( ~ ( in @ SY926 @ SV363 )
| ( in @ ( ordered_pair @ SY926 @ ( sK62_D @ SY926 @ SV363 @ SV91 ) ) @ SV91 ) ) ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2086]) ).
thf(2227,plain,
! [SV92: $i,SV364: $i,SV400: $i] :
( ( ( ~ ( ~ ( ! [SY974: $i] :
( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SY974 ) @ SV92 )
| ~ ( in @ SY974 @ SV364 ) )
| ~ ( in @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SV400 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ ( sK36_SY409 @ SV400 @ SV364 @ SV92 ) ) @ SV92 )
| ~ ( in @ ( sK36_SY409 @ SV400 @ SV364 @ SV92 ) @ SV364 ) )
| ( in @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SV400 ) ) ) )
= $true )
| ( ( SV400
= ( relation_inverse_image @ SV92 @ SV364 ) )
= $true )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2087]) ).
thf(2228,plain,
! [SV365: $i,SV92: $i,SV401: $i] :
( ( ( ( SV401
!= ( relation_inverse_image @ SV92 @ SV365 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY975: $i] :
( ! [SY931: $i] :
( ~ ( in @ ( ordered_pair @ SY975 @ SY931 ) @ SV92 )
| ~ ( in @ SY931 @ SV365 ) )
| ( in @ SY975 @ SV401 ) )
| ~ ! [SY977: $i] :
( ~ ( in @ SY977 @ SV401 )
| ~ ( ~ ( in @ ( ordered_pair @ SY977 @ ( sK34_E @ SY977 @ SV401 @ SV365 @ SV92 ) ) @ SV92 )
| ~ ( in @ ( sK34_E @ SY977 @ SV401 @ SV365 @ SV92 ) @ SV365 ) ) ) ) )
= $true )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2088]) ).
thf(2229,plain,
! [SV93: $i,SV366: $i,SV402: $i] :
( ( ( ~ ( ~ ( ! [SY978: $i] :
( ~ ( in @ ( ordered_pair @ SY978 @ ( sK38_D @ SV402 @ SV366 @ SV93 ) ) @ SV93 )
| ~ ( in @ SY978 @ SV366 ) )
| ~ ( in @ ( sK38_D @ SV402 @ SV366 @ SV93 ) @ SV402 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SV402 @ SV366 @ SV93 ) @ ( sK38_D @ SV402 @ SV366 @ SV93 ) ) @ SV93 )
| ~ ( in @ ( sK39_SY411 @ SV402 @ SV366 @ SV93 ) @ SV366 ) )
| ( in @ ( sK38_D @ SV402 @ SV366 @ SV93 ) @ SV402 ) ) ) )
= $true )
| ( ( SV402
= ( relation_image @ SV93 @ SV366 ) )
= $true )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2089]) ).
thf(2230,plain,
! [SV367: $i,SV93: $i,SV403: $i] :
( ( ( ( SV403
!= ( relation_image @ SV93 @ SV367 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY979: $i] :
( ! [SY937: $i] :
( ~ ( in @ ( ordered_pair @ SY937 @ SY979 ) @ SV93 )
| ~ ( in @ SY937 @ SV367 ) )
| ( in @ SY979 @ SV403 ) )
| ~ ! [SY981: $i] :
( ~ ( in @ SY981 @ SV403 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SY981 @ SV403 @ SV367 @ SV93 ) @ SY981 ) @ SV93 )
| ~ ( in @ ( sK37_E @ SY981 @ SV403 @ SV367 @ SV93 ) @ SV367 ) ) ) ) )
= $true )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2090]) ).
thf(2231,plain,
! [SV282: $i,SV94: $i,SV326: $i] :
( ( ( ! [SY889: $i] :
( ~ ( in @ SY889 @ ( relation_rng @ SV326 ) )
| ~ ( in @ ( ordered_pair @ SV94 @ SY889 ) @ SV326 )
| ~ ( in @ SY889 @ SV282 ) ) )
= $true )
| ( ( in @ SV94 @ ( relation_inverse_image @ SV326 @ SV282 ) )
= $true )
| ( ( relation @ SV326 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2091]) ).
thf(2232,plain,
! [SV283: $i,SV327: $i,SV94: $i] :
( ( ( ~ ( in @ SV94 @ ( relation_inverse_image @ SV327 @ SV283 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK51_D @ SV327 @ SV283 @ SV94 ) @ ( relation_rng @ SV327 ) )
| ~ ( in @ ( ordered_pair @ SV94 @ ( sK51_D @ SV327 @ SV283 @ SV94 ) ) @ SV327 ) )
| ~ ( in @ ( sK51_D @ SV327 @ SV283 @ SV94 ) @ SV283 ) ) )
= $true )
| ( ( relation @ SV327 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2092]) ).
thf(2233,plain,
! [SV175: $i,SV95: $i] :
( ( ( ! [SY731: $i] :
( ~ ( function @ SY731 )
| ~ ( relation @ SY731 )
| ~ ( in @ SV95 @ ( relation_dom @ SY731 ) )
| ~ ( in @ ( apply @ SY731 @ SV95 ) @ ( relation_dom @ SV175 ) )
| ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY731 @ SV175 ) ) ) ) )
= $true )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2093]) ).
thf(2234,plain,
! [SV175: $i,SV95: $i] :
( ( ( ~ ( ~ ! [SY732: $i] :
( ~ ( function @ SY732 )
| ~ ( relation @ SY732 )
| ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY732 @ SV175 ) ) )
| ( in @ SV95 @ ( relation_dom @ SY732 ) ) )
| ~ ! [SY733: $i] :
( ~ ( function @ SY733 )
| ~ ( relation @ SY733 )
| ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY733 @ SV175 ) ) )
| ( in @ ( apply @ SY733 @ SV95 ) @ ( relation_dom @ SV175 ) ) ) ) )
= $true )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2094]) ).
thf(2235,plain,
! [SV96: $i,SV368: $i,SV404: $i] :
( ( ( ~ ( relation @ SV404 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ SV368 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 ) )
| ~ ~ ( ~ ( ( in @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ SV368 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 ) ) ) )
| ( SV404
= ( relation_dom_restriction @ SV96 @ SV368 ) ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2095]) ).
thf(2236,plain,
! [SV369: $i,SV96: $i,SV405: $i] :
( ( ( ~ ( relation @ SV405 ) )
= $true )
| ( ( ( SV405
!= ( relation_dom_restriction @ SV96 @ SV369 ) )
| ~ ( ~ ! [SY982: $i,SY983: $i] :
( ~ ( in @ SY982 @ SV369 )
| ~ ( in @ ( ordered_pair @ SY982 @ SY983 ) @ SV96 )
| ( in @ ( ordered_pair @ SY982 @ SY983 ) @ SV405 ) )
| ~ ~ ( ~ ! [SY984: $i] :
( ! [SY985: $i] :
~ ( in @ ( ordered_pair @ SY984 @ SY985 ) @ SV405 )
| ( in @ SY984 @ SV369 ) )
| ~ ! [SY986: $i,SY987: $i] :
( ~ ( in @ ( ordered_pair @ SY986 @ SY987 ) @ SV405 )
| ( in @ ( ordered_pair @ SY986 @ SY987 ) @ SV96 ) ) ) ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2096]) ).
thf(2237,plain,
! [SV213: $i,SV284: $i] :
( ( ( relation @ SV284 )
= $false )
| ( ( empty @ SV213 )
= $false )
| ( ( empty @ ( relation_composition @ SV284 @ SV213 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2097]) ).
thf(2238,plain,
! [SV214: $i,SV285: $i] :
( ( ( relation @ SV285 )
= $false )
| ( ( empty @ SV214 )
= $false )
| ( ( relation @ ( relation_composition @ SV285 @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2098]) ).
thf(2239,plain,
! [SV97: $i,SV370: $i] :
( ( ( relation @ SV370 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SV370 @ SV97 ) @ ( sK12_SY396 @ SV370 @ SV97 ) ) @ SV370 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SV370 @ SV97 ) @ ( sK11_C @ SV370 @ SV97 ) ) @ SV97 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_C @ SV370 @ SV97 ) @ ( sK12_SY396 @ SV370 @ SV97 ) ) @ SV370 )
| ( in @ ( ordered_pair @ ( sK12_SY396 @ SV370 @ SV97 ) @ ( sK11_C @ SV370 @ SV97 ) ) @ SV97 ) ) )
| ( SV370
= ( relation_inverse @ SV97 ) ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2099]) ).
thf(2240,plain,
! [SV97: $i,SV371: $i] :
( ( ( relation @ SV371 )
= $false )
| ( ( ( SV371
!= ( relation_inverse @ SV97 ) )
| ~ ( ~ ! [SY947: $i,SY948: $i] :
( ~ ( in @ ( ordered_pair @ SY947 @ SY948 ) @ SV371 )
| ( in @ ( ordered_pair @ SY948 @ SY947 ) @ SV97 ) )
| ~ ! [SY949: $i,SY950: $i] :
( ~ ( in @ ( ordered_pair @ SY950 @ SY949 ) @ SV97 )
| ( in @ ( ordered_pair @ SY949 @ SY950 ) @ SV371 ) ) ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2100]) ).
thf(2241,plain,
! [SV98: $i,SV372: $i] :
( ( ( ~ ( ! [SY951: $i] :
~ ( in @ ( ordered_pair @ SY951 @ ( sK60_C @ SV372 @ SV98 ) ) @ SV98 )
| ~ ( in @ ( sK60_C @ SV372 @ SV98 ) @ SV372 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK61_SY417 @ SV372 @ SV98 ) @ ( sK60_C @ SV372 @ SV98 ) ) @ SV98 )
| ( in @ ( sK60_C @ SV372 @ SV98 ) @ SV372 ) ) )
= $false )
| ( ( SV372
= ( relation_rng @ SV98 ) )
= $true )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2101]) ).
thf(2242,plain,
! [SV98: $i,SV373: $i] :
( ( ( SV373
= ( relation_rng @ SV98 ) )
= $false )
| ( ( ~ ( ~ ! [SY952: $i] :
( ! [SY577: $i] :
~ ( in @ ( ordered_pair @ SY577 @ SY952 ) @ SV98 )
| ( in @ SY952 @ SV373 ) )
| ~ ! [SY954: $i] :
( ~ ( in @ SY954 @ SV373 )
| ( in @ ( ordered_pair @ ( sK59_D @ SY954 @ SV373 @ SV98 ) @ SY954 ) @ SV98 ) ) ) )
= $true )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2102]) ).
thf(2243,plain,
! [SV99: $i,SV176: $i] :
( ( ( in @ ( sK4_C @ SV176 @ SV99 ) @ SV176 )
= $false )
| ( ( in @ ( sK4_C @ SV176 @ SV99 ) @ SV99 )
= $false )
| ( ( SV99 = SV176 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2103]) ).
thf(2244,plain,
! [SV100: $i,SV286: $i,SV328: $i] :
( ( ( function @ SV328 )
= $false )
| ( ( ~ ( relation @ SV328 ) )
= $true )
| ( ( ( SV286
!= ( apply @ SV328 @ SV100 ) )
| ~ ( in @ SV100 @ ( relation_dom @ SV328 ) )
| ( in @ ( ordered_pair @ SV100 @ SV286 ) @ SV328 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2104]) ).
thf(2245,plain,
! [SV406: $i,SV100: $i,SV428: $i] :
( ( ~ ( function @ SV428 )
| ~ ( relation @ SV428 )
| ~ ( in @ ( ordered_pair @ SV100 @ SV406 ) @ SV428 )
| ( SV406
= ( apply @ SV428 @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2105]) ).
thf(2246,plain,
! [SV407: $i,SV100: $i,SV429: $i] :
( ( ~ ( function @ SV429 )
| ~ ( relation @ SV429 )
| ~ ( in @ ( ordered_pair @ SV100 @ SV407 ) @ SV429 )
| ( in @ SV100 @ ( relation_dom @ SV429 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2106]) ).
thf(2247,plain,
! [SV101: $i,SV215: $i] :
( ( ( ! [SY778: $i] :
( ~ ( relation @ SY778 )
| ~ ( ~ ( ! [SY779: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY778 @ SV215 @ SV101 ) @ SY779 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY779 @ ( sK9_SY391 @ SY778 @ SV215 @ SV101 ) ) @ SV215 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SY778 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SY778 @ SV215 @ SV101 ) ) @ SY778 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY778 @ SV215 @ SV101 ) @ ( sK10_SY395 @ SY778 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SY778 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SY778 @ SV215 @ SV101 ) ) @ SV215 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SY778 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SY778 @ SV215 @ SV101 ) ) @ SY778 ) ) )
| ( SY778
= ( relation_composition @ SV101 @ SV215 ) ) ) )
= $true )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2107]) ).
thf(2248,plain,
! [SV215: $i,SV101: $i] :
( ( ( ! [SY780: $i] :
( ~ ( relation @ SY780 )
| ( SY780
!= ( relation_composition @ SV101 @ SV215 ) )
| ~ ( ~ ! [SY781: $i,SY782: $i] :
( ! [SY783: $i] :
( ~ ( in @ ( ordered_pair @ SY781 @ SY783 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY783 @ SY782 ) @ SV215 ) )
| ( in @ ( ordered_pair @ SY781 @ SY782 ) @ SY780 ) )
| ~ ! [SY784: $i,SY785: $i] :
( ~ ( in @ ( ordered_pair @ SY784 @ SY785 ) @ SY780 )
| ~ ( ~ ( in @ ( ordered_pair @ SY784 @ ( sK7_F @ SY785 @ SY784 @ SY780 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY785 @ SY784 @ SY780 @ SV215 @ SV101 ) @ SY785 ) @ SV215 ) ) ) ) ) )
= $true )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2108]) ).
thf(2249,plain,
! [SV374: $i,SV177: $i,SV329: $i,SV102: $i] :
( ( ( ~ ( in @ SV102 @ SV329 ) )
= $true )
| ( ( ~ ( in @ SV177 @ SV374 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SV329 @ SV374 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2109]) ).
thf(2250,plain,
! [SV430: $i,SV177: $i,SV102: $i] :
( ( ! [SY1002: $i] :
~ ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SV430 @ SY1002 ) )
| ( in @ SV102 @ SV430 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2110]) ).
thf(2251,plain,
! [SV431: $i,SV177: $i,SV102: $i] :
( ( ! [SY1003: $i] :
( ~ ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SV431 @ SY1003 ) )
| ( in @ SV177 @ SY1003 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2111]) ).
thf(2252,plain,
! [SV103: $i,SV408: $i] :
( ( ( ~ ( ~ ! [SY990: $i] :
( ~ ( subset @ SY990 @ SV408 )
| ( in @ SY990 @ ( sK3_SY386 @ SV408 @ SV103 ) ) )
| ~ ( in @ ( sK3_SY386 @ SV408 @ SV103 ) @ ( sK2_B @ SV103 ) ) ) )
= $true )
| ( ( ~ ( in @ SV408 @ ( sK2_B @ SV103 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2115]) ).
thf(2253,plain,
! [SV103: $i] :
( ( ~ ! [SY605: $i,SY606: $i] :
( ~ ( in @ SY605 @ ( sK2_B @ SV103 ) )
| ~ ( subset @ SY606 @ SY605 )
| ( in @ SY606 @ ( sK2_B @ SV103 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2116]) ).
thf(2254,plain,
! [SV103: $i] :
( ( ~ ( in @ SV103 @ ( sK2_B @ SV103 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2116]) ).
thf(2255,plain,
! [SV432: $i,SV222: $i] :
( ( ( ! [SY1004: $i] :
( ( sK69_B @ SV222 )
!= ( ordered_pair @ SV432 @ SY1004 ) ) )
= $true )
| ( ( relation @ SV222 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2119]) ).
thf(2256,plain,
! [SV223: $i,SV375: $i] :
( ( ( in @ SV375 @ SV223 )
= $false )
| ( ( SV375
= ( ordered_pair @ ( sK67_C @ SV375 @ SV223 ) @ ( sK68_SY421 @ SV375 @ SV223 ) ) )
= $true )
| ( ( relation @ SV223 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2121]) ).
thf(2257,plain,
! [SV104: $i,SV376: $i] :
( ( ( relation @ SV376 )
= $false )
| ( ( ~ ( subset @ SV104 @ SV376 )
| ( subset @ ( relation_dom @ SV104 ) @ ( relation_dom @ SV376 ) ) )
= $true )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2122]) ).
thf(2258,plain,
! [SV104: $i,SV377: $i] :
( ( ( relation @ SV377 )
= $false )
| ( ( ~ ( subset @ SV104 @ SV377 )
| ( subset @ ( relation_rng @ SV104 ) @ ( relation_rng @ SV377 ) ) )
= $true )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2123]) ).
thf(2259,plain,
! [SV330: $i,SV288: $i,SV105: $i] :
( ( ( ~ ( in @ SV105 @ SV288 )
| ~ ( in @ SV105 @ ( relation_rng @ SV330 ) ) )
= $true )
| ( ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SV288 @ SV330 ) ) )
= $true )
| ( ( relation @ SV330 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2124]) ).
thf(2260,plain,
! [SV409: $i,SV105: $i,SV433: $i] :
( ( ~ ( relation @ SV433 )
| ~ ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SV409 @ SV433 ) ) )
| ( in @ SV105 @ SV409 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2125]) ).
thf(2261,plain,
! [SV410: $i,SV105: $i,SV434: $i] :
( ( ~ ( relation @ SV434 )
| ~ ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SV410 @ SV434 ) ) )
| ( in @ SV105 @ ( relation_rng @ SV434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2126]) ).
thf(2262,plain,
! [SV289: $i,SV331: $i,SV106: $i] :
( ( ( in @ SV106 @ SV331 )
= $false )
| ( ( ~ ( in @ SV289 @ SV331 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV106 @ SV289 ) @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2127]) ).
thf(2263,plain,
! [SV435: $i,SV411: $i,SV106: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV106 @ SV411 ) @ SV435 )
| ( in @ SV106 @ SV435 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2128]) ).
thf(2264,plain,
! [SV436: $i,SV412: $i,SV106: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV106 @ SV412 ) @ SV436 )
| ( in @ SV412 @ SV436 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2129]) ).
thf(2265,plain,
! [SV178: $i,SV332: $i,SV107: $i,SV378: $i] :
( ( ( relation @ SV378 )
= $false )
| ( ( ~ ( in @ SV107 @ SV332 )
| ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ SV378 )
| ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SV332 ) @ SV378 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2130]) ).
thf(2266,plain,
! [SV437: $i,SV178: $i,SV107: $i] :
( ( ! [SY1005: $i] :
( ~ ( relation @ SY1005 )
| ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SV437 ) @ SY1005 ) )
| ( in @ SV107 @ SV437 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2131]) ).
thf(2267,plain,
! [SV438: $i,SV178: $i,SV107: $i] :
( ( ! [SY1006: $i] :
( ~ ( relation @ SY1006 )
| ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SV438 ) @ SY1006 ) )
| ( in @ ( ordered_pair @ SV107 @ SV178 ) @ SY1006 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2132]) ).
thf(2268,plain,
! [SV108: $i,SV379: $i] :
( ( ( relation @ SV379 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV379 @ SV108 ) @ ( sK20_SY399 @ SV379 @ SV108 ) ) @ SV108 )
| ~ ~ ( in @ ( ordered_pair @ ( sK19_C @ SV379 @ SV108 ) @ ( sK20_SY399 @ SV379 @ SV108 ) ) @ SV379 ) )
| ( subset @ SV108 @ SV379 ) )
= $true )
| ( ( relation @ SV108 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2133]) ).
thf(2269,plain,
! [SV108: $i,SV380: $i] :
( ( ( relation @ SV380 )
= $false )
| ( ( ~ ( subset @ SV108 @ SV380 )
| ! [SY955: $i,SY956: $i] :
( ~ ( in @ ( ordered_pair @ SY955 @ SY956 ) @ SV108 )
| ( in @ ( ordered_pair @ SY955 @ SY956 ) @ SV380 ) ) )
= $true )
| ( ( relation @ SV108 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2134]) ).
thf(2270,plain,
! [SV228: $i,SV290: $i] :
( ( ( ( ( sK30_C @ SV290 @ SV228 )
!= SV228 )
| ~ ( in @ ( sK30_C @ SV290 @ SV228 ) @ SV290 ) )
= $true )
| ( ( SV290
= ( singleton @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2135]) ).
thf(2271,plain,
! [SV228: $i,SV290: $i] :
( ( ( ( ( sK30_C @ SV290 @ SV228 )
= SV228 )
| ( in @ ( sK30_C @ SV290 @ SV228 ) @ SV290 ) )
= $true )
| ( ( SV290
= ( singleton @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2136]) ).
thf(2272,plain,
! [SV291: $i,SV229: $i] :
( ( ( ~ ! [SY843: $i] :
( ( SY843 != SV229 )
| ( in @ SY843 @ SV291 ) ) )
= $false )
| ( ( SV291
= ( singleton @ SV229 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2137]) ).
thf(2273,plain,
! [SV229: $i,SV291: $i] :
( ( ( ~ ! [SY844: $i] :
( ~ ( in @ SY844 @ SV291 )
| ( SY844 = SV229 ) ) )
= $false )
| ( ( SV291
= ( singleton @ SV229 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2137]) ).
thf(2274,plain,
! [SV333: $i,SV292: $i,SV109: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV109 @ SV292 ) @ SV333 ) )
= $true )
| ( ( in @ SV109 @ ( relation_dom @ SV333 ) )
= $true )
| ( ( relation @ SV333 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2138]) ).
thf(2275,plain,
! [SV334: $i,SV293: $i,SV109: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV109 @ SV293 ) @ SV334 ) )
= $true )
| ( ( in @ SV293 @ ( relation_rng @ SV334 ) )
= $true )
| ( ( relation @ SV334 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2139]) ).
thf(2276,plain,
! [SV381: $i] :
( ( ( ~ ( empty @ SV381 )
| ~ ( relation @ SV381 ) )
= $true )
| ( ( ~ ( function @ SV381 ) )
= $true )
| ( ( function @ SV381 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2140]) ).
thf(2277,plain,
! [SV382: $i] :
( ( ( ~ ( empty @ SV382 )
| ~ ( relation @ SV382 ) )
= $true )
| ( ( ~ ( function @ SV382 ) )
= $true )
| ( ( relation @ SV382 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2141]) ).
thf(2278,plain,
! [SV230: $i] :
( ( ( relation @ SV230 )
= $false )
| ( ( empty @ SV230 )
= $false )
| ( ( ~ ( function @ SV230 ) )
= $true )
| ( ( one_to_one @ SV230 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2142]) ).
thf(2279,plain,
! [SV110: $i] :
( ( ( ~ ! [SY636: $i] :
( ~ ( function @ SY636 )
| ~ ( relation @ SY636 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SY636 @ SV110 )
= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ( ( sK70_C @ SY636 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY636 @ SV110 )
= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY636 @ SV110 )
= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ( ( sK71_SY424 @ SY636 @ SV110 )
!= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK70_C @ SY636 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK71_SY424 @ SY636 @ SV110 )
!= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY636 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK70_C @ SY636 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SY636 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SY636 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK71_SY424 @ SY636 @ SV110 )
!= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ( ( relation_dom @ SY636 )
!= ( relation_rng @ SV110 ) )
| ( SY636
= ( function_inverse @ SV110 ) ) ) )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2143]) ).
thf(2280,plain,
! [SV110: $i] :
( ( ( ~ ~ ( ~ ! [SY637: $i] :
( ~ ( function @ SY637 )
| ~ ( relation @ SY637 )
| ( SY637
!= ( function_inverse @ SV110 ) )
| ~ ( ~ ~ ( ~ ! [SY638: $i,SY639: $i] :
( ( SY639
!= ( apply @ SY637 @ SY638 ) )
| ~ ( in @ SY638 @ ( relation_rng @ SV110 ) )
| ( SY638
= ( apply @ SV110 @ SY639 ) ) )
| ~ ! [SY640: $i,SY641: $i] :
( ( SY641
!= ( apply @ SY637 @ SY640 ) )
| ~ ( in @ SY640 @ ( relation_rng @ SV110 ) )
| ( in @ SY641 @ ( relation_dom @ SV110 ) ) ) )
| ~ ~ ( ~ ! [SY642: $i,SY643: $i] :
( ( SY642
!= ( apply @ SV110 @ SY643 ) )
| ~ ( in @ SY643 @ ( relation_dom @ SV110 ) )
| ( SY643
= ( apply @ SY637 @ SY642 ) ) )
| ~ ! [SY644: $i] :
( ! [SY645: $i] :
( ( SY644
!= ( apply @ SV110 @ SY645 ) )
| ~ ( in @ SY645 @ ( relation_dom @ SV110 ) ) )
| ( in @ SY644 @ ( relation_rng @ SV110 ) ) ) ) ) )
| ~ ! [SY646: $i] :
( ~ ( function @ SY646 )
| ~ ( relation @ SY646 )
| ( SY646
!= ( function_inverse @ SV110 ) )
| ( ( relation_dom @ SY646 )
= ( relation_rng @ SV110 ) ) ) ) )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2143]) ).
thf(2281,plain,
! [SV413: $i,SV383: $i] :
( ( ( ~ ( proper_subset @ SV383 @ SV413 ) )
= $true )
| ( ( ( SV383 != SV413 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2145]) ).
thf(2282,plain,
! [SV414: $i,SV384: $i] :
( ( ( ~ ( proper_subset @ SV384 @ SV414 ) )
= $true )
| ( ( subset @ SV384 @ SV414 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2146]) ).
thf(2283,plain,
! [SV234: $i,SV295: $i] :
( ( ( in @ ( sK18_C @ SV295 @ SV234 ) @ SV234 )
= $true )
| ( ( subset @ SV234 @ SV295 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2147]) ).
thf(2284,plain,
! [SV234: $i,SV295: $i] :
( ( ( ~ ( in @ ( sK18_C @ SV295 @ SV234 ) @ SV295 ) )
= $true )
| ( ( subset @ SV234 @ SV295 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2148]) ).
thf(2285,plain,
! [SV296: $i,SV235: $i,SV415: $i] :
( ( ( ~ ( in @ SV415 @ SV235 ) )
= $true )
| ( ( in @ SV415 @ SV296 )
= $true )
| ( ( subset @ SV235 @ SV296 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2149]) ).
thf(2286,plain,
! [SV236: $i,SV297: $i] :
( ( ( in @ ( sK49_C @ SV297 @ SV236 ) @ SV236 )
= $true )
| ( ( disjoint @ SV236 @ SV297 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2150]) ).
thf(2287,plain,
! [SV236: $i,SV297: $i] :
( ( ( in @ ( sK49_C @ SV297 @ SV236 ) @ SV297 )
= $true )
| ( ( disjoint @ SV236 @ SV297 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2151]) ).
thf(2288,plain,
! [SV298: $i,SV237: $i,SV385: $i] :
( ( ( in @ SV385 @ SV237 )
= $false )
| ( ( ~ ( in @ SV385 @ SV298 ) )
= $true )
| ( ( ~ ( disjoint @ SV237 @ SV298 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2152]) ).
thf(2289,plain,
! [SV386: $i,SV179: $i,SV335: $i,SV111: $i] :
( ( ( ~ ( in @ SV111 @ SV335 ) )
= $true )
| ( ( ~ ( in @ SV179 @ SV386 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SV335 @ SV386 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2153]) ).
thf(2290,plain,
! [SV439: $i,SV179: $i,SV111: $i] :
( ( ! [SY1007: $i] :
~ ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SV439 @ SY1007 ) )
| ( in @ SV111 @ SV439 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2154]) ).
thf(2291,plain,
! [SV440: $i,SV179: $i,SV111: $i] :
( ( ! [SY1008: $i] :
( ~ ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SV440 @ SY1008 ) )
| ( in @ SV179 @ SY1008 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2155]) ).
thf(2292,plain,
! [SV416: $i,SV336: $i,SV180: $i,SV112: $i] :
( ( ( ( ordered_pair @ SV112 @ SV180 )
= ( ordered_pair @ SV336 @ SV416 ) )
= $false )
| ( ( SV112 = SV336 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2156]) ).
thf(2293,plain,
! [SV387: $i,SV337: $i,SV180: $i,SV112: $i] :
( ( ( ( ordered_pair @ SV112 @ SV180 )
= ( ordered_pair @ SV337 @ SV387 ) )
= $false )
| ( ( SV180 = SV387 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2157]) ).
thf(2294,plain,
! [SV113: $i] :
( ( ( ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ ( relation_dom @ SV113 ) )
| ! [SY660: $i] :
( ( SY660
!= ( apply @ SV113 @ SY659 ) )
| ( in @ ( ordered_pair @ SY659 @ SY660 ) @ SV113 ) ) )
| ~ ! [SY661: $i] :
( ~ ( in @ SY661 @ ( relation_dom @ SV113 ) )
| ! [SY662: $i] :
( ~ ( in @ ( ordered_pair @ SY661 @ SY662 ) @ SV113 )
| ( SY662
= ( apply @ SV113 @ SY661 ) ) ) ) )
= $false )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2158]) ).
thf(2295,plain,
! [SV113: $i] :
( ( ( ~ ! [SY663: $i] :
( ( in @ SY663 @ ( relation_dom @ SV113 ) )
| ! [SY664: $i] :
( ( SY664
!= ( apply @ SV113 @ SY663 ) )
| ( SY664 = empty_set ) ) )
| ~ ! [SY665: $i] :
( ( in @ SY665 @ ( relation_dom @ SV113 ) )
| ! [SY666: $i] :
( ( SY666 != empty_set )
| ( SY666
= ( apply @ SV113 @ SY665 ) ) ) ) )
= $false )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2159]) ).
thf(2296,plain,
! [SV114: $i,SV301: $i,SV338: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV338 )
| ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV114 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV338 )
| ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV301 ) ) ) )
= $false )
| ( ( SV338
= ( set_union2 @ SV114 @ SV301 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2161]) ).
thf(2297,plain,
! [SV114: $i,SV301: $i,SV338: $i] :
( ( ( ~ ( ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV338 )
| ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV114 )
| ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV301 ) ) )
= $false )
| ( ( SV338
= ( set_union2 @ SV114 @ SV301 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2161]) ).
thf(2298,plain,
! [SV302: $i,SV114: $i,SV339: $i] :
( ( ( ~ ! [SY895: $i] :
( ~ ( in @ SY895 @ SV339 )
| ( in @ SY895 @ SV114 )
| ( in @ SY895 @ SV302 ) )
| ~ ~ ( ~ ! [SY896: $i] :
( ~ ( in @ SY896 @ SV114 )
| ( in @ SY896 @ SV339 ) )
| ~ ! [SY897: $i] :
( ~ ( in @ SY897 @ SV302 )
| ( in @ SY897 @ SV339 ) ) ) )
= $false )
| ( ( SV339
= ( set_union2 @ SV114 @ SV302 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2162]) ).
thf(2299,plain,
! [SV340: $i,SV303: $i,SV115: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV115 @ SV303 ) @ SV340 ) )
= $true )
| ( ( in @ SV115 @ ( relation_field @ SV340 ) )
= $true )
| ( ( relation @ SV340 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2163]) ).
thf(2300,plain,
! [SV341: $i,SV304: $i,SV115: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV115 @ SV304 ) @ SV341 ) )
= $true )
| ( ( in @ SV304 @ ( relation_field @ SV341 ) )
= $true )
| ( ( relation @ SV341 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2164]) ).
thf(2301,plain,
! [SV389: $i] :
( ( ( SV389 = empty_set )
= $false )
| ( ( ! [SY959: $i] : ( subset @ SV389 @ ( singleton @ SY959 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2168]) ).
thf(2302,plain,
! [SV417: $i,SV390: $i] :
( ( ( ( SV390
!= ( singleton @ SV417 ) ) )
= $true )
| ( ( subset @ SV390 @ ( singleton @ SV417 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2169]) ).
thf(2303,plain,
! [SV116: $i,SV306: $i,SV342: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV116 )
| ~ ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV306 )
| ~ ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV342 ) ) )
= $false )
| ( ( SV342
= ( set_intersection2 @ SV116 @ SV306 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2170]) ).
thf(2304,plain,
! [SV116: $i,SV306: $i,SV342: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV116 )
| ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV342 ) )
| ~ ( ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV306 )
| ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV342 ) ) ) )
= $false )
| ( ( SV342
= ( set_intersection2 @ SV116 @ SV306 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2170]) ).
thf(2305,plain,
! [SV343: $i,SV307: $i,SV116: $i] :
( ( ( ~ ! [SY898: $i] :
( ~ ( in @ SY898 @ SV116 )
| ~ ( in @ SY898 @ SV307 )
| ( in @ SY898 @ SV343 ) )
| ~ ~ ( ~ ! [SY899: $i] :
( ~ ( in @ SY899 @ SV343 )
| ( in @ SY899 @ SV116 ) )
| ~ ! [SY900: $i] :
( ~ ( in @ SY900 @ SV343 )
| ( in @ SY900 @ SV307 ) ) ) )
= $false )
| ( ( SV343
= ( set_intersection2 @ SV116 @ SV307 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2171]) ).
thf(2306,plain,
! [SV249: $i] :
( ( ( relation @ SV249 )
= $false )
| ( ( function @ SV249 )
= $false )
| ( ( ~ ( one_to_one @ SV249 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2172]) ).
thf(2307,plain,
! [SV250: $i] :
( ( ( relation @ SV250 )
= $false )
| ( ( function @ SV250 )
= $false )
| ( ( ~ ( one_to_one @ SV250 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2173]) ).
thf(2308,plain,
! [SV251: $i,SV308: $i] :
( ( ( ~ ( ( ( sK44_C @ SV308 @ SV251 )
!= ( sK45_SY414 @ SV308 @ SV251 ) )
| ~ ( in @ ( sK44_C @ SV308 @ SV251 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 ) )
| ~ ~ ( ~ ( ( ( sK44_C @ SV308 @ SV251 )
= ( sK45_SY414 @ SV308 @ SV251 ) )
| ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 ) )
| ~ ( ( in @ ( sK44_C @ SV308 @ SV251 ) @ SV251 )
| ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 ) ) ) )
= $false )
| ( ( SV308
= ( identity_relation @ SV251 ) )
= $true )
| ( ( relation @ SV308 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2174]) ).
thf(2309,plain,
! [SV252: $i,SV309: $i] :
( ( ( SV309
= ( identity_relation @ SV252 ) )
= $false )
| ( ( ~ ( ~ ! [SY861: $i,SY862: $i] :
( ( SY861 != SY862 )
| ~ ( in @ SY861 @ SV252 )
| ( in @ ( ordered_pair @ SY861 @ SY862 ) @ SV309 ) )
| ~ ~ ( ~ ! [SY863: $i,SY864: $i] :
( ~ ( in @ ( ordered_pair @ SY863 @ SY864 ) @ SV309 )
| ( SY863 = SY864 ) )
| ~ ! [SY865: $i] :
( ! [SY866: $i] :
~ ( in @ ( ordered_pair @ SY865 @ SY866 ) @ SV309 )
| ( in @ SY865 @ SV252 ) ) ) ) )
= $true )
| ( ( relation @ SV309 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2175]) ).
thf(2310,plain,
! [SV344: $i,SV310: $i,SV117: $i] :
( ( ( ~ ( in @ SV117 @ SV310 )
| ~ ( in @ SV117 @ ( relation_dom @ SV344 ) ) )
= $true )
| ( ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SV344 @ SV310 ) ) )
= $true )
| ( ( relation @ SV344 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2176]) ).
thf(2311,plain,
! [SV418: $i,SV117: $i,SV441: $i] :
( ( ~ ( relation @ SV441 )
| ~ ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SV441 @ SV418 ) ) )
| ( in @ SV117 @ SV418 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2177]) ).
thf(2312,plain,
! [SV419: $i,SV117: $i,SV442: $i] :
( ( ~ ( relation @ SV442 )
| ~ ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SV442 @ SV419 ) ) )
| ( in @ SV117 @ ( relation_dom @ SV442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2178]) ).
thf(2313,plain,
! [SV253: $i,SV311: $i] :
( ( ( relation @ SV311 )
= $false )
| ( ( function @ SV311 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK50_C @ SV311 @ SV253 ) @ SV253 )
| ~ ( ( ( apply @ SV311 @ ( sK50_C @ SV311 @ SV253 ) )
!= ( sK50_C @ SV311 @ SV253 ) ) ) )
| ( ( relation_dom @ SV311 )
!= SV253 )
| ( SV311
= ( identity_relation @ SV253 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2179]) ).
thf(2314,plain,
! [SV391: $i,SV420: $i] :
( ( ( ~ ( function @ SV420 )
| ~ ( relation @ SV420 ) )
= $true )
| ( ( ( SV420
!= ( identity_relation @ SV391 ) )
| ! [SY997: $i] :
( ~ ( in @ SY997 @ SV391 )
| ( ( apply @ SV420 @ SY997 )
= SY997 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2180]) ).
thf(2315,plain,
! [SV392: $i,SV421: $i] :
( ( ( ~ ( function @ SV421 )
| ~ ( relation @ SV421 ) )
= $true )
| ( ( ( SV421
!= ( identity_relation @ SV392 ) )
| ( ( relation_dom @ SV421 )
= SV392 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2181]) ).
thf(2316,plain,
! [SV345: $i,SV312: $i,SV118: $i] :
( ( ( ~ ( ! [SY901: $i,SY902: $i] :
( ~ ( in @ SY901 @ SV118 )
| ~ ( in @ SY902 @ SV312 )
| ( ( sK23_D @ SV345 @ SV312 @ SV118 )
!= ( ordered_pair @ SY901 @ SY902 ) ) )
| ~ ( in @ ( sK23_D @ SV345 @ SV312 @ SV118 ) @ SV345 ) ) )
= $false )
| ( ( SV345
= ( cartesian_product2 @ SV118 @ SV312 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2182]) ).
thf(2317,plain,
! [SV118: $i,SV312: $i,SV345: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY403 @ SV345 @ SV312 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK25_SY405 @ SV345 @ SV312 @ SV118 ) @ SV312 ) )
| ( ( sK23_D @ SV345 @ SV312 @ SV118 )
!= ( ordered_pair @ ( sK24_SY403 @ SV345 @ SV312 @ SV118 ) @ ( sK25_SY405 @ SV345 @ SV312 @ SV118 ) ) ) )
| ( in @ ( sK23_D @ SV345 @ SV312 @ SV118 ) @ SV345 ) ) )
= $false )
| ( ( SV345
= ( cartesian_product2 @ SV118 @ SV312 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2182]) ).
thf(2318,plain,
! [SV346: $i,SV313: $i,SV118: $i] :
( ( ( ~ ! [SY903: $i] :
( ! [SY873: $i,SY874: $i] :
( ~ ( in @ SY873 @ SV118 )
| ~ ( in @ SY874 @ SV313 )
| ( SY903
!= ( ordered_pair @ SY873 @ SY874 ) ) )
| ( in @ SY903 @ SV346 ) )
| ~ ! [SY906: $i] :
( ~ ( in @ SY906 @ SV346 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY906 @ SV346 @ SV313 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK22_SY400 @ SY906 @ SV346 @ SV313 @ SV118 ) @ SV313 ) )
| ( SY906
!= ( ordered_pair @ ( sK21_E @ SY906 @ SV346 @ SV313 @ SV118 ) @ ( sK22_SY400 @ SY906 @ SV346 @ SV313 @ SV118 ) ) ) ) ) )
= $false )
| ( ( SV346
= ( cartesian_product2 @ SV118 @ SV313 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2183]) ).
thf(2319,plain,
! [SV254: $i,SV316: $i] :
( ( ( ! [SY878: $i] :
( ~ ( in @ ( sK15_C @ SV316 @ SV254 ) @ SY878 )
| ~ ( in @ SY878 @ SV254 ) )
| ~ ( in @ ( sK15_C @ SV316 @ SV254 ) @ SV316 ) )
= $true )
| ( ( SV316
= ( union @ SV254 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2186]) ).
thf(2320,plain,
! [SV254: $i,SV316: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_C @ SV316 @ SV254 ) @ ( sK16_SY398 @ SV316 @ SV254 ) )
| ~ ( in @ ( sK16_SY398 @ SV316 @ SV254 ) @ SV254 ) )
| ( in @ ( sK15_C @ SV316 @ SV254 ) @ SV316 ) )
= $true )
| ( ( SV316
= ( union @ SV254 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2187]) ).
thf(2321,plain,
! [SV317: $i,SV255: $i] :
( ( ( ~ ! [SY879: $i] :
( ! [SY817: $i] :
( ~ ( in @ SY879 @ SY817 )
| ~ ( in @ SY817 @ SV255 ) )
| ( in @ SY879 @ SV317 ) ) )
= $false )
| ( ( SV317
= ( union @ SV255 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2188]) ).
thf(2322,plain,
! [SV255: $i,SV317: $i] :
( ( ( ~ ! [SY881: $i] :
( ~ ( in @ SY881 @ SV317 )
| ~ ( ~ ( in @ SY881 @ ( sK14_D @ SY881 @ SV317 @ SV255 ) )
| ~ ( in @ ( sK14_D @ SY881 @ SV317 @ SV255 ) @ SV255 ) ) ) )
= $false )
| ( ( SV317
= ( union @ SV255 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2188]) ).
thf(2323,plain,
! [SV120: $i,SV393: $i] :
( ( ( relation @ SV393 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV393 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV120 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV393 ) ) )
| ( SV120 = SV393 ) )
= $true )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2189]) ).
thf(2324,plain,
! [SV120: $i,SV394: $i] :
( ( ( relation @ SV394 )
= $false )
| ( ( ( SV120 != SV394 )
| ~ ( ~ ! [SY964: $i,SY965: $i] :
( ~ ( in @ ( ordered_pair @ SY964 @ SY965 ) @ SV120 )
| ( in @ ( ordered_pair @ SY964 @ SY965 ) @ SV394 ) )
| ~ ! [SY966: $i,SY967: $i] :
( ~ ( in @ ( ordered_pair @ SY966 @ SY967 ) @ SV394 )
| ( in @ ( ordered_pair @ SY966 @ SY967 ) @ SV120 ) ) ) )
= $true )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2190]) ).
thf(2325,plain,
! [SV145: $i,SV43: $i,SV347: $i] :
( ( ( function @ SV347 )
= $false )
| ( ( ~ ( relation @ SV347 ) )
= $true )
| ( ( ~ ( in @ SV43 @ ( relation_dom @ ( relation_composition @ SV347 @ SV145 ) ) )
| ( ( apply @ ( relation_composition @ SV347 @ SV145 ) @ SV43 )
= ( apply @ SV145 @ ( apply @ SV347 @ SV43 ) ) ) )
= $true )
| ( ( function @ SV145 )
= $false )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2191]) ).
thf(2326,plain,
! [SV146: $i,SV44: $i,SV348: $i] :
( ( ( function @ SV348 )
= $false )
| ( ( ~ ( relation @ SV348 ) )
= $true )
| ( ( ~ ( in @ SV44 @ ( relation_dom @ SV146 ) )
| ( ( apply @ ( relation_composition @ SV146 @ SV348 ) @ SV44 )
= ( apply @ SV348 @ ( apply @ SV146 @ SV44 ) ) ) )
= $true )
| ( ( function @ SV146 )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2192]) ).
thf(2327,plain,
! [SV443: $i,SV349: $i] :
( ( ( subset @ SV349 @ ( singleton @ SV443 ) )
= $true )
| ( ( SV349 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2193]) ).
thf(2328,plain,
! [SV395: $i,SV350: $i] :
( ( ( SV350
= ( singleton @ SV395 ) )
= $false )
| ( ( subset @ SV350 @ ( singleton @ SV395 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2194]) ).
thf(2329,plain,
! [SV351: $i,SV424: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY406 @ SV424 @ SV351 ) @ SV351 )
| ~ ~ ( in @ ( sK32_C @ SV424 @ SV351 ) @ ( sK33_SY406 @ SV424 @ SV351 ) ) )
| ~ ( in @ ( sK32_C @ SV424 @ SV351 ) @ SV424 ) )
| ~ ( ! [SY998: $i] :
( ~ ( in @ SY998 @ SV351 )
| ( in @ ( sK32_C @ SV424 @ SV351 ) @ SY998 ) )
| ( in @ ( sK32_C @ SV424 @ SV351 ) @ SV424 ) ) ) )
= $true )
| ( ( SV424
= ( set_meet @ SV351 ) )
= $true )
| ( ( SV351 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2195]) ).
thf(2330,plain,
! [SV352: $i,SV425: $i] :
( ( ( ( SV425
!= ( set_meet @ SV352 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY999: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY999 @ SV425 @ SV352 ) @ SV352 )
| ~ ~ ( in @ SY999 @ ( sK31_D @ SY999 @ SV425 @ SV352 ) ) )
| ( in @ SY999 @ SV425 ) )
| ~ ! [SY1000: $i] :
( ~ ( in @ SY1000 @ SV425 )
| ! [SY914: $i] :
( ~ ( in @ SY914 @ SV352 )
| ( in @ SY1000 @ SY914 ) ) ) ) )
= $true )
| ( ( SV352 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2196]) ).
thf(2331,plain,
! [SV353: $i,SV444: $i] :
( ( ( ( SV444
!= ( set_meet @ SV353 ) )
| ( SV444 = empty_set ) )
= $true )
| ( ( SV353 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2197]) ).
thf(2332,plain,
! [SV354: $i,SV445: $i] :
( ( ( ( SV445 != empty_set )
| ( SV445
= ( set_meet @ SV354 ) ) )
= $true )
| ( ( SV354 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2198]) ).
thf(2333,plain,
! [SV265: $i,SV202: $i] :
( ( ( function @ SV202 )
= $false )
| ( ( ~ ( relation @ SV202 ) )
= $true )
| ( ( ~ ( relation @ SV265 ) )
= $true )
| ( ( ~ ( function @ SV265 ) )
= $true )
| ( ( function @ ( relation_composition @ SV202 @ SV265 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2200]) ).
thf(2334,plain,
! [SV266: $i,SV203: $i] :
( ( ( function @ SV203 )
= $false )
| ( ( ~ ( relation @ SV203 ) )
= $true )
| ( ( ~ ( relation @ SV266 ) )
= $true )
| ( ( ~ ( function @ SV266 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV203 @ SV266 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2201]) ).
thf(2335,plain,
! [SV271: $i,SV87: $i,SV320: $i,SV446: $i] :
( ( ( ~ ( in @ SV446 @ ( relation_dom @ SV320 ) )
| ~ ( in @ ( ordered_pair @ SV446 @ SV87 ) @ SV320 )
| ~ ( in @ SV446 @ SV271 ) )
= $true )
| ( ( in @ SV87 @ ( relation_image @ SV320 @ SV271 ) )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2204]) ).
thf(2336,plain,
! [SV272: $i,SV321: $i,SV87: $i] :
( ( ( in @ SV87 @ ( relation_image @ SV321 @ SV272 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK52_D @ SV321 @ SV272 @ SV87 ) @ ( relation_dom @ SV321 ) )
| ~ ( in @ ( ordered_pair @ ( sK52_D @ SV321 @ SV272 @ SV87 ) @ SV87 ) @ SV321 ) )
| ~ ( in @ ( sK52_D @ SV321 @ SV272 @ SV87 ) @ SV272 ) ) )
= $true )
| ( ( relation @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2205]) ).
thf(2337,plain,
! [SV396: $i,SV356: $i] :
( ( ( SV356 = SV396 )
= $false )
| ( ( subset @ SV356 @ SV396 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2207]) ).
thf(2338,plain,
! [SV397: $i,SV357: $i] :
( ( ( SV357 = SV397 )
= $false )
| ( ( subset @ SV397 @ SV357 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2208]) ).
thf(2339,plain,
! [SV88: $i,SV274: $i,SV322: $i] :
( ( ( ~ ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV88 )
| ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV274 )
| ~ ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV322 ) )
= $true )
| ( ( SV322
= ( set_difference @ SV88 @ SV274 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2209]) ).
thf(2340,plain,
! [SV88: $i,SV274: $i,SV322: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV88 )
| ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV322 ) )
| ~ ( ~ ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV274 )
| ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV322 ) ) ) )
= $true )
| ( ( SV322
= ( set_difference @ SV88 @ SV274 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2210]) ).
thf(2341,plain,
! [SV323: $i,SV275: $i,SV88: $i] :
( ( ( ~ ! [SY883: $i] :
( ~ ( in @ SY883 @ SV88 )
| ( in @ SY883 @ SV275 )
| ( in @ SY883 @ SV323 ) ) )
= $false )
| ( ( SV323
= ( set_difference @ SV88 @ SV275 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2211]) ).
thf(2342,plain,
! [SV275: $i,SV88: $i,SV323: $i] :
( ( ( ~ ~ ( ~ ! [SY884: $i] :
( ~ ( in @ SY884 @ SV323 )
| ( in @ SY884 @ SV88 ) )
| ~ ! [SY885: $i] :
( ~ ( in @ SY885 @ SV323 )
| ~ ( in @ SY885 @ SV275 ) ) ) )
= $false )
| ( ( SV323
= ( set_difference @ SV88 @ SV275 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2211]) ).
thf(2343,plain,
! [SV358: $i,SV426: $i] :
( ( ( ~ ( element @ SV426 @ SV358 ) )
= $true )
| ( ( in @ SV426 @ SV358 )
= $true )
| ( ( empty @ SV358 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2212]) ).
thf(2344,plain,
! [SV359: $i,SV427: $i] :
( ( ( ~ ( in @ SV427 @ SV359 ) )
= $true )
| ( ( element @ SV427 @ SV359 )
= $true )
| ( ( empty @ SV359 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2213]) ).
thf(2345,plain,
! [SV360: $i,SV447: $i] :
( ( ( ~ ( element @ SV447 @ SV360 )
| ( empty @ SV447 ) )
= $true )
| ( ( empty @ SV360 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2214]) ).
thf(2346,plain,
! [SV361: $i,SV448: $i] :
( ( ( ~ ( empty @ SV448 )
| ( element @ SV448 @ SV361 ) )
= $true )
| ( ( empty @ SV361 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2215]) ).
thf(2347,plain,
! [SV89: $i,SV174: $i,SV398: $i] :
( ( ( relation @ SV398 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV174 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 ) )
| ~ ~ ( ~ ( ( in @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) @ SV89 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV174 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 ) ) ) )
| ( SV398
= ( relation_rng_restriction @ SV89 @ SV174 ) ) )
= $true )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2216]) ).
thf(2348,plain,
! [SV174: $i,SV89: $i,SV399: $i] :
( ( ( relation @ SV399 )
= $false )
| ( ( ( SV399
!= ( relation_rng_restriction @ SV89 @ SV174 ) )
| ~ ( ~ ! [SY968: $i,SY969: $i] :
( ~ ( in @ SY969 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY968 @ SY969 ) @ SV174 )
| ( in @ ( ordered_pair @ SY968 @ SY969 ) @ SV399 ) )
| ~ ~ ( ~ ! [SY970: $i,SY971: $i] :
( ~ ( in @ ( ordered_pair @ SY970 @ SY971 ) @ SV399 )
| ( in @ SY971 @ SV89 ) )
| ~ ! [SY972: $i,SY973: $i] :
( ~ ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV399 )
| ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV174 ) ) ) ) )
= $true )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2217]) ).
thf(2349,plain,
! [SV90: $i,SV276: $i,SV324: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK27_D @ SV324 @ SV276 @ SV90 ) @ SV324 )
| ( ( sK27_D @ SV324 @ SV276 @ SV90 )
!= SV90 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV324 @ SV276 @ SV90 ) @ SV324 )
| ( ( sK27_D @ SV324 @ SV276 @ SV90 )
!= SV276 ) ) ) )
= $true )
| ( ( SV324
= ( unordered_pair @ SV90 @ SV276 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2218]) ).
thf(2350,plain,
! [SV90: $i,SV276: $i,SV324: $i] :
( ( ( ( in @ ( sK27_D @ SV324 @ SV276 @ SV90 ) @ SV324 )
| ( ( sK27_D @ SV324 @ SV276 @ SV90 )
= SV90 )
| ( ( sK27_D @ SV324 @ SV276 @ SV90 )
= SV276 ) )
= $true )
| ( ( SV324
= ( unordered_pair @ SV90 @ SV276 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2219]) ).
thf(2351,plain,
! [SV277: $i,SV90: $i,SV325: $i] :
( ( ( ~ ! [SY886: $i] :
( ~ ( in @ SY886 @ SV325 )
| ( SY886 = SV90 )
| ( SY886 = SV277 ) ) )
= $false )
| ( ( SV325
= ( unordered_pair @ SV90 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2220]) ).
thf(2352,plain,
! [SV277: $i,SV325: $i,SV90: $i] :
( ( ( ~ ~ ( ~ ! [SY887: $i] :
( ( SY887 != SV90 )
| ( in @ SY887 @ SV325 ) )
| ~ ! [SY888: $i] :
( ( SY888 != SV277 )
| ( in @ SY888 @ SV325 ) ) ) )
= $false )
| ( ( SV325
= ( unordered_pair @ SV90 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2220]) ).
thf(2353,plain,
! [SV209: $i,SV278: $i] :
( ( ( ~ ( in @ ( sK28_C @ SV278 @ SV209 ) @ SV278 ) )
= $true )
| ( ( ~ ( subset @ ( sK28_C @ SV278 @ SV209 ) @ SV209 ) )
= $true )
| ( ( SV278
= ( powerset @ SV209 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2221]) ).
thf(2354,plain,
! [SV209: $i,SV278: $i] :
( ( ( in @ ( sK28_C @ SV278 @ SV209 ) @ SV278 )
= $true )
| ( ( subset @ ( sK28_C @ SV278 @ SV209 ) @ SV209 )
= $true )
| ( ( SV278
= ( powerset @ SV209 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2222]) ).
thf(2355,plain,
! [SV210: $i,SV279: $i] :
( ( ( ! [SY835: $i] :
( ~ ( in @ SY835 @ SV279 )
| ( subset @ SY835 @ SV210 ) ) )
= $true )
| ( ( SV279
= ( powerset @ SV210 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2223]) ).
thf(2356,plain,
! [SV279: $i,SV210: $i] :
( ( ( ! [SY836: $i] :
( ~ ( subset @ SY836 @ SV210 )
| ( in @ SY836 @ SV279 ) ) )
= $true )
| ( ( SV279
= ( powerset @ SV210 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2224]) ).
thf(2357,plain,
! [SV91: $i,SV362: $i] :
( ( ( ~ ( ! [SY923: $i] :
~ ( in @ ( ordered_pair @ ( sK63_C @ SV362 @ SV91 ) @ SY923 ) @ SV91 )
| ~ ( in @ ( sK63_C @ SV362 @ SV91 ) @ SV362 ) ) )
= $false )
| ( ( SV362
= ( relation_dom @ SV91 ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2225]) ).
thf(2358,plain,
! [SV91: $i,SV362: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK63_C @ SV362 @ SV91 ) @ ( sK64_SY419 @ SV362 @ SV91 ) ) @ SV91 )
| ( in @ ( sK63_C @ SV362 @ SV91 ) @ SV362 ) ) )
= $false )
| ( ( SV362
= ( relation_dom @ SV91 ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2225]) ).
thf(2359,plain,
! [SV363: $i,SV91: $i] :
( ( ( ~ ! [SY924: $i] :
( ! [SY530: $i] :
~ ( in @ ( ordered_pair @ SY924 @ SY530 ) @ SV91 )
| ( in @ SY924 @ SV363 ) )
| ~ ! [SY926: $i] :
( ~ ( in @ SY926 @ SV363 )
| ( in @ ( ordered_pair @ SY926 @ ( sK62_D @ SY926 @ SV363 @ SV91 ) ) @ SV91 ) ) )
= $false )
| ( ( SV363
= ( relation_dom @ SV91 ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2226]) ).
thf(2360,plain,
! [SV92: $i,SV364: $i,SV400: $i] :
( ( ( ~ ( ! [SY974: $i] :
( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SY974 ) @ SV92 )
| ~ ( in @ SY974 @ SV364 ) )
| ~ ( in @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SV400 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ ( sK36_SY409 @ SV400 @ SV364 @ SV92 ) ) @ SV92 )
| ~ ( in @ ( sK36_SY409 @ SV400 @ SV364 @ SV92 ) @ SV364 ) )
| ( in @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SV400 ) ) )
= $false )
| ( ( SV400
= ( relation_inverse_image @ SV92 @ SV364 ) )
= $true )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2227]) ).
thf(2361,plain,
! [SV365: $i,SV92: $i,SV401: $i] :
( ( ( SV401
= ( relation_inverse_image @ SV92 @ SV365 ) )
= $false )
| ( ( ~ ( ~ ! [SY975: $i] :
( ! [SY931: $i] :
( ~ ( in @ ( ordered_pair @ SY975 @ SY931 ) @ SV92 )
| ~ ( in @ SY931 @ SV365 ) )
| ( in @ SY975 @ SV401 ) )
| ~ ! [SY977: $i] :
( ~ ( in @ SY977 @ SV401 )
| ~ ( ~ ( in @ ( ordered_pair @ SY977 @ ( sK34_E @ SY977 @ SV401 @ SV365 @ SV92 ) ) @ SV92 )
| ~ ( in @ ( sK34_E @ SY977 @ SV401 @ SV365 @ SV92 ) @ SV365 ) ) ) ) )
= $true )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2228]) ).
thf(2362,plain,
! [SV93: $i,SV366: $i,SV402: $i] :
( ( ( ~ ( ! [SY978: $i] :
( ~ ( in @ ( ordered_pair @ SY978 @ ( sK38_D @ SV402 @ SV366 @ SV93 ) ) @ SV93 )
| ~ ( in @ SY978 @ SV366 ) )
| ~ ( in @ ( sK38_D @ SV402 @ SV366 @ SV93 ) @ SV402 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SV402 @ SV366 @ SV93 ) @ ( sK38_D @ SV402 @ SV366 @ SV93 ) ) @ SV93 )
| ~ ( in @ ( sK39_SY411 @ SV402 @ SV366 @ SV93 ) @ SV366 ) )
| ( in @ ( sK38_D @ SV402 @ SV366 @ SV93 ) @ SV402 ) ) )
= $false )
| ( ( SV402
= ( relation_image @ SV93 @ SV366 ) )
= $true )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2229]) ).
thf(2363,plain,
! [SV367: $i,SV93: $i,SV403: $i] :
( ( ( SV403
= ( relation_image @ SV93 @ SV367 ) )
= $false )
| ( ( ~ ( ~ ! [SY979: $i] :
( ! [SY937: $i] :
( ~ ( in @ ( ordered_pair @ SY937 @ SY979 ) @ SV93 )
| ~ ( in @ SY937 @ SV367 ) )
| ( in @ SY979 @ SV403 ) )
| ~ ! [SY981: $i] :
( ~ ( in @ SY981 @ SV403 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SY981 @ SV403 @ SV367 @ SV93 ) @ SY981 ) @ SV93 )
| ~ ( in @ ( sK37_E @ SY981 @ SV403 @ SV367 @ SV93 ) @ SV367 ) ) ) ) )
= $true )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2230]) ).
thf(2364,plain,
! [SV282: $i,SV94: $i,SV326: $i,SV449: $i] :
( ( ( ~ ( in @ SV449 @ ( relation_rng @ SV326 ) )
| ~ ( in @ ( ordered_pair @ SV94 @ SV449 ) @ SV326 )
| ~ ( in @ SV449 @ SV282 ) )
= $true )
| ( ( in @ SV94 @ ( relation_inverse_image @ SV326 @ SV282 ) )
= $true )
| ( ( relation @ SV326 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2231]) ).
thf(2365,plain,
! [SV283: $i,SV327: $i,SV94: $i] :
( ( ( in @ SV94 @ ( relation_inverse_image @ SV327 @ SV283 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK51_D @ SV327 @ SV283 @ SV94 ) @ ( relation_rng @ SV327 ) )
| ~ ( in @ ( ordered_pair @ SV94 @ ( sK51_D @ SV327 @ SV283 @ SV94 ) ) @ SV327 ) )
| ~ ( in @ ( sK51_D @ SV327 @ SV283 @ SV94 ) @ SV283 ) ) )
= $true )
| ( ( relation @ SV327 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2232]) ).
thf(2366,plain,
! [SV175: $i,SV95: $i,SV450: $i] :
( ( ( ~ ( function @ SV450 )
| ~ ( relation @ SV450 )
| ~ ( in @ SV95 @ ( relation_dom @ SV450 ) )
| ~ ( in @ ( apply @ SV450 @ SV95 ) @ ( relation_dom @ SV175 ) )
| ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SV450 @ SV175 ) ) ) )
= $true )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2233]) ).
thf(2367,plain,
! [SV175: $i,SV95: $i] :
( ( ( ~ ! [SY732: $i] :
( ~ ( function @ SY732 )
| ~ ( relation @ SY732 )
| ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY732 @ SV175 ) ) )
| ( in @ SV95 @ ( relation_dom @ SY732 ) ) )
| ~ ! [SY733: $i] :
( ~ ( function @ SY733 )
| ~ ( relation @ SY733 )
| ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY733 @ SV175 ) ) )
| ( in @ ( apply @ SY733 @ SV95 ) @ ( relation_dom @ SV175 ) ) ) )
= $false )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2234]) ).
thf(2368,plain,
! [SV96: $i,SV368: $i,SV404: $i] :
( ( ( relation @ SV404 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ SV368 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 ) )
| ~ ~ ( ~ ( ( in @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ SV368 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 ) ) ) )
| ( SV404
= ( relation_dom_restriction @ SV96 @ SV368 ) ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2235]) ).
thf(2369,plain,
! [SV369: $i,SV96: $i,SV405: $i] :
( ( ( relation @ SV405 )
= $false )
| ( ( ( SV405
!= ( relation_dom_restriction @ SV96 @ SV369 ) )
| ~ ( ~ ! [SY982: $i,SY983: $i] :
( ~ ( in @ SY982 @ SV369 )
| ~ ( in @ ( ordered_pair @ SY982 @ SY983 ) @ SV96 )
| ( in @ ( ordered_pair @ SY982 @ SY983 ) @ SV405 ) )
| ~ ~ ( ~ ! [SY984: $i] :
( ! [SY985: $i] :
~ ( in @ ( ordered_pair @ SY984 @ SY985 ) @ SV405 )
| ( in @ SY984 @ SV369 ) )
| ~ ! [SY986: $i,SY987: $i] :
( ~ ( in @ ( ordered_pair @ SY986 @ SY987 ) @ SV405 )
| ( in @ ( ordered_pair @ SY986 @ SY987 ) @ SV96 ) ) ) ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2236]) ).
thf(2370,plain,
! [SV97: $i,SV370: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SV370 @ SV97 ) @ ( sK12_SY396 @ SV370 @ SV97 ) ) @ SV370 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SV370 @ SV97 ) @ ( sK11_C @ SV370 @ SV97 ) ) @ SV97 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_C @ SV370 @ SV97 ) @ ( sK12_SY396 @ SV370 @ SV97 ) ) @ SV370 )
| ( in @ ( ordered_pair @ ( sK12_SY396 @ SV370 @ SV97 ) @ ( sK11_C @ SV370 @ SV97 ) ) @ SV97 ) ) ) )
= $true )
| ( ( SV370
= ( relation_inverse @ SV97 ) )
= $true )
| ( ( relation @ SV370 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2239]) ).
thf(2371,plain,
! [SV97: $i,SV371: $i] :
( ( ( ( SV371
!= ( relation_inverse @ SV97 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY947: $i,SY948: $i] :
( ~ ( in @ ( ordered_pair @ SY947 @ SY948 ) @ SV371 )
| ( in @ ( ordered_pair @ SY948 @ SY947 ) @ SV97 ) )
| ~ ! [SY949: $i,SY950: $i] :
( ~ ( in @ ( ordered_pair @ SY950 @ SY949 ) @ SV97 )
| ( in @ ( ordered_pair @ SY949 @ SY950 ) @ SV371 ) ) ) )
= $true )
| ( ( relation @ SV371 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2240]) ).
thf(2372,plain,
! [SV98: $i,SV372: $i] :
( ( ( ~ ( ! [SY951: $i] :
~ ( in @ ( ordered_pair @ SY951 @ ( sK60_C @ SV372 @ SV98 ) ) @ SV98 )
| ~ ( in @ ( sK60_C @ SV372 @ SV98 ) @ SV372 ) ) )
= $false )
| ( ( SV372
= ( relation_rng @ SV98 ) )
= $true )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2241]) ).
thf(2373,plain,
! [SV98: $i,SV372: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK61_SY417 @ SV372 @ SV98 ) @ ( sK60_C @ SV372 @ SV98 ) ) @ SV98 )
| ( in @ ( sK60_C @ SV372 @ SV98 ) @ SV372 ) ) )
= $false )
| ( ( SV372
= ( relation_rng @ SV98 ) )
= $true )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2241]) ).
thf(2374,plain,
! [SV373: $i,SV98: $i] :
( ( ( ~ ! [SY952: $i] :
( ! [SY577: $i] :
~ ( in @ ( ordered_pair @ SY577 @ SY952 ) @ SV98 )
| ( in @ SY952 @ SV373 ) )
| ~ ! [SY954: $i] :
( ~ ( in @ SY954 @ SV373 )
| ( in @ ( ordered_pair @ ( sK59_D @ SY954 @ SV373 @ SV98 ) @ SY954 ) @ SV98 ) ) )
= $false )
| ( ( SV373
= ( relation_rng @ SV98 ) )
= $false )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2242]) ).
thf(2375,plain,
! [SV100: $i,SV286: $i,SV328: $i] :
( ( ( relation @ SV328 )
= $false )
| ( ( function @ SV328 )
= $false )
| ( ( ( SV286
!= ( apply @ SV328 @ SV100 ) )
| ~ ( in @ SV100 @ ( relation_dom @ SV328 ) )
| ( in @ ( ordered_pair @ SV100 @ SV286 ) @ SV328 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2244]) ).
thf(2376,plain,
! [SV406: $i,SV100: $i,SV428: $i] :
( ( ( ~ ( function @ SV428 )
| ~ ( relation @ SV428 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV100 @ SV406 ) @ SV428 )
| ( SV406
= ( apply @ SV428 @ SV100 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2245]) ).
thf(2377,plain,
! [SV407: $i,SV100: $i,SV429: $i] :
( ( ( ~ ( function @ SV429 )
| ~ ( relation @ SV429 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV100 @ SV407 ) @ SV429 )
| ( in @ SV100 @ ( relation_dom @ SV429 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2246]) ).
thf(2378,plain,
! [SV101: $i,SV215: $i,SV451: $i] :
( ( ( ~ ( relation @ SV451 )
| ~ ( ~ ( ! [SY1009: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ SY1009 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY1009 @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV215 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV451 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK10_SY395 @ SV451 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV215 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV451 ) ) )
| ( SV451
= ( relation_composition @ SV101 @ SV215 ) ) )
= $true )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2247]) ).
thf(2379,plain,
! [SV215: $i,SV101: $i,SV452: $i] :
( ( ( ~ ( relation @ SV452 )
| ( SV452
!= ( relation_composition @ SV101 @ SV215 ) )
| ~ ( ~ ! [SY1010: $i,SY1011: $i] :
( ! [SY783: $i] :
( ~ ( in @ ( ordered_pair @ SY1010 @ SY783 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY783 @ SY1011 ) @ SV215 ) )
| ( in @ ( ordered_pair @ SY1010 @ SY1011 ) @ SV452 ) )
| ~ ! [SY1013: $i,SY1014: $i] :
( ~ ( in @ ( ordered_pair @ SY1013 @ SY1014 ) @ SV452 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1013 @ ( sK7_F @ SY1014 @ SY1013 @ SV452 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY1014 @ SY1013 @ SV452 @ SV215 @ SV101 ) @ SY1014 ) @ SV215 ) ) ) ) )
= $true )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2248]) ).
thf(2380,plain,
! [SV374: $i,SV177: $i,SV329: $i,SV102: $i] :
( ( ( in @ SV102 @ SV329 )
= $false )
| ( ( ~ ( in @ SV177 @ SV374 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SV329 @ SV374 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2249]) ).
thf(2381,plain,
! [SV430: $i,SV177: $i,SV102: $i] :
( ( ( ! [SY1002: $i] :
~ ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SV430 @ SY1002 ) ) )
= $true )
| ( ( in @ SV102 @ SV430 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2250]) ).
thf(2382,plain,
! [SV453: $i,SV431: $i,SV177: $i,SV102: $i] :
( ( ~ ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SV431 @ SV453 ) )
| ( in @ SV177 @ SV453 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2251]) ).
thf(2383,plain,
! [SV103: $i,SV408: $i] :
( ( ( ~ ! [SY990: $i] :
( ~ ( subset @ SY990 @ SV408 )
| ( in @ SY990 @ ( sK3_SY386 @ SV408 @ SV103 ) ) )
| ~ ( in @ ( sK3_SY386 @ SV408 @ SV103 ) @ ( sK2_B @ SV103 ) ) )
= $false )
| ( ( ~ ( in @ SV408 @ ( sK2_B @ SV103 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2252]) ).
thf(2384,plain,
! [SV103: $i] :
( ( ! [SY605: $i,SY606: $i] :
( ~ ( in @ SY605 @ ( sK2_B @ SV103 ) )
| ~ ( subset @ SY606 @ SY605 )
| ( in @ SY606 @ ( sK2_B @ SV103 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2253]) ).
thf(2385,plain,
! [SV103: $i] :
( ( in @ SV103 @ ( sK2_B @ SV103 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2254]) ).
thf(2386,plain,
! [SV454: $i,SV432: $i,SV222: $i] :
( ( ( ( ( sK69_B @ SV222 )
!= ( ordered_pair @ SV432 @ SV454 ) ) )
= $true )
| ( ( relation @ SV222 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2255]) ).
thf(2387,plain,
! [SV376: $i,SV104: $i] :
( ( ( ~ ( subset @ SV104 @ SV376 ) )
= $true )
| ( ( subset @ ( relation_dom @ SV104 ) @ ( relation_dom @ SV376 ) )
= $true )
| ( ( relation @ SV376 )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2257]) ).
thf(2388,plain,
! [SV377: $i,SV104: $i] :
( ( ( ~ ( subset @ SV104 @ SV377 ) )
= $true )
| ( ( subset @ ( relation_rng @ SV104 ) @ ( relation_rng @ SV377 ) )
= $true )
| ( ( relation @ SV377 )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2258]) ).
thf(2389,plain,
! [SV330: $i,SV288: $i,SV105: $i] :
( ( ( ~ ( in @ SV105 @ SV288 ) )
= $true )
| ( ( ~ ( in @ SV105 @ ( relation_rng @ SV330 ) ) )
= $true )
| ( ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SV288 @ SV330 ) ) )
= $true )
| ( ( relation @ SV330 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2259]) ).
thf(2390,plain,
! [SV409: $i,SV105: $i,SV433: $i] :
( ( ( ~ ( relation @ SV433 ) )
= $true )
| ( ( ~ ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SV409 @ SV433 ) ) )
| ( in @ SV105 @ SV409 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2260]) ).
thf(2391,plain,
! [SV410: $i,SV105: $i,SV434: $i] :
( ( ( ~ ( relation @ SV434 ) )
= $true )
| ( ( ~ ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SV410 @ SV434 ) ) )
| ( in @ SV105 @ ( relation_rng @ SV434 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2261]) ).
thf(2392,plain,
! [SV106: $i,SV331: $i,SV289: $i] :
( ( ( in @ SV289 @ SV331 )
= $false )
| ( ( in @ SV106 @ SV331 )
= $false )
| ( ( subset @ ( unordered_pair @ SV106 @ SV289 ) @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2262]) ).
thf(2393,plain,
! [SV435: $i,SV411: $i,SV106: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV106 @ SV411 ) @ SV435 ) )
= $true )
| ( ( in @ SV106 @ SV435 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2263]) ).
thf(2394,plain,
! [SV436: $i,SV412: $i,SV106: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV106 @ SV412 ) @ SV436 ) )
= $true )
| ( ( in @ SV412 @ SV436 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2264]) ).
thf(2395,plain,
! [SV378: $i,SV178: $i,SV332: $i,SV107: $i] :
( ( ( ~ ( in @ SV107 @ SV332 )
| ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ SV378 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SV332 ) @ SV378 ) )
= $true )
| ( ( relation @ SV378 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2265]) ).
thf(2396,plain,
! [SV437: $i,SV178: $i,SV107: $i,SV455: $i] :
( ( ~ ( relation @ SV455 )
| ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SV437 ) @ SV455 ) )
| ( in @ SV107 @ SV437 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2266]) ).
thf(2397,plain,
! [SV438: $i,SV178: $i,SV107: $i,SV456: $i] :
( ( ~ ( relation @ SV456 )
| ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SV438 ) @ SV456 ) )
| ( in @ ( ordered_pair @ SV107 @ SV178 ) @ SV456 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2267]) ).
thf(2398,plain,
! [SV108: $i,SV379: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV379 @ SV108 ) @ ( sK20_SY399 @ SV379 @ SV108 ) ) @ SV108 )
| ~ ~ ( in @ ( ordered_pair @ ( sK19_C @ SV379 @ SV108 ) @ ( sK20_SY399 @ SV379 @ SV108 ) ) @ SV379 ) ) )
= $true )
| ( ( subset @ SV108 @ SV379 )
= $true )
| ( ( relation @ SV379 )
= $false )
| ( ( relation @ SV108 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2268]) ).
thf(2399,plain,
! [SV380: $i,SV108: $i] :
( ( ( ~ ( subset @ SV108 @ SV380 ) )
= $true )
| ( ( ! [SY955: $i,SY956: $i] :
( ~ ( in @ ( ordered_pair @ SY955 @ SY956 ) @ SV108 )
| ( in @ ( ordered_pair @ SY955 @ SY956 ) @ SV380 ) ) )
= $true )
| ( ( relation @ SV380 )
= $false )
| ( ( relation @ SV108 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2269]) ).
thf(2400,plain,
! [SV228: $i,SV290: $i] :
( ( ( ( ( sK30_C @ SV290 @ SV228 )
!= SV228 ) )
= $true )
| ( ( ~ ( in @ ( sK30_C @ SV290 @ SV228 ) @ SV290 ) )
= $true )
| ( ( SV290
= ( singleton @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2270]) ).
thf(2401,plain,
! [SV228: $i,SV290: $i] :
( ( ( ( sK30_C @ SV290 @ SV228 )
= SV228 )
= $true )
| ( ( in @ ( sK30_C @ SV290 @ SV228 ) @ SV290 )
= $true )
| ( ( SV290
= ( singleton @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2271]) ).
thf(2402,plain,
! [SV291: $i,SV229: $i] :
( ( ( ! [SY843: $i] :
( ( SY843 != SV229 )
| ( in @ SY843 @ SV291 ) ) )
= $true )
| ( ( SV291
= ( singleton @ SV229 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2272]) ).
thf(2403,plain,
! [SV229: $i,SV291: $i] :
( ( ( ! [SY844: $i] :
( ~ ( in @ SY844 @ SV291 )
| ( SY844 = SV229 ) ) )
= $true )
| ( ( SV291
= ( singleton @ SV229 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2273]) ).
thf(2404,plain,
! [SV333: $i,SV292: $i,SV109: $i] :
( ( ( in @ ( ordered_pair @ SV109 @ SV292 ) @ SV333 )
= $false )
| ( ( in @ SV109 @ ( relation_dom @ SV333 ) )
= $true )
| ( ( relation @ SV333 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2274]) ).
thf(2405,plain,
! [SV334: $i,SV293: $i,SV109: $i] :
( ( ( in @ ( ordered_pair @ SV109 @ SV293 ) @ SV334 )
= $false )
| ( ( in @ SV293 @ ( relation_rng @ SV334 ) )
= $true )
| ( ( relation @ SV334 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2275]) ).
thf(2406,plain,
! [SV381: $i] :
( ( ( ~ ( empty @ SV381 ) )
= $true )
| ( ( ~ ( relation @ SV381 ) )
= $true )
| ( ( ~ ( function @ SV381 ) )
= $true )
| ( ( function @ SV381 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2276]) ).
thf(2407,plain,
! [SV382: $i] :
( ( ( ~ ( empty @ SV382 ) )
= $true )
| ( ( ~ ( relation @ SV382 ) )
= $true )
| ( ( ~ ( function @ SV382 ) )
= $true )
| ( ( relation @ SV382 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2277]) ).
thf(2408,plain,
! [SV230: $i] :
( ( ( function @ SV230 )
= $false )
| ( ( empty @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false )
| ( ( one_to_one @ SV230 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2278]) ).
thf(2409,plain,
! [SV110: $i] :
( ( ( ! [SY636: $i] :
( ~ ( function @ SY636 )
| ~ ( relation @ SY636 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SY636 @ SV110 )
= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ( ( sK70_C @ SY636 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY636 @ SV110 )
= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY636 @ SV110 )
= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ( ( sK71_SY424 @ SY636 @ SV110 )
!= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK70_C @ SY636 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK71_SY424 @ SY636 @ SV110 )
!= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY636 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK70_C @ SY636 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SY636 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SY636 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY636 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK71_SY424 @ SY636 @ SV110 )
!= ( apply @ SY636 @ ( sK70_C @ SY636 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SY636 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ( ( relation_dom @ SY636 )
!= ( relation_rng @ SV110 ) )
| ( SY636
= ( function_inverse @ SV110 ) ) ) )
= $true )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2279]) ).
thf(2410,plain,
! [SV110: $i] :
( ( ( ~ ( ~ ! [SY637: $i] :
( ~ ( function @ SY637 )
| ~ ( relation @ SY637 )
| ( SY637
!= ( function_inverse @ SV110 ) )
| ~ ( ~ ~ ( ~ ! [SY638: $i,SY639: $i] :
( ( SY639
!= ( apply @ SY637 @ SY638 ) )
| ~ ( in @ SY638 @ ( relation_rng @ SV110 ) )
| ( SY638
= ( apply @ SV110 @ SY639 ) ) )
| ~ ! [SY640: $i,SY641: $i] :
( ( SY641
!= ( apply @ SY637 @ SY640 ) )
| ~ ( in @ SY640 @ ( relation_rng @ SV110 ) )
| ( in @ SY641 @ ( relation_dom @ SV110 ) ) ) )
| ~ ~ ( ~ ! [SY642: $i,SY643: $i] :
( ( SY642
!= ( apply @ SV110 @ SY643 ) )
| ~ ( in @ SY643 @ ( relation_dom @ SV110 ) )
| ( SY643
= ( apply @ SY637 @ SY642 ) ) )
| ~ ! [SY644: $i] :
( ! [SY645: $i] :
( ( SY644
!= ( apply @ SV110 @ SY645 ) )
| ~ ( in @ SY645 @ ( relation_dom @ SV110 ) ) )
| ( in @ SY644 @ ( relation_rng @ SV110 ) ) ) ) ) )
| ~ ! [SY646: $i] :
( ~ ( function @ SY646 )
| ~ ( relation @ SY646 )
| ( SY646
!= ( function_inverse @ SV110 ) )
| ( ( relation_dom @ SY646 )
= ( relation_rng @ SV110 ) ) ) ) )
= $true )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2280]) ).
thf(2411,plain,
! [SV413: $i,SV383: $i] :
( ( ( proper_subset @ SV383 @ SV413 )
= $false )
| ( ( ( SV383 != SV413 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2281]) ).
thf(2412,plain,
! [SV414: $i,SV384: $i] :
( ( ( proper_subset @ SV384 @ SV414 )
= $false )
| ( ( subset @ SV384 @ SV414 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2282]) ).
thf(2413,plain,
! [SV234: $i,SV295: $i] :
( ( ( in @ ( sK18_C @ SV295 @ SV234 ) @ SV295 )
= $false )
| ( ( subset @ SV234 @ SV295 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2284]) ).
thf(2414,plain,
! [SV296: $i,SV235: $i,SV415: $i] :
( ( ( in @ SV415 @ SV235 )
= $false )
| ( ( in @ SV415 @ SV296 )
= $true )
| ( ( subset @ SV235 @ SV296 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2285]) ).
thf(2415,plain,
! [SV237: $i,SV298: $i,SV385: $i] :
( ( ( in @ SV385 @ SV298 )
= $false )
| ( ( in @ SV385 @ SV237 )
= $false )
| ( ( ~ ( disjoint @ SV237 @ SV298 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2288]) ).
thf(2416,plain,
! [SV386: $i,SV179: $i,SV335: $i,SV111: $i] :
( ( ( in @ SV111 @ SV335 )
= $false )
| ( ( ~ ( in @ SV179 @ SV386 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SV335 @ SV386 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2289]) ).
thf(2417,plain,
! [SV439: $i,SV179: $i,SV111: $i] :
( ( ( ! [SY1007: $i] :
~ ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SV439 @ SY1007 ) ) )
= $true )
| ( ( in @ SV111 @ SV439 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2290]) ).
thf(2418,plain,
! [SV457: $i,SV440: $i,SV179: $i,SV111: $i] :
( ( ~ ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SV440 @ SV457 ) )
| ( in @ SV179 @ SV457 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2291]) ).
thf(2419,plain,
! [SV113: $i] :
( ( ( ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ ( relation_dom @ SV113 ) )
| ! [SY660: $i] :
( ( SY660
!= ( apply @ SV113 @ SY659 ) )
| ( in @ ( ordered_pair @ SY659 @ SY660 ) @ SV113 ) ) ) )
= $false )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2294]) ).
thf(2420,plain,
! [SV113: $i] :
( ( ( ~ ! [SY661: $i] :
( ~ ( in @ SY661 @ ( relation_dom @ SV113 ) )
| ! [SY662: $i] :
( ~ ( in @ ( ordered_pair @ SY661 @ SY662 ) @ SV113 )
| ( SY662
= ( apply @ SV113 @ SY661 ) ) ) ) )
= $false )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2294]) ).
thf(2421,plain,
! [SV113: $i] :
( ( ( ~ ! [SY663: $i] :
( ( in @ SY663 @ ( relation_dom @ SV113 ) )
| ! [SY664: $i] :
( ( SY664
!= ( apply @ SV113 @ SY663 ) )
| ( SY664 = empty_set ) ) ) )
= $false )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2295]) ).
thf(2422,plain,
! [SV113: $i] :
( ( ( ~ ! [SY665: $i] :
( ( in @ SY665 @ ( relation_dom @ SV113 ) )
| ! [SY666: $i] :
( ( SY666 != empty_set )
| ( SY666
= ( apply @ SV113 @ SY665 ) ) ) ) )
= $false )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2295]) ).
thf(2423,plain,
! [SV114: $i,SV301: $i,SV338: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV338 )
| ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV114 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV338 )
| ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV301 ) ) ) )
= $true )
| ( ( SV338
= ( set_union2 @ SV114 @ SV301 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2296]) ).
thf(2424,plain,
! [SV114: $i,SV301: $i,SV338: $i] :
( ( ( ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV338 )
| ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV114 )
| ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV301 ) )
= $true )
| ( ( SV338
= ( set_union2 @ SV114 @ SV301 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2297]) ).
thf(2425,plain,
! [SV302: $i,SV114: $i,SV339: $i] :
( ( ( ~ ! [SY895: $i] :
( ~ ( in @ SY895 @ SV339 )
| ( in @ SY895 @ SV114 )
| ( in @ SY895 @ SV302 ) ) )
= $false )
| ( ( SV339
= ( set_union2 @ SV114 @ SV302 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2298]) ).
thf(2426,plain,
! [SV302: $i,SV339: $i,SV114: $i] :
( ( ( ~ ~ ( ~ ! [SY896: $i] :
( ~ ( in @ SY896 @ SV114 )
| ( in @ SY896 @ SV339 ) )
| ~ ! [SY897: $i] :
( ~ ( in @ SY897 @ SV302 )
| ( in @ SY897 @ SV339 ) ) ) )
= $false )
| ( ( SV339
= ( set_union2 @ SV114 @ SV302 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2298]) ).
thf(2427,plain,
! [SV340: $i,SV303: $i,SV115: $i] :
( ( ( in @ ( ordered_pair @ SV115 @ SV303 ) @ SV340 )
= $false )
| ( ( in @ SV115 @ ( relation_field @ SV340 ) )
= $true )
| ( ( relation @ SV340 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2299]) ).
thf(2428,plain,
! [SV341: $i,SV304: $i,SV115: $i] :
( ( ( in @ ( ordered_pair @ SV115 @ SV304 ) @ SV341 )
= $false )
| ( ( in @ SV304 @ ( relation_field @ SV341 ) )
= $true )
| ( ( relation @ SV341 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2300]) ).
thf(2429,plain,
! [SV458: $i,SV389: $i] :
( ( ( subset @ SV389 @ ( singleton @ SV458 ) )
= $true )
| ( ( SV389 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2301]) ).
thf(2430,plain,
! [SV417: $i,SV390: $i] :
( ( ( SV390
= ( singleton @ SV417 ) )
= $false )
| ( ( subset @ SV390 @ ( singleton @ SV417 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2302]) ).
thf(2431,plain,
! [SV116: $i,SV306: $i,SV342: $i] :
( ( ( ~ ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV116 )
| ~ ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV306 )
| ~ ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV342 ) )
= $true )
| ( ( SV342
= ( set_intersection2 @ SV116 @ SV306 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2303]) ).
thf(2432,plain,
! [SV116: $i,SV306: $i,SV342: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV116 )
| ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV342 ) )
| ~ ( ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV306 )
| ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV342 ) ) ) )
= $true )
| ( ( SV342
= ( set_intersection2 @ SV116 @ SV306 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2304]) ).
thf(2433,plain,
! [SV343: $i,SV307: $i,SV116: $i] :
( ( ( ~ ! [SY898: $i] :
( ~ ( in @ SY898 @ SV116 )
| ~ ( in @ SY898 @ SV307 )
| ( in @ SY898 @ SV343 ) ) )
= $false )
| ( ( SV343
= ( set_intersection2 @ SV116 @ SV307 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2305]) ).
thf(2434,plain,
! [SV307: $i,SV116: $i,SV343: $i] :
( ( ( ~ ~ ( ~ ! [SY899: $i] :
( ~ ( in @ SY899 @ SV343 )
| ( in @ SY899 @ SV116 ) )
| ~ ! [SY900: $i] :
( ~ ( in @ SY900 @ SV343 )
| ( in @ SY900 @ SV307 ) ) ) )
= $false )
| ( ( SV343
= ( set_intersection2 @ SV116 @ SV307 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2305]) ).
thf(2435,plain,
! [SV249: $i] :
( ( ( one_to_one @ SV249 )
= $false )
| ( ( function @ SV249 )
= $false )
| ( ( relation @ SV249 )
= $false )
| ( ( function @ ( relation_inverse @ SV249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2306]) ).
thf(2436,plain,
! [SV250: $i] :
( ( ( one_to_one @ SV250 )
= $false )
| ( ( function @ SV250 )
= $false )
| ( ( relation @ SV250 )
= $false )
| ( ( relation @ ( relation_inverse @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2307]) ).
thf(2437,plain,
! [SV251: $i,SV308: $i] :
( ( ( ~ ( ( ( sK44_C @ SV308 @ SV251 )
!= ( sK45_SY414 @ SV308 @ SV251 ) )
| ~ ( in @ ( sK44_C @ SV308 @ SV251 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 ) ) )
= $false )
| ( ( SV308
= ( identity_relation @ SV251 ) )
= $true )
| ( ( relation @ SV308 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2308]) ).
thf(2438,plain,
! [SV251: $i,SV308: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK44_C @ SV308 @ SV251 )
= ( sK45_SY414 @ SV308 @ SV251 ) )
| ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 ) )
| ~ ( ( in @ ( sK44_C @ SV308 @ SV251 ) @ SV251 )
| ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 ) ) ) )
= $false )
| ( ( SV308
= ( identity_relation @ SV251 ) )
= $true )
| ( ( relation @ SV308 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2308]) ).
thf(2439,plain,
! [SV309: $i,SV252: $i] :
( ( ( ~ ! [SY861: $i,SY862: $i] :
( ( SY861 != SY862 )
| ~ ( in @ SY861 @ SV252 )
| ( in @ ( ordered_pair @ SY861 @ SY862 ) @ SV309 ) )
| ~ ~ ( ~ ! [SY863: $i,SY864: $i] :
( ~ ( in @ ( ordered_pair @ SY863 @ SY864 ) @ SV309 )
| ( SY863 = SY864 ) )
| ~ ! [SY865: $i] :
( ! [SY866: $i] :
~ ( in @ ( ordered_pair @ SY865 @ SY866 ) @ SV309 )
| ( in @ SY865 @ SV252 ) ) ) )
= $false )
| ( ( SV309
= ( identity_relation @ SV252 ) )
= $false )
| ( ( relation @ SV309 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2309]) ).
thf(2440,plain,
! [SV344: $i,SV310: $i,SV117: $i] :
( ( ( ~ ( in @ SV117 @ SV310 ) )
= $true )
| ( ( ~ ( in @ SV117 @ ( relation_dom @ SV344 ) ) )
= $true )
| ( ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SV344 @ SV310 ) ) )
= $true )
| ( ( relation @ SV344 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2310]) ).
thf(2441,plain,
! [SV418: $i,SV117: $i,SV441: $i] :
( ( ( ~ ( relation @ SV441 ) )
= $true )
| ( ( ~ ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SV441 @ SV418 ) ) )
| ( in @ SV117 @ SV418 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2311]) ).
thf(2442,plain,
! [SV419: $i,SV117: $i,SV442: $i] :
( ( ( ~ ( relation @ SV442 ) )
= $true )
| ( ( ~ ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SV442 @ SV419 ) ) )
| ( in @ SV117 @ ( relation_dom @ SV442 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2312]) ).
thf(2443,plain,
! [SV253: $i,SV311: $i] :
( ( ( ~ ( ~ ( in @ ( sK50_C @ SV311 @ SV253 ) @ SV253 )
| ~ ( ( ( apply @ SV311 @ ( sK50_C @ SV311 @ SV253 ) )
!= ( sK50_C @ SV311 @ SV253 ) ) ) )
| ( ( relation_dom @ SV311 )
!= SV253 ) )
= $true )
| ( ( SV311
= ( identity_relation @ SV253 ) )
= $true )
| ( ( function @ SV311 )
= $false )
| ( ( relation @ SV311 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2313]) ).
thf(2444,plain,
! [SV391: $i,SV420: $i] :
( ( ( ~ ( function @ SV420 ) )
= $true )
| ( ( ~ ( relation @ SV420 ) )
= $true )
| ( ( ( SV420
!= ( identity_relation @ SV391 ) )
| ! [SY997: $i] :
( ~ ( in @ SY997 @ SV391 )
| ( ( apply @ SV420 @ SY997 )
= SY997 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2314]) ).
thf(2445,plain,
! [SV392: $i,SV421: $i] :
( ( ( ~ ( function @ SV421 ) )
= $true )
| ( ( ~ ( relation @ SV421 ) )
= $true )
| ( ( ( SV421
!= ( identity_relation @ SV392 ) )
| ( ( relation_dom @ SV421 )
= SV392 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2315]) ).
thf(2446,plain,
! [SV345: $i,SV312: $i,SV118: $i] :
( ( ( ! [SY901: $i,SY902: $i] :
( ~ ( in @ SY901 @ SV118 )
| ~ ( in @ SY902 @ SV312 )
| ( ( sK23_D @ SV345 @ SV312 @ SV118 )
!= ( ordered_pair @ SY901 @ SY902 ) ) )
| ~ ( in @ ( sK23_D @ SV345 @ SV312 @ SV118 ) @ SV345 ) )
= $true )
| ( ( SV345
= ( cartesian_product2 @ SV118 @ SV312 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2316]) ).
thf(2447,plain,
! [SV118: $i,SV312: $i,SV345: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY403 @ SV345 @ SV312 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK25_SY405 @ SV345 @ SV312 @ SV118 ) @ SV312 ) )
| ( ( sK23_D @ SV345 @ SV312 @ SV118 )
!= ( ordered_pair @ ( sK24_SY403 @ SV345 @ SV312 @ SV118 ) @ ( sK25_SY405 @ SV345 @ SV312 @ SV118 ) ) ) )
| ( in @ ( sK23_D @ SV345 @ SV312 @ SV118 ) @ SV345 ) )
= $true )
| ( ( SV345
= ( cartesian_product2 @ SV118 @ SV312 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2317]) ).
thf(2448,plain,
! [SV346: $i,SV313: $i,SV118: $i] :
( ( ( ~ ! [SY903: $i] :
( ! [SY873: $i,SY874: $i] :
( ~ ( in @ SY873 @ SV118 )
| ~ ( in @ SY874 @ SV313 )
| ( SY903
!= ( ordered_pair @ SY873 @ SY874 ) ) )
| ( in @ SY903 @ SV346 ) ) )
= $false )
| ( ( SV346
= ( cartesian_product2 @ SV118 @ SV313 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2318]) ).
thf(2449,plain,
! [SV118: $i,SV313: $i,SV346: $i] :
( ( ( ~ ! [SY906: $i] :
( ~ ( in @ SY906 @ SV346 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY906 @ SV346 @ SV313 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK22_SY400 @ SY906 @ SV346 @ SV313 @ SV118 ) @ SV313 ) )
| ( SY906
!= ( ordered_pair @ ( sK21_E @ SY906 @ SV346 @ SV313 @ SV118 ) @ ( sK22_SY400 @ SY906 @ SV346 @ SV313 @ SV118 ) ) ) ) ) )
= $false )
| ( ( SV346
= ( cartesian_product2 @ SV118 @ SV313 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2318]) ).
thf(2450,plain,
! [SV254: $i,SV316: $i] :
( ( ( ! [SY878: $i] :
( ~ ( in @ ( sK15_C @ SV316 @ SV254 ) @ SY878 )
| ~ ( in @ SY878 @ SV254 ) ) )
= $true )
| ( ( ~ ( in @ ( sK15_C @ SV316 @ SV254 ) @ SV316 ) )
= $true )
| ( ( SV316
= ( union @ SV254 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2319]) ).
thf(2451,plain,
! [SV254: $i,SV316: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_C @ SV316 @ SV254 ) @ ( sK16_SY398 @ SV316 @ SV254 ) )
| ~ ( in @ ( sK16_SY398 @ SV316 @ SV254 ) @ SV254 ) ) )
= $true )
| ( ( in @ ( sK15_C @ SV316 @ SV254 ) @ SV316 )
= $true )
| ( ( SV316
= ( union @ SV254 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2320]) ).
thf(2452,plain,
! [SV317: $i,SV255: $i] :
( ( ( ! [SY879: $i] :
( ! [SY817: $i] :
( ~ ( in @ SY879 @ SY817 )
| ~ ( in @ SY817 @ SV255 ) )
| ( in @ SY879 @ SV317 ) ) )
= $true )
| ( ( SV317
= ( union @ SV255 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2321]) ).
thf(2453,plain,
! [SV255: $i,SV317: $i] :
( ( ( ! [SY881: $i] :
( ~ ( in @ SY881 @ SV317 )
| ~ ( ~ ( in @ SY881 @ ( sK14_D @ SY881 @ SV317 @ SV255 ) )
| ~ ( in @ ( sK14_D @ SY881 @ SV317 @ SV255 ) @ SV255 ) ) ) )
= $true )
| ( ( SV317
= ( union @ SV255 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2322]) ).
thf(2454,plain,
! [SV120: $i,SV393: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV393 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV120 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV393 ) ) ) )
= $true )
| ( ( SV120 = SV393 )
= $true )
| ( ( relation @ SV393 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2323]) ).
thf(2455,plain,
! [SV394: $i,SV120: $i] :
( ( ( ( SV120 != SV394 ) )
= $true )
| ( ( ~ ( ~ ! [SY964: $i,SY965: $i] :
( ~ ( in @ ( ordered_pair @ SY964 @ SY965 ) @ SV120 )
| ( in @ ( ordered_pair @ SY964 @ SY965 ) @ SV394 ) )
| ~ ! [SY966: $i,SY967: $i] :
( ~ ( in @ ( ordered_pair @ SY966 @ SY967 ) @ SV394 )
| ( in @ ( ordered_pair @ SY966 @ SY967 ) @ SV120 ) ) ) )
= $true )
| ( ( relation @ SV394 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2324]) ).
thf(2456,plain,
! [SV145: $i,SV43: $i,SV347: $i] :
( ( ( relation @ SV347 )
= $false )
| ( ( function @ SV347 )
= $false )
| ( ( ~ ( in @ SV43 @ ( relation_dom @ ( relation_composition @ SV347 @ SV145 ) ) )
| ( ( apply @ ( relation_composition @ SV347 @ SV145 ) @ SV43 )
= ( apply @ SV145 @ ( apply @ SV347 @ SV43 ) ) ) )
= $true )
| ( ( function @ SV145 )
= $false )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2325]) ).
thf(2457,plain,
! [SV146: $i,SV44: $i,SV348: $i] :
( ( ( relation @ SV348 )
= $false )
| ( ( function @ SV348 )
= $false )
| ( ( ~ ( in @ SV44 @ ( relation_dom @ SV146 ) )
| ( ( apply @ ( relation_composition @ SV146 @ SV348 ) @ SV44 )
= ( apply @ SV348 @ ( apply @ SV146 @ SV44 ) ) ) )
= $true )
| ( ( function @ SV146 )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2326]) ).
thf(2458,plain,
! [SV351: $i,SV424: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK33_SY406 @ SV424 @ SV351 ) @ SV351 )
| ~ ~ ( in @ ( sK32_C @ SV424 @ SV351 ) @ ( sK33_SY406 @ SV424 @ SV351 ) ) )
| ~ ( in @ ( sK32_C @ SV424 @ SV351 ) @ SV424 ) )
| ~ ( ! [SY998: $i] :
( ~ ( in @ SY998 @ SV351 )
| ( in @ ( sK32_C @ SV424 @ SV351 ) @ SY998 ) )
| ( in @ ( sK32_C @ SV424 @ SV351 ) @ SV424 ) ) )
= $false )
| ( ( SV424
= ( set_meet @ SV351 ) )
= $true )
| ( ( SV351 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2329]) ).
thf(2459,plain,
! [SV352: $i,SV425: $i] :
( ( ( SV425
= ( set_meet @ SV352 ) )
= $false )
| ( ( ~ ( ~ ! [SY999: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY999 @ SV425 @ SV352 ) @ SV352 )
| ~ ~ ( in @ SY999 @ ( sK31_D @ SY999 @ SV425 @ SV352 ) ) )
| ( in @ SY999 @ SV425 ) )
| ~ ! [SY1000: $i] :
( ~ ( in @ SY1000 @ SV425 )
| ! [SY914: $i] :
( ~ ( in @ SY914 @ SV352 )
| ( in @ SY1000 @ SY914 ) ) ) ) )
= $true )
| ( ( SV352 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2330]) ).
thf(2460,plain,
! [SV353: $i,SV444: $i] :
( ( ( ( SV444
!= ( set_meet @ SV353 ) ) )
= $true )
| ( ( SV444 = empty_set )
= $true )
| ( ( SV353 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2331]) ).
thf(2461,plain,
! [SV354: $i,SV445: $i] :
( ( ( ( SV445 != empty_set ) )
= $true )
| ( ( SV445
= ( set_meet @ SV354 ) )
= $true )
| ( ( SV354 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2332]) ).
thf(2462,plain,
! [SV265: $i,SV202: $i] :
( ( ( relation @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( ~ ( relation @ SV265 ) )
= $true )
| ( ( ~ ( function @ SV265 ) )
= $true )
| ( ( function @ ( relation_composition @ SV202 @ SV265 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2333]) ).
thf(2463,plain,
! [SV266: $i,SV203: $i] :
( ( ( relation @ SV203 )
= $false )
| ( ( function @ SV203 )
= $false )
| ( ( ~ ( relation @ SV266 ) )
= $true )
| ( ( ~ ( function @ SV266 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV203 @ SV266 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2334]) ).
thf(2464,plain,
! [SV271: $i,SV87: $i,SV320: $i,SV446: $i] :
( ( ( ~ ( in @ SV446 @ ( relation_dom @ SV320 ) )
| ~ ( in @ ( ordered_pair @ SV446 @ SV87 ) @ SV320 ) )
= $true )
| ( ( ~ ( in @ SV446 @ SV271 ) )
= $true )
| ( ( in @ SV87 @ ( relation_image @ SV320 @ SV271 ) )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2335]) ).
thf(2465,plain,
! [SV87: $i,SV272: $i,SV321: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK52_D @ SV321 @ SV272 @ SV87 ) @ ( relation_dom @ SV321 ) )
| ~ ( in @ ( ordered_pair @ ( sK52_D @ SV321 @ SV272 @ SV87 ) @ SV87 ) @ SV321 ) )
| ~ ( in @ ( sK52_D @ SV321 @ SV272 @ SV87 ) @ SV272 ) )
= $false )
| ( ( in @ SV87 @ ( relation_image @ SV321 @ SV272 ) )
= $false )
| ( ( relation @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2336]) ).
thf(2466,plain,
! [SV88: $i,SV274: $i,SV322: $i] :
( ( ( ~ ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV88 )
| ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV274 ) )
= $true )
| ( ( ~ ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV322 ) )
= $true )
| ( ( SV322
= ( set_difference @ SV88 @ SV274 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2339]) ).
thf(2467,plain,
! [SV88: $i,SV274: $i,SV322: $i] :
( ( ( ~ ( ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV88 )
| ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV322 ) )
| ~ ( ~ ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV274 )
| ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV322 ) ) )
= $false )
| ( ( SV322
= ( set_difference @ SV88 @ SV274 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2340]) ).
thf(2468,plain,
! [SV323: $i,SV275: $i,SV88: $i] :
( ( ( ! [SY883: $i] :
( ~ ( in @ SY883 @ SV88 )
| ( in @ SY883 @ SV275 )
| ( in @ SY883 @ SV323 ) ) )
= $true )
| ( ( SV323
= ( set_difference @ SV88 @ SV275 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2341]) ).
thf(2469,plain,
! [SV275: $i,SV88: $i,SV323: $i] :
( ( ( ~ ( ~ ! [SY884: $i] :
( ~ ( in @ SY884 @ SV323 )
| ( in @ SY884 @ SV88 ) )
| ~ ! [SY885: $i] :
( ~ ( in @ SY885 @ SV323 )
| ~ ( in @ SY885 @ SV275 ) ) ) )
= $true )
| ( ( SV323
= ( set_difference @ SV88 @ SV275 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2342]) ).
thf(2470,plain,
! [SV358: $i,SV426: $i] :
( ( ( element @ SV426 @ SV358 )
= $false )
| ( ( in @ SV426 @ SV358 )
= $true )
| ( ( empty @ SV358 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2343]) ).
thf(2471,plain,
! [SV359: $i,SV427: $i] :
( ( ( in @ SV427 @ SV359 )
= $false )
| ( ( element @ SV427 @ SV359 )
= $true )
| ( ( empty @ SV359 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2344]) ).
thf(2472,plain,
! [SV360: $i,SV447: $i] :
( ( ( ~ ( element @ SV447 @ SV360 ) )
= $true )
| ( ( empty @ SV447 )
= $true )
| ( ( empty @ SV360 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2345]) ).
thf(2473,plain,
! [SV361: $i,SV448: $i] :
( ( ( ~ ( empty @ SV448 ) )
= $true )
| ( ( element @ SV448 @ SV361 )
= $true )
| ( ( empty @ SV361 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2346]) ).
thf(2474,plain,
! [SV89: $i,SV174: $i,SV398: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV174 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 ) )
| ~ ~ ( ~ ( ( in @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) @ SV89 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV174 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 ) ) ) ) )
= $true )
| ( ( SV398
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2347]) ).
thf(2475,plain,
! [SV174: $i,SV89: $i,SV399: $i] :
( ( ( ( SV399
!= ( relation_rng_restriction @ SV89 @ SV174 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY968: $i,SY969: $i] :
( ~ ( in @ SY969 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY968 @ SY969 ) @ SV174 )
| ( in @ ( ordered_pair @ SY968 @ SY969 ) @ SV399 ) )
| ~ ~ ( ~ ! [SY970: $i,SY971: $i] :
( ~ ( in @ ( ordered_pair @ SY970 @ SY971 ) @ SV399 )
| ( in @ SY971 @ SV89 ) )
| ~ ! [SY972: $i,SY973: $i] :
( ~ ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV399 )
| ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV174 ) ) ) ) )
= $true )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2348]) ).
thf(2476,plain,
! [SV90: $i,SV276: $i,SV324: $i] :
( ( ( ~ ( ~ ( in @ ( sK27_D @ SV324 @ SV276 @ SV90 ) @ SV324 )
| ( ( sK27_D @ SV324 @ SV276 @ SV90 )
!= SV90 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV324 @ SV276 @ SV90 ) @ SV324 )
| ( ( sK27_D @ SV324 @ SV276 @ SV90 )
!= SV276 ) ) )
= $false )
| ( ( SV324
= ( unordered_pair @ SV90 @ SV276 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2349]) ).
thf(2477,plain,
! [SV90: $i,SV276: $i,SV324: $i] :
( ( ( in @ ( sK27_D @ SV324 @ SV276 @ SV90 ) @ SV324 )
= $true )
| ( ( ( ( sK27_D @ SV324 @ SV276 @ SV90 )
= SV90 )
| ( ( sK27_D @ SV324 @ SV276 @ SV90 )
= SV276 ) )
= $true )
| ( ( SV324
= ( unordered_pair @ SV90 @ SV276 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2350]) ).
thf(2478,plain,
! [SV277: $i,SV90: $i,SV325: $i] :
( ( ( ! [SY886: $i] :
( ~ ( in @ SY886 @ SV325 )
| ( SY886 = SV90 )
| ( SY886 = SV277 ) ) )
= $true )
| ( ( SV325
= ( unordered_pair @ SV90 @ SV277 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2351]) ).
thf(2479,plain,
! [SV277: $i,SV325: $i,SV90: $i] :
( ( ( ~ ( ~ ! [SY887: $i] :
( ( SY887 != SV90 )
| ( in @ SY887 @ SV325 ) )
| ~ ! [SY888: $i] :
( ( SY888 != SV277 )
| ( in @ SY888 @ SV325 ) ) ) )
= $true )
| ( ( SV325
= ( unordered_pair @ SV90 @ SV277 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2352]) ).
thf(2480,plain,
! [SV209: $i,SV278: $i] :
( ( ( in @ ( sK28_C @ SV278 @ SV209 ) @ SV278 )
= $false )
| ( ( ~ ( subset @ ( sK28_C @ SV278 @ SV209 ) @ SV209 ) )
= $true )
| ( ( SV278
= ( powerset @ SV209 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2353]) ).
thf(2481,plain,
! [SV210: $i,SV279: $i,SV459: $i] :
( ( ( ~ ( in @ SV459 @ SV279 )
| ( subset @ SV459 @ SV210 ) )
= $true )
| ( ( SV279
= ( powerset @ SV210 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2355]) ).
thf(2482,plain,
! [SV279: $i,SV210: $i,SV460: $i] :
( ( ( ~ ( subset @ SV460 @ SV210 )
| ( in @ SV460 @ SV279 ) )
= $true )
| ( ( SV279
= ( powerset @ SV210 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2356]) ).
thf(2483,plain,
! [SV91: $i,SV362: $i] :
( ( ( ! [SY923: $i] :
~ ( in @ ( ordered_pair @ ( sK63_C @ SV362 @ SV91 ) @ SY923 ) @ SV91 )
| ~ ( in @ ( sK63_C @ SV362 @ SV91 ) @ SV362 ) )
= $true )
| ( ( SV362
= ( relation_dom @ SV91 ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2357]) ).
thf(2484,plain,
! [SV91: $i,SV362: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK63_C @ SV362 @ SV91 ) @ ( sK64_SY419 @ SV362 @ SV91 ) ) @ SV91 )
| ( in @ ( sK63_C @ SV362 @ SV91 ) @ SV362 ) )
= $true )
| ( ( SV362
= ( relation_dom @ SV91 ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2358]) ).
thf(2485,plain,
! [SV363: $i,SV91: $i] :
( ( ( ~ ! [SY924: $i] :
( ! [SY530: $i] :
~ ( in @ ( ordered_pair @ SY924 @ SY530 ) @ SV91 )
| ( in @ SY924 @ SV363 ) ) )
= $false )
| ( ( SV363
= ( relation_dom @ SV91 ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2359]) ).
thf(2486,plain,
! [SV91: $i,SV363: $i] :
( ( ( ~ ! [SY926: $i] :
( ~ ( in @ SY926 @ SV363 )
| ( in @ ( ordered_pair @ SY926 @ ( sK62_D @ SY926 @ SV363 @ SV91 ) ) @ SV91 ) ) )
= $false )
| ( ( SV363
= ( relation_dom @ SV91 ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2359]) ).
thf(2487,plain,
! [SV92: $i,SV364: $i,SV400: $i] :
( ( ( ~ ( ! [SY974: $i] :
( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SY974 ) @ SV92 )
| ~ ( in @ SY974 @ SV364 ) )
| ~ ( in @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SV400 ) ) )
= $false )
| ( ( SV400
= ( relation_inverse_image @ SV92 @ SV364 ) )
= $true )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2360]) ).
thf(2488,plain,
! [SV92: $i,SV364: $i,SV400: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ ( sK36_SY409 @ SV400 @ SV364 @ SV92 ) ) @ SV92 )
| ~ ( in @ ( sK36_SY409 @ SV400 @ SV364 @ SV92 ) @ SV364 ) )
| ( in @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SV400 ) ) )
= $false )
| ( ( SV400
= ( relation_inverse_image @ SV92 @ SV364 ) )
= $true )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2360]) ).
thf(2489,plain,
! [SV401: $i,SV365: $i,SV92: $i] :
( ( ( ~ ! [SY975: $i] :
( ! [SY931: $i] :
( ~ ( in @ ( ordered_pair @ SY975 @ SY931 ) @ SV92 )
| ~ ( in @ SY931 @ SV365 ) )
| ( in @ SY975 @ SV401 ) )
| ~ ! [SY977: $i] :
( ~ ( in @ SY977 @ SV401 )
| ~ ( ~ ( in @ ( ordered_pair @ SY977 @ ( sK34_E @ SY977 @ SV401 @ SV365 @ SV92 ) ) @ SV92 )
| ~ ( in @ ( sK34_E @ SY977 @ SV401 @ SV365 @ SV92 ) @ SV365 ) ) ) )
= $false )
| ( ( SV401
= ( relation_inverse_image @ SV92 @ SV365 ) )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2361]) ).
thf(2490,plain,
! [SV93: $i,SV366: $i,SV402: $i] :
( ( ( ~ ( ! [SY978: $i] :
( ~ ( in @ ( ordered_pair @ SY978 @ ( sK38_D @ SV402 @ SV366 @ SV93 ) ) @ SV93 )
| ~ ( in @ SY978 @ SV366 ) )
| ~ ( in @ ( sK38_D @ SV402 @ SV366 @ SV93 ) @ SV402 ) ) )
= $false )
| ( ( SV402
= ( relation_image @ SV93 @ SV366 ) )
= $true )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2362]) ).
thf(2491,plain,
! [SV93: $i,SV366: $i,SV402: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SV402 @ SV366 @ SV93 ) @ ( sK38_D @ SV402 @ SV366 @ SV93 ) ) @ SV93 )
| ~ ( in @ ( sK39_SY411 @ SV402 @ SV366 @ SV93 ) @ SV366 ) )
| ( in @ ( sK38_D @ SV402 @ SV366 @ SV93 ) @ SV402 ) ) )
= $false )
| ( ( SV402
= ( relation_image @ SV93 @ SV366 ) )
= $true )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2362]) ).
thf(2492,plain,
! [SV403: $i,SV367: $i,SV93: $i] :
( ( ( ~ ! [SY979: $i] :
( ! [SY937: $i] :
( ~ ( in @ ( ordered_pair @ SY937 @ SY979 ) @ SV93 )
| ~ ( in @ SY937 @ SV367 ) )
| ( in @ SY979 @ SV403 ) )
| ~ ! [SY981: $i] :
( ~ ( in @ SY981 @ SV403 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SY981 @ SV403 @ SV367 @ SV93 ) @ SY981 ) @ SV93 )
| ~ ( in @ ( sK37_E @ SY981 @ SV403 @ SV367 @ SV93 ) @ SV367 ) ) ) )
= $false )
| ( ( SV403
= ( relation_image @ SV93 @ SV367 ) )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2363]) ).
thf(2493,plain,
! [SV282: $i,SV94: $i,SV326: $i,SV449: $i] :
( ( ( ~ ( in @ SV449 @ ( relation_rng @ SV326 ) )
| ~ ( in @ ( ordered_pair @ SV94 @ SV449 ) @ SV326 ) )
= $true )
| ( ( ~ ( in @ SV449 @ SV282 ) )
= $true )
| ( ( in @ SV94 @ ( relation_inverse_image @ SV326 @ SV282 ) )
= $true )
| ( ( relation @ SV326 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2364]) ).
thf(2494,plain,
! [SV94: $i,SV283: $i,SV327: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK51_D @ SV327 @ SV283 @ SV94 ) @ ( relation_rng @ SV327 ) )
| ~ ( in @ ( ordered_pair @ SV94 @ ( sK51_D @ SV327 @ SV283 @ SV94 ) ) @ SV327 ) )
| ~ ( in @ ( sK51_D @ SV327 @ SV283 @ SV94 ) @ SV283 ) )
= $false )
| ( ( in @ SV94 @ ( relation_inverse_image @ SV327 @ SV283 ) )
= $false )
| ( ( relation @ SV327 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2365]) ).
thf(2495,plain,
! [SV175: $i,SV95: $i,SV450: $i] :
( ( ( ~ ( function @ SV450 )
| ~ ( relation @ SV450 ) )
= $true )
| ( ( ~ ( in @ SV95 @ ( relation_dom @ SV450 ) )
| ~ ( in @ ( apply @ SV450 @ SV95 ) @ ( relation_dom @ SV175 ) )
| ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SV450 @ SV175 ) ) ) )
= $true )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2366]) ).
thf(2496,plain,
! [SV175: $i,SV95: $i] :
( ( ( ~ ! [SY732: $i] :
( ~ ( function @ SY732 )
| ~ ( relation @ SY732 )
| ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY732 @ SV175 ) ) )
| ( in @ SV95 @ ( relation_dom @ SY732 ) ) ) )
= $false )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2367]) ).
thf(2497,plain,
! [SV175: $i,SV95: $i] :
( ( ( ~ ! [SY733: $i] :
( ~ ( function @ SY733 )
| ~ ( relation @ SY733 )
| ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY733 @ SV175 ) ) )
| ( in @ ( apply @ SY733 @ SV95 ) @ ( relation_dom @ SV175 ) ) ) )
= $false )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2367]) ).
thf(2498,plain,
! [SV96: $i,SV368: $i,SV404: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ SV368 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 ) )
| ~ ~ ( ~ ( ( in @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ SV368 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 ) ) ) ) )
= $true )
| ( ( SV404
= ( relation_dom_restriction @ SV96 @ SV368 ) )
= $true )
| ( ( relation @ SV404 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2368]) ).
thf(2499,plain,
! [SV369: $i,SV96: $i,SV405: $i] :
( ( ( ( SV405
!= ( relation_dom_restriction @ SV96 @ SV369 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY982: $i,SY983: $i] :
( ~ ( in @ SY982 @ SV369 )
| ~ ( in @ ( ordered_pair @ SY982 @ SY983 ) @ SV96 )
| ( in @ ( ordered_pair @ SY982 @ SY983 ) @ SV405 ) )
| ~ ~ ( ~ ! [SY984: $i] :
( ! [SY985: $i] :
~ ( in @ ( ordered_pair @ SY984 @ SY985 ) @ SV405 )
| ( in @ SY984 @ SV369 ) )
| ~ ! [SY986: $i,SY987: $i] :
( ~ ( in @ ( ordered_pair @ SY986 @ SY987 ) @ SV405 )
| ( in @ ( ordered_pair @ SY986 @ SY987 ) @ SV96 ) ) ) ) )
= $true )
| ( ( relation @ SV405 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2369]) ).
thf(2500,plain,
! [SV97: $i,SV370: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SV370 @ SV97 ) @ ( sK12_SY396 @ SV370 @ SV97 ) ) @ SV370 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SV370 @ SV97 ) @ ( sK11_C @ SV370 @ SV97 ) ) @ SV97 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_C @ SV370 @ SV97 ) @ ( sK12_SY396 @ SV370 @ SV97 ) ) @ SV370 )
| ( in @ ( ordered_pair @ ( sK12_SY396 @ SV370 @ SV97 ) @ ( sK11_C @ SV370 @ SV97 ) ) @ SV97 ) ) )
= $false )
| ( ( SV370
= ( relation_inverse @ SV97 ) )
= $true )
| ( ( relation @ SV370 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2370]) ).
thf(2501,plain,
! [SV97: $i,SV371: $i] :
( ( ( SV371
= ( relation_inverse @ SV97 ) )
= $false )
| ( ( ~ ( ~ ! [SY947: $i,SY948: $i] :
( ~ ( in @ ( ordered_pair @ SY947 @ SY948 ) @ SV371 )
| ( in @ ( ordered_pair @ SY948 @ SY947 ) @ SV97 ) )
| ~ ! [SY949: $i,SY950: $i] :
( ~ ( in @ ( ordered_pair @ SY950 @ SY949 ) @ SV97 )
| ( in @ ( ordered_pair @ SY949 @ SY950 ) @ SV371 ) ) ) )
= $true )
| ( ( relation @ SV371 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2371]) ).
thf(2502,plain,
! [SV98: $i,SV372: $i] :
( ( ( ! [SY951: $i] :
~ ( in @ ( ordered_pair @ SY951 @ ( sK60_C @ SV372 @ SV98 ) ) @ SV98 )
| ~ ( in @ ( sK60_C @ SV372 @ SV98 ) @ SV372 ) )
= $true )
| ( ( SV372
= ( relation_rng @ SV98 ) )
= $true )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2372]) ).
thf(2503,plain,
! [SV98: $i,SV372: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK61_SY417 @ SV372 @ SV98 ) @ ( sK60_C @ SV372 @ SV98 ) ) @ SV98 )
| ( in @ ( sK60_C @ SV372 @ SV98 ) @ SV372 ) )
= $true )
| ( ( SV372
= ( relation_rng @ SV98 ) )
= $true )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2373]) ).
thf(2504,plain,
! [SV373: $i,SV98: $i] :
( ( ( ~ ! [SY952: $i] :
( ! [SY577: $i] :
~ ( in @ ( ordered_pair @ SY577 @ SY952 ) @ SV98 )
| ( in @ SY952 @ SV373 ) ) )
= $false )
| ( ( SV373
= ( relation_rng @ SV98 ) )
= $false )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2374]) ).
thf(2505,plain,
! [SV98: $i,SV373: $i] :
( ( ( ~ ! [SY954: $i] :
( ~ ( in @ SY954 @ SV373 )
| ( in @ ( ordered_pair @ ( sK59_D @ SY954 @ SV373 @ SV98 ) @ SY954 ) @ SV98 ) ) )
= $false )
| ( ( SV373
= ( relation_rng @ SV98 ) )
= $false )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2374]) ).
thf(2506,plain,
! [SV100: $i,SV328: $i,SV286: $i] :
( ( ( ( SV286
!= ( apply @ SV328 @ SV100 ) )
| ~ ( in @ SV100 @ ( relation_dom @ SV328 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV100 @ SV286 ) @ SV328 )
= $true )
| ( ( function @ SV328 )
= $false )
| ( ( relation @ SV328 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2375]) ).
thf(2507,plain,
! [SV406: $i,SV100: $i,SV428: $i] :
( ( ( ~ ( function @ SV428 ) )
= $true )
| ( ( ~ ( relation @ SV428 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV100 @ SV406 ) @ SV428 )
| ( SV406
= ( apply @ SV428 @ SV100 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2376]) ).
thf(2508,plain,
! [SV407: $i,SV100: $i,SV429: $i] :
( ( ( ~ ( function @ SV429 ) )
= $true )
| ( ( ~ ( relation @ SV429 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV100 @ SV407 ) @ SV429 )
| ( in @ SV100 @ ( relation_dom @ SV429 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2377]) ).
thf(2509,plain,
! [SV101: $i,SV215: $i,SV451: $i] :
( ( ( ~ ( relation @ SV451 ) )
= $true )
| ( ( ~ ( ~ ( ! [SY1009: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ SY1009 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY1009 @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV215 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV451 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK10_SY395 @ SV451 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV215 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV451 ) ) )
| ( SV451
= ( relation_composition @ SV101 @ SV215 ) ) )
= $true )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2378]) ).
thf(2510,plain,
! [SV215: $i,SV101: $i,SV452: $i] :
( ( ( ~ ( relation @ SV452 ) )
= $true )
| ( ( ( SV452
!= ( relation_composition @ SV101 @ SV215 ) )
| ~ ( ~ ! [SY1010: $i,SY1011: $i] :
( ! [SY783: $i] :
( ~ ( in @ ( ordered_pair @ SY1010 @ SY783 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY783 @ SY1011 ) @ SV215 ) )
| ( in @ ( ordered_pair @ SY1010 @ SY1011 ) @ SV452 ) )
| ~ ! [SY1013: $i,SY1014: $i] :
( ~ ( in @ ( ordered_pair @ SY1013 @ SY1014 ) @ SV452 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1013 @ ( sK7_F @ SY1014 @ SY1013 @ SV452 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY1014 @ SY1013 @ SV452 @ SV215 @ SV101 ) @ SY1014 ) @ SV215 ) ) ) ) )
= $true )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2379]) ).
thf(2511,plain,
! [SV329: $i,SV102: $i,SV374: $i,SV177: $i] :
( ( ( in @ SV177 @ SV374 )
= $false )
| ( ( in @ SV102 @ SV329 )
= $false )
| ( ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SV329 @ SV374 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2380]) ).
thf(2512,plain,
! [SV461: $i,SV430: $i,SV177: $i,SV102: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SV430 @ SV461 ) ) )
= $true )
| ( ( in @ SV102 @ SV430 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2381]) ).
thf(2513,plain,
! [SV453: $i,SV431: $i,SV177: $i,SV102: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SV431 @ SV453 ) ) )
= $true )
| ( ( in @ SV177 @ SV453 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2382]) ).
thf(2514,plain,
! [SV103: $i,SV408: $i] :
( ( ( ~ ! [SY990: $i] :
( ~ ( subset @ SY990 @ SV408 )
| ( in @ SY990 @ ( sK3_SY386 @ SV408 @ SV103 ) ) ) )
= $false )
| ( ( ~ ( in @ SV408 @ ( sK2_B @ SV103 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2383]) ).
thf(2515,plain,
! [SV103: $i,SV408: $i] :
( ( ( ~ ( in @ ( sK3_SY386 @ SV408 @ SV103 ) @ ( sK2_B @ SV103 ) ) )
= $false )
| ( ( ~ ( in @ SV408 @ ( sK2_B @ SV103 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2383]) ).
thf(2516,plain,
! [SV103: $i,SV462: $i] :
( ( ! [SY1015: $i] :
( ~ ( in @ SV462 @ ( sK2_B @ SV103 ) )
| ~ ( subset @ SY1015 @ SV462 )
| ( in @ SY1015 @ ( sK2_B @ SV103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2384]) ).
thf(2517,plain,
! [SV454: $i,SV432: $i,SV222: $i] :
( ( ( ( sK69_B @ SV222 )
= ( ordered_pair @ SV432 @ SV454 ) )
= $false )
| ( ( relation @ SV222 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2386]) ).
thf(2518,plain,
! [SV376: $i,SV104: $i] :
( ( ( subset @ SV104 @ SV376 )
= $false )
| ( ( subset @ ( relation_dom @ SV104 ) @ ( relation_dom @ SV376 ) )
= $true )
| ( ( relation @ SV376 )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2387]) ).
thf(2519,plain,
! [SV377: $i,SV104: $i] :
( ( ( subset @ SV104 @ SV377 )
= $false )
| ( ( subset @ ( relation_rng @ SV104 ) @ ( relation_rng @ SV377 ) )
= $true )
| ( ( relation @ SV377 )
= $false )
| ( ( relation @ SV104 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2388]) ).
thf(2520,plain,
! [SV330: $i,SV288: $i,SV105: $i] :
( ( ( in @ SV105 @ SV288 )
= $false )
| ( ( ~ ( in @ SV105 @ ( relation_rng @ SV330 ) ) )
= $true )
| ( ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SV288 @ SV330 ) ) )
= $true )
| ( ( relation @ SV330 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2389]) ).
thf(2521,plain,
! [SV409: $i,SV105: $i,SV433: $i] :
( ( ( relation @ SV433 )
= $false )
| ( ( ~ ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SV409 @ SV433 ) ) )
| ( in @ SV105 @ SV409 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2390]) ).
thf(2522,plain,
! [SV410: $i,SV105: $i,SV434: $i] :
( ( ( relation @ SV434 )
= $false )
| ( ( ~ ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SV410 @ SV434 ) ) )
| ( in @ SV105 @ ( relation_rng @ SV434 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2391]) ).
thf(2523,plain,
! [SV435: $i,SV411: $i,SV106: $i] :
( ( ( subset @ ( unordered_pair @ SV106 @ SV411 ) @ SV435 )
= $false )
| ( ( in @ SV106 @ SV435 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2393]) ).
thf(2524,plain,
! [SV436: $i,SV412: $i,SV106: $i] :
( ( ( subset @ ( unordered_pair @ SV106 @ SV412 ) @ SV436 )
= $false )
| ( ( in @ SV412 @ SV436 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2394]) ).
thf(2525,plain,
! [SV378: $i,SV178: $i,SV332: $i,SV107: $i] :
( ( ( ~ ( in @ SV107 @ SV332 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ SV378 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SV332 ) @ SV378 ) )
= $true )
| ( ( relation @ SV378 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2395]) ).
thf(2526,plain,
! [SV437: $i,SV178: $i,SV107: $i,SV455: $i] :
( ( ( ~ ( relation @ SV455 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SV437 ) @ SV455 ) )
| ( in @ SV107 @ SV437 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2396]) ).
thf(2527,plain,
! [SV438: $i,SV178: $i,SV107: $i,SV456: $i] :
( ( ( ~ ( relation @ SV456 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SV438 ) @ SV456 ) )
| ( in @ ( ordered_pair @ SV107 @ SV178 ) @ SV456 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2397]) ).
thf(2528,plain,
! [SV108: $i,SV379: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV379 @ SV108 ) @ ( sK20_SY399 @ SV379 @ SV108 ) ) @ SV108 )
| ~ ~ ( in @ ( ordered_pair @ ( sK19_C @ SV379 @ SV108 ) @ ( sK20_SY399 @ SV379 @ SV108 ) ) @ SV379 ) )
= $false )
| ( ( subset @ SV108 @ SV379 )
= $true )
| ( ( relation @ SV379 )
= $false )
| ( ( relation @ SV108 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2398]) ).
thf(2529,plain,
! [SV380: $i,SV108: $i] :
( ( ( subset @ SV108 @ SV380 )
= $false )
| ( ( ! [SY955: $i,SY956: $i] :
( ~ ( in @ ( ordered_pair @ SY955 @ SY956 ) @ SV108 )
| ( in @ ( ordered_pair @ SY955 @ SY956 ) @ SV380 ) ) )
= $true )
| ( ( relation @ SV380 )
= $false )
| ( ( relation @ SV108 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2399]) ).
thf(2530,plain,
! [SV228: $i,SV290: $i] :
( ( ( ( sK30_C @ SV290 @ SV228 )
= SV228 )
= $false )
| ( ( ~ ( in @ ( sK30_C @ SV290 @ SV228 ) @ SV290 ) )
= $true )
| ( ( SV290
= ( singleton @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2400]) ).
thf(2531,plain,
! [SV291: $i,SV229: $i,SV463: $i] :
( ( ( ( SV463 != SV229 )
| ( in @ SV463 @ SV291 ) )
= $true )
| ( ( SV291
= ( singleton @ SV229 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2402]) ).
thf(2532,plain,
! [SV229: $i,SV291: $i,SV464: $i] :
( ( ( ~ ( in @ SV464 @ SV291 )
| ( SV464 = SV229 ) )
= $true )
| ( ( SV291
= ( singleton @ SV229 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2403]) ).
thf(2533,plain,
! [SV381: $i] :
( ( ( empty @ SV381 )
= $false )
| ( ( ~ ( relation @ SV381 ) )
= $true )
| ( ( ~ ( function @ SV381 ) )
= $true )
| ( ( function @ SV381 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2406]) ).
thf(2534,plain,
! [SV382: $i] :
( ( ( empty @ SV382 )
= $false )
| ( ( ~ ( relation @ SV382 ) )
= $true )
| ( ( ~ ( function @ SV382 ) )
= $true )
| ( ( relation @ SV382 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2407]) ).
thf(2535,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ( function @ SV465 )
| ~ ( relation @ SV465 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) )
| ( SV465
= ( function_inverse @ SV110 ) ) )
= $true )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2409]) ).
thf(2536,plain,
! [SV110: $i] :
( ( ( ~ ! [SY637: $i] :
( ~ ( function @ SY637 )
| ~ ( relation @ SY637 )
| ( SY637
!= ( function_inverse @ SV110 ) )
| ~ ( ~ ~ ( ~ ! [SY638: $i,SY639: $i] :
( ( SY639
!= ( apply @ SY637 @ SY638 ) )
| ~ ( in @ SY638 @ ( relation_rng @ SV110 ) )
| ( SY638
= ( apply @ SV110 @ SY639 ) ) )
| ~ ! [SY640: $i,SY641: $i] :
( ( SY641
!= ( apply @ SY637 @ SY640 ) )
| ~ ( in @ SY640 @ ( relation_rng @ SV110 ) )
| ( in @ SY641 @ ( relation_dom @ SV110 ) ) ) )
| ~ ~ ( ~ ! [SY642: $i,SY643: $i] :
( ( SY642
!= ( apply @ SV110 @ SY643 ) )
| ~ ( in @ SY643 @ ( relation_dom @ SV110 ) )
| ( SY643
= ( apply @ SY637 @ SY642 ) ) )
| ~ ! [SY644: $i] :
( ! [SY645: $i] :
( ( SY644
!= ( apply @ SV110 @ SY645 ) )
| ~ ( in @ SY645 @ ( relation_dom @ SV110 ) ) )
| ( in @ SY644 @ ( relation_rng @ SV110 ) ) ) ) ) )
| ~ ! [SY646: $i] :
( ~ ( function @ SY646 )
| ~ ( relation @ SY646 )
| ( SY646
!= ( function_inverse @ SV110 ) )
| ( ( relation_dom @ SY646 )
= ( relation_rng @ SV110 ) ) ) )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2410]) ).
thf(2537,plain,
! [SV413: $i,SV383: $i] :
( ( ( SV383 = SV413 )
= $false )
| ( ( proper_subset @ SV383 @ SV413 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2411]) ).
thf(2538,plain,
! [SV385: $i,SV298: $i,SV237: $i] :
( ( ( disjoint @ SV237 @ SV298 )
= $false )
| ( ( in @ SV385 @ SV237 )
= $false )
| ( ( in @ SV385 @ SV298 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2415]) ).
thf(2539,plain,
! [SV335: $i,SV111: $i,SV386: $i,SV179: $i] :
( ( ( in @ SV179 @ SV386 )
= $false )
| ( ( in @ SV111 @ SV335 )
= $false )
| ( ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SV335 @ SV386 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2416]) ).
thf(2540,plain,
! [SV466: $i,SV439: $i,SV179: $i,SV111: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SV439 @ SV466 ) ) )
= $true )
| ( ( in @ SV111 @ SV439 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2417]) ).
thf(2541,plain,
! [SV457: $i,SV440: $i,SV179: $i,SV111: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SV440 @ SV457 ) ) )
= $true )
| ( ( in @ SV179 @ SV457 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2418]) ).
thf(2542,plain,
! [SV113: $i] :
( ( ( ! [SY659: $i] :
( ~ ( in @ SY659 @ ( relation_dom @ SV113 ) )
| ! [SY660: $i] :
( ( SY660
!= ( apply @ SV113 @ SY659 ) )
| ( in @ ( ordered_pair @ SY659 @ SY660 ) @ SV113 ) ) ) )
= $true )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2419]) ).
thf(2543,plain,
! [SV113: $i] :
( ( ( ! [SY661: $i] :
( ~ ( in @ SY661 @ ( relation_dom @ SV113 ) )
| ! [SY662: $i] :
( ~ ( in @ ( ordered_pair @ SY661 @ SY662 ) @ SV113 )
| ( SY662
= ( apply @ SV113 @ SY661 ) ) ) ) )
= $true )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2420]) ).
thf(2544,plain,
! [SV113: $i] :
( ( ( ! [SY663: $i] :
( ( in @ SY663 @ ( relation_dom @ SV113 ) )
| ! [SY664: $i] :
( ( SY664
!= ( apply @ SV113 @ SY663 ) )
| ( SY664 = empty_set ) ) ) )
= $true )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2421]) ).
thf(2545,plain,
! [SV113: $i] :
( ( ( ! [SY665: $i] :
( ( in @ SY665 @ ( relation_dom @ SV113 ) )
| ! [SY666: $i] :
( ( SY666 != empty_set )
| ( SY666
= ( apply @ SV113 @ SY665 ) ) ) ) )
= $true )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2422]) ).
thf(2546,plain,
! [SV114: $i,SV301: $i,SV338: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV338 )
| ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV114 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV338 )
| ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV301 ) ) )
= $false )
| ( ( SV338
= ( set_union2 @ SV114 @ SV301 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2423]) ).
thf(2547,plain,
! [SV114: $i,SV301: $i,SV338: $i] :
( ( ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV338 )
= $true )
| ( ( ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV114 )
| ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV301 ) )
= $true )
| ( ( SV338
= ( set_union2 @ SV114 @ SV301 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2424]) ).
thf(2548,plain,
! [SV302: $i,SV114: $i,SV339: $i] :
( ( ( ! [SY895: $i] :
( ~ ( in @ SY895 @ SV339 )
| ( in @ SY895 @ SV114 )
| ( in @ SY895 @ SV302 ) ) )
= $true )
| ( ( SV339
= ( set_union2 @ SV114 @ SV302 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2425]) ).
thf(2549,plain,
! [SV302: $i,SV339: $i,SV114: $i] :
( ( ( ~ ( ~ ! [SY896: $i] :
( ~ ( in @ SY896 @ SV114 )
| ( in @ SY896 @ SV339 ) )
| ~ ! [SY897: $i] :
( ~ ( in @ SY897 @ SV302 )
| ( in @ SY897 @ SV339 ) ) ) )
= $true )
| ( ( SV339
= ( set_union2 @ SV114 @ SV302 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2426]) ).
thf(2550,plain,
! [SV116: $i,SV306: $i,SV342: $i] :
( ( ( ~ ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV116 )
| ~ ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV306 ) )
= $true )
| ( ( ~ ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV342 ) )
= $true )
| ( ( SV342
= ( set_intersection2 @ SV116 @ SV306 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2431]) ).
thf(2551,plain,
! [SV116: $i,SV306: $i,SV342: $i] :
( ( ( ~ ( ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV116 )
| ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV342 ) )
| ~ ( ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV306 )
| ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV342 ) ) )
= $false )
| ( ( SV342
= ( set_intersection2 @ SV116 @ SV306 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2432]) ).
thf(2552,plain,
! [SV343: $i,SV307: $i,SV116: $i] :
( ( ( ! [SY898: $i] :
( ~ ( in @ SY898 @ SV116 )
| ~ ( in @ SY898 @ SV307 )
| ( in @ SY898 @ SV343 ) ) )
= $true )
| ( ( SV343
= ( set_intersection2 @ SV116 @ SV307 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2433]) ).
thf(2553,plain,
! [SV307: $i,SV116: $i,SV343: $i] :
( ( ( ~ ( ~ ! [SY899: $i] :
( ~ ( in @ SY899 @ SV343 )
| ( in @ SY899 @ SV116 ) )
| ~ ! [SY900: $i] :
( ~ ( in @ SY900 @ SV343 )
| ( in @ SY900 @ SV307 ) ) ) )
= $true )
| ( ( SV343
= ( set_intersection2 @ SV116 @ SV307 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2434]) ).
thf(2554,plain,
! [SV251: $i,SV308: $i] :
( ( ( ( ( sK44_C @ SV308 @ SV251 )
!= ( sK45_SY414 @ SV308 @ SV251 ) )
| ~ ( in @ ( sK44_C @ SV308 @ SV251 ) @ SV251 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 ) )
= $true )
| ( ( SV308
= ( identity_relation @ SV251 ) )
= $true )
| ( ( relation @ SV308 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2437]) ).
thf(2555,plain,
! [SV251: $i,SV308: $i] :
( ( ( ~ ( ~ ( ( ( sK44_C @ SV308 @ SV251 )
= ( sK45_SY414 @ SV308 @ SV251 ) )
| ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 ) )
| ~ ( ( in @ ( sK44_C @ SV308 @ SV251 ) @ SV251 )
| ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 ) ) ) )
= $true )
| ( ( SV308
= ( identity_relation @ SV251 ) )
= $true )
| ( ( relation @ SV308 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2438]) ).
thf(2556,plain,
! [SV309: $i,SV252: $i] :
( ( ( ~ ! [SY861: $i,SY862: $i] :
( ( SY861 != SY862 )
| ~ ( in @ SY861 @ SV252 )
| ( in @ ( ordered_pair @ SY861 @ SY862 ) @ SV309 ) ) )
= $false )
| ( ( SV309
= ( identity_relation @ SV252 ) )
= $false )
| ( ( relation @ SV309 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2439]) ).
thf(2557,plain,
! [SV252: $i,SV309: $i] :
( ( ( ~ ~ ( ~ ! [SY863: $i,SY864: $i] :
( ~ ( in @ ( ordered_pair @ SY863 @ SY864 ) @ SV309 )
| ( SY863 = SY864 ) )
| ~ ! [SY865: $i] :
( ! [SY866: $i] :
~ ( in @ ( ordered_pair @ SY865 @ SY866 ) @ SV309 )
| ( in @ SY865 @ SV252 ) ) ) )
= $false )
| ( ( SV309
= ( identity_relation @ SV252 ) )
= $false )
| ( ( relation @ SV309 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2439]) ).
thf(2558,plain,
! [SV344: $i,SV310: $i,SV117: $i] :
( ( ( in @ SV117 @ SV310 )
= $false )
| ( ( ~ ( in @ SV117 @ ( relation_dom @ SV344 ) ) )
= $true )
| ( ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SV344 @ SV310 ) ) )
= $true )
| ( ( relation @ SV344 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2440]) ).
thf(2559,plain,
! [SV418: $i,SV117: $i,SV441: $i] :
( ( ( relation @ SV441 )
= $false )
| ( ( ~ ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SV441 @ SV418 ) ) )
| ( in @ SV117 @ SV418 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2441]) ).
thf(2560,plain,
! [SV419: $i,SV117: $i,SV442: $i] :
( ( ( relation @ SV442 )
= $false )
| ( ( ~ ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SV442 @ SV419 ) ) )
| ( in @ SV117 @ ( relation_dom @ SV442 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2442]) ).
thf(2561,plain,
! [SV253: $i,SV311: $i] :
( ( ( ~ ( ~ ( in @ ( sK50_C @ SV311 @ SV253 ) @ SV253 )
| ~ ( ( ( apply @ SV311 @ ( sK50_C @ SV311 @ SV253 ) )
!= ( sK50_C @ SV311 @ SV253 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV311 )
!= SV253 ) )
= $true )
| ( ( SV311
= ( identity_relation @ SV253 ) )
= $true )
| ( ( function @ SV311 )
= $false )
| ( ( relation @ SV311 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2443]) ).
thf(2562,plain,
! [SV391: $i,SV420: $i] :
( ( ( function @ SV420 )
= $false )
| ( ( ~ ( relation @ SV420 ) )
= $true )
| ( ( ( SV420
!= ( identity_relation @ SV391 ) )
| ! [SY997: $i] :
( ~ ( in @ SY997 @ SV391 )
| ( ( apply @ SV420 @ SY997 )
= SY997 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2444]) ).
thf(2563,plain,
! [SV392: $i,SV421: $i] :
( ( ( function @ SV421 )
= $false )
| ( ( ~ ( relation @ SV421 ) )
= $true )
| ( ( ( SV421
!= ( identity_relation @ SV392 ) )
| ( ( relation_dom @ SV421 )
= SV392 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2445]) ).
thf(2564,plain,
! [SV345: $i,SV312: $i,SV118: $i] :
( ( ( ! [SY901: $i,SY902: $i] :
( ~ ( in @ SY901 @ SV118 )
| ~ ( in @ SY902 @ SV312 )
| ( ( sK23_D @ SV345 @ SV312 @ SV118 )
!= ( ordered_pair @ SY901 @ SY902 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV345 @ SV312 @ SV118 ) @ SV345 ) )
= $true )
| ( ( SV345
= ( cartesian_product2 @ SV118 @ SV312 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2446]) ).
thf(2565,plain,
! [SV118: $i,SV312: $i,SV345: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY403 @ SV345 @ SV312 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK25_SY405 @ SV345 @ SV312 @ SV118 ) @ SV312 ) )
| ( ( sK23_D @ SV345 @ SV312 @ SV118 )
!= ( ordered_pair @ ( sK24_SY403 @ SV345 @ SV312 @ SV118 ) @ ( sK25_SY405 @ SV345 @ SV312 @ SV118 ) ) ) ) )
= $true )
| ( ( in @ ( sK23_D @ SV345 @ SV312 @ SV118 ) @ SV345 )
= $true )
| ( ( SV345
= ( cartesian_product2 @ SV118 @ SV312 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2447]) ).
thf(2566,plain,
! [SV346: $i,SV313: $i,SV118: $i] :
( ( ( ! [SY903: $i] :
( ! [SY873: $i,SY874: $i] :
( ~ ( in @ SY873 @ SV118 )
| ~ ( in @ SY874 @ SV313 )
| ( SY903
!= ( ordered_pair @ SY873 @ SY874 ) ) )
| ( in @ SY903 @ SV346 ) ) )
= $true )
| ( ( SV346
= ( cartesian_product2 @ SV118 @ SV313 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2448]) ).
thf(2567,plain,
! [SV118: $i,SV313: $i,SV346: $i] :
( ( ( ! [SY906: $i] :
( ~ ( in @ SY906 @ SV346 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY906 @ SV346 @ SV313 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK22_SY400 @ SY906 @ SV346 @ SV313 @ SV118 ) @ SV313 ) )
| ( SY906
!= ( ordered_pair @ ( sK21_E @ SY906 @ SV346 @ SV313 @ SV118 ) @ ( sK22_SY400 @ SY906 @ SV346 @ SV313 @ SV118 ) ) ) ) ) )
= $true )
| ( ( SV346
= ( cartesian_product2 @ SV118 @ SV313 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2449]) ).
thf(2568,plain,
! [SV467: $i,SV254: $i,SV316: $i] :
( ( ( ~ ( in @ ( sK15_C @ SV316 @ SV254 ) @ SV467 )
| ~ ( in @ SV467 @ SV254 ) )
= $true )
| ( ( ~ ( in @ ( sK15_C @ SV316 @ SV254 ) @ SV316 ) )
= $true )
| ( ( SV316
= ( union @ SV254 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2450]) ).
thf(2569,plain,
! [SV254: $i,SV316: $i] :
( ( ( ~ ( in @ ( sK15_C @ SV316 @ SV254 ) @ ( sK16_SY398 @ SV316 @ SV254 ) )
| ~ ( in @ ( sK16_SY398 @ SV316 @ SV254 ) @ SV254 ) )
= $false )
| ( ( in @ ( sK15_C @ SV316 @ SV254 ) @ SV316 )
= $true )
| ( ( SV316
= ( union @ SV254 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2451]) ).
thf(2570,plain,
! [SV317: $i,SV255: $i,SV468: $i] :
( ( ( ! [SY1016: $i] :
( ~ ( in @ SV468 @ SY1016 )
| ~ ( in @ SY1016 @ SV255 ) )
| ( in @ SV468 @ SV317 ) )
= $true )
| ( ( SV317
= ( union @ SV255 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2452]) ).
thf(2571,plain,
! [SV255: $i,SV317: $i,SV469: $i] :
( ( ( ~ ( in @ SV469 @ SV317 )
| ~ ( ~ ( in @ SV469 @ ( sK14_D @ SV469 @ SV317 @ SV255 ) )
| ~ ( in @ ( sK14_D @ SV469 @ SV317 @ SV255 ) @ SV255 ) ) )
= $true )
| ( ( SV317
= ( union @ SV255 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2453]) ).
thf(2572,plain,
! [SV120: $i,SV393: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV393 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV120 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV393 ) ) )
= $false )
| ( ( SV120 = SV393 )
= $true )
| ( ( relation @ SV393 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2454]) ).
thf(2573,plain,
! [SV394: $i,SV120: $i] :
( ( ( SV120 = SV394 )
= $false )
| ( ( ~ ( ~ ! [SY964: $i,SY965: $i] :
( ~ ( in @ ( ordered_pair @ SY964 @ SY965 ) @ SV120 )
| ( in @ ( ordered_pair @ SY964 @ SY965 ) @ SV394 ) )
| ~ ! [SY966: $i,SY967: $i] :
( ~ ( in @ ( ordered_pair @ SY966 @ SY967 ) @ SV394 )
| ( in @ ( ordered_pair @ SY966 @ SY967 ) @ SV120 ) ) ) )
= $true )
| ( ( relation @ SV394 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2455]) ).
thf(2574,plain,
! [SV145: $i,SV347: $i,SV43: $i] :
( ( ( ~ ( in @ SV43 @ ( relation_dom @ ( relation_composition @ SV347 @ SV145 ) ) ) )
= $true )
| ( ( ( apply @ ( relation_composition @ SV347 @ SV145 ) @ SV43 )
= ( apply @ SV145 @ ( apply @ SV347 @ SV43 ) ) )
= $true )
| ( ( function @ SV347 )
= $false )
| ( ( relation @ SV347 )
= $false )
| ( ( function @ SV145 )
= $false )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2456]) ).
thf(2575,plain,
! [SV348: $i,SV146: $i,SV44: $i] :
( ( ( ~ ( in @ SV44 @ ( relation_dom @ SV146 ) ) )
= $true )
| ( ( ( apply @ ( relation_composition @ SV146 @ SV348 ) @ SV44 )
= ( apply @ SV348 @ ( apply @ SV146 @ SV44 ) ) )
= $true )
| ( ( function @ SV348 )
= $false )
| ( ( relation @ SV348 )
= $false )
| ( ( function @ SV146 )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2457]) ).
thf(2576,plain,
! [SV351: $i,SV424: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK33_SY406 @ SV424 @ SV351 ) @ SV351 )
| ~ ~ ( in @ ( sK32_C @ SV424 @ SV351 ) @ ( sK33_SY406 @ SV424 @ SV351 ) ) )
| ~ ( in @ ( sK32_C @ SV424 @ SV351 ) @ SV424 ) ) )
= $false )
| ( ( SV424
= ( set_meet @ SV351 ) )
= $true )
| ( ( SV351 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2458]) ).
thf(2577,plain,
! [SV424: $i,SV351: $i] :
( ( ( ~ ( ! [SY998: $i] :
( ~ ( in @ SY998 @ SV351 )
| ( in @ ( sK32_C @ SV424 @ SV351 ) @ SY998 ) )
| ( in @ ( sK32_C @ SV424 @ SV351 ) @ SV424 ) ) )
= $false )
| ( ( SV424
= ( set_meet @ SV351 ) )
= $true )
| ( ( SV351 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2458]) ).
thf(2578,plain,
! [SV352: $i,SV425: $i] :
( ( ( ~ ! [SY999: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY999 @ SV425 @ SV352 ) @ SV352 )
| ~ ~ ( in @ SY999 @ ( sK31_D @ SY999 @ SV425 @ SV352 ) ) )
| ( in @ SY999 @ SV425 ) )
| ~ ! [SY1000: $i] :
( ~ ( in @ SY1000 @ SV425 )
| ! [SY914: $i] :
( ~ ( in @ SY914 @ SV352 )
| ( in @ SY1000 @ SY914 ) ) ) )
= $false )
| ( ( SV425
= ( set_meet @ SV352 ) )
= $false )
| ( ( SV352 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2459]) ).
thf(2579,plain,
! [SV353: $i,SV444: $i] :
( ( ( SV444
= ( set_meet @ SV353 ) )
= $false )
| ( ( SV444 = empty_set )
= $true )
| ( ( SV353 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2460]) ).
thf(2580,plain,
! [SV354: $i,SV445: $i] :
( ( ( SV445 = empty_set )
= $false )
| ( ( SV445
= ( set_meet @ SV354 ) )
= $true )
| ( ( SV354 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2461]) ).
thf(2581,plain,
! [SV202: $i,SV265: $i] :
( ( ( relation @ SV265 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( ~ ( function @ SV265 ) )
= $true )
| ( ( function @ ( relation_composition @ SV202 @ SV265 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2462]) ).
thf(2582,plain,
! [SV203: $i,SV266: $i] :
( ( ( relation @ SV266 )
= $false )
| ( ( function @ SV203 )
= $false )
| ( ( relation @ SV203 )
= $false )
| ( ( ~ ( function @ SV266 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV203 @ SV266 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2463]) ).
thf(2583,plain,
! [SV271: $i,SV87: $i,SV320: $i,SV446: $i] :
( ( ( ~ ( in @ SV446 @ ( relation_dom @ SV320 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV446 @ SV87 ) @ SV320 ) )
= $true )
| ( ( ~ ( in @ SV446 @ SV271 ) )
= $true )
| ( ( in @ SV87 @ ( relation_image @ SV320 @ SV271 ) )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2464]) ).
thf(2584,plain,
! [SV87: $i,SV272: $i,SV321: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK52_D @ SV321 @ SV272 @ SV87 ) @ ( relation_dom @ SV321 ) )
| ~ ( in @ ( ordered_pair @ ( sK52_D @ SV321 @ SV272 @ SV87 ) @ SV87 ) @ SV321 ) ) )
= $false )
| ( ( in @ SV87 @ ( relation_image @ SV321 @ SV272 ) )
= $false )
| ( ( relation @ SV321 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2465]) ).
thf(2585,plain,
! [SV87: $i,SV272: $i,SV321: $i] :
( ( ( ~ ( in @ ( sK52_D @ SV321 @ SV272 @ SV87 ) @ SV272 ) )
= $false )
| ( ( in @ SV87 @ ( relation_image @ SV321 @ SV272 ) )
= $false )
| ( ( relation @ SV321 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2465]) ).
thf(2586,plain,
! [SV88: $i,SV274: $i,SV322: $i] :
( ( ( ~ ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV88 ) )
= $true )
| ( ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV274 )
= $true )
| ( ( ~ ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV322 ) )
= $true )
| ( ( SV322
= ( set_difference @ SV88 @ SV274 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2466]) ).
thf(2587,plain,
! [SV88: $i,SV274: $i,SV322: $i] :
( ( ( ~ ( ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV88 )
| ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV322 ) ) )
= $false )
| ( ( SV322
= ( set_difference @ SV88 @ SV274 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2467]) ).
thf(2588,plain,
! [SV88: $i,SV274: $i,SV322: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV274 )
| ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV322 ) ) )
= $false )
| ( ( SV322
= ( set_difference @ SV88 @ SV274 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2467]) ).
thf(2589,plain,
! [SV323: $i,SV275: $i,SV88: $i,SV470: $i] :
( ( ( ~ ( in @ SV470 @ SV88 )
| ( in @ SV470 @ SV275 )
| ( in @ SV470 @ SV323 ) )
= $true )
| ( ( SV323
= ( set_difference @ SV88 @ SV275 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2468]) ).
thf(2590,plain,
! [SV275: $i,SV88: $i,SV323: $i] :
( ( ( ~ ! [SY884: $i] :
( ~ ( in @ SY884 @ SV323 )
| ( in @ SY884 @ SV88 ) )
| ~ ! [SY885: $i] :
( ~ ( in @ SY885 @ SV323 )
| ~ ( in @ SY885 @ SV275 ) ) )
= $false )
| ( ( SV323
= ( set_difference @ SV88 @ SV275 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2469]) ).
thf(2591,plain,
! [SV360: $i,SV447: $i] :
( ( ( element @ SV447 @ SV360 )
= $false )
| ( ( empty @ SV447 )
= $true )
| ( ( empty @ SV360 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2472]) ).
thf(2592,plain,
! [SV361: $i,SV448: $i] :
( ( ( empty @ SV448 )
= $false )
| ( ( element @ SV448 @ SV361 )
= $true )
| ( ( empty @ SV361 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2473]) ).
thf(2593,plain,
! [SV89: $i,SV174: $i,SV398: $i] :
( ( ( ~ ( ~ ( in @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV174 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 ) )
| ~ ~ ( ~ ( ( in @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) @ SV89 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV174 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 ) ) ) )
= $false )
| ( ( SV398
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2474]) ).
thf(2594,plain,
! [SV174: $i,SV89: $i,SV399: $i] :
( ( ( SV399
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $false )
| ( ( ~ ( ~ ! [SY968: $i,SY969: $i] :
( ~ ( in @ SY969 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY968 @ SY969 ) @ SV174 )
| ( in @ ( ordered_pair @ SY968 @ SY969 ) @ SV399 ) )
| ~ ~ ( ~ ! [SY970: $i,SY971: $i] :
( ~ ( in @ ( ordered_pair @ SY970 @ SY971 ) @ SV399 )
| ( in @ SY971 @ SV89 ) )
| ~ ! [SY972: $i,SY973: $i] :
( ~ ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV399 )
| ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV174 ) ) ) ) )
= $true )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2475]) ).
thf(2595,plain,
! [SV90: $i,SV276: $i,SV324: $i] :
( ( ( ~ ( ~ ( in @ ( sK27_D @ SV324 @ SV276 @ SV90 ) @ SV324 )
| ( ( sK27_D @ SV324 @ SV276 @ SV90 )
!= SV90 ) ) )
= $false )
| ( ( SV324
= ( unordered_pair @ SV90 @ SV276 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2476]) ).
thf(2596,plain,
! [SV90: $i,SV276: $i,SV324: $i] :
( ( ( ~ ( ~ ( in @ ( sK27_D @ SV324 @ SV276 @ SV90 ) @ SV324 )
| ( ( sK27_D @ SV324 @ SV276 @ SV90 )
!= SV276 ) ) )
= $false )
| ( ( SV324
= ( unordered_pair @ SV90 @ SV276 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2476]) ).
thf(2597,plain,
! [SV90: $i,SV276: $i,SV324: $i] :
( ( ( ( sK27_D @ SV324 @ SV276 @ SV90 )
= SV90 )
= $true )
| ( ( ( sK27_D @ SV324 @ SV276 @ SV90 )
= SV276 )
= $true )
| ( ( in @ ( sK27_D @ SV324 @ SV276 @ SV90 ) @ SV324 )
= $true )
| ( ( SV324
= ( unordered_pair @ SV90 @ SV276 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2477]) ).
thf(2598,plain,
! [SV277: $i,SV90: $i,SV325: $i,SV471: $i] :
( ( ( ~ ( in @ SV471 @ SV325 )
| ( SV471 = SV90 )
| ( SV471 = SV277 ) )
= $true )
| ( ( SV325
= ( unordered_pair @ SV90 @ SV277 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2478]) ).
thf(2599,plain,
! [SV277: $i,SV325: $i,SV90: $i] :
( ( ( ~ ! [SY887: $i] :
( ( SY887 != SV90 )
| ( in @ SY887 @ SV325 ) )
| ~ ! [SY888: $i] :
( ( SY888 != SV277 )
| ( in @ SY888 @ SV325 ) ) )
= $false )
| ( ( SV325
= ( unordered_pair @ SV90 @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2479]) ).
thf(2600,plain,
! [SV209: $i,SV278: $i] :
( ( ( subset @ ( sK28_C @ SV278 @ SV209 ) @ SV209 )
= $false )
| ( ( in @ ( sK28_C @ SV278 @ SV209 ) @ SV278 )
= $false )
| ( ( SV278
= ( powerset @ SV209 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2480]) ).
thf(2601,plain,
! [SV210: $i,SV279: $i,SV459: $i] :
( ( ( ~ ( in @ SV459 @ SV279 ) )
= $true )
| ( ( subset @ SV459 @ SV210 )
= $true )
| ( ( SV279
= ( powerset @ SV210 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2481]) ).
thf(2602,plain,
! [SV279: $i,SV210: $i,SV460: $i] :
( ( ( ~ ( subset @ SV460 @ SV210 ) )
= $true )
| ( ( in @ SV460 @ SV279 )
= $true )
| ( ( SV279
= ( powerset @ SV210 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2482]) ).
thf(2603,plain,
! [SV91: $i,SV362: $i] :
( ( ( ! [SY923: $i] :
~ ( in @ ( ordered_pair @ ( sK63_C @ SV362 @ SV91 ) @ SY923 ) @ SV91 ) )
= $true )
| ( ( ~ ( in @ ( sK63_C @ SV362 @ SV91 ) @ SV362 ) )
= $true )
| ( ( SV362
= ( relation_dom @ SV91 ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2483]) ).
thf(2604,plain,
! [SV91: $i,SV362: $i] :
( ( ( in @ ( ordered_pair @ ( sK63_C @ SV362 @ SV91 ) @ ( sK64_SY419 @ SV362 @ SV91 ) ) @ SV91 )
= $true )
| ( ( in @ ( sK63_C @ SV362 @ SV91 ) @ SV362 )
= $true )
| ( ( SV362
= ( relation_dom @ SV91 ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2484]) ).
thf(2605,plain,
! [SV363: $i,SV91: $i] :
( ( ( ! [SY924: $i] :
( ! [SY530: $i] :
~ ( in @ ( ordered_pair @ SY924 @ SY530 ) @ SV91 )
| ( in @ SY924 @ SV363 ) ) )
= $true )
| ( ( SV363
= ( relation_dom @ SV91 ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2485]) ).
thf(2606,plain,
! [SV91: $i,SV363: $i] :
( ( ( ! [SY926: $i] :
( ~ ( in @ SY926 @ SV363 )
| ( in @ ( ordered_pair @ SY926 @ ( sK62_D @ SY926 @ SV363 @ SV91 ) ) @ SV91 ) ) )
= $true )
| ( ( SV363
= ( relation_dom @ SV91 ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2486]) ).
thf(2607,plain,
! [SV92: $i,SV364: $i,SV400: $i] :
( ( ( ! [SY974: $i] :
( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SY974 ) @ SV92 )
| ~ ( in @ SY974 @ SV364 ) )
| ~ ( in @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SV400 ) )
= $true )
| ( ( SV400
= ( relation_inverse_image @ SV92 @ SV364 ) )
= $true )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2487]) ).
thf(2608,plain,
! [SV92: $i,SV364: $i,SV400: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ ( sK36_SY409 @ SV400 @ SV364 @ SV92 ) ) @ SV92 )
| ~ ( in @ ( sK36_SY409 @ SV400 @ SV364 @ SV92 ) @ SV364 ) )
| ( in @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SV400 ) )
= $true )
| ( ( SV400
= ( relation_inverse_image @ SV92 @ SV364 ) )
= $true )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2488]) ).
thf(2609,plain,
! [SV401: $i,SV365: $i,SV92: $i] :
( ( ( ~ ! [SY975: $i] :
( ! [SY931: $i] :
( ~ ( in @ ( ordered_pair @ SY975 @ SY931 ) @ SV92 )
| ~ ( in @ SY931 @ SV365 ) )
| ( in @ SY975 @ SV401 ) ) )
= $false )
| ( ( SV401
= ( relation_inverse_image @ SV92 @ SV365 ) )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2489]) ).
thf(2610,plain,
! [SV92: $i,SV365: $i,SV401: $i] :
( ( ( ~ ! [SY977: $i] :
( ~ ( in @ SY977 @ SV401 )
| ~ ( ~ ( in @ ( ordered_pair @ SY977 @ ( sK34_E @ SY977 @ SV401 @ SV365 @ SV92 ) ) @ SV92 )
| ~ ( in @ ( sK34_E @ SY977 @ SV401 @ SV365 @ SV92 ) @ SV365 ) ) ) )
= $false )
| ( ( SV401
= ( relation_inverse_image @ SV92 @ SV365 ) )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2489]) ).
thf(2611,plain,
! [SV93: $i,SV366: $i,SV402: $i] :
( ( ( ! [SY978: $i] :
( ~ ( in @ ( ordered_pair @ SY978 @ ( sK38_D @ SV402 @ SV366 @ SV93 ) ) @ SV93 )
| ~ ( in @ SY978 @ SV366 ) )
| ~ ( in @ ( sK38_D @ SV402 @ SV366 @ SV93 ) @ SV402 ) )
= $true )
| ( ( SV402
= ( relation_image @ SV93 @ SV366 ) )
= $true )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2490]) ).
thf(2612,plain,
! [SV93: $i,SV366: $i,SV402: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SV402 @ SV366 @ SV93 ) @ ( sK38_D @ SV402 @ SV366 @ SV93 ) ) @ SV93 )
| ~ ( in @ ( sK39_SY411 @ SV402 @ SV366 @ SV93 ) @ SV366 ) )
| ( in @ ( sK38_D @ SV402 @ SV366 @ SV93 ) @ SV402 ) )
= $true )
| ( ( SV402
= ( relation_image @ SV93 @ SV366 ) )
= $true )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2491]) ).
thf(2613,plain,
! [SV403: $i,SV367: $i,SV93: $i] :
( ( ( ~ ! [SY979: $i] :
( ! [SY937: $i] :
( ~ ( in @ ( ordered_pair @ SY937 @ SY979 ) @ SV93 )
| ~ ( in @ SY937 @ SV367 ) )
| ( in @ SY979 @ SV403 ) ) )
= $false )
| ( ( SV403
= ( relation_image @ SV93 @ SV367 ) )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2492]) ).
thf(2614,plain,
! [SV93: $i,SV367: $i,SV403: $i] :
( ( ( ~ ! [SY981: $i] :
( ~ ( in @ SY981 @ SV403 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SY981 @ SV403 @ SV367 @ SV93 ) @ SY981 ) @ SV93 )
| ~ ( in @ ( sK37_E @ SY981 @ SV403 @ SV367 @ SV93 ) @ SV367 ) ) ) )
= $false )
| ( ( SV403
= ( relation_image @ SV93 @ SV367 ) )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2492]) ).
thf(2615,plain,
! [SV282: $i,SV94: $i,SV326: $i,SV449: $i] :
( ( ( ~ ( in @ SV449 @ ( relation_rng @ SV326 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV94 @ SV449 ) @ SV326 ) )
= $true )
| ( ( ~ ( in @ SV449 @ SV282 ) )
= $true )
| ( ( in @ SV94 @ ( relation_inverse_image @ SV326 @ SV282 ) )
= $true )
| ( ( relation @ SV326 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2493]) ).
thf(2616,plain,
! [SV94: $i,SV283: $i,SV327: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK51_D @ SV327 @ SV283 @ SV94 ) @ ( relation_rng @ SV327 ) )
| ~ ( in @ ( ordered_pair @ SV94 @ ( sK51_D @ SV327 @ SV283 @ SV94 ) ) @ SV327 ) ) )
= $false )
| ( ( in @ SV94 @ ( relation_inverse_image @ SV327 @ SV283 ) )
= $false )
| ( ( relation @ SV327 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2494]) ).
thf(2617,plain,
! [SV94: $i,SV283: $i,SV327: $i] :
( ( ( ~ ( in @ ( sK51_D @ SV327 @ SV283 @ SV94 ) @ SV283 ) )
= $false )
| ( ( in @ SV94 @ ( relation_inverse_image @ SV327 @ SV283 ) )
= $false )
| ( ( relation @ SV327 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2494]) ).
thf(2618,plain,
! [SV175: $i,SV95: $i,SV450: $i] :
( ( ( ~ ( function @ SV450 ) )
= $true )
| ( ( ~ ( relation @ SV450 ) )
= $true )
| ( ( ~ ( in @ SV95 @ ( relation_dom @ SV450 ) )
| ~ ( in @ ( apply @ SV450 @ SV95 ) @ ( relation_dom @ SV175 ) )
| ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SV450 @ SV175 ) ) ) )
= $true )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2495]) ).
thf(2619,plain,
! [SV175: $i,SV95: $i] :
( ( ( ! [SY732: $i] :
( ~ ( function @ SY732 )
| ~ ( relation @ SY732 )
| ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY732 @ SV175 ) ) )
| ( in @ SV95 @ ( relation_dom @ SY732 ) ) ) )
= $true )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2496]) ).
thf(2620,plain,
! [SV175: $i,SV95: $i] :
( ( ( ! [SY733: $i] :
( ~ ( function @ SY733 )
| ~ ( relation @ SY733 )
| ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SY733 @ SV175 ) ) )
| ( in @ ( apply @ SY733 @ SV95 ) @ ( relation_dom @ SV175 ) ) ) )
= $true )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2497]) ).
thf(2621,plain,
! [SV96: $i,SV368: $i,SV404: $i] :
( ( ( ~ ( ~ ( in @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ SV368 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 ) )
| ~ ~ ( ~ ( ( in @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ SV368 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 ) ) ) )
= $false )
| ( ( SV404
= ( relation_dom_restriction @ SV96 @ SV368 ) )
= $true )
| ( ( relation @ SV404 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2498]) ).
thf(2622,plain,
! [SV369: $i,SV96: $i,SV405: $i] :
( ( ( SV405
= ( relation_dom_restriction @ SV96 @ SV369 ) )
= $false )
| ( ( ~ ( ~ ! [SY982: $i,SY983: $i] :
( ~ ( in @ SY982 @ SV369 )
| ~ ( in @ ( ordered_pair @ SY982 @ SY983 ) @ SV96 )
| ( in @ ( ordered_pair @ SY982 @ SY983 ) @ SV405 ) )
| ~ ~ ( ~ ! [SY984: $i] :
( ! [SY985: $i] :
~ ( in @ ( ordered_pair @ SY984 @ SY985 ) @ SV405 )
| ( in @ SY984 @ SV369 ) )
| ~ ! [SY986: $i,SY987: $i] :
( ~ ( in @ ( ordered_pair @ SY986 @ SY987 ) @ SV405 )
| ( in @ ( ordered_pair @ SY986 @ SY987 ) @ SV96 ) ) ) ) )
= $true )
| ( ( relation @ SV405 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2499]) ).
thf(2623,plain,
! [SV97: $i,SV370: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SV370 @ SV97 ) @ ( sK12_SY396 @ SV370 @ SV97 ) ) @ SV370 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SV370 @ SV97 ) @ ( sK11_C @ SV370 @ SV97 ) ) @ SV97 ) ) )
= $false )
| ( ( SV370
= ( relation_inverse @ SV97 ) )
= $true )
| ( ( relation @ SV370 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2500]) ).
thf(2624,plain,
! [SV97: $i,SV370: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK11_C @ SV370 @ SV97 ) @ ( sK12_SY396 @ SV370 @ SV97 ) ) @ SV370 )
| ( in @ ( ordered_pair @ ( sK12_SY396 @ SV370 @ SV97 ) @ ( sK11_C @ SV370 @ SV97 ) ) @ SV97 ) ) )
= $false )
| ( ( SV370
= ( relation_inverse @ SV97 ) )
= $true )
| ( ( relation @ SV370 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2500]) ).
thf(2625,plain,
! [SV97: $i,SV371: $i] :
( ( ( ~ ! [SY947: $i,SY948: $i] :
( ~ ( in @ ( ordered_pair @ SY947 @ SY948 ) @ SV371 )
| ( in @ ( ordered_pair @ SY948 @ SY947 ) @ SV97 ) )
| ~ ! [SY949: $i,SY950: $i] :
( ~ ( in @ ( ordered_pair @ SY950 @ SY949 ) @ SV97 )
| ( in @ ( ordered_pair @ SY949 @ SY950 ) @ SV371 ) ) )
= $false )
| ( ( SV371
= ( relation_inverse @ SV97 ) )
= $false )
| ( ( relation @ SV371 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2501]) ).
thf(2626,plain,
! [SV98: $i,SV372: $i] :
( ( ( ! [SY951: $i] :
~ ( in @ ( ordered_pair @ SY951 @ ( sK60_C @ SV372 @ SV98 ) ) @ SV98 ) )
= $true )
| ( ( ~ ( in @ ( sK60_C @ SV372 @ SV98 ) @ SV372 ) )
= $true )
| ( ( SV372
= ( relation_rng @ SV98 ) )
= $true )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2502]) ).
thf(2627,plain,
! [SV98: $i,SV372: $i] :
( ( ( in @ ( ordered_pair @ ( sK61_SY417 @ SV372 @ SV98 ) @ ( sK60_C @ SV372 @ SV98 ) ) @ SV98 )
= $true )
| ( ( in @ ( sK60_C @ SV372 @ SV98 ) @ SV372 )
= $true )
| ( ( SV372
= ( relation_rng @ SV98 ) )
= $true )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2503]) ).
thf(2628,plain,
! [SV373: $i,SV98: $i] :
( ( ( ! [SY952: $i] :
( ! [SY577: $i] :
~ ( in @ ( ordered_pair @ SY577 @ SY952 ) @ SV98 )
| ( in @ SY952 @ SV373 ) ) )
= $true )
| ( ( SV373
= ( relation_rng @ SV98 ) )
= $false )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2504]) ).
thf(2629,plain,
! [SV98: $i,SV373: $i] :
( ( ( ! [SY954: $i] :
( ~ ( in @ SY954 @ SV373 )
| ( in @ ( ordered_pair @ ( sK59_D @ SY954 @ SV373 @ SV98 ) @ SY954 ) @ SV98 ) ) )
= $true )
| ( ( SV373
= ( relation_rng @ SV98 ) )
= $false )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2505]) ).
thf(2630,plain,
! [SV100: $i,SV328: $i,SV286: $i] :
( ( ( ( SV286
!= ( apply @ SV328 @ SV100 ) ) )
= $true )
| ( ( ~ ( in @ SV100 @ ( relation_dom @ SV328 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV100 @ SV286 ) @ SV328 )
= $true )
| ( ( function @ SV328 )
= $false )
| ( ( relation @ SV328 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2506]) ).
thf(2631,plain,
! [SV406: $i,SV100: $i,SV428: $i] :
( ( ( function @ SV428 )
= $false )
| ( ( ~ ( relation @ SV428 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV100 @ SV406 ) @ SV428 )
| ( SV406
= ( apply @ SV428 @ SV100 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2507]) ).
thf(2632,plain,
! [SV407: $i,SV100: $i,SV429: $i] :
( ( ( function @ SV429 )
= $false )
| ( ( ~ ( relation @ SV429 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV100 @ SV407 ) @ SV429 )
| ( in @ SV100 @ ( relation_dom @ SV429 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2508]) ).
thf(2633,plain,
! [SV101: $i,SV215: $i,SV451: $i] :
( ( ( relation @ SV451 )
= $false )
| ( ( ~ ( ~ ( ! [SY1009: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ SY1009 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY1009 @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV215 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV451 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK10_SY395 @ SV451 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV215 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV451 ) ) )
| ( SV451
= ( relation_composition @ SV101 @ SV215 ) ) )
= $true )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2509]) ).
thf(2634,plain,
! [SV215: $i,SV101: $i,SV452: $i] :
( ( ( relation @ SV452 )
= $false )
| ( ( ( SV452
!= ( relation_composition @ SV101 @ SV215 ) )
| ~ ( ~ ! [SY1010: $i,SY1011: $i] :
( ! [SY783: $i] :
( ~ ( in @ ( ordered_pair @ SY1010 @ SY783 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY783 @ SY1011 ) @ SV215 ) )
| ( in @ ( ordered_pair @ SY1010 @ SY1011 ) @ SV452 ) )
| ~ ! [SY1013: $i,SY1014: $i] :
( ~ ( in @ ( ordered_pair @ SY1013 @ SY1014 ) @ SV452 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1013 @ ( sK7_F @ SY1014 @ SY1013 @ SV452 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY1014 @ SY1013 @ SV452 @ SV215 @ SV101 ) @ SY1014 ) @ SV215 ) ) ) ) )
= $true )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2510]) ).
thf(2635,plain,
! [SV461: $i,SV430: $i,SV177: $i,SV102: $i] :
( ( ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SV430 @ SV461 ) )
= $false )
| ( ( in @ SV102 @ SV430 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2512]) ).
thf(2636,plain,
! [SV453: $i,SV431: $i,SV177: $i,SV102: $i] :
( ( ( in @ ( ordered_pair @ SV102 @ SV177 ) @ ( cartesian_product2 @ SV431 @ SV453 ) )
= $false )
| ( ( in @ SV177 @ SV453 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2513]) ).
thf(2637,plain,
! [SV103: $i,SV408: $i] :
( ( ( ! [SY990: $i] :
( ~ ( subset @ SY990 @ SV408 )
| ( in @ SY990 @ ( sK3_SY386 @ SV408 @ SV103 ) ) ) )
= $true )
| ( ( ~ ( in @ SV408 @ ( sK2_B @ SV103 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2514]) ).
thf(2638,plain,
! [SV103: $i,SV408: $i] :
( ( ( in @ ( sK3_SY386 @ SV408 @ SV103 ) @ ( sK2_B @ SV103 ) )
= $true )
| ( ( ~ ( in @ SV408 @ ( sK2_B @ SV103 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2515]) ).
thf(2639,plain,
! [SV472: $i,SV103: $i,SV462: $i] :
( ( ~ ( in @ SV462 @ ( sK2_B @ SV103 ) )
| ~ ( subset @ SV472 @ SV462 )
| ( in @ SV472 @ ( sK2_B @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2516]) ).
thf(2640,plain,
! [SV288: $i,SV330: $i,SV105: $i] :
( ( ( in @ SV105 @ ( relation_rng @ SV330 ) )
= $false )
| ( ( in @ SV105 @ SV288 )
= $false )
| ( ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SV288 @ SV330 ) ) )
= $true )
| ( ( relation @ SV330 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2520]) ).
thf(2641,plain,
! [SV433: $i,SV409: $i,SV105: $i] :
( ( ( ~ ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SV409 @ SV433 ) ) ) )
= $true )
| ( ( in @ SV105 @ SV409 )
= $true )
| ( ( relation @ SV433 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2521]) ).
thf(2642,plain,
! [SV434: $i,SV410: $i,SV105: $i] :
( ( ( ~ ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SV410 @ SV434 ) ) ) )
= $true )
| ( ( in @ SV105 @ ( relation_rng @ SV434 ) )
= $true )
| ( ( relation @ SV434 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2522]) ).
thf(2643,plain,
! [SV378: $i,SV178: $i,SV332: $i,SV107: $i] :
( ( ( in @ SV107 @ SV332 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ SV378 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SV332 ) @ SV378 ) )
= $true )
| ( ( relation @ SV378 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2525]) ).
thf(2644,plain,
! [SV437: $i,SV178: $i,SV107: $i,SV455: $i] :
( ( ( relation @ SV455 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SV437 ) @ SV455 ) )
| ( in @ SV107 @ SV437 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2526]) ).
thf(2645,plain,
! [SV438: $i,SV178: $i,SV107: $i,SV456: $i] :
( ( ( relation @ SV456 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SV438 ) @ SV456 ) )
| ( in @ ( ordered_pair @ SV107 @ SV178 ) @ SV456 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2527]) ).
thf(2646,plain,
! [SV108: $i,SV379: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV379 @ SV108 ) @ ( sK20_SY399 @ SV379 @ SV108 ) ) @ SV108 ) )
= $false )
| ( ( subset @ SV108 @ SV379 )
= $true )
| ( ( relation @ SV379 )
= $false )
| ( ( relation @ SV108 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2528]) ).
thf(2647,plain,
! [SV108: $i,SV379: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK19_C @ SV379 @ SV108 ) @ ( sK20_SY399 @ SV379 @ SV108 ) ) @ SV379 ) )
= $false )
| ( ( subset @ SV108 @ SV379 )
= $true )
| ( ( relation @ SV379 )
= $false )
| ( ( relation @ SV108 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2528]) ).
thf(2648,plain,
! [SV380: $i,SV108: $i,SV473: $i] :
( ( ( ! [SY1017: $i] :
( ~ ( in @ ( ordered_pair @ SV473 @ SY1017 ) @ SV108 )
| ( in @ ( ordered_pair @ SV473 @ SY1017 ) @ SV380 ) ) )
= $true )
| ( ( subset @ SV108 @ SV380 )
= $false )
| ( ( relation @ SV380 )
= $false )
| ( ( relation @ SV108 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2529]) ).
thf(2649,plain,
! [SV228: $i,SV290: $i] :
( ( ( in @ ( sK30_C @ SV290 @ SV228 ) @ SV290 )
= $false )
| ( ( ( sK30_C @ SV290 @ SV228 )
= SV228 )
= $false )
| ( ( SV290
= ( singleton @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2530]) ).
thf(2650,plain,
! [SV291: $i,SV229: $i,SV463: $i] :
( ( ( ( SV463 != SV229 ) )
= $true )
| ( ( in @ SV463 @ SV291 )
= $true )
| ( ( SV291
= ( singleton @ SV229 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2531]) ).
thf(2651,plain,
! [SV229: $i,SV291: $i,SV464: $i] :
( ( ( ~ ( in @ SV464 @ SV291 ) )
= $true )
| ( ( SV464 = SV229 )
= $true )
| ( ( SV291
= ( singleton @ SV229 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2532]) ).
thf(2652,plain,
! [SV381: $i] :
( ( ( relation @ SV381 )
= $false )
| ( ( empty @ SV381 )
= $false )
| ( ( ~ ( function @ SV381 ) )
= $true )
| ( ( function @ SV381 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2533]) ).
thf(2653,plain,
! [SV382: $i] :
( ( ( relation @ SV382 )
= $false )
| ( ( empty @ SV382 )
= $false )
| ( ( ~ ( function @ SV382 ) )
= $true )
| ( ( relation @ SV382 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2534]) ).
thf(2654,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ( function @ SV465 )
| ~ ( relation @ SV465 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) )
| ( SV465
= ( function_inverse @ SV110 ) ) )
= $true )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2535]) ).
thf(2655,plain,
! [SV110: $i] :
( ( ( ~ ! [SY637: $i] :
( ~ ( function @ SY637 )
| ~ ( relation @ SY637 )
| ( SY637
!= ( function_inverse @ SV110 ) )
| ~ ( ~ ~ ( ~ ! [SY638: $i,SY639: $i] :
( ( SY639
!= ( apply @ SY637 @ SY638 ) )
| ~ ( in @ SY638 @ ( relation_rng @ SV110 ) )
| ( SY638
= ( apply @ SV110 @ SY639 ) ) )
| ~ ! [SY640: $i,SY641: $i] :
( ( SY641
!= ( apply @ SY637 @ SY640 ) )
| ~ ( in @ SY640 @ ( relation_rng @ SV110 ) )
| ( in @ SY641 @ ( relation_dom @ SV110 ) ) ) )
| ~ ~ ( ~ ! [SY642: $i,SY643: $i] :
( ( SY642
!= ( apply @ SV110 @ SY643 ) )
| ~ ( in @ SY643 @ ( relation_dom @ SV110 ) )
| ( SY643
= ( apply @ SY637 @ SY642 ) ) )
| ~ ! [SY644: $i] :
( ! [SY645: $i] :
( ( SY644
!= ( apply @ SV110 @ SY645 ) )
| ~ ( in @ SY645 @ ( relation_dom @ SV110 ) ) )
| ( in @ SY644 @ ( relation_rng @ SV110 ) ) ) ) ) ) )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2536]) ).
thf(2656,plain,
! [SV110: $i] :
( ( ( ~ ! [SY646: $i] :
( ~ ( function @ SY646 )
| ~ ( relation @ SY646 )
| ( SY646
!= ( function_inverse @ SV110 ) )
| ( ( relation_dom @ SY646 )
= ( relation_rng @ SV110 ) ) ) )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2536]) ).
thf(2657,plain,
! [SV466: $i,SV439: $i,SV179: $i,SV111: $i] :
( ( ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SV439 @ SV466 ) )
= $false )
| ( ( in @ SV111 @ SV439 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2540]) ).
thf(2658,plain,
! [SV457: $i,SV440: $i,SV179: $i,SV111: $i] :
( ( ( in @ ( ordered_pair @ SV111 @ SV179 ) @ ( cartesian_product2 @ SV440 @ SV457 ) )
= $false )
| ( ( in @ SV179 @ SV457 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2541]) ).
thf(2659,plain,
! [SV113: $i,SV474: $i] :
( ( ( ~ ( in @ SV474 @ ( relation_dom @ SV113 ) )
| ! [SY1018: $i] :
( ( SY1018
!= ( apply @ SV113 @ SV474 ) )
| ( in @ ( ordered_pair @ SV474 @ SY1018 ) @ SV113 ) ) )
= $true )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2542]) ).
thf(2660,plain,
! [SV113: $i,SV475: $i] :
( ( ( ~ ( in @ SV475 @ ( relation_dom @ SV113 ) )
| ! [SY1019: $i] :
( ~ ( in @ ( ordered_pair @ SV475 @ SY1019 ) @ SV113 )
| ( SY1019
= ( apply @ SV113 @ SV475 ) ) ) )
= $true )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2543]) ).
thf(2661,plain,
! [SV113: $i,SV476: $i] :
( ( ( ( in @ SV476 @ ( relation_dom @ SV113 ) )
| ! [SY1020: $i] :
( ( SY1020
!= ( apply @ SV113 @ SV476 ) )
| ( SY1020 = empty_set ) ) )
= $true )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2544]) ).
thf(2662,plain,
! [SV113: $i,SV477: $i] :
( ( ( ( in @ SV477 @ ( relation_dom @ SV113 ) )
| ! [SY1021: $i] :
( ( SY1021 != empty_set )
| ( SY1021
= ( apply @ SV113 @ SV477 ) ) ) )
= $true )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2545]) ).
thf(2663,plain,
! [SV114: $i,SV301: $i,SV338: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV338 )
| ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV114 ) ) )
= $false )
| ( ( SV338
= ( set_union2 @ SV114 @ SV301 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2546]) ).
thf(2664,plain,
! [SV114: $i,SV301: $i,SV338: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV338 )
| ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV301 ) ) )
= $false )
| ( ( SV338
= ( set_union2 @ SV114 @ SV301 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2546]) ).
thf(2665,plain,
! [SV114: $i,SV301: $i,SV338: $i] :
( ( ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV114 )
= $true )
| ( ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV301 )
= $true )
| ( ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV338 )
= $true )
| ( ( SV338
= ( set_union2 @ SV114 @ SV301 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2547]) ).
thf(2666,plain,
! [SV302: $i,SV114: $i,SV339: $i,SV478: $i] :
( ( ( ~ ( in @ SV478 @ SV339 )
| ( in @ SV478 @ SV114 )
| ( in @ SV478 @ SV302 ) )
= $true )
| ( ( SV339
= ( set_union2 @ SV114 @ SV302 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2548]) ).
thf(2667,plain,
! [SV302: $i,SV339: $i,SV114: $i] :
( ( ( ~ ! [SY896: $i] :
( ~ ( in @ SY896 @ SV114 )
| ( in @ SY896 @ SV339 ) )
| ~ ! [SY897: $i] :
( ~ ( in @ SY897 @ SV302 )
| ( in @ SY897 @ SV339 ) ) )
= $false )
| ( ( SV339
= ( set_union2 @ SV114 @ SV302 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2549]) ).
thf(2668,plain,
! [SV116: $i,SV306: $i,SV342: $i] :
( ( ( ~ ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV116 ) )
= $true )
| ( ( ~ ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV306 ) )
= $true )
| ( ( ~ ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV342 ) )
= $true )
| ( ( SV342
= ( set_intersection2 @ SV116 @ SV306 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2550]) ).
thf(2669,plain,
! [SV116: $i,SV306: $i,SV342: $i] :
( ( ( ~ ( ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV116 )
| ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV342 ) ) )
= $false )
| ( ( SV342
= ( set_intersection2 @ SV116 @ SV306 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2551]) ).
thf(2670,plain,
! [SV116: $i,SV306: $i,SV342: $i] :
( ( ( ~ ( ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV306 )
| ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV342 ) ) )
= $false )
| ( ( SV342
= ( set_intersection2 @ SV116 @ SV306 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2551]) ).
thf(2671,plain,
! [SV343: $i,SV307: $i,SV116: $i,SV479: $i] :
( ( ( ~ ( in @ SV479 @ SV116 )
| ~ ( in @ SV479 @ SV307 )
| ( in @ SV479 @ SV343 ) )
= $true )
| ( ( SV343
= ( set_intersection2 @ SV116 @ SV307 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2552]) ).
thf(2672,plain,
! [SV307: $i,SV116: $i,SV343: $i] :
( ( ( ~ ! [SY899: $i] :
( ~ ( in @ SY899 @ SV343 )
| ( in @ SY899 @ SV116 ) )
| ~ ! [SY900: $i] :
( ~ ( in @ SY900 @ SV343 )
| ( in @ SY900 @ SV307 ) ) )
= $false )
| ( ( SV343
= ( set_intersection2 @ SV116 @ SV307 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2553]) ).
thf(2673,plain,
! [SV251: $i,SV308: $i] :
( ( ( ( ( sK44_C @ SV308 @ SV251 )
!= ( sK45_SY414 @ SV308 @ SV251 ) )
| ~ ( in @ ( sK44_C @ SV308 @ SV251 ) @ SV251 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 ) )
= $true )
| ( ( SV308
= ( identity_relation @ SV251 ) )
= $true )
| ( ( relation @ SV308 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2554]) ).
thf(2674,plain,
! [SV251: $i,SV308: $i] :
( ( ( ~ ( ( ( sK44_C @ SV308 @ SV251 )
= ( sK45_SY414 @ SV308 @ SV251 ) )
| ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 ) )
| ~ ( ( in @ ( sK44_C @ SV308 @ SV251 ) @ SV251 )
| ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 ) ) )
= $false )
| ( ( SV308
= ( identity_relation @ SV251 ) )
= $true )
| ( ( relation @ SV308 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2555]) ).
thf(2675,plain,
! [SV309: $i,SV252: $i] :
( ( ( ! [SY861: $i,SY862: $i] :
( ( SY861 != SY862 )
| ~ ( in @ SY861 @ SV252 )
| ( in @ ( ordered_pair @ SY861 @ SY862 ) @ SV309 ) ) )
= $true )
| ( ( SV309
= ( identity_relation @ SV252 ) )
= $false )
| ( ( relation @ SV309 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2556]) ).
thf(2676,plain,
! [SV252: $i,SV309: $i] :
( ( ( ~ ( ~ ! [SY863: $i,SY864: $i] :
( ~ ( in @ ( ordered_pair @ SY863 @ SY864 ) @ SV309 )
| ( SY863 = SY864 ) )
| ~ ! [SY865: $i] :
( ! [SY866: $i] :
~ ( in @ ( ordered_pair @ SY865 @ SY866 ) @ SV309 )
| ( in @ SY865 @ SV252 ) ) ) )
= $true )
| ( ( SV309
= ( identity_relation @ SV252 ) )
= $false )
| ( ( relation @ SV309 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2557]) ).
thf(2677,plain,
! [SV310: $i,SV344: $i,SV117: $i] :
( ( ( in @ SV117 @ ( relation_dom @ SV344 ) )
= $false )
| ( ( in @ SV117 @ SV310 )
= $false )
| ( ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SV344 @ SV310 ) ) )
= $true )
| ( ( relation @ SV344 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2558]) ).
thf(2678,plain,
! [SV418: $i,SV441: $i,SV117: $i] :
( ( ( ~ ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SV441 @ SV418 ) ) ) )
= $true )
| ( ( in @ SV117 @ SV418 )
= $true )
| ( ( relation @ SV441 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2559]) ).
thf(2679,plain,
! [SV419: $i,SV442: $i,SV117: $i] :
( ( ( ~ ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SV442 @ SV419 ) ) ) )
= $true )
| ( ( in @ SV117 @ ( relation_dom @ SV442 ) )
= $true )
| ( ( relation @ SV442 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2560]) ).
thf(2680,plain,
! [SV253: $i,SV311: $i] :
( ( ( ~ ( in @ ( sK50_C @ SV311 @ SV253 ) @ SV253 )
| ~ ( ( ( apply @ SV311 @ ( sK50_C @ SV311 @ SV253 ) )
!= ( sK50_C @ SV311 @ SV253 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV311 )
!= SV253 ) )
= $true )
| ( ( SV311
= ( identity_relation @ SV253 ) )
= $true )
| ( ( function @ SV311 )
= $false )
| ( ( relation @ SV311 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2561]) ).
thf(2681,plain,
! [SV391: $i,SV420: $i] :
( ( ( relation @ SV420 )
= $false )
| ( ( function @ SV420 )
= $false )
| ( ( ( SV420
!= ( identity_relation @ SV391 ) )
| ! [SY997: $i] :
( ~ ( in @ SY997 @ SV391 )
| ( ( apply @ SV420 @ SY997 )
= SY997 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2562]) ).
thf(2682,plain,
! [SV392: $i,SV421: $i] :
( ( ( relation @ SV421 )
= $false )
| ( ( function @ SV421 )
= $false )
| ( ( ( SV421
!= ( identity_relation @ SV392 ) )
| ( ( relation_dom @ SV421 )
= SV392 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2563]) ).
thf(2683,plain,
! [SV345: $i,SV312: $i,SV118: $i,SV480: $i] :
( ( ( ! [SY1022: $i] :
( ~ ( in @ SV480 @ SV118 )
| ~ ( in @ SY1022 @ SV312 )
| ( ( sK23_D @ SV345 @ SV312 @ SV118 )
!= ( ordered_pair @ SV480 @ SY1022 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV345 @ SV312 @ SV118 ) @ SV345 ) )
= $true )
| ( ( SV345
= ( cartesian_product2 @ SV118 @ SV312 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2564]) ).
thf(2684,plain,
! [SV118: $i,SV312: $i,SV345: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK24_SY403 @ SV345 @ SV312 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK25_SY405 @ SV345 @ SV312 @ SV118 ) @ SV312 ) )
| ( ( sK23_D @ SV345 @ SV312 @ SV118 )
!= ( ordered_pair @ ( sK24_SY403 @ SV345 @ SV312 @ SV118 ) @ ( sK25_SY405 @ SV345 @ SV312 @ SV118 ) ) ) )
= $false )
| ( ( in @ ( sK23_D @ SV345 @ SV312 @ SV118 ) @ SV345 )
= $true )
| ( ( SV345
= ( cartesian_product2 @ SV118 @ SV312 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2565]) ).
thf(2685,plain,
! [SV346: $i,SV481: $i,SV313: $i,SV118: $i] :
( ( ( ! [SY1023: $i,SY1024: $i] :
( ~ ( in @ SY1023 @ SV118 )
| ~ ( in @ SY1024 @ SV313 )
| ( SV481
!= ( ordered_pair @ SY1023 @ SY1024 ) ) )
| ( in @ SV481 @ SV346 ) )
= $true )
| ( ( SV346
= ( cartesian_product2 @ SV118 @ SV313 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2566]) ).
thf(2686,plain,
! [SV118: $i,SV313: $i,SV346: $i,SV482: $i] :
( ( ( ~ ( in @ SV482 @ SV346 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SV482 @ SV346 @ SV313 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK22_SY400 @ SV482 @ SV346 @ SV313 @ SV118 ) @ SV313 ) )
| ( SV482
!= ( ordered_pair @ ( sK21_E @ SV482 @ SV346 @ SV313 @ SV118 ) @ ( sK22_SY400 @ SV482 @ SV346 @ SV313 @ SV118 ) ) ) ) )
= $true )
| ( ( SV346
= ( cartesian_product2 @ SV118 @ SV313 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2567]) ).
thf(2687,plain,
! [SV467: $i,SV254: $i,SV316: $i] :
( ( ( ~ ( in @ ( sK15_C @ SV316 @ SV254 ) @ SV467 ) )
= $true )
| ( ( ~ ( in @ SV467 @ SV254 ) )
= $true )
| ( ( ~ ( in @ ( sK15_C @ SV316 @ SV254 ) @ SV316 ) )
= $true )
| ( ( SV316
= ( union @ SV254 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2568]) ).
thf(2688,plain,
! [SV254: $i,SV316: $i] :
( ( ( ~ ( in @ ( sK15_C @ SV316 @ SV254 ) @ ( sK16_SY398 @ SV316 @ SV254 ) ) )
= $false )
| ( ( in @ ( sK15_C @ SV316 @ SV254 ) @ SV316 )
= $true )
| ( ( SV316
= ( union @ SV254 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2569]) ).
thf(2689,plain,
! [SV254: $i,SV316: $i] :
( ( ( ~ ( in @ ( sK16_SY398 @ SV316 @ SV254 ) @ SV254 ) )
= $false )
| ( ( in @ ( sK15_C @ SV316 @ SV254 ) @ SV316 )
= $true )
| ( ( SV316
= ( union @ SV254 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2569]) ).
thf(2690,plain,
! [SV317: $i,SV255: $i,SV468: $i] :
( ( ( ! [SY1016: $i] :
( ~ ( in @ SV468 @ SY1016 )
| ~ ( in @ SY1016 @ SV255 ) ) )
= $true )
| ( ( in @ SV468 @ SV317 )
= $true )
| ( ( SV317
= ( union @ SV255 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2570]) ).
thf(2691,plain,
! [SV255: $i,SV317: $i,SV469: $i] :
( ( ( ~ ( in @ SV469 @ SV317 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV469 @ ( sK14_D @ SV469 @ SV317 @ SV255 ) )
| ~ ( in @ ( sK14_D @ SV469 @ SV317 @ SV255 ) @ SV255 ) ) )
= $true )
| ( ( SV317
= ( union @ SV255 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2571]) ).
thf(2692,plain,
! [SV120: $i,SV393: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV393 ) ) )
= $false )
| ( ( SV120 = SV393 )
= $true )
| ( ( relation @ SV393 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2572]) ).
thf(2693,plain,
! [SV120: $i,SV393: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV120 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV393 ) ) )
= $false )
| ( ( SV120 = SV393 )
= $true )
| ( ( relation @ SV393 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2572]) ).
thf(2694,plain,
! [SV394: $i,SV120: $i] :
( ( ( ~ ! [SY964: $i,SY965: $i] :
( ~ ( in @ ( ordered_pair @ SY964 @ SY965 ) @ SV120 )
| ( in @ ( ordered_pair @ SY964 @ SY965 ) @ SV394 ) )
| ~ ! [SY966: $i,SY967: $i] :
( ~ ( in @ ( ordered_pair @ SY966 @ SY967 ) @ SV394 )
| ( in @ ( ordered_pair @ SY966 @ SY967 ) @ SV120 ) ) )
= $false )
| ( ( SV120 = SV394 )
= $false )
| ( ( relation @ SV394 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2573]) ).
thf(2695,plain,
! [SV145: $i,SV347: $i,SV43: $i] :
( ( ( in @ SV43 @ ( relation_dom @ ( relation_composition @ SV347 @ SV145 ) ) )
= $false )
| ( ( ( apply @ ( relation_composition @ SV347 @ SV145 ) @ SV43 )
= ( apply @ SV145 @ ( apply @ SV347 @ SV43 ) ) )
= $true )
| ( ( function @ SV347 )
= $false )
| ( ( relation @ SV347 )
= $false )
| ( ( function @ SV145 )
= $false )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2574]) ).
thf(2696,plain,
! [SV348: $i,SV146: $i,SV44: $i] :
( ( ( in @ SV44 @ ( relation_dom @ SV146 ) )
= $false )
| ( ( ( apply @ ( relation_composition @ SV146 @ SV348 ) @ SV44 )
= ( apply @ SV348 @ ( apply @ SV146 @ SV44 ) ) )
= $true )
| ( ( function @ SV348 )
= $false )
| ( ( relation @ SV348 )
= $false )
| ( ( function @ SV146 )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2575]) ).
thf(2697,plain,
! [SV351: $i,SV424: $i] :
( ( ( ~ ( ~ ( in @ ( sK33_SY406 @ SV424 @ SV351 ) @ SV351 )
| ~ ~ ( in @ ( sK32_C @ SV424 @ SV351 ) @ ( sK33_SY406 @ SV424 @ SV351 ) ) )
| ~ ( in @ ( sK32_C @ SV424 @ SV351 ) @ SV424 ) )
= $true )
| ( ( SV424
= ( set_meet @ SV351 ) )
= $true )
| ( ( SV351 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2576]) ).
thf(2698,plain,
! [SV424: $i,SV351: $i] :
( ( ( ! [SY998: $i] :
( ~ ( in @ SY998 @ SV351 )
| ( in @ ( sK32_C @ SV424 @ SV351 ) @ SY998 ) )
| ( in @ ( sK32_C @ SV424 @ SV351 ) @ SV424 ) )
= $true )
| ( ( SV424
= ( set_meet @ SV351 ) )
= $true )
| ( ( SV351 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2577]) ).
thf(2699,plain,
! [SV352: $i,SV425: $i] :
( ( ( ~ ! [SY999: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY999 @ SV425 @ SV352 ) @ SV352 )
| ~ ~ ( in @ SY999 @ ( sK31_D @ SY999 @ SV425 @ SV352 ) ) )
| ( in @ SY999 @ SV425 ) ) )
= $false )
| ( ( SV425
= ( set_meet @ SV352 ) )
= $false )
| ( ( SV352 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2578]) ).
thf(2700,plain,
! [SV352: $i,SV425: $i] :
( ( ( ~ ! [SY1000: $i] :
( ~ ( in @ SY1000 @ SV425 )
| ! [SY914: $i] :
( ~ ( in @ SY914 @ SV352 )
| ( in @ SY1000 @ SY914 ) ) ) )
= $false )
| ( ( SV425
= ( set_meet @ SV352 ) )
= $false )
| ( ( SV352 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2578]) ).
thf(2701,plain,
! [SV202: $i,SV265: $i] :
( ( ( function @ SV265 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV265 )
= $false )
| ( ( function @ ( relation_composition @ SV202 @ SV265 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2581]) ).
thf(2702,plain,
! [SV203: $i,SV266: $i] :
( ( ( function @ SV266 )
= $false )
| ( ( relation @ SV203 )
= $false )
| ( ( function @ SV203 )
= $false )
| ( ( relation @ SV266 )
= $false )
| ( ( relation @ ( relation_composition @ SV203 @ SV266 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2582]) ).
thf(2703,plain,
! [SV271: $i,SV87: $i,SV320: $i,SV446: $i] :
( ( ( in @ SV446 @ ( relation_dom @ SV320 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV446 @ SV87 ) @ SV320 ) )
= $true )
| ( ( ~ ( in @ SV446 @ SV271 ) )
= $true )
| ( ( in @ SV87 @ ( relation_image @ SV320 @ SV271 ) )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2583]) ).
thf(2704,plain,
! [SV87: $i,SV272: $i,SV321: $i] :
( ( ( ~ ( ~ ( in @ ( sK52_D @ SV321 @ SV272 @ SV87 ) @ ( relation_dom @ SV321 ) )
| ~ ( in @ ( ordered_pair @ ( sK52_D @ SV321 @ SV272 @ SV87 ) @ SV87 ) @ SV321 ) ) )
= $true )
| ( ( in @ SV87 @ ( relation_image @ SV321 @ SV272 ) )
= $false )
| ( ( relation @ SV321 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2584]) ).
thf(2705,plain,
! [SV87: $i,SV272: $i,SV321: $i] :
( ( ( in @ ( sK52_D @ SV321 @ SV272 @ SV87 ) @ SV272 )
= $true )
| ( ( in @ SV87 @ ( relation_image @ SV321 @ SV272 ) )
= $false )
| ( ( relation @ SV321 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2585]) ).
thf(2706,plain,
! [SV88: $i,SV274: $i,SV322: $i] :
( ( ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV88 )
= $false )
| ( ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV274 )
= $true )
| ( ( ~ ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV322 ) )
= $true )
| ( ( SV322
= ( set_difference @ SV88 @ SV274 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2586]) ).
thf(2707,plain,
! [SV88: $i,SV274: $i,SV322: $i] :
( ( ( ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV88 )
| ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV322 ) )
= $true )
| ( ( SV322
= ( set_difference @ SV88 @ SV274 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2587]) ).
thf(2708,plain,
! [SV88: $i,SV274: $i,SV322: $i] :
( ( ( ~ ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV274 )
| ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV322 ) )
= $true )
| ( ( SV322
= ( set_difference @ SV88 @ SV274 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2588]) ).
thf(2709,plain,
! [SV323: $i,SV275: $i,SV88: $i,SV470: $i] :
( ( ( ~ ( in @ SV470 @ SV88 )
| ( in @ SV470 @ SV275 ) )
= $true )
| ( ( in @ SV470 @ SV323 )
= $true )
| ( ( SV323
= ( set_difference @ SV88 @ SV275 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2589]) ).
thf(2710,plain,
! [SV275: $i,SV88: $i,SV323: $i] :
( ( ( ~ ! [SY884: $i] :
( ~ ( in @ SY884 @ SV323 )
| ( in @ SY884 @ SV88 ) ) )
= $false )
| ( ( SV323
= ( set_difference @ SV88 @ SV275 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2590]) ).
thf(2711,plain,
! [SV88: $i,SV275: $i,SV323: $i] :
( ( ( ~ ! [SY885: $i] :
( ~ ( in @ SY885 @ SV323 )
| ~ ( in @ SY885 @ SV275 ) ) )
= $false )
| ( ( SV323
= ( set_difference @ SV88 @ SV275 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2590]) ).
thf(2712,plain,
! [SV89: $i,SV174: $i,SV398: $i] :
( ( ( ~ ( ~ ( in @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV174 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 ) ) )
= $false )
| ( ( SV398
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2593]) ).
thf(2713,plain,
! [SV89: $i,SV174: $i,SV398: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) @ SV89 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV174 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 ) ) ) )
= $false )
| ( ( SV398
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2593]) ).
thf(2714,plain,
! [SV399: $i,SV174: $i,SV89: $i] :
( ( ( ~ ! [SY968: $i,SY969: $i] :
( ~ ( in @ SY969 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY968 @ SY969 ) @ SV174 )
| ( in @ ( ordered_pair @ SY968 @ SY969 ) @ SV399 ) )
| ~ ~ ( ~ ! [SY970: $i,SY971: $i] :
( ~ ( in @ ( ordered_pair @ SY970 @ SY971 ) @ SV399 )
| ( in @ SY971 @ SV89 ) )
| ~ ! [SY972: $i,SY973: $i] :
( ~ ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV399 )
| ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV174 ) ) ) )
= $false )
| ( ( SV399
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2594]) ).
thf(2715,plain,
! [SV90: $i,SV276: $i,SV324: $i] :
( ( ( ~ ( in @ ( sK27_D @ SV324 @ SV276 @ SV90 ) @ SV324 )
| ( ( sK27_D @ SV324 @ SV276 @ SV90 )
!= SV90 ) )
= $true )
| ( ( SV324
= ( unordered_pair @ SV90 @ SV276 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2595]) ).
thf(2716,plain,
! [SV90: $i,SV276: $i,SV324: $i] :
( ( ( ~ ( in @ ( sK27_D @ SV324 @ SV276 @ SV90 ) @ SV324 )
| ( ( sK27_D @ SV324 @ SV276 @ SV90 )
!= SV276 ) )
= $true )
| ( ( SV324
= ( unordered_pair @ SV90 @ SV276 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2596]) ).
thf(2717,plain,
! [SV277: $i,SV90: $i,SV325: $i,SV471: $i] :
( ( ( ~ ( in @ SV471 @ SV325 ) )
= $true )
| ( ( ( SV471 = SV90 )
| ( SV471 = SV277 ) )
= $true )
| ( ( SV325
= ( unordered_pair @ SV90 @ SV277 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2598]) ).
thf(2718,plain,
! [SV277: $i,SV325: $i,SV90: $i] :
( ( ( ~ ! [SY887: $i] :
( ( SY887 != SV90 )
| ( in @ SY887 @ SV325 ) ) )
= $false )
| ( ( SV325
= ( unordered_pair @ SV90 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2599]) ).
thf(2719,plain,
! [SV90: $i,SV325: $i,SV277: $i] :
( ( ( ~ ! [SY888: $i] :
( ( SY888 != SV277 )
| ( in @ SY888 @ SV325 ) ) )
= $false )
| ( ( SV325
= ( unordered_pair @ SV90 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2599]) ).
thf(2720,plain,
! [SV210: $i,SV279: $i,SV459: $i] :
( ( ( in @ SV459 @ SV279 )
= $false )
| ( ( subset @ SV459 @ SV210 )
= $true )
| ( ( SV279
= ( powerset @ SV210 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2601]) ).
thf(2721,plain,
! [SV279: $i,SV210: $i,SV460: $i] :
( ( ( subset @ SV460 @ SV210 )
= $false )
| ( ( in @ SV460 @ SV279 )
= $true )
| ( ( SV279
= ( powerset @ SV210 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2602]) ).
thf(2722,plain,
! [SV483: $i,SV91: $i,SV362: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK63_C @ SV362 @ SV91 ) @ SV483 ) @ SV91 ) )
= $true )
| ( ( ~ ( in @ ( sK63_C @ SV362 @ SV91 ) @ SV362 ) )
= $true )
| ( ( SV362
= ( relation_dom @ SV91 ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2603]) ).
thf(2723,plain,
! [SV363: $i,SV91: $i,SV484: $i] :
( ( ( ! [SY1025: $i] :
~ ( in @ ( ordered_pair @ SV484 @ SY1025 ) @ SV91 )
| ( in @ SV484 @ SV363 ) )
= $true )
| ( ( SV363
= ( relation_dom @ SV91 ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2605]) ).
thf(2724,plain,
! [SV91: $i,SV363: $i,SV485: $i] :
( ( ( ~ ( in @ SV485 @ SV363 )
| ( in @ ( ordered_pair @ SV485 @ ( sK62_D @ SV485 @ SV363 @ SV91 ) ) @ SV91 ) )
= $true )
| ( ( SV363
= ( relation_dom @ SV91 ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2606]) ).
thf(2725,plain,
! [SV92: $i,SV364: $i,SV400: $i] :
( ( ( ! [SY974: $i] :
( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SY974 ) @ SV92 )
| ~ ( in @ SY974 @ SV364 ) ) )
= $true )
| ( ( ~ ( in @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SV400 ) )
= $true )
| ( ( SV400
= ( relation_inverse_image @ SV92 @ SV364 ) )
= $true )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2607]) ).
thf(2726,plain,
! [SV92: $i,SV364: $i,SV400: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ ( sK36_SY409 @ SV400 @ SV364 @ SV92 ) ) @ SV92 )
| ~ ( in @ ( sK36_SY409 @ SV400 @ SV364 @ SV92 ) @ SV364 ) ) )
= $true )
| ( ( in @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SV400 )
= $true )
| ( ( SV400
= ( relation_inverse_image @ SV92 @ SV364 ) )
= $true )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2608]) ).
thf(2727,plain,
! [SV401: $i,SV365: $i,SV92: $i] :
( ( ( ! [SY975: $i] :
( ! [SY931: $i] :
( ~ ( in @ ( ordered_pair @ SY975 @ SY931 ) @ SV92 )
| ~ ( in @ SY931 @ SV365 ) )
| ( in @ SY975 @ SV401 ) ) )
= $true )
| ( ( SV401
= ( relation_inverse_image @ SV92 @ SV365 ) )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2609]) ).
thf(2728,plain,
! [SV92: $i,SV365: $i,SV401: $i] :
( ( ( ! [SY977: $i] :
( ~ ( in @ SY977 @ SV401 )
| ~ ( ~ ( in @ ( ordered_pair @ SY977 @ ( sK34_E @ SY977 @ SV401 @ SV365 @ SV92 ) ) @ SV92 )
| ~ ( in @ ( sK34_E @ SY977 @ SV401 @ SV365 @ SV92 ) @ SV365 ) ) ) )
= $true )
| ( ( SV401
= ( relation_inverse_image @ SV92 @ SV365 ) )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2610]) ).
thf(2729,plain,
! [SV93: $i,SV366: $i,SV402: $i] :
( ( ( ! [SY978: $i] :
( ~ ( in @ ( ordered_pair @ SY978 @ ( sK38_D @ SV402 @ SV366 @ SV93 ) ) @ SV93 )
| ~ ( in @ SY978 @ SV366 ) ) )
= $true )
| ( ( ~ ( in @ ( sK38_D @ SV402 @ SV366 @ SV93 ) @ SV402 ) )
= $true )
| ( ( SV402
= ( relation_image @ SV93 @ SV366 ) )
= $true )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2611]) ).
thf(2730,plain,
! [SV93: $i,SV366: $i,SV402: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SV402 @ SV366 @ SV93 ) @ ( sK38_D @ SV402 @ SV366 @ SV93 ) ) @ SV93 )
| ~ ( in @ ( sK39_SY411 @ SV402 @ SV366 @ SV93 ) @ SV366 ) ) )
= $true )
| ( ( in @ ( sK38_D @ SV402 @ SV366 @ SV93 ) @ SV402 )
= $true )
| ( ( SV402
= ( relation_image @ SV93 @ SV366 ) )
= $true )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2612]) ).
thf(2731,plain,
! [SV403: $i,SV367: $i,SV93: $i] :
( ( ( ! [SY979: $i] :
( ! [SY937: $i] :
( ~ ( in @ ( ordered_pair @ SY937 @ SY979 ) @ SV93 )
| ~ ( in @ SY937 @ SV367 ) )
| ( in @ SY979 @ SV403 ) ) )
= $true )
| ( ( SV403
= ( relation_image @ SV93 @ SV367 ) )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2613]) ).
thf(2732,plain,
! [SV93: $i,SV367: $i,SV403: $i] :
( ( ( ! [SY981: $i] :
( ~ ( in @ SY981 @ SV403 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SY981 @ SV403 @ SV367 @ SV93 ) @ SY981 ) @ SV93 )
| ~ ( in @ ( sK37_E @ SY981 @ SV403 @ SV367 @ SV93 ) @ SV367 ) ) ) )
= $true )
| ( ( SV403
= ( relation_image @ SV93 @ SV367 ) )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2614]) ).
thf(2733,plain,
! [SV282: $i,SV94: $i,SV326: $i,SV449: $i] :
( ( ( in @ SV449 @ ( relation_rng @ SV326 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV94 @ SV449 ) @ SV326 ) )
= $true )
| ( ( ~ ( in @ SV449 @ SV282 ) )
= $true )
| ( ( in @ SV94 @ ( relation_inverse_image @ SV326 @ SV282 ) )
= $true )
| ( ( relation @ SV326 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2615]) ).
thf(2734,plain,
! [SV94: $i,SV283: $i,SV327: $i] :
( ( ( ~ ( ~ ( in @ ( sK51_D @ SV327 @ SV283 @ SV94 ) @ ( relation_rng @ SV327 ) )
| ~ ( in @ ( ordered_pair @ SV94 @ ( sK51_D @ SV327 @ SV283 @ SV94 ) ) @ SV327 ) ) )
= $true )
| ( ( in @ SV94 @ ( relation_inverse_image @ SV327 @ SV283 ) )
= $false )
| ( ( relation @ SV327 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2616]) ).
thf(2735,plain,
! [SV94: $i,SV283: $i,SV327: $i] :
( ( ( in @ ( sK51_D @ SV327 @ SV283 @ SV94 ) @ SV283 )
= $true )
| ( ( in @ SV94 @ ( relation_inverse_image @ SV327 @ SV283 ) )
= $false )
| ( ( relation @ SV327 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2617]) ).
thf(2736,plain,
! [SV175: $i,SV95: $i,SV450: $i] :
( ( ( function @ SV450 )
= $false )
| ( ( ~ ( relation @ SV450 ) )
= $true )
| ( ( ~ ( in @ SV95 @ ( relation_dom @ SV450 ) )
| ~ ( in @ ( apply @ SV450 @ SV95 ) @ ( relation_dom @ SV175 ) )
| ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SV450 @ SV175 ) ) ) )
= $true )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2618]) ).
thf(2737,plain,
! [SV175: $i,SV95: $i,SV486: $i] :
( ( ( ~ ( function @ SV486 )
| ~ ( relation @ SV486 )
| ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SV486 @ SV175 ) ) )
| ( in @ SV95 @ ( relation_dom @ SV486 ) ) )
= $true )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2619]) ).
thf(2738,plain,
! [SV175: $i,SV95: $i,SV487: $i] :
( ( ( ~ ( function @ SV487 )
| ~ ( relation @ SV487 )
| ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SV487 @ SV175 ) ) )
| ( in @ ( apply @ SV487 @ SV95 ) @ ( relation_dom @ SV175 ) ) )
= $true )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2620]) ).
thf(2739,plain,
! [SV96: $i,SV368: $i,SV404: $i] :
( ( ( ~ ( ~ ( in @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ SV368 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 ) ) )
= $false )
| ( ( SV404
= ( relation_dom_restriction @ SV96 @ SV368 ) )
= $true )
| ( ( relation @ SV404 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2621]) ).
thf(2740,plain,
! [SV96: $i,SV368: $i,SV404: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ SV368 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 ) ) ) )
= $false )
| ( ( SV404
= ( relation_dom_restriction @ SV96 @ SV368 ) )
= $true )
| ( ( relation @ SV404 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2621]) ).
thf(2741,plain,
! [SV405: $i,SV96: $i,SV369: $i] :
( ( ( ~ ! [SY982: $i,SY983: $i] :
( ~ ( in @ SY982 @ SV369 )
| ~ ( in @ ( ordered_pair @ SY982 @ SY983 ) @ SV96 )
| ( in @ ( ordered_pair @ SY982 @ SY983 ) @ SV405 ) )
| ~ ~ ( ~ ! [SY984: $i] :
( ! [SY985: $i] :
~ ( in @ ( ordered_pair @ SY984 @ SY985 ) @ SV405 )
| ( in @ SY984 @ SV369 ) )
| ~ ! [SY986: $i,SY987: $i] :
( ~ ( in @ ( ordered_pair @ SY986 @ SY987 ) @ SV405 )
| ( in @ ( ordered_pair @ SY986 @ SY987 ) @ SV96 ) ) ) )
= $false )
| ( ( SV405
= ( relation_dom_restriction @ SV96 @ SV369 ) )
= $false )
| ( ( relation @ SV405 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2622]) ).
thf(2742,plain,
! [SV97: $i,SV370: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SV370 @ SV97 ) @ ( sK12_SY396 @ SV370 @ SV97 ) ) @ SV370 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SV370 @ SV97 ) @ ( sK11_C @ SV370 @ SV97 ) ) @ SV97 ) )
= $true )
| ( ( SV370
= ( relation_inverse @ SV97 ) )
= $true )
| ( ( relation @ SV370 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2623]) ).
thf(2743,plain,
! [SV97: $i,SV370: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK11_C @ SV370 @ SV97 ) @ ( sK12_SY396 @ SV370 @ SV97 ) ) @ SV370 )
| ( in @ ( ordered_pair @ ( sK12_SY396 @ SV370 @ SV97 ) @ ( sK11_C @ SV370 @ SV97 ) ) @ SV97 ) )
= $true )
| ( ( SV370
= ( relation_inverse @ SV97 ) )
= $true )
| ( ( relation @ SV370 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2624]) ).
thf(2744,plain,
! [SV97: $i,SV371: $i] :
( ( ( ~ ! [SY947: $i,SY948: $i] :
( ~ ( in @ ( ordered_pair @ SY947 @ SY948 ) @ SV371 )
| ( in @ ( ordered_pair @ SY948 @ SY947 ) @ SV97 ) ) )
= $false )
| ( ( SV371
= ( relation_inverse @ SV97 ) )
= $false )
| ( ( relation @ SV371 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2625]) ).
thf(2745,plain,
! [SV371: $i,SV97: $i] :
( ( ( ~ ! [SY949: $i,SY950: $i] :
( ~ ( in @ ( ordered_pair @ SY950 @ SY949 ) @ SV97 )
| ( in @ ( ordered_pair @ SY949 @ SY950 ) @ SV371 ) ) )
= $false )
| ( ( SV371
= ( relation_inverse @ SV97 ) )
= $false )
| ( ( relation @ SV371 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2625]) ).
thf(2746,plain,
! [SV98: $i,SV372: $i,SV488: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV488 @ ( sK60_C @ SV372 @ SV98 ) ) @ SV98 ) )
= $true )
| ( ( ~ ( in @ ( sK60_C @ SV372 @ SV98 ) @ SV372 ) )
= $true )
| ( ( SV372
= ( relation_rng @ SV98 ) )
= $true )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2626]) ).
thf(2747,plain,
! [SV373: $i,SV98: $i,SV489: $i] :
( ( ( ! [SY1026: $i] :
~ ( in @ ( ordered_pair @ SY1026 @ SV489 ) @ SV98 )
| ( in @ SV489 @ SV373 ) )
= $true )
| ( ( SV373
= ( relation_rng @ SV98 ) )
= $false )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2628]) ).
thf(2748,plain,
! [SV98: $i,SV373: $i,SV490: $i] :
( ( ( ~ ( in @ SV490 @ SV373 )
| ( in @ ( ordered_pair @ ( sK59_D @ SV490 @ SV373 @ SV98 ) @ SV490 ) @ SV98 ) )
= $true )
| ( ( SV373
= ( relation_rng @ SV98 ) )
= $false )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2629]) ).
thf(2749,plain,
! [SV100: $i,SV328: $i,SV286: $i] :
( ( ( SV286
= ( apply @ SV328 @ SV100 ) )
= $false )
| ( ( ~ ( in @ SV100 @ ( relation_dom @ SV328 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV100 @ SV286 ) @ SV328 )
= $true )
| ( ( function @ SV328 )
= $false )
| ( ( relation @ SV328 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2630]) ).
thf(2750,plain,
! [SV406: $i,SV100: $i,SV428: $i] :
( ( ( relation @ SV428 )
= $false )
| ( ( function @ SV428 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV100 @ SV406 ) @ SV428 )
| ( SV406
= ( apply @ SV428 @ SV100 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2631]) ).
thf(2751,plain,
! [SV407: $i,SV100: $i,SV429: $i] :
( ( ( relation @ SV429 )
= $false )
| ( ( function @ SV429 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV100 @ SV407 ) @ SV429 )
| ( in @ SV100 @ ( relation_dom @ SV429 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2632]) ).
thf(2752,plain,
! [SV101: $i,SV215: $i,SV451: $i] :
( ( ( ~ ( ~ ( ! [SY1009: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ SY1009 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY1009 @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV215 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV451 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK10_SY395 @ SV451 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV215 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV451 ) ) ) )
= $true )
| ( ( SV451
= ( relation_composition @ SV101 @ SV215 ) )
= $true )
| ( ( relation @ SV451 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2633]) ).
thf(2753,plain,
! [SV215: $i,SV101: $i,SV452: $i] :
( ( ( ( SV452
!= ( relation_composition @ SV101 @ SV215 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1010: $i,SY1011: $i] :
( ! [SY783: $i] :
( ~ ( in @ ( ordered_pair @ SY1010 @ SY783 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY783 @ SY1011 ) @ SV215 ) )
| ( in @ ( ordered_pair @ SY1010 @ SY1011 ) @ SV452 ) )
| ~ ! [SY1013: $i,SY1014: $i] :
( ~ ( in @ ( ordered_pair @ SY1013 @ SY1014 ) @ SV452 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1013 @ ( sK7_F @ SY1014 @ SY1013 @ SV452 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY1014 @ SY1013 @ SV452 @ SV215 @ SV101 ) @ SY1014 ) @ SV215 ) ) ) ) )
= $true )
| ( ( relation @ SV452 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2634]) ).
thf(2754,plain,
! [SV103: $i,SV408: $i,SV491: $i] :
( ( ( ~ ( subset @ SV491 @ SV408 )
| ( in @ SV491 @ ( sK3_SY386 @ SV408 @ SV103 ) ) )
= $true )
| ( ( ~ ( in @ SV408 @ ( sK2_B @ SV103 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2637]) ).
thf(2755,plain,
! [SV103: $i,SV408: $i] :
( ( ( in @ SV408 @ ( sK2_B @ SV103 ) )
= $false )
| ( ( in @ ( sK3_SY386 @ SV408 @ SV103 ) @ ( sK2_B @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2638]) ).
thf(2756,plain,
! [SV472: $i,SV103: $i,SV462: $i] :
( ( ( ~ ( in @ SV462 @ ( sK2_B @ SV103 ) )
| ~ ( subset @ SV472 @ SV462 ) )
= $true )
| ( ( in @ SV472 @ ( sK2_B @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2639]) ).
thf(2757,plain,
! [SV433: $i,SV409: $i,SV105: $i] :
( ( ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SV409 @ SV433 ) ) )
= $false )
| ( ( in @ SV105 @ SV409 )
= $true )
| ( ( relation @ SV433 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2641]) ).
thf(2758,plain,
! [SV434: $i,SV410: $i,SV105: $i] :
( ( ( in @ SV105 @ ( relation_rng @ ( relation_rng_restriction @ SV410 @ SV434 ) ) )
= $false )
| ( ( in @ SV105 @ ( relation_rng @ SV434 ) )
= $true )
| ( ( relation @ SV434 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2642]) ).
thf(2759,plain,
! [SV332: $i,SV378: $i,SV178: $i,SV107: $i] :
( ( ( in @ ( ordered_pair @ SV107 @ SV178 ) @ SV378 )
= $false )
| ( ( in @ SV107 @ SV332 )
= $false )
| ( ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SV332 ) @ SV378 ) )
= $true )
| ( ( relation @ SV378 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2643]) ).
thf(2760,plain,
! [SV455: $i,SV437: $i,SV178: $i,SV107: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SV437 ) @ SV455 ) ) )
= $true )
| ( ( in @ SV107 @ SV437 )
= $true )
| ( ( relation @ SV455 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2644]) ).
thf(2761,plain,
! [SV456: $i,SV438: $i,SV178: $i,SV107: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SV438 ) @ SV456 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV107 @ SV178 ) @ SV456 )
= $true )
| ( ( relation @ SV456 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2645]) ).
thf(2762,plain,
! [SV108: $i,SV379: $i] :
( ( ( in @ ( ordered_pair @ ( sK19_C @ SV379 @ SV108 ) @ ( sK20_SY399 @ SV379 @ SV108 ) ) @ SV108 )
= $true )
| ( ( subset @ SV108 @ SV379 )
= $true )
| ( ( relation @ SV379 )
= $false )
| ( ( relation @ SV108 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2646]) ).
thf(2763,plain,
! [SV108: $i,SV379: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV379 @ SV108 ) @ ( sK20_SY399 @ SV379 @ SV108 ) ) @ SV379 ) )
= $true )
| ( ( subset @ SV108 @ SV379 )
= $true )
| ( ( relation @ SV379 )
= $false )
| ( ( relation @ SV108 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2647]) ).
thf(2764,plain,
! [SV380: $i,SV108: $i,SV492: $i,SV473: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV473 @ SV492 ) @ SV108 )
| ( in @ ( ordered_pair @ SV473 @ SV492 ) @ SV380 ) )
= $true )
| ( ( subset @ SV108 @ SV380 )
= $false )
| ( ( relation @ SV380 )
= $false )
| ( ( relation @ SV108 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2648]) ).
thf(2765,plain,
! [SV291: $i,SV229: $i,SV463: $i] :
( ( ( SV463 = SV229 )
= $false )
| ( ( in @ SV463 @ SV291 )
= $true )
| ( ( SV291
= ( singleton @ SV229 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2650]) ).
thf(2766,plain,
! [SV229: $i,SV291: $i,SV464: $i] :
( ( ( in @ SV464 @ SV291 )
= $false )
| ( ( SV464 = SV229 )
= $true )
| ( ( SV291
= ( singleton @ SV229 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2651]) ).
thf(2767,plain,
! [SV381: $i] :
( ( ( function @ SV381 )
= $false )
| ( ( empty @ SV381 )
= $false )
| ( ( relation @ SV381 )
= $false )
| ( ( function @ SV381 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2652]) ).
thf(2768,plain,
! [SV382: $i] :
( ( ( function @ SV382 )
= $false )
| ( ( empty @ SV382 )
= $false )
| ( ( relation @ SV382 )
= $false )
| ( ( relation @ SV382 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2653]) ).
thf(2769,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ( function @ SV465 ) )
= $true )
| ( ( ~ ( relation @ SV465 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) )
| ( SV465
= ( function_inverse @ SV110 ) ) )
= $true )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2654]) ).
thf(2770,plain,
! [SV110: $i] :
( ( ( ! [SY637: $i] :
( ~ ( function @ SY637 )
| ~ ( relation @ SY637 )
| ( SY637
!= ( function_inverse @ SV110 ) )
| ~ ( ~ ~ ( ~ ! [SY638: $i,SY639: $i] :
( ( SY639
!= ( apply @ SY637 @ SY638 ) )
| ~ ( in @ SY638 @ ( relation_rng @ SV110 ) )
| ( SY638
= ( apply @ SV110 @ SY639 ) ) )
| ~ ! [SY640: $i,SY641: $i] :
( ( SY641
!= ( apply @ SY637 @ SY640 ) )
| ~ ( in @ SY640 @ ( relation_rng @ SV110 ) )
| ( in @ SY641 @ ( relation_dom @ SV110 ) ) ) )
| ~ ~ ( ~ ! [SY642: $i,SY643: $i] :
( ( SY642
!= ( apply @ SV110 @ SY643 ) )
| ~ ( in @ SY643 @ ( relation_dom @ SV110 ) )
| ( SY643
= ( apply @ SY637 @ SY642 ) ) )
| ~ ! [SY644: $i] :
( ! [SY645: $i] :
( ( SY644
!= ( apply @ SV110 @ SY645 ) )
| ~ ( in @ SY645 @ ( relation_dom @ SV110 ) ) )
| ( in @ SY644 @ ( relation_rng @ SV110 ) ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2655]) ).
thf(2771,plain,
! [SV110: $i] :
( ( ( ! [SY646: $i] :
( ~ ( function @ SY646 )
| ~ ( relation @ SY646 )
| ( SY646
!= ( function_inverse @ SV110 ) )
| ( ( relation_dom @ SY646 )
= ( relation_rng @ SV110 ) ) ) )
= $true )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2656]) ).
thf(2772,plain,
! [SV113: $i,SV474: $i] :
( ( ( ~ ( in @ SV474 @ ( relation_dom @ SV113 ) ) )
= $true )
| ( ( ! [SY1018: $i] :
( ( SY1018
!= ( apply @ SV113 @ SV474 ) )
| ( in @ ( ordered_pair @ SV474 @ SY1018 ) @ SV113 ) ) )
= $true )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2659]) ).
thf(2773,plain,
! [SV113: $i,SV475: $i] :
( ( ( ~ ( in @ SV475 @ ( relation_dom @ SV113 ) ) )
= $true )
| ( ( ! [SY1019: $i] :
( ~ ( in @ ( ordered_pair @ SV475 @ SY1019 ) @ SV113 )
| ( SY1019
= ( apply @ SV113 @ SV475 ) ) ) )
= $true )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2660]) ).
thf(2774,plain,
! [SV113: $i,SV476: $i] :
( ( ( in @ SV476 @ ( relation_dom @ SV113 ) )
= $true )
| ( ( ! [SY1020: $i] :
( ( SY1020
!= ( apply @ SV113 @ SV476 ) )
| ( SY1020 = empty_set ) ) )
= $true )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2661]) ).
thf(2775,plain,
! [SV113: $i,SV477: $i] :
( ( ( in @ SV477 @ ( relation_dom @ SV113 ) )
= $true )
| ( ( ! [SY1021: $i] :
( ( SY1021 != empty_set )
| ( SY1021
= ( apply @ SV113 @ SV477 ) ) ) )
= $true )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2662]) ).
thf(2776,plain,
! [SV114: $i,SV301: $i,SV338: $i] :
( ( ( ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV338 )
| ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV114 ) )
= $true )
| ( ( SV338
= ( set_union2 @ SV114 @ SV301 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2663]) ).
thf(2777,plain,
! [SV114: $i,SV301: $i,SV338: $i] :
( ( ( ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV338 )
| ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV301 ) )
= $true )
| ( ( SV338
= ( set_union2 @ SV114 @ SV301 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2664]) ).
thf(2778,plain,
! [SV302: $i,SV114: $i,SV339: $i,SV478: $i] :
( ( ( ~ ( in @ SV478 @ SV339 ) )
= $true )
| ( ( ( in @ SV478 @ SV114 )
| ( in @ SV478 @ SV302 ) )
= $true )
| ( ( SV339
= ( set_union2 @ SV114 @ SV302 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2666]) ).
thf(2779,plain,
! [SV302: $i,SV339: $i,SV114: $i] :
( ( ( ~ ! [SY896: $i] :
( ~ ( in @ SY896 @ SV114 )
| ( in @ SY896 @ SV339 ) ) )
= $false )
| ( ( SV339
= ( set_union2 @ SV114 @ SV302 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2667]) ).
thf(2780,plain,
! [SV114: $i,SV339: $i,SV302: $i] :
( ( ( ~ ! [SY897: $i] :
( ~ ( in @ SY897 @ SV302 )
| ( in @ SY897 @ SV339 ) ) )
= $false )
| ( ( SV339
= ( set_union2 @ SV114 @ SV302 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2667]) ).
thf(2781,plain,
! [SV116: $i,SV306: $i,SV342: $i] :
( ( ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV116 )
= $false )
| ( ( ~ ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV306 ) )
= $true )
| ( ( ~ ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV342 ) )
= $true )
| ( ( SV342
= ( set_intersection2 @ SV116 @ SV306 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2668]) ).
thf(2782,plain,
! [SV116: $i,SV306: $i,SV342: $i] :
( ( ( ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV116 )
| ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV342 ) )
= $true )
| ( ( SV342
= ( set_intersection2 @ SV116 @ SV306 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2669]) ).
thf(2783,plain,
! [SV116: $i,SV306: $i,SV342: $i] :
( ( ( ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV306 )
| ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV342 ) )
= $true )
| ( ( SV342
= ( set_intersection2 @ SV116 @ SV306 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2670]) ).
thf(2784,plain,
! [SV343: $i,SV307: $i,SV116: $i,SV479: $i] :
( ( ( ~ ( in @ SV479 @ SV116 )
| ~ ( in @ SV479 @ SV307 ) )
= $true )
| ( ( in @ SV479 @ SV343 )
= $true )
| ( ( SV343
= ( set_intersection2 @ SV116 @ SV307 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2671]) ).
thf(2785,plain,
! [SV307: $i,SV116: $i,SV343: $i] :
( ( ( ~ ! [SY899: $i] :
( ~ ( in @ SY899 @ SV343 )
| ( in @ SY899 @ SV116 ) ) )
= $false )
| ( ( SV343
= ( set_intersection2 @ SV116 @ SV307 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2672]) ).
thf(2786,plain,
! [SV116: $i,SV307: $i,SV343: $i] :
( ( ( ~ ! [SY900: $i] :
( ~ ( in @ SY900 @ SV343 )
| ( in @ SY900 @ SV307 ) ) )
= $false )
| ( ( SV343
= ( set_intersection2 @ SV116 @ SV307 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2672]) ).
thf(2787,plain,
! [SV251: $i,SV308: $i] :
( ( ( ( ( sK44_C @ SV308 @ SV251 )
!= ( sK45_SY414 @ SV308 @ SV251 ) ) )
= $true )
| ( ( ~ ( in @ ( sK44_C @ SV308 @ SV251 ) @ SV251 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 ) )
= $true )
| ( ( SV308
= ( identity_relation @ SV251 ) )
= $true )
| ( ( relation @ SV308 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2673]) ).
thf(2788,plain,
! [SV251: $i,SV308: $i] :
( ( ( ~ ( ( ( sK44_C @ SV308 @ SV251 )
= ( sK45_SY414 @ SV308 @ SV251 ) )
| ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 ) ) )
= $false )
| ( ( SV308
= ( identity_relation @ SV251 ) )
= $true )
| ( ( relation @ SV308 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2674]) ).
thf(2789,plain,
! [SV251: $i,SV308: $i] :
( ( ( ~ ( ( in @ ( sK44_C @ SV308 @ SV251 ) @ SV251 )
| ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 ) ) )
= $false )
| ( ( SV308
= ( identity_relation @ SV251 ) )
= $true )
| ( ( relation @ SV308 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2674]) ).
thf(2790,plain,
! [SV309: $i,SV252: $i,SV493: $i] :
( ( ( ! [SY1027: $i] :
( ( SV493 != SY1027 )
| ~ ( in @ SV493 @ SV252 )
| ( in @ ( ordered_pair @ SV493 @ SY1027 ) @ SV309 ) ) )
= $true )
| ( ( SV309
= ( identity_relation @ SV252 ) )
= $false )
| ( ( relation @ SV309 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2675]) ).
thf(2791,plain,
! [SV252: $i,SV309: $i] :
( ( ( ~ ! [SY863: $i,SY864: $i] :
( ~ ( in @ ( ordered_pair @ SY863 @ SY864 ) @ SV309 )
| ( SY863 = SY864 ) )
| ~ ! [SY865: $i] :
( ! [SY866: $i] :
~ ( in @ ( ordered_pair @ SY865 @ SY866 ) @ SV309 )
| ( in @ SY865 @ SV252 ) ) )
= $false )
| ( ( SV309
= ( identity_relation @ SV252 ) )
= $false )
| ( ( relation @ SV309 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2676]) ).
thf(2792,plain,
! [SV418: $i,SV441: $i,SV117: $i] :
( ( ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SV441 @ SV418 ) ) )
= $false )
| ( ( in @ SV117 @ SV418 )
= $true )
| ( ( relation @ SV441 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2678]) ).
thf(2793,plain,
! [SV419: $i,SV442: $i,SV117: $i] :
( ( ( in @ SV117 @ ( relation_dom @ ( relation_dom_restriction @ SV442 @ SV419 ) ) )
= $false )
| ( ( in @ SV117 @ ( relation_dom @ SV442 ) )
= $true )
| ( ( relation @ SV442 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2679]) ).
thf(2794,plain,
! [SV253: $i,SV311: $i] :
( ( ( ~ ( in @ ( sK50_C @ SV311 @ SV253 ) @ SV253 ) )
= $false )
| ( ( ( ( relation_dom @ SV311 )
!= SV253 ) )
= $true )
| ( ( SV311
= ( identity_relation @ SV253 ) )
= $true )
| ( ( function @ SV311 )
= $false )
| ( ( relation @ SV311 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2680]) ).
thf(2795,plain,
! [SV253: $i,SV311: $i] :
( ( ( ~ ( ( ( apply @ SV311 @ ( sK50_C @ SV311 @ SV253 ) )
!= ( sK50_C @ SV311 @ SV253 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV311 )
!= SV253 ) )
= $true )
| ( ( SV311
= ( identity_relation @ SV253 ) )
= $true )
| ( ( function @ SV311 )
= $false )
| ( ( relation @ SV311 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2680]) ).
thf(2796,plain,
! [SV391: $i,SV420: $i] :
( ( ( ( SV420
!= ( identity_relation @ SV391 ) ) )
= $true )
| ( ( ! [SY997: $i] :
( ~ ( in @ SY997 @ SV391 )
| ( ( apply @ SV420 @ SY997 )
= SY997 ) ) )
= $true )
| ( ( function @ SV420 )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2681]) ).
thf(2797,plain,
! [SV392: $i,SV421: $i] :
( ( ( ( SV421
!= ( identity_relation @ SV392 ) ) )
= $true )
| ( ( ( relation_dom @ SV421 )
= SV392 )
= $true )
| ( ( function @ SV421 )
= $false )
| ( ( relation @ SV421 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2682]) ).
thf(2798,plain,
! [SV345: $i,SV312: $i,SV494: $i,SV118: $i,SV480: $i] :
( ( ( ~ ( in @ SV480 @ SV118 )
| ~ ( in @ SV494 @ SV312 )
| ( ( sK23_D @ SV345 @ SV312 @ SV118 )
!= ( ordered_pair @ SV480 @ SV494 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV345 @ SV312 @ SV118 ) @ SV345 ) )
= $true )
| ( ( SV345
= ( cartesian_product2 @ SV118 @ SV312 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2683]) ).
thf(2799,plain,
! [SV118: $i,SV312: $i,SV345: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK24_SY403 @ SV345 @ SV312 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK25_SY405 @ SV345 @ SV312 @ SV118 ) @ SV312 ) ) )
= $false )
| ( ( in @ ( sK23_D @ SV345 @ SV312 @ SV118 ) @ SV345 )
= $true )
| ( ( SV345
= ( cartesian_product2 @ SV118 @ SV312 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2684]) ).
thf(2800,plain,
! [SV118: $i,SV312: $i,SV345: $i] :
( ( ( ( ( sK23_D @ SV345 @ SV312 @ SV118 )
!= ( ordered_pair @ ( sK24_SY403 @ SV345 @ SV312 @ SV118 ) @ ( sK25_SY405 @ SV345 @ SV312 @ SV118 ) ) ) )
= $false )
| ( ( in @ ( sK23_D @ SV345 @ SV312 @ SV118 ) @ SV345 )
= $true )
| ( ( SV345
= ( cartesian_product2 @ SV118 @ SV312 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2684]) ).
thf(2801,plain,
! [SV346: $i,SV481: $i,SV313: $i,SV118: $i] :
( ( ( ! [SY1023: $i,SY1024: $i] :
( ~ ( in @ SY1023 @ SV118 )
| ~ ( in @ SY1024 @ SV313 )
| ( SV481
!= ( ordered_pair @ SY1023 @ SY1024 ) ) ) )
= $true )
| ( ( in @ SV481 @ SV346 )
= $true )
| ( ( SV346
= ( cartesian_product2 @ SV118 @ SV313 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2685]) ).
thf(2802,plain,
! [SV118: $i,SV313: $i,SV346: $i,SV482: $i] :
( ( ( ~ ( in @ SV482 @ SV346 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SV482 @ SV346 @ SV313 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK22_SY400 @ SV482 @ SV346 @ SV313 @ SV118 ) @ SV313 ) )
| ( SV482
!= ( ordered_pair @ ( sK21_E @ SV482 @ SV346 @ SV313 @ SV118 ) @ ( sK22_SY400 @ SV482 @ SV346 @ SV313 @ SV118 ) ) ) ) )
= $true )
| ( ( SV346
= ( cartesian_product2 @ SV118 @ SV313 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2686]) ).
thf(2803,plain,
! [SV467: $i,SV254: $i,SV316: $i] :
( ( ( in @ ( sK15_C @ SV316 @ SV254 ) @ SV467 )
= $false )
| ( ( ~ ( in @ SV467 @ SV254 ) )
= $true )
| ( ( ~ ( in @ ( sK15_C @ SV316 @ SV254 ) @ SV316 ) )
= $true )
| ( ( SV316
= ( union @ SV254 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2687]) ).
thf(2804,plain,
! [SV254: $i,SV316: $i] :
( ( ( in @ ( sK15_C @ SV316 @ SV254 ) @ ( sK16_SY398 @ SV316 @ SV254 ) )
= $true )
| ( ( in @ ( sK15_C @ SV316 @ SV254 ) @ SV316 )
= $true )
| ( ( SV316
= ( union @ SV254 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2688]) ).
thf(2805,plain,
! [SV254: $i,SV316: $i] :
( ( ( in @ ( sK16_SY398 @ SV316 @ SV254 ) @ SV254 )
= $true )
| ( ( in @ ( sK15_C @ SV316 @ SV254 ) @ SV316 )
= $true )
| ( ( SV316
= ( union @ SV254 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2689]) ).
thf(2806,plain,
! [SV317: $i,SV255: $i,SV495: $i,SV468: $i] :
( ( ( ~ ( in @ SV468 @ SV495 )
| ~ ( in @ SV495 @ SV255 ) )
= $true )
| ( ( in @ SV468 @ SV317 )
= $true )
| ( ( SV317
= ( union @ SV255 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2690]) ).
thf(2807,plain,
! [SV255: $i,SV317: $i,SV469: $i] :
( ( ( in @ SV469 @ SV317 )
= $false )
| ( ( ~ ( ~ ( in @ SV469 @ ( sK14_D @ SV469 @ SV317 @ SV255 ) )
| ~ ( in @ ( sK14_D @ SV469 @ SV317 @ SV255 ) @ SV255 ) ) )
= $true )
| ( ( SV317
= ( union @ SV255 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2691]) ).
thf(2808,plain,
! [SV120: $i,SV393: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV393 ) )
= $true )
| ( ( SV120 = SV393 )
= $true )
| ( ( relation @ SV393 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2692]) ).
thf(2809,plain,
! [SV120: $i,SV393: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV120 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV393 ) )
= $true )
| ( ( SV120 = SV393 )
= $true )
| ( ( relation @ SV393 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2693]) ).
thf(2810,plain,
! [SV394: $i,SV120: $i] :
( ( ( ~ ! [SY964: $i,SY965: $i] :
( ~ ( in @ ( ordered_pair @ SY964 @ SY965 ) @ SV120 )
| ( in @ ( ordered_pair @ SY964 @ SY965 ) @ SV394 ) ) )
= $false )
| ( ( SV120 = SV394 )
= $false )
| ( ( relation @ SV394 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2694]) ).
thf(2811,plain,
! [SV120: $i,SV394: $i] :
( ( ( ~ ! [SY966: $i,SY967: $i] :
( ~ ( in @ ( ordered_pair @ SY966 @ SY967 ) @ SV394 )
| ( in @ ( ordered_pair @ SY966 @ SY967 ) @ SV120 ) ) )
= $false )
| ( ( SV120 = SV394 )
= $false )
| ( ( relation @ SV394 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2694]) ).
thf(2812,plain,
! [SV351: $i,SV424: $i] :
( ( ( ~ ( ~ ( in @ ( sK33_SY406 @ SV424 @ SV351 ) @ SV351 )
| ~ ~ ( in @ ( sK32_C @ SV424 @ SV351 ) @ ( sK33_SY406 @ SV424 @ SV351 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK32_C @ SV424 @ SV351 ) @ SV424 ) )
= $true )
| ( ( SV424
= ( set_meet @ SV351 ) )
= $true )
| ( ( SV351 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2697]) ).
thf(2813,plain,
! [SV424: $i,SV351: $i] :
( ( ( ! [SY998: $i] :
( ~ ( in @ SY998 @ SV351 )
| ( in @ ( sK32_C @ SV424 @ SV351 ) @ SY998 ) ) )
= $true )
| ( ( in @ ( sK32_C @ SV424 @ SV351 ) @ SV424 )
= $true )
| ( ( SV424
= ( set_meet @ SV351 ) )
= $true )
| ( ( SV351 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2698]) ).
thf(2814,plain,
! [SV352: $i,SV425: $i] :
( ( ( ! [SY999: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY999 @ SV425 @ SV352 ) @ SV352 )
| ~ ~ ( in @ SY999 @ ( sK31_D @ SY999 @ SV425 @ SV352 ) ) )
| ( in @ SY999 @ SV425 ) ) )
= $true )
| ( ( SV425
= ( set_meet @ SV352 ) )
= $false )
| ( ( SV352 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2699]) ).
thf(2815,plain,
! [SV352: $i,SV425: $i] :
( ( ( ! [SY1000: $i] :
( ~ ( in @ SY1000 @ SV425 )
| ! [SY914: $i] :
( ~ ( in @ SY914 @ SV352 )
| ( in @ SY1000 @ SY914 ) ) ) )
= $true )
| ( ( SV425
= ( set_meet @ SV352 ) )
= $false )
| ( ( SV352 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2700]) ).
thf(2816,plain,
! [SV271: $i,SV320: $i,SV87: $i,SV446: $i] :
( ( ( in @ ( ordered_pair @ SV446 @ SV87 ) @ SV320 )
= $false )
| ( ( in @ SV446 @ ( relation_dom @ SV320 ) )
= $false )
| ( ( ~ ( in @ SV446 @ SV271 ) )
= $true )
| ( ( in @ SV87 @ ( relation_image @ SV320 @ SV271 ) )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2703]) ).
thf(2817,plain,
! [SV87: $i,SV272: $i,SV321: $i] :
( ( ( ~ ( in @ ( sK52_D @ SV321 @ SV272 @ SV87 ) @ ( relation_dom @ SV321 ) )
| ~ ( in @ ( ordered_pair @ ( sK52_D @ SV321 @ SV272 @ SV87 ) @ SV87 ) @ SV321 ) )
= $false )
| ( ( in @ SV87 @ ( relation_image @ SV321 @ SV272 ) )
= $false )
| ( ( relation @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2704]) ).
thf(2818,plain,
! [SV88: $i,SV274: $i,SV322: $i] :
( ( ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV322 )
= $false )
| ( ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV274 )
= $true )
| ( ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV88 )
= $false )
| ( ( SV322
= ( set_difference @ SV88 @ SV274 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2706]) ).
thf(2819,plain,
! [SV88: $i,SV274: $i,SV322: $i] :
( ( ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV88 )
= $true )
| ( ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV322 )
= $true )
| ( ( SV322
= ( set_difference @ SV88 @ SV274 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2707]) ).
thf(2820,plain,
! [SV88: $i,SV274: $i,SV322: $i] :
( ( ( ~ ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV274 ) )
= $true )
| ( ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV322 )
= $true )
| ( ( SV322
= ( set_difference @ SV88 @ SV274 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2708]) ).
thf(2821,plain,
! [SV323: $i,SV275: $i,SV88: $i,SV470: $i] :
( ( ( ~ ( in @ SV470 @ SV88 ) )
= $true )
| ( ( in @ SV470 @ SV275 )
= $true )
| ( ( in @ SV470 @ SV323 )
= $true )
| ( ( SV323
= ( set_difference @ SV88 @ SV275 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2709]) ).
thf(2822,plain,
! [SV275: $i,SV88: $i,SV323: $i] :
( ( ( ! [SY884: $i] :
( ~ ( in @ SY884 @ SV323 )
| ( in @ SY884 @ SV88 ) ) )
= $true )
| ( ( SV323
= ( set_difference @ SV88 @ SV275 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2710]) ).
thf(2823,plain,
! [SV88: $i,SV275: $i,SV323: $i] :
( ( ( ! [SY885: $i] :
( ~ ( in @ SY885 @ SV323 )
| ~ ( in @ SY885 @ SV275 ) ) )
= $true )
| ( ( SV323
= ( set_difference @ SV88 @ SV275 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2711]) ).
thf(2824,plain,
! [SV89: $i,SV174: $i,SV398: $i] :
( ( ( ~ ( in @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV174 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 ) )
= $true )
| ( ( SV398
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2712]) ).
thf(2825,plain,
! [SV89: $i,SV174: $i,SV398: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) @ SV89 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV174 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 ) ) ) )
= $true )
| ( ( SV398
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2713]) ).
thf(2826,plain,
! [SV399: $i,SV174: $i,SV89: $i] :
( ( ( ~ ! [SY968: $i,SY969: $i] :
( ~ ( in @ SY969 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY968 @ SY969 ) @ SV174 )
| ( in @ ( ordered_pair @ SY968 @ SY969 ) @ SV399 ) ) )
= $false )
| ( ( SV399
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2714]) ).
thf(2827,plain,
! [SV174: $i,SV89: $i,SV399: $i] :
( ( ( ~ ~ ( ~ ! [SY970: $i,SY971: $i] :
( ~ ( in @ ( ordered_pair @ SY970 @ SY971 ) @ SV399 )
| ( in @ SY971 @ SV89 ) )
| ~ ! [SY972: $i,SY973: $i] :
( ~ ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV399 )
| ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV174 ) ) ) )
= $false )
| ( ( SV399
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2714]) ).
thf(2828,plain,
! [SV90: $i,SV276: $i,SV324: $i] :
( ( ( ~ ( in @ ( sK27_D @ SV324 @ SV276 @ SV90 ) @ SV324 ) )
= $true )
| ( ( ( ( sK27_D @ SV324 @ SV276 @ SV90 )
!= SV90 ) )
= $true )
| ( ( SV324
= ( unordered_pair @ SV90 @ SV276 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2715]) ).
thf(2829,plain,
! [SV90: $i,SV276: $i,SV324: $i] :
( ( ( ~ ( in @ ( sK27_D @ SV324 @ SV276 @ SV90 ) @ SV324 ) )
= $true )
| ( ( ( ( sK27_D @ SV324 @ SV276 @ SV90 )
!= SV276 ) )
= $true )
| ( ( SV324
= ( unordered_pair @ SV90 @ SV276 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2716]) ).
thf(2830,plain,
! [SV277: $i,SV90: $i,SV325: $i,SV471: $i] :
( ( ( in @ SV471 @ SV325 )
= $false )
| ( ( ( SV471 = SV90 )
| ( SV471 = SV277 ) )
= $true )
| ( ( SV325
= ( unordered_pair @ SV90 @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2717]) ).
thf(2831,plain,
! [SV277: $i,SV325: $i,SV90: $i] :
( ( ( ! [SY887: $i] :
( ( SY887 != SV90 )
| ( in @ SY887 @ SV325 ) ) )
= $true )
| ( ( SV325
= ( unordered_pair @ SV90 @ SV277 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2718]) ).
thf(2832,plain,
! [SV90: $i,SV325: $i,SV277: $i] :
( ( ( ! [SY888: $i] :
( ( SY888 != SV277 )
| ( in @ SY888 @ SV325 ) ) )
= $true )
| ( ( SV325
= ( unordered_pair @ SV90 @ SV277 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2719]) ).
thf(2833,plain,
! [SV483: $i,SV91: $i,SV362: $i] :
( ( ( in @ ( ordered_pair @ ( sK63_C @ SV362 @ SV91 ) @ SV483 ) @ SV91 )
= $false )
| ( ( ~ ( in @ ( sK63_C @ SV362 @ SV91 ) @ SV362 ) )
= $true )
| ( ( SV362
= ( relation_dom @ SV91 ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2722]) ).
thf(2834,plain,
! [SV363: $i,SV91: $i,SV484: $i] :
( ( ( ! [SY1025: $i] :
~ ( in @ ( ordered_pair @ SV484 @ SY1025 ) @ SV91 ) )
= $true )
| ( ( in @ SV484 @ SV363 )
= $true )
| ( ( SV363
= ( relation_dom @ SV91 ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2723]) ).
thf(2835,plain,
! [SV91: $i,SV363: $i,SV485: $i] :
( ( ( ~ ( in @ SV485 @ SV363 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV485 @ ( sK62_D @ SV485 @ SV363 @ SV91 ) ) @ SV91 )
= $true )
| ( ( SV363
= ( relation_dom @ SV91 ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2724]) ).
thf(2836,plain,
! [SV496: $i,SV92: $i,SV364: $i,SV400: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SV496 ) @ SV92 )
| ~ ( in @ SV496 @ SV364 ) )
= $true )
| ( ( ~ ( in @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SV400 ) )
= $true )
| ( ( SV400
= ( relation_inverse_image @ SV92 @ SV364 ) )
= $true )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2725]) ).
thf(2837,plain,
! [SV92: $i,SV364: $i,SV400: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ ( sK36_SY409 @ SV400 @ SV364 @ SV92 ) ) @ SV92 )
| ~ ( in @ ( sK36_SY409 @ SV400 @ SV364 @ SV92 ) @ SV364 ) )
= $false )
| ( ( in @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SV400 )
= $true )
| ( ( SV400
= ( relation_inverse_image @ SV92 @ SV364 ) )
= $true )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2726]) ).
thf(2838,plain,
! [SV401: $i,SV365: $i,SV92: $i,SV497: $i] :
( ( ( ! [SY1028: $i] :
( ~ ( in @ ( ordered_pair @ SV497 @ SY1028 ) @ SV92 )
| ~ ( in @ SY1028 @ SV365 ) )
| ( in @ SV497 @ SV401 ) )
= $true )
| ( ( SV401
= ( relation_inverse_image @ SV92 @ SV365 ) )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2727]) ).
thf(2839,plain,
! [SV92: $i,SV365: $i,SV401: $i,SV498: $i] :
( ( ( ~ ( in @ SV498 @ SV401 )
| ~ ( ~ ( in @ ( ordered_pair @ SV498 @ ( sK34_E @ SV498 @ SV401 @ SV365 @ SV92 ) ) @ SV92 )
| ~ ( in @ ( sK34_E @ SV498 @ SV401 @ SV365 @ SV92 ) @ SV365 ) ) )
= $true )
| ( ( SV401
= ( relation_inverse_image @ SV92 @ SV365 ) )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2728]) ).
thf(2840,plain,
! [SV93: $i,SV366: $i,SV402: $i,SV499: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV499 @ ( sK38_D @ SV402 @ SV366 @ SV93 ) ) @ SV93 )
| ~ ( in @ SV499 @ SV366 ) )
= $true )
| ( ( ~ ( in @ ( sK38_D @ SV402 @ SV366 @ SV93 ) @ SV402 ) )
= $true )
| ( ( SV402
= ( relation_image @ SV93 @ SV366 ) )
= $true )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2729]) ).
thf(2841,plain,
! [SV93: $i,SV366: $i,SV402: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SV402 @ SV366 @ SV93 ) @ ( sK38_D @ SV402 @ SV366 @ SV93 ) ) @ SV93 )
| ~ ( in @ ( sK39_SY411 @ SV402 @ SV366 @ SV93 ) @ SV366 ) )
= $false )
| ( ( in @ ( sK38_D @ SV402 @ SV366 @ SV93 ) @ SV402 )
= $true )
| ( ( SV402
= ( relation_image @ SV93 @ SV366 ) )
= $true )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2730]) ).
thf(2842,plain,
! [SV403: $i,SV367: $i,SV93: $i,SV500: $i] :
( ( ( ! [SY1029: $i] :
( ~ ( in @ ( ordered_pair @ SY1029 @ SV500 ) @ SV93 )
| ~ ( in @ SY1029 @ SV367 ) )
| ( in @ SV500 @ SV403 ) )
= $true )
| ( ( SV403
= ( relation_image @ SV93 @ SV367 ) )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2731]) ).
thf(2843,plain,
! [SV93: $i,SV367: $i,SV403: $i,SV501: $i] :
( ( ( ~ ( in @ SV501 @ SV403 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SV501 @ SV403 @ SV367 @ SV93 ) @ SV501 ) @ SV93 )
| ~ ( in @ ( sK37_E @ SV501 @ SV403 @ SV367 @ SV93 ) @ SV367 ) ) )
= $true )
| ( ( SV403
= ( relation_image @ SV93 @ SV367 ) )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2732]) ).
thf(2844,plain,
! [SV282: $i,SV326: $i,SV449: $i,SV94: $i] :
( ( ( in @ ( ordered_pair @ SV94 @ SV449 ) @ SV326 )
= $false )
| ( ( in @ SV449 @ ( relation_rng @ SV326 ) )
= $false )
| ( ( ~ ( in @ SV449 @ SV282 ) )
= $true )
| ( ( in @ SV94 @ ( relation_inverse_image @ SV326 @ SV282 ) )
= $true )
| ( ( relation @ SV326 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2733]) ).
thf(2845,plain,
! [SV94: $i,SV283: $i,SV327: $i] :
( ( ( ~ ( in @ ( sK51_D @ SV327 @ SV283 @ SV94 ) @ ( relation_rng @ SV327 ) )
| ~ ( in @ ( ordered_pair @ SV94 @ ( sK51_D @ SV327 @ SV283 @ SV94 ) ) @ SV327 ) )
= $false )
| ( ( in @ SV94 @ ( relation_inverse_image @ SV327 @ SV283 ) )
= $false )
| ( ( relation @ SV327 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2734]) ).
thf(2846,plain,
! [SV175: $i,SV95: $i,SV450: $i] :
( ( ( relation @ SV450 )
= $false )
| ( ( function @ SV450 )
= $false )
| ( ( ~ ( in @ SV95 @ ( relation_dom @ SV450 ) )
| ~ ( in @ ( apply @ SV450 @ SV95 ) @ ( relation_dom @ SV175 ) )
| ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SV450 @ SV175 ) ) ) )
= $true )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2736]) ).
thf(2847,plain,
! [SV175: $i,SV95: $i,SV486: $i] :
( ( ( ~ ( function @ SV486 )
| ~ ( relation @ SV486 ) )
= $true )
| ( ( ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SV486 @ SV175 ) ) )
| ( in @ SV95 @ ( relation_dom @ SV486 ) ) )
= $true )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2737]) ).
thf(2848,plain,
! [SV175: $i,SV95: $i,SV487: $i] :
( ( ( ~ ( function @ SV487 )
| ~ ( relation @ SV487 ) )
= $true )
| ( ( ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SV487 @ SV175 ) ) )
| ( in @ ( apply @ SV487 @ SV95 ) @ ( relation_dom @ SV175 ) ) )
= $true )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2738]) ).
thf(2849,plain,
! [SV96: $i,SV368: $i,SV404: $i] :
( ( ( ~ ( in @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ SV368 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 ) )
= $true )
| ( ( SV404
= ( relation_dom_restriction @ SV96 @ SV368 ) )
= $true )
| ( ( relation @ SV404 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2739]) ).
thf(2850,plain,
! [SV96: $i,SV368: $i,SV404: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ SV368 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 ) ) ) )
= $true )
| ( ( SV404
= ( relation_dom_restriction @ SV96 @ SV368 ) )
= $true )
| ( ( relation @ SV404 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2740]) ).
thf(2851,plain,
! [SV405: $i,SV96: $i,SV369: $i] :
( ( ( ~ ! [SY982: $i,SY983: $i] :
( ~ ( in @ SY982 @ SV369 )
| ~ ( in @ ( ordered_pair @ SY982 @ SY983 ) @ SV96 )
| ( in @ ( ordered_pair @ SY982 @ SY983 ) @ SV405 ) ) )
= $false )
| ( ( SV405
= ( relation_dom_restriction @ SV96 @ SV369 ) )
= $false )
| ( ( relation @ SV405 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2741]) ).
thf(2852,plain,
! [SV96: $i,SV369: $i,SV405: $i] :
( ( ( ~ ~ ( ~ ! [SY984: $i] :
( ! [SY985: $i] :
~ ( in @ ( ordered_pair @ SY984 @ SY985 ) @ SV405 )
| ( in @ SY984 @ SV369 ) )
| ~ ! [SY986: $i,SY987: $i] :
( ~ ( in @ ( ordered_pair @ SY986 @ SY987 ) @ SV405 )
| ( in @ ( ordered_pair @ SY986 @ SY987 ) @ SV96 ) ) ) )
= $false )
| ( ( SV405
= ( relation_dom_restriction @ SV96 @ SV369 ) )
= $false )
| ( ( relation @ SV405 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2741]) ).
thf(2853,plain,
! [SV97: $i,SV370: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SV370 @ SV97 ) @ ( sK12_SY396 @ SV370 @ SV97 ) ) @ SV370 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SV370 @ SV97 ) @ ( sK11_C @ SV370 @ SV97 ) ) @ SV97 ) )
= $true )
| ( ( SV370
= ( relation_inverse @ SV97 ) )
= $true )
| ( ( relation @ SV370 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2742]) ).
thf(2854,plain,
! [SV97: $i,SV370: $i] :
( ( ( in @ ( ordered_pair @ ( sK11_C @ SV370 @ SV97 ) @ ( sK12_SY396 @ SV370 @ SV97 ) ) @ SV370 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK12_SY396 @ SV370 @ SV97 ) @ ( sK11_C @ SV370 @ SV97 ) ) @ SV97 )
= $true )
| ( ( SV370
= ( relation_inverse @ SV97 ) )
= $true )
| ( ( relation @ SV370 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2743]) ).
thf(2855,plain,
! [SV97: $i,SV371: $i] :
( ( ( ! [SY947: $i,SY948: $i] :
( ~ ( in @ ( ordered_pair @ SY947 @ SY948 ) @ SV371 )
| ( in @ ( ordered_pair @ SY948 @ SY947 ) @ SV97 ) ) )
= $true )
| ( ( SV371
= ( relation_inverse @ SV97 ) )
= $false )
| ( ( relation @ SV371 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2744]) ).
thf(2856,plain,
! [SV371: $i,SV97: $i] :
( ( ( ! [SY949: $i,SY950: $i] :
( ~ ( in @ ( ordered_pair @ SY950 @ SY949 ) @ SV97 )
| ( in @ ( ordered_pair @ SY949 @ SY950 ) @ SV371 ) ) )
= $true )
| ( ( SV371
= ( relation_inverse @ SV97 ) )
= $false )
| ( ( relation @ SV371 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2745]) ).
thf(2857,plain,
! [SV98: $i,SV372: $i,SV488: $i] :
( ( ( in @ ( ordered_pair @ SV488 @ ( sK60_C @ SV372 @ SV98 ) ) @ SV98 )
= $false )
| ( ( ~ ( in @ ( sK60_C @ SV372 @ SV98 ) @ SV372 ) )
= $true )
| ( ( SV372
= ( relation_rng @ SV98 ) )
= $true )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2746]) ).
thf(2858,plain,
! [SV373: $i,SV98: $i,SV489: $i] :
( ( ( ! [SY1026: $i] :
~ ( in @ ( ordered_pair @ SY1026 @ SV489 ) @ SV98 ) )
= $true )
| ( ( in @ SV489 @ SV373 )
= $true )
| ( ( SV373
= ( relation_rng @ SV98 ) )
= $false )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2747]) ).
thf(2859,plain,
! [SV98: $i,SV373: $i,SV490: $i] :
( ( ( ~ ( in @ SV490 @ SV373 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK59_D @ SV490 @ SV373 @ SV98 ) @ SV490 ) @ SV98 )
= $true )
| ( ( SV373
= ( relation_rng @ SV98 ) )
= $false )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2748]) ).
thf(2860,plain,
! [SV286: $i,SV328: $i,SV100: $i] :
( ( ( in @ SV100 @ ( relation_dom @ SV328 ) )
= $false )
| ( ( SV286
= ( apply @ SV328 @ SV100 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV100 @ SV286 ) @ SV328 )
= $true )
| ( ( function @ SV328 )
= $false )
| ( ( relation @ SV328 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2749]) ).
thf(2861,plain,
! [SV428: $i,SV406: $i,SV100: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV100 @ SV406 ) @ SV428 ) )
= $true )
| ( ( SV406
= ( apply @ SV428 @ SV100 ) )
= $true )
| ( ( function @ SV428 )
= $false )
| ( ( relation @ SV428 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2750]) ).
thf(2862,plain,
! [SV429: $i,SV407: $i,SV100: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV100 @ SV407 ) @ SV429 ) )
= $true )
| ( ( in @ SV100 @ ( relation_dom @ SV429 ) )
= $true )
| ( ( function @ SV429 )
= $false )
| ( ( relation @ SV429 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2751]) ).
thf(2863,plain,
! [SV101: $i,SV215: $i,SV451: $i] :
( ( ( ~ ( ! [SY1009: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ SY1009 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY1009 @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV215 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV451 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK10_SY395 @ SV451 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV215 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV451 ) ) )
= $false )
| ( ( SV451
= ( relation_composition @ SV101 @ SV215 ) )
= $true )
| ( ( relation @ SV451 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2752]) ).
thf(2864,plain,
! [SV215: $i,SV101: $i,SV452: $i] :
( ( ( SV452
= ( relation_composition @ SV101 @ SV215 ) )
= $false )
| ( ( ~ ( ~ ! [SY1010: $i,SY1011: $i] :
( ! [SY783: $i] :
( ~ ( in @ ( ordered_pair @ SY1010 @ SY783 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY783 @ SY1011 ) @ SV215 ) )
| ( in @ ( ordered_pair @ SY1010 @ SY1011 ) @ SV452 ) )
| ~ ! [SY1013: $i,SY1014: $i] :
( ~ ( in @ ( ordered_pair @ SY1013 @ SY1014 ) @ SV452 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1013 @ ( sK7_F @ SY1014 @ SY1013 @ SV452 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY1014 @ SY1013 @ SV452 @ SV215 @ SV101 ) @ SY1014 ) @ SV215 ) ) ) ) )
= $true )
| ( ( relation @ SV452 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2753]) ).
thf(2865,plain,
! [SV103: $i,SV408: $i,SV491: $i] :
( ( ( ~ ( subset @ SV491 @ SV408 ) )
= $true )
| ( ( in @ SV491 @ ( sK3_SY386 @ SV408 @ SV103 ) )
= $true )
| ( ( ~ ( in @ SV408 @ ( sK2_B @ SV103 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2754]) ).
thf(2866,plain,
! [SV472: $i,SV103: $i,SV462: $i] :
( ( ( ~ ( in @ SV462 @ ( sK2_B @ SV103 ) ) )
= $true )
| ( ( ~ ( subset @ SV472 @ SV462 ) )
= $true )
| ( ( in @ SV472 @ ( sK2_B @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2756]) ).
thf(2867,plain,
! [SV455: $i,SV437: $i,SV178: $i,SV107: $i] :
( ( ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SV437 ) @ SV455 ) )
= $false )
| ( ( in @ SV107 @ SV437 )
= $true )
| ( ( relation @ SV455 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2760]) ).
thf(2868,plain,
! [SV456: $i,SV438: $i,SV178: $i,SV107: $i] :
( ( ( in @ ( ordered_pair @ SV107 @ SV178 ) @ ( relation_composition @ ( identity_relation @ SV438 ) @ SV456 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV107 @ SV178 ) @ SV456 )
= $true )
| ( ( relation @ SV456 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2761]) ).
thf(2869,plain,
! [SV108: $i,SV379: $i] :
( ( ( in @ ( ordered_pair @ ( sK19_C @ SV379 @ SV108 ) @ ( sK20_SY399 @ SV379 @ SV108 ) ) @ SV379 )
= $false )
| ( ( subset @ SV108 @ SV379 )
= $true )
| ( ( relation @ SV379 )
= $false )
| ( ( relation @ SV108 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2763]) ).
thf(2870,plain,
! [SV380: $i,SV108: $i,SV492: $i,SV473: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV473 @ SV492 ) @ SV108 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV473 @ SV492 ) @ SV380 )
= $true )
| ( ( subset @ SV108 @ SV380 )
= $false )
| ( ( relation @ SV380 )
= $false )
| ( ( relation @ SV108 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2764]) ).
thf(2871,plain,
! [SV110: $i,SV465: $i] :
( ( ( function @ SV465 )
= $false )
| ( ( ~ ( relation @ SV465 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) )
| ( SV465
= ( function_inverse @ SV110 ) ) )
= $true )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2769]) ).
thf(2872,plain,
! [SV110: $i,SV502: $i] :
( ( ( ~ ( function @ SV502 )
| ~ ( relation @ SV502 )
| ( SV502
!= ( function_inverse @ SV110 ) )
| ~ ( ~ ~ ( ~ ! [SY1030: $i,SY1031: $i] :
( ( SY1031
!= ( apply @ SV502 @ SY1030 ) )
| ~ ( in @ SY1030 @ ( relation_rng @ SV110 ) )
| ( SY1030
= ( apply @ SV110 @ SY1031 ) ) )
| ~ ! [SY1032: $i,SY1033: $i] :
( ( SY1033
!= ( apply @ SV502 @ SY1032 ) )
| ~ ( in @ SY1032 @ ( relation_rng @ SV110 ) )
| ( in @ SY1033 @ ( relation_dom @ SV110 ) ) ) )
| ~ ~ ( ~ ! [SY1034: $i,SY1035: $i] :
( ( SY1034
!= ( apply @ SV110 @ SY1035 ) )
| ~ ( in @ SY1035 @ ( relation_dom @ SV110 ) )
| ( SY1035
= ( apply @ SV502 @ SY1034 ) ) )
| ~ ! [SY644: $i] :
( ! [SY645: $i] :
( ( SY644
!= ( apply @ SV110 @ SY645 ) )
| ~ ( in @ SY645 @ ( relation_dom @ SV110 ) ) )
| ( in @ SY644 @ ( relation_rng @ SV110 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2770]) ).
thf(2873,plain,
! [SV110: $i,SV503: $i] :
( ( ( ~ ( function @ SV503 )
| ~ ( relation @ SV503 )
| ( SV503
!= ( function_inverse @ SV110 ) )
| ( ( relation_dom @ SV503 )
= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2771]) ).
thf(2874,plain,
! [SV113: $i,SV474: $i] :
( ( ( in @ SV474 @ ( relation_dom @ SV113 ) )
= $false )
| ( ( ! [SY1018: $i] :
( ( SY1018
!= ( apply @ SV113 @ SV474 ) )
| ( in @ ( ordered_pair @ SV474 @ SY1018 ) @ SV113 ) ) )
= $true )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2772]) ).
thf(2875,plain,
! [SV113: $i,SV475: $i] :
( ( ( in @ SV475 @ ( relation_dom @ SV113 ) )
= $false )
| ( ( ! [SY1019: $i] :
( ~ ( in @ ( ordered_pair @ SV475 @ SY1019 ) @ SV113 )
| ( SY1019
= ( apply @ SV113 @ SV475 ) ) ) )
= $true )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2773]) ).
thf(2876,plain,
! [SV476: $i,SV113: $i,SV504: $i] :
( ( ( ( SV504
!= ( apply @ SV113 @ SV476 ) )
| ( SV504 = empty_set ) )
= $true )
| ( ( in @ SV476 @ ( relation_dom @ SV113 ) )
= $true )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2774]) ).
thf(2877,plain,
! [SV477: $i,SV113: $i,SV505: $i] :
( ( ( ( SV505 != empty_set )
| ( SV505
= ( apply @ SV113 @ SV477 ) ) )
= $true )
| ( ( in @ SV477 @ ( relation_dom @ SV113 ) )
= $true )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2775]) ).
thf(2878,plain,
! [SV114: $i,SV301: $i,SV338: $i] :
( ( ( ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV338 ) )
= $true )
| ( ( ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV114 ) )
= $true )
| ( ( SV338
= ( set_union2 @ SV114 @ SV301 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2776]) ).
thf(2879,plain,
! [SV114: $i,SV301: $i,SV338: $i] :
( ( ( ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV338 ) )
= $true )
| ( ( ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV301 ) )
= $true )
| ( ( SV338
= ( set_union2 @ SV114 @ SV301 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2777]) ).
thf(2880,plain,
! [SV302: $i,SV114: $i,SV339: $i,SV478: $i] :
( ( ( in @ SV478 @ SV339 )
= $false )
| ( ( ( in @ SV478 @ SV114 )
| ( in @ SV478 @ SV302 ) )
= $true )
| ( ( SV339
= ( set_union2 @ SV114 @ SV302 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2778]) ).
thf(2881,plain,
! [SV302: $i,SV339: $i,SV114: $i] :
( ( ( ! [SY896: $i] :
( ~ ( in @ SY896 @ SV114 )
| ( in @ SY896 @ SV339 ) ) )
= $true )
| ( ( SV339
= ( set_union2 @ SV114 @ SV302 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2779]) ).
thf(2882,plain,
! [SV114: $i,SV339: $i,SV302: $i] :
( ( ( ! [SY897: $i] :
( ~ ( in @ SY897 @ SV302 )
| ( in @ SY897 @ SV339 ) ) )
= $true )
| ( ( SV339
= ( set_union2 @ SV114 @ SV302 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2780]) ).
thf(2883,plain,
! [SV116: $i,SV306: $i,SV342: $i] :
( ( ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV306 )
= $false )
| ( ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV116 )
= $false )
| ( ( ~ ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV342 ) )
= $true )
| ( ( SV342
= ( set_intersection2 @ SV116 @ SV306 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2781]) ).
thf(2884,plain,
! [SV116: $i,SV306: $i,SV342: $i] :
( ( ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV116 )
= $true )
| ( ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV342 )
= $true )
| ( ( SV342
= ( set_intersection2 @ SV116 @ SV306 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2782]) ).
thf(2885,plain,
! [SV116: $i,SV306: $i,SV342: $i] :
( ( ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV306 )
= $true )
| ( ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV342 )
= $true )
| ( ( SV342
= ( set_intersection2 @ SV116 @ SV306 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2783]) ).
thf(2886,plain,
! [SV343: $i,SV307: $i,SV116: $i,SV479: $i] :
( ( ( ~ ( in @ SV479 @ SV116 ) )
= $true )
| ( ( ~ ( in @ SV479 @ SV307 ) )
= $true )
| ( ( in @ SV479 @ SV343 )
= $true )
| ( ( SV343
= ( set_intersection2 @ SV116 @ SV307 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2784]) ).
thf(2887,plain,
! [SV307: $i,SV116: $i,SV343: $i] :
( ( ( ! [SY899: $i] :
( ~ ( in @ SY899 @ SV343 )
| ( in @ SY899 @ SV116 ) ) )
= $true )
| ( ( SV343
= ( set_intersection2 @ SV116 @ SV307 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2785]) ).
thf(2888,plain,
! [SV116: $i,SV307: $i,SV343: $i] :
( ( ( ! [SY900: $i] :
( ~ ( in @ SY900 @ SV343 )
| ( in @ SY900 @ SV307 ) ) )
= $true )
| ( ( SV343
= ( set_intersection2 @ SV116 @ SV307 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2786]) ).
thf(2889,plain,
! [SV251: $i,SV308: $i] :
( ( ( ( sK44_C @ SV308 @ SV251 )
= ( sK45_SY414 @ SV308 @ SV251 ) )
= $false )
| ( ( ~ ( in @ ( sK44_C @ SV308 @ SV251 ) @ SV251 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 ) )
= $true )
| ( ( SV308
= ( identity_relation @ SV251 ) )
= $true )
| ( ( relation @ SV308 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2787]) ).
thf(2890,plain,
! [SV251: $i,SV308: $i] :
( ( ( ( ( sK44_C @ SV308 @ SV251 )
= ( sK45_SY414 @ SV308 @ SV251 ) )
| ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 ) )
= $true )
| ( ( SV308
= ( identity_relation @ SV251 ) )
= $true )
| ( ( relation @ SV308 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2788]) ).
thf(2891,plain,
! [SV251: $i,SV308: $i] :
( ( ( ( in @ ( sK44_C @ SV308 @ SV251 ) @ SV251 )
| ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 ) )
= $true )
| ( ( SV308
= ( identity_relation @ SV251 ) )
= $true )
| ( ( relation @ SV308 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2789]) ).
thf(2892,plain,
! [SV309: $i,SV252: $i,SV506: $i,SV493: $i] :
( ( ( ( SV493 != SV506 )
| ~ ( in @ SV493 @ SV252 )
| ( in @ ( ordered_pair @ SV493 @ SV506 ) @ SV309 ) )
= $true )
| ( ( SV309
= ( identity_relation @ SV252 ) )
= $false )
| ( ( relation @ SV309 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2790]) ).
thf(2893,plain,
! [SV252: $i,SV309: $i] :
( ( ( ~ ! [SY863: $i,SY864: $i] :
( ~ ( in @ ( ordered_pair @ SY863 @ SY864 ) @ SV309 )
| ( SY863 = SY864 ) ) )
= $false )
| ( ( SV309
= ( identity_relation @ SV252 ) )
= $false )
| ( ( relation @ SV309 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2791]) ).
thf(2894,plain,
! [SV252: $i,SV309: $i] :
( ( ( ~ ! [SY865: $i] :
( ! [SY866: $i] :
~ ( in @ ( ordered_pair @ SY865 @ SY866 ) @ SV309 )
| ( in @ SY865 @ SV252 ) ) )
= $false )
| ( ( SV309
= ( identity_relation @ SV252 ) )
= $false )
| ( ( relation @ SV309 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2791]) ).
thf(2895,plain,
! [SV253: $i,SV311: $i] :
( ( ( in @ ( sK50_C @ SV311 @ SV253 ) @ SV253 )
= $true )
| ( ( ( ( relation_dom @ SV311 )
!= SV253 ) )
= $true )
| ( ( SV311
= ( identity_relation @ SV253 ) )
= $true )
| ( ( function @ SV311 )
= $false )
| ( ( relation @ SV311 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2794]) ).
thf(2896,plain,
! [SV253: $i,SV311: $i] :
( ( ( ( ( apply @ SV311 @ ( sK50_C @ SV311 @ SV253 ) )
!= ( sK50_C @ SV311 @ SV253 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV311 )
!= SV253 ) )
= $true )
| ( ( SV311
= ( identity_relation @ SV253 ) )
= $true )
| ( ( function @ SV311 )
= $false )
| ( ( relation @ SV311 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2795]) ).
thf(2897,plain,
! [SV391: $i,SV420: $i] :
( ( ( SV420
= ( identity_relation @ SV391 ) )
= $false )
| ( ( ! [SY997: $i] :
( ~ ( in @ SY997 @ SV391 )
| ( ( apply @ SV420 @ SY997 )
= SY997 ) ) )
= $true )
| ( ( function @ SV420 )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2796]) ).
thf(2898,plain,
! [SV392: $i,SV421: $i] :
( ( ( SV421
= ( identity_relation @ SV392 ) )
= $false )
| ( ( ( relation_dom @ SV421 )
= SV392 )
= $true )
| ( ( function @ SV421 )
= $false )
| ( ( relation @ SV421 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2797]) ).
thf(2899,plain,
! [SV345: $i,SV312: $i,SV494: $i,SV118: $i,SV480: $i] :
( ( ( ~ ( in @ SV480 @ SV118 )
| ~ ( in @ SV494 @ SV312 ) )
= $true )
| ( ( ( ( sK23_D @ SV345 @ SV312 @ SV118 )
!= ( ordered_pair @ SV480 @ SV494 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV345 @ SV312 @ SV118 ) @ SV345 ) )
= $true )
| ( ( SV345
= ( cartesian_product2 @ SV118 @ SV312 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2798]) ).
thf(2900,plain,
! [SV118: $i,SV312: $i,SV345: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_SY403 @ SV345 @ SV312 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK25_SY405 @ SV345 @ SV312 @ SV118 ) @ SV312 ) ) )
= $true )
| ( ( in @ ( sK23_D @ SV345 @ SV312 @ SV118 ) @ SV345 )
= $true )
| ( ( SV345
= ( cartesian_product2 @ SV118 @ SV312 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2799]) ).
thf(2901,plain,
! [SV118: $i,SV312: $i,SV345: $i] :
( ( ( ( sK23_D @ SV345 @ SV312 @ SV118 )
= ( ordered_pair @ ( sK24_SY403 @ SV345 @ SV312 @ SV118 ) @ ( sK25_SY405 @ SV345 @ SV312 @ SV118 ) ) )
= $true )
| ( ( in @ ( sK23_D @ SV345 @ SV312 @ SV118 ) @ SV345 )
= $true )
| ( ( SV345
= ( cartesian_product2 @ SV118 @ SV312 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2800]) ).
thf(2902,plain,
! [SV346: $i,SV481: $i,SV313: $i,SV118: $i,SV507: $i] :
( ( ( ! [SY1038: $i] :
( ~ ( in @ SV507 @ SV118 )
| ~ ( in @ SY1038 @ SV313 )
| ( SV481
!= ( ordered_pair @ SV507 @ SY1038 ) ) ) )
= $true )
| ( ( in @ SV481 @ SV346 )
= $true )
| ( ( SV346
= ( cartesian_product2 @ SV118 @ SV313 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2801]) ).
thf(2903,plain,
! [SV118: $i,SV313: $i,SV346: $i,SV482: $i] :
( ( ( in @ SV482 @ SV346 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SV482 @ SV346 @ SV313 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK22_SY400 @ SV482 @ SV346 @ SV313 @ SV118 ) @ SV313 ) )
| ( SV482
!= ( ordered_pair @ ( sK21_E @ SV482 @ SV346 @ SV313 @ SV118 ) @ ( sK22_SY400 @ SV482 @ SV346 @ SV313 @ SV118 ) ) ) ) )
= $true )
| ( ( SV346
= ( cartesian_product2 @ SV118 @ SV313 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2802]) ).
thf(2904,plain,
! [SV316: $i,SV254: $i,SV467: $i] :
( ( ( in @ SV467 @ SV254 )
= $false )
| ( ( in @ ( sK15_C @ SV316 @ SV254 ) @ SV467 )
= $false )
| ( ( ~ ( in @ ( sK15_C @ SV316 @ SV254 ) @ SV316 ) )
= $true )
| ( ( SV316
= ( union @ SV254 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2803]) ).
thf(2905,plain,
! [SV317: $i,SV255: $i,SV495: $i,SV468: $i] :
( ( ( ~ ( in @ SV468 @ SV495 ) )
= $true )
| ( ( ~ ( in @ SV495 @ SV255 ) )
= $true )
| ( ( in @ SV468 @ SV317 )
= $true )
| ( ( SV317
= ( union @ SV255 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2806]) ).
thf(2906,plain,
! [SV255: $i,SV317: $i,SV469: $i] :
( ( ( ~ ( in @ SV469 @ ( sK14_D @ SV469 @ SV317 @ SV255 ) )
| ~ ( in @ ( sK14_D @ SV469 @ SV317 @ SV255 ) @ SV255 ) )
= $false )
| ( ( in @ SV469 @ SV317 )
= $false )
| ( ( SV317
= ( union @ SV255 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2807]) ).
thf(2907,plain,
! [SV120: $i,SV393: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV120 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV393 ) )
= $true )
| ( ( SV120 = SV393 )
= $true )
| ( ( relation @ SV393 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2808]) ).
thf(2908,plain,
! [SV120: $i,SV393: $i] :
( ( ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV120 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV393 )
= $true )
| ( ( SV120 = SV393 )
= $true )
| ( ( relation @ SV393 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2809]) ).
thf(2909,plain,
! [SV394: $i,SV120: $i] :
( ( ( ! [SY964: $i,SY965: $i] :
( ~ ( in @ ( ordered_pair @ SY964 @ SY965 ) @ SV120 )
| ( in @ ( ordered_pair @ SY964 @ SY965 ) @ SV394 ) ) )
= $true )
| ( ( SV120 = SV394 )
= $false )
| ( ( relation @ SV394 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2810]) ).
thf(2910,plain,
! [SV120: $i,SV394: $i] :
( ( ( ! [SY966: $i,SY967: $i] :
( ~ ( in @ ( ordered_pair @ SY966 @ SY967 ) @ SV394 )
| ( in @ ( ordered_pair @ SY966 @ SY967 ) @ SV120 ) ) )
= $true )
| ( ( SV120 = SV394 )
= $false )
| ( ( relation @ SV394 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2811]) ).
thf(2911,plain,
! [SV351: $i,SV424: $i] :
( ( ( ~ ( in @ ( sK33_SY406 @ SV424 @ SV351 ) @ SV351 )
| ~ ~ ( in @ ( sK32_C @ SV424 @ SV351 ) @ ( sK33_SY406 @ SV424 @ SV351 ) ) )
= $false )
| ( ( ~ ( in @ ( sK32_C @ SV424 @ SV351 ) @ SV424 ) )
= $true )
| ( ( SV424
= ( set_meet @ SV351 ) )
= $true )
| ( ( SV351 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2812]) ).
thf(2912,plain,
! [SV424: $i,SV351: $i,SV508: $i] :
( ( ( ~ ( in @ SV508 @ SV351 )
| ( in @ ( sK32_C @ SV424 @ SV351 ) @ SV508 ) )
= $true )
| ( ( in @ ( sK32_C @ SV424 @ SV351 ) @ SV424 )
= $true )
| ( ( SV424
= ( set_meet @ SV351 ) )
= $true )
| ( ( SV351 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2813]) ).
thf(2913,plain,
! [SV352: $i,SV425: $i,SV509: $i] :
( ( ( ~ ( ~ ( in @ ( sK31_D @ SV509 @ SV425 @ SV352 ) @ SV352 )
| ~ ~ ( in @ SV509 @ ( sK31_D @ SV509 @ SV425 @ SV352 ) ) )
| ( in @ SV509 @ SV425 ) )
= $true )
| ( ( SV425
= ( set_meet @ SV352 ) )
= $false )
| ( ( SV352 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2814]) ).
thf(2914,plain,
! [SV352: $i,SV425: $i,SV510: $i] :
( ( ( ~ ( in @ SV510 @ SV425 )
| ! [SY1039: $i] :
( ~ ( in @ SY1039 @ SV352 )
| ( in @ SV510 @ SY1039 ) ) )
= $true )
| ( ( SV425
= ( set_meet @ SV352 ) )
= $false )
| ( ( SV352 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2815]) ).
thf(2915,plain,
! [SV87: $i,SV320: $i,SV271: $i,SV446: $i] :
( ( ( in @ SV446 @ SV271 )
= $false )
| ( ( in @ SV446 @ ( relation_dom @ SV320 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV446 @ SV87 ) @ SV320 )
= $false )
| ( ( in @ SV87 @ ( relation_image @ SV320 @ SV271 ) )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2816]) ).
thf(2916,plain,
! [SV87: $i,SV272: $i,SV321: $i] :
( ( ( ~ ( in @ ( sK52_D @ SV321 @ SV272 @ SV87 ) @ ( relation_dom @ SV321 ) ) )
= $false )
| ( ( in @ SV87 @ ( relation_image @ SV321 @ SV272 ) )
= $false )
| ( ( relation @ SV321 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2817]) ).
thf(2917,plain,
! [SV87: $i,SV272: $i,SV321: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV321 @ SV272 @ SV87 ) @ SV87 ) @ SV321 ) )
= $false )
| ( ( in @ SV87 @ ( relation_image @ SV321 @ SV272 ) )
= $false )
| ( ( relation @ SV321 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2817]) ).
thf(2918,plain,
! [SV88: $i,SV274: $i,SV322: $i] :
( ( ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV274 )
= $false )
| ( ( in @ ( sK13_D @ SV322 @ SV274 @ SV88 ) @ SV322 )
= $true )
| ( ( SV322
= ( set_difference @ SV88 @ SV274 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2820]) ).
thf(2919,plain,
! [SV323: $i,SV275: $i,SV88: $i,SV470: $i] :
( ( ( in @ SV470 @ SV88 )
= $false )
| ( ( in @ SV470 @ SV275 )
= $true )
| ( ( in @ SV470 @ SV323 )
= $true )
| ( ( SV323
= ( set_difference @ SV88 @ SV275 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2821]) ).
thf(2920,plain,
! [SV275: $i,SV88: $i,SV323: $i,SV511: $i] :
( ( ( ~ ( in @ SV511 @ SV323 )
| ( in @ SV511 @ SV88 ) )
= $true )
| ( ( SV323
= ( set_difference @ SV88 @ SV275 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2822]) ).
thf(2921,plain,
! [SV88: $i,SV275: $i,SV323: $i,SV512: $i] :
( ( ( ~ ( in @ SV512 @ SV323 )
| ~ ( in @ SV512 @ SV275 ) )
= $true )
| ( ( SV323
= ( set_difference @ SV88 @ SV275 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2823]) ).
thf(2922,plain,
! [SV89: $i,SV174: $i,SV398: $i] :
( ( ( ~ ( in @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV174 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 ) )
= $true )
| ( ( SV398
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2824]) ).
thf(2923,plain,
! [SV89: $i,SV174: $i,SV398: $i] :
( ( ( ~ ( ( in @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) @ SV89 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV174 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 ) ) )
= $false )
| ( ( SV398
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2825]) ).
thf(2924,plain,
! [SV399: $i,SV174: $i,SV89: $i] :
( ( ( ! [SY968: $i,SY969: $i] :
( ~ ( in @ SY969 @ SV89 )
| ~ ( in @ ( ordered_pair @ SY968 @ SY969 ) @ SV174 )
| ( in @ ( ordered_pair @ SY968 @ SY969 ) @ SV399 ) ) )
= $true )
| ( ( SV399
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2826]) ).
thf(2925,plain,
! [SV174: $i,SV89: $i,SV399: $i] :
( ( ( ~ ( ~ ! [SY970: $i,SY971: $i] :
( ~ ( in @ ( ordered_pair @ SY970 @ SY971 ) @ SV399 )
| ( in @ SY971 @ SV89 ) )
| ~ ! [SY972: $i,SY973: $i] :
( ~ ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV399 )
| ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV174 ) ) ) )
= $true )
| ( ( SV399
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2827]) ).
thf(2926,plain,
! [SV90: $i,SV276: $i,SV324: $i] :
( ( ( in @ ( sK27_D @ SV324 @ SV276 @ SV90 ) @ SV324 )
= $false )
| ( ( ( ( sK27_D @ SV324 @ SV276 @ SV90 )
!= SV90 ) )
= $true )
| ( ( SV324
= ( unordered_pair @ SV90 @ SV276 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2828]) ).
thf(2927,plain,
! [SV90: $i,SV276: $i,SV324: $i] :
( ( ( in @ ( sK27_D @ SV324 @ SV276 @ SV90 ) @ SV324 )
= $false )
| ( ( ( ( sK27_D @ SV324 @ SV276 @ SV90 )
!= SV276 ) )
= $true )
| ( ( SV324
= ( unordered_pair @ SV90 @ SV276 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2829]) ).
thf(2928,plain,
! [SV325: $i,SV277: $i,SV90: $i,SV471: $i] :
( ( ( SV471 = SV90 )
= $true )
| ( ( SV471 = SV277 )
= $true )
| ( ( in @ SV471 @ SV325 )
= $false )
| ( ( SV325
= ( unordered_pair @ SV90 @ SV277 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2830]) ).
thf(2929,plain,
! [SV277: $i,SV325: $i,SV90: $i,SV513: $i] :
( ( ( ( SV513 != SV90 )
| ( in @ SV513 @ SV325 ) )
= $true )
| ( ( SV325
= ( unordered_pair @ SV90 @ SV277 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2831]) ).
thf(2930,plain,
! [SV90: $i,SV325: $i,SV277: $i,SV514: $i] :
( ( ( ( SV514 != SV277 )
| ( in @ SV514 @ SV325 ) )
= $true )
| ( ( SV325
= ( unordered_pair @ SV90 @ SV277 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2832]) ).
thf(2931,plain,
! [SV483: $i,SV91: $i,SV362: $i] :
( ( ( in @ ( sK63_C @ SV362 @ SV91 ) @ SV362 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK63_C @ SV362 @ SV91 ) @ SV483 ) @ SV91 )
= $false )
| ( ( SV362
= ( relation_dom @ SV91 ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2833]) ).
thf(2932,plain,
! [SV363: $i,SV91: $i,SV515: $i,SV484: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV484 @ SV515 ) @ SV91 ) )
= $true )
| ( ( in @ SV484 @ SV363 )
= $true )
| ( ( SV363
= ( relation_dom @ SV91 ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2834]) ).
thf(2933,plain,
! [SV91: $i,SV363: $i,SV485: $i] :
( ( ( in @ SV485 @ SV363 )
= $false )
| ( ( in @ ( ordered_pair @ SV485 @ ( sK62_D @ SV485 @ SV363 @ SV91 ) ) @ SV91 )
= $true )
| ( ( SV363
= ( relation_dom @ SV91 ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2835]) ).
thf(2934,plain,
! [SV496: $i,SV92: $i,SV364: $i,SV400: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SV496 ) @ SV92 ) )
= $true )
| ( ( ~ ( in @ SV496 @ SV364 ) )
= $true )
| ( ( ~ ( in @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SV400 ) )
= $true )
| ( ( SV400
= ( relation_inverse_image @ SV92 @ SV364 ) )
= $true )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2836]) ).
thf(2935,plain,
! [SV92: $i,SV364: $i,SV400: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ ( sK36_SY409 @ SV400 @ SV364 @ SV92 ) ) @ SV92 ) )
= $false )
| ( ( in @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SV400 )
= $true )
| ( ( SV400
= ( relation_inverse_image @ SV92 @ SV364 ) )
= $true )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2837]) ).
thf(2936,plain,
! [SV92: $i,SV364: $i,SV400: $i] :
( ( ( ~ ( in @ ( sK36_SY409 @ SV400 @ SV364 @ SV92 ) @ SV364 ) )
= $false )
| ( ( in @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SV400 )
= $true )
| ( ( SV400
= ( relation_inverse_image @ SV92 @ SV364 ) )
= $true )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2837]) ).
thf(2937,plain,
! [SV401: $i,SV365: $i,SV92: $i,SV497: $i] :
( ( ( ! [SY1028: $i] :
( ~ ( in @ ( ordered_pair @ SV497 @ SY1028 ) @ SV92 )
| ~ ( in @ SY1028 @ SV365 ) ) )
= $true )
| ( ( in @ SV497 @ SV401 )
= $true )
| ( ( SV401
= ( relation_inverse_image @ SV92 @ SV365 ) )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2838]) ).
thf(2938,plain,
! [SV92: $i,SV365: $i,SV401: $i,SV498: $i] :
( ( ( ~ ( in @ SV498 @ SV401 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV498 @ ( sK34_E @ SV498 @ SV401 @ SV365 @ SV92 ) ) @ SV92 )
| ~ ( in @ ( sK34_E @ SV498 @ SV401 @ SV365 @ SV92 ) @ SV365 ) ) )
= $true )
| ( ( SV401
= ( relation_inverse_image @ SV92 @ SV365 ) )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2839]) ).
thf(2939,plain,
! [SV93: $i,SV366: $i,SV402: $i,SV499: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV499 @ ( sK38_D @ SV402 @ SV366 @ SV93 ) ) @ SV93 ) )
= $true )
| ( ( ~ ( in @ SV499 @ SV366 ) )
= $true )
| ( ( ~ ( in @ ( sK38_D @ SV402 @ SV366 @ SV93 ) @ SV402 ) )
= $true )
| ( ( SV402
= ( relation_image @ SV93 @ SV366 ) )
= $true )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2840]) ).
thf(2940,plain,
! [SV93: $i,SV366: $i,SV402: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SV402 @ SV366 @ SV93 ) @ ( sK38_D @ SV402 @ SV366 @ SV93 ) ) @ SV93 ) )
= $false )
| ( ( in @ ( sK38_D @ SV402 @ SV366 @ SV93 ) @ SV402 )
= $true )
| ( ( SV402
= ( relation_image @ SV93 @ SV366 ) )
= $true )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2841]) ).
thf(2941,plain,
! [SV93: $i,SV366: $i,SV402: $i] :
( ( ( ~ ( in @ ( sK39_SY411 @ SV402 @ SV366 @ SV93 ) @ SV366 ) )
= $false )
| ( ( in @ ( sK38_D @ SV402 @ SV366 @ SV93 ) @ SV402 )
= $true )
| ( ( SV402
= ( relation_image @ SV93 @ SV366 ) )
= $true )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2841]) ).
thf(2942,plain,
! [SV403: $i,SV367: $i,SV93: $i,SV500: $i] :
( ( ( ! [SY1029: $i] :
( ~ ( in @ ( ordered_pair @ SY1029 @ SV500 ) @ SV93 )
| ~ ( in @ SY1029 @ SV367 ) ) )
= $true )
| ( ( in @ SV500 @ SV403 )
= $true )
| ( ( SV403
= ( relation_image @ SV93 @ SV367 ) )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2842]) ).
thf(2943,plain,
! [SV93: $i,SV367: $i,SV403: $i,SV501: $i] :
( ( ( ~ ( in @ SV501 @ SV403 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SV501 @ SV403 @ SV367 @ SV93 ) @ SV501 ) @ SV93 )
| ~ ( in @ ( sK37_E @ SV501 @ SV403 @ SV367 @ SV93 ) @ SV367 ) ) )
= $true )
| ( ( SV403
= ( relation_image @ SV93 @ SV367 ) )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2843]) ).
thf(2944,plain,
! [SV94: $i,SV326: $i,SV282: $i,SV449: $i] :
( ( ( in @ SV449 @ SV282 )
= $false )
| ( ( in @ SV449 @ ( relation_rng @ SV326 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV94 @ SV449 ) @ SV326 )
= $false )
| ( ( in @ SV94 @ ( relation_inverse_image @ SV326 @ SV282 ) )
= $true )
| ( ( relation @ SV326 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2844]) ).
thf(2945,plain,
! [SV94: $i,SV283: $i,SV327: $i] :
( ( ( ~ ( in @ ( sK51_D @ SV327 @ SV283 @ SV94 ) @ ( relation_rng @ SV327 ) ) )
= $false )
| ( ( in @ SV94 @ ( relation_inverse_image @ SV327 @ SV283 ) )
= $false )
| ( ( relation @ SV327 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2845]) ).
thf(2946,plain,
! [SV283: $i,SV327: $i,SV94: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV94 @ ( sK51_D @ SV327 @ SV283 @ SV94 ) ) @ SV327 ) )
= $false )
| ( ( in @ SV94 @ ( relation_inverse_image @ SV327 @ SV283 ) )
= $false )
| ( ( relation @ SV327 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2845]) ).
thf(2947,plain,
! [SV175: $i,SV450: $i,SV95: $i] :
( ( ( ~ ( in @ SV95 @ ( relation_dom @ SV450 ) )
| ~ ( in @ ( apply @ SV450 @ SV95 ) @ ( relation_dom @ SV175 ) ) )
= $true )
| ( ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SV450 @ SV175 ) ) )
= $true )
| ( ( function @ SV450 )
= $false )
| ( ( relation @ SV450 )
= $false )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2846]) ).
thf(2948,plain,
! [SV175: $i,SV95: $i,SV486: $i] :
( ( ( ~ ( function @ SV486 ) )
= $true )
| ( ( ~ ( relation @ SV486 ) )
= $true )
| ( ( ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SV486 @ SV175 ) ) )
| ( in @ SV95 @ ( relation_dom @ SV486 ) ) )
= $true )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2847]) ).
thf(2949,plain,
! [SV175: $i,SV95: $i,SV487: $i] :
( ( ( ~ ( function @ SV487 ) )
= $true )
| ( ( ~ ( relation @ SV487 ) )
= $true )
| ( ( ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SV487 @ SV175 ) ) )
| ( in @ ( apply @ SV487 @ SV95 ) @ ( relation_dom @ SV175 ) ) )
= $true )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2848]) ).
thf(2950,plain,
! [SV96: $i,SV368: $i,SV404: $i] :
( ( ( ~ ( in @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ SV368 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV96 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 ) )
= $true )
| ( ( SV404
= ( relation_dom_restriction @ SV96 @ SV368 ) )
= $true )
| ( ( relation @ SV404 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2849]) ).
thf(2951,plain,
! [SV96: $i,SV368: $i,SV404: $i] :
( ( ( ~ ( ( in @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ SV368 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 ) ) )
= $false )
| ( ( SV404
= ( relation_dom_restriction @ SV96 @ SV368 ) )
= $true )
| ( ( relation @ SV404 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2850]) ).
thf(2952,plain,
! [SV405: $i,SV96: $i,SV369: $i] :
( ( ( ! [SY982: $i,SY983: $i] :
( ~ ( in @ SY982 @ SV369 )
| ~ ( in @ ( ordered_pair @ SY982 @ SY983 ) @ SV96 )
| ( in @ ( ordered_pair @ SY982 @ SY983 ) @ SV405 ) ) )
= $true )
| ( ( SV405
= ( relation_dom_restriction @ SV96 @ SV369 ) )
= $false )
| ( ( relation @ SV405 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2851]) ).
thf(2953,plain,
! [SV96: $i,SV369: $i,SV405: $i] :
( ( ( ~ ( ~ ! [SY984: $i] :
( ! [SY985: $i] :
~ ( in @ ( ordered_pair @ SY984 @ SY985 ) @ SV405 )
| ( in @ SY984 @ SV369 ) )
| ~ ! [SY986: $i,SY987: $i] :
( ~ ( in @ ( ordered_pair @ SY986 @ SY987 ) @ SV405 )
| ( in @ ( ordered_pair @ SY986 @ SY987 ) @ SV96 ) ) ) )
= $true )
| ( ( SV405
= ( relation_dom_restriction @ SV96 @ SV369 ) )
= $false )
| ( ( relation @ SV405 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2852]) ).
thf(2954,plain,
! [SV97: $i,SV370: $i] :
( ( ( in @ ( ordered_pair @ ( sK11_C @ SV370 @ SV97 ) @ ( sK12_SY396 @ SV370 @ SV97 ) ) @ SV370 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SV370 @ SV97 ) @ ( sK11_C @ SV370 @ SV97 ) ) @ SV97 ) )
= $true )
| ( ( SV370
= ( relation_inverse @ SV97 ) )
= $true )
| ( ( relation @ SV370 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2853]) ).
thf(2955,plain,
! [SV97: $i,SV371: $i,SV516: $i] :
( ( ( ! [SY1040: $i] :
( ~ ( in @ ( ordered_pair @ SV516 @ SY1040 ) @ SV371 )
| ( in @ ( ordered_pair @ SY1040 @ SV516 ) @ SV97 ) ) )
= $true )
| ( ( SV371
= ( relation_inverse @ SV97 ) )
= $false )
| ( ( relation @ SV371 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2855]) ).
thf(2956,plain,
! [SV371: $i,SV97: $i,SV517: $i] :
( ( ( ! [SY1041: $i] :
( ~ ( in @ ( ordered_pair @ SY1041 @ SV517 ) @ SV97 )
| ( in @ ( ordered_pair @ SV517 @ SY1041 ) @ SV371 ) ) )
= $true )
| ( ( SV371
= ( relation_inverse @ SV97 ) )
= $false )
| ( ( relation @ SV371 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2856]) ).
thf(2957,plain,
! [SV488: $i,SV98: $i,SV372: $i] :
( ( ( in @ ( sK60_C @ SV372 @ SV98 ) @ SV372 )
= $false )
| ( ( in @ ( ordered_pair @ SV488 @ ( sK60_C @ SV372 @ SV98 ) ) @ SV98 )
= $false )
| ( ( SV372
= ( relation_rng @ SV98 ) )
= $true )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2857]) ).
thf(2958,plain,
! [SV373: $i,SV98: $i,SV489: $i,SV518: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV518 @ SV489 ) @ SV98 ) )
= $true )
| ( ( in @ SV489 @ SV373 )
= $true )
| ( ( SV373
= ( relation_rng @ SV98 ) )
= $false )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2858]) ).
thf(2959,plain,
! [SV98: $i,SV373: $i,SV490: $i] :
( ( ( in @ SV490 @ SV373 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK59_D @ SV490 @ SV373 @ SV98 ) @ SV490 ) @ SV98 )
= $true )
| ( ( SV373
= ( relation_rng @ SV98 ) )
= $false )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2859]) ).
thf(2960,plain,
! [SV428: $i,SV406: $i,SV100: $i] :
( ( ( in @ ( ordered_pair @ SV100 @ SV406 ) @ SV428 )
= $false )
| ( ( SV406
= ( apply @ SV428 @ SV100 ) )
= $true )
| ( ( function @ SV428 )
= $false )
| ( ( relation @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2861]) ).
thf(2961,plain,
! [SV429: $i,SV407: $i,SV100: $i] :
( ( ( in @ ( ordered_pair @ SV100 @ SV407 ) @ SV429 )
= $false )
| ( ( in @ SV100 @ ( relation_dom @ SV429 ) )
= $true )
| ( ( function @ SV429 )
= $false )
| ( ( relation @ SV429 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2862]) ).
thf(2962,plain,
! [SV101: $i,SV215: $i,SV451: $i] :
( ( ( ~ ( ! [SY1009: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ SY1009 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY1009 @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV215 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV451 ) ) )
= $false )
| ( ( SV451
= ( relation_composition @ SV101 @ SV215 ) )
= $true )
| ( ( relation @ SV451 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2863]) ).
thf(2963,plain,
! [SV101: $i,SV215: $i,SV451: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK10_SY395 @ SV451 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV215 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV451 ) ) )
= $false )
| ( ( SV451
= ( relation_composition @ SV101 @ SV215 ) )
= $true )
| ( ( relation @ SV451 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2863]) ).
thf(2964,plain,
! [SV452: $i,SV215: $i,SV101: $i] :
( ( ( ~ ! [SY1010: $i,SY1011: $i] :
( ! [SY783: $i] :
( ~ ( in @ ( ordered_pair @ SY1010 @ SY783 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY783 @ SY1011 ) @ SV215 ) )
| ( in @ ( ordered_pair @ SY1010 @ SY1011 ) @ SV452 ) )
| ~ ! [SY1013: $i,SY1014: $i] :
( ~ ( in @ ( ordered_pair @ SY1013 @ SY1014 ) @ SV452 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1013 @ ( sK7_F @ SY1014 @ SY1013 @ SV452 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY1014 @ SY1013 @ SV452 @ SV215 @ SV101 ) @ SY1014 ) @ SV215 ) ) ) )
= $false )
| ( ( SV452
= ( relation_composition @ SV101 @ SV215 ) )
= $false )
| ( ( relation @ SV452 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2864]) ).
thf(2965,plain,
! [SV103: $i,SV408: $i,SV491: $i] :
( ( ( subset @ SV491 @ SV408 )
= $false )
| ( ( in @ SV491 @ ( sK3_SY386 @ SV408 @ SV103 ) )
= $true )
| ( ( ~ ( in @ SV408 @ ( sK2_B @ SV103 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2865]) ).
thf(2966,plain,
! [SV472: $i,SV103: $i,SV462: $i] :
( ( ( in @ SV462 @ ( sK2_B @ SV103 ) )
= $false )
| ( ( ~ ( subset @ SV472 @ SV462 ) )
= $true )
| ( ( in @ SV472 @ ( sK2_B @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2866]) ).
thf(2967,plain,
! [SV380: $i,SV108: $i,SV492: $i,SV473: $i] :
( ( ( in @ ( ordered_pair @ SV473 @ SV492 ) @ SV108 )
= $false )
| ( ( in @ ( ordered_pair @ SV473 @ SV492 ) @ SV380 )
= $true )
| ( ( subset @ SV108 @ SV380 )
= $false )
| ( ( relation @ SV380 )
= $false )
| ( ( relation @ SV108 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2870]) ).
thf(2968,plain,
! [SV110: $i,SV465: $i] :
( ( ( relation @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) )
| ( SV465
= ( function_inverse @ SV110 ) ) )
= $true )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2871]) ).
thf(2969,plain,
! [SV110: $i,SV502: $i] :
( ( ( ~ ( function @ SV502 )
| ~ ( relation @ SV502 ) )
= $true )
| ( ( ( SV502
!= ( function_inverse @ SV110 ) )
| ~ ( ~ ~ ( ~ ! [SY1030: $i,SY1031: $i] :
( ( SY1031
!= ( apply @ SV502 @ SY1030 ) )
| ~ ( in @ SY1030 @ ( relation_rng @ SV110 ) )
| ( SY1030
= ( apply @ SV110 @ SY1031 ) ) )
| ~ ! [SY1032: $i,SY1033: $i] :
( ( SY1033
!= ( apply @ SV502 @ SY1032 ) )
| ~ ( in @ SY1032 @ ( relation_rng @ SV110 ) )
| ( in @ SY1033 @ ( relation_dom @ SV110 ) ) ) )
| ~ ~ ( ~ ! [SY1034: $i,SY1035: $i] :
( ( SY1034
!= ( apply @ SV110 @ SY1035 ) )
| ~ ( in @ SY1035 @ ( relation_dom @ SV110 ) )
| ( SY1035
= ( apply @ SV502 @ SY1034 ) ) )
| ~ ! [SY644: $i] :
( ! [SY645: $i] :
( ( SY644
!= ( apply @ SV110 @ SY645 ) )
| ~ ( in @ SY645 @ ( relation_dom @ SV110 ) ) )
| ( in @ SY644 @ ( relation_rng @ SV110 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2872]) ).
thf(2970,plain,
! [SV110: $i,SV503: $i] :
( ( ( ~ ( function @ SV503 )
| ~ ( relation @ SV503 ) )
= $true )
| ( ( ( SV503
!= ( function_inverse @ SV110 ) )
| ( ( relation_dom @ SV503 )
= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2873]) ).
thf(2971,plain,
! [SV474: $i,SV113: $i,SV519: $i] :
( ( ( ( SV519
!= ( apply @ SV113 @ SV474 ) )
| ( in @ ( ordered_pair @ SV474 @ SV519 ) @ SV113 ) )
= $true )
| ( ( in @ SV474 @ ( relation_dom @ SV113 ) )
= $false )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2874]) ).
thf(2972,plain,
! [SV113: $i,SV520: $i,SV475: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV475 @ SV520 ) @ SV113 )
| ( SV520
= ( apply @ SV113 @ SV475 ) ) )
= $true )
| ( ( in @ SV475 @ ( relation_dom @ SV113 ) )
= $false )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2875]) ).
thf(2973,plain,
! [SV476: $i,SV113: $i,SV504: $i] :
( ( ( ( SV504
!= ( apply @ SV113 @ SV476 ) ) )
= $true )
| ( ( SV504 = empty_set )
= $true )
| ( ( in @ SV476 @ ( relation_dom @ SV113 ) )
= $true )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2876]) ).
thf(2974,plain,
! [SV477: $i,SV113: $i,SV505: $i] :
( ( ( ( SV505 != empty_set ) )
= $true )
| ( ( SV505
= ( apply @ SV113 @ SV477 ) )
= $true )
| ( ( in @ SV477 @ ( relation_dom @ SV113 ) )
= $true )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2877]) ).
thf(2975,plain,
! [SV114: $i,SV301: $i,SV338: $i] :
( ( ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV338 )
= $false )
| ( ( ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV114 ) )
= $true )
| ( ( SV338
= ( set_union2 @ SV114 @ SV301 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2878]) ).
thf(2976,plain,
! [SV114: $i,SV301: $i,SV338: $i] :
( ( ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV338 )
= $false )
| ( ( ~ ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV301 ) )
= $true )
| ( ( SV338
= ( set_union2 @ SV114 @ SV301 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2879]) ).
thf(2977,plain,
! [SV339: $i,SV302: $i,SV114: $i,SV478: $i] :
( ( ( in @ SV478 @ SV114 )
= $true )
| ( ( in @ SV478 @ SV302 )
= $true )
| ( ( in @ SV478 @ SV339 )
= $false )
| ( ( SV339
= ( set_union2 @ SV114 @ SV302 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2880]) ).
thf(2978,plain,
! [SV302: $i,SV339: $i,SV114: $i,SV521: $i] :
( ( ( ~ ( in @ SV521 @ SV114 )
| ( in @ SV521 @ SV339 ) )
= $true )
| ( ( SV339
= ( set_union2 @ SV114 @ SV302 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2881]) ).
thf(2979,plain,
! [SV114: $i,SV339: $i,SV302: $i,SV522: $i] :
( ( ( ~ ( in @ SV522 @ SV302 )
| ( in @ SV522 @ SV339 ) )
= $true )
| ( ( SV339
= ( set_union2 @ SV114 @ SV302 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2882]) ).
thf(2980,plain,
! [SV116: $i,SV306: $i,SV342: $i] :
( ( ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV342 )
= $false )
| ( ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV116 )
= $false )
| ( ( in @ ( sK17_D @ SV342 @ SV306 @ SV116 ) @ SV306 )
= $false )
| ( ( SV342
= ( set_intersection2 @ SV116 @ SV306 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2883]) ).
thf(2981,plain,
! [SV343: $i,SV307: $i,SV116: $i,SV479: $i] :
( ( ( in @ SV479 @ SV116 )
= $false )
| ( ( ~ ( in @ SV479 @ SV307 ) )
= $true )
| ( ( in @ SV479 @ SV343 )
= $true )
| ( ( SV343
= ( set_intersection2 @ SV116 @ SV307 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2886]) ).
thf(2982,plain,
! [SV307: $i,SV116: $i,SV343: $i,SV523: $i] :
( ( ( ~ ( in @ SV523 @ SV343 )
| ( in @ SV523 @ SV116 ) )
= $true )
| ( ( SV343
= ( set_intersection2 @ SV116 @ SV307 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2887]) ).
thf(2983,plain,
! [SV116: $i,SV307: $i,SV343: $i,SV524: $i] :
( ( ( ~ ( in @ SV524 @ SV343 )
| ( in @ SV524 @ SV307 ) )
= $true )
| ( ( SV343
= ( set_intersection2 @ SV116 @ SV307 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2888]) ).
thf(2984,plain,
! [SV251: $i,SV308: $i] :
( ( ( in @ ( sK44_C @ SV308 @ SV251 ) @ SV251 )
= $false )
| ( ( ( sK44_C @ SV308 @ SV251 )
= ( sK45_SY414 @ SV308 @ SV251 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 ) )
= $true )
| ( ( SV308
= ( identity_relation @ SV251 ) )
= $true )
| ( ( relation @ SV308 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2889]) ).
thf(2985,plain,
! [SV251: $i,SV308: $i] :
( ( ( ( sK44_C @ SV308 @ SV251 )
= ( sK45_SY414 @ SV308 @ SV251 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 )
= $true )
| ( ( SV308
= ( identity_relation @ SV251 ) )
= $true )
| ( ( relation @ SV308 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2890]) ).
thf(2986,plain,
! [SV251: $i,SV308: $i] :
( ( ( in @ ( sK44_C @ SV308 @ SV251 ) @ SV251 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 )
= $true )
| ( ( SV308
= ( identity_relation @ SV251 ) )
= $true )
| ( ( relation @ SV308 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2891]) ).
thf(2987,plain,
! [SV309: $i,SV252: $i,SV506: $i,SV493: $i] :
( ( ( ( SV493 != SV506 )
| ~ ( in @ SV493 @ SV252 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV493 @ SV506 ) @ SV309 )
= $true )
| ( ( SV309
= ( identity_relation @ SV252 ) )
= $false )
| ( ( relation @ SV309 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2892]) ).
thf(2988,plain,
! [SV252: $i,SV309: $i] :
( ( ( ! [SY863: $i,SY864: $i] :
( ~ ( in @ ( ordered_pair @ SY863 @ SY864 ) @ SV309 )
| ( SY863 = SY864 ) ) )
= $true )
| ( ( SV309
= ( identity_relation @ SV252 ) )
= $false )
| ( ( relation @ SV309 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2893]) ).
thf(2989,plain,
! [SV252: $i,SV309: $i] :
( ( ( ! [SY865: $i] :
( ! [SY866: $i] :
~ ( in @ ( ordered_pair @ SY865 @ SY866 ) @ SV309 )
| ( in @ SY865 @ SV252 ) ) )
= $true )
| ( ( SV309
= ( identity_relation @ SV252 ) )
= $false )
| ( ( relation @ SV309 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2894]) ).
thf(2990,plain,
! [SV253: $i,SV311: $i] :
( ( ( ( relation_dom @ SV311 )
= SV253 )
= $false )
| ( ( in @ ( sK50_C @ SV311 @ SV253 ) @ SV253 )
= $true )
| ( ( SV311
= ( identity_relation @ SV253 ) )
= $true )
| ( ( function @ SV311 )
= $false )
| ( ( relation @ SV311 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2895]) ).
thf(2991,plain,
! [SV253: $i,SV311: $i] :
( ( ( ( apply @ SV311 @ ( sK50_C @ SV311 @ SV253 ) )
= ( sK50_C @ SV311 @ SV253 ) )
= $false )
| ( ( ( ( relation_dom @ SV311 )
!= SV253 ) )
= $true )
| ( ( SV311
= ( identity_relation @ SV253 ) )
= $true )
| ( ( function @ SV311 )
= $false )
| ( ( relation @ SV311 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2896]) ).
thf(2992,plain,
! [SV420: $i,SV391: $i,SV525: $i] :
( ( ( ~ ( in @ SV525 @ SV391 )
| ( ( apply @ SV420 @ SV525 )
= SV525 ) )
= $true )
| ( ( SV420
= ( identity_relation @ SV391 ) )
= $false )
| ( ( function @ SV420 )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2897]) ).
thf(2993,plain,
! [SV345: $i,SV312: $i,SV494: $i,SV118: $i,SV480: $i] :
( ( ( ~ ( in @ SV480 @ SV118 ) )
= $true )
| ( ( ~ ( in @ SV494 @ SV312 ) )
= $true )
| ( ( ( ( sK23_D @ SV345 @ SV312 @ SV118 )
!= ( ordered_pair @ SV480 @ SV494 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV345 @ SV312 @ SV118 ) @ SV345 ) )
= $true )
| ( ( SV345
= ( cartesian_product2 @ SV118 @ SV312 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2899]) ).
thf(2994,plain,
! [SV118: $i,SV312: $i,SV345: $i] :
( ( ( ~ ( in @ ( sK24_SY403 @ SV345 @ SV312 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK25_SY405 @ SV345 @ SV312 @ SV118 ) @ SV312 ) )
= $false )
| ( ( in @ ( sK23_D @ SV345 @ SV312 @ SV118 ) @ SV345 )
= $true )
| ( ( SV345
= ( cartesian_product2 @ SV118 @ SV312 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2900]) ).
thf(2995,plain,
! [SV346: $i,SV481: $i,SV313: $i,SV526: $i,SV118: $i,SV507: $i] :
( ( ( ~ ( in @ SV507 @ SV118 )
| ~ ( in @ SV526 @ SV313 )
| ( SV481
!= ( ordered_pair @ SV507 @ SV526 ) ) )
= $true )
| ( ( in @ SV481 @ SV346 )
= $true )
| ( ( SV346
= ( cartesian_product2 @ SV118 @ SV313 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2902]) ).
thf(2996,plain,
! [SV118: $i,SV313: $i,SV346: $i,SV482: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK21_E @ SV482 @ SV346 @ SV313 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK22_SY400 @ SV482 @ SV346 @ SV313 @ SV118 ) @ SV313 ) )
| ( SV482
!= ( ordered_pair @ ( sK21_E @ SV482 @ SV346 @ SV313 @ SV118 ) @ ( sK22_SY400 @ SV482 @ SV346 @ SV313 @ SV118 ) ) ) )
= $false )
| ( ( in @ SV482 @ SV346 )
= $false )
| ( ( SV346
= ( cartesian_product2 @ SV118 @ SV313 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2903]) ).
thf(2997,plain,
! [SV467: $i,SV254: $i,SV316: $i] :
( ( ( in @ ( sK15_C @ SV316 @ SV254 ) @ SV316 )
= $false )
| ( ( in @ ( sK15_C @ SV316 @ SV254 ) @ SV467 )
= $false )
| ( ( in @ SV467 @ SV254 )
= $false )
| ( ( SV316
= ( union @ SV254 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2904]) ).
thf(2998,plain,
! [SV317: $i,SV255: $i,SV495: $i,SV468: $i] :
( ( ( in @ SV468 @ SV495 )
= $false )
| ( ( ~ ( in @ SV495 @ SV255 ) )
= $true )
| ( ( in @ SV468 @ SV317 )
= $true )
| ( ( SV317
= ( union @ SV255 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2905]) ).
thf(2999,plain,
! [SV255: $i,SV317: $i,SV469: $i] :
( ( ( ~ ( in @ SV469 @ ( sK14_D @ SV469 @ SV317 @ SV255 ) ) )
= $false )
| ( ( in @ SV469 @ SV317 )
= $false )
| ( ( SV317
= ( union @ SV255 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2906]) ).
thf(3000,plain,
! [SV255: $i,SV317: $i,SV469: $i] :
( ( ( ~ ( in @ ( sK14_D @ SV469 @ SV317 @ SV255 ) @ SV255 ) )
= $false )
| ( ( in @ SV469 @ SV317 )
= $false )
| ( ( SV317
= ( union @ SV255 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2906]) ).
thf(3001,plain,
! [SV120: $i,SV393: $i] :
( ( ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV120 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV393 ) )
= $true )
| ( ( SV120 = SV393 )
= $true )
| ( ( relation @ SV393 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2907]) ).
thf(3002,plain,
! [SV394: $i,SV120: $i,SV527: $i] :
( ( ( ! [SY1042: $i] :
( ~ ( in @ ( ordered_pair @ SV527 @ SY1042 ) @ SV120 )
| ( in @ ( ordered_pair @ SV527 @ SY1042 ) @ SV394 ) ) )
= $true )
| ( ( SV120 = SV394 )
= $false )
| ( ( relation @ SV394 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2909]) ).
thf(3003,plain,
! [SV120: $i,SV394: $i,SV528: $i] :
( ( ( ! [SY1043: $i] :
( ~ ( in @ ( ordered_pair @ SV528 @ SY1043 ) @ SV394 )
| ( in @ ( ordered_pair @ SV528 @ SY1043 ) @ SV120 ) ) )
= $true )
| ( ( SV120 = SV394 )
= $false )
| ( ( relation @ SV394 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2910]) ).
thf(3004,plain,
! [SV351: $i,SV424: $i] :
( ( ( ~ ( in @ ( sK33_SY406 @ SV424 @ SV351 ) @ SV351 ) )
= $false )
| ( ( ~ ( in @ ( sK32_C @ SV424 @ SV351 ) @ SV424 ) )
= $true )
| ( ( SV424
= ( set_meet @ SV351 ) )
= $true )
| ( ( SV351 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2911]) ).
thf(3005,plain,
! [SV351: $i,SV424: $i] :
( ( ( ~ ~ ( in @ ( sK32_C @ SV424 @ SV351 ) @ ( sK33_SY406 @ SV424 @ SV351 ) ) )
= $false )
| ( ( ~ ( in @ ( sK32_C @ SV424 @ SV351 ) @ SV424 ) )
= $true )
| ( ( SV424
= ( set_meet @ SV351 ) )
= $true )
| ( ( SV351 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2911]) ).
thf(3006,plain,
! [SV424: $i,SV351: $i,SV508: $i] :
( ( ( ~ ( in @ SV508 @ SV351 ) )
= $true )
| ( ( in @ ( sK32_C @ SV424 @ SV351 ) @ SV508 )
= $true )
| ( ( in @ ( sK32_C @ SV424 @ SV351 ) @ SV424 )
= $true )
| ( ( SV424
= ( set_meet @ SV351 ) )
= $true )
| ( ( SV351 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2912]) ).
thf(3007,plain,
! [SV352: $i,SV425: $i,SV509: $i] :
( ( ( ~ ( ~ ( in @ ( sK31_D @ SV509 @ SV425 @ SV352 ) @ SV352 )
| ~ ~ ( in @ SV509 @ ( sK31_D @ SV509 @ SV425 @ SV352 ) ) ) )
= $true )
| ( ( in @ SV509 @ SV425 )
= $true )
| ( ( SV425
= ( set_meet @ SV352 ) )
= $false )
| ( ( SV352 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2913]) ).
thf(3008,plain,
! [SV352: $i,SV425: $i,SV510: $i] :
( ( ( ~ ( in @ SV510 @ SV425 ) )
= $true )
| ( ( ! [SY1039: $i] :
( ~ ( in @ SY1039 @ SV352 )
| ( in @ SV510 @ SY1039 ) ) )
= $true )
| ( ( SV425
= ( set_meet @ SV352 ) )
= $false )
| ( ( SV352 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2914]) ).
thf(3009,plain,
! [SV87: $i,SV272: $i,SV321: $i] :
( ( ( in @ ( sK52_D @ SV321 @ SV272 @ SV87 ) @ ( relation_dom @ SV321 ) )
= $true )
| ( ( in @ SV87 @ ( relation_image @ SV321 @ SV272 ) )
= $false )
| ( ( relation @ SV321 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2916]) ).
thf(3010,plain,
! [SV87: $i,SV272: $i,SV321: $i] :
( ( ( in @ ( ordered_pair @ ( sK52_D @ SV321 @ SV272 @ SV87 ) @ SV87 ) @ SV321 )
= $true )
| ( ( in @ SV87 @ ( relation_image @ SV321 @ SV272 ) )
= $false )
| ( ( relation @ SV321 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2917]) ).
thf(3011,plain,
! [SV275: $i,SV88: $i,SV323: $i,SV511: $i] :
( ( ( ~ ( in @ SV511 @ SV323 ) )
= $true )
| ( ( in @ SV511 @ SV88 )
= $true )
| ( ( SV323
= ( set_difference @ SV88 @ SV275 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2920]) ).
thf(3012,plain,
! [SV88: $i,SV275: $i,SV323: $i,SV512: $i] :
( ( ( ~ ( in @ SV512 @ SV323 ) )
= $true )
| ( ( ~ ( in @ SV512 @ SV275 ) )
= $true )
| ( ( SV323
= ( set_difference @ SV88 @ SV275 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2921]) ).
thf(3013,plain,
! [SV89: $i,SV174: $i,SV398: $i] :
( ( ( ~ ( in @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) @ SV89 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV174 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 ) )
= $true )
| ( ( SV398
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2922]) ).
thf(3014,plain,
! [SV89: $i,SV174: $i,SV398: $i] :
( ( ( ~ ( ( in @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) @ SV89 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 ) ) )
= $false )
| ( ( SV398
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2923]) ).
thf(3015,plain,
! [SV89: $i,SV174: $i,SV398: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV174 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 ) ) )
= $false )
| ( ( SV398
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2923]) ).
thf(3016,plain,
! [SV399: $i,SV174: $i,SV529: $i,SV89: $i] :
( ( ( ! [SY1044: $i] :
( ~ ( in @ SY1044 @ SV89 )
| ~ ( in @ ( ordered_pair @ SV529 @ SY1044 ) @ SV174 )
| ( in @ ( ordered_pair @ SV529 @ SY1044 ) @ SV399 ) ) )
= $true )
| ( ( SV399
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2924]) ).
thf(3017,plain,
! [SV174: $i,SV89: $i,SV399: $i] :
( ( ( ~ ! [SY970: $i,SY971: $i] :
( ~ ( in @ ( ordered_pair @ SY970 @ SY971 ) @ SV399 )
| ( in @ SY971 @ SV89 ) )
| ~ ! [SY972: $i,SY973: $i] :
( ~ ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV399 )
| ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV174 ) ) )
= $false )
| ( ( SV399
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2925]) ).
thf(3018,plain,
! [SV90: $i,SV276: $i,SV324: $i] :
( ( ( ( sK27_D @ SV324 @ SV276 @ SV90 )
= SV90 )
= $false )
| ( ( in @ ( sK27_D @ SV324 @ SV276 @ SV90 ) @ SV324 )
= $false )
| ( ( SV324
= ( unordered_pair @ SV90 @ SV276 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2926]) ).
thf(3019,plain,
! [SV90: $i,SV276: $i,SV324: $i] :
( ( ( ( sK27_D @ SV324 @ SV276 @ SV90 )
= SV276 )
= $false )
| ( ( in @ ( sK27_D @ SV324 @ SV276 @ SV90 ) @ SV324 )
= $false )
| ( ( SV324
= ( unordered_pair @ SV90 @ SV276 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2927]) ).
thf(3020,plain,
! [SV277: $i,SV325: $i,SV90: $i,SV513: $i] :
( ( ( ( SV513 != SV90 ) )
= $true )
| ( ( in @ SV513 @ SV325 )
= $true )
| ( ( SV325
= ( unordered_pair @ SV90 @ SV277 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2929]) ).
thf(3021,plain,
! [SV90: $i,SV325: $i,SV277: $i,SV514: $i] :
( ( ( ( SV514 != SV277 ) )
= $true )
| ( ( in @ SV514 @ SV325 )
= $true )
| ( ( SV325
= ( unordered_pair @ SV90 @ SV277 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2930]) ).
thf(3022,plain,
! [SV363: $i,SV91: $i,SV515: $i,SV484: $i] :
( ( ( in @ ( ordered_pair @ SV484 @ SV515 ) @ SV91 )
= $false )
| ( ( in @ SV484 @ SV363 )
= $true )
| ( ( SV363
= ( relation_dom @ SV91 ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2932]) ).
thf(3023,plain,
! [SV496: $i,SV92: $i,SV364: $i,SV400: $i] :
( ( ( in @ ( ordered_pair @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SV496 ) @ SV92 )
= $false )
| ( ( ~ ( in @ SV496 @ SV364 ) )
= $true )
| ( ( ~ ( in @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SV400 ) )
= $true )
| ( ( SV400
= ( relation_inverse_image @ SV92 @ SV364 ) )
= $true )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2934]) ).
thf(3024,plain,
! [SV92: $i,SV364: $i,SV400: $i] :
( ( ( in @ ( ordered_pair @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ ( sK36_SY409 @ SV400 @ SV364 @ SV92 ) ) @ SV92 )
= $true )
| ( ( in @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SV400 )
= $true )
| ( ( SV400
= ( relation_inverse_image @ SV92 @ SV364 ) )
= $true )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2935]) ).
thf(3025,plain,
! [SV92: $i,SV364: $i,SV400: $i] :
( ( ( in @ ( sK36_SY409 @ SV400 @ SV364 @ SV92 ) @ SV364 )
= $true )
| ( ( in @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SV400 )
= $true )
| ( ( SV400
= ( relation_inverse_image @ SV92 @ SV364 ) )
= $true )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2936]) ).
thf(3026,plain,
! [SV401: $i,SV365: $i,SV92: $i,SV530: $i,SV497: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV497 @ SV530 ) @ SV92 )
| ~ ( in @ SV530 @ SV365 ) )
= $true )
| ( ( in @ SV497 @ SV401 )
= $true )
| ( ( SV401
= ( relation_inverse_image @ SV92 @ SV365 ) )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2937]) ).
thf(3027,plain,
! [SV92: $i,SV365: $i,SV401: $i,SV498: $i] :
( ( ( in @ SV498 @ SV401 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV498 @ ( sK34_E @ SV498 @ SV401 @ SV365 @ SV92 ) ) @ SV92 )
| ~ ( in @ ( sK34_E @ SV498 @ SV401 @ SV365 @ SV92 ) @ SV365 ) ) )
= $true )
| ( ( SV401
= ( relation_inverse_image @ SV92 @ SV365 ) )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2938]) ).
thf(3028,plain,
! [SV93: $i,SV366: $i,SV402: $i,SV499: $i] :
( ( ( in @ ( ordered_pair @ SV499 @ ( sK38_D @ SV402 @ SV366 @ SV93 ) ) @ SV93 )
= $false )
| ( ( ~ ( in @ SV499 @ SV366 ) )
= $true )
| ( ( ~ ( in @ ( sK38_D @ SV402 @ SV366 @ SV93 ) @ SV402 ) )
= $true )
| ( ( SV402
= ( relation_image @ SV93 @ SV366 ) )
= $true )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2939]) ).
thf(3029,plain,
! [SV93: $i,SV366: $i,SV402: $i] :
( ( ( in @ ( ordered_pair @ ( sK39_SY411 @ SV402 @ SV366 @ SV93 ) @ ( sK38_D @ SV402 @ SV366 @ SV93 ) ) @ SV93 )
= $true )
| ( ( in @ ( sK38_D @ SV402 @ SV366 @ SV93 ) @ SV402 )
= $true )
| ( ( SV402
= ( relation_image @ SV93 @ SV366 ) )
= $true )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2940]) ).
thf(3030,plain,
! [SV93: $i,SV366: $i,SV402: $i] :
( ( ( in @ ( sK39_SY411 @ SV402 @ SV366 @ SV93 ) @ SV366 )
= $true )
| ( ( in @ ( sK38_D @ SV402 @ SV366 @ SV93 ) @ SV402 )
= $true )
| ( ( SV402
= ( relation_image @ SV93 @ SV366 ) )
= $true )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2941]) ).
thf(3031,plain,
! [SV403: $i,SV367: $i,SV93: $i,SV500: $i,SV531: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV531 @ SV500 ) @ SV93 )
| ~ ( in @ SV531 @ SV367 ) )
= $true )
| ( ( in @ SV500 @ SV403 )
= $true )
| ( ( SV403
= ( relation_image @ SV93 @ SV367 ) )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2942]) ).
thf(3032,plain,
! [SV93: $i,SV367: $i,SV403: $i,SV501: $i] :
( ( ( in @ SV501 @ SV403 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SV501 @ SV403 @ SV367 @ SV93 ) @ SV501 ) @ SV93 )
| ~ ( in @ ( sK37_E @ SV501 @ SV403 @ SV367 @ SV93 ) @ SV367 ) ) )
= $true )
| ( ( SV403
= ( relation_image @ SV93 @ SV367 ) )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2943]) ).
thf(3033,plain,
! [SV94: $i,SV283: $i,SV327: $i] :
( ( ( in @ ( sK51_D @ SV327 @ SV283 @ SV94 ) @ ( relation_rng @ SV327 ) )
= $true )
| ( ( in @ SV94 @ ( relation_inverse_image @ SV327 @ SV283 ) )
= $false )
| ( ( relation @ SV327 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2945]) ).
thf(3034,plain,
! [SV283: $i,SV327: $i,SV94: $i] :
( ( ( in @ ( ordered_pair @ SV94 @ ( sK51_D @ SV327 @ SV283 @ SV94 ) ) @ SV327 )
= $true )
| ( ( in @ SV94 @ ( relation_inverse_image @ SV327 @ SV283 ) )
= $false )
| ( ( relation @ SV327 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2946]) ).
thf(3035,plain,
! [SV175: $i,SV450: $i,SV95: $i] :
( ( ( ~ ( in @ SV95 @ ( relation_dom @ SV450 ) ) )
= $true )
| ( ( ~ ( in @ ( apply @ SV450 @ SV95 ) @ ( relation_dom @ SV175 ) ) )
= $true )
| ( ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SV450 @ SV175 ) ) )
= $true )
| ( ( function @ SV450 )
= $false )
| ( ( relation @ SV450 )
= $false )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2947]) ).
thf(3036,plain,
! [SV175: $i,SV95: $i,SV486: $i] :
( ( ( function @ SV486 )
= $false )
| ( ( ~ ( relation @ SV486 ) )
= $true )
| ( ( ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SV486 @ SV175 ) ) )
| ( in @ SV95 @ ( relation_dom @ SV486 ) ) )
= $true )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2948]) ).
thf(3037,plain,
! [SV175: $i,SV95: $i,SV487: $i] :
( ( ( function @ SV487 )
= $false )
| ( ( ~ ( relation @ SV487 ) )
= $true )
| ( ( ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SV487 @ SV175 ) ) )
| ( in @ ( apply @ SV487 @ SV95 ) @ ( relation_dom @ SV175 ) ) )
= $true )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2949]) ).
thf(3038,plain,
! [SV96: $i,SV368: $i,SV404: $i] :
( ( ( ~ ( in @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ SV368 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV96 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 ) )
= $true )
| ( ( SV404
= ( relation_dom_restriction @ SV96 @ SV368 ) )
= $true )
| ( ( relation @ SV404 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2950]) ).
thf(3039,plain,
! [SV96: $i,SV368: $i,SV404: $i] :
( ( ( ~ ( ( in @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ SV368 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 ) ) )
= $false )
| ( ( SV404
= ( relation_dom_restriction @ SV96 @ SV368 ) )
= $true )
| ( ( relation @ SV404 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2951]) ).
thf(3040,plain,
! [SV96: $i,SV368: $i,SV404: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 ) ) )
= $false )
| ( ( SV404
= ( relation_dom_restriction @ SV96 @ SV368 ) )
= $true )
| ( ( relation @ SV404 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2951]) ).
thf(3041,plain,
! [SV405: $i,SV96: $i,SV369: $i,SV532: $i] :
( ( ( ! [SY1045: $i] :
( ~ ( in @ SV532 @ SV369 )
| ~ ( in @ ( ordered_pair @ SV532 @ SY1045 ) @ SV96 )
| ( in @ ( ordered_pair @ SV532 @ SY1045 ) @ SV405 ) ) )
= $true )
| ( ( SV405
= ( relation_dom_restriction @ SV96 @ SV369 ) )
= $false )
| ( ( relation @ SV405 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2952]) ).
thf(3042,plain,
! [SV96: $i,SV369: $i,SV405: $i] :
( ( ( ~ ! [SY984: $i] :
( ! [SY985: $i] :
~ ( in @ ( ordered_pair @ SY984 @ SY985 ) @ SV405 )
| ( in @ SY984 @ SV369 ) )
| ~ ! [SY986: $i,SY987: $i] :
( ~ ( in @ ( ordered_pair @ SY986 @ SY987 ) @ SV405 )
| ( in @ ( ordered_pair @ SY986 @ SY987 ) @ SV96 ) ) )
= $false )
| ( ( SV405
= ( relation_dom_restriction @ SV96 @ SV369 ) )
= $false )
| ( ( relation @ SV405 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2953]) ).
thf(3043,plain,
! [SV97: $i,SV370: $i] :
( ( ( in @ ( ordered_pair @ ( sK12_SY396 @ SV370 @ SV97 ) @ ( sK11_C @ SV370 @ SV97 ) ) @ SV97 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK11_C @ SV370 @ SV97 ) @ ( sK12_SY396 @ SV370 @ SV97 ) ) @ SV370 )
= $false )
| ( ( SV370
= ( relation_inverse @ SV97 ) )
= $true )
| ( ( relation @ SV370 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2954]) ).
thf(3044,plain,
! [SV97: $i,SV371: $i,SV533: $i,SV516: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV516 @ SV533 ) @ SV371 )
| ( in @ ( ordered_pair @ SV533 @ SV516 ) @ SV97 ) )
= $true )
| ( ( SV371
= ( relation_inverse @ SV97 ) )
= $false )
| ( ( relation @ SV371 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2955]) ).
thf(3045,plain,
! [SV371: $i,SV97: $i,SV517: $i,SV534: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV534 @ SV517 ) @ SV97 )
| ( in @ ( ordered_pair @ SV517 @ SV534 ) @ SV371 ) )
= $true )
| ( ( SV371
= ( relation_inverse @ SV97 ) )
= $false )
| ( ( relation @ SV371 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2956]) ).
thf(3046,plain,
! [SV373: $i,SV98: $i,SV489: $i,SV518: $i] :
( ( ( in @ ( ordered_pair @ SV518 @ SV489 ) @ SV98 )
= $false )
| ( ( in @ SV489 @ SV373 )
= $true )
| ( ( SV373
= ( relation_rng @ SV98 ) )
= $false )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2958]) ).
thf(3047,plain,
! [SV101: $i,SV215: $i,SV451: $i] :
( ( ( ! [SY1009: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ SY1009 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY1009 @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV215 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV451 ) )
= $true )
| ( ( SV451
= ( relation_composition @ SV101 @ SV215 ) )
= $true )
| ( ( relation @ SV451 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2962]) ).
thf(3048,plain,
! [SV101: $i,SV215: $i,SV451: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK10_SY395 @ SV451 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV215 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV451 ) )
= $true )
| ( ( SV451
= ( relation_composition @ SV101 @ SV215 ) )
= $true )
| ( ( relation @ SV451 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2963]) ).
thf(3049,plain,
! [SV452: $i,SV215: $i,SV101: $i] :
( ( ( ~ ! [SY1010: $i,SY1011: $i] :
( ! [SY783: $i] :
( ~ ( in @ ( ordered_pair @ SY1010 @ SY783 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY783 @ SY1011 ) @ SV215 ) )
| ( in @ ( ordered_pair @ SY1010 @ SY1011 ) @ SV452 ) ) )
= $false )
| ( ( SV452
= ( relation_composition @ SV101 @ SV215 ) )
= $false )
| ( ( relation @ SV452 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2964]) ).
thf(3050,plain,
! [SV101: $i,SV215: $i,SV452: $i] :
( ( ( ~ ! [SY1013: $i,SY1014: $i] :
( ~ ( in @ ( ordered_pair @ SY1013 @ SY1014 ) @ SV452 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1013 @ ( sK7_F @ SY1014 @ SY1013 @ SV452 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY1014 @ SY1013 @ SV452 @ SV215 @ SV101 ) @ SY1014 ) @ SV215 ) ) ) )
= $false )
| ( ( SV452
= ( relation_composition @ SV101 @ SV215 ) )
= $false )
| ( ( relation @ SV452 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2964]) ).
thf(3051,plain,
! [SV491: $i,SV103: $i,SV408: $i] :
( ( ( in @ SV408 @ ( sK2_B @ SV103 ) )
= $false )
| ( ( in @ SV491 @ ( sK3_SY386 @ SV408 @ SV103 ) )
= $true )
| ( ( subset @ SV491 @ SV408 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2965]) ).
thf(3052,plain,
! [SV103: $i,SV462: $i,SV472: $i] :
( ( ( subset @ SV472 @ SV462 )
= $false )
| ( ( in @ SV462 @ ( sK2_B @ SV103 ) )
= $false )
| ( ( in @ SV472 @ ( sK2_B @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2966]) ).
thf(3053,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2968]) ).
thf(3054,plain,
! [SV110: $i,SV502: $i] :
( ( ( ~ ( function @ SV502 ) )
= $true )
| ( ( ~ ( relation @ SV502 ) )
= $true )
| ( ( ( SV502
!= ( function_inverse @ SV110 ) )
| ~ ( ~ ~ ( ~ ! [SY1030: $i,SY1031: $i] :
( ( SY1031
!= ( apply @ SV502 @ SY1030 ) )
| ~ ( in @ SY1030 @ ( relation_rng @ SV110 ) )
| ( SY1030
= ( apply @ SV110 @ SY1031 ) ) )
| ~ ! [SY1032: $i,SY1033: $i] :
( ( SY1033
!= ( apply @ SV502 @ SY1032 ) )
| ~ ( in @ SY1032 @ ( relation_rng @ SV110 ) )
| ( in @ SY1033 @ ( relation_dom @ SV110 ) ) ) )
| ~ ~ ( ~ ! [SY1034: $i,SY1035: $i] :
( ( SY1034
!= ( apply @ SV110 @ SY1035 ) )
| ~ ( in @ SY1035 @ ( relation_dom @ SV110 ) )
| ( SY1035
= ( apply @ SV502 @ SY1034 ) ) )
| ~ ! [SY644: $i] :
( ! [SY645: $i] :
( ( SY644
!= ( apply @ SV110 @ SY645 ) )
| ~ ( in @ SY645 @ ( relation_dom @ SV110 ) ) )
| ( in @ SY644 @ ( relation_rng @ SV110 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2969]) ).
thf(3055,plain,
! [SV110: $i,SV503: $i] :
( ( ( ~ ( function @ SV503 ) )
= $true )
| ( ( ~ ( relation @ SV503 ) )
= $true )
| ( ( ( SV503
!= ( function_inverse @ SV110 ) )
| ( ( relation_dom @ SV503 )
= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2970]) ).
thf(3056,plain,
! [SV474: $i,SV113: $i,SV519: $i] :
( ( ( ( SV519
!= ( apply @ SV113 @ SV474 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV474 @ SV519 ) @ SV113 )
= $true )
| ( ( in @ SV474 @ ( relation_dom @ SV113 ) )
= $false )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2971]) ).
thf(3057,plain,
! [SV113: $i,SV520: $i,SV475: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV475 @ SV520 ) @ SV113 ) )
= $true )
| ( ( SV520
= ( apply @ SV113 @ SV475 ) )
= $true )
| ( ( in @ SV475 @ ( relation_dom @ SV113 ) )
= $false )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2972]) ).
thf(3058,plain,
! [SV476: $i,SV113: $i,SV504: $i] :
( ( ( SV504
= ( apply @ SV113 @ SV476 ) )
= $false )
| ( ( SV504 = empty_set )
= $true )
| ( ( in @ SV476 @ ( relation_dom @ SV113 ) )
= $true )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2973]) ).
thf(3059,plain,
! [SV477: $i,SV113: $i,SV505: $i] :
( ( ( SV505 = empty_set )
= $false )
| ( ( SV505
= ( apply @ SV113 @ SV477 ) )
= $true )
| ( ( in @ SV477 @ ( relation_dom @ SV113 ) )
= $true )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2974]) ).
thf(3060,plain,
! [SV114: $i,SV301: $i,SV338: $i] :
( ( ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV114 )
= $false )
| ( ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV338 )
= $false )
| ( ( SV338
= ( set_union2 @ SV114 @ SV301 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2975]) ).
thf(3061,plain,
! [SV114: $i,SV301: $i,SV338: $i] :
( ( ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV301 )
= $false )
| ( ( in @ ( sK26_D @ SV338 @ SV301 @ SV114 ) @ SV338 )
= $false )
| ( ( SV338
= ( set_union2 @ SV114 @ SV301 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2976]) ).
thf(3062,plain,
! [SV302: $i,SV339: $i,SV114: $i,SV521: $i] :
( ( ( ~ ( in @ SV521 @ SV114 ) )
= $true )
| ( ( in @ SV521 @ SV339 )
= $true )
| ( ( SV339
= ( set_union2 @ SV114 @ SV302 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2978]) ).
thf(3063,plain,
! [SV114: $i,SV339: $i,SV302: $i,SV522: $i] :
( ( ( ~ ( in @ SV522 @ SV302 ) )
= $true )
| ( ( in @ SV522 @ SV339 )
= $true )
| ( ( SV339
= ( set_union2 @ SV114 @ SV302 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2979]) ).
thf(3064,plain,
! [SV343: $i,SV116: $i,SV307: $i,SV479: $i] :
( ( ( in @ SV479 @ SV307 )
= $false )
| ( ( in @ SV479 @ SV116 )
= $false )
| ( ( in @ SV479 @ SV343 )
= $true )
| ( ( SV343
= ( set_intersection2 @ SV116 @ SV307 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2981]) ).
thf(3065,plain,
! [SV307: $i,SV116: $i,SV343: $i,SV523: $i] :
( ( ( ~ ( in @ SV523 @ SV343 ) )
= $true )
| ( ( in @ SV523 @ SV116 )
= $true )
| ( ( SV343
= ( set_intersection2 @ SV116 @ SV307 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2982]) ).
thf(3066,plain,
! [SV116: $i,SV307: $i,SV343: $i,SV524: $i] :
( ( ( ~ ( in @ SV524 @ SV343 ) )
= $true )
| ( ( in @ SV524 @ SV307 )
= $true )
| ( ( SV343
= ( set_intersection2 @ SV116 @ SV307 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2983]) ).
thf(3067,plain,
! [SV251: $i,SV308: $i] :
( ( ( in @ ( ordered_pair @ ( sK44_C @ SV308 @ SV251 ) @ ( sK45_SY414 @ SV308 @ SV251 ) ) @ SV308 )
= $false )
| ( ( ( sK44_C @ SV308 @ SV251 )
= ( sK45_SY414 @ SV308 @ SV251 ) )
= $false )
| ( ( in @ ( sK44_C @ SV308 @ SV251 ) @ SV251 )
= $false )
| ( ( SV308
= ( identity_relation @ SV251 ) )
= $true )
| ( ( relation @ SV308 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2984]) ).
thf(3068,plain,
! [SV309: $i,SV252: $i,SV506: $i,SV493: $i] :
( ( ( ( SV493 != SV506 ) )
= $true )
| ( ( ~ ( in @ SV493 @ SV252 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV493 @ SV506 ) @ SV309 )
= $true )
| ( ( SV309
= ( identity_relation @ SV252 ) )
= $false )
| ( ( relation @ SV309 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2987]) ).
thf(3069,plain,
! [SV252: $i,SV309: $i,SV535: $i] :
( ( ( ! [SY1046: $i] :
( ~ ( in @ ( ordered_pair @ SV535 @ SY1046 ) @ SV309 )
| ( SV535 = SY1046 ) ) )
= $true )
| ( ( SV309
= ( identity_relation @ SV252 ) )
= $false )
| ( ( relation @ SV309 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2988]) ).
thf(3070,plain,
! [SV252: $i,SV309: $i,SV536: $i] :
( ( ( ! [SY1047: $i] :
~ ( in @ ( ordered_pair @ SV536 @ SY1047 ) @ SV309 )
| ( in @ SV536 @ SV252 ) )
= $true )
| ( ( SV309
= ( identity_relation @ SV252 ) )
= $false )
| ( ( relation @ SV309 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2989]) ).
thf(3071,plain,
! [SV253: $i,SV311: $i] :
( ( ( ( relation_dom @ SV311 )
= SV253 )
= $false )
| ( ( ( apply @ SV311 @ ( sK50_C @ SV311 @ SV253 ) )
= ( sK50_C @ SV311 @ SV253 ) )
= $false )
| ( ( SV311
= ( identity_relation @ SV253 ) )
= $true )
| ( ( function @ SV311 )
= $false )
| ( ( relation @ SV311 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2991]) ).
thf(3072,plain,
! [SV420: $i,SV391: $i,SV525: $i] :
( ( ( ~ ( in @ SV525 @ SV391 ) )
= $true )
| ( ( ( apply @ SV420 @ SV525 )
= SV525 )
= $true )
| ( ( SV420
= ( identity_relation @ SV391 ) )
= $false )
| ( ( function @ SV420 )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2992]) ).
thf(3073,plain,
! [SV345: $i,SV312: $i,SV494: $i,SV118: $i,SV480: $i] :
( ( ( in @ SV480 @ SV118 )
= $false )
| ( ( ~ ( in @ SV494 @ SV312 ) )
= $true )
| ( ( ( ( sK23_D @ SV345 @ SV312 @ SV118 )
!= ( ordered_pair @ SV480 @ SV494 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV345 @ SV312 @ SV118 ) @ SV345 ) )
= $true )
| ( ( SV345
= ( cartesian_product2 @ SV118 @ SV312 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2993]) ).
thf(3074,plain,
! [SV118: $i,SV312: $i,SV345: $i] :
( ( ( ~ ( in @ ( sK24_SY403 @ SV345 @ SV312 @ SV118 ) @ SV118 ) )
= $false )
| ( ( in @ ( sK23_D @ SV345 @ SV312 @ SV118 ) @ SV345 )
= $true )
| ( ( SV345
= ( cartesian_product2 @ SV118 @ SV312 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2994]) ).
thf(3075,plain,
! [SV118: $i,SV312: $i,SV345: $i] :
( ( ( ~ ( in @ ( sK25_SY405 @ SV345 @ SV312 @ SV118 ) @ SV312 ) )
= $false )
| ( ( in @ ( sK23_D @ SV345 @ SV312 @ SV118 ) @ SV345 )
= $true )
| ( ( SV345
= ( cartesian_product2 @ SV118 @ SV312 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2994]) ).
thf(3076,plain,
! [SV346: $i,SV481: $i,SV313: $i,SV526: $i,SV118: $i,SV507: $i] :
( ( ( ~ ( in @ SV507 @ SV118 )
| ~ ( in @ SV526 @ SV313 ) )
= $true )
| ( ( ( SV481
!= ( ordered_pair @ SV507 @ SV526 ) ) )
= $true )
| ( ( in @ SV481 @ SV346 )
= $true )
| ( ( SV346
= ( cartesian_product2 @ SV118 @ SV313 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2995]) ).
thf(3077,plain,
! [SV118: $i,SV313: $i,SV346: $i,SV482: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK21_E @ SV482 @ SV346 @ SV313 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK22_SY400 @ SV482 @ SV346 @ SV313 @ SV118 ) @ SV313 ) ) )
= $false )
| ( ( in @ SV482 @ SV346 )
= $false )
| ( ( SV346
= ( cartesian_product2 @ SV118 @ SV313 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2996]) ).
thf(3078,plain,
! [SV118: $i,SV313: $i,SV346: $i,SV482: $i] :
( ( ( ( SV482
!= ( ordered_pair @ ( sK21_E @ SV482 @ SV346 @ SV313 @ SV118 ) @ ( sK22_SY400 @ SV482 @ SV346 @ SV313 @ SV118 ) ) ) )
= $false )
| ( ( in @ SV482 @ SV346 )
= $false )
| ( ( SV346
= ( cartesian_product2 @ SV118 @ SV313 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2996]) ).
thf(3079,plain,
! [SV317: $i,SV468: $i,SV255: $i,SV495: $i] :
( ( ( in @ SV495 @ SV255 )
= $false )
| ( ( in @ SV468 @ SV495 )
= $false )
| ( ( in @ SV468 @ SV317 )
= $true )
| ( ( SV317
= ( union @ SV255 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2998]) ).
thf(3080,plain,
! [SV255: $i,SV317: $i,SV469: $i] :
( ( ( in @ SV469 @ ( sK14_D @ SV469 @ SV317 @ SV255 ) )
= $true )
| ( ( in @ SV469 @ SV317 )
= $false )
| ( ( SV317
= ( union @ SV255 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2999]) ).
thf(3081,plain,
! [SV255: $i,SV317: $i,SV469: $i] :
( ( ( in @ ( sK14_D @ SV469 @ SV317 @ SV255 ) @ SV255 )
= $true )
| ( ( in @ SV469 @ SV317 )
= $false )
| ( ( SV317
= ( union @ SV255 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3000]) ).
thf(3082,plain,
! [SV120: $i,SV393: $i] :
( ( ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV393 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK65_C @ SV393 @ SV120 ) @ ( sK66_SY420 @ SV393 @ SV120 ) ) @ SV120 )
= $false )
| ( ( SV120 = SV393 )
= $true )
| ( ( relation @ SV393 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3001]) ).
thf(3083,plain,
! [SV394: $i,SV120: $i,SV537: $i,SV527: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV527 @ SV537 ) @ SV120 )
| ( in @ ( ordered_pair @ SV527 @ SV537 ) @ SV394 ) )
= $true )
| ( ( SV120 = SV394 )
= $false )
| ( ( relation @ SV394 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3002]) ).
thf(3084,plain,
! [SV120: $i,SV394: $i,SV538: $i,SV528: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV528 @ SV538 ) @ SV394 )
| ( in @ ( ordered_pair @ SV528 @ SV538 ) @ SV120 ) )
= $true )
| ( ( SV120 = SV394 )
= $false )
| ( ( relation @ SV394 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3003]) ).
thf(3085,plain,
! [SV351: $i,SV424: $i] :
( ( ( in @ ( sK33_SY406 @ SV424 @ SV351 ) @ SV351 )
= $true )
| ( ( ~ ( in @ ( sK32_C @ SV424 @ SV351 ) @ SV424 ) )
= $true )
| ( ( SV424
= ( set_meet @ SV351 ) )
= $true )
| ( ( SV351 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3004]) ).
thf(3086,plain,
! [SV351: $i,SV424: $i] :
( ( ( ~ ( in @ ( sK32_C @ SV424 @ SV351 ) @ ( sK33_SY406 @ SV424 @ SV351 ) ) )
= $true )
| ( ( ~ ( in @ ( sK32_C @ SV424 @ SV351 ) @ SV424 ) )
= $true )
| ( ( SV424
= ( set_meet @ SV351 ) )
= $true )
| ( ( SV351 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3005]) ).
thf(3087,plain,
! [SV424: $i,SV351: $i,SV508: $i] :
( ( ( in @ SV508 @ SV351 )
= $false )
| ( ( in @ ( sK32_C @ SV424 @ SV351 ) @ SV508 )
= $true )
| ( ( in @ ( sK32_C @ SV424 @ SV351 ) @ SV424 )
= $true )
| ( ( SV424
= ( set_meet @ SV351 ) )
= $true )
| ( ( SV351 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3006]) ).
thf(3088,plain,
! [SV352: $i,SV425: $i,SV509: $i] :
( ( ( ~ ( in @ ( sK31_D @ SV509 @ SV425 @ SV352 ) @ SV352 )
| ~ ~ ( in @ SV509 @ ( sK31_D @ SV509 @ SV425 @ SV352 ) ) )
= $false )
| ( ( in @ SV509 @ SV425 )
= $true )
| ( ( SV425
= ( set_meet @ SV352 ) )
= $false )
| ( ( SV352 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3007]) ).
thf(3089,plain,
! [SV352: $i,SV425: $i,SV510: $i] :
( ( ( in @ SV510 @ SV425 )
= $false )
| ( ( ! [SY1039: $i] :
( ~ ( in @ SY1039 @ SV352 )
| ( in @ SV510 @ SY1039 ) ) )
= $true )
| ( ( SV425
= ( set_meet @ SV352 ) )
= $false )
| ( ( SV352 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3008]) ).
thf(3090,plain,
! [SV275: $i,SV88: $i,SV323: $i,SV511: $i] :
( ( ( in @ SV511 @ SV323 )
= $false )
| ( ( in @ SV511 @ SV88 )
= $true )
| ( ( SV323
= ( set_difference @ SV88 @ SV275 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3011]) ).
thf(3091,plain,
! [SV88: $i,SV275: $i,SV323: $i,SV512: $i] :
( ( ( in @ SV512 @ SV323 )
= $false )
| ( ( ~ ( in @ SV512 @ SV275 ) )
= $true )
| ( ( SV323
= ( set_difference @ SV88 @ SV275 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3012]) ).
thf(3092,plain,
! [SV89: $i,SV174: $i,SV398: $i] :
( ( ( in @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) @ SV89 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV174 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 ) )
= $true )
| ( ( SV398
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3013]) ).
thf(3093,plain,
! [SV89: $i,SV174: $i,SV398: $i] :
( ( ( ( in @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) @ SV89 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 ) )
= $true )
| ( ( SV398
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3014]) ).
thf(3094,plain,
! [SV89: $i,SV174: $i,SV398: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV174 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 ) )
= $true )
| ( ( SV398
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3015]) ).
thf(3095,plain,
! [SV399: $i,SV174: $i,SV529: $i,SV89: $i,SV539: $i] :
( ( ( ~ ( in @ SV539 @ SV89 )
| ~ ( in @ ( ordered_pair @ SV529 @ SV539 ) @ SV174 )
| ( in @ ( ordered_pair @ SV529 @ SV539 ) @ SV399 ) )
= $true )
| ( ( SV399
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3016]) ).
thf(3096,plain,
! [SV174: $i,SV89: $i,SV399: $i] :
( ( ( ~ ! [SY970: $i,SY971: $i] :
( ~ ( in @ ( ordered_pair @ SY970 @ SY971 ) @ SV399 )
| ( in @ SY971 @ SV89 ) ) )
= $false )
| ( ( SV399
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3017]) ).
thf(3097,plain,
! [SV89: $i,SV174: $i,SV399: $i] :
( ( ( ~ ! [SY972: $i,SY973: $i] :
( ~ ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV399 )
| ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV174 ) ) )
= $false )
| ( ( SV399
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3017]) ).
thf(3098,plain,
! [SV277: $i,SV325: $i,SV90: $i,SV513: $i] :
( ( ( SV513 = SV90 )
= $false )
| ( ( in @ SV513 @ SV325 )
= $true )
| ( ( SV325
= ( unordered_pair @ SV90 @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3020]) ).
thf(3099,plain,
! [SV90: $i,SV325: $i,SV277: $i,SV514: $i] :
( ( ( SV514 = SV277 )
= $false )
| ( ( in @ SV514 @ SV325 )
= $true )
| ( ( SV325
= ( unordered_pair @ SV90 @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3021]) ).
thf(3100,plain,
! [SV92: $i,SV400: $i,SV364: $i,SV496: $i] :
( ( ( in @ SV496 @ SV364 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SV496 ) @ SV92 )
= $false )
| ( ( ~ ( in @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SV400 ) )
= $true )
| ( ( SV400
= ( relation_inverse_image @ SV92 @ SV364 ) )
= $true )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3023]) ).
thf(3101,plain,
! [SV401: $i,SV365: $i,SV92: $i,SV530: $i,SV497: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV497 @ SV530 ) @ SV92 ) )
= $true )
| ( ( ~ ( in @ SV530 @ SV365 ) )
= $true )
| ( ( in @ SV497 @ SV401 )
= $true )
| ( ( SV401
= ( relation_inverse_image @ SV92 @ SV365 ) )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3026]) ).
thf(3102,plain,
! [SV92: $i,SV365: $i,SV401: $i,SV498: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV498 @ ( sK34_E @ SV498 @ SV401 @ SV365 @ SV92 ) ) @ SV92 )
| ~ ( in @ ( sK34_E @ SV498 @ SV401 @ SV365 @ SV92 ) @ SV365 ) )
= $false )
| ( ( in @ SV498 @ SV401 )
= $false )
| ( ( SV401
= ( relation_inverse_image @ SV92 @ SV365 ) )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3027]) ).
thf(3103,plain,
! [SV93: $i,SV402: $i,SV366: $i,SV499: $i] :
( ( ( in @ SV499 @ SV366 )
= $false )
| ( ( in @ ( ordered_pair @ SV499 @ ( sK38_D @ SV402 @ SV366 @ SV93 ) ) @ SV93 )
= $false )
| ( ( ~ ( in @ ( sK38_D @ SV402 @ SV366 @ SV93 ) @ SV402 ) )
= $true )
| ( ( SV402
= ( relation_image @ SV93 @ SV366 ) )
= $true )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3028]) ).
thf(3104,plain,
! [SV403: $i,SV367: $i,SV93: $i,SV500: $i,SV531: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV531 @ SV500 ) @ SV93 ) )
= $true )
| ( ( ~ ( in @ SV531 @ SV367 ) )
= $true )
| ( ( in @ SV500 @ SV403 )
= $true )
| ( ( SV403
= ( relation_image @ SV93 @ SV367 ) )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3031]) ).
thf(3105,plain,
! [SV93: $i,SV367: $i,SV403: $i,SV501: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SV501 @ SV403 @ SV367 @ SV93 ) @ SV501 ) @ SV93 )
| ~ ( in @ ( sK37_E @ SV501 @ SV403 @ SV367 @ SV93 ) @ SV367 ) )
= $false )
| ( ( in @ SV501 @ SV403 )
= $false )
| ( ( SV403
= ( relation_image @ SV93 @ SV367 ) )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3032]) ).
thf(3106,plain,
! [SV175: $i,SV450: $i,SV95: $i] :
( ( ( in @ SV95 @ ( relation_dom @ SV450 ) )
= $false )
| ( ( ~ ( in @ ( apply @ SV450 @ SV95 ) @ ( relation_dom @ SV175 ) ) )
= $true )
| ( ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SV450 @ SV175 ) ) )
= $true )
| ( ( function @ SV450 )
= $false )
| ( ( relation @ SV450 )
= $false )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3035]) ).
thf(3107,plain,
! [SV175: $i,SV95: $i,SV486: $i] :
( ( ( relation @ SV486 )
= $false )
| ( ( function @ SV486 )
= $false )
| ( ( ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SV486 @ SV175 ) ) )
| ( in @ SV95 @ ( relation_dom @ SV486 ) ) )
= $true )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3036]) ).
thf(3108,plain,
! [SV175: $i,SV95: $i,SV487: $i] :
( ( ( relation @ SV487 )
= $false )
| ( ( function @ SV487 )
= $false )
| ( ( ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SV487 @ SV175 ) ) )
| ( in @ ( apply @ SV487 @ SV95 ) @ ( relation_dom @ SV175 ) ) )
= $true )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3037]) ).
thf(3109,plain,
! [SV96: $i,SV368: $i,SV404: $i] :
( ( ( in @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ SV368 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV96 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 ) )
= $true )
| ( ( SV404
= ( relation_dom_restriction @ SV96 @ SV368 ) )
= $true )
| ( ( relation @ SV404 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3038]) ).
thf(3110,plain,
! [SV96: $i,SV368: $i,SV404: $i] :
( ( ( ( in @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ SV368 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 ) )
= $true )
| ( ( SV404
= ( relation_dom_restriction @ SV96 @ SV368 ) )
= $true )
| ( ( relation @ SV404 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3039]) ).
thf(3111,plain,
! [SV96: $i,SV368: $i,SV404: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 ) )
= $true )
| ( ( SV404
= ( relation_dom_restriction @ SV96 @ SV368 ) )
= $true )
| ( ( relation @ SV404 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3040]) ).
thf(3112,plain,
! [SV405: $i,SV96: $i,SV540: $i,SV369: $i,SV532: $i] :
( ( ( ~ ( in @ SV532 @ SV369 )
| ~ ( in @ ( ordered_pair @ SV532 @ SV540 ) @ SV96 )
| ( in @ ( ordered_pair @ SV532 @ SV540 ) @ SV405 ) )
= $true )
| ( ( SV405
= ( relation_dom_restriction @ SV96 @ SV369 ) )
= $false )
| ( ( relation @ SV405 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3041]) ).
thf(3113,plain,
! [SV96: $i,SV369: $i,SV405: $i] :
( ( ( ~ ! [SY984: $i] :
( ! [SY985: $i] :
~ ( in @ ( ordered_pair @ SY984 @ SY985 ) @ SV405 )
| ( in @ SY984 @ SV369 ) ) )
= $false )
| ( ( SV405
= ( relation_dom_restriction @ SV96 @ SV369 ) )
= $false )
| ( ( relation @ SV405 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3042]) ).
thf(3114,plain,
! [SV369: $i,SV96: $i,SV405: $i] :
( ( ( ~ ! [SY986: $i,SY987: $i] :
( ~ ( in @ ( ordered_pair @ SY986 @ SY987 ) @ SV405 )
| ( in @ ( ordered_pair @ SY986 @ SY987 ) @ SV96 ) ) )
= $false )
| ( ( SV405
= ( relation_dom_restriction @ SV96 @ SV369 ) )
= $false )
| ( ( relation @ SV405 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3042]) ).
thf(3115,plain,
! [SV97: $i,SV371: $i,SV533: $i,SV516: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV516 @ SV533 ) @ SV371 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV533 @ SV516 ) @ SV97 )
= $true )
| ( ( SV371
= ( relation_inverse @ SV97 ) )
= $false )
| ( ( relation @ SV371 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3044]) ).
thf(3116,plain,
! [SV371: $i,SV97: $i,SV517: $i,SV534: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV534 @ SV517 ) @ SV97 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV517 @ SV534 ) @ SV371 )
= $true )
| ( ( SV371
= ( relation_inverse @ SV97 ) )
= $false )
| ( ( relation @ SV371 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3045]) ).
thf(3117,plain,
! [SV101: $i,SV215: $i,SV451: $i] :
( ( ( ! [SY1009: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ SY1009 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY1009 @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV215 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV451 ) )
= $true )
| ( ( SV451
= ( relation_composition @ SV101 @ SV215 ) )
= $true )
| ( ( relation @ SV451 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3047]) ).
thf(3118,plain,
! [SV101: $i,SV215: $i,SV451: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK10_SY395 @ SV451 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV215 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV451 )
= $true )
| ( ( SV451
= ( relation_composition @ SV101 @ SV215 ) )
= $true )
| ( ( relation @ SV451 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3048]) ).
thf(3119,plain,
! [SV452: $i,SV215: $i,SV101: $i] :
( ( ( ! [SY1010: $i,SY1011: $i] :
( ! [SY783: $i] :
( ~ ( in @ ( ordered_pair @ SY1010 @ SY783 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY783 @ SY1011 ) @ SV215 ) )
| ( in @ ( ordered_pair @ SY1010 @ SY1011 ) @ SV452 ) ) )
= $true )
| ( ( SV452
= ( relation_composition @ SV101 @ SV215 ) )
= $false )
| ( ( relation @ SV452 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3049]) ).
thf(3120,plain,
! [SV101: $i,SV215: $i,SV452: $i] :
( ( ( ! [SY1013: $i,SY1014: $i] :
( ~ ( in @ ( ordered_pair @ SY1013 @ SY1014 ) @ SV452 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1013 @ ( sK7_F @ SY1014 @ SY1013 @ SV452 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY1014 @ SY1013 @ SV452 @ SV215 @ SV101 ) @ SY1014 ) @ SV215 ) ) ) )
= $true )
| ( ( SV452
= ( relation_composition @ SV101 @ SV215 ) )
= $false )
| ( ( relation @ SV452 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3050]) ).
thf(3121,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3053]) ).
thf(3122,plain,
! [SV110: $i,SV502: $i] :
( ( ( function @ SV502 )
= $false )
| ( ( ~ ( relation @ SV502 ) )
= $true )
| ( ( ( SV502
!= ( function_inverse @ SV110 ) )
| ~ ( ~ ~ ( ~ ! [SY1030: $i,SY1031: $i] :
( ( SY1031
!= ( apply @ SV502 @ SY1030 ) )
| ~ ( in @ SY1030 @ ( relation_rng @ SV110 ) )
| ( SY1030
= ( apply @ SV110 @ SY1031 ) ) )
| ~ ! [SY1032: $i,SY1033: $i] :
( ( SY1033
!= ( apply @ SV502 @ SY1032 ) )
| ~ ( in @ SY1032 @ ( relation_rng @ SV110 ) )
| ( in @ SY1033 @ ( relation_dom @ SV110 ) ) ) )
| ~ ~ ( ~ ! [SY1034: $i,SY1035: $i] :
( ( SY1034
!= ( apply @ SV110 @ SY1035 ) )
| ~ ( in @ SY1035 @ ( relation_dom @ SV110 ) )
| ( SY1035
= ( apply @ SV502 @ SY1034 ) ) )
| ~ ! [SY644: $i] :
( ! [SY645: $i] :
( ( SY644
!= ( apply @ SV110 @ SY645 ) )
| ~ ( in @ SY645 @ ( relation_dom @ SV110 ) ) )
| ( in @ SY644 @ ( relation_rng @ SV110 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3054]) ).
thf(3123,plain,
! [SV110: $i,SV503: $i] :
( ( ( function @ SV503 )
= $false )
| ( ( ~ ( relation @ SV503 ) )
= $true )
| ( ( ( SV503
!= ( function_inverse @ SV110 ) )
| ( ( relation_dom @ SV503 )
= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3055]) ).
thf(3124,plain,
! [SV474: $i,SV113: $i,SV519: $i] :
( ( ( SV519
= ( apply @ SV113 @ SV474 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV474 @ SV519 ) @ SV113 )
= $true )
| ( ( in @ SV474 @ ( relation_dom @ SV113 ) )
= $false )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3056]) ).
thf(3125,plain,
! [SV113: $i,SV520: $i,SV475: $i] :
( ( ( in @ ( ordered_pair @ SV475 @ SV520 ) @ SV113 )
= $false )
| ( ( SV520
= ( apply @ SV113 @ SV475 ) )
= $true )
| ( ( in @ SV475 @ ( relation_dom @ SV113 ) )
= $false )
| ( ( function @ SV113 )
= $false )
| ( ( relation @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3057]) ).
thf(3126,plain,
! [SV302: $i,SV339: $i,SV114: $i,SV521: $i] :
( ( ( in @ SV521 @ SV114 )
= $false )
| ( ( in @ SV521 @ SV339 )
= $true )
| ( ( SV339
= ( set_union2 @ SV114 @ SV302 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3062]) ).
thf(3127,plain,
! [SV114: $i,SV339: $i,SV302: $i,SV522: $i] :
( ( ( in @ SV522 @ SV302 )
= $false )
| ( ( in @ SV522 @ SV339 )
= $true )
| ( ( SV339
= ( set_union2 @ SV114 @ SV302 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3063]) ).
thf(3128,plain,
! [SV307: $i,SV116: $i,SV343: $i,SV523: $i] :
( ( ( in @ SV523 @ SV343 )
= $false )
| ( ( in @ SV523 @ SV116 )
= $true )
| ( ( SV343
= ( set_intersection2 @ SV116 @ SV307 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3065]) ).
thf(3129,plain,
! [SV116: $i,SV307: $i,SV343: $i,SV524: $i] :
( ( ( in @ SV524 @ SV343 )
= $false )
| ( ( in @ SV524 @ SV307 )
= $true )
| ( ( SV343
= ( set_intersection2 @ SV116 @ SV307 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3066]) ).
thf(3130,plain,
! [SV309: $i,SV252: $i,SV506: $i,SV493: $i] :
( ( ( SV493 = SV506 )
= $false )
| ( ( ~ ( in @ SV493 @ SV252 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV493 @ SV506 ) @ SV309 )
= $true )
| ( ( SV309
= ( identity_relation @ SV252 ) )
= $false )
| ( ( relation @ SV309 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3068]) ).
thf(3131,plain,
! [SV252: $i,SV309: $i,SV541: $i,SV535: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV535 @ SV541 ) @ SV309 )
| ( SV535 = SV541 ) )
= $true )
| ( ( SV309
= ( identity_relation @ SV252 ) )
= $false )
| ( ( relation @ SV309 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3069]) ).
thf(3132,plain,
! [SV252: $i,SV309: $i,SV536: $i] :
( ( ( ! [SY1047: $i] :
~ ( in @ ( ordered_pair @ SV536 @ SY1047 ) @ SV309 ) )
= $true )
| ( ( in @ SV536 @ SV252 )
= $true )
| ( ( SV309
= ( identity_relation @ SV252 ) )
= $false )
| ( ( relation @ SV309 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3070]) ).
thf(3133,plain,
! [SV420: $i,SV391: $i,SV525: $i] :
( ( ( in @ SV525 @ SV391 )
= $false )
| ( ( ( apply @ SV420 @ SV525 )
= SV525 )
= $true )
| ( ( SV420
= ( identity_relation @ SV391 ) )
= $false )
| ( ( function @ SV420 )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3072]) ).
thf(3134,plain,
! [SV345: $i,SV118: $i,SV480: $i,SV312: $i,SV494: $i] :
( ( ( in @ SV494 @ SV312 )
= $false )
| ( ( in @ SV480 @ SV118 )
= $false )
| ( ( ( ( sK23_D @ SV345 @ SV312 @ SV118 )
!= ( ordered_pair @ SV480 @ SV494 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV345 @ SV312 @ SV118 ) @ SV345 ) )
= $true )
| ( ( SV345
= ( cartesian_product2 @ SV118 @ SV312 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3073]) ).
thf(3135,plain,
! [SV118: $i,SV312: $i,SV345: $i] :
( ( ( in @ ( sK24_SY403 @ SV345 @ SV312 @ SV118 ) @ SV118 )
= $true )
| ( ( in @ ( sK23_D @ SV345 @ SV312 @ SV118 ) @ SV345 )
= $true )
| ( ( SV345
= ( cartesian_product2 @ SV118 @ SV312 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3074]) ).
thf(3136,plain,
! [SV118: $i,SV312: $i,SV345: $i] :
( ( ( in @ ( sK25_SY405 @ SV345 @ SV312 @ SV118 ) @ SV312 )
= $true )
| ( ( in @ ( sK23_D @ SV345 @ SV312 @ SV118 ) @ SV345 )
= $true )
| ( ( SV345
= ( cartesian_product2 @ SV118 @ SV312 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3075]) ).
thf(3137,plain,
! [SV346: $i,SV481: $i,SV313: $i,SV526: $i,SV118: $i,SV507: $i] :
( ( ( ~ ( in @ SV507 @ SV118 ) )
= $true )
| ( ( ~ ( in @ SV526 @ SV313 ) )
= $true )
| ( ( ( SV481
!= ( ordered_pair @ SV507 @ SV526 ) ) )
= $true )
| ( ( in @ SV481 @ SV346 )
= $true )
| ( ( SV346
= ( cartesian_product2 @ SV118 @ SV313 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3076]) ).
thf(3138,plain,
! [SV118: $i,SV313: $i,SV346: $i,SV482: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_E @ SV482 @ SV346 @ SV313 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK22_SY400 @ SV482 @ SV346 @ SV313 @ SV118 ) @ SV313 ) ) )
= $true )
| ( ( in @ SV482 @ SV346 )
= $false )
| ( ( SV346
= ( cartesian_product2 @ SV118 @ SV313 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3077]) ).
thf(3139,plain,
! [SV118: $i,SV313: $i,SV346: $i,SV482: $i] :
( ( ( SV482
= ( ordered_pair @ ( sK21_E @ SV482 @ SV346 @ SV313 @ SV118 ) @ ( sK22_SY400 @ SV482 @ SV346 @ SV313 @ SV118 ) ) )
= $true )
| ( ( in @ SV482 @ SV346 )
= $false )
| ( ( SV346
= ( cartesian_product2 @ SV118 @ SV313 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3078]) ).
thf(3140,plain,
! [SV394: $i,SV120: $i,SV537: $i,SV527: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV527 @ SV537 ) @ SV120 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV527 @ SV537 ) @ SV394 )
= $true )
| ( ( SV120 = SV394 )
= $false )
| ( ( relation @ SV394 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3083]) ).
thf(3141,plain,
! [SV120: $i,SV394: $i,SV538: $i,SV528: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV528 @ SV538 ) @ SV394 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV528 @ SV538 ) @ SV120 )
= $true )
| ( ( SV120 = SV394 )
= $false )
| ( ( relation @ SV394 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3084]) ).
thf(3142,plain,
! [SV351: $i,SV424: $i] :
( ( ( in @ ( sK32_C @ SV424 @ SV351 ) @ SV424 )
= $false )
| ( ( in @ ( sK33_SY406 @ SV424 @ SV351 ) @ SV351 )
= $true )
| ( ( SV424
= ( set_meet @ SV351 ) )
= $true )
| ( ( SV351 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3085]) ).
thf(3143,plain,
! [SV351: $i,SV424: $i] :
( ( ( in @ ( sK32_C @ SV424 @ SV351 ) @ ( sK33_SY406 @ SV424 @ SV351 ) )
= $false )
| ( ( ~ ( in @ ( sK32_C @ SV424 @ SV351 ) @ SV424 ) )
= $true )
| ( ( SV424
= ( set_meet @ SV351 ) )
= $true )
| ( ( SV351 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3086]) ).
thf(3144,plain,
! [SV352: $i,SV425: $i,SV509: $i] :
( ( ( ~ ( in @ ( sK31_D @ SV509 @ SV425 @ SV352 ) @ SV352 ) )
= $false )
| ( ( in @ SV509 @ SV425 )
= $true )
| ( ( SV425
= ( set_meet @ SV352 ) )
= $false )
| ( ( SV352 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3088]) ).
thf(3145,plain,
! [SV352: $i,SV425: $i,SV509: $i] :
( ( ( ~ ~ ( in @ SV509 @ ( sK31_D @ SV509 @ SV425 @ SV352 ) ) )
= $false )
| ( ( in @ SV509 @ SV425 )
= $true )
| ( ( SV425
= ( set_meet @ SV352 ) )
= $false )
| ( ( SV352 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3088]) ).
thf(3146,plain,
! [SV425: $i,SV510: $i,SV352: $i,SV542: $i] :
( ( ( ~ ( in @ SV542 @ SV352 )
| ( in @ SV510 @ SV542 ) )
= $true )
| ( ( in @ SV510 @ SV425 )
= $false )
| ( ( SV425
= ( set_meet @ SV352 ) )
= $false )
| ( ( SV352 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3089]) ).
thf(3147,plain,
! [SV88: $i,SV323: $i,SV275: $i,SV512: $i] :
( ( ( in @ SV512 @ SV275 )
= $false )
| ( ( in @ SV512 @ SV323 )
= $false )
| ( ( SV323
= ( set_difference @ SV88 @ SV275 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3091]) ).
thf(3148,plain,
! [SV89: $i,SV174: $i,SV398: $i] :
( ( ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV174 )
= $false )
| ( ( in @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) @ SV89 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 ) )
= $true )
| ( ( SV398
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3092]) ).
thf(3149,plain,
! [SV89: $i,SV174: $i,SV398: $i] :
( ( ( in @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) @ SV89 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 )
= $true )
| ( ( SV398
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3093]) ).
thf(3150,plain,
! [SV89: $i,SV174: $i,SV398: $i] :
( ( ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV174 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 )
= $true )
| ( ( SV398
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3094]) ).
thf(3151,plain,
! [SV399: $i,SV174: $i,SV529: $i,SV89: $i,SV539: $i] :
( ( ( ~ ( in @ SV539 @ SV89 )
| ~ ( in @ ( ordered_pair @ SV529 @ SV539 ) @ SV174 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV529 @ SV539 ) @ SV399 )
= $true )
| ( ( SV399
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3095]) ).
thf(3152,plain,
! [SV174: $i,SV89: $i,SV399: $i] :
( ( ( ! [SY970: $i,SY971: $i] :
( ~ ( in @ ( ordered_pair @ SY970 @ SY971 ) @ SV399 )
| ( in @ SY971 @ SV89 ) ) )
= $true )
| ( ( SV399
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3096]) ).
thf(3153,plain,
! [SV89: $i,SV174: $i,SV399: $i] :
( ( ( ! [SY972: $i,SY973: $i] :
( ~ ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV399 )
| ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV174 ) ) )
= $true )
| ( ( SV399
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3097]) ).
thf(3154,plain,
! [SV496: $i,SV92: $i,SV364: $i,SV400: $i] :
( ( ( in @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SV400 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK35_D @ SV400 @ SV364 @ SV92 ) @ SV496 ) @ SV92 )
= $false )
| ( ( in @ SV496 @ SV364 )
= $false )
| ( ( SV400
= ( relation_inverse_image @ SV92 @ SV364 ) )
= $true )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3100]) ).
thf(3155,plain,
! [SV401: $i,SV365: $i,SV92: $i,SV530: $i,SV497: $i] :
( ( ( in @ ( ordered_pair @ SV497 @ SV530 ) @ SV92 )
= $false )
| ( ( ~ ( in @ SV530 @ SV365 ) )
= $true )
| ( ( in @ SV497 @ SV401 )
= $true )
| ( ( SV401
= ( relation_inverse_image @ SV92 @ SV365 ) )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3101]) ).
thf(3156,plain,
! [SV92: $i,SV365: $i,SV401: $i,SV498: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV498 @ ( sK34_E @ SV498 @ SV401 @ SV365 @ SV92 ) ) @ SV92 ) )
= $false )
| ( ( in @ SV498 @ SV401 )
= $false )
| ( ( SV401
= ( relation_inverse_image @ SV92 @ SV365 ) )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3102]) ).
thf(3157,plain,
! [SV92: $i,SV365: $i,SV401: $i,SV498: $i] :
( ( ( ~ ( in @ ( sK34_E @ SV498 @ SV401 @ SV365 @ SV92 ) @ SV365 ) )
= $false )
| ( ( in @ SV498 @ SV401 )
= $false )
| ( ( SV401
= ( relation_inverse_image @ SV92 @ SV365 ) )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3102]) ).
thf(3158,plain,
! [SV499: $i,SV93: $i,SV366: $i,SV402: $i] :
( ( ( in @ ( sK38_D @ SV402 @ SV366 @ SV93 ) @ SV402 )
= $false )
| ( ( in @ ( ordered_pair @ SV499 @ ( sK38_D @ SV402 @ SV366 @ SV93 ) ) @ SV93 )
= $false )
| ( ( in @ SV499 @ SV366 )
= $false )
| ( ( SV402
= ( relation_image @ SV93 @ SV366 ) )
= $true )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3103]) ).
thf(3159,plain,
! [SV403: $i,SV367: $i,SV93: $i,SV500: $i,SV531: $i] :
( ( ( in @ ( ordered_pair @ SV531 @ SV500 ) @ SV93 )
= $false )
| ( ( ~ ( in @ SV531 @ SV367 ) )
= $true )
| ( ( in @ SV500 @ SV403 )
= $true )
| ( ( SV403
= ( relation_image @ SV93 @ SV367 ) )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3104]) ).
thf(3160,plain,
! [SV93: $i,SV367: $i,SV403: $i,SV501: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SV501 @ SV403 @ SV367 @ SV93 ) @ SV501 ) @ SV93 ) )
= $false )
| ( ( in @ SV501 @ SV403 )
= $false )
| ( ( SV403
= ( relation_image @ SV93 @ SV367 ) )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3105]) ).
thf(3161,plain,
! [SV93: $i,SV367: $i,SV403: $i,SV501: $i] :
( ( ( ~ ( in @ ( sK37_E @ SV501 @ SV403 @ SV367 @ SV93 ) @ SV367 ) )
= $false )
| ( ( in @ SV501 @ SV403 )
= $false )
| ( ( SV403
= ( relation_image @ SV93 @ SV367 ) )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3105]) ).
thf(3162,plain,
! [SV175: $i,SV95: $i,SV450: $i] :
( ( ( in @ ( apply @ SV450 @ SV95 ) @ ( relation_dom @ SV175 ) )
= $false )
| ( ( in @ SV95 @ ( relation_dom @ SV450 ) )
= $false )
| ( ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SV450 @ SV175 ) ) )
= $true )
| ( ( function @ SV450 )
= $false )
| ( ( relation @ SV450 )
= $false )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3106]) ).
thf(3163,plain,
! [SV175: $i,SV486: $i,SV95: $i] :
( ( ( ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SV486 @ SV175 ) ) ) )
= $true )
| ( ( in @ SV95 @ ( relation_dom @ SV486 ) )
= $true )
| ( ( function @ SV486 )
= $false )
| ( ( relation @ SV486 )
= $false )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3107]) ).
thf(3164,plain,
! [SV175: $i,SV487: $i,SV95: $i] :
( ( ( ~ ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SV487 @ SV175 ) ) ) )
= $true )
| ( ( in @ ( apply @ SV487 @ SV95 ) @ ( relation_dom @ SV175 ) )
= $true )
| ( ( function @ SV487 )
= $false )
| ( ( relation @ SV487 )
= $false )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3108]) ).
thf(3165,plain,
! [SV96: $i,SV368: $i,SV404: $i] :
( ( ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV96 )
= $false )
| ( ( in @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ SV368 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 ) )
= $true )
| ( ( SV404
= ( relation_dom_restriction @ SV96 @ SV368 ) )
= $true )
| ( ( relation @ SV404 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3109]) ).
thf(3166,plain,
! [SV96: $i,SV368: $i,SV404: $i] :
( ( ( in @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ SV368 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 )
= $true )
| ( ( SV404
= ( relation_dom_restriction @ SV96 @ SV368 ) )
= $true )
| ( ( relation @ SV404 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3110]) ).
thf(3167,plain,
! [SV96: $i,SV368: $i,SV404: $i] :
( ( ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV96 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 )
= $true )
| ( ( SV404
= ( relation_dom_restriction @ SV96 @ SV368 ) )
= $true )
| ( ( relation @ SV404 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3111]) ).
thf(3168,plain,
! [SV405: $i,SV96: $i,SV540: $i,SV369: $i,SV532: $i] :
( ( ( ~ ( in @ SV532 @ SV369 )
| ~ ( in @ ( ordered_pair @ SV532 @ SV540 ) @ SV96 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV532 @ SV540 ) @ SV405 )
= $true )
| ( ( SV405
= ( relation_dom_restriction @ SV96 @ SV369 ) )
= $false )
| ( ( relation @ SV405 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3112]) ).
thf(3169,plain,
! [SV96: $i,SV369: $i,SV405: $i] :
( ( ( ! [SY984: $i] :
( ! [SY985: $i] :
~ ( in @ ( ordered_pair @ SY984 @ SY985 ) @ SV405 )
| ( in @ SY984 @ SV369 ) ) )
= $true )
| ( ( SV405
= ( relation_dom_restriction @ SV96 @ SV369 ) )
= $false )
| ( ( relation @ SV405 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3113]) ).
thf(3170,plain,
! [SV369: $i,SV96: $i,SV405: $i] :
( ( ( ! [SY986: $i,SY987: $i] :
( ~ ( in @ ( ordered_pair @ SY986 @ SY987 ) @ SV405 )
| ( in @ ( ordered_pair @ SY986 @ SY987 ) @ SV96 ) ) )
= $true )
| ( ( SV405
= ( relation_dom_restriction @ SV96 @ SV369 ) )
= $false )
| ( ( relation @ SV405 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3114]) ).
thf(3171,plain,
! [SV97: $i,SV371: $i,SV533: $i,SV516: $i] :
( ( ( in @ ( ordered_pair @ SV516 @ SV533 ) @ SV371 )
= $false )
| ( ( in @ ( ordered_pair @ SV533 @ SV516 ) @ SV97 )
= $true )
| ( ( SV371
= ( relation_inverse @ SV97 ) )
= $false )
| ( ( relation @ SV371 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3115]) ).
thf(3172,plain,
! [SV371: $i,SV97: $i,SV517: $i,SV534: $i] :
( ( ( in @ ( ordered_pair @ SV534 @ SV517 ) @ SV97 )
= $false )
| ( ( in @ ( ordered_pair @ SV517 @ SV534 ) @ SV371 )
= $true )
| ( ( SV371
= ( relation_inverse @ SV97 ) )
= $false )
| ( ( relation @ SV371 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3116]) ).
thf(3173,plain,
! [SV543: $i,SV101: $i,SV215: $i,SV451: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ SV543 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SV543 @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV215 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV451 ) )
= $true )
| ( ( SV451
= ( relation_composition @ SV101 @ SV215 ) )
= $true )
| ( ( relation @ SV451 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3117]) ).
thf(3174,plain,
! [SV101: $i,SV215: $i,SV451: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK10_SY395 @ SV451 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV215 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV451 )
= $true )
| ( ( SV451
= ( relation_composition @ SV101 @ SV215 ) )
= $true )
| ( ( relation @ SV451 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3118]) ).
thf(3175,plain,
! [SV452: $i,SV215: $i,SV101: $i,SV544: $i] :
( ( ( ! [SY1048: $i] :
( ! [SY1049: $i] :
( ~ ( in @ ( ordered_pair @ SV544 @ SY1049 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY1049 @ SY1048 ) @ SV215 ) )
| ( in @ ( ordered_pair @ SV544 @ SY1048 ) @ SV452 ) ) )
= $true )
| ( ( SV452
= ( relation_composition @ SV101 @ SV215 ) )
= $false )
| ( ( relation @ SV452 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3119]) ).
thf(3176,plain,
! [SV101: $i,SV215: $i,SV452: $i,SV545: $i] :
( ( ( ! [SY1050: $i] :
( ~ ( in @ ( ordered_pair @ SV545 @ SY1050 ) @ SV452 )
| ~ ( ~ ( in @ ( ordered_pair @ SV545 @ ( sK7_F @ SY1050 @ SV545 @ SV452 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY1050 @ SV545 @ SV452 @ SV215 @ SV101 ) @ SY1050 ) @ SV215 ) ) ) )
= $true )
| ( ( SV452
= ( relation_composition @ SV101 @ SV215 ) )
= $false )
| ( ( relation @ SV452 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3120]) ).
thf(3177,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3121]) ).
thf(3178,plain,
! [SV110: $i,SV502: $i] :
( ( ( relation @ SV502 )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( ( SV502
!= ( function_inverse @ SV110 ) )
| ~ ( ~ ~ ( ~ ! [SY1030: $i,SY1031: $i] :
( ( SY1031
!= ( apply @ SV502 @ SY1030 ) )
| ~ ( in @ SY1030 @ ( relation_rng @ SV110 ) )
| ( SY1030
= ( apply @ SV110 @ SY1031 ) ) )
| ~ ! [SY1032: $i,SY1033: $i] :
( ( SY1033
!= ( apply @ SV502 @ SY1032 ) )
| ~ ( in @ SY1032 @ ( relation_rng @ SV110 ) )
| ( in @ SY1033 @ ( relation_dom @ SV110 ) ) ) )
| ~ ~ ( ~ ! [SY1034: $i,SY1035: $i] :
( ( SY1034
!= ( apply @ SV110 @ SY1035 ) )
| ~ ( in @ SY1035 @ ( relation_dom @ SV110 ) )
| ( SY1035
= ( apply @ SV502 @ SY1034 ) ) )
| ~ ! [SY644: $i] :
( ! [SY645: $i] :
( ( SY644
!= ( apply @ SV110 @ SY645 ) )
| ~ ( in @ SY645 @ ( relation_dom @ SV110 ) ) )
| ( in @ SY644 @ ( relation_rng @ SV110 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3122]) ).
thf(3179,plain,
! [SV110: $i,SV503: $i] :
( ( ( relation @ SV503 )
= $false )
| ( ( function @ SV503 )
= $false )
| ( ( ( SV503
!= ( function_inverse @ SV110 ) )
| ( ( relation_dom @ SV503 )
= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3123]) ).
thf(3180,plain,
! [SV309: $i,SV506: $i,SV252: $i,SV493: $i] :
( ( ( in @ SV493 @ SV252 )
= $false )
| ( ( SV493 = SV506 )
= $false )
| ( ( in @ ( ordered_pair @ SV493 @ SV506 ) @ SV309 )
= $true )
| ( ( SV309
= ( identity_relation @ SV252 ) )
= $false )
| ( ( relation @ SV309 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3130]) ).
thf(3181,plain,
! [SV252: $i,SV309: $i,SV541: $i,SV535: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV535 @ SV541 ) @ SV309 ) )
= $true )
| ( ( SV535 = SV541 )
= $true )
| ( ( SV309
= ( identity_relation @ SV252 ) )
= $false )
| ( ( relation @ SV309 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3131]) ).
thf(3182,plain,
! [SV252: $i,SV309: $i,SV546: $i,SV536: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV536 @ SV546 ) @ SV309 ) )
= $true )
| ( ( in @ SV536 @ SV252 )
= $true )
| ( ( SV309
= ( identity_relation @ SV252 ) )
= $false )
| ( ( relation @ SV309 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3132]) ).
thf(3183,plain,
! [SV494: $i,SV480: $i,SV118: $i,SV312: $i,SV345: $i] :
( ( ( ( sK23_D @ SV345 @ SV312 @ SV118 )
= ( ordered_pair @ SV480 @ SV494 ) )
= $false )
| ( ( in @ SV480 @ SV118 )
= $false )
| ( ( in @ SV494 @ SV312 )
= $false )
| ( ( ~ ( in @ ( sK23_D @ SV345 @ SV312 @ SV118 ) @ SV345 ) )
= $true )
| ( ( SV345
= ( cartesian_product2 @ SV118 @ SV312 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3134]) ).
thf(3184,plain,
! [SV346: $i,SV481: $i,SV313: $i,SV526: $i,SV118: $i,SV507: $i] :
( ( ( in @ SV507 @ SV118 )
= $false )
| ( ( ~ ( in @ SV526 @ SV313 ) )
= $true )
| ( ( ( SV481
!= ( ordered_pair @ SV507 @ SV526 ) ) )
= $true )
| ( ( in @ SV481 @ SV346 )
= $true )
| ( ( SV346
= ( cartesian_product2 @ SV118 @ SV313 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3137]) ).
thf(3185,plain,
! [SV118: $i,SV313: $i,SV346: $i,SV482: $i] :
( ( ( ~ ( in @ ( sK21_E @ SV482 @ SV346 @ SV313 @ SV118 ) @ SV118 )
| ~ ( in @ ( sK22_SY400 @ SV482 @ SV346 @ SV313 @ SV118 ) @ SV313 ) )
= $false )
| ( ( in @ SV482 @ SV346 )
= $false )
| ( ( SV346
= ( cartesian_product2 @ SV118 @ SV313 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3138]) ).
thf(3186,plain,
! [SV394: $i,SV120: $i,SV537: $i,SV527: $i] :
( ( ( in @ ( ordered_pair @ SV527 @ SV537 ) @ SV120 )
= $false )
| ( ( in @ ( ordered_pair @ SV527 @ SV537 ) @ SV394 )
= $true )
| ( ( SV120 = SV394 )
= $false )
| ( ( relation @ SV394 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3140]) ).
thf(3187,plain,
! [SV120: $i,SV394: $i,SV538: $i,SV528: $i] :
( ( ( in @ ( ordered_pair @ SV528 @ SV538 ) @ SV394 )
= $false )
| ( ( in @ ( ordered_pair @ SV528 @ SV538 ) @ SV120 )
= $true )
| ( ( SV120 = SV394 )
= $false )
| ( ( relation @ SV394 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3141]) ).
thf(3188,plain,
! [SV351: $i,SV424: $i] :
( ( ( in @ ( sK32_C @ SV424 @ SV351 ) @ SV424 )
= $false )
| ( ( in @ ( sK32_C @ SV424 @ SV351 ) @ ( sK33_SY406 @ SV424 @ SV351 ) )
= $false )
| ( ( SV424
= ( set_meet @ SV351 ) )
= $true )
| ( ( SV351 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3143]) ).
thf(3189,plain,
! [SV352: $i,SV425: $i,SV509: $i] :
( ( ( in @ ( sK31_D @ SV509 @ SV425 @ SV352 ) @ SV352 )
= $true )
| ( ( in @ SV509 @ SV425 )
= $true )
| ( ( SV425
= ( set_meet @ SV352 ) )
= $false )
| ( ( SV352 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3144]) ).
thf(3190,plain,
! [SV352: $i,SV425: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ ( sK31_D @ SV509 @ SV425 @ SV352 ) ) )
= $true )
| ( ( in @ SV509 @ SV425 )
= $true )
| ( ( SV425
= ( set_meet @ SV352 ) )
= $false )
| ( ( SV352 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3145]) ).
thf(3191,plain,
! [SV425: $i,SV510: $i,SV352: $i,SV542: $i] :
( ( ( ~ ( in @ SV542 @ SV352 ) )
= $true )
| ( ( in @ SV510 @ SV542 )
= $true )
| ( ( in @ SV510 @ SV425 )
= $false )
| ( ( SV425
= ( set_meet @ SV352 ) )
= $false )
| ( ( SV352 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3146]) ).
thf(3192,plain,
! [SV89: $i,SV174: $i,SV398: $i] :
( ( ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV398 )
= $false )
| ( ( in @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) @ SV89 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK40_D @ SV398 @ SV174 @ SV89 ) @ ( sK41_SY412 @ SV398 @ SV174 @ SV89 ) ) @ SV174 )
= $false )
| ( ( SV398
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3148]) ).
thf(3193,plain,
! [SV399: $i,SV174: $i,SV529: $i,SV89: $i,SV539: $i] :
( ( ( ~ ( in @ SV539 @ SV89 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV529 @ SV539 ) @ SV174 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV529 @ SV539 ) @ SV399 )
= $true )
| ( ( SV399
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3151]) ).
thf(3194,plain,
! [SV174: $i,SV89: $i,SV399: $i,SV547: $i] :
( ( ( ! [SY1051: $i] :
( ~ ( in @ ( ordered_pair @ SV547 @ SY1051 ) @ SV399 )
| ( in @ SY1051 @ SV89 ) ) )
= $true )
| ( ( SV399
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3152]) ).
thf(3195,plain,
! [SV89: $i,SV174: $i,SV399: $i,SV548: $i] :
( ( ( ! [SY1052: $i] :
( ~ ( in @ ( ordered_pair @ SV548 @ SY1052 ) @ SV399 )
| ( in @ ( ordered_pair @ SV548 @ SY1052 ) @ SV174 ) ) )
= $true )
| ( ( SV399
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3153]) ).
thf(3196,plain,
! [SV401: $i,SV92: $i,SV497: $i,SV365: $i,SV530: $i] :
( ( ( in @ SV530 @ SV365 )
= $false )
| ( ( in @ ( ordered_pair @ SV497 @ SV530 ) @ SV92 )
= $false )
| ( ( in @ SV497 @ SV401 )
= $true )
| ( ( SV401
= ( relation_inverse_image @ SV92 @ SV365 ) )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3155]) ).
thf(3197,plain,
! [SV92: $i,SV365: $i,SV401: $i,SV498: $i] :
( ( ( in @ ( ordered_pair @ SV498 @ ( sK34_E @ SV498 @ SV401 @ SV365 @ SV92 ) ) @ SV92 )
= $true )
| ( ( in @ SV498 @ SV401 )
= $false )
| ( ( SV401
= ( relation_inverse_image @ SV92 @ SV365 ) )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3156]) ).
thf(3198,plain,
! [SV92: $i,SV365: $i,SV401: $i,SV498: $i] :
( ( ( in @ ( sK34_E @ SV498 @ SV401 @ SV365 @ SV92 ) @ SV365 )
= $true )
| ( ( in @ SV498 @ SV401 )
= $false )
| ( ( SV401
= ( relation_inverse_image @ SV92 @ SV365 ) )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3157]) ).
thf(3199,plain,
! [SV403: $i,SV93: $i,SV500: $i,SV367: $i,SV531: $i] :
( ( ( in @ SV531 @ SV367 )
= $false )
| ( ( in @ ( ordered_pair @ SV531 @ SV500 ) @ SV93 )
= $false )
| ( ( in @ SV500 @ SV403 )
= $true )
| ( ( SV403
= ( relation_image @ SV93 @ SV367 ) )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3159]) ).
thf(3200,plain,
! [SV93: $i,SV367: $i,SV403: $i,SV501: $i] :
( ( ( in @ ( ordered_pair @ ( sK37_E @ SV501 @ SV403 @ SV367 @ SV93 ) @ SV501 ) @ SV93 )
= $true )
| ( ( in @ SV501 @ SV403 )
= $false )
| ( ( SV403
= ( relation_image @ SV93 @ SV367 ) )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3160]) ).
thf(3201,plain,
! [SV93: $i,SV367: $i,SV403: $i,SV501: $i] :
( ( ( in @ ( sK37_E @ SV501 @ SV403 @ SV367 @ SV93 ) @ SV367 )
= $true )
| ( ( in @ SV501 @ SV403 )
= $false )
| ( ( SV403
= ( relation_image @ SV93 @ SV367 ) )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3161]) ).
thf(3202,plain,
! [SV175: $i,SV486: $i,SV95: $i] :
( ( ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SV486 @ SV175 ) ) )
= $false )
| ( ( in @ SV95 @ ( relation_dom @ SV486 ) )
= $true )
| ( ( function @ SV486 )
= $false )
| ( ( relation @ SV486 )
= $false )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3163]) ).
thf(3203,plain,
! [SV175: $i,SV487: $i,SV95: $i] :
( ( ( in @ SV95 @ ( relation_dom @ ( relation_composition @ SV487 @ SV175 ) ) )
= $false )
| ( ( in @ ( apply @ SV487 @ SV95 ) @ ( relation_dom @ SV175 ) )
= $true )
| ( ( function @ SV487 )
= $false )
| ( ( relation @ SV487 )
= $false )
| ( ( function @ SV175 )
= $false )
| ( ( relation @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3164]) ).
thf(3204,plain,
! [SV96: $i,SV368: $i,SV404: $i] :
( ( ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV404 )
= $false )
| ( ( in @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ SV368 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_D @ SV404 @ SV368 @ SV96 ) @ ( sK43_SY413 @ SV404 @ SV368 @ SV96 ) ) @ SV96 )
= $false )
| ( ( SV404
= ( relation_dom_restriction @ SV96 @ SV368 ) )
= $true )
| ( ( relation @ SV404 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3165]) ).
thf(3205,plain,
! [SV405: $i,SV96: $i,SV540: $i,SV369: $i,SV532: $i] :
( ( ( ~ ( in @ SV532 @ SV369 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV532 @ SV540 ) @ SV96 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV532 @ SV540 ) @ SV405 )
= $true )
| ( ( SV405
= ( relation_dom_restriction @ SV96 @ SV369 ) )
= $false )
| ( ( relation @ SV405 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3168]) ).
thf(3206,plain,
! [SV96: $i,SV369: $i,SV405: $i,SV549: $i] :
( ( ( ! [SY1053: $i] :
~ ( in @ ( ordered_pair @ SV549 @ SY1053 ) @ SV405 )
| ( in @ SV549 @ SV369 ) )
= $true )
| ( ( SV405
= ( relation_dom_restriction @ SV96 @ SV369 ) )
= $false )
| ( ( relation @ SV405 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3169]) ).
thf(3207,plain,
! [SV369: $i,SV96: $i,SV405: $i,SV550: $i] :
( ( ( ! [SY1054: $i] :
( ~ ( in @ ( ordered_pair @ SV550 @ SY1054 ) @ SV405 )
| ( in @ ( ordered_pair @ SV550 @ SY1054 ) @ SV96 ) ) )
= $true )
| ( ( SV405
= ( relation_dom_restriction @ SV96 @ SV369 ) )
= $false )
| ( ( relation @ SV405 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3170]) ).
thf(3208,plain,
! [SV543: $i,SV101: $i,SV215: $i,SV451: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ SV543 ) @ SV101 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV543 @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV215 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV451 ) )
= $true )
| ( ( SV451
= ( relation_composition @ SV101 @ SV215 ) )
= $true )
| ( ( relation @ SV451 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3173]) ).
thf(3209,plain,
! [SV101: $i,SV215: $i,SV451: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK10_SY395 @ SV451 @ SV215 @ SV101 ) ) @ SV101 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV451 )
= $true )
| ( ( SV451
= ( relation_composition @ SV101 @ SV215 ) )
= $true )
| ( ( relation @ SV451 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3174]) ).
thf(3210,plain,
! [SV101: $i,SV215: $i,SV451: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV215 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV451 )
= $true )
| ( ( SV451
= ( relation_composition @ SV101 @ SV215 ) )
= $true )
| ( ( relation @ SV451 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3174]) ).
thf(3211,plain,
! [SV452: $i,SV215: $i,SV551: $i,SV101: $i,SV544: $i] :
( ( ( ! [SY1055: $i] :
( ~ ( in @ ( ordered_pair @ SV544 @ SY1055 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY1055 @ SV551 ) @ SV215 ) )
| ( in @ ( ordered_pair @ SV544 @ SV551 ) @ SV452 ) )
= $true )
| ( ( SV452
= ( relation_composition @ SV101 @ SV215 ) )
= $false )
| ( ( relation @ SV452 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3175]) ).
thf(3212,plain,
! [SV101: $i,SV215: $i,SV452: $i,SV552: $i,SV545: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV545 @ SV552 ) @ SV452 )
| ~ ( ~ ( in @ ( ordered_pair @ SV545 @ ( sK7_F @ SV552 @ SV545 @ SV452 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SV552 @ SV545 @ SV452 @ SV215 @ SV101 ) @ SV552 ) @ SV215 ) ) )
= $true )
| ( ( SV452
= ( relation_composition @ SV101 @ SV215 ) )
= $false )
| ( ( relation @ SV452 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3176]) ).
thf(3213,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3177]) ).
thf(3214,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3177]) ).
thf(3215,plain,
! [SV110: $i,SV502: $i] :
( ( ( ( SV502
!= ( function_inverse @ SV110 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY1030: $i,SY1031: $i] :
( ( SY1031
!= ( apply @ SV502 @ SY1030 ) )
| ~ ( in @ SY1030 @ ( relation_rng @ SV110 ) )
| ( SY1030
= ( apply @ SV110 @ SY1031 ) ) )
| ~ ! [SY1032: $i,SY1033: $i] :
( ( SY1033
!= ( apply @ SV502 @ SY1032 ) )
| ~ ( in @ SY1032 @ ( relation_rng @ SV110 ) )
| ( in @ SY1033 @ ( relation_dom @ SV110 ) ) ) )
| ~ ~ ( ~ ! [SY1034: $i,SY1035: $i] :
( ( SY1034
!= ( apply @ SV110 @ SY1035 ) )
| ~ ( in @ SY1035 @ ( relation_dom @ SV110 ) )
| ( SY1035
= ( apply @ SV502 @ SY1034 ) ) )
| ~ ! [SY644: $i] :
( ! [SY645: $i] :
( ( SY644
!= ( apply @ SV110 @ SY645 ) )
| ~ ( in @ SY645 @ ( relation_dom @ SV110 ) ) )
| ( in @ SY644 @ ( relation_rng @ SV110 ) ) ) ) ) )
= $true )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3178]) ).
thf(3216,plain,
! [SV110: $i,SV503: $i] :
( ( ( ( SV503
!= ( function_inverse @ SV110 ) ) )
= $true )
| ( ( ( relation_dom @ SV503 )
= ( relation_rng @ SV110 ) )
= $true )
| ( ( function @ SV503 )
= $false )
| ( ( relation @ SV503 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3179]) ).
thf(3217,plain,
! [SV252: $i,SV309: $i,SV541: $i,SV535: $i] :
( ( ( in @ ( ordered_pair @ SV535 @ SV541 ) @ SV309 )
= $false )
| ( ( SV535 = SV541 )
= $true )
| ( ( SV309
= ( identity_relation @ SV252 ) )
= $false )
| ( ( relation @ SV309 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3181]) ).
thf(3218,plain,
! [SV252: $i,SV309: $i,SV546: $i,SV536: $i] :
( ( ( in @ ( ordered_pair @ SV536 @ SV546 ) @ SV309 )
= $false )
| ( ( in @ SV536 @ SV252 )
= $true )
| ( ( SV309
= ( identity_relation @ SV252 ) )
= $false )
| ( ( relation @ SV309 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3182]) ).
thf(3219,plain,
! [SV480: $i,SV494: $i,SV118: $i,SV312: $i,SV345: $i] :
( ( ( in @ ( sK23_D @ SV345 @ SV312 @ SV118 ) @ SV345 )
= $false )
| ( ( in @ SV494 @ SV312 )
= $false )
| ( ( in @ SV480 @ SV118 )
= $false )
| ( ( ( sK23_D @ SV345 @ SV312 @ SV118 )
= ( ordered_pair @ SV480 @ SV494 ) )
= $false )
| ( ( SV345
= ( cartesian_product2 @ SV118 @ SV312 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3183]) ).
thf(3220,plain,
! [SV346: $i,SV481: $i,SV118: $i,SV507: $i,SV313: $i,SV526: $i] :
( ( ( in @ SV526 @ SV313 )
= $false )
| ( ( in @ SV507 @ SV118 )
= $false )
| ( ( ( SV481
!= ( ordered_pair @ SV507 @ SV526 ) ) )
= $true )
| ( ( in @ SV481 @ SV346 )
= $true )
| ( ( SV346
= ( cartesian_product2 @ SV118 @ SV313 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3184]) ).
thf(3221,plain,
! [SV118: $i,SV313: $i,SV346: $i,SV482: $i] :
( ( ( ~ ( in @ ( sK21_E @ SV482 @ SV346 @ SV313 @ SV118 ) @ SV118 ) )
= $false )
| ( ( in @ SV482 @ SV346 )
= $false )
| ( ( SV346
= ( cartesian_product2 @ SV118 @ SV313 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3185]) ).
thf(3222,plain,
! [SV118: $i,SV313: $i,SV346: $i,SV482: $i] :
( ( ( ~ ( in @ ( sK22_SY400 @ SV482 @ SV346 @ SV313 @ SV118 ) @ SV313 ) )
= $false )
| ( ( in @ SV482 @ SV346 )
= $false )
| ( ( SV346
= ( cartesian_product2 @ SV118 @ SV313 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3185]) ).
thf(3223,plain,
! [SV352: $i,SV425: $i,SV509: $i] :
( ( ( in @ SV509 @ ( sK31_D @ SV509 @ SV425 @ SV352 ) )
= $false )
| ( ( in @ SV509 @ SV425 )
= $true )
| ( ( SV425
= ( set_meet @ SV352 ) )
= $false )
| ( ( SV352 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3190]) ).
thf(3224,plain,
! [SV425: $i,SV510: $i,SV352: $i,SV542: $i] :
( ( ( in @ SV542 @ SV352 )
= $false )
| ( ( in @ SV510 @ SV542 )
= $true )
| ( ( in @ SV510 @ SV425 )
= $false )
| ( ( SV425
= ( set_meet @ SV352 ) )
= $false )
| ( ( SV352 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3191]) ).
thf(3225,plain,
! [SV399: $i,SV174: $i,SV529: $i,SV89: $i,SV539: $i] :
( ( ( in @ SV539 @ SV89 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV529 @ SV539 ) @ SV174 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV529 @ SV539 ) @ SV399 )
= $true )
| ( ( SV399
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3193]) ).
thf(3226,plain,
! [SV174: $i,SV89: $i,SV399: $i,SV553: $i,SV547: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV547 @ SV553 ) @ SV399 )
| ( in @ SV553 @ SV89 ) )
= $true )
| ( ( SV399
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3194]) ).
thf(3227,plain,
! [SV89: $i,SV174: $i,SV399: $i,SV554: $i,SV548: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV548 @ SV554 ) @ SV399 )
| ( in @ ( ordered_pair @ SV548 @ SV554 ) @ SV174 ) )
= $true )
| ( ( SV399
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3195]) ).
thf(3228,plain,
! [SV405: $i,SV96: $i,SV540: $i,SV369: $i,SV532: $i] :
( ( ( in @ SV532 @ SV369 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV532 @ SV540 ) @ SV96 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV532 @ SV540 ) @ SV405 )
= $true )
| ( ( SV405
= ( relation_dom_restriction @ SV96 @ SV369 ) )
= $false )
| ( ( relation @ SV405 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3205]) ).
thf(3229,plain,
! [SV96: $i,SV369: $i,SV405: $i,SV549: $i] :
( ( ( ! [SY1053: $i] :
~ ( in @ ( ordered_pair @ SV549 @ SY1053 ) @ SV405 ) )
= $true )
| ( ( in @ SV549 @ SV369 )
= $true )
| ( ( SV405
= ( relation_dom_restriction @ SV96 @ SV369 ) )
= $false )
| ( ( relation @ SV405 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3206]) ).
thf(3230,plain,
! [SV369: $i,SV96: $i,SV405: $i,SV555: $i,SV550: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV550 @ SV555 ) @ SV405 )
| ( in @ ( ordered_pair @ SV550 @ SV555 ) @ SV96 ) )
= $true )
| ( ( SV405
= ( relation_dom_restriction @ SV96 @ SV369 ) )
= $false )
| ( ( relation @ SV405 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3207]) ).
thf(3231,plain,
! [SV543: $i,SV101: $i,SV215: $i,SV451: $i] :
( ( ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ SV543 ) @ SV101 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV543 @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV215 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV451 ) )
= $true )
| ( ( SV451
= ( relation_composition @ SV101 @ SV215 ) )
= $true )
| ( ( relation @ SV451 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3208]) ).
thf(3232,plain,
! [SV101: $i,SV215: $i,SV451: $i] :
( ( ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK10_SY395 @ SV451 @ SV215 @ SV101 ) ) @ SV101 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV451 )
= $true )
| ( ( SV451
= ( relation_composition @ SV101 @ SV215 ) )
= $true )
| ( ( relation @ SV451 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3209]) ).
thf(3233,plain,
! [SV101: $i,SV215: $i,SV451: $i] :
( ( ( in @ ( ordered_pair @ ( sK10_SY395 @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV215 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV451 )
= $true )
| ( ( SV451
= ( relation_composition @ SV101 @ SV215 ) )
= $true )
| ( ( relation @ SV451 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3210]) ).
thf(3234,plain,
! [SV452: $i,SV215: $i,SV551: $i,SV101: $i,SV544: $i] :
( ( ( ! [SY1055: $i] :
( ~ ( in @ ( ordered_pair @ SV544 @ SY1055 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SY1055 @ SV551 ) @ SV215 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV544 @ SV551 ) @ SV452 )
= $true )
| ( ( SV452
= ( relation_composition @ SV101 @ SV215 ) )
= $false )
| ( ( relation @ SV452 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3211]) ).
thf(3235,plain,
! [SV101: $i,SV215: $i,SV452: $i,SV552: $i,SV545: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV545 @ SV552 ) @ SV452 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV545 @ ( sK7_F @ SV552 @ SV545 @ SV452 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SV552 @ SV545 @ SV452 @ SV215 @ SV101 ) @ SV552 ) @ SV215 ) ) )
= $true )
| ( ( SV452
= ( relation_composition @ SV101 @ SV215 ) )
= $false )
| ( ( relation @ SV452 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3212]) ).
thf(3236,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3213]) ).
thf(3237,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3214]) ).
thf(3238,plain,
! [SV110: $i,SV502: $i] :
( ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY1030: $i,SY1031: $i] :
( ( SY1031
!= ( apply @ SV502 @ SY1030 ) )
| ~ ( in @ SY1030 @ ( relation_rng @ SV110 ) )
| ( SY1030
= ( apply @ SV110 @ SY1031 ) ) )
| ~ ! [SY1032: $i,SY1033: $i] :
( ( SY1033
!= ( apply @ SV502 @ SY1032 ) )
| ~ ( in @ SY1032 @ ( relation_rng @ SV110 ) )
| ( in @ SY1033 @ ( relation_dom @ SV110 ) ) ) )
| ~ ~ ( ~ ! [SY1034: $i,SY1035: $i] :
( ( SY1034
!= ( apply @ SV110 @ SY1035 ) )
| ~ ( in @ SY1035 @ ( relation_dom @ SV110 ) )
| ( SY1035
= ( apply @ SV502 @ SY1034 ) ) )
| ~ ! [SY644: $i] :
( ! [SY645: $i] :
( ( SY644
!= ( apply @ SV110 @ SY645 ) )
| ~ ( in @ SY645 @ ( relation_dom @ SV110 ) ) )
| ( in @ SY644 @ ( relation_rng @ SV110 ) ) ) ) ) )
= $true )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3215]) ).
thf(3239,plain,
! [SV110: $i,SV503: $i] :
( ( ( SV503
= ( function_inverse @ SV110 ) )
= $false )
| ( ( ( relation_dom @ SV503 )
= ( relation_rng @ SV110 ) )
= $true )
| ( ( function @ SV503 )
= $false )
| ( ( relation @ SV503 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3216]) ).
thf(3240,plain,
! [SV346: $i,SV313: $i,SV118: $i,SV526: $i,SV507: $i,SV481: $i] :
( ( ( SV481
= ( ordered_pair @ SV507 @ SV526 ) )
= $false )
| ( ( in @ SV507 @ SV118 )
= $false )
| ( ( in @ SV526 @ SV313 )
= $false )
| ( ( in @ SV481 @ SV346 )
= $true )
| ( ( SV346
= ( cartesian_product2 @ SV118 @ SV313 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3220]) ).
thf(3241,plain,
! [SV118: $i,SV313: $i,SV346: $i,SV482: $i] :
( ( ( in @ ( sK21_E @ SV482 @ SV346 @ SV313 @ SV118 ) @ SV118 )
= $true )
| ( ( in @ SV482 @ SV346 )
= $false )
| ( ( SV346
= ( cartesian_product2 @ SV118 @ SV313 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3221]) ).
thf(3242,plain,
! [SV118: $i,SV313: $i,SV346: $i,SV482: $i] :
( ( ( in @ ( sK22_SY400 @ SV482 @ SV346 @ SV313 @ SV118 ) @ SV313 )
= $true )
| ( ( in @ SV482 @ SV346 )
= $false )
| ( ( SV346
= ( cartesian_product2 @ SV118 @ SV313 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3222]) ).
thf(3243,plain,
! [SV399: $i,SV89: $i,SV174: $i,SV539: $i,SV529: $i] :
( ( ( in @ ( ordered_pair @ SV529 @ SV539 ) @ SV174 )
= $false )
| ( ( in @ SV539 @ SV89 )
= $false )
| ( ( in @ ( ordered_pair @ SV529 @ SV539 ) @ SV399 )
= $true )
| ( ( SV399
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3225]) ).
thf(3244,plain,
! [SV174: $i,SV89: $i,SV399: $i,SV553: $i,SV547: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV547 @ SV553 ) @ SV399 ) )
= $true )
| ( ( in @ SV553 @ SV89 )
= $true )
| ( ( SV399
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3226]) ).
thf(3245,plain,
! [SV89: $i,SV174: $i,SV399: $i,SV554: $i,SV548: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV548 @ SV554 ) @ SV399 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV548 @ SV554 ) @ SV174 )
= $true )
| ( ( SV399
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3227]) ).
thf(3246,plain,
! [SV405: $i,SV369: $i,SV96: $i,SV540: $i,SV532: $i] :
( ( ( in @ ( ordered_pair @ SV532 @ SV540 ) @ SV96 )
= $false )
| ( ( in @ SV532 @ SV369 )
= $false )
| ( ( in @ ( ordered_pair @ SV532 @ SV540 ) @ SV405 )
= $true )
| ( ( SV405
= ( relation_dom_restriction @ SV96 @ SV369 ) )
= $false )
| ( ( relation @ SV405 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3228]) ).
thf(3247,plain,
! [SV96: $i,SV369: $i,SV405: $i,SV556: $i,SV549: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV549 @ SV556 ) @ SV405 ) )
= $true )
| ( ( in @ SV549 @ SV369 )
= $true )
| ( ( SV405
= ( relation_dom_restriction @ SV96 @ SV369 ) )
= $false )
| ( ( relation @ SV405 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3229]) ).
thf(3248,plain,
! [SV369: $i,SV96: $i,SV405: $i,SV555: $i,SV550: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV550 @ SV555 ) @ SV405 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV550 @ SV555 ) @ SV96 )
= $true )
| ( ( SV405
= ( relation_dom_restriction @ SV96 @ SV369 ) )
= $false )
| ( ( relation @ SV405 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3230]) ).
thf(3249,plain,
! [SV101: $i,SV215: $i,SV451: $i,SV543: $i] :
( ( ( in @ ( ordered_pair @ SV543 @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV215 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ SV543 ) @ SV101 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV451 ) )
= $true )
| ( ( SV451
= ( relation_composition @ SV101 @ SV215 ) )
= $true )
| ( ( relation @ SV451 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3231]) ).
thf(3250,plain,
! [SV452: $i,SV215: $i,SV551: $i,SV101: $i,SV557: $i,SV544: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV544 @ SV557 ) @ SV101 )
| ~ ( in @ ( ordered_pair @ SV557 @ SV551 ) @ SV215 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV544 @ SV551 ) @ SV452 )
= $true )
| ( ( SV452
= ( relation_composition @ SV101 @ SV215 ) )
= $false )
| ( ( relation @ SV452 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3234]) ).
thf(3251,plain,
! [SV101: $i,SV215: $i,SV452: $i,SV552: $i,SV545: $i] :
( ( ( in @ ( ordered_pair @ SV545 @ SV552 ) @ SV452 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV545 @ ( sK7_F @ SV552 @ SV545 @ SV452 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SV552 @ SV545 @ SV452 @ SV215 @ SV101 ) @ SV552 ) @ SV215 ) ) )
= $true )
| ( ( SV452
= ( relation_composition @ SV101 @ SV215 ) )
= $false )
| ( ( relation @ SV452 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3235]) ).
thf(3252,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3236]) ).
thf(3253,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3237]) ).
thf(3254,plain,
! [SV110: $i,SV502: $i] :
( ( ( ~ ~ ( ~ ! [SY1030: $i,SY1031: $i] :
( ( SY1031
!= ( apply @ SV502 @ SY1030 ) )
| ~ ( in @ SY1030 @ ( relation_rng @ SV110 ) )
| ( SY1030
= ( apply @ SV110 @ SY1031 ) ) )
| ~ ! [SY1032: $i,SY1033: $i] :
( ( SY1033
!= ( apply @ SV502 @ SY1032 ) )
| ~ ( in @ SY1032 @ ( relation_rng @ SV110 ) )
| ( in @ SY1033 @ ( relation_dom @ SV110 ) ) ) )
| ~ ~ ( ~ ! [SY1034: $i,SY1035: $i] :
( ( SY1034
!= ( apply @ SV110 @ SY1035 ) )
| ~ ( in @ SY1035 @ ( relation_dom @ SV110 ) )
| ( SY1035
= ( apply @ SV502 @ SY1034 ) ) )
| ~ ! [SY644: $i] :
( ! [SY645: $i] :
( ( SY644
!= ( apply @ SV110 @ SY645 ) )
| ~ ( in @ SY645 @ ( relation_dom @ SV110 ) ) )
| ( in @ SY644 @ ( relation_rng @ SV110 ) ) ) ) )
= $false )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3238]) ).
thf(3255,plain,
! [SV174: $i,SV89: $i,SV399: $i,SV553: $i,SV547: $i] :
( ( ( in @ ( ordered_pair @ SV547 @ SV553 ) @ SV399 )
= $false )
| ( ( in @ SV553 @ SV89 )
= $true )
| ( ( SV399
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3244]) ).
thf(3256,plain,
! [SV89: $i,SV174: $i,SV399: $i,SV554: $i,SV548: $i] :
( ( ( in @ ( ordered_pair @ SV548 @ SV554 ) @ SV399 )
= $false )
| ( ( in @ ( ordered_pair @ SV548 @ SV554 ) @ SV174 )
= $true )
| ( ( SV399
= ( relation_rng_restriction @ SV89 @ SV174 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3245]) ).
thf(3257,plain,
! [SV96: $i,SV369: $i,SV405: $i,SV556: $i,SV549: $i] :
( ( ( in @ ( ordered_pair @ SV549 @ SV556 ) @ SV405 )
= $false )
| ( ( in @ SV549 @ SV369 )
= $true )
| ( ( SV405
= ( relation_dom_restriction @ SV96 @ SV369 ) )
= $false )
| ( ( relation @ SV405 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3247]) ).
thf(3258,plain,
! [SV369: $i,SV96: $i,SV405: $i,SV555: $i,SV550: $i] :
( ( ( in @ ( ordered_pair @ SV550 @ SV555 ) @ SV405 )
= $false )
| ( ( in @ ( ordered_pair @ SV550 @ SV555 ) @ SV96 )
= $true )
| ( ( SV405
= ( relation_dom_restriction @ SV96 @ SV369 ) )
= $false )
| ( ( relation @ SV405 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3248]) ).
thf(3259,plain,
! [SV543: $i,SV101: $i,SV215: $i,SV451: $i] :
( ( ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV451 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_D @ SV451 @ SV215 @ SV101 ) @ SV543 ) @ SV101 )
= $false )
| ( ( in @ ( ordered_pair @ SV543 @ ( sK9_SY391 @ SV451 @ SV215 @ SV101 ) ) @ SV215 )
= $false )
| ( ( SV451
= ( relation_composition @ SV101 @ SV215 ) )
= $true )
| ( ( relation @ SV451 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3249]) ).
thf(3260,plain,
! [SV452: $i,SV215: $i,SV551: $i,SV101: $i,SV557: $i,SV544: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV544 @ SV557 ) @ SV101 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV557 @ SV551 ) @ SV215 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV544 @ SV551 ) @ SV452 )
= $true )
| ( ( SV452
= ( relation_composition @ SV101 @ SV215 ) )
= $false )
| ( ( relation @ SV452 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3250]) ).
thf(3261,plain,
! [SV101: $i,SV215: $i,SV452: $i,SV552: $i,SV545: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV545 @ ( sK7_F @ SV552 @ SV545 @ SV452 @ SV215 @ SV101 ) ) @ SV101 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SV552 @ SV545 @ SV452 @ SV215 @ SV101 ) @ SV552 ) @ SV215 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV545 @ SV552 ) @ SV452 )
= $false )
| ( ( SV452
= ( relation_composition @ SV101 @ SV215 ) )
= $false )
| ( ( relation @ SV452 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3251]) ).
thf(3262,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3252]) ).
thf(3263,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3252]) ).
thf(3264,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3253]) ).
thf(3265,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3253]) ).
thf(3266,plain,
! [SV110: $i,SV502: $i] :
( ( ( ~ ~ ( ~ ! [SY1030: $i,SY1031: $i] :
( ( SY1031
!= ( apply @ SV502 @ SY1030 ) )
| ~ ( in @ SY1030 @ ( relation_rng @ SV110 ) )
| ( SY1030
= ( apply @ SV110 @ SY1031 ) ) )
| ~ ! [SY1032: $i,SY1033: $i] :
( ( SY1033
!= ( apply @ SV502 @ SY1032 ) )
| ~ ( in @ SY1032 @ ( relation_rng @ SV110 ) )
| ( in @ SY1033 @ ( relation_dom @ SV110 ) ) ) ) )
= $false )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3254]) ).
thf(3267,plain,
! [SV502: $i,SV110: $i] :
( ( ( ~ ~ ( ~ ! [SY1034: $i,SY1035: $i] :
( ( SY1034
!= ( apply @ SV110 @ SY1035 ) )
| ~ ( in @ SY1035 @ ( relation_dom @ SV110 ) )
| ( SY1035
= ( apply @ SV502 @ SY1034 ) ) )
| ~ ! [SY644: $i] :
( ! [SY645: $i] :
( ( SY644
!= ( apply @ SV110 @ SY645 ) )
| ~ ( in @ SY645 @ ( relation_dom @ SV110 ) ) )
| ( in @ SY644 @ ( relation_rng @ SV110 ) ) ) ) )
= $false )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3254]) ).
thf(3268,plain,
! [SV452: $i,SV215: $i,SV551: $i,SV101: $i,SV557: $i,SV544: $i] :
( ( ( in @ ( ordered_pair @ SV544 @ SV557 ) @ SV101 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV557 @ SV551 ) @ SV215 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV544 @ SV551 ) @ SV452 )
= $true )
| ( ( SV452
= ( relation_composition @ SV101 @ SV215 ) )
= $false )
| ( ( relation @ SV452 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3260]) ).
thf(3269,plain,
! [SV101: $i,SV215: $i,SV452: $i,SV552: $i,SV545: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV545 @ ( sK7_F @ SV552 @ SV545 @ SV452 @ SV215 @ SV101 ) ) @ SV101 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV545 @ SV552 ) @ SV452 )
= $false )
| ( ( SV452
= ( relation_composition @ SV101 @ SV215 ) )
= $false )
| ( ( relation @ SV452 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3261]) ).
thf(3270,plain,
! [SV101: $i,SV215: $i,SV452: $i,SV545: $i,SV552: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK7_F @ SV552 @ SV545 @ SV452 @ SV215 @ SV101 ) @ SV552 ) @ SV215 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV545 @ SV552 ) @ SV452 )
= $false )
| ( ( SV452
= ( relation_composition @ SV101 @ SV215 ) )
= $false )
| ( ( relation @ SV452 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3261]) ).
thf(3271,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3262]) ).
thf(3272,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3263]) ).
thf(3273,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ( ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3264]) ).
thf(3274,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3265]) ).
thf(3275,plain,
! [SV110: $i,SV502: $i] :
( ( ( ~ ( ~ ! [SY1030: $i,SY1031: $i] :
( ( SY1031
!= ( apply @ SV502 @ SY1030 ) )
| ~ ( in @ SY1030 @ ( relation_rng @ SV110 ) )
| ( SY1030
= ( apply @ SV110 @ SY1031 ) ) )
| ~ ! [SY1032: $i,SY1033: $i] :
( ( SY1033
!= ( apply @ SV502 @ SY1032 ) )
| ~ ( in @ SY1032 @ ( relation_rng @ SV110 ) )
| ( in @ SY1033 @ ( relation_dom @ SV110 ) ) ) ) )
= $true )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3266]) ).
thf(3276,plain,
! [SV502: $i,SV110: $i] :
( ( ( ~ ( ~ ! [SY1034: $i,SY1035: $i] :
( ( SY1034
!= ( apply @ SV110 @ SY1035 ) )
| ~ ( in @ SY1035 @ ( relation_dom @ SV110 ) )
| ( SY1035
= ( apply @ SV502 @ SY1034 ) ) )
| ~ ! [SY644: $i] :
( ! [SY645: $i] :
( ( SY644
!= ( apply @ SV110 @ SY645 ) )
| ~ ( in @ SY645 @ ( relation_dom @ SV110 ) ) )
| ( in @ SY644 @ ( relation_rng @ SV110 ) ) ) ) )
= $true )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3267]) ).
thf(3277,plain,
! [SV452: $i,SV101: $i,SV544: $i,SV215: $i,SV551: $i,SV557: $i] :
( ( ( in @ ( ordered_pair @ SV557 @ SV551 ) @ SV215 )
= $false )
| ( ( in @ ( ordered_pair @ SV544 @ SV557 ) @ SV101 )
= $false )
| ( ( in @ ( ordered_pair @ SV544 @ SV551 ) @ SV452 )
= $true )
| ( ( SV452
= ( relation_composition @ SV101 @ SV215 ) )
= $false )
| ( ( relation @ SV452 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3268]) ).
thf(3278,plain,
! [SV101: $i,SV215: $i,SV452: $i,SV552: $i,SV545: $i] :
( ( ( in @ ( ordered_pair @ SV545 @ ( sK7_F @ SV552 @ SV545 @ SV452 @ SV215 @ SV101 ) ) @ SV101 )
= $true )
| ( ( in @ ( ordered_pair @ SV545 @ SV552 ) @ SV452 )
= $false )
| ( ( SV452
= ( relation_composition @ SV101 @ SV215 ) )
= $false )
| ( ( relation @ SV452 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3269]) ).
thf(3279,plain,
! [SV101: $i,SV215: $i,SV452: $i,SV545: $i,SV552: $i] :
( ( ( in @ ( ordered_pair @ ( sK7_F @ SV552 @ SV545 @ SV452 @ SV215 @ SV101 ) @ SV552 ) @ SV215 )
= $true )
| ( ( in @ ( ordered_pair @ SV545 @ SV552 ) @ SV452 )
= $false )
| ( ( SV452
= ( relation_composition @ SV101 @ SV215 ) )
= $false )
| ( ( relation @ SV452 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV101 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3270]) ).
thf(3280,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3271]) ).
thf(3281,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3272]) ).
thf(3282,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3273]) ).
thf(3283,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) )
= $true )
| ( ( ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3274]) ).
thf(3284,plain,
! [SV110: $i,SV502: $i] :
( ( ( ~ ! [SY1030: $i,SY1031: $i] :
( ( SY1031
!= ( apply @ SV502 @ SY1030 ) )
| ~ ( in @ SY1030 @ ( relation_rng @ SV110 ) )
| ( SY1030
= ( apply @ SV110 @ SY1031 ) ) )
| ~ ! [SY1032: $i,SY1033: $i] :
( ( SY1033
!= ( apply @ SV502 @ SY1032 ) )
| ~ ( in @ SY1032 @ ( relation_rng @ SV110 ) )
| ( in @ SY1033 @ ( relation_dom @ SV110 ) ) ) )
= $false )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3275]) ).
thf(3285,plain,
! [SV502: $i,SV110: $i] :
( ( ( ~ ! [SY1034: $i,SY1035: $i] :
( ( SY1034
!= ( apply @ SV110 @ SY1035 ) )
| ~ ( in @ SY1035 @ ( relation_dom @ SV110 ) )
| ( SY1035
= ( apply @ SV502 @ SY1034 ) ) )
| ~ ! [SY644: $i] :
( ! [SY645: $i] :
( ( SY644
!= ( apply @ SV110 @ SY645 ) )
| ~ ( in @ SY645 @ ( relation_dom @ SV110 ) ) )
| ( in @ SY644 @ ( relation_rng @ SV110 ) ) ) )
= $false )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3276]) ).
thf(3286,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3280]) ).
thf(3287,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3280]) ).
thf(3288,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3281]) ).
thf(3289,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3281]) ).
thf(3290,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3282]) ).
thf(3291,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3282]) ).
thf(3292,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) )
= $true )
| ( ( ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3283]) ).
thf(3293,plain,
! [SV110: $i,SV502: $i] :
( ( ( ~ ! [SY1030: $i,SY1031: $i] :
( ( SY1031
!= ( apply @ SV502 @ SY1030 ) )
| ~ ( in @ SY1030 @ ( relation_rng @ SV110 ) )
| ( SY1030
= ( apply @ SV110 @ SY1031 ) ) ) )
= $false )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3284]) ).
thf(3294,plain,
! [SV110: $i,SV502: $i] :
( ( ( ~ ! [SY1032: $i,SY1033: $i] :
( ( SY1033
!= ( apply @ SV502 @ SY1032 ) )
| ~ ( in @ SY1032 @ ( relation_rng @ SV110 ) )
| ( in @ SY1033 @ ( relation_dom @ SV110 ) ) ) )
= $false )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3284]) ).
thf(3295,plain,
! [SV502: $i,SV110: $i] :
( ( ( ~ ! [SY1034: $i,SY1035: $i] :
( ( SY1034
!= ( apply @ SV110 @ SY1035 ) )
| ~ ( in @ SY1035 @ ( relation_dom @ SV110 ) )
| ( SY1035
= ( apply @ SV502 @ SY1034 ) ) ) )
= $false )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3285]) ).
thf(3296,plain,
! [SV502: $i,SV110: $i] :
( ( ( ~ ! [SY644: $i] :
( ! [SY645: $i] :
( ( SY644
!= ( apply @ SV110 @ SY645 ) )
| ~ ( in @ SY645 @ ( relation_dom @ SV110 ) ) )
| ( in @ SY644 @ ( relation_rng @ SV110 ) ) ) )
= $false )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3285]) ).
thf(3297,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ( ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3286]) ).
thf(3298,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3287]) ).
thf(3299,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3288]) ).
thf(3300,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3289]) ).
thf(3301,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3290]) ).
thf(3302,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3291]) ).
thf(3303,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
= $false )
| ( ( ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) )
= $true )
| ( ( ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3292]) ).
thf(3304,plain,
! [SV110: $i,SV502: $i] :
( ( ( ! [SY1030: $i,SY1031: $i] :
( ( SY1031
!= ( apply @ SV502 @ SY1030 ) )
| ~ ( in @ SY1030 @ ( relation_rng @ SV110 ) )
| ( SY1030
= ( apply @ SV110 @ SY1031 ) ) ) )
= $true )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3293]) ).
thf(3305,plain,
! [SV110: $i,SV502: $i] :
( ( ( ! [SY1032: $i,SY1033: $i] :
( ( SY1033
!= ( apply @ SV502 @ SY1032 ) )
| ~ ( in @ SY1032 @ ( relation_rng @ SV110 ) )
| ( in @ SY1033 @ ( relation_dom @ SV110 ) ) ) )
= $true )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3294]) ).
thf(3306,plain,
! [SV502: $i,SV110: $i] :
( ( ( ! [SY1034: $i,SY1035: $i] :
( ( SY1034
!= ( apply @ SV110 @ SY1035 ) )
| ~ ( in @ SY1035 @ ( relation_dom @ SV110 ) )
| ( SY1035
= ( apply @ SV502 @ SY1034 ) ) ) )
= $true )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3295]) ).
thf(3307,plain,
! [SV502: $i,SV110: $i] :
( ( ( ! [SY644: $i] :
( ! [SY645: $i] :
( ( SY644
!= ( apply @ SV110 @ SY645 ) )
| ~ ( in @ SY645 @ ( relation_dom @ SV110 ) ) )
| ( in @ SY644 @ ( relation_rng @ SV110 ) ) ) )
= $true )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3296]) ).
thf(3308,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3297]) ).
thf(3309,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
= $true )
| ( ( ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3298]) ).
thf(3310,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3299]) ).
thf(3311,plain,
! [SV110: $i,SV465: $i] :
( ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
= $true )
| ( ( ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3300]) ).
thf(3312,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) )
= $true )
| ( ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3301]) ).
thf(3313,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) )
= $true )
| ( ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3302]) ).
thf(3314,plain,
! [SV110: $i,SV465: $i] :
( ( ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
= $false )
| ( ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
= $false )
| ( ( ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3303]) ).
thf(3315,plain,
! [SV110: $i,SV558: $i,SV502: $i] :
( ( ( ! [SY1056: $i] :
( ( SY1056
!= ( apply @ SV502 @ SV558 ) )
| ~ ( in @ SV558 @ ( relation_rng @ SV110 ) )
| ( SV558
= ( apply @ SV110 @ SY1056 ) ) ) )
= $true )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3304]) ).
thf(3316,plain,
! [SV110: $i,SV559: $i,SV502: $i] :
( ( ( ! [SY1057: $i] :
( ( SY1057
!= ( apply @ SV502 @ SV559 ) )
| ~ ( in @ SV559 @ ( relation_rng @ SV110 ) )
| ( in @ SY1057 @ ( relation_dom @ SV110 ) ) ) )
= $true )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3305]) ).
thf(3317,plain,
! [SV502: $i,SV110: $i,SV560: $i] :
( ( ( ! [SY1058: $i] :
( ( SV560
!= ( apply @ SV110 @ SY1058 ) )
| ~ ( in @ SY1058 @ ( relation_dom @ SV110 ) )
| ( SY1058
= ( apply @ SV502 @ SV560 ) ) ) )
= $true )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3306]) ).
thf(3318,plain,
! [SV502: $i,SV110: $i,SV561: $i] :
( ( ( ! [SY1059: $i] :
( ( SV561
!= ( apply @ SV110 @ SY1059 ) )
| ~ ( in @ SY1059 @ ( relation_dom @ SV110 ) ) )
| ( in @ SV561 @ ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3307]) ).
thf(3319,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3308]) ).
thf(3320,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3308]) ).
thf(3321,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) )
= $true )
| ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3309]) ).
thf(3322,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3310]) ).
thf(3323,plain,
! [SV110: $i,SV465: $i] :
( ( ( ~ ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3310]) ).
thf(3324,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) )
= $true )
| ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3311]) ).
thf(3325,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) )
= $true )
| ( ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3312]) ).
thf(3326,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( ( sK70_C @ SV465 @ SV110 )
!= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) )
= $true )
| ( ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3313]) ).
thf(3327,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( ( sK71_SY424 @ SV465 @ SV110 )
!= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) )
= $true )
| ( ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
= $false )
| ( ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
= $false )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3314]) ).
thf(3328,plain,
! [SV110: $i,SV558: $i,SV502: $i,SV562: $i] :
( ( ( ( SV562
!= ( apply @ SV502 @ SV558 ) )
| ~ ( in @ SV558 @ ( relation_rng @ SV110 ) )
| ( SV558
= ( apply @ SV110 @ SV562 ) ) )
= $true )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3315]) ).
thf(3329,plain,
! [SV110: $i,SV559: $i,SV502: $i,SV563: $i] :
( ( ( ( SV563
!= ( apply @ SV502 @ SV559 ) )
| ~ ( in @ SV559 @ ( relation_rng @ SV110 ) )
| ( in @ SV563 @ ( relation_dom @ SV110 ) ) )
= $true )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3316]) ).
thf(3330,plain,
! [SV502: $i,SV564: $i,SV110: $i,SV560: $i] :
( ( ( ( SV560
!= ( apply @ SV110 @ SV564 ) )
| ~ ( in @ SV564 @ ( relation_dom @ SV110 ) )
| ( SV564
= ( apply @ SV502 @ SV560 ) ) )
= $true )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3317]) ).
thf(3331,plain,
! [SV502: $i,SV110: $i,SV561: $i] :
( ( ( ! [SY1059: $i] :
( ( SV561
!= ( apply @ SV110 @ SY1059 ) )
| ~ ( in @ SY1059 @ ( relation_dom @ SV110 ) ) ) )
= $true )
| ( ( in @ SV561 @ ( relation_rng @ SV110 ) )
= $true )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3318]) ).
thf(3332,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3319]) ).
thf(3333,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3320]) ).
thf(3334,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
= $false )
| ( ( ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) )
= $true )
| ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3321]) ).
thf(3335,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3322]) ).
thf(3336,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
| ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3323]) ).
thf(3337,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
= $false )
| ( ( ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) )
= $true )
| ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3324]) ).
thf(3338,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
= $false )
| ( ( ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) )
= $true )
| ( ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3325]) ).
thf(3339,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
= $false )
| ( ( ~ ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) ) )
= $true )
| ( ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3326]) ).
thf(3340,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
= $false )
| ( ( ~ ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) ) )
= $true )
| ( ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
= $false )
| ( ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
= $false )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3327]) ).
thf(3341,plain,
! [SV110: $i,SV558: $i,SV502: $i,SV562: $i] :
( ( ( ( SV562
!= ( apply @ SV502 @ SV558 ) )
| ~ ( in @ SV558 @ ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV558
= ( apply @ SV110 @ SV562 ) )
= $true )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3328]) ).
thf(3342,plain,
! [SV110: $i,SV559: $i,SV502: $i,SV563: $i] :
( ( ( ( SV563
!= ( apply @ SV502 @ SV559 ) )
| ~ ( in @ SV559 @ ( relation_rng @ SV110 ) ) )
= $true )
| ( ( in @ SV563 @ ( relation_dom @ SV110 ) )
= $true )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3329]) ).
thf(3343,plain,
! [SV502: $i,SV564: $i,SV110: $i,SV560: $i] :
( ( ( ( SV560
!= ( apply @ SV110 @ SV564 ) )
| ~ ( in @ SV564 @ ( relation_dom @ SV110 ) ) )
= $true )
| ( ( SV564
= ( apply @ SV502 @ SV560 ) )
= $true )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3330]) ).
thf(3344,plain,
! [SV502: $i,SV565: $i,SV110: $i,SV561: $i] :
( ( ( ( SV561
!= ( apply @ SV110 @ SV565 ) )
| ~ ( in @ SV565 @ ( relation_dom @ SV110 ) ) )
= $true )
| ( ( in @ SV561 @ ( relation_rng @ SV110 ) )
= $true )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3331]) ).
thf(3345,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
= $true )
| ( ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3332]) ).
thf(3346,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
= $true )
| ( ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3333]) ).
thf(3347,plain,
! [SV110: $i,SV465: $i] :
( ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
= $false )
| ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
= $false )
| ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3334]) ).
thf(3348,plain,
! [SV110: $i,SV465: $i] :
( ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
= $true )
| ( ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3335]) ).
thf(3349,plain,
! [SV110: $i,SV465: $i] :
( ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
= $true )
| ( ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3336]) ).
thf(3350,plain,
! [SV110: $i,SV465: $i] :
( ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
= $false )
| ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
= $false )
| ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3337]) ).
thf(3351,plain,
! [SV110: $i,SV465: $i] :
( ( ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
= $false )
| ( ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
= $false )
| ( ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3338]) ).
thf(3352,plain,
! [SV110: $i,SV465: $i] :
( ( ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
= $false )
| ( ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
= $false )
| ( ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
= $true )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3339]) ).
thf(3353,plain,
! [SV110: $i,SV465: $i] :
( ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
= $false )
| ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
= $false )
| ( ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
= $false )
| ( ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
= $false )
| ( ( ( ( relation_dom @ SV465 )
!= ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3340]) ).
thf(3354,plain,
! [SV110: $i,SV558: $i,SV502: $i,SV562: $i] :
( ( ( ( SV562
!= ( apply @ SV502 @ SV558 ) ) )
= $true )
| ( ( ~ ( in @ SV558 @ ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV558
= ( apply @ SV110 @ SV562 ) )
= $true )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3341]) ).
thf(3355,plain,
! [SV110: $i,SV559: $i,SV502: $i,SV563: $i] :
( ( ( ( SV563
!= ( apply @ SV502 @ SV559 ) ) )
= $true )
| ( ( ~ ( in @ SV559 @ ( relation_rng @ SV110 ) ) )
= $true )
| ( ( in @ SV563 @ ( relation_dom @ SV110 ) )
= $true )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3342]) ).
thf(3356,plain,
! [SV502: $i,SV564: $i,SV110: $i,SV560: $i] :
( ( ( ( SV560
!= ( apply @ SV110 @ SV564 ) ) )
= $true )
| ( ( ~ ( in @ SV564 @ ( relation_dom @ SV110 ) ) )
= $true )
| ( ( SV564
= ( apply @ SV502 @ SV560 ) )
= $true )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3343]) ).
thf(3357,plain,
! [SV502: $i,SV565: $i,SV110: $i,SV561: $i] :
( ( ( ( SV561
!= ( apply @ SV110 @ SV565 ) ) )
= $true )
| ( ( ~ ( in @ SV565 @ ( relation_dom @ SV110 ) ) )
= $true )
| ( ( in @ SV561 @ ( relation_rng @ SV110 ) )
= $true )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3344]) ).
thf(3358,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( relation_dom @ SV465 )
= ( relation_rng @ SV110 ) )
= $false )
| ( ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
= $true )
| ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3345]) ).
thf(3359,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( relation_dom @ SV465 )
= ( relation_rng @ SV110 ) )
= $false )
| ( ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
= $true )
| ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3346]) ).
thf(3360,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( relation_dom @ SV465 )
= ( relation_rng @ SV110 ) )
= $false )
| ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
= $true )
| ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
= $false )
| ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
= $false )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3347]) ).
thf(3361,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( relation_dom @ SV465 )
= ( relation_rng @ SV110 ) )
= $false )
| ( ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
= $true )
| ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3348]) ).
thf(3362,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( relation_dom @ SV465 )
= ( relation_rng @ SV110 ) )
= $false )
| ( ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
= $true )
| ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
= $true )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3349]) ).
thf(3363,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( relation_dom @ SV465 )
= ( relation_rng @ SV110 ) )
= $false )
| ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
= $true )
| ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
= $false )
| ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
= $false )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3350]) ).
thf(3364,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( relation_dom @ SV465 )
= ( relation_rng @ SV110 ) )
= $false )
| ( ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
= $true )
| ( ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
= $false )
| ( ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
= $false )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3351]) ).
thf(3365,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( relation_dom @ SV465 )
= ( relation_rng @ SV110 ) )
= $false )
| ( ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
= $true )
| ( ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
= $false )
| ( ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
= $false )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3352]) ).
thf(3366,plain,
! [SV110: $i,SV465: $i] :
( ( ( ( relation_dom @ SV465 )
= ( relation_rng @ SV110 ) )
= $false )
| ( ( in @ ( sK71_SY424 @ SV465 @ SV110 ) @ ( relation_dom @ SV110 ) )
= $false )
| ( ( ( sK70_C @ SV465 @ SV110 )
= ( apply @ SV110 @ ( sK71_SY424 @ SV465 @ SV110 ) ) )
= $false )
| ( ( ( sK71_SY424 @ SV465 @ SV110 )
= ( apply @ SV465 @ ( sK70_C @ SV465 @ SV110 ) ) )
= $false )
| ( ( in @ ( sK70_C @ SV465 @ SV110 ) @ ( relation_rng @ SV110 ) )
= $false )
| ( ( SV465
= ( function_inverse @ SV110 ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3353]) ).
thf(3367,plain,
! [SV110: $i,SV558: $i,SV502: $i,SV562: $i] :
( ( ( SV562
= ( apply @ SV502 @ SV558 ) )
= $false )
| ( ( ~ ( in @ SV558 @ ( relation_rng @ SV110 ) ) )
= $true )
| ( ( SV558
= ( apply @ SV110 @ SV562 ) )
= $true )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3354]) ).
thf(3368,plain,
! [SV110: $i,SV559: $i,SV502: $i,SV563: $i] :
( ( ( SV563
= ( apply @ SV502 @ SV559 ) )
= $false )
| ( ( ~ ( in @ SV559 @ ( relation_rng @ SV110 ) ) )
= $true )
| ( ( in @ SV563 @ ( relation_dom @ SV110 ) )
= $true )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3355]) ).
thf(3369,plain,
! [SV502: $i,SV564: $i,SV110: $i,SV560: $i] :
( ( ( SV560
= ( apply @ SV110 @ SV564 ) )
= $false )
| ( ( ~ ( in @ SV564 @ ( relation_dom @ SV110 ) ) )
= $true )
| ( ( SV564
= ( apply @ SV502 @ SV560 ) )
= $true )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3356]) ).
thf(3370,plain,
! [SV502: $i,SV565: $i,SV110: $i,SV561: $i] :
( ( ( SV561
= ( apply @ SV110 @ SV565 ) )
= $false )
| ( ( ~ ( in @ SV565 @ ( relation_dom @ SV110 ) ) )
= $true )
| ( ( in @ SV561 @ ( relation_rng @ SV110 ) )
= $true )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3357]) ).
thf(3371,plain,
! [SV502: $i,SV562: $i,SV110: $i,SV558: $i] :
( ( ( in @ SV558 @ ( relation_rng @ SV110 ) )
= $false )
| ( ( SV562
= ( apply @ SV502 @ SV558 ) )
= $false )
| ( ( SV558
= ( apply @ SV110 @ SV562 ) )
= $true )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3367]) ).
thf(3372,plain,
! [SV502: $i,SV563: $i,SV110: $i,SV559: $i] :
( ( ( in @ SV559 @ ( relation_rng @ SV110 ) )
= $false )
| ( ( SV563
= ( apply @ SV502 @ SV559 ) )
= $false )
| ( ( in @ SV563 @ ( relation_dom @ SV110 ) )
= $true )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3368]) ).
thf(3373,plain,
! [SV502: $i,SV560: $i,SV110: $i,SV564: $i] :
( ( ( in @ SV564 @ ( relation_dom @ SV110 ) )
= $false )
| ( ( SV560
= ( apply @ SV110 @ SV564 ) )
= $false )
| ( ( SV564
= ( apply @ SV502 @ SV560 ) )
= $true )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3369]) ).
thf(3374,plain,
! [SV502: $i,SV561: $i,SV110: $i,SV565: $i] :
( ( ( in @ SV565 @ ( relation_dom @ SV110 ) )
= $false )
| ( ( SV561
= ( apply @ SV110 @ SV565 ) )
= $false )
| ( ( in @ SV561 @ ( relation_rng @ SV110 ) )
= $true )
| ( ( SV502
= ( function_inverse @ SV110 ) )
= $false )
| ( ( function @ SV502 )
= $false )
| ( ( relation @ SV502 )
= $false )
| ( ( one_to_one @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3370]) ).
thf(3375,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[699,3374,3373,3372,3371,3366,3365,3364,3363,3362,3361,3360,3359,3358,3279,3278,3277,3259,3258,3257,3256,3255,3246,3243,3242,3241,3240,3239,3233,3232,3224,3223,3219,3218,3217,3204,3203,3202,3201,3200,3199,3198,3197,3196,3192,3189,3188,3187,3186,3180,3172,3171,3167,3166,3162,3158,3154,3150,3149,3147,3142,3139,3136,3135,3133,3129,3128,3127,3126,3125,3124,3099,3098,3090,3087,3082,3081,3080,3079,3071,3067,3064,3061,3060,3059,3058,3052,3051,3046,3043,3034,3033,3030,3029,3025,3024,3022,3019,3018,3010,3009,2997,2990,2986,2985,2980,2977,2967,2961,2960,2959,2957,2944,2933,2931,2928,2919,2918,2915,2908,2901,2898,2885,2884,2869,2868,2867,2860,2854,2819,2818,2805,2804,2793,2792,2768,2767,2766,2765,2762,2759,2758,2757,2755,2735,2721,2720,2705,2702,2701,2696,2695,2677,2665,2658,2657,2649,2640,2636,2635,2627,2604,2600,2597,2592,2591,2580,2579,2539,2538,2537,2524,2523,2519,2518,2517,2511,2471,2470,2436,2435,2430,2429,2428,2427,2414,2413,2412,2408,2405,2404,2401,2392,2385,2354,2338,2337,2328,2327,2293,2292,2287,2286,2283,2256,2243,2238,2237,2206,2203,2202,2199,2185,2184,2167,2166,2165,2160,2144,2120,2118,2117,2114,2113,2112,2055,2052,2051,2050,2049,2046,2045,2016,2015,1962,1943,1942,1922,1921,1910,1909,1908,1907,1904,1903,1900,1897,1880,1879,1865,1864,1858,1857,1844,1843,1841,1840,1825,1824,1816,1815,1756,1746,1737,1736,1735,1731,1730,1728,1692,1581,1580,1579,1578,1575,1574,1573,1566,1565,1554,1508,1494,1493,1490,1489,1423,1421,1420,1418,1417,1415,1412,1411,1410,1409,1407,1400,1398,1397,1392,1391,1388,1387,1386,1380,1378,1377,1375,1374,1373,1372,1358,1333,1332,1330,1329,1328,1327,1321,1314,1298,1260,1259,1254,1253,1232,1227,1225,1214,1200,1192,1190,1189,1188,1180,1176,1037,1035,1034,1033,1028,1023,1020,1018,1017,1008,1002,891,887,886,884,882,881,880,879,878,850,829,724,723,722,708]) ).
thf(3376,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)],[554]) ).
thf(3377,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[553]) ).
thf(3378,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[552]) ).
thf(3379,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[551]) ).
thf(3380,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)],[550]) ).
thf(3381,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)],[549]) ).
thf(3382,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[548]) ).
thf(3383,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)],[547]) ).
thf(3384,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[546]) ).
thf(3385,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)],[545]) ).
thf(3386,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[544]) ).
thf(3387,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)],[543]) ).
thf(3388,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)],[542]) ).
thf(3389,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[541]) ).
thf(3390,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)],[540]) ).
thf(3391,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)],[539]) ).
thf(3392,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[538]) ).
thf(3393,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[537]) ).
thf(3394,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)],[536]) ).
thf(3395,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)],[535]) ).
thf(3396,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ! [B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ( ( ( sK71_SY424 @ B @ A )
= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ( ( sK70_C @ B @ A )
= ( apply @ A @ ( sK71_SY424 @ B @ A ) ) ) )
& ( ( ( sK71_SY424 @ B @ A )
= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ( in @ ( sK71_SY424 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( ( sK71_SY424 @ B @ A )
= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ( ( sK71_SY424 @ B @ A )
!= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ~ ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) ) )
& ( ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) )
| ( ( sK70_C @ B @ A )
= ( apply @ A @ ( sK71_SY424 @ B @ A ) ) ) )
& ( ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) )
| ( in @ ( sK71_SY424 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) )
| ( ( sK71_SY424 @ B @ A )
!= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ~ ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) ) )
& ( ( ( sK70_C @ B @ A )
!= ( apply @ A @ ( sK71_SY424 @ B @ A ) ) )
| ~ ( in @ ( sK71_SY424 @ B @ A ) @ ( relation_dom @ A ) )
| ( ( sK70_C @ B @ A )
= ( apply @ A @ ( sK71_SY424 @ B @ A ) ) ) )
& ( ( ( sK70_C @ B @ A )
!= ( apply @ A @ ( sK71_SY424 @ B @ A ) ) )
| ~ ( in @ ( sK71_SY424 @ B @ A ) @ ( relation_dom @ A ) )
| ( in @ ( sK71_SY424 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( ( sK70_C @ B @ A )
!= ( apply @ A @ ( sK71_SY424 @ B @ A ) ) )
| ~ ( in @ ( sK71_SY424 @ B @ A ) @ ( relation_dom @ A ) )
| ( ( sK71_SY424 @ B @ A )
!= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ~ ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) ) ) )
| ( ( relation_dom @ B )
!= ( relation_rng @ A ) )
| ( B
= ( function_inverse @ A ) ) )
& ! [B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( B
!= ( function_inverse @ A ) )
| ( ! [C: $i,D: $i] :
( ( D
!= ( apply @ B @ C ) )
| ~ ( in @ C @ ( relation_rng @ A ) )
| ( C
= ( apply @ A @ D ) ) )
& ! [C: $i,D: $i] :
( ( D
!= ( apply @ B @ C ) )
| ~ ( in @ C @ ( relation_rng @ A ) )
| ( in @ D @ ( relation_dom @ A ) ) )
& ! [C: $i,D: $i] :
( ( C
!= ( apply @ A @ D ) )
| ~ ( in @ D @ ( relation_dom @ A ) )
| ( D
= ( apply @ B @ C ) ) )
& ! [C: $i] :
( ! [D: $i] :
( ( C
!= ( apply @ A @ D ) )
| ~ ( in @ D @ ( relation_dom @ A ) ) )
| ( in @ C @ ( relation_rng @ A ) ) ) ) )
& ! [B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( B
!= ( function_inverse @ A ) )
| ( ( relation_dom @ B )
= ( relation_rng @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[534]) ).
thf(3397,plain,
( ( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(3398,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)],[533]) ).
thf(3399,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)],[532]) ).
thf(3400,plain,
( ( ! [A: $i] :
( ( relation_dom @ ( identity_relation @ A ) )
= A )
& ! [A: $i] :
( ( relation_rng @ ( identity_relation @ A ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[531]) ).
thf(3401,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)],[530]) ).
thf(3402,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[529]) ).
thf(3403,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)],[528]) ).
thf(3404,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[527]) ).
thf(3405,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[526]) ).
thf(3406,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[525]) ).
thf(3407,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)],[524]) ).
thf(3408,plain,
( ( ! [A: $i] :
( ( ! [SY422: $i,SY423: $i] :
( ( sK69_B @ A )
!= ( ordered_pair @ SY422 @ SY423 ) )
& ( in @ ( sK69_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK67_C @ B @ A ) @ ( sK68_SY421 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[523]) ).
thf(3409,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK65_C @ B @ A ) @ ( sK66_SY420 @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ B @ A ) @ ( sK66_SY420 @ B @ A ) ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK65_C @ B @ A ) @ ( sK66_SY420 @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK65_C @ B @ A ) @ ( sK66_SY420 @ 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)],[522]) ).
thf(3410,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY418: $i] :
~ ( in @ ( ordered_pair @ ( sK63_C @ B @ A ) @ SY418 ) @ A )
| ~ ( in @ ( sK63_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK63_C @ B @ A ) @ ( sK64_SY419 @ B @ A ) ) @ A )
| ( in @ ( sK63_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 @ ( sK62_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[521]) ).
thf(3411,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY416: $i] :
~ ( in @ ( ordered_pair @ SY416 @ ( sK60_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK60_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK61_SY417 @ B @ A ) @ ( sK60_C @ B @ A ) ) @ A )
| ( in @ ( sK60_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 @ ( sK59_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[520]) ).
thf(3412,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[519]) ).
thf(3413,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ( function_inverse @ A )
= ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[518]) ).
thf(3414,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)],[517]) ).
thf(3415,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[516]) ).
thf(3416,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[515]) ).
thf(3417,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(3418,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[514]) ).
thf(3419,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[513]) ).
thf(3420,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)],[512]) ).
thf(3421,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_inverse @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[511]) ).
thf(3422,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)],[510]) ).
thf(3423,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[509]) ).
thf(3424,plain,
( ( ! [A: $i] : ( function @ ( identity_relation @ A ) )
& ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[508]) ).
thf(3425,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[507]) ).
thf(3426,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)],[506]) ).
thf(3427,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[349]) ).
thf(3428,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[505]) ).
thf(3429,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[504]) ).
thf(3430,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[503]) ).
thf(3431,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[502]) ).
thf(3432,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)],[501]) ).
thf(3433,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[500]) ).
thf(3434,plain,
( ( ( function @ sK58_A )
& ( relation @ sK58_A ) )
= $true ),
inference(copy,[status(thm)],[499]) ).
thf(3435,plain,
( ( ( empty @ sK57_A )
& ( relation @ sK57_A ) )
= $true ),
inference(copy,[status(thm)],[498]) ).
thf(3436,plain,
( ( ( empty @ sK56_A )
& ( relation @ sK56_A )
& ( function @ sK56_A ) )
= $true ),
inference(copy,[status(thm)],[497]) ).
thf(3437,plain,
( ( ~ ( empty @ sK55_A )
& ( relation @ sK55_A ) )
= $true ),
inference(copy,[status(thm)],[496]) ).
thf(3438,plain,
( ( ( function @ sK54_A )
& ( relation @ sK54_A )
& ( one_to_one @ sK54_A ) )
= $true ),
inference(copy,[status(thm)],[495]) ).
thf(3439,plain,
( ( ( relation @ sK53_A )
& ( relation_empty_yielding @ sK53_A ) )
= $true ),
inference(copy,[status(thm)],[494]) ).
thf(3440,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[493]) ).
thf(3441,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[492]) ).
thf(3442,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)],[491]) ).
thf(3443,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)],[490]) ).
thf(3444,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)],[489]) ).
thf(3445,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[488]) ).
thf(3446,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)],[487]) ).
thf(3447,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)],[486]) ).
thf(3448,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)],[485]) ).
thf(3449,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)],[484]) ).
thf(3450,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[483]) ).
thf(3451,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 @ ( sK52_D @ C @ B @ A ) @ ( relation_dom @ C ) )
& ( in @ ( ordered_pair @ ( sK52_D @ C @ B @ A ) @ A ) @ C )
& ( in @ ( sK52_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[482]) ).
thf(3452,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 @ ( sK51_D @ C @ B @ A ) @ ( relation_rng @ C ) )
& ( in @ ( ordered_pair @ A @ ( sK51_D @ C @ B @ A ) ) @ C )
& ( in @ ( sK51_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[481]) ).
thf(3453,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)],[480]) ).
thf(3454,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[322]) ).
thf(3455,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[479]) ).
thf(3456,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[478]) ).
thf(3457,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)],[477]) ).
thf(3458,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)],[476]) ).
thf(3459,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)],[475]) ).
thf(3460,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[474]) ).
thf(3461,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[473]) ).
thf(3462,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[314]) ).
thf(3463,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)],[472]) ).
thf(3464,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[471]) ).
thf(3465,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)],[470]) ).
thf(3466,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ( in @ ( sK50_C @ B @ A ) @ A )
& ( ( apply @ B @ ( sK50_C @ B @ A ) )
!= ( sK50_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)],[469]) ).
thf(3467,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ A )
| ( ( apply @ ( identity_relation @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[468]) ).
thf(3468,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[308]) ).
thf(3469,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)],[467]) ).
thf(3470,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)],[466]) ).
thf(3471,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)],[465]) ).
thf(3472,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[304]) ).
thf(3473,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)],[464]) ).
thf(3474,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK49_C @ B @ A ) @ A )
& ( in @ ( sK49_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[463]) ).
thf(3475,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[462]) ).
thf(3476,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[300]) ).
thf(3477,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[461]) ).
thf(3478,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[460]) ).
thf(3479,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[297]) ).
thf(3480,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK48_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)],[459]) ).
thf(3481,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK46_B @ A ) @ ( sK47_SY415 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[458]) ).
thf(3482,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[457]) ).
thf(3483,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[456]) ).
thf(3484,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[455]) ).
thf(3485,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)],[454]) ).
thf(3486,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[290]) ).
thf(3487,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)],[453]) ).
thf(3488,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[452]) ).
thf(3489,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[451]) ).
thf(3490,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( relation_dom_restriction @ B @ A )
= ( relation_composition @ ( identity_relation @ A ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[450]) ).
thf(3491,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[449]) ).
thf(3492,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[284]) ).
thf(3493,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[283]) ).
thf(3494,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( ( ( sK44_C @ B @ A )
!= ( sK45_SY414 @ B @ A ) )
| ~ ( in @ ( sK44_C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ B @ A ) @ ( sK45_SY414 @ B @ A ) ) @ B ) )
& ( ( ( sK44_C @ B @ A )
= ( sK45_SY414 @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK44_C @ B @ A ) @ ( sK45_SY414 @ B @ A ) ) @ B ) )
& ( ( in @ ( sK44_C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK44_C @ B @ A ) @ ( sK45_SY414 @ 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)],[448]) ).
thf(3495,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)],[447]) ).
thf(3496,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK42_D @ C @ B @ A ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ C @ B @ A ) @ ( sK43_SY413 @ C @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ C @ B @ A ) @ ( sK43_SY413 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK42_D @ C @ B @ A ) @ B )
| ( in @ ( ordered_pair @ ( sK42_D @ C @ B @ A ) @ ( sK43_SY413 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK42_D @ C @ B @ A ) @ ( sK43_SY413 @ C @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK42_D @ C @ B @ A ) @ ( sK43_SY413 @ 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)],[446]) ).
thf(3497,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK41_SY412 @ C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ C @ B @ A ) @ ( sK41_SY412 @ C @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ C @ B @ A ) @ ( sK41_SY412 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK41_SY412 @ C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK40_D @ C @ B @ A ) @ ( sK41_SY412 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK40_D @ C @ B @ A ) @ ( sK41_SY412 @ C @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK40_D @ C @ B @ A ) @ ( sK41_SY412 @ 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)],[445]) ).
thf(3498,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY410: $i] :
( ~ ( in @ ( ordered_pair @ SY410 @ ( sK38_D @ C @ B @ A ) ) @ A )
| ~ ( in @ SY410 @ B ) )
| ~ ( in @ ( sK38_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK39_SY411 @ C @ B @ A ) @ ( sK38_D @ C @ B @ A ) ) @ A )
& ( in @ ( sK39_SY411 @ C @ B @ A ) @ B ) )
| ( in @ ( sK38_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 @ ( sK37_E @ D @ C @ B @ A ) @ D ) @ A )
& ( in @ ( sK37_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[444]) ).
thf(3499,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY408: $i] :
( ~ ( in @ ( ordered_pair @ ( sK35_D @ C @ B @ A ) @ SY408 ) @ A )
| ~ ( in @ SY408 @ B ) )
| ~ ( in @ ( sK35_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK35_D @ C @ B @ A ) @ ( sK36_SY409 @ C @ B @ A ) ) @ A )
& ( in @ ( sK36_SY409 @ C @ B @ A ) @ B ) )
| ( in @ ( sK35_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 @ ( sK34_E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( sK34_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[443]) ).
thf(3500,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( ( ( ( in @ ( sK33_SY406 @ B @ A ) @ A )
& ~ ( in @ ( sK32_C @ B @ A ) @ ( sK33_SY406 @ B @ A ) ) )
| ~ ( in @ ( sK32_C @ B @ A ) @ B ) )
& ( ! [SY407: $i] :
( ~ ( in @ SY407 @ A )
| ( in @ ( sK32_C @ B @ A ) @ SY407 ) )
| ( in @ ( sK32_C @ B @ A ) @ B ) ) )
| ( B
= ( set_meet @ A ) ) ) )
& ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( ! [C: $i] :
( ( ( in @ ( sK31_D @ C @ B @ A ) @ A )
& ~ ( in @ C @ ( sK31_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)],[442]) ).
thf(3501,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK30_C @ B @ A )
!= A )
| ~ ( in @ ( sK30_C @ B @ A ) @ B ) )
& ( ( ( sK30_C @ B @ A )
= A )
| ( in @ ( sK30_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)],[441]) ).
thf(3502,plain,
( ( ! [A: $i] :
( ( in @ ( sK29_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[440]) ).
thf(3503,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK28_C @ B @ A ) @ B )
| ~ ( subset @ ( sK28_C @ B @ A ) @ A ) )
& ( ( in @ ( sK28_C @ B @ A ) @ B )
| ( subset @ ( sK28_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)],[439]) ).
thf(3504,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)],[438]) ).
thf(3505,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK27_D @ C @ B @ A ) @ C )
| ( ( sK27_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK27_D @ C @ B @ A ) @ C )
| ( ( sK27_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK27_D @ C @ B @ A ) @ C )
| ( ( sK27_D @ C @ B @ A )
= A )
| ( ( sK27_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)],[437]) ).
thf(3506,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK26_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK26_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK26_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK26_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK26_D @ C @ B @ A ) @ C )
| ( in @ ( sK26_D @ C @ B @ A ) @ A )
| ( in @ ( sK26_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)],[436]) ).
thf(3507,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY401: $i,SY402: $i] :
( ~ ( in @ SY401 @ A )
| ~ ( in @ SY402 @ B )
| ( ( sK23_D @ C @ B @ A )
!= ( ordered_pair @ SY401 @ SY402 ) ) )
| ~ ( in @ ( sK23_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK24_SY403 @ C @ B @ A ) @ A )
& ( in @ ( sK25_SY405 @ C @ B @ A ) @ B )
& ( ( sK23_D @ C @ B @ A )
= ( ordered_pair @ ( sK24_SY403 @ C @ B @ A ) @ ( sK25_SY405 @ C @ B @ A ) ) ) )
| ( in @ ( sK23_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 @ ( sK21_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK22_SY400 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK21_E @ D @ C @ B @ A ) @ ( sK22_SY400 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(3508,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( in @ ( ordered_pair @ ( sK19_C @ B @ A ) @ ( sK20_SY399 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK19_C @ B @ A ) @ ( sK20_SY399 @ 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)],[434]) ).
thf(3509,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK18_C @ B @ A ) @ A )
& ~ ( in @ ( sK18_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)],[433]) ).
thf(3510,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK17_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK17_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK17_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK17_D @ C @ B @ A ) @ A )
| ( in @ ( sK17_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK17_D @ C @ B @ A ) @ B )
| ( in @ ( sK17_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)],[432]) ).
thf(3511,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)],[431]) ).
thf(3512,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY397: $i] :
( ~ ( in @ ( sK15_C @ B @ A ) @ SY397 )
| ~ ( in @ SY397 @ A ) )
| ~ ( in @ ( sK15_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK15_C @ B @ A ) @ ( sK16_SY398 @ B @ A ) )
& ( in @ ( sK16_SY398 @ B @ A ) @ A ) )
| ( in @ ( sK15_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 @ ( sK14_D @ C @ B @ A ) )
& ( in @ ( sK14_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[430]) ).
thf(3513,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK13_D @ C @ B @ A ) @ A )
| ( in @ ( sK13_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK13_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK13_D @ C @ B @ A ) @ A )
| ( in @ ( sK13_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK13_D @ C @ B @ A ) @ B )
| ( in @ ( sK13_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)],[429]) ).
thf(3514,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK11_C @ B @ A ) @ ( sK12_SY396 @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ B @ A ) @ ( sK11_C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( sK11_C @ B @ A ) @ ( sK12_SY396 @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK12_SY396 @ B @ A ) @ ( sK11_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)],[428]) ).
thf(3515,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)],[427]) ).
thf(3516,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ! [SY394: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ C @ B @ A ) @ SY394 ) @ A )
| ~ ( in @ ( ordered_pair @ SY394 @ ( sK9_SY391 @ C @ B @ A ) ) @ B ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ C @ B @ A ) @ ( sK9_SY391 @ C @ B @ A ) ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK8_D @ C @ B @ A ) @ ( sK10_SY395 @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK10_SY395 @ C @ B @ A ) @ ( sK9_SY391 @ C @ B @ A ) ) @ B ) )
| ( in @ ( ordered_pair @ ( sK8_D @ C @ B @ A ) @ ( sK9_SY391 @ 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 @ ( sK7_F @ E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK7_F @ E @ D @ C @ B @ A ) @ E ) @ B ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(3517,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)],[425]) ).
thf(3518,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[258]) ).
thf(3519,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[257]) ).
thf(3520,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[256]) ).
thf(3521,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[255]) ).
thf(3522,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[254]) ).
thf(3523,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[424]) ).
thf(3524,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[252]) ).
thf(3525,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(3526,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(3527,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(3528,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(3529,plain,
( ( empty @ sK6_A )
= $true ),
inference(copy,[status(thm)],[419]) ).
thf(3530,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(copy,[status(thm)],[418]) ).
thf(3531,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(3532,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[244]) ).
thf(3533,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(3534,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(3535,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(3536,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)],[414]) ).
thf(3537,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[239]) ).
thf(3538,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(3539,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(3540,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(3541,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(3542,plain,
( ( ! [A: $i] :
( ! [SY384: $i] :
( ~ ( subset @ SY384 @ ( sK2_B @ A ) )
| ( are_equipotent @ SY384 @ ( sK2_B @ A ) )
| ( in @ SY384 @ ( sK2_B @ A ) ) )
& ! [SY385: $i] :
( ( ! [SY390: $i] :
( ~ ( subset @ SY390 @ SY385 )
| ( in @ SY390 @ ( sK3_SY386 @ SY385 @ A ) ) )
& ( in @ ( sK3_SY386 @ SY385 @ A ) @ ( sK2_B @ A ) ) )
| ~ ( in @ SY385 @ ( sK2_B @ A ) ) )
& ! [SY388: $i,SY389: $i] :
( ~ ( in @ SY388 @ ( sK2_B @ A ) )
| ~ ( subset @ SY389 @ SY388 )
| ( in @ SY389 @ ( sK2_B @ A ) ) )
& ( in @ A @ ( sK2_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(3543,plain,
( ( one_to_one @ sK1_A )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(3544,plain,
( ( function @ sK1_A )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(3545,plain,
( ( relation @ sK1_A )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(3546,plain,
( ( ( ( relation_dom @ sK1_A )
!= ( relation_rng @ ( function_inverse @ sK1_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(3547,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK17_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK17_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK17_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK17_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK17_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ( in @ ( sK17_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK17_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)],[3510]) ).
thf(3548,plain,
( ( ~ ( ~ ( empty @ sK57_A )
| ~ ( relation @ sK57_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3435]) ).
thf(3549,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)],[3399]) ).
thf(3550,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SX1 @ SX0 )
= ( apply @ SX1 @ ( sK70_C @ SX1 @ SX0 ) ) )
| ( ( sK70_C @ SX1 @ SX0 )
= ( apply @ SX0 @ ( sK71_SY424 @ SX1 @ SX0 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SX1 @ SX0 )
= ( apply @ SX1 @ ( sK70_C @ SX1 @ SX0 ) ) )
| ( in @ ( sK71_SY424 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SX1 @ SX0 )
= ( apply @ SX1 @ ( sK70_C @ SX1 @ SX0 ) ) )
| ( ( sK71_SY424 @ SX1 @ SX0 )
!= ( apply @ SX1 @ ( sK70_C @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK70_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) )
| ( ( sK70_C @ SX1 @ SX0 )
= ( apply @ SX0 @ ( sK71_SY424 @ SX1 @ SX0 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) )
| ( in @ ( sK71_SY424 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) )
| ( ( sK71_SY424 @ SX1 @ SX0 )
!= ( apply @ SX1 @ ( sK70_C @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK70_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK71_SY424 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK71_SY424 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ( ( sK70_C @ SX1 @ SX0 )
= ( apply @ SX0 @ ( sK71_SY424 @ SX1 @ SX0 ) ) ) )
| ~ ( ( ( sK70_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK71_SY424 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK71_SY424 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ( in @ ( sK71_SY424 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) ) )
| ~ ( ( ( sK70_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK71_SY424 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK71_SY424 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ( ( sK71_SY424 @ SX1 @ SX0 )
!= ( apply @ SX1 @ ( sK70_C @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK70_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) ) ) ) )
| ( ( relation_dom @ SX1 )
!= ( relation_rng @ SX0 ) )
| ( SX1
= ( function_inverse @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( function_inverse @ SX0 ) )
| ~ ( ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX3
!= ( apply @ SX1 @ SX2 ) )
| ~ ( in @ SX2 @ ( relation_rng @ SX0 ) )
| ( SX2
= ( apply @ SX0 @ SX3 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( SX3
!= ( apply @ SX1 @ SX2 ) )
| ~ ( in @ SX2 @ ( relation_rng @ SX0 ) )
| ( in @ SX3 @ ( relation_dom @ SX0 ) ) ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX2
!= ( apply @ SX0 @ SX3 ) )
| ~ ( in @ SX3 @ ( relation_dom @ SX0 ) )
| ( SX3
= ( apply @ SX1 @ SX2 ) ) )
| ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ( SX2
!= ( apply @ SX0 @ SX3 ) )
| ~ ( in @ SX3 @ ( relation_dom @ SX0 ) ) )
| ( in @ SX2 @ ( relation_rng @ SX0 ) ) ) ) ) )
| ~ ! [SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( function_inverse @ SX0 ) )
| ( ( relation_dom @ SX1 )
= ( relation_rng @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3396]) ).
thf(3551,plain,
( ( ~ ( ~ ~ ( ~ ( function @ sK54_A )
| ~ ( relation @ sK54_A ) )
| ~ ( one_to_one @ sK54_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3438]) ).
thf(3552,plain,
( ( ~ ( ~ ~ ( empty @ sK55_A )
| ~ ( relation @ sK55_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3437]) ).
thf(3553,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)],[3504]) ).
thf(3554,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)],[3515]) ).
thf(3555,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)],[3473]) ).
thf(3556,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( relation_dom @ ( identity_relation @ SX0 ) )
= SX0 )
| ~ ! [SX0: $i] :
( ( relation_rng @ ( identity_relation @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3400]) ).
thf(3557,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)],[3470]) ).
thf(3558,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3430]) ).
thf(3559,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)],[3443]) ).
thf(3560,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)],[3485]) ).
thf(3561,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ ( sK41_SY412 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SX2 @ SX1 @ SX0 ) @ ( sK41_SY412 @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SX2 @ SX1 @ SX0 ) @ ( sK41_SY412 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK41_SY412 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK40_D @ SX2 @ SX1 @ SX0 ) @ ( sK41_SY412 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SX2 @ SX1 @ SX0 ) @ ( sK41_SY412 @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK40_D @ SX2 @ SX1 @ SX0 ) @ ( sK41_SY412 @ 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)],[3497]) ).
thf(3562,plain,
( ( ~ ( ~ ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) )
| ~ ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3424]) ).
thf(3563,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)],[3465]) ).
thf(3564,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ ( sK35_D @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ~ ( in @ ( sK35_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SX2 @ SX1 @ SX0 ) @ ( sK36_SY409 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK36_SY409 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( in @ ( sK35_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 @ ( sK34_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK34_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3499]) ).
thf(3565,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ ( sK38_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ~ ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SX2 @ SX1 @ SX0 ) @ ( sK38_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK39_SY411 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( in @ ( sK38_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 @ ( sK37_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ ( sK37_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3498]) ).
thf(3566,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)],[3517]) ).
thf(3567,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)],[3420]) ).
thf(3568,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)],[3407]) ).
thf(3569,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK69_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK69_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK67_C @ SX1 @ SX0 ) @ ( sK68_SY421 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3408]) ).
thf(3570,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)],[3471]) ).
thf(3571,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ ( sK9_SY391 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ ( sK9_SY391 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ ( sK10_SY395 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SX2 @ SX1 @ SX0 ) @ ( sK9_SY391 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ ( sK9_SY391 @ 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 @ ( sK7_F @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX4 ) @ SX1 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3516]) ).
thf(3572,plain,
( ( ~ ( ~ ( relation @ sK53_A )
| ~ ( relation_empty_yielding @ sK53_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3439]) ).
thf(3573,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( in @ ( sK29_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3502]) ).
thf(3574,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3431]) ).
thf(3575,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)],[3391]) ).
thf(3576,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ SX2 @ ( sK60_C @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK60_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK61_SY417 @ SX1 @ SX0 ) @ ( sK60_C @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK60_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 @ ( sK59_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3411]) ).
thf(3577,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK13_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK13_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK13_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK13_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK13_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( in @ ( sK13_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK13_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)],[3513]) ).
thf(3578,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)],[3422]) ).
thf(3579,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)],[3376]) ).
thf(3580,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)],[3511]) ).
thf(3581,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SX1 @ SX0 ) @ ( sK20_SY399 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( in @ ( ordered_pair @ ( sK19_C @ SX1 @ SX0 ) @ ( sK20_SY399 @ 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)],[3508]) ).
thf(3582,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)],[3457]) ).
thf(3583,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 @ ( sK51_D @ SX2 @ SX1 @ SX0 ) @ ( relation_rng @ SX2 ) )
| ~ ( in @ ( ordered_pair @ SX0 @ ( sK51_D @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( in @ ( sK51_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3452]) ).
thf(3584,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK49_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK49_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)],[3474]) ).
thf(3585,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3421]) ).
thf(3586,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)],[3401]) ).
thf(3587,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK26_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ~ ( in @ ( sK26_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK26_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ( ( in @ ( sK26_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( in @ ( sK26_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK26_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)],[3506]) ).
thf(3588,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY406 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ ( sK33_SY406 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK31_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)],[3500]) ).
thf(3589,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i,SX4: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX4 @ SX1 )
| ( ( sK23_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ SX3 @ SX4 ) ) )
| ~ ( in @ ( sK23_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY403 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK25_SY405 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( sK23_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ ( sK24_SY403 @ SX2 @ SX1 @ SX0 ) @ ( sK25_SY405 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( in @ ( sK23_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 @ ( sK21_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK22_SY400 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( SX3
!= ( ordered_pair @ ( sK21_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK22_SY400 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3507]) ).
thf(3590,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)],[3487]) ).
thf(3591,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SX1 @ SX0 ) @ ( sK12_SY396 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SX1 @ SX0 ) @ ( sK11_C @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_C @ SX1 @ SX0 ) @ ( sK12_SY396 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK12_SY396 @ SX1 @ SX0 ) @ ( sK11_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)],[3514]) ).
thf(3592,plain,
( ( ~ ( ~ ( function @ sK58_A )
| ~ ( relation @ sK58_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3434]) ).
thf(3593,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)],[3469]) ).
thf(3594,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)],[3426]) ).
thf(3595,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)],[3388]) ).
thf(3596,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)],[3447]) ).
thf(3597,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK27_D @ SX2 @ SX1 @ SX0 )
!= SX0 ) )
| ~ ( ~ ( in @ ( sK27_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK27_D @ SX2 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ( ( in @ ( sK27_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK27_D @ SX2 @ SX1 @ SX0 )
= SX0 )
| ( ( sK27_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)],[3505]) ).
thf(3598,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)],[3446]) ).
thf(3599,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK48_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)],[3480]) ).
thf(3600,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)],[3414]) ).
thf(3601,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)],[3536]) ).
thf(3602,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)],[3448]) ).
thf(3603,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ ( sK16_SY398 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK16_SY398 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK15_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 @ ( sK14_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK14_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3512]) ).
thf(3604,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ ( sK63_C @ SX1 @ SX0 ) @ SX2 ) @ SX0 )
| ~ ( in @ ( sK63_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_C @ SX1 @ SX0 ) @ ( sK64_SY419 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK63_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 @ ( sK62_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3410]) ).
thf(3605,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)],[3463]) ).
thf(3606,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK44_C @ SX1 @ SX0 )
!= ( sK45_SY414 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY414 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK44_C @ SX1 @ SX0 )
= ( sK45_SY414 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY414 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY414 @ 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)],[3494]) ).
thf(3607,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ ( sK42_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SX2 @ SX1 @ SX0 ) @ ( sK43_SY413 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SX2 @ SX1 @ SX0 ) @ ( sK43_SY413 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK42_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK42_D @ SX2 @ SX1 @ SX0 ) @ ( sK43_SY413 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SX2 @ SX1 @ SX0 ) @ ( sK43_SY413 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK42_D @ SX2 @ SX1 @ SX0 ) @ ( sK43_SY413 @ 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)],[3496]) ).
thf(3608,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK30_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK30_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK30_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK30_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)],[3501]) ).
thf(3609,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3427]) ).
thf(3610,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 @ ( sK52_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX2 ) )
| ~ ( in @ ( ordered_pair @ ( sK52_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) @ SX2 ) )
| ~ ( in @ ( sK52_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3451]) ).
thf(3611,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3518]) ).
thf(3612,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)],[3390]) ).
thf(3613,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)],[3432]) ).
thf(3614,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY420 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY420 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY420 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY420 @ 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)],[3409]) ).
thf(3615,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX1 @ ( sK2_B @ SX0 ) )
| ( are_equipotent @ SX1 @ ( sK2_B @ SX0 ) )
| ( in @ SX1 @ ( sK2_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK3_SY386 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK3_SY386 @ SX1 @ SX0 ) @ ( sK2_B @ SX0 ) ) )
| ~ ( in @ SX1 @ ( sK2_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK2_B @ SX0 ) )
| ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK2_B @ SX0 ) ) )
| ~ ( in @ SX0 @ ( sK2_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3542]) ).
thf(3616,plain,
( ( ~ ( ( ( relation_dom @ empty_set )
!= empty_set )
| ( ( relation_rng @ empty_set )
!= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3397]) ).
thf(3617,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)],[3495]) ).
thf(3618,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK28_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK28_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)],[3503]) ).
thf(3619,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)],[3444]) ).
thf(3620,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)],[3398]) ).
thf(3621,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ sK56_A )
| ~ ( relation @ sK56_A ) )
| ~ ( function @ sK56_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3436]) ).
thf(3622,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK50_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK50_C @ SX1 @ SX0 ) )
!= ( sK50_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)],[3466]) ).
thf(3623,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)],[3442]) ).
thf(3624,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK18_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK18_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)],[3509]) ).
thf(3625,plain,
! [SV566: $i] :
( ( ! [SY1060: $i] :
( ~ ( relation @ SY1060 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV566 @ SY1060 ) ) @ SV566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3377]) ).
thf(3626,plain,
! [SV567: $i] :
( ( ! [SY1061: $i] :
( ~ ( relation @ SY1061 )
| ( subset @ ( relation_rng_restriction @ SV567 @ SY1061 ) @ SY1061 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3378]) ).
thf(3627,plain,
! [SV568: $i] :
( ( ! [SY1062: $i] :
( ~ ( relation @ SY1062 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV568 @ SY1062 ) ) @ ( relation_rng @ SY1062 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3379]) ).
thf(3628,plain,
! [SV569: $i] :
( ( ! [SY1063: $i] :
( ~ ( relation @ SY1063 )
| ( ( relation_rng @ ( relation_rng_restriction @ SV569 @ SY1063 ) )
= ( set_intersection2 @ ( relation_rng @ SY1063 ) @ SV569 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3380]) ).
thf(3629,plain,
! [SV570: $i] :
( ( ! [SY1064: $i,SY1065: $i] :
( ~ ( relation @ SY1065 )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV570 @ SY1065 ) @ SY1064 )
= ( relation_rng_restriction @ SV570 @ ( relation_dom_restriction @ SY1065 @ SY1064 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3381]) ).
thf(3630,plain,
! [SV571: $i] :
( ( ! [SY1066: $i] :
( ~ ( relation @ SY1066 )
| ( subset @ ( relation_image @ SY1066 @ SV571 ) @ ( relation_rng @ SY1066 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3382]) ).
thf(3631,plain,
! [SV572: $i] :
( ( ! [SY1067: $i] :
( ~ ( relation @ SY1067 )
| ( ( relation_image @ SY1067 @ SV572 )
= ( relation_image @ SY1067 @ ( set_intersection2 @ ( relation_dom @ SY1067 ) @ SV572 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3383]) ).
thf(3632,plain,
! [SV573: $i] :
( ( ~ ( relation @ SV573 )
| ( ( relation_image @ SV573 @ ( relation_dom @ SV573 ) )
= ( relation_rng @ SV573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3384]) ).
thf(3633,plain,
! [SV574: $i] :
( ( ~ ( relation @ SV574 )
| ! [SY1068: $i] :
( ~ ( relation @ SY1068 )
| ( ( relation_rng @ ( relation_composition @ SV574 @ SY1068 ) )
= ( relation_image @ SY1068 @ ( relation_rng @ SV574 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3385]) ).
thf(3634,plain,
! [SV575: $i] :
( ( ! [SY1069: $i] :
( ~ ( relation @ SY1069 )
| ( subset @ ( relation_inverse_image @ SY1069 @ SV575 ) @ ( relation_dom @ SY1069 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3386]) ).
thf(3635,plain,
! [SV576: $i] :
( ( ! [SY1070: $i,SY1071: $i] :
( ~ ( relation @ SY1071 )
| ~ ( subset @ SV576 @ SY1070 )
| ( subset @ ( relation_inverse_image @ SY1071 @ SV576 ) @ ( relation_inverse_image @ SY1071 @ SY1070 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3387]) ).
thf(3636,plain,
! [SV577: $i] :
( ( ~ ( relation @ SV577 )
| ( subset @ SV577 @ ( cartesian_product2 @ ( relation_dom @ SV577 ) @ ( relation_rng @ SV577 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3389]) ).
thf(3637,plain,
! [SV578: $i] :
( ( ~ ( relation @ SV578 )
| ! [SY1072: $i] :
( ~ ( relation @ SY1072 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV578 @ SY1072 ) ) @ ( relation_dom @ SV578 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3392]) ).
thf(3638,plain,
! [SV579: $i] :
( ( ~ ( relation @ SV579 )
| ! [SY1073: $i] :
( ~ ( relation @ SY1073 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV579 @ SY1073 ) ) @ ( relation_rng @ SY1073 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3393]) ).
thf(3639,plain,
! [SV580: $i] :
( ( ~ ( relation @ SV580 )
| ! [SY1074: $i] :
( ~ ( relation @ SY1074 )
| ~ ( subset @ ( relation_rng @ SV580 ) @ ( relation_dom @ SY1074 ) )
| ( ( relation_dom @ ( relation_composition @ SV580 @ SY1074 ) )
= ( relation_dom @ SV580 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3394]) ).
thf(3640,plain,
! [SV581: $i] :
( ( ~ ( relation @ SV581 )
| ! [SY1075: $i] :
( ~ ( relation @ SY1075 )
| ~ ( subset @ ( relation_dom @ SV581 ) @ ( relation_rng @ SY1075 ) )
| ( ( relation_rng @ ( relation_composition @ SY1075 @ SV581 ) )
= ( relation_rng @ SV581 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3395]) ).
thf(3641,plain,
! [SV582: $i] :
( ( ! [SY1076: $i] :
( ~ ( relation @ SY1076 )
| ( subset @ ( relation_dom_restriction @ SY1076 @ SV582 ) @ SY1076 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3402]) ).
thf(3642,plain,
! [SV583: $i] :
( ( ! [SY1077: $i] :
( ~ ( relation @ SY1077 )
| ( ( relation_dom @ ( relation_dom_restriction @ SY1077 @ SV583 ) )
= ( set_intersection2 @ ( relation_dom @ SY1077 ) @ SV583 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3403]) ).
thf(3643,plain,
! [SV584: $i] :
( ( ! [SY1078: $i] :
( ~ ( relation @ SY1078 )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ SY1078 @ SV584 ) ) @ ( relation_rng @ SY1078 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3404]) ).
thf(3644,plain,
! [SV585: $i] :
( ( ~ ( empty @ SV585 )
| ( function @ SV585 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3405]) ).
thf(3645,plain,
! [SV586: $i] :
( ( ~ ( empty @ SV586 )
| ( relation @ SV586 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3406]) ).
thf(3646,plain,
! [SV587: $i] :
( ( ~ ( relation @ SV587 )
| ( ( relation_field @ SV587 )
= ( set_union2 @ ( relation_dom @ SV587 ) @ ( relation_rng @ SV587 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3412]) ).
thf(3647,plain,
! [SV588: $i] :
( ( ~ ( function @ SV588 )
| ~ ( relation @ SV588 )
| ~ ( one_to_one @ SV588 )
| ( ( function_inverse @ SV588 )
= ( relation_inverse @ SV588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3413]) ).
thf(3648,plain,
! [SV589: $i] :
( ( ~ ( relation @ SV589 )
| ( relation @ ( relation_inverse @ SV589 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3415]) ).
thf(3649,plain,
! [SV590: $i] :
( ( ! [SY1079: $i] :
( ~ ( relation @ SV590 )
| ~ ( relation @ SY1079 )
| ( relation @ ( relation_composition @ SV590 @ SY1079 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3416]) ).
thf(3650,plain,
! [SV591: $i] :
( ( relation @ ( identity_relation @ SV591 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3417]) ).
thf(3651,plain,
! [SV592: $i] :
( ( ~ ( relation @ SV592 )
| ! [SY1080: $i] : ( relation @ ( relation_dom_restriction @ SV592 @ SY1080 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3418]) ).
thf(3652,plain,
! [SV593: $i] :
( ( ! [SY1081: $i] :
( ~ ( relation @ SY1081 )
| ( relation @ ( relation_rng_restriction @ SV593 @ SY1081 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3419]) ).
thf(3653,plain,
! [SV594: $i] :
( ( ! [SY1082: $i] :
( ~ ( relation @ SV594 )
| ~ ( relation @ SY1082 )
| ( relation @ ( set_intersection2 @ SV594 @ SY1082 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3423]) ).
thf(3654,plain,
! [SV595: $i] :
( ( ! [SY1083: $i] :
( ~ ( relation @ SV595 )
| ~ ( relation @ SY1083 )
| ( relation @ ( set_union2 @ SV595 @ SY1083 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3425]) ).
thf(3655,plain,
! [SV596: $i] :
( ( ( empty @ SV596 )
| ~ ( relation @ SV596 )
| ~ ( empty @ ( relation_dom @ SV596 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3428]) ).
thf(3656,plain,
! [SV597: $i] :
( ( ( empty @ SV597 )
| ~ ( relation @ SV597 )
| ~ ( empty @ ( relation_rng @ SV597 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3429]) ).
thf(3657,plain,
! [SV598: $i] :
( ( ~ ( relation @ SV598 )
| ( ( relation_inverse @ ( relation_inverse @ SV598 ) )
= SV598 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3433]) ).
thf(3658,plain,
! [SV599: $i] :
( ( ( ( singleton @ SV599 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3440]) ).
thf(3659,plain,
! [SV600: $i] :
( ( ! [SY1084: $i] :
( ~ ( in @ SV600 @ SY1084 )
| ( ( set_union2 @ ( singleton @ SV600 ) @ SY1084 )
= SY1084 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3441]) ).
thf(3660,plain,
! [SV601: $i] :
( ( ! [SY1085: $i] :
( ~ ( in @ SV601 @ SY1085 )
| ( subset @ SV601 @ ( union @ SY1085 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3445]) ).
thf(3661,plain,
! [SV602: $i] :
( ( ! [SY1086: $i,SY1087: $i,SY1088: $i] :
( ~ ( subset @ SV602 @ SY1086 )
| ~ ( subset @ SY1087 @ SY1088 )
| ( subset @ ( cartesian_product2 @ SV602 @ SY1087 ) @ ( cartesian_product2 @ SY1086 @ SY1088 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3449]) ).
thf(3662,plain,
! [SV603: $i] :
( ( ! [SY1089: $i] :
( ~ ( subset @ SV603 @ SY1089 )
| ( ( set_union2 @ SV603 @ SY1089 )
= SY1089 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3450]) ).
thf(3663,plain,
! [SV604: $i] :
( ( ! [SY1090: $i] :
( ~ ( relation @ SY1090 )
| ( SV604 = empty_set )
| ~ ( subset @ SV604 @ ( relation_rng @ SY1090 ) )
| ( ( relation_inverse_image @ SY1090 @ SV604 )
!= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3453]) ).
thf(3664,plain,
! [SV605: $i] :
( ( ! [SY1091: $i] : ( subset @ ( set_intersection2 @ SV605 @ SY1091 ) @ SV605 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3454]) ).
thf(3665,plain,
! [SV606: $i] :
( ( ! [SY1092: $i,SY1093: $i] :
( ~ ( subset @ SV606 @ SY1092 )
| ~ ( subset @ SV606 @ SY1093 )
| ( subset @ SV606 @ ( set_intersection2 @ SY1092 @ SY1093 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3455]) ).
thf(3666,plain,
! [SV607: $i] :
( ( ! [SY1094: $i,SY1095: $i] :
( ~ ( subset @ SV607 @ SY1094 )
| ~ ( subset @ SY1094 @ SY1095 )
| ( subset @ SV607 @ SY1095 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3456]) ).
thf(3667,plain,
! [SV608: $i] :
( ( ! [SY1096: $i] :
( ~ ( function @ SY1096 )
| ~ ( relation @ SY1096 )
| ! [SY1097: $i] :
( ~ ( function @ SY1097 )
| ~ ( relation @ SY1097 )
| ~ ( in @ SV608 @ ( relation_dom @ ( relation_composition @ SY1097 @ SY1096 ) ) )
| ( ( apply @ ( relation_composition @ SY1097 @ SY1096 ) @ SV608 )
= ( apply @ SY1096 @ ( apply @ SY1097 @ SV608 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3458]) ).
thf(3668,plain,
! [SV609: $i] :
( ( ! [SY1098: $i] :
( ~ ( function @ SY1098 )
| ~ ( relation @ SY1098 )
| ! [SY1099: $i] :
( ~ ( function @ SY1099 )
| ~ ( relation @ SY1099 )
| ~ ( in @ SV609 @ ( relation_dom @ SY1098 ) )
| ( ( apply @ ( relation_composition @ SY1098 @ SY1099 ) @ SV609 )
= ( apply @ SY1099 @ ( apply @ SY1098 @ SV609 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3459]) ).
thf(3669,plain,
! [SV610: $i] :
( ( ! [SY1100: $i] :
( ~ ( subset @ SV610 @ SY1100 )
| ! [SY1101: $i] : ( subset @ ( set_intersection2 @ SV610 @ SY1101 ) @ ( set_intersection2 @ SY1100 @ SY1101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3460]) ).
thf(3670,plain,
! [SV611: $i] :
( ( ! [SY1102: $i] :
( ~ ( subset @ SV611 @ SY1102 )
| ( ( set_intersection2 @ SV611 @ SY1102 )
= SV611 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3461]) ).
thf(3671,plain,
! [SV612: $i] :
( ( subset @ empty_set @ SV612 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3462]) ).
thf(3672,plain,
! [SV613: $i] :
( ( ! [SY1103: $i] :
( ~ ( subset @ SV613 @ SY1103 )
| ! [SY1104: $i] : ( subset @ ( set_difference @ SV613 @ SY1104 ) @ ( set_difference @ SY1103 @ SY1104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3464]) ).
thf(3673,plain,
! [SV614: $i] :
( ( ! [SY1105: $i] :
( ~ ( in @ SY1105 @ SV614 )
| ( ( apply @ ( identity_relation @ SV614 ) @ SY1105 )
= SY1105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3467]) ).
thf(3674,plain,
! [SV615: $i] :
( ( ! [SY1106: $i] : ( subset @ ( set_difference @ SV615 @ SY1106 ) @ SV615 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3468]) ).
thf(3675,plain,
! [SV616: $i] :
( ( ! [SY1107: $i] :
( ( set_union2 @ SV616 @ ( set_difference @ SY1107 @ SV616 ) )
= ( set_union2 @ SV616 @ SY1107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3472]) ).
thf(3676,plain,
! [SV617: $i] :
( ( ~ ( subset @ SV617 @ empty_set )
| ( SV617 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3475]) ).
thf(3677,plain,
! [SV618: $i] :
( ( ! [SY1108: $i] :
( ( set_difference @ ( set_union2 @ SV618 @ SY1108 ) @ SY1108 )
= ( set_difference @ SV618 @ SY1108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3476]) ).
thf(3678,plain,
! [SV619: $i] :
( ( ! [SY1109: $i] :
( ~ ( subset @ SV619 @ SY1109 )
| ( SY1109
= ( set_union2 @ SV619 @ ( set_difference @ SY1109 @ SV619 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3477]) ).
thf(3679,plain,
! [SV620: $i] :
( ( ! [SY1110: $i] :
( ~ ( in @ SV620 @ SY1110 )
| ( ( set_union2 @ ( singleton @ SV620 ) @ SY1110 )
= SY1110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3478]) ).
thf(3680,plain,
! [SV621: $i] :
( ( ! [SY1111: $i] :
( ( set_difference @ SV621 @ ( set_difference @ SV621 @ SY1111 ) )
= ( set_intersection2 @ SV621 @ SY1111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3479]) ).
thf(3681,plain,
! [SV622: $i] :
( ( ~ ( relation @ SV622 )
| ( in @ ( ordered_pair @ ( sK46_B @ SV622 ) @ ( sK47_SY415 @ SV622 ) ) @ SV622 )
| ( SV622 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3481]) ).
thf(3682,plain,
! [SV623: $i] :
( ( ! [SY1112: $i] :
( ~ ( proper_subset @ SY1112 @ SV623 )
| ~ ( subset @ SV623 @ SY1112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3482]) ).
thf(3683,plain,
! [SV624: $i] :
( ( ! [SY1113: $i,SY1114: $i] :
( ~ ( disjoint @ SY1113 @ SY1114 )
| ~ ( subset @ SV624 @ SY1113 )
| ( disjoint @ SV624 @ SY1114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3483]) ).
thf(3684,plain,
! [SV625: $i] :
( ( ! [SY1115: $i] :
( ~ ( subset @ ( singleton @ SV625 ) @ ( singleton @ SY1115 ) )
| ( SV625 = SY1115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3484]) ).
thf(3685,plain,
! [SV626: $i] :
( ( ! [SY1116: $i] : ( subset @ SV626 @ ( set_union2 @ SV626 @ SY1116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3486]) ).
thf(3686,plain,
! [SV627: $i] :
( ( ! [SY1117: $i,SY1118: $i] :
( ~ ( subset @ SV627 @ SY1117 )
| ~ ( subset @ SY1118 @ SY1117 )
| ( subset @ ( set_union2 @ SV627 @ SY1118 ) @ SY1117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3488]) ).
thf(3687,plain,
! [SV628: $i] :
( ( ! [SY1119: $i] :
( ~ ( in @ SV628 @ SY1119 )
| ( subset @ SV628 @ ( union @ SY1119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3489]) ).
thf(3688,plain,
! [SV629: $i] :
( ( ! [SY1120: $i] :
( ~ ( relation @ SY1120 )
| ( ( relation_dom_restriction @ SY1120 @ SV629 )
= ( relation_composition @ ( identity_relation @ SV629 ) @ SY1120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3490]) ).
thf(3689,plain,
! [SV630: $i] :
( ( ! [SY1121: $i] :
( ~ ( in @ SV630 @ SY1121 )
| ~ ( in @ SY1121 @ SV630 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3491]) ).
thf(3690,plain,
! [SV631: $i] :
( ( ! [SY1122: $i] :
( ( set_union2 @ SV631 @ SY1122 )
= ( set_union2 @ SY1122 @ SV631 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3492]) ).
thf(3691,plain,
! [SV632: $i] :
( ( ! [SY1123: $i] :
( ( set_intersection2 @ SV632 @ SY1123 )
= ( set_intersection2 @ SY1123 @ SV632 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3493]) ).
thf(3692,plain,
! [SV633: $i] :
( ( ~ ( empty @ ( powerset @ SV633 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3519]) ).
thf(3693,plain,
! [SV634: $i] :
( ( ! [SY1124: $i] :
~ ( empty @ ( ordered_pair @ SV634 @ SY1124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3521]) ).
thf(3694,plain,
! [SV635: $i] :
( ( ~ ( empty @ ( singleton @ SV635 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3522]) ).
thf(3695,plain,
! [SV636: $i] :
( ( ( empty @ SV636 )
| ! [SY1125: $i] :
~ ( empty @ ( set_union2 @ SV636 @ SY1125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3523]) ).
thf(3696,plain,
! [SV637: $i] :
( ( ! [SY1126: $i] :
~ ( empty @ ( unordered_pair @ SV637 @ SY1126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3524]) ).
thf(3697,plain,
! [SV638: $i] :
( ( ( empty @ SV638 )
| ! [SY1127: $i] :
~ ( empty @ ( set_union2 @ SY1127 @ SV638 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3525]) ).
thf(3698,plain,
! [SV639: $i] :
( ( ! [SY1128: $i] :
( ( empty @ SV639 )
| ( empty @ SY1128 )
| ~ ( empty @ ( cartesian_product2 @ SV639 @ SY1128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3526]) ).
thf(3699,plain,
! [SV640: $i] :
( ( ( set_union2 @ SV640 @ SV640 )
= SV640 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3527]) ).
thf(3700,plain,
! [SV641: $i] :
( ( ( set_intersection2 @ SV641 @ SV641 )
= SV641 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3528]) ).
thf(3701,plain,
( ( empty @ sK5_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3530]) ).
thf(3702,plain,
! [SV642: $i] :
( ( subset @ SV642 @ SV642 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3531]) ).
thf(3703,plain,
! [SV643: $i] :
( ( ( set_union2 @ SV643 @ empty_set )
= SV643 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3532]) ).
thf(3704,plain,
! [SV644: $i] :
( ( ! [SY1129: $i] :
( ~ ( in @ SV644 @ SY1129 )
| ( element @ SV644 @ SY1129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3533]) ).
thf(3705,plain,
! [SV645: $i] :
( ( ( set_intersection2 @ SV645 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3534]) ).
thf(3706,plain,
! [SV646: $i] :
( ( ! [SY1130: $i] :
( ~ ( element @ SV646 @ SY1130 )
| ( empty @ SY1130 )
| ( in @ SV646 @ SY1130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3535]) ).
thf(3707,plain,
! [SV647: $i] :
( ( ( set_difference @ SV647 @ empty_set )
= SV647 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3537]) ).
thf(3708,plain,
! [SV648: $i] :
( ( ( set_difference @ empty_set @ SV648 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3538]) ).
thf(3709,plain,
! [SV649: $i] :
( ( ~ ( empty @ SV649 )
| ( SV649 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3539]) ).
thf(3710,plain,
! [SV650: $i] :
( ( ! [SY1131: $i] :
( ~ ( empty @ SY1131 )
| ~ ( in @ SV650 @ SY1131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3540]) ).
thf(3711,plain,
! [SV651: $i] :
( ( ! [SY1132: $i] :
( ( SV651 = SY1132 )
| ~ ( empty @ SV651 )
| ~ ( empty @ SY1132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3541]) ).
thf(3712,plain,
( ( ( relation_dom @ sK1_A )
= ( relation_rng @ ( function_inverse @ sK1_A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3546]) ).
thf(3713,plain,
! [SV652: $i] :
( ( ~ ( ~ ! [SY1133: $i,SY1134: $i] :
( ~ ( ~ ( ~ ( in @ ( sK17_D @ SY1134 @ SY1133 @ SV652 ) @ SV652 )
| ~ ( in @ ( sK17_D @ SY1134 @ SY1133 @ SV652 ) @ SY1133 )
| ~ ( in @ ( sK17_D @ SY1134 @ SY1133 @ SV652 ) @ SY1134 ) )
| ~ ~ ( ~ ( ( in @ ( sK17_D @ SY1134 @ SY1133 @ SV652 ) @ SV652 )
| ( in @ ( sK17_D @ SY1134 @ SY1133 @ SV652 ) @ SY1134 ) )
| ~ ( ( in @ ( sK17_D @ SY1134 @ SY1133 @ SV652 ) @ SY1133 )
| ( in @ ( sK17_D @ SY1134 @ SY1133 @ SV652 ) @ SY1134 ) ) ) )
| ( SY1134
= ( set_intersection2 @ SV652 @ SY1133 ) ) )
| ~ ! [SY1135: $i,SY1136: $i] :
( ( SY1136
!= ( set_intersection2 @ SV652 @ SY1135 ) )
| ~ ( ~ ! [SY1137: $i] :
( ~ ( in @ SY1137 @ SV652 )
| ~ ( in @ SY1137 @ SY1135 )
| ( in @ SY1137 @ SY1136 ) )
| ~ ~ ( ~ ! [SY1138: $i] :
( ~ ( in @ SY1138 @ SY1136 )
| ( in @ SY1138 @ SV652 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1136 )
| ( in @ SX3 @ SY1135 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3547]) ).
thf(3714,plain,
( ( ~ ( empty @ sK57_A )
| ~ ( relation @ sK57_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3548]) ).
thf(3715,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)],[3549]) ).
thf(3716,plain,
! [SV653: $i] :
( ( ~ ( function @ SV653 )
| ~ ( relation @ SV653 )
| ~ ( one_to_one @ SV653 )
| ~ ( ~ ! [SY1140: $i] :
( ~ ( function @ SY1140 )
| ~ ( relation @ SY1140 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SY1140 @ SV653 )
= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ( ( sK70_C @ SY1140 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY1140 @ SV653 )
= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY1140 @ SV653 )
= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ( ( sK71_SY424 @ SY1140 @ SV653 )
!= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK70_C @ SY1140 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK71_SY424 @ SY1140 @ SV653 )
!= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY1140 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK70_C @ SY1140 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SY1140 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SY1140 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK71_SY424 @ SY1140 @ SV653 )
!= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ( ( relation_dom @ SY1140 )
!= ( relation_rng @ SV653 ) )
| ( SY1140
= ( function_inverse @ SV653 ) ) )
| ~ ~ ( ~ ! [SY1141: $i] :
( ~ ( function @ SY1141 )
| ~ ( relation @ SY1141 )
| ( SY1141
!= ( function_inverse @ SV653 ) )
| ~ ( ~ ~ ( ~ ! [SY1142: $i,SY1143: $i] :
( ( SY1143
!= ( apply @ SY1141 @ SY1142 ) )
| ~ ( in @ SY1142 @ ( relation_rng @ SV653 ) )
| ( SY1142
= ( apply @ SV653 @ SY1143 ) ) )
| ~ ! [SY1144: $i,SY1145: $i] :
( ( SY1145
!= ( apply @ SY1141 @ SY1144 ) )
| ~ ( in @ SY1144 @ ( relation_rng @ SV653 ) )
| ( in @ SY1145 @ ( relation_dom @ SV653 ) ) ) )
| ~ ~ ( ~ ! [SY1146: $i,SY1147: $i] :
( ( SY1146
!= ( apply @ SV653 @ SY1147 ) )
| ~ ( in @ SY1147 @ ( relation_dom @ SV653 ) )
| ( SY1147
= ( apply @ SY1141 @ SY1146 ) ) )
| ~ ! [SY1148: $i] :
( ! [SY1149: $i] :
( ( SY1148
!= ( apply @ SV653 @ SY1149 ) )
| ~ ( in @ SY1149 @ ( relation_dom @ SV653 ) ) )
| ( in @ SY1148 @ ( relation_rng @ SV653 ) ) ) ) ) )
| ~ ! [SY1150: $i] :
( ~ ( function @ SY1150 )
| ~ ( relation @ SY1150 )
| ( SY1150
!= ( function_inverse @ SV653 ) )
| ( ( relation_dom @ SY1150 )
= ( relation_rng @ SV653 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3550]) ).
thf(3717,plain,
( ( ~ ~ ( ~ ( function @ sK54_A )
| ~ ( relation @ sK54_A ) )
| ~ ( one_to_one @ sK54_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3551]) ).
thf(3718,plain,
( ( ~ ~ ( empty @ sK55_A )
| ~ ( relation @ sK55_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3552]) ).
thf(3719,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)],[3553]) ).
thf(3720,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)],[3554]) ).
thf(3721,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)],[3555]) ).
thf(3722,plain,
( ( ~ ! [SX0: $i] :
( ( relation_dom @ ( identity_relation @ SX0 ) )
= SX0 )
| ~ ! [SX0: $i] :
( ( relation_rng @ ( identity_relation @ SX0 ) )
= SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3556]) ).
thf(3723,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)],[3557]) ).
thf(3724,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3558]) ).
thf(3725,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)],[3559]) ).
thf(3726,plain,
! [SV654: $i] :
( ( ! [SY1151: $i] :
~ ( ~ ! [SY1152: $i,SY1153: $i] :
( ~ ( relation @ SY1153 )
| ~ ( in @ SV654 @ SY1152 )
| ~ ( in @ ( ordered_pair @ SV654 @ SY1151 ) @ SY1153 )
| ( in @ ( ordered_pair @ SV654 @ SY1151 ) @ ( relation_composition @ ( identity_relation @ SY1152 ) @ SY1153 ) ) )
| ~ ~ ( ~ ! [SY1154: $i,SY1155: $i] :
( ~ ( relation @ SY1155 )
| ~ ( in @ ( ordered_pair @ SV654 @ SY1151 ) @ ( relation_composition @ ( identity_relation @ SY1154 ) @ SY1155 ) )
| ( in @ SV654 @ SY1154 ) )
| ~ ! [SY1156: $i,SY1157: $i] :
( ~ ( relation @ SY1157 )
| ~ ( in @ ( ordered_pair @ SV654 @ SY1151 ) @ ( relation_composition @ ( identity_relation @ SY1156 ) @ SY1157 ) )
| ( in @ ( ordered_pair @ SV654 @ SY1151 ) @ SY1157 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3560]) ).
thf(3727,plain,
! [SV655: $i] :
( ( ! [SY1158: $i] :
( ~ ( relation @ SY1158 )
| ~ ( ~ ! [SY1159: $i] :
( ~ ( relation @ SY1159 )
| ~ ( ~ ( ~ ( in @ ( sK41_SY412 @ SY1159 @ SY1158 @ SV655 ) @ SV655 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY1159 @ SY1158 @ SV655 ) @ ( sK41_SY412 @ SY1159 @ SY1158 @ SV655 ) ) @ SY1158 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY1159 @ SY1158 @ SV655 ) @ ( sK41_SY412 @ SY1159 @ SY1158 @ SV655 ) ) @ SY1159 ) )
| ~ ~ ( ~ ( ( in @ ( sK41_SY412 @ SY1159 @ SY1158 @ SV655 ) @ SV655 )
| ( in @ ( ordered_pair @ ( sK40_D @ SY1159 @ SY1158 @ SV655 ) @ ( sK41_SY412 @ SY1159 @ SY1158 @ SV655 ) ) @ SY1159 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SY1159 @ SY1158 @ SV655 ) @ ( sK41_SY412 @ SY1159 @ SY1158 @ SV655 ) ) @ SY1158 )
| ( in @ ( ordered_pair @ ( sK40_D @ SY1159 @ SY1158 @ SV655 ) @ ( sK41_SY412 @ SY1159 @ SY1158 @ SV655 ) ) @ SY1159 ) ) ) )
| ( SY1159
= ( relation_rng_restriction @ SV655 @ SY1158 ) ) )
| ~ ! [SY1160: $i] :
( ~ ( relation @ SY1160 )
| ( SY1160
!= ( relation_rng_restriction @ SV655 @ SY1158 ) )
| ~ ( ~ ! [SY1161: $i,SY1162: $i] :
( ~ ( in @ SY1162 @ SV655 )
| ~ ( in @ ( ordered_pair @ SY1161 @ SY1162 ) @ SY1158 )
| ( in @ ( ordered_pair @ SY1161 @ SY1162 ) @ SY1160 ) )
| ~ ~ ( ~ ! [SY1163: $i,SY1164: $i] :
( ~ ( in @ ( ordered_pair @ SY1163 @ SY1164 ) @ SY1160 )
| ( in @ SY1164 @ SV655 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY1160 )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY1158 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3561]) ).
thf(3728,plain,
( ( ~ ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) )
| ~ ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3562]) ).
thf(3729,plain,
! [SV656: $i] :
( ( ! [SY1167: $i] :
~ ( ~ ! [SY1168: $i] :
( ! [SY1169: $i] :
( ( ordered_pair @ SV656 @ SY1167 )
!= ( ordered_pair @ SY1168 @ SY1169 ) )
| ( SV656 = SY1168 ) )
| ~ ! [SY1170: $i,SY1171: $i] :
( ( ( ordered_pair @ SV656 @ SY1167 )
!= ( ordered_pair @ SY1170 @ SY1171 ) )
| ( SY1167 = SY1171 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3563]) ).
thf(3730,plain,
! [SV657: $i] :
( ( ~ ( relation @ SV657 )
| ~ ( ~ ! [SY1172: $i,SY1173: $i] :
( ~ ( ~ ( ! [SY1174: $i] :
( ~ ( in @ ( ordered_pair @ ( sK35_D @ SY1173 @ SY1172 @ SV657 ) @ SY1174 ) @ SV657 )
| ~ ( in @ SY1174 @ SY1172 ) )
| ~ ( in @ ( sK35_D @ SY1173 @ SY1172 @ SV657 ) @ SY1173 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SY1173 @ SY1172 @ SV657 ) @ ( sK36_SY409 @ SY1173 @ SY1172 @ SV657 ) ) @ SV657 )
| ~ ( in @ ( sK36_SY409 @ SY1173 @ SY1172 @ SV657 ) @ SY1172 ) )
| ( in @ ( sK35_D @ SY1173 @ SY1172 @ SV657 ) @ SY1173 ) ) )
| ( SY1173
= ( relation_inverse_image @ SV657 @ SY1172 ) ) )
| ~ ! [SY1175: $i,SY1176: $i] :
( ( SY1176
!= ( relation_inverse_image @ SV657 @ SY1175 ) )
| ~ ( ~ ! [SY1177: $i] :
( ! [SY1178: $i] :
( ~ ( in @ ( ordered_pair @ SY1177 @ SY1178 ) @ SV657 )
| ~ ( in @ SY1178 @ SY1175 ) )
| ( in @ SY1177 @ SY1176 ) )
| ~ ! [SY1179: $i] :
( ~ ( in @ SY1179 @ SY1176 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1179 @ ( sK34_E @ SY1179 @ SY1176 @ SY1175 @ SV657 ) ) @ SV657 )
| ~ ( in @ ( sK34_E @ SY1179 @ SY1176 @ SY1175 @ SV657 ) @ SY1175 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3564]) ).
thf(3731,plain,
! [SV658: $i] :
( ( ~ ( relation @ SV658 )
| ~ ( ~ ! [SY1180: $i,SY1181: $i] :
( ~ ( ~ ( ! [SY1182: $i] :
( ~ ( in @ ( ordered_pair @ SY1182 @ ( sK38_D @ SY1181 @ SY1180 @ SV658 ) ) @ SV658 )
| ~ ( in @ SY1182 @ SY1180 ) )
| ~ ( in @ ( sK38_D @ SY1181 @ SY1180 @ SV658 ) @ SY1181 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SY1181 @ SY1180 @ SV658 ) @ ( sK38_D @ SY1181 @ SY1180 @ SV658 ) ) @ SV658 )
| ~ ( in @ ( sK39_SY411 @ SY1181 @ SY1180 @ SV658 ) @ SY1180 ) )
| ( in @ ( sK38_D @ SY1181 @ SY1180 @ SV658 ) @ SY1181 ) ) )
| ( SY1181
= ( relation_image @ SV658 @ SY1180 ) ) )
| ~ ! [SY1183: $i,SY1184: $i] :
( ( SY1184
!= ( relation_image @ SV658 @ SY1183 ) )
| ~ ( ~ ! [SY1185: $i] :
( ! [SY1186: $i] :
( ~ ( in @ ( ordered_pair @ SY1186 @ SY1185 ) @ SV658 )
| ~ ( in @ SY1186 @ SY1183 ) )
| ( in @ SY1185 @ SY1184 ) )
| ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ SY1184 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SY1187 @ SY1184 @ SY1183 @ SV658 ) @ SY1187 ) @ SV658 )
| ~ ( in @ ( sK37_E @ SY1187 @ SY1184 @ SY1183 @ SV658 ) @ SY1183 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3565]) ).
thf(3732,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)],[3566]) ).
thf(3733,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)],[3567]) ).
thf(3734,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)],[3568]) ).
thf(3735,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK69_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK69_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK67_C @ SX1 @ SX0 ) @ ( sK68_SY421 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3569]) ).
thf(3736,plain,
! [SV659: $i] :
( ( ~ ( ~ ! [SY1188: $i,SY1189: $i] :
( ~ ( in @ SV659 @ SY1189 )
| ~ ( in @ SY1188 @ SY1189 )
| ( subset @ ( unordered_pair @ SV659 @ SY1188 ) @ SY1189 ) )
| ~ ~ ( ~ ! [SY1190: $i,SY1191: $i] :
( ~ ( subset @ ( unordered_pair @ SV659 @ SY1190 ) @ SY1191 )
| ( in @ SV659 @ SY1191 ) )
| ~ ! [SY1192: $i,SY1193: $i] :
( ~ ( subset @ ( unordered_pair @ SV659 @ SY1192 ) @ SY1193 )
| ( in @ SY1192 @ SY1193 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3570]) ).
thf(3737,plain,
! [SV660: $i] :
( ( ~ ( relation @ SV660 )
| ! [SY1194: $i] :
( ~ ( relation @ SY1194 )
| ~ ( ~ ! [SY1195: $i] :
( ~ ( relation @ SY1195 )
| ~ ( ~ ( ! [SY1196: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY1195 @ SY1194 @ SV660 ) @ SY1196 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1196 @ ( sK9_SY391 @ SY1195 @ SY1194 @ SV660 ) ) @ SY1194 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SY1195 @ SY1194 @ SV660 ) @ ( sK9_SY391 @ SY1195 @ SY1194 @ SV660 ) ) @ SY1195 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY1195 @ SY1194 @ SV660 ) @ ( sK10_SY395 @ SY1195 @ SY1194 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SY1195 @ SY1194 @ SV660 ) @ ( sK9_SY391 @ SY1195 @ SY1194 @ SV660 ) ) @ SY1194 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SY1195 @ SY1194 @ SV660 ) @ ( sK9_SY391 @ SY1195 @ SY1194 @ SV660 ) ) @ SY1195 ) ) )
| ( SY1195
= ( relation_composition @ SV660 @ SY1194 ) ) )
| ~ ! [SY1197: $i] :
( ~ ( relation @ SY1197 )
| ( SY1197
!= ( relation_composition @ SV660 @ SY1194 ) )
| ~ ( ~ ! [SY1198: $i,SY1199: $i] :
( ! [SY1200: $i] :
( ~ ( in @ ( ordered_pair @ SY1198 @ SY1200 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1200 @ SY1199 ) @ SY1194 ) )
| ( in @ ( ordered_pair @ SY1198 @ SY1199 ) @ SY1197 ) )
| ~ ! [SY1201: $i,SY1202: $i] :
( ~ ( in @ ( ordered_pair @ SY1201 @ SY1202 ) @ SY1197 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1201 @ ( sK7_F @ SY1202 @ SY1201 @ SY1197 @ SY1194 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY1202 @ SY1201 @ SY1197 @ SY1194 @ SV660 ) @ SY1202 ) @ SY1194 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3571]) ).
thf(3738,plain,
( ( ~ ( relation @ sK53_A )
| ~ ( relation_empty_yielding @ sK53_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3572]) ).
thf(3739,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK29_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3573]) ).
thf(3740,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3574]) ).
thf(3741,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)],[3575]) ).
thf(3742,plain,
! [SV661: $i] :
( ( ~ ( relation @ SV661 )
| ~ ( ~ ! [SY1203: $i] :
( ~ ( ~ ( ! [SY1204: $i] :
~ ( in @ ( ordered_pair @ SY1204 @ ( sK60_C @ SY1203 @ SV661 ) ) @ SV661 )
| ~ ( in @ ( sK60_C @ SY1203 @ SV661 ) @ SY1203 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK61_SY417 @ SY1203 @ SV661 ) @ ( sK60_C @ SY1203 @ SV661 ) ) @ SV661 )
| ( in @ ( sK60_C @ SY1203 @ SV661 ) @ SY1203 ) ) )
| ( SY1203
= ( relation_rng @ SV661 ) ) )
| ~ ! [SY1205: $i] :
( ( SY1205
!= ( relation_rng @ SV661 ) )
| ~ ( ~ ! [SY1206: $i] :
( ! [SY1207: $i] :
~ ( in @ ( ordered_pair @ SY1207 @ SY1206 ) @ SV661 )
| ( in @ SY1206 @ SY1205 ) )
| ~ ! [SY1208: $i] :
( ~ ( in @ SY1208 @ SY1205 )
| ( in @ ( ordered_pair @ ( sK59_D @ SY1208 @ SY1205 @ SV661 ) @ SY1208 ) @ SV661 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3576]) ).
thf(3743,plain,
! [SV662: $i] :
( ( ~ ( ~ ! [SY1209: $i,SY1210: $i] :
( ~ ( ~ ( ~ ( in @ ( sK13_D @ SY1210 @ SY1209 @ SV662 ) @ SV662 )
| ( in @ ( sK13_D @ SY1210 @ SY1209 @ SV662 ) @ SY1209 )
| ~ ( in @ ( sK13_D @ SY1210 @ SY1209 @ SV662 ) @ SY1210 ) )
| ~ ~ ( ~ ( ( in @ ( sK13_D @ SY1210 @ SY1209 @ SV662 ) @ SV662 )
| ( in @ ( sK13_D @ SY1210 @ SY1209 @ SV662 ) @ SY1210 ) )
| ~ ( ~ ( in @ ( sK13_D @ SY1210 @ SY1209 @ SV662 ) @ SY1209 )
| ( in @ ( sK13_D @ SY1210 @ SY1209 @ SV662 ) @ SY1210 ) ) ) )
| ( SY1210
= ( set_difference @ SV662 @ SY1209 ) ) )
| ~ ! [SY1211: $i,SY1212: $i] :
( ( SY1212
!= ( set_difference @ SV662 @ SY1211 ) )
| ~ ( ~ ! [SY1213: $i] :
( ~ ( in @ SY1213 @ SV662 )
| ( in @ SY1213 @ SY1211 )
| ( in @ SY1213 @ SY1212 ) )
| ~ ~ ( ~ ! [SY1214: $i] :
( ~ ( in @ SY1214 @ SY1212 )
| ( in @ SY1214 @ SV662 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1212 )
| ~ ( in @ SX3 @ SY1211 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3577]) ).
thf(3744,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)],[3578]) ).
thf(3745,plain,
! [SV663: $i] :
( ( ~ ( ~ ! [SY1216: $i,SY1217: $i] :
( ~ ( relation @ SY1217 )
| ~ ( in @ SV663 @ SY1216 )
| ~ ( in @ SV663 @ ( relation_rng @ SY1217 ) )
| ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SY1216 @ SY1217 ) ) ) )
| ~ ~ ( ~ ! [SY1218: $i,SY1219: $i] :
( ~ ( relation @ SY1219 )
| ~ ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SY1218 @ SY1219 ) ) )
| ( in @ SV663 @ SY1218 ) )
| ~ ! [SY1220: $i,SY1221: $i] :
( ~ ( relation @ SY1221 )
| ~ ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SY1220 @ SY1221 ) ) )
| ( in @ SV663 @ ( relation_rng @ SY1221 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3579]) ).
thf(3746,plain,
! [SV664: $i] :
( ( ~ ( function @ SV664 )
| ~ ( relation @ SV664 )
| ~ ( ~ ~ ( ~ ! [SY1222: $i] :
( ~ ( in @ SY1222 @ ( relation_dom @ SV664 ) )
| ! [SY1223: $i] :
( ( SY1223
!= ( apply @ SV664 @ SY1222 ) )
| ( in @ ( ordered_pair @ SY1222 @ SY1223 ) @ SV664 ) ) )
| ~ ! [SY1224: $i] :
( ~ ( in @ SY1224 @ ( relation_dom @ SV664 ) )
| ! [SY1225: $i] :
( ~ ( in @ ( ordered_pair @ SY1224 @ SY1225 ) @ SV664 )
| ( SY1225
= ( apply @ SV664 @ SY1224 ) ) ) ) )
| ~ ~ ( ~ ! [SY1226: $i] :
( ( in @ SY1226 @ ( relation_dom @ SV664 ) )
| ! [SY1227: $i] :
( ( SY1227
!= ( apply @ SV664 @ SY1226 ) )
| ( SY1227 = empty_set ) ) )
| ~ ! [SY1228: $i] :
( ( in @ SY1228 @ ( relation_dom @ SV664 ) )
| ! [SY1229: $i] :
( ( SY1229 != empty_set )
| ( SY1229
= ( apply @ SV664 @ SY1228 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3580]) ).
thf(3747,plain,
! [SV665: $i] :
( ( ~ ( relation @ SV665 )
| ~ ( ~ ! [SY1230: $i] :
( ~ ( relation @ SY1230 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SY1230 @ SV665 ) @ ( sK20_SY399 @ SY1230 @ SV665 ) ) @ SV665 )
| ~ ~ ( in @ ( ordered_pair @ ( sK19_C @ SY1230 @ SV665 ) @ ( sK20_SY399 @ SY1230 @ SV665 ) ) @ SY1230 ) )
| ( subset @ SV665 @ SY1230 ) )
| ~ ! [SY1231: $i] :
( ~ ( relation @ SY1231 )
| ~ ( subset @ SV665 @ SY1231 )
| ! [SY1232: $i,SY1233: $i] :
( ~ ( in @ ( ordered_pair @ SY1232 @ SY1233 ) @ SV665 )
| ( in @ ( ordered_pair @ SY1232 @ SY1233 ) @ SY1231 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3581]) ).
thf(3748,plain,
! [SV666: $i] :
( ( ! [SY1234: $i] :
( ~ ( function @ SY1234 )
| ~ ( relation @ SY1234 )
| ~ ( ~ ! [SY1235: $i] :
( ~ ( function @ SY1235 )
| ~ ( relation @ SY1235 )
| ~ ( in @ SV666 @ ( relation_dom @ SY1235 ) )
| ~ ( in @ ( apply @ SY1235 @ SV666 ) @ ( relation_dom @ SY1234 ) )
| ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1235 @ SY1234 ) ) ) )
| ~ ~ ( ~ ! [SY1236: $i] :
( ~ ( function @ SY1236 )
| ~ ( relation @ SY1236 )
| ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1236 @ SY1234 ) ) )
| ( in @ SV666 @ ( relation_dom @ SY1236 ) ) )
| ~ ! [SY1237: $i] :
( ~ ( function @ SY1237 )
| ~ ( relation @ SY1237 )
| ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1237 @ SY1234 ) ) )
| ( in @ ( apply @ SY1237 @ SV666 ) @ ( relation_dom @ SY1234 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3582]) ).
thf(3749,plain,
! [SV667: $i] :
( ( ~ ( ~ ! [SY1238: $i,SY1239: $i] :
( ~ ( relation @ SY1239 )
| ! [SY1240: $i] :
( ~ ( in @ SY1240 @ ( relation_rng @ SY1239 ) )
| ~ ( in @ ( ordered_pair @ SV667 @ SY1240 ) @ SY1239 )
| ~ ( in @ SY1240 @ SY1238 ) )
| ( in @ SV667 @ ( relation_inverse_image @ SY1239 @ SY1238 ) ) )
| ~ ! [SY1241: $i,SY1242: $i] :
( ~ ( relation @ SY1242 )
| ~ ( in @ SV667 @ ( relation_inverse_image @ SY1242 @ SY1241 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK51_D @ SY1242 @ SY1241 @ SV667 ) @ ( relation_rng @ SY1242 ) )
| ~ ( in @ ( ordered_pair @ SV667 @ ( sK51_D @ SY1242 @ SY1241 @ SV667 ) ) @ SY1242 ) )
| ~ ( in @ ( sK51_D @ SY1242 @ SY1241 @ SV667 ) @ SY1241 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3583]) ).
thf(3750,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK49_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK49_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)],[3584]) ).
thf(3751,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3585]) ).
thf(3752,plain,
! [SV668: $i] :
( ( ~ ( ~ ! [SY1243: $i,SY1244: $i] :
( ~ ( relation @ SY1244 )
| ~ ( in @ SV668 @ SY1243 )
| ~ ( in @ SV668 @ ( relation_dom @ SY1244 ) )
| ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SY1244 @ SY1243 ) ) ) )
| ~ ~ ( ~ ! [SY1245: $i,SY1246: $i] :
( ~ ( relation @ SY1246 )
| ~ ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SY1246 @ SY1245 ) ) )
| ( in @ SV668 @ SY1245 ) )
| ~ ! [SY1247: $i,SY1248: $i] :
( ~ ( relation @ SY1248 )
| ~ ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SY1248 @ SY1247 ) ) )
| ( in @ SV668 @ ( relation_dom @ SY1248 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3586]) ).
thf(3753,plain,
! [SV669: $i] :
( ( ~ ( ~ ! [SY1249: $i,SY1250: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY1250 @ SY1249 @ SV669 ) @ SY1250 )
| ~ ( in @ ( sK26_D @ SY1250 @ SY1249 @ SV669 ) @ SV669 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY1250 @ SY1249 @ SV669 ) @ SY1250 )
| ~ ( in @ ( sK26_D @ SY1250 @ SY1249 @ SV669 ) @ SY1249 ) ) )
| ~ ( ( in @ ( sK26_D @ SY1250 @ SY1249 @ SV669 ) @ SY1250 )
| ( in @ ( sK26_D @ SY1250 @ SY1249 @ SV669 ) @ SV669 )
| ( in @ ( sK26_D @ SY1250 @ SY1249 @ SV669 ) @ SY1249 ) ) )
| ( SY1250
= ( set_union2 @ SV669 @ SY1249 ) ) )
| ~ ! [SY1251: $i,SY1252: $i] :
( ( SY1252
!= ( set_union2 @ SV669 @ SY1251 ) )
| ~ ( ~ ! [SY1253: $i] :
( ~ ( in @ SY1253 @ SY1252 )
| ( in @ SY1253 @ SV669 )
| ( in @ SY1253 @ SY1251 ) )
| ~ ~ ( ~ ! [SY1254: $i] :
( ~ ( in @ SY1254 @ SV669 )
| ( in @ SY1254 @ SY1252 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1251 )
| ( in @ SX3 @ SY1252 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3587]) ).
thf(3754,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY406 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ ( sK33_SY406 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK31_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)],[3588]) ).
thf(3755,plain,
! [SV670: $i] :
( ( ~ ( ~ ! [SY1256: $i,SY1257: $i] :
( ~ ( ~ ( ! [SY1258: $i,SY1259: $i] :
( ~ ( in @ SY1258 @ SV670 )
| ~ ( in @ SY1259 @ SY1256 )
| ( ( sK23_D @ SY1257 @ SY1256 @ SV670 )
!= ( ordered_pair @ SY1258 @ SY1259 ) ) )
| ~ ( in @ ( sK23_D @ SY1257 @ SY1256 @ SV670 ) @ SY1257 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY403 @ SY1257 @ SY1256 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK25_SY405 @ SY1257 @ SY1256 @ SV670 ) @ SY1256 ) )
| ( ( sK23_D @ SY1257 @ SY1256 @ SV670 )
!= ( ordered_pair @ ( sK24_SY403 @ SY1257 @ SY1256 @ SV670 ) @ ( sK25_SY405 @ SY1257 @ SY1256 @ SV670 ) ) ) )
| ( in @ ( sK23_D @ SY1257 @ SY1256 @ SV670 ) @ SY1257 ) ) )
| ( SY1257
= ( cartesian_product2 @ SV670 @ SY1256 ) ) )
| ~ ! [SY1260: $i,SY1261: $i] :
( ( SY1261
!= ( cartesian_product2 @ SV670 @ SY1260 ) )
| ~ ( ~ ! [SY1262: $i] :
( ! [SY1263: $i,SY1264: $i] :
( ~ ( in @ SY1263 @ SV670 )
| ~ ( in @ SY1264 @ SY1260 )
| ( SY1262
!= ( ordered_pair @ SY1263 @ SY1264 ) ) )
| ( in @ SY1262 @ SY1261 ) )
| ~ ! [SY1265: $i] :
( ~ ( in @ SY1265 @ SY1261 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY1265 @ SY1261 @ SY1260 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK22_SY400 @ SY1265 @ SY1261 @ SY1260 @ SV670 ) @ SY1260 ) )
| ( SY1265
!= ( ordered_pair @ ( sK21_E @ SY1265 @ SY1261 @ SY1260 @ SV670 ) @ ( sK22_SY400 @ SY1265 @ SY1261 @ SY1260 @ SV670 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3589]) ).
thf(3756,plain,
! [SV671: $i] :
( ( ~ ( ~ ! [SY1266: $i,SY1267: $i] :
( ~ ( function @ SY1267 )
| ~ ( relation @ SY1267 )
| ( SY1266
!= ( apply @ SY1267 @ SV671 ) )
| ~ ( in @ SV671 @ ( relation_dom @ SY1267 ) )
| ( in @ ( ordered_pair @ SV671 @ SY1266 ) @ SY1267 ) )
| ~ ~ ( ~ ! [SY1268: $i,SY1269: $i] :
( ~ ( function @ SY1269 )
| ~ ( relation @ SY1269 )
| ~ ( in @ ( ordered_pair @ SV671 @ SY1268 ) @ SY1269 )
| ( SY1268
= ( apply @ SY1269 @ SV671 ) ) )
| ~ ! [SY1270: $i,SY1271: $i] :
( ~ ( function @ SY1271 )
| ~ ( relation @ SY1271 )
| ~ ( in @ ( ordered_pair @ SV671 @ SY1270 ) @ SY1271 )
| ( in @ SV671 @ ( relation_dom @ SY1271 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3590]) ).
thf(3757,plain,
! [SV672: $i] :
( ( ~ ( relation @ SV672 )
| ~ ( ~ ! [SY1272: $i] :
( ~ ( relation @ SY1272 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SY1272 @ SV672 ) @ ( sK12_SY396 @ SY1272 @ SV672 ) ) @ SY1272 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SY1272 @ SV672 ) @ ( sK11_C @ SY1272 @ SV672 ) ) @ SV672 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_C @ SY1272 @ SV672 ) @ ( sK12_SY396 @ SY1272 @ SV672 ) ) @ SY1272 )
| ( in @ ( ordered_pair @ ( sK12_SY396 @ SY1272 @ SV672 ) @ ( sK11_C @ SY1272 @ SV672 ) ) @ SV672 ) ) )
| ( SY1272
= ( relation_inverse @ SV672 ) ) )
| ~ ! [SY1273: $i] :
( ~ ( relation @ SY1273 )
| ( SY1273
!= ( relation_inverse @ SV672 ) )
| ~ ( ~ ! [SY1274: $i,SY1275: $i] :
( ~ ( in @ ( ordered_pair @ SY1274 @ SY1275 ) @ SY1273 )
| ( in @ ( ordered_pair @ SY1275 @ SY1274 ) @ SV672 ) )
| ~ ! [SY1276: $i,SY1277: $i] :
( ~ ( in @ ( ordered_pair @ SY1277 @ SY1276 ) @ SV672 )
| ( in @ ( ordered_pair @ SY1276 @ SY1277 ) @ SY1273 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3591]) ).
thf(3758,plain,
( ( ~ ( function @ sK58_A )
| ~ ( relation @ sK58_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3592]) ).
thf(3759,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)],[3593]) ).
thf(3760,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)],[3594]) ).
thf(3761,plain,
! [SV673: $i] :
( ( ~ ( ~ ! [SY1278: $i,SY1279: $i] :
( ~ ( relation @ SY1279 )
| ~ ( in @ ( ordered_pair @ SV673 @ SY1278 ) @ SY1279 )
| ( in @ SV673 @ ( relation_dom @ SY1279 ) ) )
| ~ ! [SY1280: $i,SY1281: $i] :
( ~ ( relation @ SY1281 )
| ~ ( in @ ( ordered_pair @ SV673 @ SY1280 ) @ SY1281 )
| ( in @ SY1280 @ ( relation_rng @ SY1281 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3595]) ).
thf(3762,plain,
! [SV674: $i] :
( ( ! [SY1282: $i] :
~ ( ~ ! [SY1283: $i,SY1284: $i] :
( ~ ( in @ SV674 @ SY1283 )
| ~ ( in @ SY1282 @ SY1284 )
| ( in @ ( ordered_pair @ SV674 @ SY1282 ) @ ( cartesian_product2 @ SY1283 @ SY1284 ) ) )
| ~ ~ ( ~ ! [SY1285: $i] :
( ! [SY1286: $i] :
~ ( in @ ( ordered_pair @ SV674 @ SY1282 ) @ ( cartesian_product2 @ SY1285 @ SY1286 ) )
| ( in @ SV674 @ SY1285 ) )
| ~ ! [SY1287: $i,SY1288: $i] :
( ~ ( in @ ( ordered_pair @ SV674 @ SY1282 ) @ ( cartesian_product2 @ SY1287 @ SY1288 ) )
| ( in @ SY1282 @ SY1288 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3596]) ).
thf(3763,plain,
! [SV675: $i] :
( ( ~ ( ~ ! [SY1289: $i,SY1290: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY1290 @ SY1289 @ SV675 ) @ SY1290 )
| ( ( sK27_D @ SY1290 @ SY1289 @ SV675 )
!= SV675 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY1290 @ SY1289 @ SV675 ) @ SY1290 )
| ( ( sK27_D @ SY1290 @ SY1289 @ SV675 )
!= SY1289 ) ) )
| ~ ( ( in @ ( sK27_D @ SY1290 @ SY1289 @ SV675 ) @ SY1290 )
| ( ( sK27_D @ SY1290 @ SY1289 @ SV675 )
= SV675 )
| ( ( sK27_D @ SY1290 @ SY1289 @ SV675 )
= SY1289 ) ) )
| ( SY1290
= ( unordered_pair @ SV675 @ SY1289 ) ) )
| ~ ! [SY1291: $i,SY1292: $i] :
( ( SY1292
!= ( unordered_pair @ SV675 @ SY1291 ) )
| ~ ( ~ ! [SY1293: $i] :
( ~ ( in @ SY1293 @ SY1292 )
| ( SY1293 = SV675 )
| ( SY1293 = SY1291 ) )
| ~ ~ ( ~ ! [SY1294: $i] :
( ( SY1294 != SV675 )
| ( in @ SY1294 @ SY1292 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY1291 )
| ( in @ SX3 @ SY1292 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3597]) ).
thf(3764,plain,
! [SV676: $i] :
( ( ! [SY1296: $i] :
~ ( ~ ! [SY1297: $i,SY1298: $i] :
( ~ ( in @ SV676 @ SY1297 )
| ~ ( in @ SY1296 @ SY1298 )
| ( in @ ( ordered_pair @ SV676 @ SY1296 ) @ ( cartesian_product2 @ SY1297 @ SY1298 ) ) )
| ~ ~ ( ~ ! [SY1299: $i] :
( ! [SY1300: $i] :
~ ( in @ ( ordered_pair @ SV676 @ SY1296 ) @ ( cartesian_product2 @ SY1299 @ SY1300 ) )
| ( in @ SV676 @ SY1299 ) )
| ~ ! [SY1301: $i,SY1302: $i] :
( ~ ( in @ ( ordered_pair @ SV676 @ SY1296 ) @ ( cartesian_product2 @ SY1301 @ SY1302 ) )
| ( in @ SY1296 @ SY1302 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3598]) ).
thf(3765,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK48_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)],[3599]) ).
thf(3766,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)],[3600]) ).
thf(3767,plain,
! [SV677: $i] :
( ( ! [SY1303: $i] :
( ~ ( ~ ( ~ ( in @ ( sK4_C @ SY1303 @ SV677 ) @ SV677 )
| ~ ( in @ ( sK4_C @ SY1303 @ SV677 ) @ SY1303 ) )
| ~ ( ( in @ ( sK4_C @ SY1303 @ SV677 ) @ SV677 )
| ( in @ ( sK4_C @ SY1303 @ SV677 ) @ SY1303 ) ) )
| ( SV677 = SY1303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3601]) ).
thf(3768,plain,
! [SV678: $i] :
( ( ~ ( ~ ! [SY1304: $i] :
( ~ ( subset @ SV678 @ SY1304 )
| ! [SY1305: $i] : ( subset @ ( cartesian_product2 @ SV678 @ SY1305 ) @ ( cartesian_product2 @ SY1304 @ SY1305 ) ) )
| ~ ! [SY1306: $i] :
( ~ ( subset @ SV678 @ SY1306 )
| ! [SY1307: $i] : ( subset @ ( cartesian_product2 @ SY1307 @ SV678 ) @ ( cartesian_product2 @ SY1307 @ SY1306 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3602]) ).
thf(3769,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ ( sK16_SY398 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK16_SY398 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK15_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 @ ( sK14_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK14_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3603]) ).
thf(3770,plain,
! [SV679: $i] :
( ( ~ ( relation @ SV679 )
| ~ ( ~ ! [SY1308: $i] :
( ~ ( ~ ( ! [SY1309: $i] :
~ ( in @ ( ordered_pair @ ( sK63_C @ SY1308 @ SV679 ) @ SY1309 ) @ SV679 )
| ~ ( in @ ( sK63_C @ SY1308 @ SV679 ) @ SY1308 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_C @ SY1308 @ SV679 ) @ ( sK64_SY419 @ SY1308 @ SV679 ) ) @ SV679 )
| ( in @ ( sK63_C @ SY1308 @ SV679 ) @ SY1308 ) ) )
| ( SY1308
= ( relation_dom @ SV679 ) ) )
| ~ ! [SY1310: $i] :
( ( SY1310
!= ( relation_dom @ SV679 ) )
| ~ ( ~ ! [SY1311: $i] :
( ! [SY1312: $i] :
~ ( in @ ( ordered_pair @ SY1311 @ SY1312 ) @ SV679 )
| ( in @ SY1311 @ SY1310 ) )
| ~ ! [SY1313: $i] :
( ~ ( in @ SY1313 @ SY1310 )
| ( in @ ( ordered_pair @ SY1313 @ ( sK62_D @ SY1313 @ SY1310 @ SV679 ) ) @ SV679 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3604]) ).
thf(3771,plain,
! [SV680: $i] :
( ( ~ ( ~ ! [SY1314: $i,SY1315: $i] :
( ~ ( relation @ SY1315 )
| ~ ( in @ ( ordered_pair @ SV680 @ SY1314 ) @ SY1315 )
| ( in @ SV680 @ ( relation_field @ SY1315 ) ) )
| ~ ! [SY1316: $i,SY1317: $i] :
( ~ ( relation @ SY1317 )
| ~ ( in @ ( ordered_pair @ SV680 @ SY1316 ) @ SY1317 )
| ( in @ SY1316 @ ( relation_field @ SY1317 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3605]) ).
thf(3772,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK44_C @ SX1 @ SX0 )
!= ( sK45_SY414 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY414 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK44_C @ SX1 @ SX0 )
= ( sK45_SY414 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY414 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY414 @ 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)],[3606]) ).
thf(3773,plain,
! [SV681: $i] :
( ( ~ ( relation @ SV681 )
| ~ ( ~ ! [SY1318: $i,SY1319: $i] :
( ~ ( relation @ SY1319 )
| ~ ( ~ ( ~ ( in @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ SY1318 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ ( sK43_SY413 @ SY1319 @ SY1318 @ SV681 ) ) @ SV681 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ ( sK43_SY413 @ SY1319 @ SY1318 @ SV681 ) ) @ SY1319 ) )
| ~ ~ ( ~ ( ( in @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ SY1318 )
| ( in @ ( ordered_pair @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ ( sK43_SY413 @ SY1319 @ SY1318 @ SV681 ) ) @ SY1319 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ ( sK43_SY413 @ SY1319 @ SY1318 @ SV681 ) ) @ SV681 )
| ( in @ ( ordered_pair @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ ( sK43_SY413 @ SY1319 @ SY1318 @ SV681 ) ) @ SY1319 ) ) ) )
| ( SY1319
= ( relation_dom_restriction @ SV681 @ SY1318 ) ) )
| ~ ! [SY1320: $i,SY1321: $i] :
( ~ ( relation @ SY1321 )
| ( SY1321
!= ( relation_dom_restriction @ SV681 @ SY1320 ) )
| ~ ( ~ ! [SY1322: $i,SY1323: $i] :
( ~ ( in @ SY1322 @ SY1320 )
| ~ ( in @ ( ordered_pair @ SY1322 @ SY1323 ) @ SV681 )
| ( in @ ( ordered_pair @ SY1322 @ SY1323 ) @ SY1321 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY1321 )
| ( in @ SX3 @ SY1320 ) )
| ~ ! [SY1326: $i,SY1327: $i] :
( ~ ( in @ ( ordered_pair @ SY1326 @ SY1327 ) @ SY1321 )
| ( in @ ( ordered_pair @ SY1326 @ SY1327 ) @ SV681 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3607]) ).
thf(3774,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK30_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK30_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK30_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK30_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)],[3608]) ).
thf(3775,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3609]) ).
thf(3776,plain,
! [SV682: $i] :
( ( ~ ( ~ ! [SY1328: $i,SY1329: $i] :
( ~ ( relation @ SY1329 )
| ! [SY1330: $i] :
( ~ ( in @ SY1330 @ ( relation_dom @ SY1329 ) )
| ~ ( in @ ( ordered_pair @ SY1330 @ SV682 ) @ SY1329 )
| ~ ( in @ SY1330 @ SY1328 ) )
| ( in @ SV682 @ ( relation_image @ SY1329 @ SY1328 ) ) )
| ~ ! [SY1331: $i,SY1332: $i] :
( ~ ( relation @ SY1332 )
| ~ ( in @ SV682 @ ( relation_image @ SY1332 @ SY1331 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK52_D @ SY1332 @ SY1331 @ SV682 ) @ ( relation_dom @ SY1332 ) )
| ~ ( in @ ( ordered_pair @ ( sK52_D @ SY1332 @ SY1331 @ SV682 ) @ SV682 ) @ SY1332 ) )
| ~ ( in @ ( sK52_D @ SY1332 @ SY1331 @ SV682 ) @ SY1331 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3610]) ).
thf(3777,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3611]) ).
thf(3778,plain,
! [SV683: $i] :
( ( ~ ( relation @ SV683 )
| ~ ( ~ ! [SY1333: $i] :
( ~ ( relation @ SY1333 )
| ~ ( subset @ SV683 @ SY1333 )
| ( subset @ ( relation_dom @ SV683 ) @ ( relation_dom @ SY1333 ) ) )
| ~ ! [SY1334: $i] :
( ~ ( relation @ SY1334 )
| ~ ( subset @ SV683 @ SY1334 )
| ( subset @ ( relation_rng @ SV683 ) @ ( relation_rng @ SY1334 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3612]) ).
thf(3779,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)],[3613]) ).
thf(3780,plain,
! [SV684: $i] :
( ( ~ ( relation @ SV684 )
| ~ ( ~ ! [SY1335: $i] :
( ~ ( relation @ SY1335 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SY1335 @ SV684 ) @ ( sK66_SY420 @ SY1335 @ SV684 ) ) @ SV684 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SY1335 @ SV684 ) @ ( sK66_SY420 @ SY1335 @ SV684 ) ) @ SY1335 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_C @ SY1335 @ SV684 ) @ ( sK66_SY420 @ SY1335 @ SV684 ) ) @ SV684 )
| ( in @ ( ordered_pair @ ( sK65_C @ SY1335 @ SV684 ) @ ( sK66_SY420 @ SY1335 @ SV684 ) ) @ SY1335 ) ) )
| ( SV684 = SY1335 ) )
| ~ ! [SY1336: $i] :
( ~ ( relation @ SY1336 )
| ( SV684 != SY1336 )
| ~ ( ~ ! [SY1337: $i,SY1338: $i] :
( ~ ( in @ ( ordered_pair @ SY1337 @ SY1338 ) @ SV684 )
| ( in @ ( ordered_pair @ SY1337 @ SY1338 ) @ SY1336 ) )
| ~ ! [SY1339: $i,SY1340: $i] :
( ~ ( in @ ( ordered_pair @ SY1339 @ SY1340 ) @ SY1336 )
| ( in @ ( ordered_pair @ SY1339 @ SY1340 ) @ SV684 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3614]) ).
thf(3781,plain,
! [SV685: $i] :
( ( ~ ( ~ ! [SY1341: $i] :
( ~ ( subset @ SY1341 @ ( sK2_B @ SV685 ) )
| ( are_equipotent @ SY1341 @ ( sK2_B @ SV685 ) )
| ( in @ SY1341 @ ( sK2_B @ SV685 ) ) )
| ~ ~ ( ~ ! [SY1342: $i] :
( ~ ( ~ ! [SY1343: $i] :
( ~ ( subset @ SY1343 @ SY1342 )
| ( in @ SY1343 @ ( sK3_SY386 @ SY1342 @ SV685 ) ) )
| ~ ( in @ ( sK3_SY386 @ SY1342 @ SV685 ) @ ( sK2_B @ SV685 ) ) )
| ~ ( in @ SY1342 @ ( sK2_B @ SV685 ) ) )
| ~ ~ ( ~ ! [SY1344: $i,SY1345: $i] :
( ~ ( in @ SY1344 @ ( sK2_B @ SV685 ) )
| ~ ( subset @ SY1345 @ SY1344 )
| ( in @ SY1345 @ ( sK2_B @ SV685 ) ) )
| ~ ( in @ SV685 @ ( sK2_B @ SV685 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3615]) ).
thf(3782,plain,
( ( ( ( relation_dom @ empty_set )
!= empty_set )
| ( ( relation_rng @ empty_set )
!= empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3616]) ).
thf(3783,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)],[3617]) ).
thf(3784,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK28_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK28_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)],[3618]) ).
thf(3785,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)],[3619]) ).
thf(3786,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)],[3620]) ).
thf(3787,plain,
( ( ~ ~ ( ~ ( empty @ sK56_A )
| ~ ( relation @ sK56_A ) )
| ~ ( function @ sK56_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3621]) ).
thf(3788,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK50_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK50_C @ SX1 @ SX0 ) )
!= ( sK50_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)],[3622]) ).
thf(3789,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)],[3623]) ).
thf(3790,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK18_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK18_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)],[3624]) ).
thf(3791,plain,
! [SV566: $i,SV686: $i] :
( ( ~ ( relation @ SV686 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV566 @ SV686 ) ) @ SV566 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3625]) ).
thf(3792,plain,
! [SV567: $i,SV687: $i] :
( ( ~ ( relation @ SV687 )
| ( subset @ ( relation_rng_restriction @ SV567 @ SV687 ) @ SV687 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3626]) ).
thf(3793,plain,
! [SV568: $i,SV688: $i] :
( ( ~ ( relation @ SV688 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV568 @ SV688 ) ) @ ( relation_rng @ SV688 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3627]) ).
thf(3794,plain,
! [SV569: $i,SV689: $i] :
( ( ~ ( relation @ SV689 )
| ( ( relation_rng @ ( relation_rng_restriction @ SV569 @ SV689 ) )
= ( set_intersection2 @ ( relation_rng @ SV689 ) @ SV569 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3628]) ).
thf(3795,plain,
! [SV690: $i,SV570: $i] :
( ( ! [SY1346: $i] :
( ~ ( relation @ SY1346 )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV570 @ SY1346 ) @ SV690 )
= ( relation_rng_restriction @ SV570 @ ( relation_dom_restriction @ SY1346 @ SV690 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3629]) ).
thf(3796,plain,
! [SV571: $i,SV691: $i] :
( ( ~ ( relation @ SV691 )
| ( subset @ ( relation_image @ SV691 @ SV571 ) @ ( relation_rng @ SV691 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3630]) ).
thf(3797,plain,
! [SV572: $i,SV692: $i] :
( ( ~ ( relation @ SV692 )
| ( ( relation_image @ SV692 @ SV572 )
= ( relation_image @ SV692 @ ( set_intersection2 @ ( relation_dom @ SV692 ) @ SV572 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3631]) ).
thf(3798,plain,
! [SV573: $i] :
( ( ( ~ ( relation @ SV573 ) )
= $true )
| ( ( ( relation_image @ SV573 @ ( relation_dom @ SV573 ) )
= ( relation_rng @ SV573 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3632]) ).
thf(3799,plain,
! [SV574: $i] :
( ( ( ~ ( relation @ SV574 ) )
= $true )
| ( ( ! [SY1068: $i] :
( ~ ( relation @ SY1068 )
| ( ( relation_rng @ ( relation_composition @ SV574 @ SY1068 ) )
= ( relation_image @ SY1068 @ ( relation_rng @ SV574 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3633]) ).
thf(3800,plain,
! [SV575: $i,SV693: $i] :
( ( ~ ( relation @ SV693 )
| ( subset @ ( relation_inverse_image @ SV693 @ SV575 ) @ ( relation_dom @ SV693 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3634]) ).
thf(3801,plain,
! [SV694: $i,SV576: $i] :
( ( ! [SY1347: $i] :
( ~ ( relation @ SY1347 )
| ~ ( subset @ SV576 @ SV694 )
| ( subset @ ( relation_inverse_image @ SY1347 @ SV576 ) @ ( relation_inverse_image @ SY1347 @ SV694 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3635]) ).
thf(3802,plain,
! [SV577: $i] :
( ( ( ~ ( relation @ SV577 ) )
= $true )
| ( ( subset @ SV577 @ ( cartesian_product2 @ ( relation_dom @ SV577 ) @ ( relation_rng @ SV577 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3636]) ).
thf(3803,plain,
! [SV578: $i] :
( ( ( ~ ( relation @ SV578 ) )
= $true )
| ( ( ! [SY1072: $i] :
( ~ ( relation @ SY1072 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV578 @ SY1072 ) ) @ ( relation_dom @ SV578 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3637]) ).
thf(3804,plain,
! [SV579: $i] :
( ( ( ~ ( relation @ SV579 ) )
= $true )
| ( ( ! [SY1073: $i] :
( ~ ( relation @ SY1073 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV579 @ SY1073 ) ) @ ( relation_rng @ SY1073 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3638]) ).
thf(3805,plain,
! [SV580: $i] :
( ( ( ~ ( relation @ SV580 ) )
= $true )
| ( ( ! [SY1074: $i] :
( ~ ( relation @ SY1074 )
| ~ ( subset @ ( relation_rng @ SV580 ) @ ( relation_dom @ SY1074 ) )
| ( ( relation_dom @ ( relation_composition @ SV580 @ SY1074 ) )
= ( relation_dom @ SV580 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3639]) ).
thf(3806,plain,
! [SV581: $i] :
( ( ( ~ ( relation @ SV581 ) )
= $true )
| ( ( ! [SY1075: $i] :
( ~ ( relation @ SY1075 )
| ~ ( subset @ ( relation_dom @ SV581 ) @ ( relation_rng @ SY1075 ) )
| ( ( relation_rng @ ( relation_composition @ SY1075 @ SV581 ) )
= ( relation_rng @ SV581 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3640]) ).
thf(3807,plain,
! [SV582: $i,SV695: $i] :
( ( ~ ( relation @ SV695 )
| ( subset @ ( relation_dom_restriction @ SV695 @ SV582 ) @ SV695 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3641]) ).
thf(3808,plain,
! [SV583: $i,SV696: $i] :
( ( ~ ( relation @ SV696 )
| ( ( relation_dom @ ( relation_dom_restriction @ SV696 @ SV583 ) )
= ( set_intersection2 @ ( relation_dom @ SV696 ) @ SV583 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3642]) ).
thf(3809,plain,
! [SV584: $i,SV697: $i] :
( ( ~ ( relation @ SV697 )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV697 @ SV584 ) ) @ ( relation_rng @ SV697 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3643]) ).
thf(3810,plain,
! [SV585: $i] :
( ( ( ~ ( empty @ SV585 ) )
= $true )
| ( ( function @ SV585 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3644]) ).
thf(3811,plain,
! [SV586: $i] :
( ( ( ~ ( empty @ SV586 ) )
= $true )
| ( ( relation @ SV586 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3645]) ).
thf(3812,plain,
! [SV587: $i] :
( ( ( ~ ( relation @ SV587 ) )
= $true )
| ( ( ( relation_field @ SV587 )
= ( set_union2 @ ( relation_dom @ SV587 ) @ ( relation_rng @ SV587 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3646]) ).
thf(3813,plain,
! [SV588: $i] :
( ( ( ~ ( function @ SV588 )
| ~ ( relation @ SV588 ) )
= $true )
| ( ( ~ ( one_to_one @ SV588 )
| ( ( function_inverse @ SV588 )
= ( relation_inverse @ SV588 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3647]) ).
thf(3814,plain,
! [SV589: $i] :
( ( ( ~ ( relation @ SV589 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV589 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3648]) ).
thf(3815,plain,
! [SV698: $i,SV590: $i] :
( ( ~ ( relation @ SV590 )
| ~ ( relation @ SV698 )
| ( relation @ ( relation_composition @ SV590 @ SV698 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3649]) ).
thf(3816,plain,
! [SV592: $i] :
( ( ( ~ ( relation @ SV592 ) )
= $true )
| ( ( ! [SY1080: $i] : ( relation @ ( relation_dom_restriction @ SV592 @ SY1080 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3651]) ).
thf(3817,plain,
! [SV593: $i,SV699: $i] :
( ( ~ ( relation @ SV699 )
| ( relation @ ( relation_rng_restriction @ SV593 @ SV699 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3652]) ).
thf(3818,plain,
! [SV700: $i,SV594: $i] :
( ( ~ ( relation @ SV594 )
| ~ ( relation @ SV700 )
| ( relation @ ( set_intersection2 @ SV594 @ SV700 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3653]) ).
thf(3819,plain,
! [SV701: $i,SV595: $i] :
( ( ~ ( relation @ SV595 )
| ~ ( relation @ SV701 )
| ( relation @ ( set_union2 @ SV595 @ SV701 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3654]) ).
thf(3820,plain,
! [SV596: $i] :
( ( ( ( empty @ SV596 )
| ~ ( relation @ SV596 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV596 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3655]) ).
thf(3821,plain,
! [SV597: $i] :
( ( ( ( empty @ SV597 )
| ~ ( relation @ SV597 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV597 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3656]) ).
thf(3822,plain,
! [SV598: $i] :
( ( ( ~ ( relation @ SV598 ) )
= $true )
| ( ( ( relation_inverse @ ( relation_inverse @ SV598 ) )
= SV598 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3657]) ).
thf(3823,plain,
! [SV599: $i] :
( ( ( singleton @ SV599 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3658]) ).
thf(3824,plain,
! [SV702: $i,SV600: $i] :
( ( ~ ( in @ SV600 @ SV702 )
| ( ( set_union2 @ ( singleton @ SV600 ) @ SV702 )
= SV702 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3659]) ).
thf(3825,plain,
! [SV703: $i,SV601: $i] :
( ( ~ ( in @ SV601 @ SV703 )
| ( subset @ SV601 @ ( union @ SV703 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3660]) ).
thf(3826,plain,
! [SV704: $i,SV602: $i] :
( ( ! [SY1348: $i,SY1349: $i] :
( ~ ( subset @ SV602 @ SV704 )
| ~ ( subset @ SY1348 @ SY1349 )
| ( subset @ ( cartesian_product2 @ SV602 @ SY1348 ) @ ( cartesian_product2 @ SV704 @ SY1349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3661]) ).
thf(3827,plain,
! [SV705: $i,SV603: $i] :
( ( ~ ( subset @ SV603 @ SV705 )
| ( ( set_union2 @ SV603 @ SV705 )
= SV705 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3662]) ).
thf(3828,plain,
! [SV604: $i,SV706: $i] :
( ( ~ ( relation @ SV706 )
| ( SV604 = empty_set )
| ~ ( subset @ SV604 @ ( relation_rng @ SV706 ) )
| ( ( relation_inverse_image @ SV706 @ SV604 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3663]) ).
thf(3829,plain,
! [SV707: $i,SV605: $i] :
( ( subset @ ( set_intersection2 @ SV605 @ SV707 ) @ SV605 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3664]) ).
thf(3830,plain,
! [SV708: $i,SV606: $i] :
( ( ! [SY1350: $i] :
( ~ ( subset @ SV606 @ SV708 )
| ~ ( subset @ SV606 @ SY1350 )
| ( subset @ SV606 @ ( set_intersection2 @ SV708 @ SY1350 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3665]) ).
thf(3831,plain,
! [SV709: $i,SV607: $i] :
( ( ! [SY1351: $i] :
( ~ ( subset @ SV607 @ SV709 )
| ~ ( subset @ SV709 @ SY1351 )
| ( subset @ SV607 @ SY1351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3666]) ).
thf(3832,plain,
! [SV608: $i,SV710: $i] :
( ( ~ ( function @ SV710 )
| ~ ( relation @ SV710 )
| ! [SY1352: $i] :
( ~ ( function @ SY1352 )
| ~ ( relation @ SY1352 )
| ~ ( in @ SV608 @ ( relation_dom @ ( relation_composition @ SY1352 @ SV710 ) ) )
| ( ( apply @ ( relation_composition @ SY1352 @ SV710 ) @ SV608 )
= ( apply @ SV710 @ ( apply @ SY1352 @ SV608 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3667]) ).
thf(3833,plain,
! [SV609: $i,SV711: $i] :
( ( ~ ( function @ SV711 )
| ~ ( relation @ SV711 )
| ! [SY1353: $i] :
( ~ ( function @ SY1353 )
| ~ ( relation @ SY1353 )
| ~ ( in @ SV609 @ ( relation_dom @ SV711 ) )
| ( ( apply @ ( relation_composition @ SV711 @ SY1353 ) @ SV609 )
= ( apply @ SY1353 @ ( apply @ SV711 @ SV609 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3668]) ).
thf(3834,plain,
! [SV712: $i,SV610: $i] :
( ( ~ ( subset @ SV610 @ SV712 )
| ! [SY1354: $i] : ( subset @ ( set_intersection2 @ SV610 @ SY1354 ) @ ( set_intersection2 @ SV712 @ SY1354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3669]) ).
thf(3835,plain,
! [SV713: $i,SV611: $i] :
( ( ~ ( subset @ SV611 @ SV713 )
| ( ( set_intersection2 @ SV611 @ SV713 )
= SV611 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3670]) ).
thf(3836,plain,
! [SV714: $i,SV613: $i] :
( ( ~ ( subset @ SV613 @ SV714 )
| ! [SY1355: $i] : ( subset @ ( set_difference @ SV613 @ SY1355 ) @ ( set_difference @ SV714 @ SY1355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3672]) ).
thf(3837,plain,
! [SV614: $i,SV715: $i] :
( ( ~ ( in @ SV715 @ SV614 )
| ( ( apply @ ( identity_relation @ SV614 ) @ SV715 )
= SV715 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3673]) ).
thf(3838,plain,
! [SV716: $i,SV615: $i] :
( ( subset @ ( set_difference @ SV615 @ SV716 ) @ SV615 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3674]) ).
thf(3839,plain,
! [SV717: $i,SV616: $i] :
( ( ( set_union2 @ SV616 @ ( set_difference @ SV717 @ SV616 ) )
= ( set_union2 @ SV616 @ SV717 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3675]) ).
thf(3840,plain,
! [SV617: $i] :
( ( ( ~ ( subset @ SV617 @ empty_set ) )
= $true )
| ( ( SV617 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3676]) ).
thf(3841,plain,
! [SV718: $i,SV618: $i] :
( ( ( set_difference @ ( set_union2 @ SV618 @ SV718 ) @ SV718 )
= ( set_difference @ SV618 @ SV718 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3677]) ).
thf(3842,plain,
! [SV719: $i,SV619: $i] :
( ( ~ ( subset @ SV619 @ SV719 )
| ( SV719
= ( set_union2 @ SV619 @ ( set_difference @ SV719 @ SV619 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3678]) ).
thf(3843,plain,
! [SV720: $i,SV620: $i] :
( ( ~ ( in @ SV620 @ SV720 )
| ( ( set_union2 @ ( singleton @ SV620 ) @ SV720 )
= SV720 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3679]) ).
thf(3844,plain,
! [SV721: $i,SV621: $i] :
( ( ( set_difference @ SV621 @ ( set_difference @ SV621 @ SV721 ) )
= ( set_intersection2 @ SV621 @ SV721 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3680]) ).
thf(3845,plain,
! [SV622: $i] :
( ( ( ~ ( relation @ SV622 ) )
= $true )
| ( ( ( in @ ( ordered_pair @ ( sK46_B @ SV622 ) @ ( sK47_SY415 @ SV622 ) ) @ SV622 )
| ( SV622 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3681]) ).
thf(3846,plain,
! [SV623: $i,SV722: $i] :
( ( ~ ( proper_subset @ SV722 @ SV623 )
| ~ ( subset @ SV623 @ SV722 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3682]) ).
thf(3847,plain,
! [SV624: $i,SV723: $i] :
( ( ! [SY1356: $i] :
( ~ ( disjoint @ SV723 @ SY1356 )
| ~ ( subset @ SV624 @ SV723 )
| ( disjoint @ SV624 @ SY1356 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3683]) ).
thf(3848,plain,
! [SV724: $i,SV625: $i] :
( ( ~ ( subset @ ( singleton @ SV625 ) @ ( singleton @ SV724 ) )
| ( SV625 = SV724 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3684]) ).
thf(3849,plain,
! [SV725: $i,SV626: $i] :
( ( subset @ SV626 @ ( set_union2 @ SV626 @ SV725 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3685]) ).
thf(3850,plain,
! [SV726: $i,SV627: $i] :
( ( ! [SY1357: $i] :
( ~ ( subset @ SV627 @ SV726 )
| ~ ( subset @ SY1357 @ SV726 )
| ( subset @ ( set_union2 @ SV627 @ SY1357 ) @ SV726 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3686]) ).
thf(3851,plain,
! [SV727: $i,SV628: $i] :
( ( ~ ( in @ SV628 @ SV727 )
| ( subset @ SV628 @ ( union @ SV727 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3687]) ).
thf(3852,plain,
! [SV629: $i,SV728: $i] :
( ( ~ ( relation @ SV728 )
| ( ( relation_dom_restriction @ SV728 @ SV629 )
= ( relation_composition @ ( identity_relation @ SV629 ) @ SV728 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3688]) ).
thf(3853,plain,
! [SV729: $i,SV630: $i] :
( ( ~ ( in @ SV630 @ SV729 )
| ~ ( in @ SV729 @ SV630 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3689]) ).
thf(3854,plain,
! [SV730: $i,SV631: $i] :
( ( ( set_union2 @ SV631 @ SV730 )
= ( set_union2 @ SV730 @ SV631 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3690]) ).
thf(3855,plain,
! [SV731: $i,SV632: $i] :
( ( ( set_intersection2 @ SV632 @ SV731 )
= ( set_intersection2 @ SV731 @ SV632 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3691]) ).
thf(3856,plain,
! [SV633: $i] :
( ( empty @ ( powerset @ SV633 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3692]) ).
thf(3857,plain,
! [SV732: $i,SV634: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV634 @ SV732 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3693]) ).
thf(3858,plain,
! [SV635: $i] :
( ( empty @ ( singleton @ SV635 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3694]) ).
thf(3859,plain,
! [SV636: $i] :
( ( ( empty @ SV636 )
= $true )
| ( ( ! [SY1125: $i] :
~ ( empty @ ( set_union2 @ SV636 @ SY1125 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3695]) ).
thf(3860,plain,
! [SV733: $i,SV637: $i] :
( ( ~ ( empty @ ( unordered_pair @ SV637 @ SV733 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3696]) ).
thf(3861,plain,
! [SV638: $i] :
( ( ( empty @ SV638 )
= $true )
| ( ( ! [SY1127: $i] :
~ ( empty @ ( set_union2 @ SY1127 @ SV638 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3697]) ).
thf(3862,plain,
! [SV734: $i,SV639: $i] :
( ( ( empty @ SV639 )
| ( empty @ SV734 )
| ~ ( empty @ ( cartesian_product2 @ SV639 @ SV734 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3698]) ).
thf(3863,plain,
! [SV735: $i,SV644: $i] :
( ( ~ ( in @ SV644 @ SV735 )
| ( element @ SV644 @ SV735 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3704]) ).
thf(3864,plain,
! [SV736: $i,SV646: $i] :
( ( ~ ( element @ SV646 @ SV736 )
| ( empty @ SV736 )
| ( in @ SV646 @ SV736 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3706]) ).
thf(3865,plain,
! [SV649: $i] :
( ( ( ~ ( empty @ SV649 ) )
= $true )
| ( ( SV649 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3709]) ).
thf(3866,plain,
! [SV650: $i,SV737: $i] :
( ( ~ ( empty @ SV737 )
| ~ ( in @ SV650 @ SV737 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3710]) ).
thf(3867,plain,
! [SV738: $i,SV651: $i] :
( ( ( SV651 = SV738 )
| ~ ( empty @ SV651 )
| ~ ( empty @ SV738 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3711]) ).
thf(3868,plain,
! [SV652: $i] :
( ( ~ ! [SY1133: $i,SY1134: $i] :
( ~ ( ~ ( ~ ( in @ ( sK17_D @ SY1134 @ SY1133 @ SV652 ) @ SV652 )
| ~ ( in @ ( sK17_D @ SY1134 @ SY1133 @ SV652 ) @ SY1133 )
| ~ ( in @ ( sK17_D @ SY1134 @ SY1133 @ SV652 ) @ SY1134 ) )
| ~ ~ ( ~ ( ( in @ ( sK17_D @ SY1134 @ SY1133 @ SV652 ) @ SV652 )
| ( in @ ( sK17_D @ SY1134 @ SY1133 @ SV652 ) @ SY1134 ) )
| ~ ( ( in @ ( sK17_D @ SY1134 @ SY1133 @ SV652 ) @ SY1133 )
| ( in @ ( sK17_D @ SY1134 @ SY1133 @ SV652 ) @ SY1134 ) ) ) )
| ( SY1134
= ( set_intersection2 @ SV652 @ SY1133 ) ) )
| ~ ! [SY1135: $i,SY1136: $i] :
( ( SY1136
!= ( set_intersection2 @ SV652 @ SY1135 ) )
| ~ ( ~ ! [SY1137: $i] :
( ~ ( in @ SY1137 @ SV652 )
| ~ ( in @ SY1137 @ SY1135 )
| ( in @ SY1137 @ SY1136 ) )
| ~ ~ ( ~ ! [SY1138: $i] :
( ~ ( in @ SY1138 @ SY1136 )
| ( in @ SY1138 @ SV652 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1136 )
| ( in @ SX3 @ SY1135 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3713]) ).
thf(3869,plain,
( ( ~ ( empty @ sK57_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3714]) ).
thf(3870,plain,
( ( ~ ( relation @ sK57_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3714]) ).
thf(3871,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( ( relation_rng @ SX0 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3715]) ).
thf(3872,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( ( relation_dom @ SX0 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3715]) ).
thf(3873,plain,
! [SV653: $i] :
( ( ( ~ ( function @ SV653 )
| ~ ( relation @ SV653 ) )
= $true )
| ( ( ~ ( one_to_one @ SV653 )
| ~ ( ~ ! [SY1140: $i] :
( ~ ( function @ SY1140 )
| ~ ( relation @ SY1140 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SY1140 @ SV653 )
= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ( ( sK70_C @ SY1140 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY1140 @ SV653 )
= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY1140 @ SV653 )
= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ( ( sK71_SY424 @ SY1140 @ SV653 )
!= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK70_C @ SY1140 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK71_SY424 @ SY1140 @ SV653 )
!= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY1140 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK70_C @ SY1140 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SY1140 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SY1140 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK71_SY424 @ SY1140 @ SV653 )
!= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ( ( relation_dom @ SY1140 )
!= ( relation_rng @ SV653 ) )
| ( SY1140
= ( function_inverse @ SV653 ) ) )
| ~ ~ ( ~ ! [SY1141: $i] :
( ~ ( function @ SY1141 )
| ~ ( relation @ SY1141 )
| ( SY1141
!= ( function_inverse @ SV653 ) )
| ~ ( ~ ~ ( ~ ! [SY1142: $i,SY1143: $i] :
( ( SY1143
!= ( apply @ SY1141 @ SY1142 ) )
| ~ ( in @ SY1142 @ ( relation_rng @ SV653 ) )
| ( SY1142
= ( apply @ SV653 @ SY1143 ) ) )
| ~ ! [SY1144: $i,SY1145: $i] :
( ( SY1145
!= ( apply @ SY1141 @ SY1144 ) )
| ~ ( in @ SY1144 @ ( relation_rng @ SV653 ) )
| ( in @ SY1145 @ ( relation_dom @ SV653 ) ) ) )
| ~ ~ ( ~ ! [SY1146: $i,SY1147: $i] :
( ( SY1146
!= ( apply @ SV653 @ SY1147 ) )
| ~ ( in @ SY1147 @ ( relation_dom @ SV653 ) )
| ( SY1147
= ( apply @ SY1141 @ SY1146 ) ) )
| ~ ! [SY1148: $i] :
( ! [SY1149: $i] :
( ( SY1148
!= ( apply @ SV653 @ SY1149 ) )
| ~ ( in @ SY1149 @ ( relation_dom @ SV653 ) ) )
| ( in @ SY1148 @ ( relation_rng @ SV653 ) ) ) ) ) )
| ~ ! [SY1150: $i] :
( ~ ( function @ SY1150 )
| ~ ( relation @ SY1150 )
| ( SY1150
!= ( function_inverse @ SV653 ) )
| ( ( relation_dom @ SY1150 )
= ( relation_rng @ SV653 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3716]) ).
thf(3874,plain,
( ( ~ ~ ( ~ ( function @ sK54_A )
| ~ ( relation @ sK54_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3717]) ).
thf(3875,plain,
( ( ~ ( one_to_one @ sK54_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3717]) ).
thf(3876,plain,
( ( ~ ~ ( empty @ sK55_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3718]) ).
thf(3877,plain,
( ( ~ ( relation @ sK55_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3718]) ).
thf(3878,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)],[3719]) ).
thf(3879,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)],[3719]) ).
thf(3880,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3720]) ).
thf(3881,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3720]) ).
thf(3882,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3721]) ).
thf(3883,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)],[3721]) ).
thf(3884,plain,
( ( ~ ! [SX0: $i] :
( ( relation_dom @ ( identity_relation @ SX0 ) )
= SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3722]) ).
thf(3885,plain,
( ( ~ ! [SX0: $i] :
( ( relation_rng @ ( identity_relation @ SX0 ) )
= SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3722]) ).
thf(3886,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3723]) ).
thf(3887,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3723]) ).
thf(3888,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3724]) ).
thf(3889,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3724]) ).
thf(3890,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3725]) ).
thf(3891,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3725]) ).
thf(3892,plain,
! [SV739: $i,SV654: $i] :
( ( ~ ( ~ ! [SY1358: $i,SY1359: $i] :
( ~ ( relation @ SY1359 )
| ~ ( in @ SV654 @ SY1358 )
| ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ SY1359 )
| ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SY1358 ) @ SY1359 ) ) )
| ~ ~ ( ~ ! [SY1360: $i,SY1361: $i] :
( ~ ( relation @ SY1361 )
| ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SY1360 ) @ SY1361 ) )
| ( in @ SV654 @ SY1360 ) )
| ~ ! [SY1362: $i,SY1363: $i] :
( ~ ( relation @ SY1363 )
| ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SY1362 ) @ SY1363 ) )
| ( in @ ( ordered_pair @ SV654 @ SV739 ) @ SY1363 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3726]) ).
thf(3893,plain,
! [SV655: $i,SV740: $i] :
( ( ~ ( relation @ SV740 )
| ~ ( ~ ! [SY1364: $i] :
( ~ ( relation @ SY1364 )
| ~ ( ~ ( ~ ( in @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) @ SV655 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY1364 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) ) @ SV740 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY1364 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) ) @ SY1364 ) )
| ~ ~ ( ~ ( ( in @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) @ SV655 )
| ( in @ ( ordered_pair @ ( sK40_D @ SY1364 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) ) @ SY1364 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SY1364 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) ) @ SV740 )
| ( in @ ( ordered_pair @ ( sK40_D @ SY1364 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) ) @ SY1364 ) ) ) )
| ( SY1364
= ( relation_rng_restriction @ SV655 @ SV740 ) ) )
| ~ ! [SY1365: $i] :
( ~ ( relation @ SY1365 )
| ( SY1365
!= ( relation_rng_restriction @ SV655 @ SV740 ) )
| ~ ( ~ ! [SY1366: $i,SY1367: $i] :
( ~ ( in @ SY1367 @ SV655 )
| ~ ( in @ ( ordered_pair @ SY1366 @ SY1367 ) @ SV740 )
| ( in @ ( ordered_pair @ SY1366 @ SY1367 ) @ SY1365 ) )
| ~ ~ ( ~ ! [SY1163: $i,SY1164: $i] :
( ~ ( in @ ( ordered_pair @ SY1163 @ SY1164 ) @ SY1365 )
| ( in @ SY1164 @ SV655 ) )
| ~ ! [SY1370: $i,SY1371: $i] :
( ~ ( in @ ( ordered_pair @ SY1370 @ SY1371 ) @ SY1365 )
| ( in @ ( ordered_pair @ SY1370 @ SY1371 ) @ SV740 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3727]) ).
thf(3894,plain,
( ( ~ ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3728]) ).
thf(3895,plain,
( ( ~ ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3728]) ).
thf(3896,plain,
! [SV741: $i,SV656: $i] :
( ( ~ ( ~ ! [SY1372: $i] :
( ! [SY1373: $i] :
( ( ordered_pair @ SV656 @ SV741 )
!= ( ordered_pair @ SY1372 @ SY1373 ) )
| ( SV656 = SY1372 ) )
| ~ ! [SY1374: $i,SY1375: $i] :
( ( ( ordered_pair @ SV656 @ SV741 )
!= ( ordered_pair @ SY1374 @ SY1375 ) )
| ( SV741 = SY1375 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3729]) ).
thf(3897,plain,
! [SV657: $i] :
( ( ( ~ ( relation @ SV657 ) )
= $true )
| ( ( ~ ( ~ ! [SY1172: $i,SY1173: $i] :
( ~ ( ~ ( ! [SY1174: $i] :
( ~ ( in @ ( ordered_pair @ ( sK35_D @ SY1173 @ SY1172 @ SV657 ) @ SY1174 ) @ SV657 )
| ~ ( in @ SY1174 @ SY1172 ) )
| ~ ( in @ ( sK35_D @ SY1173 @ SY1172 @ SV657 ) @ SY1173 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SY1173 @ SY1172 @ SV657 ) @ ( sK36_SY409 @ SY1173 @ SY1172 @ SV657 ) ) @ SV657 )
| ~ ( in @ ( sK36_SY409 @ SY1173 @ SY1172 @ SV657 ) @ SY1172 ) )
| ( in @ ( sK35_D @ SY1173 @ SY1172 @ SV657 ) @ SY1173 ) ) )
| ( SY1173
= ( relation_inverse_image @ SV657 @ SY1172 ) ) )
| ~ ! [SY1175: $i,SY1176: $i] :
( ( SY1176
!= ( relation_inverse_image @ SV657 @ SY1175 ) )
| ~ ( ~ ! [SY1177: $i] :
( ! [SY1178: $i] :
( ~ ( in @ ( ordered_pair @ SY1177 @ SY1178 ) @ SV657 )
| ~ ( in @ SY1178 @ SY1175 ) )
| ( in @ SY1177 @ SY1176 ) )
| ~ ! [SY1179: $i] :
( ~ ( in @ SY1179 @ SY1176 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1179 @ ( sK34_E @ SY1179 @ SY1176 @ SY1175 @ SV657 ) ) @ SV657 )
| ~ ( in @ ( sK34_E @ SY1179 @ SY1176 @ SY1175 @ SV657 ) @ SY1175 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3730]) ).
thf(3898,plain,
! [SV658: $i] :
( ( ( ~ ( relation @ SV658 ) )
= $true )
| ( ( ~ ( ~ ! [SY1180: $i,SY1181: $i] :
( ~ ( ~ ( ! [SY1182: $i] :
( ~ ( in @ ( ordered_pair @ SY1182 @ ( sK38_D @ SY1181 @ SY1180 @ SV658 ) ) @ SV658 )
| ~ ( in @ SY1182 @ SY1180 ) )
| ~ ( in @ ( sK38_D @ SY1181 @ SY1180 @ SV658 ) @ SY1181 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SY1181 @ SY1180 @ SV658 ) @ ( sK38_D @ SY1181 @ SY1180 @ SV658 ) ) @ SV658 )
| ~ ( in @ ( sK39_SY411 @ SY1181 @ SY1180 @ SV658 ) @ SY1180 ) )
| ( in @ ( sK38_D @ SY1181 @ SY1180 @ SV658 ) @ SY1181 ) ) )
| ( SY1181
= ( relation_image @ SV658 @ SY1180 ) ) )
| ~ ! [SY1183: $i,SY1184: $i] :
( ( SY1184
!= ( relation_image @ SV658 @ SY1183 ) )
| ~ ( ~ ! [SY1185: $i] :
( ! [SY1186: $i] :
( ~ ( in @ ( ordered_pair @ SY1186 @ SY1185 ) @ SV658 )
| ~ ( in @ SY1186 @ SY1183 ) )
| ( in @ SY1185 @ SY1184 ) )
| ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ SY1184 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SY1187 @ SY1184 @ SY1183 @ SV658 ) @ SY1187 ) @ SV658 )
| ~ ( in @ ( sK37_E @ SY1187 @ SY1184 @ SY1183 @ SV658 ) @ SY1183 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3731]) ).
thf(3899,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3732]) ).
thf(3900,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)],[3732]) ).
thf(3901,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3733]) ).
thf(3902,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3733]) ).
thf(3903,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)],[3734]) ).
thf(3904,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3734]) ).
thf(3905,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK69_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK69_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3735]) ).
thf(3906,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK67_C @ SX1 @ SX0 ) @ ( sK68_SY421 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3735]) ).
thf(3907,plain,
! [SV659: $i] :
( ( ~ ! [SY1188: $i,SY1189: $i] :
( ~ ( in @ SV659 @ SY1189 )
| ~ ( in @ SY1188 @ SY1189 )
| ( subset @ ( unordered_pair @ SV659 @ SY1188 ) @ SY1189 ) )
| ~ ~ ( ~ ! [SY1190: $i,SY1191: $i] :
( ~ ( subset @ ( unordered_pair @ SV659 @ SY1190 ) @ SY1191 )
| ( in @ SV659 @ SY1191 ) )
| ~ ! [SY1192: $i,SY1193: $i] :
( ~ ( subset @ ( unordered_pair @ SV659 @ SY1192 ) @ SY1193 )
| ( in @ SY1192 @ SY1193 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3736]) ).
thf(3908,plain,
! [SV660: $i] :
( ( ( ~ ( relation @ SV660 ) )
= $true )
| ( ( ! [SY1194: $i] :
( ~ ( relation @ SY1194 )
| ~ ( ~ ! [SY1195: $i] :
( ~ ( relation @ SY1195 )
| ~ ( ~ ( ! [SY1196: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY1195 @ SY1194 @ SV660 ) @ SY1196 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1196 @ ( sK9_SY391 @ SY1195 @ SY1194 @ SV660 ) ) @ SY1194 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SY1195 @ SY1194 @ SV660 ) @ ( sK9_SY391 @ SY1195 @ SY1194 @ SV660 ) ) @ SY1195 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY1195 @ SY1194 @ SV660 ) @ ( sK10_SY395 @ SY1195 @ SY1194 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SY1195 @ SY1194 @ SV660 ) @ ( sK9_SY391 @ SY1195 @ SY1194 @ SV660 ) ) @ SY1194 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SY1195 @ SY1194 @ SV660 ) @ ( sK9_SY391 @ SY1195 @ SY1194 @ SV660 ) ) @ SY1195 ) ) )
| ( SY1195
= ( relation_composition @ SV660 @ SY1194 ) ) )
| ~ ! [SY1197: $i] :
( ~ ( relation @ SY1197 )
| ( SY1197
!= ( relation_composition @ SV660 @ SY1194 ) )
| ~ ( ~ ! [SY1198: $i,SY1199: $i] :
( ! [SY1200: $i] :
( ~ ( in @ ( ordered_pair @ SY1198 @ SY1200 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1200 @ SY1199 ) @ SY1194 ) )
| ( in @ ( ordered_pair @ SY1198 @ SY1199 ) @ SY1197 ) )
| ~ ! [SY1201: $i,SY1202: $i] :
( ~ ( in @ ( ordered_pair @ SY1201 @ SY1202 ) @ SY1197 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1201 @ ( sK7_F @ SY1202 @ SY1201 @ SY1197 @ SY1194 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY1202 @ SY1201 @ SY1197 @ SY1194 @ SV660 ) @ SY1202 ) @ SY1194 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3737]) ).
thf(3909,plain,
( ( ~ ( relation @ sK53_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3738]) ).
thf(3910,plain,
( ( ~ ( relation_empty_yielding @ sK53_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3738]) ).
thf(3911,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK29_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3739]) ).
thf(3912,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3739]) ).
thf(3913,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3740]) ).
thf(3914,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3740]) ).
thf(3915,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3741]) ).
thf(3916,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3741]) ).
thf(3917,plain,
! [SV661: $i] :
( ( ( ~ ( relation @ SV661 ) )
= $true )
| ( ( ~ ( ~ ! [SY1203: $i] :
( ~ ( ~ ( ! [SY1204: $i] :
~ ( in @ ( ordered_pair @ SY1204 @ ( sK60_C @ SY1203 @ SV661 ) ) @ SV661 )
| ~ ( in @ ( sK60_C @ SY1203 @ SV661 ) @ SY1203 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK61_SY417 @ SY1203 @ SV661 ) @ ( sK60_C @ SY1203 @ SV661 ) ) @ SV661 )
| ( in @ ( sK60_C @ SY1203 @ SV661 ) @ SY1203 ) ) )
| ( SY1203
= ( relation_rng @ SV661 ) ) )
| ~ ! [SY1205: $i] :
( ( SY1205
!= ( relation_rng @ SV661 ) )
| ~ ( ~ ! [SY1206: $i] :
( ! [SY1207: $i] :
~ ( in @ ( ordered_pair @ SY1207 @ SY1206 ) @ SV661 )
| ( in @ SY1206 @ SY1205 ) )
| ~ ! [SY1208: $i] :
( ~ ( in @ SY1208 @ SY1205 )
| ( in @ ( ordered_pair @ ( sK59_D @ SY1208 @ SY1205 @ SV661 ) @ SY1208 ) @ SV661 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3742]) ).
thf(3918,plain,
! [SV662: $i] :
( ( ~ ! [SY1209: $i,SY1210: $i] :
( ~ ( ~ ( ~ ( in @ ( sK13_D @ SY1210 @ SY1209 @ SV662 ) @ SV662 )
| ( in @ ( sK13_D @ SY1210 @ SY1209 @ SV662 ) @ SY1209 )
| ~ ( in @ ( sK13_D @ SY1210 @ SY1209 @ SV662 ) @ SY1210 ) )
| ~ ~ ( ~ ( ( in @ ( sK13_D @ SY1210 @ SY1209 @ SV662 ) @ SV662 )
| ( in @ ( sK13_D @ SY1210 @ SY1209 @ SV662 ) @ SY1210 ) )
| ~ ( ~ ( in @ ( sK13_D @ SY1210 @ SY1209 @ SV662 ) @ SY1209 )
| ( in @ ( sK13_D @ SY1210 @ SY1209 @ SV662 ) @ SY1210 ) ) ) )
| ( SY1210
= ( set_difference @ SV662 @ SY1209 ) ) )
| ~ ! [SY1211: $i,SY1212: $i] :
( ( SY1212
!= ( set_difference @ SV662 @ SY1211 ) )
| ~ ( ~ ! [SY1213: $i] :
( ~ ( in @ SY1213 @ SV662 )
| ( in @ SY1213 @ SY1211 )
| ( in @ SY1213 @ SY1212 ) )
| ~ ~ ( ~ ! [SY1214: $i] :
( ~ ( in @ SY1214 @ SY1212 )
| ( in @ SY1214 @ SV662 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1212 )
| ~ ( in @ SX3 @ SY1211 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3743]) ).
thf(3919,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)],[3744]) ).
thf(3920,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)],[3744]) ).
thf(3921,plain,
! [SV663: $i] :
( ( ~ ! [SY1216: $i,SY1217: $i] :
( ~ ( relation @ SY1217 )
| ~ ( in @ SV663 @ SY1216 )
| ~ ( in @ SV663 @ ( relation_rng @ SY1217 ) )
| ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SY1216 @ SY1217 ) ) ) )
| ~ ~ ( ~ ! [SY1218: $i,SY1219: $i] :
( ~ ( relation @ SY1219 )
| ~ ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SY1218 @ SY1219 ) ) )
| ( in @ SV663 @ SY1218 ) )
| ~ ! [SY1220: $i,SY1221: $i] :
( ~ ( relation @ SY1221 )
| ~ ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SY1220 @ SY1221 ) ) )
| ( in @ SV663 @ ( relation_rng @ SY1221 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3745]) ).
thf(3922,plain,
! [SV664: $i] :
( ( ( ~ ( function @ SV664 )
| ~ ( relation @ SV664 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY1222: $i] :
( ~ ( in @ SY1222 @ ( relation_dom @ SV664 ) )
| ! [SY1223: $i] :
( ( SY1223
!= ( apply @ SV664 @ SY1222 ) )
| ( in @ ( ordered_pair @ SY1222 @ SY1223 ) @ SV664 ) ) )
| ~ ! [SY1224: $i] :
( ~ ( in @ SY1224 @ ( relation_dom @ SV664 ) )
| ! [SY1225: $i] :
( ~ ( in @ ( ordered_pair @ SY1224 @ SY1225 ) @ SV664 )
| ( SY1225
= ( apply @ SV664 @ SY1224 ) ) ) ) )
| ~ ~ ( ~ ! [SY1226: $i] :
( ( in @ SY1226 @ ( relation_dom @ SV664 ) )
| ! [SY1227: $i] :
( ( SY1227
!= ( apply @ SV664 @ SY1226 ) )
| ( SY1227 = empty_set ) ) )
| ~ ! [SY1228: $i] :
( ( in @ SY1228 @ ( relation_dom @ SV664 ) )
| ! [SY1229: $i] :
( ( SY1229 != empty_set )
| ( SY1229
= ( apply @ SV664 @ SY1228 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3746]) ).
thf(3923,plain,
! [SV665: $i] :
( ( ( ~ ( relation @ SV665 ) )
= $true )
| ( ( ~ ( ~ ! [SY1230: $i] :
( ~ ( relation @ SY1230 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SY1230 @ SV665 ) @ ( sK20_SY399 @ SY1230 @ SV665 ) ) @ SV665 )
| ~ ~ ( in @ ( ordered_pair @ ( sK19_C @ SY1230 @ SV665 ) @ ( sK20_SY399 @ SY1230 @ SV665 ) ) @ SY1230 ) )
| ( subset @ SV665 @ SY1230 ) )
| ~ ! [SY1231: $i] :
( ~ ( relation @ SY1231 )
| ~ ( subset @ SV665 @ SY1231 )
| ! [SY1232: $i,SY1233: $i] :
( ~ ( in @ ( ordered_pair @ SY1232 @ SY1233 ) @ SV665 )
| ( in @ ( ordered_pair @ SY1232 @ SY1233 ) @ SY1231 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3747]) ).
thf(3924,plain,
! [SV666: $i,SV742: $i] :
( ( ~ ( function @ SV742 )
| ~ ( relation @ SV742 )
| ~ ( ~ ! [SY1376: $i] :
( ~ ( function @ SY1376 )
| ~ ( relation @ SY1376 )
| ~ ( in @ SV666 @ ( relation_dom @ SY1376 ) )
| ~ ( in @ ( apply @ SY1376 @ SV666 ) @ ( relation_dom @ SV742 ) )
| ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1376 @ SV742 ) ) ) )
| ~ ~ ( ~ ! [SY1377: $i] :
( ~ ( function @ SY1377 )
| ~ ( relation @ SY1377 )
| ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1377 @ SV742 ) ) )
| ( in @ SV666 @ ( relation_dom @ SY1377 ) ) )
| ~ ! [SY1378: $i] :
( ~ ( function @ SY1378 )
| ~ ( relation @ SY1378 )
| ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1378 @ SV742 ) ) )
| ( in @ ( apply @ SY1378 @ SV666 ) @ ( relation_dom @ SV742 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3748]) ).
thf(3925,plain,
! [SV667: $i] :
( ( ~ ! [SY1238: $i,SY1239: $i] :
( ~ ( relation @ SY1239 )
| ! [SY1240: $i] :
( ~ ( in @ SY1240 @ ( relation_rng @ SY1239 ) )
| ~ ( in @ ( ordered_pair @ SV667 @ SY1240 ) @ SY1239 )
| ~ ( in @ SY1240 @ SY1238 ) )
| ( in @ SV667 @ ( relation_inverse_image @ SY1239 @ SY1238 ) ) )
| ~ ! [SY1241: $i,SY1242: $i] :
( ~ ( relation @ SY1242 )
| ~ ( in @ SV667 @ ( relation_inverse_image @ SY1242 @ SY1241 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK51_D @ SY1242 @ SY1241 @ SV667 ) @ ( relation_rng @ SY1242 ) )
| ~ ( in @ ( ordered_pair @ SV667 @ ( sK51_D @ SY1242 @ SY1241 @ SV667 ) ) @ SY1242 ) )
| ~ ( in @ ( sK51_D @ SY1242 @ SY1241 @ SV667 ) @ SY1241 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3749]) ).
thf(3926,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK49_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK49_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3750]) ).
thf(3927,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3750]) ).
thf(3928,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3751]) ).
thf(3929,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3751]) ).
thf(3930,plain,
! [SV668: $i] :
( ( ~ ! [SY1243: $i,SY1244: $i] :
( ~ ( relation @ SY1244 )
| ~ ( in @ SV668 @ SY1243 )
| ~ ( in @ SV668 @ ( relation_dom @ SY1244 ) )
| ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SY1244 @ SY1243 ) ) ) )
| ~ ~ ( ~ ! [SY1245: $i,SY1246: $i] :
( ~ ( relation @ SY1246 )
| ~ ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SY1246 @ SY1245 ) ) )
| ( in @ SV668 @ SY1245 ) )
| ~ ! [SY1247: $i,SY1248: $i] :
( ~ ( relation @ SY1248 )
| ~ ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SY1248 @ SY1247 ) ) )
| ( in @ SV668 @ ( relation_dom @ SY1248 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3752]) ).
thf(3931,plain,
! [SV669: $i] :
( ( ~ ! [SY1249: $i,SY1250: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY1250 @ SY1249 @ SV669 ) @ SY1250 )
| ~ ( in @ ( sK26_D @ SY1250 @ SY1249 @ SV669 ) @ SV669 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY1250 @ SY1249 @ SV669 ) @ SY1250 )
| ~ ( in @ ( sK26_D @ SY1250 @ SY1249 @ SV669 ) @ SY1249 ) ) )
| ~ ( ( in @ ( sK26_D @ SY1250 @ SY1249 @ SV669 ) @ SY1250 )
| ( in @ ( sK26_D @ SY1250 @ SY1249 @ SV669 ) @ SV669 )
| ( in @ ( sK26_D @ SY1250 @ SY1249 @ SV669 ) @ SY1249 ) ) )
| ( SY1250
= ( set_union2 @ SV669 @ SY1249 ) ) )
| ~ ! [SY1251: $i,SY1252: $i] :
( ( SY1252
!= ( set_union2 @ SV669 @ SY1251 ) )
| ~ ( ~ ! [SY1253: $i] :
( ~ ( in @ SY1253 @ SY1252 )
| ( in @ SY1253 @ SV669 )
| ( in @ SY1253 @ SY1251 ) )
| ~ ~ ( ~ ! [SY1254: $i] :
( ~ ( in @ SY1254 @ SV669 )
| ( in @ SY1254 @ SY1252 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1251 )
| ( in @ SX3 @ SY1252 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3753]) ).
thf(3932,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY406 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ ( sK33_SY406 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK31_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)],[3754]) ).
thf(3933,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)],[3754]) ).
thf(3934,plain,
! [SV670: $i] :
( ( ~ ! [SY1256: $i,SY1257: $i] :
( ~ ( ~ ( ! [SY1258: $i,SY1259: $i] :
( ~ ( in @ SY1258 @ SV670 )
| ~ ( in @ SY1259 @ SY1256 )
| ( ( sK23_D @ SY1257 @ SY1256 @ SV670 )
!= ( ordered_pair @ SY1258 @ SY1259 ) ) )
| ~ ( in @ ( sK23_D @ SY1257 @ SY1256 @ SV670 ) @ SY1257 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY403 @ SY1257 @ SY1256 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK25_SY405 @ SY1257 @ SY1256 @ SV670 ) @ SY1256 ) )
| ( ( sK23_D @ SY1257 @ SY1256 @ SV670 )
!= ( ordered_pair @ ( sK24_SY403 @ SY1257 @ SY1256 @ SV670 ) @ ( sK25_SY405 @ SY1257 @ SY1256 @ SV670 ) ) ) )
| ( in @ ( sK23_D @ SY1257 @ SY1256 @ SV670 ) @ SY1257 ) ) )
| ( SY1257
= ( cartesian_product2 @ SV670 @ SY1256 ) ) )
| ~ ! [SY1260: $i,SY1261: $i] :
( ( SY1261
!= ( cartesian_product2 @ SV670 @ SY1260 ) )
| ~ ( ~ ! [SY1262: $i] :
( ! [SY1263: $i,SY1264: $i] :
( ~ ( in @ SY1263 @ SV670 )
| ~ ( in @ SY1264 @ SY1260 )
| ( SY1262
!= ( ordered_pair @ SY1263 @ SY1264 ) ) )
| ( in @ SY1262 @ SY1261 ) )
| ~ ! [SY1265: $i] :
( ~ ( in @ SY1265 @ SY1261 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY1265 @ SY1261 @ SY1260 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK22_SY400 @ SY1265 @ SY1261 @ SY1260 @ SV670 ) @ SY1260 ) )
| ( SY1265
!= ( ordered_pair @ ( sK21_E @ SY1265 @ SY1261 @ SY1260 @ SV670 ) @ ( sK22_SY400 @ SY1265 @ SY1261 @ SY1260 @ SV670 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3755]) ).
thf(3935,plain,
! [SV671: $i] :
( ( ~ ! [SY1266: $i,SY1267: $i] :
( ~ ( function @ SY1267 )
| ~ ( relation @ SY1267 )
| ( SY1266
!= ( apply @ SY1267 @ SV671 ) )
| ~ ( in @ SV671 @ ( relation_dom @ SY1267 ) )
| ( in @ ( ordered_pair @ SV671 @ SY1266 ) @ SY1267 ) )
| ~ ~ ( ~ ! [SY1268: $i,SY1269: $i] :
( ~ ( function @ SY1269 )
| ~ ( relation @ SY1269 )
| ~ ( in @ ( ordered_pair @ SV671 @ SY1268 ) @ SY1269 )
| ( SY1268
= ( apply @ SY1269 @ SV671 ) ) )
| ~ ! [SY1270: $i,SY1271: $i] :
( ~ ( function @ SY1271 )
| ~ ( relation @ SY1271 )
| ~ ( in @ ( ordered_pair @ SV671 @ SY1270 ) @ SY1271 )
| ( in @ SV671 @ ( relation_dom @ SY1271 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3756]) ).
thf(3936,plain,
! [SV672: $i] :
( ( ( ~ ( relation @ SV672 ) )
= $true )
| ( ( ~ ( ~ ! [SY1272: $i] :
( ~ ( relation @ SY1272 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SY1272 @ SV672 ) @ ( sK12_SY396 @ SY1272 @ SV672 ) ) @ SY1272 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SY1272 @ SV672 ) @ ( sK11_C @ SY1272 @ SV672 ) ) @ SV672 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_C @ SY1272 @ SV672 ) @ ( sK12_SY396 @ SY1272 @ SV672 ) ) @ SY1272 )
| ( in @ ( ordered_pair @ ( sK12_SY396 @ SY1272 @ SV672 ) @ ( sK11_C @ SY1272 @ SV672 ) ) @ SV672 ) ) )
| ( SY1272
= ( relation_inverse @ SV672 ) ) )
| ~ ! [SY1273: $i] :
( ~ ( relation @ SY1273 )
| ( SY1273
!= ( relation_inverse @ SV672 ) )
| ~ ( ~ ! [SY1274: $i,SY1275: $i] :
( ~ ( in @ ( ordered_pair @ SY1274 @ SY1275 ) @ SY1273 )
| ( in @ ( ordered_pair @ SY1275 @ SY1274 ) @ SV672 ) )
| ~ ! [SY1276: $i,SY1277: $i] :
( ~ ( in @ ( ordered_pair @ SY1277 @ SY1276 ) @ SV672 )
| ( in @ ( ordered_pair @ SY1276 @ SY1277 ) @ SY1273 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3757]) ).
thf(3937,plain,
( ( ~ ( function @ sK58_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3758]) ).
thf(3938,plain,
( ( ~ ( relation @ sK58_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3758]) ).
thf(3939,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3759]) ).
thf(3940,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3759]) ).
thf(3941,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( function @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3760]) ).
thf(3942,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3760]) ).
thf(3943,plain,
! [SV673: $i] :
( ( ~ ! [SY1278: $i,SY1279: $i] :
( ~ ( relation @ SY1279 )
| ~ ( in @ ( ordered_pair @ SV673 @ SY1278 ) @ SY1279 )
| ( in @ SV673 @ ( relation_dom @ SY1279 ) ) )
| ~ ! [SY1280: $i,SY1281: $i] :
( ~ ( relation @ SY1281 )
| ~ ( in @ ( ordered_pair @ SV673 @ SY1280 ) @ SY1281 )
| ( in @ SY1280 @ ( relation_rng @ SY1281 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3761]) ).
thf(3944,plain,
! [SV743: $i,SV674: $i] :
( ( ~ ( ~ ! [SY1379: $i,SY1380: $i] :
( ~ ( in @ SV674 @ SY1379 )
| ~ ( in @ SV743 @ SY1380 )
| ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SY1379 @ SY1380 ) ) )
| ~ ~ ( ~ ! [SY1381: $i] :
( ! [SY1382: $i] :
~ ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SY1381 @ SY1382 ) )
| ( in @ SV674 @ SY1381 ) )
| ~ ! [SY1383: $i,SY1384: $i] :
( ~ ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SY1383 @ SY1384 ) )
| ( in @ SV743 @ SY1384 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3762]) ).
thf(3945,plain,
! [SV675: $i] :
( ( ~ ! [SY1289: $i,SY1290: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY1290 @ SY1289 @ SV675 ) @ SY1290 )
| ( ( sK27_D @ SY1290 @ SY1289 @ SV675 )
!= SV675 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY1290 @ SY1289 @ SV675 ) @ SY1290 )
| ( ( sK27_D @ SY1290 @ SY1289 @ SV675 )
!= SY1289 ) ) )
| ~ ( ( in @ ( sK27_D @ SY1290 @ SY1289 @ SV675 ) @ SY1290 )
| ( ( sK27_D @ SY1290 @ SY1289 @ SV675 )
= SV675 )
| ( ( sK27_D @ SY1290 @ SY1289 @ SV675 )
= SY1289 ) ) )
| ( SY1290
= ( unordered_pair @ SV675 @ SY1289 ) ) )
| ~ ! [SY1291: $i,SY1292: $i] :
( ( SY1292
!= ( unordered_pair @ SV675 @ SY1291 ) )
| ~ ( ~ ! [SY1293: $i] :
( ~ ( in @ SY1293 @ SY1292 )
| ( SY1293 = SV675 )
| ( SY1293 = SY1291 ) )
| ~ ~ ( ~ ! [SY1294: $i] :
( ( SY1294 != SV675 )
| ( in @ SY1294 @ SY1292 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY1291 )
| ( in @ SX3 @ SY1292 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3763]) ).
thf(3946,plain,
! [SV744: $i,SV676: $i] :
( ( ~ ( ~ ! [SY1385: $i,SY1386: $i] :
( ~ ( in @ SV676 @ SY1385 )
| ~ ( in @ SV744 @ SY1386 )
| ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SY1385 @ SY1386 ) ) )
| ~ ~ ( ~ ! [SY1387: $i] :
( ! [SY1388: $i] :
~ ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SY1387 @ SY1388 ) )
| ( in @ SV676 @ SY1387 ) )
| ~ ! [SY1389: $i,SY1390: $i] :
( ~ ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SY1389 @ SY1390 ) )
| ( in @ SV744 @ SY1390 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3764]) ).
thf(3947,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK48_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3765]) ).
thf(3948,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3765]) ).
thf(3949,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( function @ ( function_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3766]) ).
thf(3950,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( relation @ ( function_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3766]) ).
thf(3951,plain,
! [SV677: $i,SV745: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK4_C @ SV745 @ SV677 ) @ SV677 )
| ~ ( in @ ( sK4_C @ SV745 @ SV677 ) @ SV745 ) )
| ~ ( ( in @ ( sK4_C @ SV745 @ SV677 ) @ SV677 )
| ( in @ ( sK4_C @ SV745 @ SV677 ) @ SV745 ) ) )
| ( SV677 = SV745 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3767]) ).
thf(3952,plain,
! [SV678: $i] :
( ( ~ ! [SY1304: $i] :
( ~ ( subset @ SV678 @ SY1304 )
| ! [SY1305: $i] : ( subset @ ( cartesian_product2 @ SV678 @ SY1305 ) @ ( cartesian_product2 @ SY1304 @ SY1305 ) ) )
| ~ ! [SY1306: $i] :
( ~ ( subset @ SV678 @ SY1306 )
| ! [SY1307: $i] : ( subset @ ( cartesian_product2 @ SY1307 @ SV678 ) @ ( cartesian_product2 @ SY1307 @ SY1306 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3768]) ).
thf(3953,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ ( sK16_SY398 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK16_SY398 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK15_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3769]) ).
thf(3954,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 @ ( sK14_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK14_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3769]) ).
thf(3955,plain,
! [SV679: $i] :
( ( ( ~ ( relation @ SV679 ) )
= $true )
| ( ( ~ ( ~ ! [SY1308: $i] :
( ~ ( ~ ( ! [SY1309: $i] :
~ ( in @ ( ordered_pair @ ( sK63_C @ SY1308 @ SV679 ) @ SY1309 ) @ SV679 )
| ~ ( in @ ( sK63_C @ SY1308 @ SV679 ) @ SY1308 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_C @ SY1308 @ SV679 ) @ ( sK64_SY419 @ SY1308 @ SV679 ) ) @ SV679 )
| ( in @ ( sK63_C @ SY1308 @ SV679 ) @ SY1308 ) ) )
| ( SY1308
= ( relation_dom @ SV679 ) ) )
| ~ ! [SY1310: $i] :
( ( SY1310
!= ( relation_dom @ SV679 ) )
| ~ ( ~ ! [SY1311: $i] :
( ! [SY1312: $i] :
~ ( in @ ( ordered_pair @ SY1311 @ SY1312 ) @ SV679 )
| ( in @ SY1311 @ SY1310 ) )
| ~ ! [SY1313: $i] :
( ~ ( in @ SY1313 @ SY1310 )
| ( in @ ( ordered_pair @ SY1313 @ ( sK62_D @ SY1313 @ SY1310 @ SV679 ) ) @ SV679 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3770]) ).
thf(3956,plain,
! [SV680: $i] :
( ( ~ ! [SY1314: $i,SY1315: $i] :
( ~ ( relation @ SY1315 )
| ~ ( in @ ( ordered_pair @ SV680 @ SY1314 ) @ SY1315 )
| ( in @ SV680 @ ( relation_field @ SY1315 ) ) )
| ~ ! [SY1316: $i,SY1317: $i] :
( ~ ( relation @ SY1317 )
| ~ ( in @ ( ordered_pair @ SV680 @ SY1316 ) @ SY1317 )
| ( in @ SY1316 @ ( relation_field @ SY1317 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3771]) ).
thf(3957,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK44_C @ SX1 @ SX0 )
!= ( sK45_SY414 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY414 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK44_C @ SX1 @ SX0 )
= ( sK45_SY414 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY414 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY414 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3772]) ).
thf(3958,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)],[3772]) ).
thf(3959,plain,
! [SV681: $i] :
( ( ( ~ ( relation @ SV681 ) )
= $true )
| ( ( ~ ( ~ ! [SY1318: $i,SY1319: $i] :
( ~ ( relation @ SY1319 )
| ~ ( ~ ( ~ ( in @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ SY1318 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ ( sK43_SY413 @ SY1319 @ SY1318 @ SV681 ) ) @ SV681 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ ( sK43_SY413 @ SY1319 @ SY1318 @ SV681 ) ) @ SY1319 ) )
| ~ ~ ( ~ ( ( in @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ SY1318 )
| ( in @ ( ordered_pair @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ ( sK43_SY413 @ SY1319 @ SY1318 @ SV681 ) ) @ SY1319 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ ( sK43_SY413 @ SY1319 @ SY1318 @ SV681 ) ) @ SV681 )
| ( in @ ( ordered_pair @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ ( sK43_SY413 @ SY1319 @ SY1318 @ SV681 ) ) @ SY1319 ) ) ) )
| ( SY1319
= ( relation_dom_restriction @ SV681 @ SY1318 ) ) )
| ~ ! [SY1320: $i,SY1321: $i] :
( ~ ( relation @ SY1321 )
| ( SY1321
!= ( relation_dom_restriction @ SV681 @ SY1320 ) )
| ~ ( ~ ! [SY1322: $i,SY1323: $i] :
( ~ ( in @ SY1322 @ SY1320 )
| ~ ( in @ ( ordered_pair @ SY1322 @ SY1323 ) @ SV681 )
| ( in @ ( ordered_pair @ SY1322 @ SY1323 ) @ SY1321 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY1321 )
| ( in @ SX3 @ SY1320 ) )
| ~ ! [SY1326: $i,SY1327: $i] :
( ~ ( in @ ( ordered_pair @ SY1326 @ SY1327 ) @ SY1321 )
| ( in @ ( ordered_pair @ SY1326 @ SY1327 ) @ SV681 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3773]) ).
thf(3960,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK30_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK30_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK30_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK30_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3774]) ).
thf(3961,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)],[3774]) ).
thf(3962,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3775]) ).
thf(3963,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3775]) ).
thf(3964,plain,
! [SV682: $i] :
( ( ~ ! [SY1328: $i,SY1329: $i] :
( ~ ( relation @ SY1329 )
| ! [SY1330: $i] :
( ~ ( in @ SY1330 @ ( relation_dom @ SY1329 ) )
| ~ ( in @ ( ordered_pair @ SY1330 @ SV682 ) @ SY1329 )
| ~ ( in @ SY1330 @ SY1328 ) )
| ( in @ SV682 @ ( relation_image @ SY1329 @ SY1328 ) ) )
| ~ ! [SY1331: $i,SY1332: $i] :
( ~ ( relation @ SY1332 )
| ~ ( in @ SV682 @ ( relation_image @ SY1332 @ SY1331 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK52_D @ SY1332 @ SY1331 @ SV682 ) @ ( relation_dom @ SY1332 ) )
| ~ ( in @ ( ordered_pair @ ( sK52_D @ SY1332 @ SY1331 @ SV682 ) @ SV682 ) @ SY1332 ) )
| ~ ( in @ ( sK52_D @ SY1332 @ SY1331 @ SV682 ) @ SY1331 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3776]) ).
thf(3965,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3777]) ).
thf(3966,plain,
( ( ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3777]) ).
thf(3967,plain,
! [SV683: $i] :
( ( ( ~ ( relation @ SV683 ) )
= $true )
| ( ( ~ ( ~ ! [SY1333: $i] :
( ~ ( relation @ SY1333 )
| ~ ( subset @ SV683 @ SY1333 )
| ( subset @ ( relation_dom @ SV683 ) @ ( relation_dom @ SY1333 ) ) )
| ~ ! [SY1334: $i] :
( ~ ( relation @ SY1334 )
| ~ ( subset @ SV683 @ SY1334 )
| ( subset @ ( relation_rng @ SV683 ) @ ( relation_rng @ SY1334 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3778]) ).
thf(3968,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3779]) ).
thf(3969,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3779]) ).
thf(3970,plain,
! [SV684: $i] :
( ( ( ~ ( relation @ SV684 ) )
= $true )
| ( ( ~ ( ~ ! [SY1335: $i] :
( ~ ( relation @ SY1335 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SY1335 @ SV684 ) @ ( sK66_SY420 @ SY1335 @ SV684 ) ) @ SV684 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SY1335 @ SV684 ) @ ( sK66_SY420 @ SY1335 @ SV684 ) ) @ SY1335 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_C @ SY1335 @ SV684 ) @ ( sK66_SY420 @ SY1335 @ SV684 ) ) @ SV684 )
| ( in @ ( ordered_pair @ ( sK65_C @ SY1335 @ SV684 ) @ ( sK66_SY420 @ SY1335 @ SV684 ) ) @ SY1335 ) ) )
| ( SV684 = SY1335 ) )
| ~ ! [SY1336: $i] :
( ~ ( relation @ SY1336 )
| ( SV684 != SY1336 )
| ~ ( ~ ! [SY1337: $i,SY1338: $i] :
( ~ ( in @ ( ordered_pair @ SY1337 @ SY1338 ) @ SV684 )
| ( in @ ( ordered_pair @ SY1337 @ SY1338 ) @ SY1336 ) )
| ~ ! [SY1339: $i,SY1340: $i] :
( ~ ( in @ ( ordered_pair @ SY1339 @ SY1340 ) @ SY1336 )
| ( in @ ( ordered_pair @ SY1339 @ SY1340 ) @ SV684 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3780]) ).
thf(3971,plain,
! [SV685: $i] :
( ( ~ ! [SY1341: $i] :
( ~ ( subset @ SY1341 @ ( sK2_B @ SV685 ) )
| ( are_equipotent @ SY1341 @ ( sK2_B @ SV685 ) )
| ( in @ SY1341 @ ( sK2_B @ SV685 ) ) )
| ~ ~ ( ~ ! [SY1342: $i] :
( ~ ( ~ ! [SY1343: $i] :
( ~ ( subset @ SY1343 @ SY1342 )
| ( in @ SY1343 @ ( sK3_SY386 @ SY1342 @ SV685 ) ) )
| ~ ( in @ ( sK3_SY386 @ SY1342 @ SV685 ) @ ( sK2_B @ SV685 ) ) )
| ~ ( in @ SY1342 @ ( sK2_B @ SV685 ) ) )
| ~ ~ ( ~ ! [SY1344: $i,SY1345: $i] :
( ~ ( in @ SY1344 @ ( sK2_B @ SV685 ) )
| ~ ( subset @ SY1345 @ SY1344 )
| ( in @ SY1345 @ ( sK2_B @ SV685 ) ) )
| ~ ( in @ SV685 @ ( sK2_B @ SV685 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3781]) ).
thf(3972,plain,
( ( ( ( relation_dom @ empty_set )
!= empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3782]) ).
thf(3973,plain,
( ( ( ( relation_rng @ empty_set )
!= empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3782]) ).
thf(3974,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3783]) ).
thf(3975,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)],[3783]) ).
thf(3976,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK28_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK28_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3784]) ).
thf(3977,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)],[3784]) ).
thf(3978,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3785]) ).
thf(3979,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)],[3785]) ).
thf(3980,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3786]) ).
thf(3981,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3786]) ).
thf(3982,plain,
( ( ~ ~ ( ~ ( empty @ sK56_A )
| ~ ( relation @ sK56_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3787]) ).
thf(3983,plain,
( ( ~ ( function @ sK56_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3787]) ).
thf(3984,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK50_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK50_C @ SX1 @ SX0 ) )
!= ( sK50_C @ SX1 @ SX0 ) ) ) )
| ( ( relation_dom @ SX1 )
!= SX0 )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3788]) ).
thf(3985,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)],[3788]) ).
thf(3986,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3789]) ).
thf(3987,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3789]) ).
thf(3988,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK18_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK18_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3790]) ).
thf(3989,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3790]) ).
thf(3990,plain,
! [SV566: $i,SV686: $i] :
( ( ( ~ ( relation @ SV686 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV566 @ SV686 ) ) @ SV566 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3791]) ).
thf(3991,plain,
! [SV567: $i,SV687: $i] :
( ( ( ~ ( relation @ SV687 ) )
= $true )
| ( ( subset @ ( relation_rng_restriction @ SV567 @ SV687 ) @ SV687 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3792]) ).
thf(3992,plain,
! [SV568: $i,SV688: $i] :
( ( ( ~ ( relation @ SV688 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV568 @ SV688 ) ) @ ( relation_rng @ SV688 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3793]) ).
thf(3993,plain,
! [SV569: $i,SV689: $i] :
( ( ( ~ ( relation @ SV689 ) )
= $true )
| ( ( ( relation_rng @ ( relation_rng_restriction @ SV569 @ SV689 ) )
= ( set_intersection2 @ ( relation_rng @ SV689 ) @ SV569 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3794]) ).
thf(3994,plain,
! [SV690: $i,SV570: $i,SV746: $i] :
( ( ~ ( relation @ SV746 )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV570 @ SV746 ) @ SV690 )
= ( relation_rng_restriction @ SV570 @ ( relation_dom_restriction @ SV746 @ SV690 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3795]) ).
thf(3995,plain,
! [SV571: $i,SV691: $i] :
( ( ( ~ ( relation @ SV691 ) )
= $true )
| ( ( subset @ ( relation_image @ SV691 @ SV571 ) @ ( relation_rng @ SV691 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3796]) ).
thf(3996,plain,
! [SV572: $i,SV692: $i] :
( ( ( ~ ( relation @ SV692 ) )
= $true )
| ( ( ( relation_image @ SV692 @ SV572 )
= ( relation_image @ SV692 @ ( set_intersection2 @ ( relation_dom @ SV692 ) @ SV572 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3797]) ).
thf(3997,plain,
! [SV573: $i] :
( ( ( relation @ SV573 )
= $false )
| ( ( ( relation_image @ SV573 @ ( relation_dom @ SV573 ) )
= ( relation_rng @ SV573 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3798]) ).
thf(3998,plain,
! [SV574: $i] :
( ( ( relation @ SV574 )
= $false )
| ( ( ! [SY1068: $i] :
( ~ ( relation @ SY1068 )
| ( ( relation_rng @ ( relation_composition @ SV574 @ SY1068 ) )
= ( relation_image @ SY1068 @ ( relation_rng @ SV574 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3799]) ).
thf(3999,plain,
! [SV575: $i,SV693: $i] :
( ( ( ~ ( relation @ SV693 ) )
= $true )
| ( ( subset @ ( relation_inverse_image @ SV693 @ SV575 ) @ ( relation_dom @ SV693 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3800]) ).
thf(4000,plain,
! [SV694: $i,SV576: $i,SV747: $i] :
( ( ~ ( relation @ SV747 )
| ~ ( subset @ SV576 @ SV694 )
| ( subset @ ( relation_inverse_image @ SV747 @ SV576 ) @ ( relation_inverse_image @ SV747 @ SV694 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3801]) ).
thf(4001,plain,
! [SV577: $i] :
( ( ( relation @ SV577 )
= $false )
| ( ( subset @ SV577 @ ( cartesian_product2 @ ( relation_dom @ SV577 ) @ ( relation_rng @ SV577 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3802]) ).
thf(4002,plain,
! [SV578: $i] :
( ( ( relation @ SV578 )
= $false )
| ( ( ! [SY1072: $i] :
( ~ ( relation @ SY1072 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV578 @ SY1072 ) ) @ ( relation_dom @ SV578 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3803]) ).
thf(4003,plain,
! [SV579: $i] :
( ( ( relation @ SV579 )
= $false )
| ( ( ! [SY1073: $i] :
( ~ ( relation @ SY1073 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV579 @ SY1073 ) ) @ ( relation_rng @ SY1073 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3804]) ).
thf(4004,plain,
! [SV580: $i] :
( ( ( relation @ SV580 )
= $false )
| ( ( ! [SY1074: $i] :
( ~ ( relation @ SY1074 )
| ~ ( subset @ ( relation_rng @ SV580 ) @ ( relation_dom @ SY1074 ) )
| ( ( relation_dom @ ( relation_composition @ SV580 @ SY1074 ) )
= ( relation_dom @ SV580 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3805]) ).
thf(4005,plain,
! [SV581: $i] :
( ( ( relation @ SV581 )
= $false )
| ( ( ! [SY1075: $i] :
( ~ ( relation @ SY1075 )
| ~ ( subset @ ( relation_dom @ SV581 ) @ ( relation_rng @ SY1075 ) )
| ( ( relation_rng @ ( relation_composition @ SY1075 @ SV581 ) )
= ( relation_rng @ SV581 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3806]) ).
thf(4006,plain,
! [SV582: $i,SV695: $i] :
( ( ( ~ ( relation @ SV695 ) )
= $true )
| ( ( subset @ ( relation_dom_restriction @ SV695 @ SV582 ) @ SV695 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3807]) ).
thf(4007,plain,
! [SV583: $i,SV696: $i] :
( ( ( ~ ( relation @ SV696 ) )
= $true )
| ( ( ( relation_dom @ ( relation_dom_restriction @ SV696 @ SV583 ) )
= ( set_intersection2 @ ( relation_dom @ SV696 ) @ SV583 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3808]) ).
thf(4008,plain,
! [SV584: $i,SV697: $i] :
( ( ( ~ ( relation @ SV697 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV697 @ SV584 ) ) @ ( relation_rng @ SV697 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3809]) ).
thf(4009,plain,
! [SV585: $i] :
( ( ( empty @ SV585 )
= $false )
| ( ( function @ SV585 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3810]) ).
thf(4010,plain,
! [SV586: $i] :
( ( ( empty @ SV586 )
= $false )
| ( ( relation @ SV586 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3811]) ).
thf(4011,plain,
! [SV587: $i] :
( ( ( relation @ SV587 )
= $false )
| ( ( ( relation_field @ SV587 )
= ( set_union2 @ ( relation_dom @ SV587 ) @ ( relation_rng @ SV587 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3812]) ).
thf(4012,plain,
! [SV588: $i] :
( ( ( ~ ( function @ SV588 ) )
= $true )
| ( ( ~ ( relation @ SV588 ) )
= $true )
| ( ( ~ ( one_to_one @ SV588 )
| ( ( function_inverse @ SV588 )
= ( relation_inverse @ SV588 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3813]) ).
thf(4013,plain,
! [SV589: $i] :
( ( ( relation @ SV589 )
= $false )
| ( ( relation @ ( relation_inverse @ SV589 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3814]) ).
thf(4014,plain,
! [SV698: $i,SV590: $i] :
( ( ( ~ ( relation @ SV590 )
| ~ ( relation @ SV698 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV590 @ SV698 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3815]) ).
thf(4015,plain,
! [SV592: $i] :
( ( ( relation @ SV592 )
= $false )
| ( ( ! [SY1080: $i] : ( relation @ ( relation_dom_restriction @ SV592 @ SY1080 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3816]) ).
thf(4016,plain,
! [SV593: $i,SV699: $i] :
( ( ( ~ ( relation @ SV699 ) )
= $true )
| ( ( relation @ ( relation_rng_restriction @ SV593 @ SV699 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3817]) ).
thf(4017,plain,
! [SV700: $i,SV594: $i] :
( ( ( ~ ( relation @ SV594 )
| ~ ( relation @ SV700 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV594 @ SV700 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3818]) ).
thf(4018,plain,
! [SV701: $i,SV595: $i] :
( ( ( ~ ( relation @ SV595 )
| ~ ( relation @ SV701 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV595 @ SV701 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3819]) ).
thf(4019,plain,
! [SV596: $i] :
( ( ( empty @ SV596 )
= $true )
| ( ( ~ ( relation @ SV596 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV596 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3820]) ).
thf(4020,plain,
! [SV597: $i] :
( ( ( empty @ SV597 )
= $true )
| ( ( ~ ( relation @ SV597 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV597 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3821]) ).
thf(4021,plain,
! [SV598: $i] :
( ( ( relation @ SV598 )
= $false )
| ( ( ( relation_inverse @ ( relation_inverse @ SV598 ) )
= SV598 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3822]) ).
thf(4022,plain,
! [SV702: $i,SV600: $i] :
( ( ( ~ ( in @ SV600 @ SV702 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV600 ) @ SV702 )
= SV702 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3824]) ).
thf(4023,plain,
! [SV703: $i,SV601: $i] :
( ( ( ~ ( in @ SV601 @ SV703 ) )
= $true )
| ( ( subset @ SV601 @ ( union @ SV703 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3825]) ).
thf(4024,plain,
! [SV748: $i,SV704: $i,SV602: $i] :
( ( ! [SY1391: $i] :
( ~ ( subset @ SV602 @ SV704 )
| ~ ( subset @ SV748 @ SY1391 )
| ( subset @ ( cartesian_product2 @ SV602 @ SV748 ) @ ( cartesian_product2 @ SV704 @ SY1391 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3826]) ).
thf(4025,plain,
! [SV705: $i,SV603: $i] :
( ( ( ~ ( subset @ SV603 @ SV705 ) )
= $true )
| ( ( ( set_union2 @ SV603 @ SV705 )
= SV705 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3827]) ).
thf(4026,plain,
! [SV604: $i,SV706: $i] :
( ( ( ~ ( relation @ SV706 ) )
= $true )
| ( ( ( SV604 = empty_set )
| ~ ( subset @ SV604 @ ( relation_rng @ SV706 ) )
| ( ( relation_inverse_image @ SV706 @ SV604 )
!= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3828]) ).
thf(4027,plain,
! [SV749: $i,SV708: $i,SV606: $i] :
( ( ~ ( subset @ SV606 @ SV708 )
| ~ ( subset @ SV606 @ SV749 )
| ( subset @ SV606 @ ( set_intersection2 @ SV708 @ SV749 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3830]) ).
thf(4028,plain,
! [SV750: $i,SV709: $i,SV607: $i] :
( ( ~ ( subset @ SV607 @ SV709 )
| ~ ( subset @ SV709 @ SV750 )
| ( subset @ SV607 @ SV750 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3831]) ).
thf(4029,plain,
! [SV608: $i,SV710: $i] :
( ( ( ~ ( function @ SV710 )
| ~ ( relation @ SV710 ) )
= $true )
| ( ( ! [SY1352: $i] :
( ~ ( function @ SY1352 )
| ~ ( relation @ SY1352 )
| ~ ( in @ SV608 @ ( relation_dom @ ( relation_composition @ SY1352 @ SV710 ) ) )
| ( ( apply @ ( relation_composition @ SY1352 @ SV710 ) @ SV608 )
= ( apply @ SV710 @ ( apply @ SY1352 @ SV608 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3832]) ).
thf(4030,plain,
! [SV609: $i,SV711: $i] :
( ( ( ~ ( function @ SV711 )
| ~ ( relation @ SV711 ) )
= $true )
| ( ( ! [SY1353: $i] :
( ~ ( function @ SY1353 )
| ~ ( relation @ SY1353 )
| ~ ( in @ SV609 @ ( relation_dom @ SV711 ) )
| ( ( apply @ ( relation_composition @ SV711 @ SY1353 ) @ SV609 )
= ( apply @ SY1353 @ ( apply @ SV711 @ SV609 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3833]) ).
thf(4031,plain,
! [SV712: $i,SV610: $i] :
( ( ( ~ ( subset @ SV610 @ SV712 ) )
= $true )
| ( ( ! [SY1354: $i] : ( subset @ ( set_intersection2 @ SV610 @ SY1354 ) @ ( set_intersection2 @ SV712 @ SY1354 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3834]) ).
thf(4032,plain,
! [SV713: $i,SV611: $i] :
( ( ( ~ ( subset @ SV611 @ SV713 ) )
= $true )
| ( ( ( set_intersection2 @ SV611 @ SV713 )
= SV611 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3835]) ).
thf(4033,plain,
! [SV714: $i,SV613: $i] :
( ( ( ~ ( subset @ SV613 @ SV714 ) )
= $true )
| ( ( ! [SY1355: $i] : ( subset @ ( set_difference @ SV613 @ SY1355 ) @ ( set_difference @ SV714 @ SY1355 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3836]) ).
thf(4034,plain,
! [SV614: $i,SV715: $i] :
( ( ( ~ ( in @ SV715 @ SV614 ) )
= $true )
| ( ( ( apply @ ( identity_relation @ SV614 ) @ SV715 )
= SV715 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3837]) ).
thf(4035,plain,
! [SV617: $i] :
( ( ( subset @ SV617 @ empty_set )
= $false )
| ( ( SV617 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3840]) ).
thf(4036,plain,
! [SV719: $i,SV619: $i] :
( ( ( ~ ( subset @ SV619 @ SV719 ) )
= $true )
| ( ( SV719
= ( set_union2 @ SV619 @ ( set_difference @ SV719 @ SV619 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3842]) ).
thf(4037,plain,
! [SV720: $i,SV620: $i] :
( ( ( ~ ( in @ SV620 @ SV720 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV620 ) @ SV720 )
= SV720 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3843]) ).
thf(4038,plain,
! [SV622: $i] :
( ( ( relation @ SV622 )
= $false )
| ( ( ( in @ ( ordered_pair @ ( sK46_B @ SV622 ) @ ( sK47_SY415 @ SV622 ) ) @ SV622 )
| ( SV622 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3845]) ).
thf(4039,plain,
! [SV623: $i,SV722: $i] :
( ( ( ~ ( proper_subset @ SV722 @ SV623 ) )
= $true )
| ( ( ~ ( subset @ SV623 @ SV722 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3846]) ).
thf(4040,plain,
! [SV624: $i,SV751: $i,SV723: $i] :
( ( ~ ( disjoint @ SV723 @ SV751 )
| ~ ( subset @ SV624 @ SV723 )
| ( disjoint @ SV624 @ SV751 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3847]) ).
thf(4041,plain,
! [SV724: $i,SV625: $i] :
( ( ( ~ ( subset @ ( singleton @ SV625 ) @ ( singleton @ SV724 ) ) )
= $true )
| ( ( SV625 = SV724 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3848]) ).
thf(4042,plain,
! [SV752: $i,SV726: $i,SV627: $i] :
( ( ~ ( subset @ SV627 @ SV726 )
| ~ ( subset @ SV752 @ SV726 )
| ( subset @ ( set_union2 @ SV627 @ SV752 ) @ SV726 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3850]) ).
thf(4043,plain,
! [SV727: $i,SV628: $i] :
( ( ( ~ ( in @ SV628 @ SV727 ) )
= $true )
| ( ( subset @ SV628 @ ( union @ SV727 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3851]) ).
thf(4044,plain,
! [SV629: $i,SV728: $i] :
( ( ( ~ ( relation @ SV728 ) )
= $true )
| ( ( ( relation_dom_restriction @ SV728 @ SV629 )
= ( relation_composition @ ( identity_relation @ SV629 ) @ SV728 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3852]) ).
thf(4045,plain,
! [SV729: $i,SV630: $i] :
( ( ( ~ ( in @ SV630 @ SV729 ) )
= $true )
| ( ( ~ ( in @ SV729 @ SV630 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3853]) ).
thf(4046,plain,
! [SV732: $i,SV634: $i] :
( ( empty @ ( ordered_pair @ SV634 @ SV732 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3857]) ).
thf(4047,plain,
! [SV753: $i,SV636: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV636 @ SV753 ) ) )
= $true )
| ( ( empty @ SV636 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3859]) ).
thf(4048,plain,
! [SV733: $i,SV637: $i] :
( ( empty @ ( unordered_pair @ SV637 @ SV733 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3860]) ).
thf(4049,plain,
! [SV638: $i,SV754: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV754 @ SV638 ) ) )
= $true )
| ( ( empty @ SV638 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3861]) ).
thf(4050,plain,
! [SV734: $i,SV639: $i] :
( ( ( ( empty @ SV639 )
| ( empty @ SV734 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV639 @ SV734 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3862]) ).
thf(4051,plain,
! [SV735: $i,SV644: $i] :
( ( ( ~ ( in @ SV644 @ SV735 ) )
= $true )
| ( ( element @ SV644 @ SV735 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3863]) ).
thf(4052,plain,
! [SV736: $i,SV646: $i] :
( ( ( ~ ( element @ SV646 @ SV736 ) )
= $true )
| ( ( ( empty @ SV736 )
| ( in @ SV646 @ SV736 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3864]) ).
thf(4053,plain,
! [SV649: $i] :
( ( ( empty @ SV649 )
= $false )
| ( ( SV649 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3865]) ).
thf(4054,plain,
! [SV650: $i,SV737: $i] :
( ( ( ~ ( empty @ SV737 ) )
= $true )
| ( ( ~ ( in @ SV650 @ SV737 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3866]) ).
thf(4055,plain,
! [SV738: $i,SV651: $i] :
( ( ( ( SV651 = SV738 )
| ~ ( empty @ SV651 ) )
= $true )
| ( ( ~ ( empty @ SV738 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3867]) ).
thf(4056,plain,
! [SV652: $i] :
( ( ~ ! [SY1133: $i,SY1134: $i] :
( ~ ( ~ ( ~ ( in @ ( sK17_D @ SY1134 @ SY1133 @ SV652 ) @ SV652 )
| ~ ( in @ ( sK17_D @ SY1134 @ SY1133 @ SV652 ) @ SY1133 )
| ~ ( in @ ( sK17_D @ SY1134 @ SY1133 @ SV652 ) @ SY1134 ) )
| ~ ~ ( ~ ( ( in @ ( sK17_D @ SY1134 @ SY1133 @ SV652 ) @ SV652 )
| ( in @ ( sK17_D @ SY1134 @ SY1133 @ SV652 ) @ SY1134 ) )
| ~ ( ( in @ ( sK17_D @ SY1134 @ SY1133 @ SV652 ) @ SY1133 )
| ( in @ ( sK17_D @ SY1134 @ SY1133 @ SV652 ) @ SY1134 ) ) ) )
| ( SY1134
= ( set_intersection2 @ SV652 @ SY1133 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3868]) ).
thf(4057,plain,
! [SV652: $i] :
( ( ~ ! [SY1135: $i,SY1136: $i] :
( ( SY1136
!= ( set_intersection2 @ SV652 @ SY1135 ) )
| ~ ( ~ ! [SY1137: $i] :
( ~ ( in @ SY1137 @ SV652 )
| ~ ( in @ SY1137 @ SY1135 )
| ( in @ SY1137 @ SY1136 ) )
| ~ ~ ( ~ ! [SY1138: $i] :
( ~ ( in @ SY1138 @ SY1136 )
| ( in @ SY1138 @ SV652 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1136 )
| ( in @ SX3 @ SY1135 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3868]) ).
thf(4058,plain,
( ( empty @ sK57_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3869]) ).
thf(4059,plain,
( ( relation @ sK57_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3870]) ).
thf(4060,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( ( relation_rng @ SX0 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3871]) ).
thf(4061,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( ( relation_dom @ SX0 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3872]) ).
thf(4062,plain,
! [SV653: $i] :
( ( ( ~ ( function @ SV653 ) )
= $true )
| ( ( ~ ( relation @ SV653 ) )
= $true )
| ( ( ~ ( one_to_one @ SV653 )
| ~ ( ~ ! [SY1140: $i] :
( ~ ( function @ SY1140 )
| ~ ( relation @ SY1140 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SY1140 @ SV653 )
= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ( ( sK70_C @ SY1140 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY1140 @ SV653 )
= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY1140 @ SV653 )
= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ( ( sK71_SY424 @ SY1140 @ SV653 )
!= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK70_C @ SY1140 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK71_SY424 @ SY1140 @ SV653 )
!= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY1140 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK70_C @ SY1140 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SY1140 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SY1140 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK71_SY424 @ SY1140 @ SV653 )
!= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ( ( relation_dom @ SY1140 )
!= ( relation_rng @ SV653 ) )
| ( SY1140
= ( function_inverse @ SV653 ) ) )
| ~ ~ ( ~ ! [SY1141: $i] :
( ~ ( function @ SY1141 )
| ~ ( relation @ SY1141 )
| ( SY1141
!= ( function_inverse @ SV653 ) )
| ~ ( ~ ~ ( ~ ! [SY1142: $i,SY1143: $i] :
( ( SY1143
!= ( apply @ SY1141 @ SY1142 ) )
| ~ ( in @ SY1142 @ ( relation_rng @ SV653 ) )
| ( SY1142
= ( apply @ SV653 @ SY1143 ) ) )
| ~ ! [SY1144: $i,SY1145: $i] :
( ( SY1145
!= ( apply @ SY1141 @ SY1144 ) )
| ~ ( in @ SY1144 @ ( relation_rng @ SV653 ) )
| ( in @ SY1145 @ ( relation_dom @ SV653 ) ) ) )
| ~ ~ ( ~ ! [SY1146: $i,SY1147: $i] :
( ( SY1146
!= ( apply @ SV653 @ SY1147 ) )
| ~ ( in @ SY1147 @ ( relation_dom @ SV653 ) )
| ( SY1147
= ( apply @ SY1141 @ SY1146 ) ) )
| ~ ! [SY1148: $i] :
( ! [SY1149: $i] :
( ( SY1148
!= ( apply @ SV653 @ SY1149 ) )
| ~ ( in @ SY1149 @ ( relation_dom @ SV653 ) ) )
| ( in @ SY1148 @ ( relation_rng @ SV653 ) ) ) ) ) )
| ~ ! [SY1150: $i] :
( ~ ( function @ SY1150 )
| ~ ( relation @ SY1150 )
| ( SY1150
!= ( function_inverse @ SV653 ) )
| ( ( relation_dom @ SY1150 )
= ( relation_rng @ SV653 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3873]) ).
thf(4063,plain,
( ( ~ ( ~ ( function @ sK54_A )
| ~ ( relation @ sK54_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3874]) ).
thf(4064,plain,
( ( one_to_one @ sK54_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3875]) ).
thf(4065,plain,
( ( ~ ( empty @ sK55_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3876]) ).
thf(4066,plain,
( ( relation @ sK55_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3877]) ).
thf(4067,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)],[3878]) ).
thf(4068,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)],[3879]) ).
thf(4069,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3880]) ).
thf(4070,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3881]) ).
thf(4071,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3882]) ).
thf(4072,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)],[3883]) ).
thf(4073,plain,
( ( ! [SX0: $i] :
( ( relation_dom @ ( identity_relation @ SX0 ) )
= SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3884]) ).
thf(4074,plain,
( ( ! [SX0: $i] :
( ( relation_rng @ ( identity_relation @ SX0 ) )
= SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3885]) ).
thf(4075,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3886]) ).
thf(4076,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3887]) ).
thf(4077,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3888]) ).
thf(4078,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3889]) ).
thf(4079,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3890]) ).
thf(4080,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3891]) ).
thf(4081,plain,
! [SV739: $i,SV654: $i] :
( ( ~ ! [SY1358: $i,SY1359: $i] :
( ~ ( relation @ SY1359 )
| ~ ( in @ SV654 @ SY1358 )
| ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ SY1359 )
| ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SY1358 ) @ SY1359 ) ) )
| ~ ~ ( ~ ! [SY1360: $i,SY1361: $i] :
( ~ ( relation @ SY1361 )
| ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SY1360 ) @ SY1361 ) )
| ( in @ SV654 @ SY1360 ) )
| ~ ! [SY1362: $i,SY1363: $i] :
( ~ ( relation @ SY1363 )
| ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SY1362 ) @ SY1363 ) )
| ( in @ ( ordered_pair @ SV654 @ SV739 ) @ SY1363 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3892]) ).
thf(4082,plain,
! [SV655: $i,SV740: $i] :
( ( ( ~ ( relation @ SV740 ) )
= $true )
| ( ( ~ ( ~ ! [SY1364: $i] :
( ~ ( relation @ SY1364 )
| ~ ( ~ ( ~ ( in @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) @ SV655 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY1364 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) ) @ SV740 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY1364 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) ) @ SY1364 ) )
| ~ ~ ( ~ ( ( in @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) @ SV655 )
| ( in @ ( ordered_pair @ ( sK40_D @ SY1364 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) ) @ SY1364 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SY1364 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) ) @ SV740 )
| ( in @ ( ordered_pair @ ( sK40_D @ SY1364 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) ) @ SY1364 ) ) ) )
| ( SY1364
= ( relation_rng_restriction @ SV655 @ SV740 ) ) )
| ~ ! [SY1365: $i] :
( ~ ( relation @ SY1365 )
| ( SY1365
!= ( relation_rng_restriction @ SV655 @ SV740 ) )
| ~ ( ~ ! [SY1366: $i,SY1367: $i] :
( ~ ( in @ SY1367 @ SV655 )
| ~ ( in @ ( ordered_pair @ SY1366 @ SY1367 ) @ SV740 )
| ( in @ ( ordered_pair @ SY1366 @ SY1367 ) @ SY1365 ) )
| ~ ~ ( ~ ! [SY1163: $i,SY1164: $i] :
( ~ ( in @ ( ordered_pair @ SY1163 @ SY1164 ) @ SY1365 )
| ( in @ SY1164 @ SV655 ) )
| ~ ! [SY1370: $i,SY1371: $i] :
( ~ ( in @ ( ordered_pair @ SY1370 @ SY1371 ) @ SY1365 )
| ( in @ ( ordered_pair @ SY1370 @ SY1371 ) @ SV740 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3893]) ).
thf(4083,plain,
( ( ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3894]) ).
thf(4084,plain,
( ( ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3895]) ).
thf(4085,plain,
! [SV741: $i,SV656: $i] :
( ( ~ ! [SY1372: $i] :
( ! [SY1373: $i] :
( ( ordered_pair @ SV656 @ SV741 )
!= ( ordered_pair @ SY1372 @ SY1373 ) )
| ( SV656 = SY1372 ) )
| ~ ! [SY1374: $i,SY1375: $i] :
( ( ( ordered_pair @ SV656 @ SV741 )
!= ( ordered_pair @ SY1374 @ SY1375 ) )
| ( SV741 = SY1375 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3896]) ).
thf(4086,plain,
! [SV657: $i] :
( ( ( relation @ SV657 )
= $false )
| ( ( ~ ( ~ ! [SY1172: $i,SY1173: $i] :
( ~ ( ~ ( ! [SY1174: $i] :
( ~ ( in @ ( ordered_pair @ ( sK35_D @ SY1173 @ SY1172 @ SV657 ) @ SY1174 ) @ SV657 )
| ~ ( in @ SY1174 @ SY1172 ) )
| ~ ( in @ ( sK35_D @ SY1173 @ SY1172 @ SV657 ) @ SY1173 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SY1173 @ SY1172 @ SV657 ) @ ( sK36_SY409 @ SY1173 @ SY1172 @ SV657 ) ) @ SV657 )
| ~ ( in @ ( sK36_SY409 @ SY1173 @ SY1172 @ SV657 ) @ SY1172 ) )
| ( in @ ( sK35_D @ SY1173 @ SY1172 @ SV657 ) @ SY1173 ) ) )
| ( SY1173
= ( relation_inverse_image @ SV657 @ SY1172 ) ) )
| ~ ! [SY1175: $i,SY1176: $i] :
( ( SY1176
!= ( relation_inverse_image @ SV657 @ SY1175 ) )
| ~ ( ~ ! [SY1177: $i] :
( ! [SY1178: $i] :
( ~ ( in @ ( ordered_pair @ SY1177 @ SY1178 ) @ SV657 )
| ~ ( in @ SY1178 @ SY1175 ) )
| ( in @ SY1177 @ SY1176 ) )
| ~ ! [SY1179: $i] :
( ~ ( in @ SY1179 @ SY1176 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1179 @ ( sK34_E @ SY1179 @ SY1176 @ SY1175 @ SV657 ) ) @ SV657 )
| ~ ( in @ ( sK34_E @ SY1179 @ SY1176 @ SY1175 @ SV657 ) @ SY1175 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3897]) ).
thf(4087,plain,
! [SV658: $i] :
( ( ( relation @ SV658 )
= $false )
| ( ( ~ ( ~ ! [SY1180: $i,SY1181: $i] :
( ~ ( ~ ( ! [SY1182: $i] :
( ~ ( in @ ( ordered_pair @ SY1182 @ ( sK38_D @ SY1181 @ SY1180 @ SV658 ) ) @ SV658 )
| ~ ( in @ SY1182 @ SY1180 ) )
| ~ ( in @ ( sK38_D @ SY1181 @ SY1180 @ SV658 ) @ SY1181 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SY1181 @ SY1180 @ SV658 ) @ ( sK38_D @ SY1181 @ SY1180 @ SV658 ) ) @ SV658 )
| ~ ( in @ ( sK39_SY411 @ SY1181 @ SY1180 @ SV658 ) @ SY1180 ) )
| ( in @ ( sK38_D @ SY1181 @ SY1180 @ SV658 ) @ SY1181 ) ) )
| ( SY1181
= ( relation_image @ SV658 @ SY1180 ) ) )
| ~ ! [SY1183: $i,SY1184: $i] :
( ( SY1184
!= ( relation_image @ SV658 @ SY1183 ) )
| ~ ( ~ ! [SY1185: $i] :
( ! [SY1186: $i] :
( ~ ( in @ ( ordered_pair @ SY1186 @ SY1185 ) @ SV658 )
| ~ ( in @ SY1186 @ SY1183 ) )
| ( in @ SY1185 @ SY1184 ) )
| ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ SY1184 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SY1187 @ SY1184 @ SY1183 @ SV658 ) @ SY1187 ) @ SV658 )
| ~ ( in @ ( sK37_E @ SY1187 @ SY1184 @ SY1183 @ SV658 ) @ SY1183 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3898]) ).
thf(4088,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3899]) ).
thf(4089,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)],[3900]) ).
thf(4090,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3901]) ).
thf(4091,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3902]) ).
thf(4092,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)],[3903]) ).
thf(4093,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3904]) ).
thf(4094,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK69_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK69_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3905]) ).
thf(4095,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK67_C @ SX1 @ SX0 ) @ ( sK68_SY421 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3906]) ).
thf(4096,plain,
! [SV659: $i] :
( ( ~ ! [SY1188: $i,SY1189: $i] :
( ~ ( in @ SV659 @ SY1189 )
| ~ ( in @ SY1188 @ SY1189 )
| ( subset @ ( unordered_pair @ SV659 @ SY1188 ) @ SY1189 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3907]) ).
thf(4097,plain,
! [SV659: $i] :
( ( ~ ~ ( ~ ! [SY1190: $i,SY1191: $i] :
( ~ ( subset @ ( unordered_pair @ SV659 @ SY1190 ) @ SY1191 )
| ( in @ SV659 @ SY1191 ) )
| ~ ! [SY1192: $i,SY1193: $i] :
( ~ ( subset @ ( unordered_pair @ SV659 @ SY1192 ) @ SY1193 )
| ( in @ SY1192 @ SY1193 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3907]) ).
thf(4098,plain,
! [SV660: $i] :
( ( ( relation @ SV660 )
= $false )
| ( ( ! [SY1194: $i] :
( ~ ( relation @ SY1194 )
| ~ ( ~ ! [SY1195: $i] :
( ~ ( relation @ SY1195 )
| ~ ( ~ ( ! [SY1196: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY1195 @ SY1194 @ SV660 ) @ SY1196 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1196 @ ( sK9_SY391 @ SY1195 @ SY1194 @ SV660 ) ) @ SY1194 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SY1195 @ SY1194 @ SV660 ) @ ( sK9_SY391 @ SY1195 @ SY1194 @ SV660 ) ) @ SY1195 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY1195 @ SY1194 @ SV660 ) @ ( sK10_SY395 @ SY1195 @ SY1194 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SY1195 @ SY1194 @ SV660 ) @ ( sK9_SY391 @ SY1195 @ SY1194 @ SV660 ) ) @ SY1194 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SY1195 @ SY1194 @ SV660 ) @ ( sK9_SY391 @ SY1195 @ SY1194 @ SV660 ) ) @ SY1195 ) ) )
| ( SY1195
= ( relation_composition @ SV660 @ SY1194 ) ) )
| ~ ! [SY1197: $i] :
( ~ ( relation @ SY1197 )
| ( SY1197
!= ( relation_composition @ SV660 @ SY1194 ) )
| ~ ( ~ ! [SY1198: $i,SY1199: $i] :
( ! [SY1200: $i] :
( ~ ( in @ ( ordered_pair @ SY1198 @ SY1200 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1200 @ SY1199 ) @ SY1194 ) )
| ( in @ ( ordered_pair @ SY1198 @ SY1199 ) @ SY1197 ) )
| ~ ! [SY1201: $i,SY1202: $i] :
( ~ ( in @ ( ordered_pair @ SY1201 @ SY1202 ) @ SY1197 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1201 @ ( sK7_F @ SY1202 @ SY1201 @ SY1197 @ SY1194 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY1202 @ SY1201 @ SY1197 @ SY1194 @ SV660 ) @ SY1202 ) @ SY1194 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3908]) ).
thf(4099,plain,
( ( relation @ sK53_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3909]) ).
thf(4100,plain,
( ( relation_empty_yielding @ sK53_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3910]) ).
thf(4101,plain,
( ( ! [SX0: $i] :
( ( in @ ( sK29_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3911]) ).
thf(4102,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3912]) ).
thf(4103,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3913]) ).
thf(4104,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3914]) ).
thf(4105,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3915]) ).
thf(4106,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3916]) ).
thf(4107,plain,
! [SV661: $i] :
( ( ( relation @ SV661 )
= $false )
| ( ( ~ ( ~ ! [SY1203: $i] :
( ~ ( ~ ( ! [SY1204: $i] :
~ ( in @ ( ordered_pair @ SY1204 @ ( sK60_C @ SY1203 @ SV661 ) ) @ SV661 )
| ~ ( in @ ( sK60_C @ SY1203 @ SV661 ) @ SY1203 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK61_SY417 @ SY1203 @ SV661 ) @ ( sK60_C @ SY1203 @ SV661 ) ) @ SV661 )
| ( in @ ( sK60_C @ SY1203 @ SV661 ) @ SY1203 ) ) )
| ( SY1203
= ( relation_rng @ SV661 ) ) )
| ~ ! [SY1205: $i] :
( ( SY1205
!= ( relation_rng @ SV661 ) )
| ~ ( ~ ! [SY1206: $i] :
( ! [SY1207: $i] :
~ ( in @ ( ordered_pair @ SY1207 @ SY1206 ) @ SV661 )
| ( in @ SY1206 @ SY1205 ) )
| ~ ! [SY1208: $i] :
( ~ ( in @ SY1208 @ SY1205 )
| ( in @ ( ordered_pair @ ( sK59_D @ SY1208 @ SY1205 @ SV661 ) @ SY1208 ) @ SV661 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3917]) ).
thf(4108,plain,
! [SV662: $i] :
( ( ~ ! [SY1209: $i,SY1210: $i] :
( ~ ( ~ ( ~ ( in @ ( sK13_D @ SY1210 @ SY1209 @ SV662 ) @ SV662 )
| ( in @ ( sK13_D @ SY1210 @ SY1209 @ SV662 ) @ SY1209 )
| ~ ( in @ ( sK13_D @ SY1210 @ SY1209 @ SV662 ) @ SY1210 ) )
| ~ ~ ( ~ ( ( in @ ( sK13_D @ SY1210 @ SY1209 @ SV662 ) @ SV662 )
| ( in @ ( sK13_D @ SY1210 @ SY1209 @ SV662 ) @ SY1210 ) )
| ~ ( ~ ( in @ ( sK13_D @ SY1210 @ SY1209 @ SV662 ) @ SY1209 )
| ( in @ ( sK13_D @ SY1210 @ SY1209 @ SV662 ) @ SY1210 ) ) ) )
| ( SY1210
= ( set_difference @ SV662 @ SY1209 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3918]) ).
thf(4109,plain,
! [SV662: $i] :
( ( ~ ! [SY1211: $i,SY1212: $i] :
( ( SY1212
!= ( set_difference @ SV662 @ SY1211 ) )
| ~ ( ~ ! [SY1213: $i] :
( ~ ( in @ SY1213 @ SV662 )
| ( in @ SY1213 @ SY1211 )
| ( in @ SY1213 @ SY1212 ) )
| ~ ~ ( ~ ! [SY1214: $i] :
( ~ ( in @ SY1214 @ SY1212 )
| ( in @ SY1214 @ SV662 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1212 )
| ~ ( in @ SX3 @ SY1211 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3918]) ).
thf(4110,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)],[3919]) ).
thf(4111,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)],[3920]) ).
thf(4112,plain,
! [SV663: $i] :
( ( ~ ! [SY1216: $i,SY1217: $i] :
( ~ ( relation @ SY1217 )
| ~ ( in @ SV663 @ SY1216 )
| ~ ( in @ SV663 @ ( relation_rng @ SY1217 ) )
| ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SY1216 @ SY1217 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3921]) ).
thf(4113,plain,
! [SV663: $i] :
( ( ~ ~ ( ~ ! [SY1218: $i,SY1219: $i] :
( ~ ( relation @ SY1219 )
| ~ ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SY1218 @ SY1219 ) ) )
| ( in @ SV663 @ SY1218 ) )
| ~ ! [SY1220: $i,SY1221: $i] :
( ~ ( relation @ SY1221 )
| ~ ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SY1220 @ SY1221 ) ) )
| ( in @ SV663 @ ( relation_rng @ SY1221 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3921]) ).
thf(4114,plain,
! [SV664: $i] :
( ( ( ~ ( function @ SV664 ) )
= $true )
| ( ( ~ ( relation @ SV664 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY1222: $i] :
( ~ ( in @ SY1222 @ ( relation_dom @ SV664 ) )
| ! [SY1223: $i] :
( ( SY1223
!= ( apply @ SV664 @ SY1222 ) )
| ( in @ ( ordered_pair @ SY1222 @ SY1223 ) @ SV664 ) ) )
| ~ ! [SY1224: $i] :
( ~ ( in @ SY1224 @ ( relation_dom @ SV664 ) )
| ! [SY1225: $i] :
( ~ ( in @ ( ordered_pair @ SY1224 @ SY1225 ) @ SV664 )
| ( SY1225
= ( apply @ SV664 @ SY1224 ) ) ) ) )
| ~ ~ ( ~ ! [SY1226: $i] :
( ( in @ SY1226 @ ( relation_dom @ SV664 ) )
| ! [SY1227: $i] :
( ( SY1227
!= ( apply @ SV664 @ SY1226 ) )
| ( SY1227 = empty_set ) ) )
| ~ ! [SY1228: $i] :
( ( in @ SY1228 @ ( relation_dom @ SV664 ) )
| ! [SY1229: $i] :
( ( SY1229 != empty_set )
| ( SY1229
= ( apply @ SV664 @ SY1228 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3922]) ).
thf(4115,plain,
! [SV665: $i] :
( ( ( relation @ SV665 )
= $false )
| ( ( ~ ( ~ ! [SY1230: $i] :
( ~ ( relation @ SY1230 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SY1230 @ SV665 ) @ ( sK20_SY399 @ SY1230 @ SV665 ) ) @ SV665 )
| ~ ~ ( in @ ( ordered_pair @ ( sK19_C @ SY1230 @ SV665 ) @ ( sK20_SY399 @ SY1230 @ SV665 ) ) @ SY1230 ) )
| ( subset @ SV665 @ SY1230 ) )
| ~ ! [SY1231: $i] :
( ~ ( relation @ SY1231 )
| ~ ( subset @ SV665 @ SY1231 )
| ! [SY1232: $i,SY1233: $i] :
( ~ ( in @ ( ordered_pair @ SY1232 @ SY1233 ) @ SV665 )
| ( in @ ( ordered_pair @ SY1232 @ SY1233 ) @ SY1231 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3923]) ).
thf(4116,plain,
! [SV666: $i,SV742: $i] :
( ( ( ~ ( function @ SV742 )
| ~ ( relation @ SV742 ) )
= $true )
| ( ( ~ ( ~ ! [SY1376: $i] :
( ~ ( function @ SY1376 )
| ~ ( relation @ SY1376 )
| ~ ( in @ SV666 @ ( relation_dom @ SY1376 ) )
| ~ ( in @ ( apply @ SY1376 @ SV666 ) @ ( relation_dom @ SV742 ) )
| ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1376 @ SV742 ) ) ) )
| ~ ~ ( ~ ! [SY1377: $i] :
( ~ ( function @ SY1377 )
| ~ ( relation @ SY1377 )
| ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1377 @ SV742 ) ) )
| ( in @ SV666 @ ( relation_dom @ SY1377 ) ) )
| ~ ! [SY1378: $i] :
( ~ ( function @ SY1378 )
| ~ ( relation @ SY1378 )
| ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1378 @ SV742 ) ) )
| ( in @ ( apply @ SY1378 @ SV666 ) @ ( relation_dom @ SV742 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3924]) ).
thf(4117,plain,
! [SV667: $i] :
( ( ~ ! [SY1238: $i,SY1239: $i] :
( ~ ( relation @ SY1239 )
| ! [SY1240: $i] :
( ~ ( in @ SY1240 @ ( relation_rng @ SY1239 ) )
| ~ ( in @ ( ordered_pair @ SV667 @ SY1240 ) @ SY1239 )
| ~ ( in @ SY1240 @ SY1238 ) )
| ( in @ SV667 @ ( relation_inverse_image @ SY1239 @ SY1238 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3925]) ).
thf(4118,plain,
! [SV667: $i] :
( ( ~ ! [SY1241: $i,SY1242: $i] :
( ~ ( relation @ SY1242 )
| ~ ( in @ SV667 @ ( relation_inverse_image @ SY1242 @ SY1241 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK51_D @ SY1242 @ SY1241 @ SV667 ) @ ( relation_rng @ SY1242 ) )
| ~ ( in @ ( ordered_pair @ SV667 @ ( sK51_D @ SY1242 @ SY1241 @ SV667 ) ) @ SY1242 ) )
| ~ ( in @ ( sK51_D @ SY1242 @ SY1241 @ SV667 ) @ SY1241 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3925]) ).
thf(4119,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK49_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK49_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3926]) ).
thf(4120,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3927]) ).
thf(4121,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3928]) ).
thf(4122,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3929]) ).
thf(4123,plain,
! [SV668: $i] :
( ( ~ ! [SY1243: $i,SY1244: $i] :
( ~ ( relation @ SY1244 )
| ~ ( in @ SV668 @ SY1243 )
| ~ ( in @ SV668 @ ( relation_dom @ SY1244 ) )
| ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SY1244 @ SY1243 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3930]) ).
thf(4124,plain,
! [SV668: $i] :
( ( ~ ~ ( ~ ! [SY1245: $i,SY1246: $i] :
( ~ ( relation @ SY1246 )
| ~ ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SY1246 @ SY1245 ) ) )
| ( in @ SV668 @ SY1245 ) )
| ~ ! [SY1247: $i,SY1248: $i] :
( ~ ( relation @ SY1248 )
| ~ ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SY1248 @ SY1247 ) ) )
| ( in @ SV668 @ ( relation_dom @ SY1248 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3930]) ).
thf(4125,plain,
! [SV669: $i] :
( ( ~ ! [SY1249: $i,SY1250: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY1250 @ SY1249 @ SV669 ) @ SY1250 )
| ~ ( in @ ( sK26_D @ SY1250 @ SY1249 @ SV669 ) @ SV669 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY1250 @ SY1249 @ SV669 ) @ SY1250 )
| ~ ( in @ ( sK26_D @ SY1250 @ SY1249 @ SV669 ) @ SY1249 ) ) )
| ~ ( ( in @ ( sK26_D @ SY1250 @ SY1249 @ SV669 ) @ SY1250 )
| ( in @ ( sK26_D @ SY1250 @ SY1249 @ SV669 ) @ SV669 )
| ( in @ ( sK26_D @ SY1250 @ SY1249 @ SV669 ) @ SY1249 ) ) )
| ( SY1250
= ( set_union2 @ SV669 @ SY1249 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3931]) ).
thf(4126,plain,
! [SV669: $i] :
( ( ~ ! [SY1251: $i,SY1252: $i] :
( ( SY1252
!= ( set_union2 @ SV669 @ SY1251 ) )
| ~ ( ~ ! [SY1253: $i] :
( ~ ( in @ SY1253 @ SY1252 )
| ( in @ SY1253 @ SV669 )
| ( in @ SY1253 @ SY1251 ) )
| ~ ~ ( ~ ! [SY1254: $i] :
( ~ ( in @ SY1254 @ SV669 )
| ( in @ SY1254 @ SY1252 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1251 )
| ( in @ SX3 @ SY1252 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3931]) ).
thf(4127,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY406 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ ( sK33_SY406 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK31_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)],[3932]) ).
thf(4128,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)],[3933]) ).
thf(4129,plain,
! [SV670: $i] :
( ( ~ ! [SY1256: $i,SY1257: $i] :
( ~ ( ~ ( ! [SY1258: $i,SY1259: $i] :
( ~ ( in @ SY1258 @ SV670 )
| ~ ( in @ SY1259 @ SY1256 )
| ( ( sK23_D @ SY1257 @ SY1256 @ SV670 )
!= ( ordered_pair @ SY1258 @ SY1259 ) ) )
| ~ ( in @ ( sK23_D @ SY1257 @ SY1256 @ SV670 ) @ SY1257 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY403 @ SY1257 @ SY1256 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK25_SY405 @ SY1257 @ SY1256 @ SV670 ) @ SY1256 ) )
| ( ( sK23_D @ SY1257 @ SY1256 @ SV670 )
!= ( ordered_pair @ ( sK24_SY403 @ SY1257 @ SY1256 @ SV670 ) @ ( sK25_SY405 @ SY1257 @ SY1256 @ SV670 ) ) ) )
| ( in @ ( sK23_D @ SY1257 @ SY1256 @ SV670 ) @ SY1257 ) ) )
| ( SY1257
= ( cartesian_product2 @ SV670 @ SY1256 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3934]) ).
thf(4130,plain,
! [SV670: $i] :
( ( ~ ! [SY1260: $i,SY1261: $i] :
( ( SY1261
!= ( cartesian_product2 @ SV670 @ SY1260 ) )
| ~ ( ~ ! [SY1262: $i] :
( ! [SY1263: $i,SY1264: $i] :
( ~ ( in @ SY1263 @ SV670 )
| ~ ( in @ SY1264 @ SY1260 )
| ( SY1262
!= ( ordered_pair @ SY1263 @ SY1264 ) ) )
| ( in @ SY1262 @ SY1261 ) )
| ~ ! [SY1265: $i] :
( ~ ( in @ SY1265 @ SY1261 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY1265 @ SY1261 @ SY1260 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK22_SY400 @ SY1265 @ SY1261 @ SY1260 @ SV670 ) @ SY1260 ) )
| ( SY1265
!= ( ordered_pair @ ( sK21_E @ SY1265 @ SY1261 @ SY1260 @ SV670 ) @ ( sK22_SY400 @ SY1265 @ SY1261 @ SY1260 @ SV670 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3934]) ).
thf(4131,plain,
! [SV671: $i] :
( ( ~ ! [SY1266: $i,SY1267: $i] :
( ~ ( function @ SY1267 )
| ~ ( relation @ SY1267 )
| ( SY1266
!= ( apply @ SY1267 @ SV671 ) )
| ~ ( in @ SV671 @ ( relation_dom @ SY1267 ) )
| ( in @ ( ordered_pair @ SV671 @ SY1266 ) @ SY1267 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3935]) ).
thf(4132,plain,
! [SV671: $i] :
( ( ~ ~ ( ~ ! [SY1268: $i,SY1269: $i] :
( ~ ( function @ SY1269 )
| ~ ( relation @ SY1269 )
| ~ ( in @ ( ordered_pair @ SV671 @ SY1268 ) @ SY1269 )
| ( SY1268
= ( apply @ SY1269 @ SV671 ) ) )
| ~ ! [SY1270: $i,SY1271: $i] :
( ~ ( function @ SY1271 )
| ~ ( relation @ SY1271 )
| ~ ( in @ ( ordered_pair @ SV671 @ SY1270 ) @ SY1271 )
| ( in @ SV671 @ ( relation_dom @ SY1271 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3935]) ).
thf(4133,plain,
! [SV672: $i] :
( ( ( relation @ SV672 )
= $false )
| ( ( ~ ( ~ ! [SY1272: $i] :
( ~ ( relation @ SY1272 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SY1272 @ SV672 ) @ ( sK12_SY396 @ SY1272 @ SV672 ) ) @ SY1272 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SY1272 @ SV672 ) @ ( sK11_C @ SY1272 @ SV672 ) ) @ SV672 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_C @ SY1272 @ SV672 ) @ ( sK12_SY396 @ SY1272 @ SV672 ) ) @ SY1272 )
| ( in @ ( ordered_pair @ ( sK12_SY396 @ SY1272 @ SV672 ) @ ( sK11_C @ SY1272 @ SV672 ) ) @ SV672 ) ) )
| ( SY1272
= ( relation_inverse @ SV672 ) ) )
| ~ ! [SY1273: $i] :
( ~ ( relation @ SY1273 )
| ( SY1273
!= ( relation_inverse @ SV672 ) )
| ~ ( ~ ! [SY1274: $i,SY1275: $i] :
( ~ ( in @ ( ordered_pair @ SY1274 @ SY1275 ) @ SY1273 )
| ( in @ ( ordered_pair @ SY1275 @ SY1274 ) @ SV672 ) )
| ~ ! [SY1276: $i,SY1277: $i] :
( ~ ( in @ ( ordered_pair @ SY1277 @ SY1276 ) @ SV672 )
| ( in @ ( ordered_pair @ SY1276 @ SY1277 ) @ SY1273 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3936]) ).
thf(4134,plain,
( ( function @ sK58_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3937]) ).
thf(4135,plain,
( ( relation @ sK58_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3938]) ).
thf(4136,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3939]) ).
thf(4137,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3940]) ).
thf(4138,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( function @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3941]) ).
thf(4139,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3942]) ).
thf(4140,plain,
! [SV673: $i] :
( ( ~ ! [SY1278: $i,SY1279: $i] :
( ~ ( relation @ SY1279 )
| ~ ( in @ ( ordered_pair @ SV673 @ SY1278 ) @ SY1279 )
| ( in @ SV673 @ ( relation_dom @ SY1279 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3943]) ).
thf(4141,plain,
! [SV673: $i] :
( ( ~ ! [SY1280: $i,SY1281: $i] :
( ~ ( relation @ SY1281 )
| ~ ( in @ ( ordered_pair @ SV673 @ SY1280 ) @ SY1281 )
| ( in @ SY1280 @ ( relation_rng @ SY1281 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3943]) ).
thf(4142,plain,
! [SV743: $i,SV674: $i] :
( ( ~ ! [SY1379: $i,SY1380: $i] :
( ~ ( in @ SV674 @ SY1379 )
| ~ ( in @ SV743 @ SY1380 )
| ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SY1379 @ SY1380 ) ) )
| ~ ~ ( ~ ! [SY1381: $i] :
( ! [SY1382: $i] :
~ ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SY1381 @ SY1382 ) )
| ( in @ SV674 @ SY1381 ) )
| ~ ! [SY1383: $i,SY1384: $i] :
( ~ ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SY1383 @ SY1384 ) )
| ( in @ SV743 @ SY1384 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3944]) ).
thf(4143,plain,
! [SV675: $i] :
( ( ~ ! [SY1289: $i,SY1290: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY1290 @ SY1289 @ SV675 ) @ SY1290 )
| ( ( sK27_D @ SY1290 @ SY1289 @ SV675 )
!= SV675 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY1290 @ SY1289 @ SV675 ) @ SY1290 )
| ( ( sK27_D @ SY1290 @ SY1289 @ SV675 )
!= SY1289 ) ) )
| ~ ( ( in @ ( sK27_D @ SY1290 @ SY1289 @ SV675 ) @ SY1290 )
| ( ( sK27_D @ SY1290 @ SY1289 @ SV675 )
= SV675 )
| ( ( sK27_D @ SY1290 @ SY1289 @ SV675 )
= SY1289 ) ) )
| ( SY1290
= ( unordered_pair @ SV675 @ SY1289 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3945]) ).
thf(4144,plain,
! [SV675: $i] :
( ( ~ ! [SY1291: $i,SY1292: $i] :
( ( SY1292
!= ( unordered_pair @ SV675 @ SY1291 ) )
| ~ ( ~ ! [SY1293: $i] :
( ~ ( in @ SY1293 @ SY1292 )
| ( SY1293 = SV675 )
| ( SY1293 = SY1291 ) )
| ~ ~ ( ~ ! [SY1294: $i] :
( ( SY1294 != SV675 )
| ( in @ SY1294 @ SY1292 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY1291 )
| ( in @ SX3 @ SY1292 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3945]) ).
thf(4145,plain,
! [SV744: $i,SV676: $i] :
( ( ~ ! [SY1385: $i,SY1386: $i] :
( ~ ( in @ SV676 @ SY1385 )
| ~ ( in @ SV744 @ SY1386 )
| ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SY1385 @ SY1386 ) ) )
| ~ ~ ( ~ ! [SY1387: $i] :
( ! [SY1388: $i] :
~ ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SY1387 @ SY1388 ) )
| ( in @ SV676 @ SY1387 ) )
| ~ ! [SY1389: $i,SY1390: $i] :
( ~ ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SY1389 @ SY1390 ) )
| ( in @ SV744 @ SY1390 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3946]) ).
thf(4146,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK48_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3947]) ).
thf(4147,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3948]) ).
thf(4148,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( function @ ( function_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3949]) ).
thf(4149,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( relation @ ( function_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3950]) ).
thf(4150,plain,
! [SV677: $i,SV745: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK4_C @ SV745 @ SV677 ) @ SV677 )
| ~ ( in @ ( sK4_C @ SV745 @ SV677 ) @ SV745 ) )
| ~ ( ( in @ ( sK4_C @ SV745 @ SV677 ) @ SV677 )
| ( in @ ( sK4_C @ SV745 @ SV677 ) @ SV745 ) ) ) )
= $true )
| ( ( SV677 = SV745 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3951]) ).
thf(4151,plain,
! [SV678: $i] :
( ( ~ ! [SY1304: $i] :
( ~ ( subset @ SV678 @ SY1304 )
| ! [SY1305: $i] : ( subset @ ( cartesian_product2 @ SV678 @ SY1305 ) @ ( cartesian_product2 @ SY1304 @ SY1305 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3952]) ).
thf(4152,plain,
! [SV678: $i] :
( ( ~ ! [SY1306: $i] :
( ~ ( subset @ SV678 @ SY1306 )
| ! [SY1307: $i] : ( subset @ ( cartesian_product2 @ SY1307 @ SV678 ) @ ( cartesian_product2 @ SY1307 @ SY1306 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3952]) ).
thf(4153,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ ( sK16_SY398 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK16_SY398 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK15_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3953]) ).
thf(4154,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 @ ( sK14_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK14_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3954]) ).
thf(4155,plain,
! [SV679: $i] :
( ( ( relation @ SV679 )
= $false )
| ( ( ~ ( ~ ! [SY1308: $i] :
( ~ ( ~ ( ! [SY1309: $i] :
~ ( in @ ( ordered_pair @ ( sK63_C @ SY1308 @ SV679 ) @ SY1309 ) @ SV679 )
| ~ ( in @ ( sK63_C @ SY1308 @ SV679 ) @ SY1308 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_C @ SY1308 @ SV679 ) @ ( sK64_SY419 @ SY1308 @ SV679 ) ) @ SV679 )
| ( in @ ( sK63_C @ SY1308 @ SV679 ) @ SY1308 ) ) )
| ( SY1308
= ( relation_dom @ SV679 ) ) )
| ~ ! [SY1310: $i] :
( ( SY1310
!= ( relation_dom @ SV679 ) )
| ~ ( ~ ! [SY1311: $i] :
( ! [SY1312: $i] :
~ ( in @ ( ordered_pair @ SY1311 @ SY1312 ) @ SV679 )
| ( in @ SY1311 @ SY1310 ) )
| ~ ! [SY1313: $i] :
( ~ ( in @ SY1313 @ SY1310 )
| ( in @ ( ordered_pair @ SY1313 @ ( sK62_D @ SY1313 @ SY1310 @ SV679 ) ) @ SV679 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3955]) ).
thf(4156,plain,
! [SV680: $i] :
( ( ~ ! [SY1314: $i,SY1315: $i] :
( ~ ( relation @ SY1315 )
| ~ ( in @ ( ordered_pair @ SV680 @ SY1314 ) @ SY1315 )
| ( in @ SV680 @ ( relation_field @ SY1315 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3956]) ).
thf(4157,plain,
! [SV680: $i] :
( ( ~ ! [SY1316: $i,SY1317: $i] :
( ~ ( relation @ SY1317 )
| ~ ( in @ ( ordered_pair @ SV680 @ SY1316 ) @ SY1317 )
| ( in @ SY1316 @ ( relation_field @ SY1317 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3956]) ).
thf(4158,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK44_C @ SX1 @ SX0 )
!= ( sK45_SY414 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY414 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK44_C @ SX1 @ SX0 )
= ( sK45_SY414 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY414 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY414 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3957]) ).
thf(4159,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)],[3958]) ).
thf(4160,plain,
! [SV681: $i] :
( ( ( relation @ SV681 )
= $false )
| ( ( ~ ( ~ ! [SY1318: $i,SY1319: $i] :
( ~ ( relation @ SY1319 )
| ~ ( ~ ( ~ ( in @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ SY1318 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ ( sK43_SY413 @ SY1319 @ SY1318 @ SV681 ) ) @ SV681 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ ( sK43_SY413 @ SY1319 @ SY1318 @ SV681 ) ) @ SY1319 ) )
| ~ ~ ( ~ ( ( in @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ SY1318 )
| ( in @ ( ordered_pair @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ ( sK43_SY413 @ SY1319 @ SY1318 @ SV681 ) ) @ SY1319 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ ( sK43_SY413 @ SY1319 @ SY1318 @ SV681 ) ) @ SV681 )
| ( in @ ( ordered_pair @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ ( sK43_SY413 @ SY1319 @ SY1318 @ SV681 ) ) @ SY1319 ) ) ) )
| ( SY1319
= ( relation_dom_restriction @ SV681 @ SY1318 ) ) )
| ~ ! [SY1320: $i,SY1321: $i] :
( ~ ( relation @ SY1321 )
| ( SY1321
!= ( relation_dom_restriction @ SV681 @ SY1320 ) )
| ~ ( ~ ! [SY1322: $i,SY1323: $i] :
( ~ ( in @ SY1322 @ SY1320 )
| ~ ( in @ ( ordered_pair @ SY1322 @ SY1323 ) @ SV681 )
| ( in @ ( ordered_pair @ SY1322 @ SY1323 ) @ SY1321 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY1321 )
| ( in @ SX3 @ SY1320 ) )
| ~ ! [SY1326: $i,SY1327: $i] :
( ~ ( in @ ( ordered_pair @ SY1326 @ SY1327 ) @ SY1321 )
| ( in @ ( ordered_pair @ SY1326 @ SY1327 ) @ SV681 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3959]) ).
thf(4161,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK30_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK30_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK30_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK30_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3960]) ).
thf(4162,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)],[3961]) ).
thf(4163,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3962]) ).
thf(4164,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3963]) ).
thf(4165,plain,
! [SV682: $i] :
( ( ~ ! [SY1328: $i,SY1329: $i] :
( ~ ( relation @ SY1329 )
| ! [SY1330: $i] :
( ~ ( in @ SY1330 @ ( relation_dom @ SY1329 ) )
| ~ ( in @ ( ordered_pair @ SY1330 @ SV682 ) @ SY1329 )
| ~ ( in @ SY1330 @ SY1328 ) )
| ( in @ SV682 @ ( relation_image @ SY1329 @ SY1328 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3964]) ).
thf(4166,plain,
! [SV682: $i] :
( ( ~ ! [SY1331: $i,SY1332: $i] :
( ~ ( relation @ SY1332 )
| ~ ( in @ SV682 @ ( relation_image @ SY1332 @ SY1331 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK52_D @ SY1332 @ SY1331 @ SV682 ) @ ( relation_dom @ SY1332 ) )
| ~ ( in @ ( ordered_pair @ ( sK52_D @ SY1332 @ SY1331 @ SV682 ) @ SV682 ) @ SY1332 ) )
| ~ ( in @ ( sK52_D @ SY1332 @ SY1331 @ SV682 ) @ SY1331 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3964]) ).
thf(4167,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3965]) ).
thf(4168,plain,
( ( relation_empty_yielding @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3966]) ).
thf(4169,plain,
! [SV683: $i] :
( ( ( relation @ SV683 )
= $false )
| ( ( ~ ( ~ ! [SY1333: $i] :
( ~ ( relation @ SY1333 )
| ~ ( subset @ SV683 @ SY1333 )
| ( subset @ ( relation_dom @ SV683 ) @ ( relation_dom @ SY1333 ) ) )
| ~ ! [SY1334: $i] :
( ~ ( relation @ SY1334 )
| ~ ( subset @ SV683 @ SY1334 )
| ( subset @ ( relation_rng @ SV683 ) @ ( relation_rng @ SY1334 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3967]) ).
thf(4170,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3968]) ).
thf(4171,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3969]) ).
thf(4172,plain,
! [SV684: $i] :
( ( ( relation @ SV684 )
= $false )
| ( ( ~ ( ~ ! [SY1335: $i] :
( ~ ( relation @ SY1335 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SY1335 @ SV684 ) @ ( sK66_SY420 @ SY1335 @ SV684 ) ) @ SV684 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SY1335 @ SV684 ) @ ( sK66_SY420 @ SY1335 @ SV684 ) ) @ SY1335 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_C @ SY1335 @ SV684 ) @ ( sK66_SY420 @ SY1335 @ SV684 ) ) @ SV684 )
| ( in @ ( ordered_pair @ ( sK65_C @ SY1335 @ SV684 ) @ ( sK66_SY420 @ SY1335 @ SV684 ) ) @ SY1335 ) ) )
| ( SV684 = SY1335 ) )
| ~ ! [SY1336: $i] :
( ~ ( relation @ SY1336 )
| ( SV684 != SY1336 )
| ~ ( ~ ! [SY1337: $i,SY1338: $i] :
( ~ ( in @ ( ordered_pair @ SY1337 @ SY1338 ) @ SV684 )
| ( in @ ( ordered_pair @ SY1337 @ SY1338 ) @ SY1336 ) )
| ~ ! [SY1339: $i,SY1340: $i] :
( ~ ( in @ ( ordered_pair @ SY1339 @ SY1340 ) @ SY1336 )
| ( in @ ( ordered_pair @ SY1339 @ SY1340 ) @ SV684 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3970]) ).
thf(4173,plain,
! [SV685: $i] :
( ( ~ ! [SY1341: $i] :
( ~ ( subset @ SY1341 @ ( sK2_B @ SV685 ) )
| ( are_equipotent @ SY1341 @ ( sK2_B @ SV685 ) )
| ( in @ SY1341 @ ( sK2_B @ SV685 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3971]) ).
thf(4174,plain,
! [SV685: $i] :
( ( ~ ~ ( ~ ! [SY1342: $i] :
( ~ ( ~ ! [SY1343: $i] :
( ~ ( subset @ SY1343 @ SY1342 )
| ( in @ SY1343 @ ( sK3_SY386 @ SY1342 @ SV685 ) ) )
| ~ ( in @ ( sK3_SY386 @ SY1342 @ SV685 ) @ ( sK2_B @ SV685 ) ) )
| ~ ( in @ SY1342 @ ( sK2_B @ SV685 ) ) )
| ~ ~ ( ~ ! [SY1344: $i,SY1345: $i] :
( ~ ( in @ SY1344 @ ( sK2_B @ SV685 ) )
| ~ ( subset @ SY1345 @ SY1344 )
| ( in @ SY1345 @ ( sK2_B @ SV685 ) ) )
| ~ ( in @ SV685 @ ( sK2_B @ SV685 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3971]) ).
thf(4175,plain,
( ( ( relation_dom @ empty_set )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3972]) ).
thf(4176,plain,
( ( ( relation_rng @ empty_set )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3973]) ).
thf(4177,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3974]) ).
thf(4178,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)],[3975]) ).
thf(4179,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK28_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK28_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3976]) ).
thf(4180,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)],[3977]) ).
thf(4181,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3978]) ).
thf(4182,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)],[3979]) ).
thf(4183,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3980]) ).
thf(4184,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3981]) ).
thf(4185,plain,
( ( ~ ( ~ ( empty @ sK56_A )
| ~ ( relation @ sK56_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3982]) ).
thf(4186,plain,
( ( function @ sK56_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3983]) ).
thf(4187,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK50_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK50_C @ SX1 @ SX0 ) )
!= ( sK50_C @ SX1 @ SX0 ) ) ) )
| ( ( relation_dom @ SX1 )
!= SX0 )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3984]) ).
thf(4188,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)],[3985]) ).
thf(4189,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3986]) ).
thf(4190,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3987]) ).
thf(4191,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK18_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK18_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3988]) ).
thf(4192,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3989]) ).
thf(4193,plain,
! [SV566: $i,SV686: $i] :
( ( ( relation @ SV686 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV566 @ SV686 ) ) @ SV566 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3990]) ).
thf(4194,plain,
! [SV567: $i,SV687: $i] :
( ( ( relation @ SV687 )
= $false )
| ( ( subset @ ( relation_rng_restriction @ SV567 @ SV687 ) @ SV687 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3991]) ).
thf(4195,plain,
! [SV568: $i,SV688: $i] :
( ( ( relation @ SV688 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV568 @ SV688 ) ) @ ( relation_rng @ SV688 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3992]) ).
thf(4196,plain,
! [SV569: $i,SV689: $i] :
( ( ( relation @ SV689 )
= $false )
| ( ( ( relation_rng @ ( relation_rng_restriction @ SV569 @ SV689 ) )
= ( set_intersection2 @ ( relation_rng @ SV689 ) @ SV569 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3993]) ).
thf(4197,plain,
! [SV690: $i,SV570: $i,SV746: $i] :
( ( ( ~ ( relation @ SV746 ) )
= $true )
| ( ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV570 @ SV746 ) @ SV690 )
= ( relation_rng_restriction @ SV570 @ ( relation_dom_restriction @ SV746 @ SV690 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3994]) ).
thf(4198,plain,
! [SV571: $i,SV691: $i] :
( ( ( relation @ SV691 )
= $false )
| ( ( subset @ ( relation_image @ SV691 @ SV571 ) @ ( relation_rng @ SV691 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3995]) ).
thf(4199,plain,
! [SV572: $i,SV692: $i] :
( ( ( relation @ SV692 )
= $false )
| ( ( ( relation_image @ SV692 @ SV572 )
= ( relation_image @ SV692 @ ( set_intersection2 @ ( relation_dom @ SV692 ) @ SV572 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3996]) ).
thf(4200,plain,
! [SV574: $i,SV755: $i] :
( ( ( ~ ( relation @ SV755 )
| ( ( relation_rng @ ( relation_composition @ SV574 @ SV755 ) )
= ( relation_image @ SV755 @ ( relation_rng @ SV574 ) ) ) )
= $true )
| ( ( relation @ SV574 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3998]) ).
thf(4201,plain,
! [SV575: $i,SV693: $i] :
( ( ( relation @ SV693 )
= $false )
| ( ( subset @ ( relation_inverse_image @ SV693 @ SV575 ) @ ( relation_dom @ SV693 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3999]) ).
thf(4202,plain,
! [SV694: $i,SV576: $i,SV747: $i] :
( ( ( ~ ( relation @ SV747 ) )
= $true )
| ( ( ~ ( subset @ SV576 @ SV694 )
| ( subset @ ( relation_inverse_image @ SV747 @ SV576 ) @ ( relation_inverse_image @ SV747 @ SV694 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4000]) ).
thf(4203,plain,
! [SV578: $i,SV756: $i] :
( ( ( ~ ( relation @ SV756 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV578 @ SV756 ) ) @ ( relation_dom @ SV578 ) ) )
= $true )
| ( ( relation @ SV578 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4002]) ).
thf(4204,plain,
! [SV579: $i,SV757: $i] :
( ( ( ~ ( relation @ SV757 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV579 @ SV757 ) ) @ ( relation_rng @ SV757 ) ) )
= $true )
| ( ( relation @ SV579 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4003]) ).
thf(4205,plain,
! [SV580: $i,SV758: $i] :
( ( ( ~ ( relation @ SV758 )
| ~ ( subset @ ( relation_rng @ SV580 ) @ ( relation_dom @ SV758 ) )
| ( ( relation_dom @ ( relation_composition @ SV580 @ SV758 ) )
= ( relation_dom @ SV580 ) ) )
= $true )
| ( ( relation @ SV580 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4004]) ).
thf(4206,plain,
! [SV581: $i,SV759: $i] :
( ( ( ~ ( relation @ SV759 )
| ~ ( subset @ ( relation_dom @ SV581 ) @ ( relation_rng @ SV759 ) )
| ( ( relation_rng @ ( relation_composition @ SV759 @ SV581 ) )
= ( relation_rng @ SV581 ) ) )
= $true )
| ( ( relation @ SV581 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4005]) ).
thf(4207,plain,
! [SV582: $i,SV695: $i] :
( ( ( relation @ SV695 )
= $false )
| ( ( subset @ ( relation_dom_restriction @ SV695 @ SV582 ) @ SV695 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4006]) ).
thf(4208,plain,
! [SV583: $i,SV696: $i] :
( ( ( relation @ SV696 )
= $false )
| ( ( ( relation_dom @ ( relation_dom_restriction @ SV696 @ SV583 ) )
= ( set_intersection2 @ ( relation_dom @ SV696 ) @ SV583 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4007]) ).
thf(4209,plain,
! [SV584: $i,SV697: $i] :
( ( ( relation @ SV697 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV697 @ SV584 ) ) @ ( relation_rng @ SV697 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4008]) ).
thf(4210,plain,
! [SV588: $i] :
( ( ( function @ SV588 )
= $false )
| ( ( ~ ( relation @ SV588 ) )
= $true )
| ( ( ~ ( one_to_one @ SV588 )
| ( ( function_inverse @ SV588 )
= ( relation_inverse @ SV588 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4012]) ).
thf(4211,plain,
! [SV698: $i,SV590: $i] :
( ( ( ~ ( relation @ SV590 ) )
= $true )
| ( ( ~ ( relation @ SV698 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV590 @ SV698 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4014]) ).
thf(4212,plain,
! [SV760: $i,SV592: $i] :
( ( ( relation @ ( relation_dom_restriction @ SV592 @ SV760 ) )
= $true )
| ( ( relation @ SV592 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4015]) ).
thf(4213,plain,
! [SV593: $i,SV699: $i] :
( ( ( relation @ SV699 )
= $false )
| ( ( relation @ ( relation_rng_restriction @ SV593 @ SV699 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4016]) ).
thf(4214,plain,
! [SV700: $i,SV594: $i] :
( ( ( ~ ( relation @ SV594 ) )
= $true )
| ( ( ~ ( relation @ SV700 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV594 @ SV700 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4017]) ).
thf(4215,plain,
! [SV701: $i,SV595: $i] :
( ( ( ~ ( relation @ SV595 ) )
= $true )
| ( ( ~ ( relation @ SV701 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV595 @ SV701 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4018]) ).
thf(4216,plain,
! [SV596: $i] :
( ( ( relation @ SV596 )
= $false )
| ( ( empty @ SV596 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV596 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4019]) ).
thf(4217,plain,
! [SV597: $i] :
( ( ( relation @ SV597 )
= $false )
| ( ( empty @ SV597 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV597 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4020]) ).
thf(4218,plain,
! [SV702: $i,SV600: $i] :
( ( ( in @ SV600 @ SV702 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV600 ) @ SV702 )
= SV702 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4022]) ).
thf(4219,plain,
! [SV703: $i,SV601: $i] :
( ( ( in @ SV601 @ SV703 )
= $false )
| ( ( subset @ SV601 @ ( union @ SV703 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4023]) ).
thf(4220,plain,
! [SV761: $i,SV748: $i,SV704: $i,SV602: $i] :
( ( ~ ( subset @ SV602 @ SV704 )
| ~ ( subset @ SV748 @ SV761 )
| ( subset @ ( cartesian_product2 @ SV602 @ SV748 ) @ ( cartesian_product2 @ SV704 @ SV761 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4024]) ).
thf(4221,plain,
! [SV705: $i,SV603: $i] :
( ( ( subset @ SV603 @ SV705 )
= $false )
| ( ( ( set_union2 @ SV603 @ SV705 )
= SV705 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4025]) ).
thf(4222,plain,
! [SV604: $i,SV706: $i] :
( ( ( relation @ SV706 )
= $false )
| ( ( ( SV604 = empty_set )
| ~ ( subset @ SV604 @ ( relation_rng @ SV706 ) )
| ( ( relation_inverse_image @ SV706 @ SV604 )
!= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4026]) ).
thf(4223,plain,
! [SV749: $i,SV708: $i,SV606: $i] :
( ( ( ~ ( subset @ SV606 @ SV708 )
| ~ ( subset @ SV606 @ SV749 ) )
= $true )
| ( ( subset @ SV606 @ ( set_intersection2 @ SV708 @ SV749 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4027]) ).
thf(4224,plain,
! [SV750: $i,SV709: $i,SV607: $i] :
( ( ( ~ ( subset @ SV607 @ SV709 )
| ~ ( subset @ SV709 @ SV750 ) )
= $true )
| ( ( subset @ SV607 @ SV750 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4028]) ).
thf(4225,plain,
! [SV608: $i,SV710: $i] :
( ( ( ~ ( function @ SV710 ) )
= $true )
| ( ( ~ ( relation @ SV710 ) )
= $true )
| ( ( ! [SY1352: $i] :
( ~ ( function @ SY1352 )
| ~ ( relation @ SY1352 )
| ~ ( in @ SV608 @ ( relation_dom @ ( relation_composition @ SY1352 @ SV710 ) ) )
| ( ( apply @ ( relation_composition @ SY1352 @ SV710 ) @ SV608 )
= ( apply @ SV710 @ ( apply @ SY1352 @ SV608 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4029]) ).
thf(4226,plain,
! [SV609: $i,SV711: $i] :
( ( ( ~ ( function @ SV711 ) )
= $true )
| ( ( ~ ( relation @ SV711 ) )
= $true )
| ( ( ! [SY1353: $i] :
( ~ ( function @ SY1353 )
| ~ ( relation @ SY1353 )
| ~ ( in @ SV609 @ ( relation_dom @ SV711 ) )
| ( ( apply @ ( relation_composition @ SV711 @ SY1353 ) @ SV609 )
= ( apply @ SY1353 @ ( apply @ SV711 @ SV609 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4030]) ).
thf(4227,plain,
! [SV712: $i,SV610: $i] :
( ( ( subset @ SV610 @ SV712 )
= $false )
| ( ( ! [SY1354: $i] : ( subset @ ( set_intersection2 @ SV610 @ SY1354 ) @ ( set_intersection2 @ SV712 @ SY1354 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4031]) ).
thf(4228,plain,
! [SV713: $i,SV611: $i] :
( ( ( subset @ SV611 @ SV713 )
= $false )
| ( ( ( set_intersection2 @ SV611 @ SV713 )
= SV611 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4032]) ).
thf(4229,plain,
! [SV714: $i,SV613: $i] :
( ( ( subset @ SV613 @ SV714 )
= $false )
| ( ( ! [SY1355: $i] : ( subset @ ( set_difference @ SV613 @ SY1355 ) @ ( set_difference @ SV714 @ SY1355 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4033]) ).
thf(4230,plain,
! [SV614: $i,SV715: $i] :
( ( ( in @ SV715 @ SV614 )
= $false )
| ( ( ( apply @ ( identity_relation @ SV614 ) @ SV715 )
= SV715 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4034]) ).
thf(4231,plain,
! [SV719: $i,SV619: $i] :
( ( ( subset @ SV619 @ SV719 )
= $false )
| ( ( SV719
= ( set_union2 @ SV619 @ ( set_difference @ SV719 @ SV619 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4036]) ).
thf(4232,plain,
! [SV720: $i,SV620: $i] :
( ( ( in @ SV620 @ SV720 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV620 ) @ SV720 )
= SV720 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4037]) ).
thf(4233,plain,
! [SV622: $i] :
( ( ( in @ ( ordered_pair @ ( sK46_B @ SV622 ) @ ( sK47_SY415 @ SV622 ) ) @ SV622 )
= $true )
| ( ( SV622 = empty_set )
= $true )
| ( ( relation @ SV622 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4038]) ).
thf(4234,plain,
! [SV623: $i,SV722: $i] :
( ( ( proper_subset @ SV722 @ SV623 )
= $false )
| ( ( ~ ( subset @ SV623 @ SV722 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4039]) ).
thf(4235,plain,
! [SV624: $i,SV751: $i,SV723: $i] :
( ( ( ~ ( disjoint @ SV723 @ SV751 )
| ~ ( subset @ SV624 @ SV723 ) )
= $true )
| ( ( disjoint @ SV624 @ SV751 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4040]) ).
thf(4236,plain,
! [SV724: $i,SV625: $i] :
( ( ( subset @ ( singleton @ SV625 ) @ ( singleton @ SV724 ) )
= $false )
| ( ( SV625 = SV724 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4041]) ).
thf(4237,plain,
! [SV752: $i,SV726: $i,SV627: $i] :
( ( ( ~ ( subset @ SV627 @ SV726 )
| ~ ( subset @ SV752 @ SV726 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV627 @ SV752 ) @ SV726 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4042]) ).
thf(4238,plain,
! [SV727: $i,SV628: $i] :
( ( ( in @ SV628 @ SV727 )
= $false )
| ( ( subset @ SV628 @ ( union @ SV727 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4043]) ).
thf(4239,plain,
! [SV629: $i,SV728: $i] :
( ( ( relation @ SV728 )
= $false )
| ( ( ( relation_dom_restriction @ SV728 @ SV629 )
= ( relation_composition @ ( identity_relation @ SV629 ) @ SV728 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4044]) ).
thf(4240,plain,
! [SV729: $i,SV630: $i] :
( ( ( in @ SV630 @ SV729 )
= $false )
| ( ( ~ ( in @ SV729 @ SV630 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4045]) ).
thf(4241,plain,
! [SV753: $i,SV636: $i] :
( ( ( empty @ ( set_union2 @ SV636 @ SV753 ) )
= $false )
| ( ( empty @ SV636 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4047]) ).
thf(4242,plain,
! [SV638: $i,SV754: $i] :
( ( ( empty @ ( set_union2 @ SV754 @ SV638 ) )
= $false )
| ( ( empty @ SV638 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4049]) ).
thf(4243,plain,
! [SV734: $i,SV639: $i] :
( ( ( empty @ SV639 )
= $true )
| ( ( empty @ SV734 )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV639 @ SV734 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4050]) ).
thf(4244,plain,
! [SV735: $i,SV644: $i] :
( ( ( in @ SV644 @ SV735 )
= $false )
| ( ( element @ SV644 @ SV735 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4051]) ).
thf(4245,plain,
! [SV736: $i,SV646: $i] :
( ( ( element @ SV646 @ SV736 )
= $false )
| ( ( ( empty @ SV736 )
| ( in @ SV646 @ SV736 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4052]) ).
thf(4246,plain,
! [SV650: $i,SV737: $i] :
( ( ( empty @ SV737 )
= $false )
| ( ( ~ ( in @ SV650 @ SV737 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4054]) ).
thf(4247,plain,
! [SV738: $i,SV651: $i] :
( ( ( SV651 = SV738 )
= $true )
| ( ( ~ ( empty @ SV651 ) )
= $true )
| ( ( ~ ( empty @ SV738 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4055]) ).
thf(4248,plain,
! [SV652: $i] :
( ( ! [SY1133: $i,SY1134: $i] :
( ~ ( ~ ( ~ ( in @ ( sK17_D @ SY1134 @ SY1133 @ SV652 ) @ SV652 )
| ~ ( in @ ( sK17_D @ SY1134 @ SY1133 @ SV652 ) @ SY1133 )
| ~ ( in @ ( sK17_D @ SY1134 @ SY1133 @ SV652 ) @ SY1134 ) )
| ~ ~ ( ~ ( ( in @ ( sK17_D @ SY1134 @ SY1133 @ SV652 ) @ SV652 )
| ( in @ ( sK17_D @ SY1134 @ SY1133 @ SV652 ) @ SY1134 ) )
| ~ ( ( in @ ( sK17_D @ SY1134 @ SY1133 @ SV652 ) @ SY1133 )
| ( in @ ( sK17_D @ SY1134 @ SY1133 @ SV652 ) @ SY1134 ) ) ) )
| ( SY1134
= ( set_intersection2 @ SV652 @ SY1133 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4056]) ).
thf(4249,plain,
! [SV652: $i] :
( ( ! [SY1135: $i,SY1136: $i] :
( ( SY1136
!= ( set_intersection2 @ SV652 @ SY1135 ) )
| ~ ( ~ ! [SY1137: $i] :
( ~ ( in @ SY1137 @ SV652 )
| ~ ( in @ SY1137 @ SY1135 )
| ( in @ SY1137 @ SY1136 ) )
| ~ ~ ( ~ ! [SY1138: $i] :
( ~ ( in @ SY1138 @ SY1136 )
| ( in @ SY1138 @ SV652 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1136 )
| ( in @ SX3 @ SY1135 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4057]) ).
thf(4250,plain,
! [SV762: $i] :
( ( ~ ( relation @ SV762 )
| ( ( relation_dom @ SV762 )
!= empty_set )
| ( ( relation_rng @ SV762 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4060]) ).
thf(4251,plain,
! [SV763: $i] :
( ( ~ ( relation @ SV763 )
| ( ( relation_rng @ SV763 )
!= empty_set )
| ( ( relation_dom @ SV763 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4061]) ).
thf(4252,plain,
! [SV653: $i] :
( ( ( function @ SV653 )
= $false )
| ( ( ~ ( relation @ SV653 ) )
= $true )
| ( ( ~ ( one_to_one @ SV653 )
| ~ ( ~ ! [SY1140: $i] :
( ~ ( function @ SY1140 )
| ~ ( relation @ SY1140 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SY1140 @ SV653 )
= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ( ( sK70_C @ SY1140 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY1140 @ SV653 )
= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY1140 @ SV653 )
= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ( ( sK71_SY424 @ SY1140 @ SV653 )
!= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK70_C @ SY1140 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK71_SY424 @ SY1140 @ SV653 )
!= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY1140 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK70_C @ SY1140 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SY1140 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SY1140 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK71_SY424 @ SY1140 @ SV653 )
!= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ( ( relation_dom @ SY1140 )
!= ( relation_rng @ SV653 ) )
| ( SY1140
= ( function_inverse @ SV653 ) ) )
| ~ ~ ( ~ ! [SY1141: $i] :
( ~ ( function @ SY1141 )
| ~ ( relation @ SY1141 )
| ( SY1141
!= ( function_inverse @ SV653 ) )
| ~ ( ~ ~ ( ~ ! [SY1142: $i,SY1143: $i] :
( ( SY1143
!= ( apply @ SY1141 @ SY1142 ) )
| ~ ( in @ SY1142 @ ( relation_rng @ SV653 ) )
| ( SY1142
= ( apply @ SV653 @ SY1143 ) ) )
| ~ ! [SY1144: $i,SY1145: $i] :
( ( SY1145
!= ( apply @ SY1141 @ SY1144 ) )
| ~ ( in @ SY1144 @ ( relation_rng @ SV653 ) )
| ( in @ SY1145 @ ( relation_dom @ SV653 ) ) ) )
| ~ ~ ( ~ ! [SY1146: $i,SY1147: $i] :
( ( SY1146
!= ( apply @ SV653 @ SY1147 ) )
| ~ ( in @ SY1147 @ ( relation_dom @ SV653 ) )
| ( SY1147
= ( apply @ SY1141 @ SY1146 ) ) )
| ~ ! [SY1148: $i] :
( ! [SY1149: $i] :
( ( SY1148
!= ( apply @ SV653 @ SY1149 ) )
| ~ ( in @ SY1149 @ ( relation_dom @ SV653 ) ) )
| ( in @ SY1148 @ ( relation_rng @ SV653 ) ) ) ) ) )
| ~ ! [SY1150: $i] :
( ~ ( function @ SY1150 )
| ~ ( relation @ SY1150 )
| ( SY1150
!= ( function_inverse @ SV653 ) )
| ( ( relation_dom @ SY1150 )
= ( relation_rng @ SV653 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4062]) ).
thf(4253,plain,
( ( ~ ( function @ sK54_A )
| ~ ( relation @ sK54_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4063]) ).
thf(4254,plain,
( ( empty @ sK55_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4065]) ).
thf(4255,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)],[4067]) ).
thf(4256,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)],[4068]) ).
thf(4257,plain,
! [SV764: $i] :
( ( ! [SY1392: $i] :
( ( ( set_intersection2 @ SV764 @ SY1392 )
!= empty_set )
| ( disjoint @ SV764 @ SY1392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4069]) ).
thf(4258,plain,
! [SV765: $i] :
( ( ! [SY1393: $i] :
( ~ ( disjoint @ SV765 @ SY1393 )
| ( ( set_intersection2 @ SV765 @ SY1393 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4070]) ).
thf(4259,plain,
! [SV766: $i] :
( ( ! [SY1394: $i] :
( ~ ( subset @ SV766 @ ( singleton @ SY1394 ) )
| ( SV766 = empty_set )
| ( SV766
= ( singleton @ SY1394 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4071]) ).
thf(4260,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)],[4072]) ).
thf(4261,plain,
! [SV767: $i] :
( ( ( relation_dom @ ( identity_relation @ SV767 ) )
= SV767 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4073]) ).
thf(4262,plain,
! [SV768: $i] :
( ( ( relation_rng @ ( identity_relation @ SV768 ) )
= SV768 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4074]) ).
thf(4263,plain,
! [SV769: $i] :
( ( ! [SY1395: $i] :
( ~ ( in @ SV769 @ SY1395 )
| ( subset @ ( singleton @ SV769 ) @ SY1395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4075]) ).
thf(4264,plain,
! [SV770: $i] :
( ( ! [SY1396: $i] :
( ~ ( subset @ ( singleton @ SV770 ) @ SY1396 )
| ( in @ SV770 @ SY1396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4076]) ).
thf(4265,plain,
! [SV771: $i] :
( ( ~ ( empty @ SV771 )
| ( empty @ ( relation_dom @ SV771 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4077]) ).
thf(4266,plain,
! [SV772: $i] :
( ( ~ ( empty @ SV772 )
| ( relation @ ( relation_dom @ SV772 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4078]) ).
thf(4267,plain,
! [SV773: $i] :
( ( ! [SY1397: $i] :
( ( ( set_difference @ SV773 @ SY1397 )
!= empty_set )
| ( subset @ SV773 @ SY1397 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4079]) ).
thf(4268,plain,
! [SV774: $i] :
( ( ! [SY1398: $i] :
( ~ ( subset @ SV774 @ SY1398 )
| ( ( set_difference @ SV774 @ SY1398 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4080]) ).
thf(4269,plain,
! [SV739: $i,SV654: $i] :
( ( ~ ! [SY1358: $i,SY1359: $i] :
( ~ ( relation @ SY1359 )
| ~ ( in @ SV654 @ SY1358 )
| ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ SY1359 )
| ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SY1358 ) @ SY1359 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4081]) ).
thf(4270,plain,
! [SV739: $i,SV654: $i] :
( ( ~ ~ ( ~ ! [SY1360: $i,SY1361: $i] :
( ~ ( relation @ SY1361 )
| ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SY1360 ) @ SY1361 ) )
| ( in @ SV654 @ SY1360 ) )
| ~ ! [SY1362: $i,SY1363: $i] :
( ~ ( relation @ SY1363 )
| ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SY1362 ) @ SY1363 ) )
| ( in @ ( ordered_pair @ SV654 @ SV739 ) @ SY1363 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4081]) ).
thf(4271,plain,
! [SV655: $i,SV740: $i] :
( ( ( relation @ SV740 )
= $false )
| ( ( ~ ( ~ ! [SY1364: $i] :
( ~ ( relation @ SY1364 )
| ~ ( ~ ( ~ ( in @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) @ SV655 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY1364 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) ) @ SV740 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY1364 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) ) @ SY1364 ) )
| ~ ~ ( ~ ( ( in @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) @ SV655 )
| ( in @ ( ordered_pair @ ( sK40_D @ SY1364 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) ) @ SY1364 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SY1364 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) ) @ SV740 )
| ( in @ ( ordered_pair @ ( sK40_D @ SY1364 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) ) @ SY1364 ) ) ) )
| ( SY1364
= ( relation_rng_restriction @ SV655 @ SV740 ) ) )
| ~ ! [SY1365: $i] :
( ~ ( relation @ SY1365 )
| ( SY1365
!= ( relation_rng_restriction @ SV655 @ SV740 ) )
| ~ ( ~ ! [SY1366: $i,SY1367: $i] :
( ~ ( in @ SY1367 @ SV655 )
| ~ ( in @ ( ordered_pair @ SY1366 @ SY1367 ) @ SV740 )
| ( in @ ( ordered_pair @ SY1366 @ SY1367 ) @ SY1365 ) )
| ~ ~ ( ~ ! [SY1163: $i,SY1164: $i] :
( ~ ( in @ ( ordered_pair @ SY1163 @ SY1164 ) @ SY1365 )
| ( in @ SY1164 @ SV655 ) )
| ~ ! [SY1370: $i,SY1371: $i] :
( ~ ( in @ ( ordered_pair @ SY1370 @ SY1371 ) @ SY1365 )
| ( in @ ( ordered_pair @ SY1370 @ SY1371 ) @ SV740 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4082]) ).
thf(4272,plain,
! [SV775: $i] :
( ( function @ ( identity_relation @ SV775 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4083]) ).
thf(4273,plain,
! [SV776: $i] :
( ( relation @ ( identity_relation @ SV776 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4084]) ).
thf(4274,plain,
! [SV741: $i,SV656: $i] :
( ( ~ ! [SY1372: $i] :
( ! [SY1373: $i] :
( ( ordered_pair @ SV656 @ SV741 )
!= ( ordered_pair @ SY1372 @ SY1373 ) )
| ( SV656 = SY1372 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4085]) ).
thf(4275,plain,
! [SV741: $i,SV656: $i] :
( ( ~ ! [SY1374: $i,SY1375: $i] :
( ( ( ordered_pair @ SV656 @ SV741 )
!= ( ordered_pair @ SY1374 @ SY1375 ) )
| ( SV741 = SY1375 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4085]) ).
thf(4276,plain,
! [SV657: $i] :
( ( ( ~ ! [SY1172: $i,SY1173: $i] :
( ~ ( ~ ( ! [SY1174: $i] :
( ~ ( in @ ( ordered_pair @ ( sK35_D @ SY1173 @ SY1172 @ SV657 ) @ SY1174 ) @ SV657 )
| ~ ( in @ SY1174 @ SY1172 ) )
| ~ ( in @ ( sK35_D @ SY1173 @ SY1172 @ SV657 ) @ SY1173 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SY1173 @ SY1172 @ SV657 ) @ ( sK36_SY409 @ SY1173 @ SY1172 @ SV657 ) ) @ SV657 )
| ~ ( in @ ( sK36_SY409 @ SY1173 @ SY1172 @ SV657 ) @ SY1172 ) )
| ( in @ ( sK35_D @ SY1173 @ SY1172 @ SV657 ) @ SY1173 ) ) )
| ( SY1173
= ( relation_inverse_image @ SV657 @ SY1172 ) ) )
| ~ ! [SY1175: $i,SY1176: $i] :
( ( SY1176
!= ( relation_inverse_image @ SV657 @ SY1175 ) )
| ~ ( ~ ! [SY1177: $i] :
( ! [SY1178: $i] :
( ~ ( in @ ( ordered_pair @ SY1177 @ SY1178 ) @ SV657 )
| ~ ( in @ SY1178 @ SY1175 ) )
| ( in @ SY1177 @ SY1176 ) )
| ~ ! [SY1179: $i] :
( ~ ( in @ SY1179 @ SY1176 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1179 @ ( sK34_E @ SY1179 @ SY1176 @ SY1175 @ SV657 ) ) @ SV657 )
| ~ ( in @ ( sK34_E @ SY1179 @ SY1176 @ SY1175 @ SV657 ) @ SY1175 ) ) ) ) ) )
= $false )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4086]) ).
thf(4277,plain,
! [SV658: $i] :
( ( ( ~ ! [SY1180: $i,SY1181: $i] :
( ~ ( ~ ( ! [SY1182: $i] :
( ~ ( in @ ( ordered_pair @ SY1182 @ ( sK38_D @ SY1181 @ SY1180 @ SV658 ) ) @ SV658 )
| ~ ( in @ SY1182 @ SY1180 ) )
| ~ ( in @ ( sK38_D @ SY1181 @ SY1180 @ SV658 ) @ SY1181 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SY1181 @ SY1180 @ SV658 ) @ ( sK38_D @ SY1181 @ SY1180 @ SV658 ) ) @ SV658 )
| ~ ( in @ ( sK39_SY411 @ SY1181 @ SY1180 @ SV658 ) @ SY1180 ) )
| ( in @ ( sK38_D @ SY1181 @ SY1180 @ SV658 ) @ SY1181 ) ) )
| ( SY1181
= ( relation_image @ SV658 @ SY1180 ) ) )
| ~ ! [SY1183: $i,SY1184: $i] :
( ( SY1184
!= ( relation_image @ SV658 @ SY1183 ) )
| ~ ( ~ ! [SY1185: $i] :
( ! [SY1186: $i] :
( ~ ( in @ ( ordered_pair @ SY1186 @ SY1185 ) @ SV658 )
| ~ ( in @ SY1186 @ SY1183 ) )
| ( in @ SY1185 @ SY1184 ) )
| ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ SY1184 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SY1187 @ SY1184 @ SY1183 @ SV658 ) @ SY1187 ) @ SV658 )
| ~ ( in @ ( sK37_E @ SY1187 @ SY1184 @ SY1183 @ SV658 ) @ SY1183 ) ) ) ) ) )
= $false )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4087]) ).
thf(4278,plain,
! [SV777: $i] :
( ( ! [SY1399: $i] :
( ( SV777 = SY1399 )
| ~ ( subset @ SV777 @ SY1399 )
| ( proper_subset @ SV777 @ SY1399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4088]) ).
thf(4279,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)],[4089]) ).
thf(4280,plain,
! [SV778: $i] :
( ( ! [SY1400: $i] :
( ~ ( empty @ SV778 )
| ~ ( relation @ SY1400 )
| ( empty @ ( relation_composition @ SY1400 @ SV778 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4090]) ).
thf(4281,plain,
! [SV779: $i] :
( ( ! [SY1401: $i] :
( ~ ( empty @ SV779 )
| ~ ( relation @ SY1401 )
| ( relation @ ( relation_composition @ SY1401 @ SV779 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4091]) ).
thf(4282,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)],[4092]) ).
thf(4283,plain,
! [SV780: $i] :
( ( ~ ( empty @ SV780 )
| ~ ( relation @ SV780 )
| ~ ( function @ SV780 )
| ( one_to_one @ SV780 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4093]) ).
thf(4284,plain,
! [SV781: $i] :
( ( ~ ( ~ ! [SY1402: $i,SY1403: $i] :
( ( sK69_B @ SV781 )
!= ( ordered_pair @ SY1402 @ SY1403 ) )
| ~ ( in @ ( sK69_B @ SV781 ) @ SV781 ) )
| ( relation @ SV781 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4094]) ).
thf(4285,plain,
! [SV782: $i] :
( ( ~ ( relation @ SV782 )
| ! [SY1404: $i] :
( ( SY1404
= ( ordered_pair @ ( sK67_C @ SY1404 @ SV782 ) @ ( sK68_SY421 @ SY1404 @ SV782 ) ) )
| ~ ( in @ SY1404 @ SV782 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4095]) ).
thf(4286,plain,
! [SV659: $i] :
( ( ! [SY1188: $i,SY1189: $i] :
( ~ ( in @ SV659 @ SY1189 )
| ~ ( in @ SY1188 @ SY1189 )
| ( subset @ ( unordered_pair @ SV659 @ SY1188 ) @ SY1189 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4096]) ).
thf(4287,plain,
! [SV659: $i] :
( ( ~ ( ~ ! [SY1190: $i,SY1191: $i] :
( ~ ( subset @ ( unordered_pair @ SV659 @ SY1190 ) @ SY1191 )
| ( in @ SV659 @ SY1191 ) )
| ~ ! [SY1192: $i,SY1193: $i] :
( ~ ( subset @ ( unordered_pair @ SV659 @ SY1192 ) @ SY1193 )
| ( in @ SY1192 @ SY1193 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4097]) ).
thf(4288,plain,
! [SV660: $i,SV783: $i] :
( ( ( ~ ( relation @ SV783 )
| ~ ( ~ ! [SY1405: $i] :
( ~ ( relation @ SY1405 )
| ~ ( ~ ( ! [SY1406: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY1405 @ SV783 @ SV660 ) @ SY1406 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1406 @ ( sK9_SY391 @ SY1405 @ SV783 @ SV660 ) ) @ SV783 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SY1405 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SY1405 @ SV783 @ SV660 ) ) @ SY1405 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY1405 @ SV783 @ SV660 ) @ ( sK10_SY395 @ SY1405 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SY1405 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SY1405 @ SV783 @ SV660 ) ) @ SV783 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SY1405 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SY1405 @ SV783 @ SV660 ) ) @ SY1405 ) ) )
| ( SY1405
= ( relation_composition @ SV660 @ SV783 ) ) )
| ~ ! [SY1407: $i] :
( ~ ( relation @ SY1407 )
| ( SY1407
!= ( relation_composition @ SV660 @ SV783 ) )
| ~ ( ~ ! [SY1408: $i,SY1409: $i] :
( ! [SY1410: $i] :
( ~ ( in @ ( ordered_pair @ SY1408 @ SY1410 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1410 @ SY1409 ) @ SV783 ) )
| ( in @ ( ordered_pair @ SY1408 @ SY1409 ) @ SY1407 ) )
| ~ ! [SY1411: $i,SY1412: $i] :
( ~ ( in @ ( ordered_pair @ SY1411 @ SY1412 ) @ SY1407 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1411 @ ( sK7_F @ SY1412 @ SY1411 @ SY1407 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY1412 @ SY1411 @ SY1407 @ SV783 @ SV660 ) @ SY1412 ) @ SV783 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4098]) ).
thf(4289,plain,
! [SV784: $i] :
( ( ( in @ ( sK29_B @ SV784 ) @ SV784 )
| ( SV784 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4101]) ).
thf(4290,plain,
! [SV785: $i] :
( ( ( SV785 != empty_set )
| ! [SY1413: $i] :
~ ( in @ SY1413 @ SV785 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4102]) ).
thf(4291,plain,
! [SV786: $i] :
( ( ~ ( empty @ SV786 )
| ( empty @ ( relation_rng @ SV786 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4103]) ).
thf(4292,plain,
! [SV787: $i] :
( ( ~ ( empty @ SV787 )
| ( relation @ ( relation_rng @ SV787 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4104]) ).
thf(4293,plain,
! [SV788: $i] :
( ( ~ ( relation @ SV788 )
| ( ( relation_rng @ SV788 )
= ( relation_dom @ ( relation_inverse @ SV788 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4105]) ).
thf(4294,plain,
! [SV789: $i] :
( ( ~ ( relation @ SV789 )
| ( ( relation_dom @ SV789 )
= ( relation_rng @ ( relation_inverse @ SV789 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4106]) ).
thf(4295,plain,
! [SV661: $i] :
( ( ( ~ ! [SY1203: $i] :
( ~ ( ~ ( ! [SY1204: $i] :
~ ( in @ ( ordered_pair @ SY1204 @ ( sK60_C @ SY1203 @ SV661 ) ) @ SV661 )
| ~ ( in @ ( sK60_C @ SY1203 @ SV661 ) @ SY1203 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK61_SY417 @ SY1203 @ SV661 ) @ ( sK60_C @ SY1203 @ SV661 ) ) @ SV661 )
| ( in @ ( sK60_C @ SY1203 @ SV661 ) @ SY1203 ) ) )
| ( SY1203
= ( relation_rng @ SV661 ) ) )
| ~ ! [SY1205: $i] :
( ( SY1205
!= ( relation_rng @ SV661 ) )
| ~ ( ~ ! [SY1206: $i] :
( ! [SY1207: $i] :
~ ( in @ ( ordered_pair @ SY1207 @ SY1206 ) @ SV661 )
| ( in @ SY1206 @ SY1205 ) )
| ~ ! [SY1208: $i] :
( ~ ( in @ SY1208 @ SY1205 )
| ( in @ ( ordered_pair @ ( sK59_D @ SY1208 @ SY1205 @ SV661 ) @ SY1208 ) @ SV661 ) ) ) ) )
= $false )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4107]) ).
thf(4296,plain,
! [SV662: $i] :
( ( ! [SY1209: $i,SY1210: $i] :
( ~ ( ~ ( ~ ( in @ ( sK13_D @ SY1210 @ SY1209 @ SV662 ) @ SV662 )
| ( in @ ( sK13_D @ SY1210 @ SY1209 @ SV662 ) @ SY1209 )
| ~ ( in @ ( sK13_D @ SY1210 @ SY1209 @ SV662 ) @ SY1210 ) )
| ~ ~ ( ~ ( ( in @ ( sK13_D @ SY1210 @ SY1209 @ SV662 ) @ SV662 )
| ( in @ ( sK13_D @ SY1210 @ SY1209 @ SV662 ) @ SY1210 ) )
| ~ ( ~ ( in @ ( sK13_D @ SY1210 @ SY1209 @ SV662 ) @ SY1209 )
| ( in @ ( sK13_D @ SY1210 @ SY1209 @ SV662 ) @ SY1210 ) ) ) )
| ( SY1210
= ( set_difference @ SV662 @ SY1209 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4108]) ).
thf(4297,plain,
! [SV662: $i] :
( ( ! [SY1211: $i,SY1212: $i] :
( ( SY1212
!= ( set_difference @ SV662 @ SY1211 ) )
| ~ ( ~ ! [SY1213: $i] :
( ~ ( in @ SY1213 @ SV662 )
| ( in @ SY1213 @ SY1211 )
| ( in @ SY1213 @ SY1212 ) )
| ~ ~ ( ~ ! [SY1214: $i] :
( ~ ( in @ SY1214 @ SY1212 )
| ( in @ SY1214 @ SV662 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1212 )
| ~ ( in @ SX3 @ SY1211 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4109]) ).
thf(4298,plain,
! [SV790: $i] :
( ( ! [SY1414: $i] :
( ~ ( function @ SV790 )
| ~ ( relation @ SV790 )
| ~ ( relation @ SY1414 )
| ~ ( function @ SY1414 )
| ( function @ ( relation_composition @ SV790 @ SY1414 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4110]) ).
thf(4299,plain,
! [SV791: $i] :
( ( ! [SY1415: $i] :
( ~ ( function @ SV791 )
| ~ ( relation @ SV791 )
| ~ ( relation @ SY1415 )
| ~ ( function @ SY1415 )
| ( relation @ ( relation_composition @ SV791 @ SY1415 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4111]) ).
thf(4300,plain,
! [SV663: $i] :
( ( ! [SY1216: $i,SY1217: $i] :
( ~ ( relation @ SY1217 )
| ~ ( in @ SV663 @ SY1216 )
| ~ ( in @ SV663 @ ( relation_rng @ SY1217 ) )
| ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SY1216 @ SY1217 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4112]) ).
thf(4301,plain,
! [SV663: $i] :
( ( ~ ( ~ ! [SY1218: $i,SY1219: $i] :
( ~ ( relation @ SY1219 )
| ~ ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SY1218 @ SY1219 ) ) )
| ( in @ SV663 @ SY1218 ) )
| ~ ! [SY1220: $i,SY1221: $i] :
( ~ ( relation @ SY1221 )
| ~ ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SY1220 @ SY1221 ) ) )
| ( in @ SV663 @ ( relation_rng @ SY1221 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4113]) ).
thf(4302,plain,
! [SV664: $i] :
( ( ( function @ SV664 )
= $false )
| ( ( ~ ( relation @ SV664 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY1222: $i] :
( ~ ( in @ SY1222 @ ( relation_dom @ SV664 ) )
| ! [SY1223: $i] :
( ( SY1223
!= ( apply @ SV664 @ SY1222 ) )
| ( in @ ( ordered_pair @ SY1222 @ SY1223 ) @ SV664 ) ) )
| ~ ! [SY1224: $i] :
( ~ ( in @ SY1224 @ ( relation_dom @ SV664 ) )
| ! [SY1225: $i] :
( ~ ( in @ ( ordered_pair @ SY1224 @ SY1225 ) @ SV664 )
| ( SY1225
= ( apply @ SV664 @ SY1224 ) ) ) ) )
| ~ ~ ( ~ ! [SY1226: $i] :
( ( in @ SY1226 @ ( relation_dom @ SV664 ) )
| ! [SY1227: $i] :
( ( SY1227
!= ( apply @ SV664 @ SY1226 ) )
| ( SY1227 = empty_set ) ) )
| ~ ! [SY1228: $i] :
( ( in @ SY1228 @ ( relation_dom @ SV664 ) )
| ! [SY1229: $i] :
( ( SY1229 != empty_set )
| ( SY1229
= ( apply @ SV664 @ SY1228 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4114]) ).
thf(4303,plain,
! [SV665: $i] :
( ( ( ~ ! [SY1230: $i] :
( ~ ( relation @ SY1230 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SY1230 @ SV665 ) @ ( sK20_SY399 @ SY1230 @ SV665 ) ) @ SV665 )
| ~ ~ ( in @ ( ordered_pair @ ( sK19_C @ SY1230 @ SV665 ) @ ( sK20_SY399 @ SY1230 @ SV665 ) ) @ SY1230 ) )
| ( subset @ SV665 @ SY1230 ) )
| ~ ! [SY1231: $i] :
( ~ ( relation @ SY1231 )
| ~ ( subset @ SV665 @ SY1231 )
| ! [SY1232: $i,SY1233: $i] :
( ~ ( in @ ( ordered_pair @ SY1232 @ SY1233 ) @ SV665 )
| ( in @ ( ordered_pair @ SY1232 @ SY1233 ) @ SY1231 ) ) ) )
= $false )
| ( ( relation @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4115]) ).
thf(4304,plain,
! [SV666: $i,SV742: $i] :
( ( ( ~ ( function @ SV742 ) )
= $true )
| ( ( ~ ( relation @ SV742 ) )
= $true )
| ( ( ~ ( ~ ! [SY1376: $i] :
( ~ ( function @ SY1376 )
| ~ ( relation @ SY1376 )
| ~ ( in @ SV666 @ ( relation_dom @ SY1376 ) )
| ~ ( in @ ( apply @ SY1376 @ SV666 ) @ ( relation_dom @ SV742 ) )
| ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1376 @ SV742 ) ) ) )
| ~ ~ ( ~ ! [SY1377: $i] :
( ~ ( function @ SY1377 )
| ~ ( relation @ SY1377 )
| ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1377 @ SV742 ) ) )
| ( in @ SV666 @ ( relation_dom @ SY1377 ) ) )
| ~ ! [SY1378: $i] :
( ~ ( function @ SY1378 )
| ~ ( relation @ SY1378 )
| ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1378 @ SV742 ) ) )
| ( in @ ( apply @ SY1378 @ SV666 ) @ ( relation_dom @ SV742 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4116]) ).
thf(4305,plain,
! [SV667: $i] :
( ( ! [SY1238: $i,SY1239: $i] :
( ~ ( relation @ SY1239 )
| ! [SY1240: $i] :
( ~ ( in @ SY1240 @ ( relation_rng @ SY1239 ) )
| ~ ( in @ ( ordered_pair @ SV667 @ SY1240 ) @ SY1239 )
| ~ ( in @ SY1240 @ SY1238 ) )
| ( in @ SV667 @ ( relation_inverse_image @ SY1239 @ SY1238 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4117]) ).
thf(4306,plain,
! [SV667: $i] :
( ( ! [SY1241: $i,SY1242: $i] :
( ~ ( relation @ SY1242 )
| ~ ( in @ SV667 @ ( relation_inverse_image @ SY1242 @ SY1241 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK51_D @ SY1242 @ SY1241 @ SV667 ) @ ( relation_rng @ SY1242 ) )
| ~ ( in @ ( ordered_pair @ SV667 @ ( sK51_D @ SY1242 @ SY1241 @ SV667 ) ) @ SY1242 ) )
| ~ ( in @ ( sK51_D @ SY1242 @ SY1241 @ SV667 ) @ SY1241 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4118]) ).
thf(4307,plain,
! [SV792: $i] :
( ( ! [SY1416: $i] :
( ( disjoint @ SV792 @ SY1416 )
| ~ ( ~ ( in @ ( sK49_C @ SY1416 @ SV792 ) @ SV792 )
| ~ ( in @ ( sK49_C @ SY1416 @ SV792 ) @ SY1416 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4119]) ).
thf(4308,plain,
! [SV793: $i] :
( ( ! [SY1417: $i] :
( ! [SY1418: $i] :
( ~ ( in @ SY1418 @ SV793 )
| ~ ( in @ SY1418 @ SY1417 ) )
| ~ ( disjoint @ SV793 @ SY1417 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4120]) ).
thf(4309,plain,
! [SV794: $i] :
( ( ~ ( empty @ SV794 )
| ( empty @ ( relation_inverse @ SV794 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4121]) ).
thf(4310,plain,
! [SV795: $i] :
( ( ~ ( empty @ SV795 )
| ( relation @ ( relation_inverse @ SV795 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4122]) ).
thf(4311,plain,
! [SV668: $i] :
( ( ! [SY1243: $i,SY1244: $i] :
( ~ ( relation @ SY1244 )
| ~ ( in @ SV668 @ SY1243 )
| ~ ( in @ SV668 @ ( relation_dom @ SY1244 ) )
| ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SY1244 @ SY1243 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4123]) ).
thf(4312,plain,
! [SV668: $i] :
( ( ~ ( ~ ! [SY1245: $i,SY1246: $i] :
( ~ ( relation @ SY1246 )
| ~ ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SY1246 @ SY1245 ) ) )
| ( in @ SV668 @ SY1245 ) )
| ~ ! [SY1247: $i,SY1248: $i] :
( ~ ( relation @ SY1248 )
| ~ ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SY1248 @ SY1247 ) ) )
| ( in @ SV668 @ ( relation_dom @ SY1248 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4124]) ).
thf(4313,plain,
! [SV669: $i] :
( ( ! [SY1249: $i,SY1250: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY1250 @ SY1249 @ SV669 ) @ SY1250 )
| ~ ( in @ ( sK26_D @ SY1250 @ SY1249 @ SV669 ) @ SV669 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY1250 @ SY1249 @ SV669 ) @ SY1250 )
| ~ ( in @ ( sK26_D @ SY1250 @ SY1249 @ SV669 ) @ SY1249 ) ) )
| ~ ( ( in @ ( sK26_D @ SY1250 @ SY1249 @ SV669 ) @ SY1250 )
| ( in @ ( sK26_D @ SY1250 @ SY1249 @ SV669 ) @ SV669 )
| ( in @ ( sK26_D @ SY1250 @ SY1249 @ SV669 ) @ SY1249 ) ) )
| ( SY1250
= ( set_union2 @ SV669 @ SY1249 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4125]) ).
thf(4314,plain,
! [SV669: $i] :
( ( ! [SY1251: $i,SY1252: $i] :
( ( SY1252
!= ( set_union2 @ SV669 @ SY1251 ) )
| ~ ( ~ ! [SY1253: $i] :
( ~ ( in @ SY1253 @ SY1252 )
| ( in @ SY1253 @ SV669 )
| ( in @ SY1253 @ SY1251 ) )
| ~ ~ ( ~ ! [SY1254: $i] :
( ~ ( in @ SY1254 @ SV669 )
| ( in @ SY1254 @ SY1252 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1251 )
| ( in @ SX3 @ SY1252 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4126]) ).
thf(4315,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY406 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ ( sK33_SY406 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK31_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)],[4127]) ).
thf(4316,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)],[4128]) ).
thf(4317,plain,
! [SV670: $i] :
( ( ! [SY1256: $i,SY1257: $i] :
( ~ ( ~ ( ! [SY1258: $i,SY1259: $i] :
( ~ ( in @ SY1258 @ SV670 )
| ~ ( in @ SY1259 @ SY1256 )
| ( ( sK23_D @ SY1257 @ SY1256 @ SV670 )
!= ( ordered_pair @ SY1258 @ SY1259 ) ) )
| ~ ( in @ ( sK23_D @ SY1257 @ SY1256 @ SV670 ) @ SY1257 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY403 @ SY1257 @ SY1256 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK25_SY405 @ SY1257 @ SY1256 @ SV670 ) @ SY1256 ) )
| ( ( sK23_D @ SY1257 @ SY1256 @ SV670 )
!= ( ordered_pair @ ( sK24_SY403 @ SY1257 @ SY1256 @ SV670 ) @ ( sK25_SY405 @ SY1257 @ SY1256 @ SV670 ) ) ) )
| ( in @ ( sK23_D @ SY1257 @ SY1256 @ SV670 ) @ SY1257 ) ) )
| ( SY1257
= ( cartesian_product2 @ SV670 @ SY1256 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4129]) ).
thf(4318,plain,
! [SV670: $i] :
( ( ! [SY1260: $i,SY1261: $i] :
( ( SY1261
!= ( cartesian_product2 @ SV670 @ SY1260 ) )
| ~ ( ~ ! [SY1262: $i] :
( ! [SY1263: $i,SY1264: $i] :
( ~ ( in @ SY1263 @ SV670 )
| ~ ( in @ SY1264 @ SY1260 )
| ( SY1262
!= ( ordered_pair @ SY1263 @ SY1264 ) ) )
| ( in @ SY1262 @ SY1261 ) )
| ~ ! [SY1265: $i] :
( ~ ( in @ SY1265 @ SY1261 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY1265 @ SY1261 @ SY1260 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK22_SY400 @ SY1265 @ SY1261 @ SY1260 @ SV670 ) @ SY1260 ) )
| ( SY1265
!= ( ordered_pair @ ( sK21_E @ SY1265 @ SY1261 @ SY1260 @ SV670 ) @ ( sK22_SY400 @ SY1265 @ SY1261 @ SY1260 @ SV670 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4130]) ).
thf(4319,plain,
! [SV671: $i] :
( ( ! [SY1266: $i,SY1267: $i] :
( ~ ( function @ SY1267 )
| ~ ( relation @ SY1267 )
| ( SY1266
!= ( apply @ SY1267 @ SV671 ) )
| ~ ( in @ SV671 @ ( relation_dom @ SY1267 ) )
| ( in @ ( ordered_pair @ SV671 @ SY1266 ) @ SY1267 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4131]) ).
thf(4320,plain,
! [SV671: $i] :
( ( ~ ( ~ ! [SY1268: $i,SY1269: $i] :
( ~ ( function @ SY1269 )
| ~ ( relation @ SY1269 )
| ~ ( in @ ( ordered_pair @ SV671 @ SY1268 ) @ SY1269 )
| ( SY1268
= ( apply @ SY1269 @ SV671 ) ) )
| ~ ! [SY1270: $i,SY1271: $i] :
( ~ ( function @ SY1271 )
| ~ ( relation @ SY1271 )
| ~ ( in @ ( ordered_pair @ SV671 @ SY1270 ) @ SY1271 )
| ( in @ SV671 @ ( relation_dom @ SY1271 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4132]) ).
thf(4321,plain,
! [SV672: $i] :
( ( ( ~ ! [SY1272: $i] :
( ~ ( relation @ SY1272 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SY1272 @ SV672 ) @ ( sK12_SY396 @ SY1272 @ SV672 ) ) @ SY1272 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SY1272 @ SV672 ) @ ( sK11_C @ SY1272 @ SV672 ) ) @ SV672 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_C @ SY1272 @ SV672 ) @ ( sK12_SY396 @ SY1272 @ SV672 ) ) @ SY1272 )
| ( in @ ( ordered_pair @ ( sK12_SY396 @ SY1272 @ SV672 ) @ ( sK11_C @ SY1272 @ SV672 ) ) @ SV672 ) ) )
| ( SY1272
= ( relation_inverse @ SV672 ) ) )
| ~ ! [SY1273: $i] :
( ~ ( relation @ SY1273 )
| ( SY1273
!= ( relation_inverse @ SV672 ) )
| ~ ( ~ ! [SY1274: $i,SY1275: $i] :
( ~ ( in @ ( ordered_pair @ SY1274 @ SY1275 ) @ SY1273 )
| ( in @ ( ordered_pair @ SY1275 @ SY1274 ) @ SV672 ) )
| ~ ! [SY1276: $i,SY1277: $i] :
( ~ ( in @ ( ordered_pair @ SY1277 @ SY1276 ) @ SV672 )
| ( in @ ( ordered_pair @ SY1276 @ SY1277 ) @ SY1273 ) ) ) ) )
= $false )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4133]) ).
thf(4322,plain,
! [SV796: $i] :
( ( ! [SY1419: $i] :
( ( ( set_difference @ SV796 @ SY1419 )
!= empty_set )
| ( subset @ SV796 @ SY1419 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4136]) ).
thf(4323,plain,
! [SV797: $i] :
( ( ! [SY1420: $i] :
( ~ ( subset @ SV797 @ SY1420 )
| ( ( set_difference @ SV797 @ SY1420 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4137]) ).
thf(4324,plain,
! [SV798: $i] :
( ( ~ ( function @ SV798 )
| ~ ( relation @ SV798 )
| ~ ( one_to_one @ SV798 )
| ( function @ ( relation_inverse @ SV798 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4138]) ).
thf(4325,plain,
! [SV799: $i] :
( ( ~ ( function @ SV799 )
| ~ ( relation @ SV799 )
| ~ ( one_to_one @ SV799 )
| ( relation @ ( relation_inverse @ SV799 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4139]) ).
thf(4326,plain,
! [SV673: $i] :
( ( ! [SY1278: $i,SY1279: $i] :
( ~ ( relation @ SY1279 )
| ~ ( in @ ( ordered_pair @ SV673 @ SY1278 ) @ SY1279 )
| ( in @ SV673 @ ( relation_dom @ SY1279 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4140]) ).
thf(4327,plain,
! [SV673: $i] :
( ( ! [SY1280: $i,SY1281: $i] :
( ~ ( relation @ SY1281 )
| ~ ( in @ ( ordered_pair @ SV673 @ SY1280 ) @ SY1281 )
| ( in @ SY1280 @ ( relation_rng @ SY1281 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4141]) ).
thf(4328,plain,
! [SV743: $i,SV674: $i] :
( ( ~ ! [SY1379: $i,SY1380: $i] :
( ~ ( in @ SV674 @ SY1379 )
| ~ ( in @ SV743 @ SY1380 )
| ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SY1379 @ SY1380 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4142]) ).
thf(4329,plain,
! [SV743: $i,SV674: $i] :
( ( ~ ~ ( ~ ! [SY1381: $i] :
( ! [SY1382: $i] :
~ ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SY1381 @ SY1382 ) )
| ( in @ SV674 @ SY1381 ) )
| ~ ! [SY1383: $i,SY1384: $i] :
( ~ ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SY1383 @ SY1384 ) )
| ( in @ SV743 @ SY1384 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4142]) ).
thf(4330,plain,
! [SV675: $i] :
( ( ! [SY1289: $i,SY1290: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY1290 @ SY1289 @ SV675 ) @ SY1290 )
| ( ( sK27_D @ SY1290 @ SY1289 @ SV675 )
!= SV675 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY1290 @ SY1289 @ SV675 ) @ SY1290 )
| ( ( sK27_D @ SY1290 @ SY1289 @ SV675 )
!= SY1289 ) ) )
| ~ ( ( in @ ( sK27_D @ SY1290 @ SY1289 @ SV675 ) @ SY1290 )
| ( ( sK27_D @ SY1290 @ SY1289 @ SV675 )
= SV675 )
| ( ( sK27_D @ SY1290 @ SY1289 @ SV675 )
= SY1289 ) ) )
| ( SY1290
= ( unordered_pair @ SV675 @ SY1289 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4143]) ).
thf(4331,plain,
! [SV675: $i] :
( ( ! [SY1291: $i,SY1292: $i] :
( ( SY1292
!= ( unordered_pair @ SV675 @ SY1291 ) )
| ~ ( ~ ! [SY1293: $i] :
( ~ ( in @ SY1293 @ SY1292 )
| ( SY1293 = SV675 )
| ( SY1293 = SY1291 ) )
| ~ ~ ( ~ ! [SY1294: $i] :
( ( SY1294 != SV675 )
| ( in @ SY1294 @ SY1292 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY1291 )
| ( in @ SX3 @ SY1292 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4144]) ).
thf(4332,plain,
! [SV744: $i,SV676: $i] :
( ( ~ ! [SY1385: $i,SY1386: $i] :
( ~ ( in @ SV676 @ SY1385 )
| ~ ( in @ SV744 @ SY1386 )
| ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SY1385 @ SY1386 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4145]) ).
thf(4333,plain,
! [SV744: $i,SV676: $i] :
( ( ~ ~ ( ~ ! [SY1387: $i] :
( ! [SY1388: $i] :
~ ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SY1387 @ SY1388 ) )
| ( in @ SV676 @ SY1387 ) )
| ~ ! [SY1389: $i,SY1390: $i] :
( ~ ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SY1389 @ SY1390 ) )
| ( in @ SV744 @ SY1390 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4145]) ).
thf(4334,plain,
! [SV800: $i] :
( ( ! [SY1421: $i] :
( ( disjoint @ SV800 @ SY1421 )
| ( in @ ( sK48_C @ SY1421 @ SV800 ) @ ( set_intersection2 @ SV800 @ SY1421 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4146]) ).
thf(4335,plain,
! [SV801: $i] :
( ( ! [SY1422: $i] :
( ! [SY1423: $i] :
~ ( in @ SY1423 @ ( set_intersection2 @ SV801 @ SY1422 ) )
| ~ ( disjoint @ SV801 @ SY1422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4147]) ).
thf(4336,plain,
! [SV802: $i] :
( ( ~ ( function @ SV802 )
| ~ ( relation @ SV802 )
| ( function @ ( function_inverse @ SV802 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4148]) ).
thf(4337,plain,
! [SV803: $i] :
( ( ~ ( function @ SV803 )
| ~ ( relation @ SV803 )
| ( relation @ ( function_inverse @ SV803 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4149]) ).
thf(4338,plain,
! [SV677: $i,SV745: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_C @ SV745 @ SV677 ) @ SV677 )
| ~ ( in @ ( sK4_C @ SV745 @ SV677 ) @ SV745 ) )
| ~ ( ( in @ ( sK4_C @ SV745 @ SV677 ) @ SV677 )
| ( in @ ( sK4_C @ SV745 @ SV677 ) @ SV745 ) ) )
= $false )
| ( ( SV677 = SV745 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4150]) ).
thf(4339,plain,
! [SV678: $i] :
( ( ! [SY1304: $i] :
( ~ ( subset @ SV678 @ SY1304 )
| ! [SY1305: $i] : ( subset @ ( cartesian_product2 @ SV678 @ SY1305 ) @ ( cartesian_product2 @ SY1304 @ SY1305 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4151]) ).
thf(4340,plain,
! [SV678: $i] :
( ( ! [SY1306: $i] :
( ~ ( subset @ SV678 @ SY1306 )
| ! [SY1307: $i] : ( subset @ ( cartesian_product2 @ SY1307 @ SV678 ) @ ( cartesian_product2 @ SY1307 @ SY1306 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4152]) ).
thf(4341,plain,
! [SV804: $i] :
( ( ! [SY1424: $i] :
( ~ ( ~ ( ! [SY1425: $i] :
( ~ ( in @ ( sK15_C @ SY1424 @ SV804 ) @ SY1425 )
| ~ ( in @ SY1425 @ SV804 ) )
| ~ ( in @ ( sK15_C @ SY1424 @ SV804 ) @ SY1424 ) )
| ~ ( ~ ( ~ ( in @ ( sK15_C @ SY1424 @ SV804 ) @ ( sK16_SY398 @ SY1424 @ SV804 ) )
| ~ ( in @ ( sK16_SY398 @ SY1424 @ SV804 ) @ SV804 ) )
| ( in @ ( sK15_C @ SY1424 @ SV804 ) @ SY1424 ) ) )
| ( SY1424
= ( union @ SV804 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4153]) ).
thf(4342,plain,
! [SV805: $i] :
( ( ! [SY1426: $i] :
( ( SY1426
!= ( union @ SV805 ) )
| ~ ( ~ ! [SY1427: $i] :
( ! [SY1428: $i] :
( ~ ( in @ SY1427 @ SY1428 )
| ~ ( in @ SY1428 @ SV805 ) )
| ( in @ SY1427 @ SY1426 ) )
| ~ ! [SY1429: $i] :
( ~ ( in @ SY1429 @ SY1426 )
| ~ ( ~ ( in @ SY1429 @ ( sK14_D @ SY1429 @ SY1426 @ SV805 ) )
| ~ ( in @ ( sK14_D @ SY1429 @ SY1426 @ SV805 ) @ SV805 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4154]) ).
thf(4343,plain,
! [SV679: $i] :
( ( ( ~ ! [SY1308: $i] :
( ~ ( ~ ( ! [SY1309: $i] :
~ ( in @ ( ordered_pair @ ( sK63_C @ SY1308 @ SV679 ) @ SY1309 ) @ SV679 )
| ~ ( in @ ( sK63_C @ SY1308 @ SV679 ) @ SY1308 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_C @ SY1308 @ SV679 ) @ ( sK64_SY419 @ SY1308 @ SV679 ) ) @ SV679 )
| ( in @ ( sK63_C @ SY1308 @ SV679 ) @ SY1308 ) ) )
| ( SY1308
= ( relation_dom @ SV679 ) ) )
| ~ ! [SY1310: $i] :
( ( SY1310
!= ( relation_dom @ SV679 ) )
| ~ ( ~ ! [SY1311: $i] :
( ! [SY1312: $i] :
~ ( in @ ( ordered_pair @ SY1311 @ SY1312 ) @ SV679 )
| ( in @ SY1311 @ SY1310 ) )
| ~ ! [SY1313: $i] :
( ~ ( in @ SY1313 @ SY1310 )
| ( in @ ( ordered_pair @ SY1313 @ ( sK62_D @ SY1313 @ SY1310 @ SV679 ) ) @ SV679 ) ) ) ) )
= $false )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4155]) ).
thf(4344,plain,
! [SV680: $i] :
( ( ! [SY1314: $i,SY1315: $i] :
( ~ ( relation @ SY1315 )
| ~ ( in @ ( ordered_pair @ SV680 @ SY1314 ) @ SY1315 )
| ( in @ SV680 @ ( relation_field @ SY1315 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4156]) ).
thf(4345,plain,
! [SV680: $i] :
( ( ! [SY1316: $i,SY1317: $i] :
( ~ ( relation @ SY1317 )
| ~ ( in @ ( ordered_pair @ SV680 @ SY1316 ) @ SY1317 )
| ( in @ SY1316 @ ( relation_field @ SY1317 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4157]) ).
thf(4346,plain,
! [SV806: $i] :
( ( ! [SY1430: $i] :
( ~ ( relation @ SY1430 )
| ~ ( ~ ( ( ( sK44_C @ SY1430 @ SV806 )
!= ( sK45_SY414 @ SY1430 @ SV806 ) )
| ~ ( in @ ( sK44_C @ SY1430 @ SV806 ) @ SV806 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SY1430 @ SV806 ) @ ( sK45_SY414 @ SY1430 @ SV806 ) ) @ SY1430 ) )
| ~ ~ ( ~ ( ( ( sK44_C @ SY1430 @ SV806 )
= ( sK45_SY414 @ SY1430 @ SV806 ) )
| ( in @ ( ordered_pair @ ( sK44_C @ SY1430 @ SV806 ) @ ( sK45_SY414 @ SY1430 @ SV806 ) ) @ SY1430 ) )
| ~ ( ( in @ ( sK44_C @ SY1430 @ SV806 ) @ SV806 )
| ( in @ ( ordered_pair @ ( sK44_C @ SY1430 @ SV806 ) @ ( sK45_SY414 @ SY1430 @ SV806 ) ) @ SY1430 ) ) ) )
| ( SY1430
= ( identity_relation @ SV806 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4158]) ).
thf(4347,plain,
! [SV807: $i] :
( ( ! [SY1431: $i] :
( ~ ( relation @ SY1431 )
| ( SY1431
!= ( identity_relation @ SV807 ) )
| ~ ( ~ ! [SY1432: $i,SY1433: $i] :
( ( SY1432 != SY1433 )
| ~ ( in @ SY1432 @ SV807 )
| ( in @ ( ordered_pair @ SY1432 @ SY1433 ) @ SY1431 ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SY1431 )
| ( SX2 = SX3 ) )
| ~ ! [SY1436: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SY1436 @ SX3 ) @ SY1431 )
| ( in @ SY1436 @ SV807 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4159]) ).
thf(4348,plain,
! [SV681: $i] :
( ( ( ~ ! [SY1318: $i,SY1319: $i] :
( ~ ( relation @ SY1319 )
| ~ ( ~ ( ~ ( in @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ SY1318 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ ( sK43_SY413 @ SY1319 @ SY1318 @ SV681 ) ) @ SV681 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ ( sK43_SY413 @ SY1319 @ SY1318 @ SV681 ) ) @ SY1319 ) )
| ~ ~ ( ~ ( ( in @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ SY1318 )
| ( in @ ( ordered_pair @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ ( sK43_SY413 @ SY1319 @ SY1318 @ SV681 ) ) @ SY1319 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ ( sK43_SY413 @ SY1319 @ SY1318 @ SV681 ) ) @ SV681 )
| ( in @ ( ordered_pair @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ ( sK43_SY413 @ SY1319 @ SY1318 @ SV681 ) ) @ SY1319 ) ) ) )
| ( SY1319
= ( relation_dom_restriction @ SV681 @ SY1318 ) ) )
| ~ ! [SY1320: $i,SY1321: $i] :
( ~ ( relation @ SY1321 )
| ( SY1321
!= ( relation_dom_restriction @ SV681 @ SY1320 ) )
| ~ ( ~ ! [SY1322: $i,SY1323: $i] :
( ~ ( in @ SY1322 @ SY1320 )
| ~ ( in @ ( ordered_pair @ SY1322 @ SY1323 ) @ SV681 )
| ( in @ ( ordered_pair @ SY1322 @ SY1323 ) @ SY1321 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY1321 )
| ( in @ SX3 @ SY1320 ) )
| ~ ! [SY1326: $i,SY1327: $i] :
( ~ ( in @ ( ordered_pair @ SY1326 @ SY1327 ) @ SY1321 )
| ( in @ ( ordered_pair @ SY1326 @ SY1327 ) @ SV681 ) ) ) ) ) )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4160]) ).
thf(4349,plain,
! [SV808: $i] :
( ( ! [SY1438: $i] :
( ~ ( ~ ( ( ( sK30_C @ SY1438 @ SV808 )
!= SV808 )
| ~ ( in @ ( sK30_C @ SY1438 @ SV808 ) @ SY1438 ) )
| ~ ( ( ( sK30_C @ SY1438 @ SV808 )
= SV808 )
| ( in @ ( sK30_C @ SY1438 @ SV808 ) @ SY1438 ) ) )
| ( SY1438
= ( singleton @ SV808 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4161]) ).
thf(4350,plain,
! [SV809: $i] :
( ( ! [SY1439: $i] :
( ( SY1439
!= ( singleton @ SV809 ) )
| ~ ( ~ ! [SY1440: $i] :
( ( SY1440 != SV809 )
| ( in @ SY1440 @ SY1439 ) )
| ~ ! [SY1441: $i] :
( ~ ( in @ SY1441 @ SY1439 )
| ( SY1441 = SV809 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4162]) ).
thf(4351,plain,
! [SV682: $i] :
( ( ! [SY1328: $i,SY1329: $i] :
( ~ ( relation @ SY1329 )
| ! [SY1330: $i] :
( ~ ( in @ SY1330 @ ( relation_dom @ SY1329 ) )
| ~ ( in @ ( ordered_pair @ SY1330 @ SV682 ) @ SY1329 )
| ~ ( in @ SY1330 @ SY1328 ) )
| ( in @ SV682 @ ( relation_image @ SY1329 @ SY1328 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4165]) ).
thf(4352,plain,
! [SV682: $i] :
( ( ! [SY1331: $i,SY1332: $i] :
( ~ ( relation @ SY1332 )
| ~ ( in @ SV682 @ ( relation_image @ SY1332 @ SY1331 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK52_D @ SY1332 @ SY1331 @ SV682 ) @ ( relation_dom @ SY1332 ) )
| ~ ( in @ ( ordered_pair @ ( sK52_D @ SY1332 @ SY1331 @ SV682 ) @ SV682 ) @ SY1332 ) )
| ~ ( in @ ( sK52_D @ SY1332 @ SY1331 @ SV682 ) @ SY1331 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4166]) ).
thf(4353,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4167]) ).
thf(4354,plain,
! [SV683: $i] :
( ( ( ~ ! [SY1333: $i] :
( ~ ( relation @ SY1333 )
| ~ ( subset @ SV683 @ SY1333 )
| ( subset @ ( relation_dom @ SV683 ) @ ( relation_dom @ SY1333 ) ) )
| ~ ! [SY1334: $i] :
( ~ ( relation @ SY1334 )
| ~ ( subset @ SV683 @ SY1334 )
| ( subset @ ( relation_rng @ SV683 ) @ ( relation_rng @ SY1334 ) ) ) )
= $false )
| ( ( relation @ SV683 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4169]) ).
thf(4355,plain,
! [SV810: $i] :
( ( ! [SY1442: $i] :
( ~ ( empty @ SV810 )
| ~ ( relation @ SY1442 )
| ( empty @ ( relation_composition @ SV810 @ SY1442 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4170]) ).
thf(4356,plain,
! [SV811: $i] :
( ( ! [SY1443: $i] :
( ~ ( empty @ SV811 )
| ~ ( relation @ SY1443 )
| ( relation @ ( relation_composition @ SV811 @ SY1443 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4171]) ).
thf(4357,plain,
! [SV684: $i] :
( ( ( ~ ! [SY1335: $i] :
( ~ ( relation @ SY1335 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SY1335 @ SV684 ) @ ( sK66_SY420 @ SY1335 @ SV684 ) ) @ SV684 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SY1335 @ SV684 ) @ ( sK66_SY420 @ SY1335 @ SV684 ) ) @ SY1335 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_C @ SY1335 @ SV684 ) @ ( sK66_SY420 @ SY1335 @ SV684 ) ) @ SV684 )
| ( in @ ( ordered_pair @ ( sK65_C @ SY1335 @ SV684 ) @ ( sK66_SY420 @ SY1335 @ SV684 ) ) @ SY1335 ) ) )
| ( SV684 = SY1335 ) )
| ~ ! [SY1336: $i] :
( ~ ( relation @ SY1336 )
| ( SV684 != SY1336 )
| ~ ( ~ ! [SY1337: $i,SY1338: $i] :
( ~ ( in @ ( ordered_pair @ SY1337 @ SY1338 ) @ SV684 )
| ( in @ ( ordered_pair @ SY1337 @ SY1338 ) @ SY1336 ) )
| ~ ! [SY1339: $i,SY1340: $i] :
( ~ ( in @ ( ordered_pair @ SY1339 @ SY1340 ) @ SY1336 )
| ( in @ ( ordered_pair @ SY1339 @ SY1340 ) @ SV684 ) ) ) ) )
= $false )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4172]) ).
thf(4358,plain,
! [SV685: $i] :
( ( ! [SY1341: $i] :
( ~ ( subset @ SY1341 @ ( sK2_B @ SV685 ) )
| ( are_equipotent @ SY1341 @ ( sK2_B @ SV685 ) )
| ( in @ SY1341 @ ( sK2_B @ SV685 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4173]) ).
thf(4359,plain,
! [SV685: $i] :
( ( ~ ( ~ ! [SY1342: $i] :
( ~ ( ~ ! [SY1343: $i] :
( ~ ( subset @ SY1343 @ SY1342 )
| ( in @ SY1343 @ ( sK3_SY386 @ SY1342 @ SV685 ) ) )
| ~ ( in @ ( sK3_SY386 @ SY1342 @ SV685 ) @ ( sK2_B @ SV685 ) ) )
| ~ ( in @ SY1342 @ ( sK2_B @ SV685 ) ) )
| ~ ~ ( ~ ! [SY1344: $i,SY1345: $i] :
( ~ ( in @ SY1344 @ ( sK2_B @ SV685 ) )
| ~ ( subset @ SY1345 @ SY1344 )
| ( in @ SY1345 @ ( sK2_B @ SV685 ) ) )
| ~ ( in @ SV685 @ ( sK2_B @ SV685 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4174]) ).
thf(4360,plain,
! [SV812: $i] :
( ( ! [SY1444: $i] :
( ~ ( subset @ SV812 @ SY1444 )
| ~ ( subset @ SY1444 @ SV812 )
| ( SV812 = SY1444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4177]) ).
thf(4361,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)],[4178]) ).
thf(4362,plain,
! [SV813: $i] :
( ( ! [SY1445: $i] :
( ~ ( ~ ( ~ ( in @ ( sK28_C @ SY1445 @ SV813 ) @ SY1445 )
| ~ ( subset @ ( sK28_C @ SY1445 @ SV813 ) @ SV813 ) )
| ~ ( ( in @ ( sK28_C @ SY1445 @ SV813 ) @ SY1445 )
| ( subset @ ( sK28_C @ SY1445 @ SV813 ) @ SV813 ) ) )
| ( SY1445
= ( powerset @ SV813 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4179]) ).
thf(4363,plain,
! [SV814: $i] :
( ( ! [SY1446: $i] :
( ( SY1446
!= ( powerset @ SV814 ) )
| ~ ( ~ ! [SY1447: $i] :
( ~ ( in @ SY1447 @ SY1446 )
| ( subset @ SY1447 @ SV814 ) )
| ~ ! [SY1448: $i] :
( ~ ( subset @ SY1448 @ SV814 )
| ( in @ SY1448 @ SY1446 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4180]) ).
thf(4364,plain,
! [SV815: $i] :
( ( ! [SY1449: $i] :
( ~ ( subset @ SV815 @ ( singleton @ SY1449 ) )
| ( SV815 = empty_set )
| ( SV815
= ( singleton @ SY1449 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4181]) ).
thf(4365,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)],[4182]) ).
thf(4366,plain,
! [SV816: $i] :
( ( ~ ( relation @ SV816 )
| ( ( relation_dom @ SV816 )
!= empty_set )
| ( SV816 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4183]) ).
thf(4367,plain,
! [SV817: $i] :
( ( ~ ( relation @ SV817 )
| ( ( relation_rng @ SV817 )
!= empty_set )
| ( SV817 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4184]) ).
thf(4368,plain,
( ( ~ ( empty @ sK56_A )
| ~ ( relation @ sK56_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4185]) ).
thf(4369,plain,
! [SV818: $i] :
( ( ! [SY1450: $i] :
( ~ ( function @ SY1450 )
| ~ ( relation @ SY1450 )
| ~ ( ~ ( in @ ( sK50_C @ SY1450 @ SV818 ) @ SV818 )
| ~ ( ( ( apply @ SY1450 @ ( sK50_C @ SY1450 @ SV818 ) )
!= ( sK50_C @ SY1450 @ SV818 ) ) ) )
| ( ( relation_dom @ SY1450 )
!= SV818 )
| ( SY1450
= ( identity_relation @ SV818 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4187]) ).
thf(4370,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)],[4188]) ).
thf(4371,plain,
! [SV819: $i] :
( ( ! [SY1451: $i] :
( ~ ( in @ SV819 @ SY1451 )
| ( subset @ ( singleton @ SV819 ) @ SY1451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4189]) ).
thf(4372,plain,
! [SV820: $i] :
( ( ! [SY1452: $i] :
( ~ ( subset @ ( singleton @ SV820 ) @ SY1452 )
| ( in @ SV820 @ SY1452 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4190]) ).
thf(4373,plain,
! [SV821: $i] :
( ( ! [SY1453: $i] :
( ~ ( ~ ( in @ ( sK18_C @ SY1453 @ SV821 ) @ SV821 )
| ~ ~ ( in @ ( sK18_C @ SY1453 @ SV821 ) @ SY1453 ) )
| ( subset @ SV821 @ SY1453 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4191]) ).
thf(4374,plain,
! [SV822: $i] :
( ( ! [SY1454: $i] :
( ~ ( subset @ SV822 @ SY1454 )
| ! [SY1455: $i] :
( ~ ( in @ SY1455 @ SV822 )
| ( in @ SY1455 @ SY1454 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4192]) ).
thf(4375,plain,
! [SV690: $i,SV570: $i,SV746: $i] :
( ( ( relation @ SV746 )
= $false )
| ( ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV570 @ SV746 ) @ SV690 )
= ( relation_rng_restriction @ SV570 @ ( relation_dom_restriction @ SV746 @ SV690 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4197]) ).
thf(4376,plain,
! [SV574: $i,SV755: $i] :
( ( ( ~ ( relation @ SV755 ) )
= $true )
| ( ( ( relation_rng @ ( relation_composition @ SV574 @ SV755 ) )
= ( relation_image @ SV755 @ ( relation_rng @ SV574 ) ) )
= $true )
| ( ( relation @ SV574 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4200]) ).
thf(4377,plain,
! [SV694: $i,SV576: $i,SV747: $i] :
( ( ( relation @ SV747 )
= $false )
| ( ( ~ ( subset @ SV576 @ SV694 )
| ( subset @ ( relation_inverse_image @ SV747 @ SV576 ) @ ( relation_inverse_image @ SV747 @ SV694 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4202]) ).
thf(4378,plain,
! [SV578: $i,SV756: $i] :
( ( ( ~ ( relation @ SV756 ) )
= $true )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV578 @ SV756 ) ) @ ( relation_dom @ SV578 ) )
= $true )
| ( ( relation @ SV578 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4203]) ).
thf(4379,plain,
! [SV579: $i,SV757: $i] :
( ( ( ~ ( relation @ SV757 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV579 @ SV757 ) ) @ ( relation_rng @ SV757 ) )
= $true )
| ( ( relation @ SV579 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4204]) ).
thf(4380,plain,
! [SV580: $i,SV758: $i] :
( ( ( ~ ( relation @ SV758 ) )
= $true )
| ( ( ~ ( subset @ ( relation_rng @ SV580 ) @ ( relation_dom @ SV758 ) )
| ( ( relation_dom @ ( relation_composition @ SV580 @ SV758 ) )
= ( relation_dom @ SV580 ) ) )
= $true )
| ( ( relation @ SV580 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4205]) ).
thf(4381,plain,
! [SV581: $i,SV759: $i] :
( ( ( ~ ( relation @ SV759 ) )
= $true )
| ( ( ~ ( subset @ ( relation_dom @ SV581 ) @ ( relation_rng @ SV759 ) )
| ( ( relation_rng @ ( relation_composition @ SV759 @ SV581 ) )
= ( relation_rng @ SV581 ) ) )
= $true )
| ( ( relation @ SV581 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4206]) ).
thf(4382,plain,
! [SV588: $i] :
( ( ( relation @ SV588 )
= $false )
| ( ( function @ SV588 )
= $false )
| ( ( ~ ( one_to_one @ SV588 )
| ( ( function_inverse @ SV588 )
= ( relation_inverse @ SV588 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4210]) ).
thf(4383,plain,
! [SV698: $i,SV590: $i] :
( ( ( relation @ SV590 )
= $false )
| ( ( ~ ( relation @ SV698 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV590 @ SV698 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4211]) ).
thf(4384,plain,
! [SV700: $i,SV594: $i] :
( ( ( relation @ SV594 )
= $false )
| ( ( ~ ( relation @ SV700 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV594 @ SV700 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4214]) ).
thf(4385,plain,
! [SV701: $i,SV595: $i] :
( ( ( relation @ SV595 )
= $false )
| ( ( ~ ( relation @ SV701 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV595 @ SV701 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4215]) ).
thf(4386,plain,
! [SV596: $i] :
( ( ( empty @ ( relation_dom @ SV596 ) )
= $false )
| ( ( empty @ SV596 )
= $true )
| ( ( relation @ SV596 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4216]) ).
thf(4387,plain,
! [SV597: $i] :
( ( ( empty @ ( relation_rng @ SV597 ) )
= $false )
| ( ( empty @ SV597 )
= $true )
| ( ( relation @ SV597 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4217]) ).
thf(4388,plain,
! [SV761: $i,SV748: $i,SV704: $i,SV602: $i] :
( ( ( ~ ( subset @ SV602 @ SV704 )
| ~ ( subset @ SV748 @ SV761 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV602 @ SV748 ) @ ( cartesian_product2 @ SV704 @ SV761 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4220]) ).
thf(4389,plain,
! [SV706: $i,SV604: $i] :
( ( ( ( SV604 = empty_set )
| ~ ( subset @ SV604 @ ( relation_rng @ SV706 ) ) )
= $true )
| ( ( ( ( relation_inverse_image @ SV706 @ SV604 )
!= empty_set ) )
= $true )
| ( ( relation @ SV706 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4222]) ).
thf(4390,plain,
! [SV749: $i,SV708: $i,SV606: $i] :
( ( ( ~ ( subset @ SV606 @ SV708 ) )
= $true )
| ( ( ~ ( subset @ SV606 @ SV749 ) )
= $true )
| ( ( subset @ SV606 @ ( set_intersection2 @ SV708 @ SV749 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4223]) ).
thf(4391,plain,
! [SV750: $i,SV709: $i,SV607: $i] :
( ( ( ~ ( subset @ SV607 @ SV709 ) )
= $true )
| ( ( ~ ( subset @ SV709 @ SV750 ) )
= $true )
| ( ( subset @ SV607 @ SV750 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4224]) ).
thf(4392,plain,
! [SV608: $i,SV710: $i] :
( ( ( function @ SV710 )
= $false )
| ( ( ~ ( relation @ SV710 ) )
= $true )
| ( ( ! [SY1352: $i] :
( ~ ( function @ SY1352 )
| ~ ( relation @ SY1352 )
| ~ ( in @ SV608 @ ( relation_dom @ ( relation_composition @ SY1352 @ SV710 ) ) )
| ( ( apply @ ( relation_composition @ SY1352 @ SV710 ) @ SV608 )
= ( apply @ SV710 @ ( apply @ SY1352 @ SV608 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4225]) ).
thf(4393,plain,
! [SV609: $i,SV711: $i] :
( ( ( function @ SV711 )
= $false )
| ( ( ~ ( relation @ SV711 ) )
= $true )
| ( ( ! [SY1353: $i] :
( ~ ( function @ SY1353 )
| ~ ( relation @ SY1353 )
| ~ ( in @ SV609 @ ( relation_dom @ SV711 ) )
| ( ( apply @ ( relation_composition @ SV711 @ SY1353 ) @ SV609 )
= ( apply @ SY1353 @ ( apply @ SV711 @ SV609 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4226]) ).
thf(4394,plain,
! [SV712: $i,SV823: $i,SV610: $i] :
( ( ( subset @ ( set_intersection2 @ SV610 @ SV823 ) @ ( set_intersection2 @ SV712 @ SV823 ) )
= $true )
| ( ( subset @ SV610 @ SV712 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4227]) ).
thf(4395,plain,
! [SV714: $i,SV824: $i,SV613: $i] :
( ( ( subset @ ( set_difference @ SV613 @ SV824 ) @ ( set_difference @ SV714 @ SV824 ) )
= $true )
| ( ( subset @ SV613 @ SV714 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4229]) ).
thf(4396,plain,
! [SV722: $i,SV623: $i] :
( ( ( subset @ SV623 @ SV722 )
= $false )
| ( ( proper_subset @ SV722 @ SV623 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4234]) ).
thf(4397,plain,
! [SV624: $i,SV751: $i,SV723: $i] :
( ( ( ~ ( disjoint @ SV723 @ SV751 ) )
= $true )
| ( ( ~ ( subset @ SV624 @ SV723 ) )
= $true )
| ( ( disjoint @ SV624 @ SV751 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4235]) ).
thf(4398,plain,
! [SV752: $i,SV726: $i,SV627: $i] :
( ( ( ~ ( subset @ SV627 @ SV726 ) )
= $true )
| ( ( ~ ( subset @ SV752 @ SV726 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV627 @ SV752 ) @ SV726 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4237]) ).
thf(4399,plain,
! [SV630: $i,SV729: $i] :
( ( ( in @ SV729 @ SV630 )
= $false )
| ( ( in @ SV630 @ SV729 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4240]) ).
thf(4400,plain,
! [SV734: $i,SV639: $i] :
( ( ( empty @ ( cartesian_product2 @ SV639 @ SV734 ) )
= $false )
| ( ( empty @ SV734 )
= $true )
| ( ( empty @ SV639 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4243]) ).
thf(4401,plain,
! [SV646: $i,SV736: $i] :
( ( ( empty @ SV736 )
= $true )
| ( ( in @ SV646 @ SV736 )
= $true )
| ( ( element @ SV646 @ SV736 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4245]) ).
thf(4402,plain,
! [SV737: $i,SV650: $i] :
( ( ( in @ SV650 @ SV737 )
= $false )
| ( ( empty @ SV737 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4246]) ).
thf(4403,plain,
! [SV738: $i,SV651: $i] :
( ( ( empty @ SV651 )
= $false )
| ( ( SV651 = SV738 )
= $true )
| ( ( ~ ( empty @ SV738 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4247]) ).
thf(4404,plain,
! [SV652: $i,SV825: $i] :
( ( ! [SY1456: $i] :
( ~ ( ~ ( ~ ( in @ ( sK17_D @ SY1456 @ SV825 @ SV652 ) @ SV652 )
| ~ ( in @ ( sK17_D @ SY1456 @ SV825 @ SV652 ) @ SV825 )
| ~ ( in @ ( sK17_D @ SY1456 @ SV825 @ SV652 ) @ SY1456 ) )
| ~ ~ ( ~ ( ( in @ ( sK17_D @ SY1456 @ SV825 @ SV652 ) @ SV652 )
| ( in @ ( sK17_D @ SY1456 @ SV825 @ SV652 ) @ SY1456 ) )
| ~ ( ( in @ ( sK17_D @ SY1456 @ SV825 @ SV652 ) @ SV825 )
| ( in @ ( sK17_D @ SY1456 @ SV825 @ SV652 ) @ SY1456 ) ) ) )
| ( SY1456
= ( set_intersection2 @ SV652 @ SV825 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4248]) ).
thf(4405,plain,
! [SV826: $i,SV652: $i] :
( ( ! [SY1457: $i] :
( ( SY1457
!= ( set_intersection2 @ SV652 @ SV826 ) )
| ~ ( ~ ! [SY1458: $i] :
( ~ ( in @ SY1458 @ SV652 )
| ~ ( in @ SY1458 @ SV826 )
| ( in @ SY1458 @ SY1457 ) )
| ~ ~ ( ~ ! [SY1138: $i] :
( ~ ( in @ SY1138 @ SY1457 )
| ( in @ SY1138 @ SV652 ) )
| ~ ! [SY1460: $i] :
( ~ ( in @ SY1460 @ SY1457 )
| ( in @ SY1460 @ SV826 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4249]) ).
thf(4406,plain,
! [SV762: $i] :
( ( ( ~ ( relation @ SV762 ) )
= $true )
| ( ( ( ( relation_dom @ SV762 )
!= empty_set )
| ( ( relation_rng @ SV762 )
= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4250]) ).
thf(4407,plain,
! [SV763: $i] :
( ( ( ~ ( relation @ SV763 ) )
= $true )
| ( ( ( ( relation_rng @ SV763 )
!= empty_set )
| ( ( relation_dom @ SV763 )
= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4251]) ).
thf(4408,plain,
! [SV653: $i] :
( ( ( relation @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( ~ ( one_to_one @ SV653 )
| ~ ( ~ ! [SY1140: $i] :
( ~ ( function @ SY1140 )
| ~ ( relation @ SY1140 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SY1140 @ SV653 )
= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ( ( sK70_C @ SY1140 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY1140 @ SV653 )
= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY1140 @ SV653 )
= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ( ( sK71_SY424 @ SY1140 @ SV653 )
!= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK70_C @ SY1140 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK71_SY424 @ SY1140 @ SV653 )
!= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY1140 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK70_C @ SY1140 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SY1140 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SY1140 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK71_SY424 @ SY1140 @ SV653 )
!= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ( ( relation_dom @ SY1140 )
!= ( relation_rng @ SV653 ) )
| ( SY1140
= ( function_inverse @ SV653 ) ) )
| ~ ~ ( ~ ! [SY1141: $i] :
( ~ ( function @ SY1141 )
| ~ ( relation @ SY1141 )
| ( SY1141
!= ( function_inverse @ SV653 ) )
| ~ ( ~ ~ ( ~ ! [SY1142: $i,SY1143: $i] :
( ( SY1143
!= ( apply @ SY1141 @ SY1142 ) )
| ~ ( in @ SY1142 @ ( relation_rng @ SV653 ) )
| ( SY1142
= ( apply @ SV653 @ SY1143 ) ) )
| ~ ! [SY1144: $i,SY1145: $i] :
( ( SY1145
!= ( apply @ SY1141 @ SY1144 ) )
| ~ ( in @ SY1144 @ ( relation_rng @ SV653 ) )
| ( in @ SY1145 @ ( relation_dom @ SV653 ) ) ) )
| ~ ~ ( ~ ! [SY1146: $i,SY1147: $i] :
( ( SY1146
!= ( apply @ SV653 @ SY1147 ) )
| ~ ( in @ SY1147 @ ( relation_dom @ SV653 ) )
| ( SY1147
= ( apply @ SY1141 @ SY1146 ) ) )
| ~ ! [SY1148: $i] :
( ! [SY1149: $i] :
( ( SY1148
!= ( apply @ SV653 @ SY1149 ) )
| ~ ( in @ SY1149 @ ( relation_dom @ SV653 ) ) )
| ( in @ SY1148 @ ( relation_rng @ SV653 ) ) ) ) ) )
| ~ ! [SY1150: $i] :
( ~ ( function @ SY1150 )
| ~ ( relation @ SY1150 )
| ( SY1150
!= ( function_inverse @ SV653 ) )
| ( ( relation_dom @ SY1150 )
= ( relation_rng @ SV653 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4252]) ).
thf(4409,plain,
( ( ~ ( function @ sK54_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4253]) ).
thf(4410,plain,
( ( ~ ( relation @ sK54_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4253]) ).
thf(4411,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4255]) ).
thf(4412,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4255]) ).
thf(4413,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4256]) ).
thf(4414,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4256]) ).
thf(4415,plain,
! [SV827: $i,SV764: $i] :
( ( ( ( set_intersection2 @ SV764 @ SV827 )
!= empty_set )
| ( disjoint @ SV764 @ SV827 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4257]) ).
thf(4416,plain,
! [SV828: $i,SV765: $i] :
( ( ~ ( disjoint @ SV765 @ SV828 )
| ( ( set_intersection2 @ SV765 @ SV828 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4258]) ).
thf(4417,plain,
! [SV829: $i,SV766: $i] :
( ( ~ ( subset @ SV766 @ ( singleton @ SV829 ) )
| ( SV766 = empty_set )
| ( SV766
= ( singleton @ SV829 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4259]) ).
thf(4418,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4260]) ).
thf(4419,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4260]) ).
thf(4420,plain,
! [SV830: $i,SV769: $i] :
( ( ~ ( in @ SV769 @ SV830 )
| ( subset @ ( singleton @ SV769 ) @ SV830 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4263]) ).
thf(4421,plain,
! [SV831: $i,SV770: $i] :
( ( ~ ( subset @ ( singleton @ SV770 ) @ SV831 )
| ( in @ SV770 @ SV831 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4264]) ).
thf(4422,plain,
! [SV771: $i] :
( ( ( ~ ( empty @ SV771 ) )
= $true )
| ( ( empty @ ( relation_dom @ SV771 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4265]) ).
thf(4423,plain,
! [SV772: $i] :
( ( ( ~ ( empty @ SV772 ) )
= $true )
| ( ( relation @ ( relation_dom @ SV772 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4266]) ).
thf(4424,plain,
! [SV832: $i,SV773: $i] :
( ( ( ( set_difference @ SV773 @ SV832 )
!= empty_set )
| ( subset @ SV773 @ SV832 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4267]) ).
thf(4425,plain,
! [SV833: $i,SV774: $i] :
( ( ~ ( subset @ SV774 @ SV833 )
| ( ( set_difference @ SV774 @ SV833 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4268]) ).
thf(4426,plain,
! [SV739: $i,SV654: $i] :
( ( ! [SY1358: $i,SY1359: $i] :
( ~ ( relation @ SY1359 )
| ~ ( in @ SV654 @ SY1358 )
| ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ SY1359 )
| ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SY1358 ) @ SY1359 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4269]) ).
thf(4427,plain,
! [SV739: $i,SV654: $i] :
( ( ~ ( ~ ! [SY1360: $i,SY1361: $i] :
( ~ ( relation @ SY1361 )
| ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SY1360 ) @ SY1361 ) )
| ( in @ SV654 @ SY1360 ) )
| ~ ! [SY1362: $i,SY1363: $i] :
( ~ ( relation @ SY1363 )
| ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SY1362 ) @ SY1363 ) )
| ( in @ ( ordered_pair @ SV654 @ SV739 ) @ SY1363 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4270]) ).
thf(4428,plain,
! [SV655: $i,SV740: $i] :
( ( ( ~ ! [SY1364: $i] :
( ~ ( relation @ SY1364 )
| ~ ( ~ ( ~ ( in @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) @ SV655 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY1364 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) ) @ SV740 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY1364 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) ) @ SY1364 ) )
| ~ ~ ( ~ ( ( in @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) @ SV655 )
| ( in @ ( ordered_pair @ ( sK40_D @ SY1364 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) ) @ SY1364 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SY1364 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) ) @ SV740 )
| ( in @ ( ordered_pair @ ( sK40_D @ SY1364 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) ) @ SY1364 ) ) ) )
| ( SY1364
= ( relation_rng_restriction @ SV655 @ SV740 ) ) )
| ~ ! [SY1365: $i] :
( ~ ( relation @ SY1365 )
| ( SY1365
!= ( relation_rng_restriction @ SV655 @ SV740 ) )
| ~ ( ~ ! [SY1366: $i,SY1367: $i] :
( ~ ( in @ SY1367 @ SV655 )
| ~ ( in @ ( ordered_pair @ SY1366 @ SY1367 ) @ SV740 )
| ( in @ ( ordered_pair @ SY1366 @ SY1367 ) @ SY1365 ) )
| ~ ~ ( ~ ! [SY1163: $i,SY1164: $i] :
( ~ ( in @ ( ordered_pair @ SY1163 @ SY1164 ) @ SY1365 )
| ( in @ SY1164 @ SV655 ) )
| ~ ! [SY1370: $i,SY1371: $i] :
( ~ ( in @ ( ordered_pair @ SY1370 @ SY1371 ) @ SY1365 )
| ( in @ ( ordered_pair @ SY1370 @ SY1371 ) @ SV740 ) ) ) ) ) )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4271]) ).
thf(4429,plain,
! [SV741: $i,SV656: $i] :
( ( ! [SY1372: $i] :
( ! [SY1373: $i] :
( ( ordered_pair @ SV656 @ SV741 )
!= ( ordered_pair @ SY1372 @ SY1373 ) )
| ( SV656 = SY1372 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4274]) ).
thf(4430,plain,
! [SV741: $i,SV656: $i] :
( ( ! [SY1374: $i,SY1375: $i] :
( ( ( ordered_pair @ SV656 @ SV741 )
!= ( ordered_pair @ SY1374 @ SY1375 ) )
| ( SV741 = SY1375 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4275]) ).
thf(4431,plain,
! [SV657: $i] :
( ( ( ~ ! [SY1172: $i,SY1173: $i] :
( ~ ( ~ ( ! [SY1174: $i] :
( ~ ( in @ ( ordered_pair @ ( sK35_D @ SY1173 @ SY1172 @ SV657 ) @ SY1174 ) @ SV657 )
| ~ ( in @ SY1174 @ SY1172 ) )
| ~ ( in @ ( sK35_D @ SY1173 @ SY1172 @ SV657 ) @ SY1173 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SY1173 @ SY1172 @ SV657 ) @ ( sK36_SY409 @ SY1173 @ SY1172 @ SV657 ) ) @ SV657 )
| ~ ( in @ ( sK36_SY409 @ SY1173 @ SY1172 @ SV657 ) @ SY1172 ) )
| ( in @ ( sK35_D @ SY1173 @ SY1172 @ SV657 ) @ SY1173 ) ) )
| ( SY1173
= ( relation_inverse_image @ SV657 @ SY1172 ) ) ) )
= $false )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4276]) ).
thf(4432,plain,
! [SV657: $i] :
( ( ( ~ ! [SY1175: $i,SY1176: $i] :
( ( SY1176
!= ( relation_inverse_image @ SV657 @ SY1175 ) )
| ~ ( ~ ! [SY1177: $i] :
( ! [SY1178: $i] :
( ~ ( in @ ( ordered_pair @ SY1177 @ SY1178 ) @ SV657 )
| ~ ( in @ SY1178 @ SY1175 ) )
| ( in @ SY1177 @ SY1176 ) )
| ~ ! [SY1179: $i] :
( ~ ( in @ SY1179 @ SY1176 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1179 @ ( sK34_E @ SY1179 @ SY1176 @ SY1175 @ SV657 ) ) @ SV657 )
| ~ ( in @ ( sK34_E @ SY1179 @ SY1176 @ SY1175 @ SV657 ) @ SY1175 ) ) ) ) ) )
= $false )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4276]) ).
thf(4433,plain,
! [SV658: $i] :
( ( ( ~ ! [SY1180: $i,SY1181: $i] :
( ~ ( ~ ( ! [SY1182: $i] :
( ~ ( in @ ( ordered_pair @ SY1182 @ ( sK38_D @ SY1181 @ SY1180 @ SV658 ) ) @ SV658 )
| ~ ( in @ SY1182 @ SY1180 ) )
| ~ ( in @ ( sK38_D @ SY1181 @ SY1180 @ SV658 ) @ SY1181 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SY1181 @ SY1180 @ SV658 ) @ ( sK38_D @ SY1181 @ SY1180 @ SV658 ) ) @ SV658 )
| ~ ( in @ ( sK39_SY411 @ SY1181 @ SY1180 @ SV658 ) @ SY1180 ) )
| ( in @ ( sK38_D @ SY1181 @ SY1180 @ SV658 ) @ SY1181 ) ) )
| ( SY1181
= ( relation_image @ SV658 @ SY1180 ) ) ) )
= $false )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4277]) ).
thf(4434,plain,
! [SV658: $i] :
( ( ( ~ ! [SY1183: $i,SY1184: $i] :
( ( SY1184
!= ( relation_image @ SV658 @ SY1183 ) )
| ~ ( ~ ! [SY1185: $i] :
( ! [SY1186: $i] :
( ~ ( in @ ( ordered_pair @ SY1186 @ SY1185 ) @ SV658 )
| ~ ( in @ SY1186 @ SY1183 ) )
| ( in @ SY1185 @ SY1184 ) )
| ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ SY1184 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SY1187 @ SY1184 @ SY1183 @ SV658 ) @ SY1187 ) @ SV658 )
| ~ ( in @ ( sK37_E @ SY1187 @ SY1184 @ SY1183 @ SV658 ) @ SY1183 ) ) ) ) ) )
= $false )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4277]) ).
thf(4435,plain,
! [SV834: $i,SV777: $i] :
( ( ( SV777 = SV834 )
| ~ ( subset @ SV777 @ SV834 )
| ( proper_subset @ SV777 @ SV834 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4278]) ).
thf(4436,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4279]) ).
thf(4437,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4279]) ).
thf(4438,plain,
! [SV835: $i,SV778: $i] :
( ( ~ ( empty @ SV778 )
| ~ ( relation @ SV835 )
| ( empty @ ( relation_composition @ SV835 @ SV778 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4280]) ).
thf(4439,plain,
! [SV836: $i,SV779: $i] :
( ( ~ ( empty @ SV779 )
| ~ ( relation @ SV836 )
| ( relation @ ( relation_composition @ SV836 @ SV779 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4281]) ).
thf(4440,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4282]) ).
thf(4441,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4282]) ).
thf(4442,plain,
! [SV780: $i] :
( ( ( ~ ( empty @ SV780 )
| ~ ( relation @ SV780 )
| ~ ( function @ SV780 ) )
= $true )
| ( ( one_to_one @ SV780 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4283]) ).
thf(4443,plain,
! [SV781: $i] :
( ( ( ~ ( ~ ! [SY1402: $i,SY1403: $i] :
( ( sK69_B @ SV781 )
!= ( ordered_pair @ SY1402 @ SY1403 ) )
| ~ ( in @ ( sK69_B @ SV781 ) @ SV781 ) ) )
= $true )
| ( ( relation @ SV781 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4284]) ).
thf(4444,plain,
! [SV782: $i] :
( ( ( ~ ( relation @ SV782 ) )
= $true )
| ( ( ! [SY1404: $i] :
( ( SY1404
= ( ordered_pair @ ( sK67_C @ SY1404 @ SV782 ) @ ( sK68_SY421 @ SY1404 @ SV782 ) ) )
| ~ ( in @ SY1404 @ SV782 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4285]) ).
thf(4445,plain,
! [SV837: $i,SV659: $i] :
( ( ! [SY1461: $i] :
( ~ ( in @ SV659 @ SY1461 )
| ~ ( in @ SV837 @ SY1461 )
| ( subset @ ( unordered_pair @ SV659 @ SV837 ) @ SY1461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4286]) ).
thf(4446,plain,
! [SV659: $i] :
( ( ~ ! [SY1190: $i,SY1191: $i] :
( ~ ( subset @ ( unordered_pair @ SV659 @ SY1190 ) @ SY1191 )
| ( in @ SV659 @ SY1191 ) )
| ~ ! [SY1192: $i,SY1193: $i] :
( ~ ( subset @ ( unordered_pair @ SV659 @ SY1192 ) @ SY1193 )
| ( in @ SY1192 @ SY1193 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4287]) ).
thf(4447,plain,
! [SV660: $i,SV783: $i] :
( ( ( ~ ( relation @ SV783 ) )
= $true )
| ( ( ~ ( ~ ! [SY1405: $i] :
( ~ ( relation @ SY1405 )
| ~ ( ~ ( ! [SY1406: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY1405 @ SV783 @ SV660 ) @ SY1406 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1406 @ ( sK9_SY391 @ SY1405 @ SV783 @ SV660 ) ) @ SV783 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SY1405 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SY1405 @ SV783 @ SV660 ) ) @ SY1405 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY1405 @ SV783 @ SV660 ) @ ( sK10_SY395 @ SY1405 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SY1405 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SY1405 @ SV783 @ SV660 ) ) @ SV783 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SY1405 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SY1405 @ SV783 @ SV660 ) ) @ SY1405 ) ) )
| ( SY1405
= ( relation_composition @ SV660 @ SV783 ) ) )
| ~ ! [SY1407: $i] :
( ~ ( relation @ SY1407 )
| ( SY1407
!= ( relation_composition @ SV660 @ SV783 ) )
| ~ ( ~ ! [SY1408: $i,SY1409: $i] :
( ! [SY1410: $i] :
( ~ ( in @ ( ordered_pair @ SY1408 @ SY1410 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1410 @ SY1409 ) @ SV783 ) )
| ( in @ ( ordered_pair @ SY1408 @ SY1409 ) @ SY1407 ) )
| ~ ! [SY1411: $i,SY1412: $i] :
( ~ ( in @ ( ordered_pair @ SY1411 @ SY1412 ) @ SY1407 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1411 @ ( sK7_F @ SY1412 @ SY1411 @ SY1407 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY1412 @ SY1411 @ SY1407 @ SV783 @ SV660 ) @ SY1412 ) @ SV783 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4288]) ).
thf(4448,plain,
! [SV784: $i] :
( ( ( in @ ( sK29_B @ SV784 ) @ SV784 )
= $true )
| ( ( SV784 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4289]) ).
thf(4449,plain,
! [SV785: $i] :
( ( ( ( SV785 != empty_set ) )
= $true )
| ( ( ! [SY1413: $i] :
~ ( in @ SY1413 @ SV785 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4290]) ).
thf(4450,plain,
! [SV786: $i] :
( ( ( ~ ( empty @ SV786 ) )
= $true )
| ( ( empty @ ( relation_rng @ SV786 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4291]) ).
thf(4451,plain,
! [SV787: $i] :
( ( ( ~ ( empty @ SV787 ) )
= $true )
| ( ( relation @ ( relation_rng @ SV787 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4292]) ).
thf(4452,plain,
! [SV788: $i] :
( ( ( ~ ( relation @ SV788 ) )
= $true )
| ( ( ( relation_rng @ SV788 )
= ( relation_dom @ ( relation_inverse @ SV788 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4293]) ).
thf(4453,plain,
! [SV789: $i] :
( ( ( ~ ( relation @ SV789 ) )
= $true )
| ( ( ( relation_dom @ SV789 )
= ( relation_rng @ ( relation_inverse @ SV789 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4294]) ).
thf(4454,plain,
! [SV661: $i] :
( ( ( ~ ! [SY1203: $i] :
( ~ ( ~ ( ! [SY1204: $i] :
~ ( in @ ( ordered_pair @ SY1204 @ ( sK60_C @ SY1203 @ SV661 ) ) @ SV661 )
| ~ ( in @ ( sK60_C @ SY1203 @ SV661 ) @ SY1203 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK61_SY417 @ SY1203 @ SV661 ) @ ( sK60_C @ SY1203 @ SV661 ) ) @ SV661 )
| ( in @ ( sK60_C @ SY1203 @ SV661 ) @ SY1203 ) ) )
| ( SY1203
= ( relation_rng @ SV661 ) ) ) )
= $false )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4295]) ).
thf(4455,plain,
! [SV661: $i] :
( ( ( ~ ! [SY1205: $i] :
( ( SY1205
!= ( relation_rng @ SV661 ) )
| ~ ( ~ ! [SY1206: $i] :
( ! [SY1207: $i] :
~ ( in @ ( ordered_pair @ SY1207 @ SY1206 ) @ SV661 )
| ( in @ SY1206 @ SY1205 ) )
| ~ ! [SY1208: $i] :
( ~ ( in @ SY1208 @ SY1205 )
| ( in @ ( ordered_pair @ ( sK59_D @ SY1208 @ SY1205 @ SV661 ) @ SY1208 ) @ SV661 ) ) ) ) )
= $false )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4295]) ).
thf(4456,plain,
! [SV662: $i,SV838: $i] :
( ( ! [SY1462: $i] :
( ~ ( ~ ( ~ ( in @ ( sK13_D @ SY1462 @ SV838 @ SV662 ) @ SV662 )
| ( in @ ( sK13_D @ SY1462 @ SV838 @ SV662 ) @ SV838 )
| ~ ( in @ ( sK13_D @ SY1462 @ SV838 @ SV662 ) @ SY1462 ) )
| ~ ~ ( ~ ( ( in @ ( sK13_D @ SY1462 @ SV838 @ SV662 ) @ SV662 )
| ( in @ ( sK13_D @ SY1462 @ SV838 @ SV662 ) @ SY1462 ) )
| ~ ( ~ ( in @ ( sK13_D @ SY1462 @ SV838 @ SV662 ) @ SV838 )
| ( in @ ( sK13_D @ SY1462 @ SV838 @ SV662 ) @ SY1462 ) ) ) )
| ( SY1462
= ( set_difference @ SV662 @ SV838 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4296]) ).
thf(4457,plain,
! [SV839: $i,SV662: $i] :
( ( ! [SY1463: $i] :
( ( SY1463
!= ( set_difference @ SV662 @ SV839 ) )
| ~ ( ~ ! [SY1464: $i] :
( ~ ( in @ SY1464 @ SV662 )
| ( in @ SY1464 @ SV839 )
| ( in @ SY1464 @ SY1463 ) )
| ~ ~ ( ~ ! [SY1214: $i] :
( ~ ( in @ SY1214 @ SY1463 )
| ( in @ SY1214 @ SV662 ) )
| ~ ! [SY1466: $i] :
( ~ ( in @ SY1466 @ SY1463 )
| ~ ( in @ SY1466 @ SV839 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4297]) ).
thf(4458,plain,
! [SV840: $i,SV790: $i] :
( ( ~ ( function @ SV790 )
| ~ ( relation @ SV790 )
| ~ ( relation @ SV840 )
| ~ ( function @ SV840 )
| ( function @ ( relation_composition @ SV790 @ SV840 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4298]) ).
thf(4459,plain,
! [SV841: $i,SV791: $i] :
( ( ~ ( function @ SV791 )
| ~ ( relation @ SV791 )
| ~ ( relation @ SV841 )
| ~ ( function @ SV841 )
| ( relation @ ( relation_composition @ SV791 @ SV841 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4299]) ).
thf(4460,plain,
! [SV842: $i,SV663: $i] :
( ( ! [SY1467: $i] :
( ~ ( relation @ SY1467 )
| ~ ( in @ SV663 @ SV842 )
| ~ ( in @ SV663 @ ( relation_rng @ SY1467 ) )
| ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SV842 @ SY1467 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4300]) ).
thf(4461,plain,
! [SV663: $i] :
( ( ~ ! [SY1218: $i,SY1219: $i] :
( ~ ( relation @ SY1219 )
| ~ ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SY1218 @ SY1219 ) ) )
| ( in @ SV663 @ SY1218 ) )
| ~ ! [SY1220: $i,SY1221: $i] :
( ~ ( relation @ SY1221 )
| ~ ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SY1220 @ SY1221 ) ) )
| ( in @ SV663 @ ( relation_rng @ SY1221 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4301]) ).
thf(4462,plain,
! [SV664: $i] :
( ( ( relation @ SV664 )
= $false )
| ( ( function @ SV664 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY1222: $i] :
( ~ ( in @ SY1222 @ ( relation_dom @ SV664 ) )
| ! [SY1223: $i] :
( ( SY1223
!= ( apply @ SV664 @ SY1222 ) )
| ( in @ ( ordered_pair @ SY1222 @ SY1223 ) @ SV664 ) ) )
| ~ ! [SY1224: $i] :
( ~ ( in @ SY1224 @ ( relation_dom @ SV664 ) )
| ! [SY1225: $i] :
( ~ ( in @ ( ordered_pair @ SY1224 @ SY1225 ) @ SV664 )
| ( SY1225
= ( apply @ SV664 @ SY1224 ) ) ) ) )
| ~ ~ ( ~ ! [SY1226: $i] :
( ( in @ SY1226 @ ( relation_dom @ SV664 ) )
| ! [SY1227: $i] :
( ( SY1227
!= ( apply @ SV664 @ SY1226 ) )
| ( SY1227 = empty_set ) ) )
| ~ ! [SY1228: $i] :
( ( in @ SY1228 @ ( relation_dom @ SV664 ) )
| ! [SY1229: $i] :
( ( SY1229 != empty_set )
| ( SY1229
= ( apply @ SV664 @ SY1228 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4302]) ).
thf(4463,plain,
! [SV665: $i] :
( ( ( ~ ! [SY1230: $i] :
( ~ ( relation @ SY1230 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SY1230 @ SV665 ) @ ( sK20_SY399 @ SY1230 @ SV665 ) ) @ SV665 )
| ~ ~ ( in @ ( ordered_pair @ ( sK19_C @ SY1230 @ SV665 ) @ ( sK20_SY399 @ SY1230 @ SV665 ) ) @ SY1230 ) )
| ( subset @ SV665 @ SY1230 ) ) )
= $false )
| ( ( relation @ SV665 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4303]) ).
thf(4464,plain,
! [SV665: $i] :
( ( ( ~ ! [SY1231: $i] :
( ~ ( relation @ SY1231 )
| ~ ( subset @ SV665 @ SY1231 )
| ! [SY1232: $i,SY1233: $i] :
( ~ ( in @ ( ordered_pair @ SY1232 @ SY1233 ) @ SV665 )
| ( in @ ( ordered_pair @ SY1232 @ SY1233 ) @ SY1231 ) ) ) )
= $false )
| ( ( relation @ SV665 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4303]) ).
thf(4465,plain,
! [SV666: $i,SV742: $i] :
( ( ( function @ SV742 )
= $false )
| ( ( ~ ( relation @ SV742 ) )
= $true )
| ( ( ~ ( ~ ! [SY1376: $i] :
( ~ ( function @ SY1376 )
| ~ ( relation @ SY1376 )
| ~ ( in @ SV666 @ ( relation_dom @ SY1376 ) )
| ~ ( in @ ( apply @ SY1376 @ SV666 ) @ ( relation_dom @ SV742 ) )
| ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1376 @ SV742 ) ) ) )
| ~ ~ ( ~ ! [SY1377: $i] :
( ~ ( function @ SY1377 )
| ~ ( relation @ SY1377 )
| ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1377 @ SV742 ) ) )
| ( in @ SV666 @ ( relation_dom @ SY1377 ) ) )
| ~ ! [SY1378: $i] :
( ~ ( function @ SY1378 )
| ~ ( relation @ SY1378 )
| ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1378 @ SV742 ) ) )
| ( in @ ( apply @ SY1378 @ SV666 ) @ ( relation_dom @ SV742 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4304]) ).
thf(4466,plain,
! [SV843: $i,SV667: $i] :
( ( ! [SY1468: $i] :
( ~ ( relation @ SY1468 )
| ! [SY1469: $i] :
( ~ ( in @ SY1469 @ ( relation_rng @ SY1468 ) )
| ~ ( in @ ( ordered_pair @ SV667 @ SY1469 ) @ SY1468 )
| ~ ( in @ SY1469 @ SV843 ) )
| ( in @ SV667 @ ( relation_inverse_image @ SY1468 @ SV843 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4305]) ).
thf(4467,plain,
! [SV844: $i,SV667: $i] :
( ( ! [SY1470: $i] :
( ~ ( relation @ SY1470 )
| ~ ( in @ SV667 @ ( relation_inverse_image @ SY1470 @ SV844 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK51_D @ SY1470 @ SV844 @ SV667 ) @ ( relation_rng @ SY1470 ) )
| ~ ( in @ ( ordered_pair @ SV667 @ ( sK51_D @ SY1470 @ SV844 @ SV667 ) ) @ SY1470 ) )
| ~ ( in @ ( sK51_D @ SY1470 @ SV844 @ SV667 ) @ SV844 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4306]) ).
thf(4468,plain,
! [SV845: $i,SV792: $i] :
( ( ( disjoint @ SV792 @ SV845 )
| ~ ( ~ ( in @ ( sK49_C @ SV845 @ SV792 ) @ SV792 )
| ~ ( in @ ( sK49_C @ SV845 @ SV792 ) @ SV845 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4307]) ).
thf(4469,plain,
! [SV846: $i,SV793: $i] :
( ( ! [SY1471: $i] :
( ~ ( in @ SY1471 @ SV793 )
| ~ ( in @ SY1471 @ SV846 ) )
| ~ ( disjoint @ SV793 @ SV846 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4308]) ).
thf(4470,plain,
! [SV794: $i] :
( ( ( ~ ( empty @ SV794 ) )
= $true )
| ( ( empty @ ( relation_inverse @ SV794 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4309]) ).
thf(4471,plain,
! [SV795: $i] :
( ( ( ~ ( empty @ SV795 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV795 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4310]) ).
thf(4472,plain,
! [SV847: $i,SV668: $i] :
( ( ! [SY1472: $i] :
( ~ ( relation @ SY1472 )
| ~ ( in @ SV668 @ SV847 )
| ~ ( in @ SV668 @ ( relation_dom @ SY1472 ) )
| ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SY1472 @ SV847 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4311]) ).
thf(4473,plain,
! [SV668: $i] :
( ( ~ ! [SY1245: $i,SY1246: $i] :
( ~ ( relation @ SY1246 )
| ~ ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SY1246 @ SY1245 ) ) )
| ( in @ SV668 @ SY1245 ) )
| ~ ! [SY1247: $i,SY1248: $i] :
( ~ ( relation @ SY1248 )
| ~ ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SY1248 @ SY1247 ) ) )
| ( in @ SV668 @ ( relation_dom @ SY1248 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4312]) ).
thf(4474,plain,
! [SV669: $i,SV848: $i] :
( ( ! [SY1473: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SY1473 @ SV848 @ SV669 ) @ SY1473 )
| ~ ( in @ ( sK26_D @ SY1473 @ SV848 @ SV669 ) @ SV669 ) )
| ~ ( ~ ( in @ ( sK26_D @ SY1473 @ SV848 @ SV669 ) @ SY1473 )
| ~ ( in @ ( sK26_D @ SY1473 @ SV848 @ SV669 ) @ SV848 ) ) )
| ~ ( ( in @ ( sK26_D @ SY1473 @ SV848 @ SV669 ) @ SY1473 )
| ( in @ ( sK26_D @ SY1473 @ SV848 @ SV669 ) @ SV669 )
| ( in @ ( sK26_D @ SY1473 @ SV848 @ SV669 ) @ SV848 ) ) )
| ( SY1473
= ( set_union2 @ SV669 @ SV848 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4313]) ).
thf(4475,plain,
! [SV849: $i,SV669: $i] :
( ( ! [SY1474: $i] :
( ( SY1474
!= ( set_union2 @ SV669 @ SV849 ) )
| ~ ( ~ ! [SY1475: $i] :
( ~ ( in @ SY1475 @ SY1474 )
| ( in @ SY1475 @ SV669 )
| ( in @ SY1475 @ SV849 ) )
| ~ ~ ( ~ ! [SY1254: $i] :
( ~ ( in @ SY1254 @ SV669 )
| ( in @ SY1254 @ SY1474 ) )
| ~ ! [SY1477: $i] :
( ~ ( in @ SY1477 @ SV849 )
| ( in @ SY1477 @ SY1474 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4314]) ).
thf(4476,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY406 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ ( sK33_SY406 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4315]) ).
thf(4477,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK31_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)],[4315]) ).
thf(4478,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4316]) ).
thf(4479,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4316]) ).
thf(4480,plain,
! [SV850: $i,SV670: $i] :
( ( ! [SY1478: $i] :
( ~ ( ~ ( ! [SY1479: $i,SY1480: $i] :
( ~ ( in @ SY1479 @ SV670 )
| ~ ( in @ SY1480 @ SV850 )
| ( ( sK23_D @ SY1478 @ SV850 @ SV670 )
!= ( ordered_pair @ SY1479 @ SY1480 ) ) )
| ~ ( in @ ( sK23_D @ SY1478 @ SV850 @ SV670 ) @ SY1478 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY403 @ SY1478 @ SV850 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK25_SY405 @ SY1478 @ SV850 @ SV670 ) @ SV850 ) )
| ( ( sK23_D @ SY1478 @ SV850 @ SV670 )
!= ( ordered_pair @ ( sK24_SY403 @ SY1478 @ SV850 @ SV670 ) @ ( sK25_SY405 @ SY1478 @ SV850 @ SV670 ) ) ) )
| ( in @ ( sK23_D @ SY1478 @ SV850 @ SV670 ) @ SY1478 ) ) )
| ( SY1478
= ( cartesian_product2 @ SV670 @ SV850 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4317]) ).
thf(4481,plain,
! [SV851: $i,SV670: $i] :
( ( ! [SY1481: $i] :
( ( SY1481
!= ( cartesian_product2 @ SV670 @ SV851 ) )
| ~ ( ~ ! [SY1482: $i] :
( ! [SY1483: $i,SY1484: $i] :
( ~ ( in @ SY1483 @ SV670 )
| ~ ( in @ SY1484 @ SV851 )
| ( SY1482
!= ( ordered_pair @ SY1483 @ SY1484 ) ) )
| ( in @ SY1482 @ SY1481 ) )
| ~ ! [SY1485: $i] :
( ~ ( in @ SY1485 @ SY1481 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY1485 @ SY1481 @ SV851 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK22_SY400 @ SY1485 @ SY1481 @ SV851 @ SV670 ) @ SV851 ) )
| ( SY1485
!= ( ordered_pair @ ( sK21_E @ SY1485 @ SY1481 @ SV851 @ SV670 ) @ ( sK22_SY400 @ SY1485 @ SY1481 @ SV851 @ SV670 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4318]) ).
thf(4482,plain,
! [SV671: $i,SV852: $i] :
( ( ! [SY1486: $i] :
( ~ ( function @ SY1486 )
| ~ ( relation @ SY1486 )
| ( SV852
!= ( apply @ SY1486 @ SV671 ) )
| ~ ( in @ SV671 @ ( relation_dom @ SY1486 ) )
| ( in @ ( ordered_pair @ SV671 @ SV852 ) @ SY1486 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4319]) ).
thf(4483,plain,
! [SV671: $i] :
( ( ~ ! [SY1268: $i,SY1269: $i] :
( ~ ( function @ SY1269 )
| ~ ( relation @ SY1269 )
| ~ ( in @ ( ordered_pair @ SV671 @ SY1268 ) @ SY1269 )
| ( SY1268
= ( apply @ SY1269 @ SV671 ) ) )
| ~ ! [SY1270: $i,SY1271: $i] :
( ~ ( function @ SY1271 )
| ~ ( relation @ SY1271 )
| ~ ( in @ ( ordered_pair @ SV671 @ SY1270 ) @ SY1271 )
| ( in @ SV671 @ ( relation_dom @ SY1271 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4320]) ).
thf(4484,plain,
! [SV672: $i] :
( ( ( ~ ! [SY1272: $i] :
( ~ ( relation @ SY1272 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SY1272 @ SV672 ) @ ( sK12_SY396 @ SY1272 @ SV672 ) ) @ SY1272 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SY1272 @ SV672 ) @ ( sK11_C @ SY1272 @ SV672 ) ) @ SV672 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_C @ SY1272 @ SV672 ) @ ( sK12_SY396 @ SY1272 @ SV672 ) ) @ SY1272 )
| ( in @ ( ordered_pair @ ( sK12_SY396 @ SY1272 @ SV672 ) @ ( sK11_C @ SY1272 @ SV672 ) ) @ SV672 ) ) )
| ( SY1272
= ( relation_inverse @ SV672 ) ) ) )
= $false )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4321]) ).
thf(4485,plain,
! [SV672: $i] :
( ( ( ~ ! [SY1273: $i] :
( ~ ( relation @ SY1273 )
| ( SY1273
!= ( relation_inverse @ SV672 ) )
| ~ ( ~ ! [SY1274: $i,SY1275: $i] :
( ~ ( in @ ( ordered_pair @ SY1274 @ SY1275 ) @ SY1273 )
| ( in @ ( ordered_pair @ SY1275 @ SY1274 ) @ SV672 ) )
| ~ ! [SY1276: $i,SY1277: $i] :
( ~ ( in @ ( ordered_pair @ SY1277 @ SY1276 ) @ SV672 )
| ( in @ ( ordered_pair @ SY1276 @ SY1277 ) @ SY1273 ) ) ) ) )
= $false )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4321]) ).
thf(4486,plain,
! [SV853: $i,SV796: $i] :
( ( ( ( set_difference @ SV796 @ SV853 )
!= empty_set )
| ( subset @ SV796 @ SV853 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4322]) ).
thf(4487,plain,
! [SV854: $i,SV797: $i] :
( ( ~ ( subset @ SV797 @ SV854 )
| ( ( set_difference @ SV797 @ SV854 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4323]) ).
thf(4488,plain,
! [SV798: $i] :
( ( ( ~ ( function @ SV798 )
| ~ ( relation @ SV798 )
| ~ ( one_to_one @ SV798 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV798 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4324]) ).
thf(4489,plain,
! [SV799: $i] :
( ( ( ~ ( function @ SV799 )
| ~ ( relation @ SV799 )
| ~ ( one_to_one @ SV799 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV799 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4325]) ).
thf(4490,plain,
! [SV855: $i,SV673: $i] :
( ( ! [SY1487: $i] :
( ~ ( relation @ SY1487 )
| ~ ( in @ ( ordered_pair @ SV673 @ SV855 ) @ SY1487 )
| ( in @ SV673 @ ( relation_dom @ SY1487 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4326]) ).
thf(4491,plain,
! [SV856: $i,SV673: $i] :
( ( ! [SY1488: $i] :
( ~ ( relation @ SY1488 )
| ~ ( in @ ( ordered_pair @ SV673 @ SV856 ) @ SY1488 )
| ( in @ SV856 @ ( relation_rng @ SY1488 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4327]) ).
thf(4492,plain,
! [SV743: $i,SV674: $i] :
( ( ! [SY1379: $i,SY1380: $i] :
( ~ ( in @ SV674 @ SY1379 )
| ~ ( in @ SV743 @ SY1380 )
| ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SY1379 @ SY1380 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4328]) ).
thf(4493,plain,
! [SV743: $i,SV674: $i] :
( ( ~ ( ~ ! [SY1381: $i] :
( ! [SY1382: $i] :
~ ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SY1381 @ SY1382 ) )
| ( in @ SV674 @ SY1381 ) )
| ~ ! [SY1383: $i,SY1384: $i] :
( ~ ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SY1383 @ SY1384 ) )
| ( in @ SV743 @ SY1384 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4329]) ).
thf(4494,plain,
! [SV675: $i,SV857: $i] :
( ( ! [SY1489: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SY1489 @ SV857 @ SV675 ) @ SY1489 )
| ( ( sK27_D @ SY1489 @ SV857 @ SV675 )
!= SV675 ) )
| ~ ( ~ ( in @ ( sK27_D @ SY1489 @ SV857 @ SV675 ) @ SY1489 )
| ( ( sK27_D @ SY1489 @ SV857 @ SV675 )
!= SV857 ) ) )
| ~ ( ( in @ ( sK27_D @ SY1489 @ SV857 @ SV675 ) @ SY1489 )
| ( ( sK27_D @ SY1489 @ SV857 @ SV675 )
= SV675 )
| ( ( sK27_D @ SY1489 @ SV857 @ SV675 )
= SV857 ) ) )
| ( SY1489
= ( unordered_pair @ SV675 @ SV857 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4330]) ).
thf(4495,plain,
! [SV858: $i,SV675: $i] :
( ( ! [SY1490: $i] :
( ( SY1490
!= ( unordered_pair @ SV675 @ SV858 ) )
| ~ ( ~ ! [SY1491: $i] :
( ~ ( in @ SY1491 @ SY1490 )
| ( SY1491 = SV675 )
| ( SY1491 = SV858 ) )
| ~ ~ ( ~ ! [SY1294: $i] :
( ( SY1294 != SV675 )
| ( in @ SY1294 @ SY1490 ) )
| ~ ! [SY1493: $i] :
( ( SY1493 != SV858 )
| ( in @ SY1493 @ SY1490 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4331]) ).
thf(4496,plain,
! [SV744: $i,SV676: $i] :
( ( ! [SY1385: $i,SY1386: $i] :
( ~ ( in @ SV676 @ SY1385 )
| ~ ( in @ SV744 @ SY1386 )
| ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SY1385 @ SY1386 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4332]) ).
thf(4497,plain,
! [SV744: $i,SV676: $i] :
( ( ~ ( ~ ! [SY1387: $i] :
( ! [SY1388: $i] :
~ ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SY1387 @ SY1388 ) )
| ( in @ SV676 @ SY1387 ) )
| ~ ! [SY1389: $i,SY1390: $i] :
( ~ ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SY1389 @ SY1390 ) )
| ( in @ SV744 @ SY1390 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4333]) ).
thf(4498,plain,
! [SV859: $i,SV800: $i] :
( ( ( disjoint @ SV800 @ SV859 )
| ( in @ ( sK48_C @ SV859 @ SV800 ) @ ( set_intersection2 @ SV800 @ SV859 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4334]) ).
thf(4499,plain,
! [SV860: $i,SV801: $i] :
( ( ! [SY1494: $i] :
~ ( in @ SY1494 @ ( set_intersection2 @ SV801 @ SV860 ) )
| ~ ( disjoint @ SV801 @ SV860 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4335]) ).
thf(4500,plain,
! [SV802: $i] :
( ( ( ~ ( function @ SV802 )
| ~ ( relation @ SV802 ) )
= $true )
| ( ( function @ ( function_inverse @ SV802 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4336]) ).
thf(4501,plain,
! [SV803: $i] :
( ( ( ~ ( function @ SV803 )
| ~ ( relation @ SV803 ) )
= $true )
| ( ( relation @ ( function_inverse @ SV803 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4337]) ).
thf(4502,plain,
! [SV677: $i,SV745: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_C @ SV745 @ SV677 ) @ SV677 )
| ~ ( in @ ( sK4_C @ SV745 @ SV677 ) @ SV745 ) ) )
= $false )
| ( ( SV677 = SV745 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4338]) ).
thf(4503,plain,
! [SV677: $i,SV745: $i] :
( ( ( ~ ( ( in @ ( sK4_C @ SV745 @ SV677 ) @ SV677 )
| ( in @ ( sK4_C @ SV745 @ SV677 ) @ SV745 ) ) )
= $false )
| ( ( SV677 = SV745 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4338]) ).
thf(4504,plain,
! [SV861: $i,SV678: $i] :
( ( ~ ( subset @ SV678 @ SV861 )
| ! [SY1495: $i] : ( subset @ ( cartesian_product2 @ SV678 @ SY1495 ) @ ( cartesian_product2 @ SV861 @ SY1495 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4339]) ).
thf(4505,plain,
! [SV862: $i,SV678: $i] :
( ( ~ ( subset @ SV678 @ SV862 )
| ! [SY1496: $i] : ( subset @ ( cartesian_product2 @ SY1496 @ SV678 ) @ ( cartesian_product2 @ SY1496 @ SV862 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4340]) ).
thf(4506,plain,
! [SV804: $i,SV863: $i] :
( ( ~ ( ~ ( ! [SY1497: $i] :
( ~ ( in @ ( sK15_C @ SV863 @ SV804 ) @ SY1497 )
| ~ ( in @ SY1497 @ SV804 ) )
| ~ ( in @ ( sK15_C @ SV863 @ SV804 ) @ SV863 ) )
| ~ ( ~ ( ~ ( in @ ( sK15_C @ SV863 @ SV804 ) @ ( sK16_SY398 @ SV863 @ SV804 ) )
| ~ ( in @ ( sK16_SY398 @ SV863 @ SV804 ) @ SV804 ) )
| ( in @ ( sK15_C @ SV863 @ SV804 ) @ SV863 ) ) )
| ( SV863
= ( union @ SV804 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4341]) ).
thf(4507,plain,
! [SV805: $i,SV864: $i] :
( ( ( SV864
!= ( union @ SV805 ) )
| ~ ( ~ ! [SY1498: $i] :
( ! [SY1428: $i] :
( ~ ( in @ SY1498 @ SY1428 )
| ~ ( in @ SY1428 @ SV805 ) )
| ( in @ SY1498 @ SV864 ) )
| ~ ! [SY1500: $i] :
( ~ ( in @ SY1500 @ SV864 )
| ~ ( ~ ( in @ SY1500 @ ( sK14_D @ SY1500 @ SV864 @ SV805 ) )
| ~ ( in @ ( sK14_D @ SY1500 @ SV864 @ SV805 ) @ SV805 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4342]) ).
thf(4508,plain,
! [SV679: $i] :
( ( ( ~ ! [SY1308: $i] :
( ~ ( ~ ( ! [SY1309: $i] :
~ ( in @ ( ordered_pair @ ( sK63_C @ SY1308 @ SV679 ) @ SY1309 ) @ SV679 )
| ~ ( in @ ( sK63_C @ SY1308 @ SV679 ) @ SY1308 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_C @ SY1308 @ SV679 ) @ ( sK64_SY419 @ SY1308 @ SV679 ) ) @ SV679 )
| ( in @ ( sK63_C @ SY1308 @ SV679 ) @ SY1308 ) ) )
| ( SY1308
= ( relation_dom @ SV679 ) ) ) )
= $false )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4343]) ).
thf(4509,plain,
! [SV679: $i] :
( ( ( ~ ! [SY1310: $i] :
( ( SY1310
!= ( relation_dom @ SV679 ) )
| ~ ( ~ ! [SY1311: $i] :
( ! [SY1312: $i] :
~ ( in @ ( ordered_pair @ SY1311 @ SY1312 ) @ SV679 )
| ( in @ SY1311 @ SY1310 ) )
| ~ ! [SY1313: $i] :
( ~ ( in @ SY1313 @ SY1310 )
| ( in @ ( ordered_pair @ SY1313 @ ( sK62_D @ SY1313 @ SY1310 @ SV679 ) ) @ SV679 ) ) ) ) )
= $false )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4343]) ).
thf(4510,plain,
! [SV865: $i,SV680: $i] :
( ( ! [SY1501: $i] :
( ~ ( relation @ SY1501 )
| ~ ( in @ ( ordered_pair @ SV680 @ SV865 ) @ SY1501 )
| ( in @ SV680 @ ( relation_field @ SY1501 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4344]) ).
thf(4511,plain,
! [SV866: $i,SV680: $i] :
( ( ! [SY1502: $i] :
( ~ ( relation @ SY1502 )
| ~ ( in @ ( ordered_pair @ SV680 @ SV866 ) @ SY1502 )
| ( in @ SV866 @ ( relation_field @ SY1502 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4345]) ).
thf(4512,plain,
! [SV806: $i,SV867: $i] :
( ( ~ ( relation @ SV867 )
| ~ ( ~ ( ( ( sK44_C @ SV867 @ SV806 )
!= ( sK45_SY414 @ SV867 @ SV806 ) )
| ~ ( in @ ( sK44_C @ SV867 @ SV806 ) @ SV806 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 ) )
| ~ ~ ( ~ ( ( ( sK44_C @ SV867 @ SV806 )
= ( sK45_SY414 @ SV867 @ SV806 ) )
| ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 ) )
| ~ ( ( in @ ( sK44_C @ SV867 @ SV806 ) @ SV806 )
| ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 ) ) ) )
| ( SV867
= ( identity_relation @ SV806 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4346]) ).
thf(4513,plain,
! [SV807: $i,SV868: $i] :
( ( ~ ( relation @ SV868 )
| ( SV868
!= ( identity_relation @ SV807 ) )
| ~ ( ~ ! [SY1503: $i,SY1504: $i] :
( ( SY1503 != SY1504 )
| ~ ( in @ SY1503 @ SV807 )
| ( in @ ( ordered_pair @ SY1503 @ SY1504 ) @ SV868 ) )
| ~ ~ ( ~ ! [SY1505: $i,SY1506: $i] :
( ~ ( in @ ( ordered_pair @ SY1505 @ SY1506 ) @ SV868 )
| ( SY1505 = SY1506 ) )
| ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
~ ( in @ ( ordered_pair @ SY1507 @ SY1508 ) @ SV868 )
| ( in @ SY1507 @ SV807 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4347]) ).
thf(4514,plain,
! [SV681: $i] :
( ( ( ~ ! [SY1318: $i,SY1319: $i] :
( ~ ( relation @ SY1319 )
| ~ ( ~ ( ~ ( in @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ SY1318 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ ( sK43_SY413 @ SY1319 @ SY1318 @ SV681 ) ) @ SV681 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ ( sK43_SY413 @ SY1319 @ SY1318 @ SV681 ) ) @ SY1319 ) )
| ~ ~ ( ~ ( ( in @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ SY1318 )
| ( in @ ( ordered_pair @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ ( sK43_SY413 @ SY1319 @ SY1318 @ SV681 ) ) @ SY1319 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ ( sK43_SY413 @ SY1319 @ SY1318 @ SV681 ) ) @ SV681 )
| ( in @ ( ordered_pair @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ ( sK43_SY413 @ SY1319 @ SY1318 @ SV681 ) ) @ SY1319 ) ) ) )
| ( SY1319
= ( relation_dom_restriction @ SV681 @ SY1318 ) ) ) )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4348]) ).
thf(4515,plain,
! [SV681: $i] :
( ( ( ~ ! [SY1320: $i,SY1321: $i] :
( ~ ( relation @ SY1321 )
| ( SY1321
!= ( relation_dom_restriction @ SV681 @ SY1320 ) )
| ~ ( ~ ! [SY1322: $i,SY1323: $i] :
( ~ ( in @ SY1322 @ SY1320 )
| ~ ( in @ ( ordered_pair @ SY1322 @ SY1323 ) @ SV681 )
| ( in @ ( ordered_pair @ SY1322 @ SY1323 ) @ SY1321 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY1321 )
| ( in @ SX3 @ SY1320 ) )
| ~ ! [SY1326: $i,SY1327: $i] :
( ~ ( in @ ( ordered_pair @ SY1326 @ SY1327 ) @ SY1321 )
| ( in @ ( ordered_pair @ SY1326 @ SY1327 ) @ SV681 ) ) ) ) ) )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4348]) ).
thf(4516,plain,
! [SV808: $i,SV869: $i] :
( ( ~ ( ~ ( ( ( sK30_C @ SV869 @ SV808 )
!= SV808 )
| ~ ( in @ ( sK30_C @ SV869 @ SV808 ) @ SV869 ) )
| ~ ( ( ( sK30_C @ SV869 @ SV808 )
= SV808 )
| ( in @ ( sK30_C @ SV869 @ SV808 ) @ SV869 ) ) )
| ( SV869
= ( singleton @ SV808 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4349]) ).
thf(4517,plain,
! [SV809: $i,SV870: $i] :
( ( ( SV870
!= ( singleton @ SV809 ) )
| ~ ( ~ ! [SY1509: $i] :
( ( SY1509 != SV809 )
| ( in @ SY1509 @ SV870 ) )
| ~ ! [SY1510: $i] :
( ~ ( in @ SY1510 @ SV870 )
| ( SY1510 = SV809 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4350]) ).
thf(4518,plain,
! [SV871: $i,SV682: $i] :
( ( ! [SY1511: $i] :
( ~ ( relation @ SY1511 )
| ! [SY1512: $i] :
( ~ ( in @ SY1512 @ ( relation_dom @ SY1511 ) )
| ~ ( in @ ( ordered_pair @ SY1512 @ SV682 ) @ SY1511 )
| ~ ( in @ SY1512 @ SV871 ) )
| ( in @ SV682 @ ( relation_image @ SY1511 @ SV871 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4351]) ).
thf(4519,plain,
! [SV872: $i,SV682: $i] :
( ( ! [SY1513: $i] :
( ~ ( relation @ SY1513 )
| ~ ( in @ SV682 @ ( relation_image @ SY1513 @ SV872 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK52_D @ SY1513 @ SV872 @ SV682 ) @ ( relation_dom @ SY1513 ) )
| ~ ( in @ ( ordered_pair @ ( sK52_D @ SY1513 @ SV872 @ SV682 ) @ SV682 ) @ SY1513 ) )
| ~ ( in @ ( sK52_D @ SY1513 @ SV872 @ SV682 ) @ SV872 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4352]) ).
thf(4520,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4353]) ).
thf(4521,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4353]) ).
thf(4522,plain,
! [SV683: $i] :
( ( ( ~ ! [SY1333: $i] :
( ~ ( relation @ SY1333 )
| ~ ( subset @ SV683 @ SY1333 )
| ( subset @ ( relation_dom @ SV683 ) @ ( relation_dom @ SY1333 ) ) ) )
= $false )
| ( ( relation @ SV683 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4354]) ).
thf(4523,plain,
! [SV683: $i] :
( ( ( ~ ! [SY1334: $i] :
( ~ ( relation @ SY1334 )
| ~ ( subset @ SV683 @ SY1334 )
| ( subset @ ( relation_rng @ SV683 ) @ ( relation_rng @ SY1334 ) ) ) )
= $false )
| ( ( relation @ SV683 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4354]) ).
thf(4524,plain,
! [SV873: $i,SV810: $i] :
( ( ~ ( empty @ SV810 )
| ~ ( relation @ SV873 )
| ( empty @ ( relation_composition @ SV810 @ SV873 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4355]) ).
thf(4525,plain,
! [SV874: $i,SV811: $i] :
( ( ~ ( empty @ SV811 )
| ~ ( relation @ SV874 )
| ( relation @ ( relation_composition @ SV811 @ SV874 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4356]) ).
thf(4526,plain,
! [SV684: $i] :
( ( ( ~ ! [SY1335: $i] :
( ~ ( relation @ SY1335 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SY1335 @ SV684 ) @ ( sK66_SY420 @ SY1335 @ SV684 ) ) @ SV684 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SY1335 @ SV684 ) @ ( sK66_SY420 @ SY1335 @ SV684 ) ) @ SY1335 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_C @ SY1335 @ SV684 ) @ ( sK66_SY420 @ SY1335 @ SV684 ) ) @ SV684 )
| ( in @ ( ordered_pair @ ( sK65_C @ SY1335 @ SV684 ) @ ( sK66_SY420 @ SY1335 @ SV684 ) ) @ SY1335 ) ) )
| ( SV684 = SY1335 ) ) )
= $false )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4357]) ).
thf(4527,plain,
! [SV684: $i] :
( ( ( ~ ! [SY1336: $i] :
( ~ ( relation @ SY1336 )
| ( SV684 != SY1336 )
| ~ ( ~ ! [SY1337: $i,SY1338: $i] :
( ~ ( in @ ( ordered_pair @ SY1337 @ SY1338 ) @ SV684 )
| ( in @ ( ordered_pair @ SY1337 @ SY1338 ) @ SY1336 ) )
| ~ ! [SY1339: $i,SY1340: $i] :
( ~ ( in @ ( ordered_pair @ SY1339 @ SY1340 ) @ SY1336 )
| ( in @ ( ordered_pair @ SY1339 @ SY1340 ) @ SV684 ) ) ) ) )
= $false )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4357]) ).
thf(4528,plain,
! [SV685: $i,SV875: $i] :
( ( ~ ( subset @ SV875 @ ( sK2_B @ SV685 ) )
| ( are_equipotent @ SV875 @ ( sK2_B @ SV685 ) )
| ( in @ SV875 @ ( sK2_B @ SV685 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4358]) ).
thf(4529,plain,
! [SV685: $i] :
( ( ~ ! [SY1342: $i] :
( ~ ( ~ ! [SY1343: $i] :
( ~ ( subset @ SY1343 @ SY1342 )
| ( in @ SY1343 @ ( sK3_SY386 @ SY1342 @ SV685 ) ) )
| ~ ( in @ ( sK3_SY386 @ SY1342 @ SV685 ) @ ( sK2_B @ SV685 ) ) )
| ~ ( in @ SY1342 @ ( sK2_B @ SV685 ) ) )
| ~ ~ ( ~ ! [SY1344: $i,SY1345: $i] :
( ~ ( in @ SY1344 @ ( sK2_B @ SV685 ) )
| ~ ( subset @ SY1345 @ SY1344 )
| ( in @ SY1345 @ ( sK2_B @ SV685 ) ) )
| ~ ( in @ SV685 @ ( sK2_B @ SV685 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4359]) ).
thf(4530,plain,
! [SV876: $i,SV812: $i] :
( ( ~ ( subset @ SV812 @ SV876 )
| ~ ( subset @ SV876 @ SV812 )
| ( SV812 = SV876 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4360]) ).
thf(4531,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4361]) ).
thf(4532,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4361]) ).
thf(4533,plain,
! [SV813: $i,SV877: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK28_C @ SV877 @ SV813 ) @ SV877 )
| ~ ( subset @ ( sK28_C @ SV877 @ SV813 ) @ SV813 ) )
| ~ ( ( in @ ( sK28_C @ SV877 @ SV813 ) @ SV877 )
| ( subset @ ( sK28_C @ SV877 @ SV813 ) @ SV813 ) ) )
| ( SV877
= ( powerset @ SV813 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4362]) ).
thf(4534,plain,
! [SV814: $i,SV878: $i] :
( ( ( SV878
!= ( powerset @ SV814 ) )
| ~ ( ~ ! [SY1514: $i] :
( ~ ( in @ SY1514 @ SV878 )
| ( subset @ SY1514 @ SV814 ) )
| ~ ! [SY1515: $i] :
( ~ ( subset @ SY1515 @ SV814 )
| ( in @ SY1515 @ SV878 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4363]) ).
thf(4535,plain,
! [SV879: $i,SV815: $i] :
( ( ~ ( subset @ SV815 @ ( singleton @ SV879 ) )
| ( SV815 = empty_set )
| ( SV815
= ( singleton @ SV879 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4364]) ).
thf(4536,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4365]) ).
thf(4537,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4365]) ).
thf(4538,plain,
! [SV816: $i] :
( ( ( ~ ( relation @ SV816 ) )
= $true )
| ( ( ( ( relation_dom @ SV816 )
!= empty_set )
| ( SV816 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4366]) ).
thf(4539,plain,
! [SV817: $i] :
( ( ( ~ ( relation @ SV817 ) )
= $true )
| ( ( ( ( relation_rng @ SV817 )
!= empty_set )
| ( SV817 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4367]) ).
thf(4540,plain,
( ( ~ ( empty @ sK56_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4368]) ).
thf(4541,plain,
( ( ~ ( relation @ sK56_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4368]) ).
thf(4542,plain,
! [SV818: $i,SV880: $i] :
( ( ~ ( function @ SV880 )
| ~ ( relation @ SV880 )
| ~ ( ~ ( in @ ( sK50_C @ SV880 @ SV818 ) @ SV818 )
| ~ ( ( ( apply @ SV880 @ ( sK50_C @ SV880 @ SV818 ) )
!= ( sK50_C @ SV880 @ SV818 ) ) ) )
| ( ( relation_dom @ SV880 )
!= SV818 )
| ( SV880
= ( identity_relation @ SV818 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4369]) ).
thf(4543,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)],[4370]) ).
thf(4544,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4370]) ).
thf(4545,plain,
! [SV881: $i,SV819: $i] :
( ( ~ ( in @ SV819 @ SV881 )
| ( subset @ ( singleton @ SV819 ) @ SV881 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4371]) ).
thf(4546,plain,
! [SV882: $i,SV820: $i] :
( ( ~ ( subset @ ( singleton @ SV820 ) @ SV882 )
| ( in @ SV820 @ SV882 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4372]) ).
thf(4547,plain,
! [SV821: $i,SV883: $i] :
( ( ~ ( ~ ( in @ ( sK18_C @ SV883 @ SV821 ) @ SV821 )
| ~ ~ ( in @ ( sK18_C @ SV883 @ SV821 ) @ SV883 ) )
| ( subset @ SV821 @ SV883 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4373]) ).
thf(4548,plain,
! [SV884: $i,SV822: $i] :
( ( ~ ( subset @ SV822 @ SV884 )
| ! [SY1516: $i] :
( ~ ( in @ SY1516 @ SV822 )
| ( in @ SY1516 @ SV884 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4374]) ).
thf(4549,plain,
! [SV574: $i,SV755: $i] :
( ( ( relation @ SV755 )
= $false )
| ( ( ( relation_rng @ ( relation_composition @ SV574 @ SV755 ) )
= ( relation_image @ SV755 @ ( relation_rng @ SV574 ) ) )
= $true )
| ( ( relation @ SV574 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4376]) ).
thf(4550,plain,
! [SV747: $i,SV694: $i,SV576: $i] :
( ( ( ~ ( subset @ SV576 @ SV694 ) )
= $true )
| ( ( subset @ ( relation_inverse_image @ SV747 @ SV576 ) @ ( relation_inverse_image @ SV747 @ SV694 ) )
= $true )
| ( ( relation @ SV747 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4377]) ).
thf(4551,plain,
! [SV578: $i,SV756: $i] :
( ( ( relation @ SV756 )
= $false )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV578 @ SV756 ) ) @ ( relation_dom @ SV578 ) )
= $true )
| ( ( relation @ SV578 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4378]) ).
thf(4552,plain,
! [SV579: $i,SV757: $i] :
( ( ( relation @ SV757 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV579 @ SV757 ) ) @ ( relation_rng @ SV757 ) )
= $true )
| ( ( relation @ SV579 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4379]) ).
thf(4553,plain,
! [SV580: $i,SV758: $i] :
( ( ( relation @ SV758 )
= $false )
| ( ( ~ ( subset @ ( relation_rng @ SV580 ) @ ( relation_dom @ SV758 ) )
| ( ( relation_dom @ ( relation_composition @ SV580 @ SV758 ) )
= ( relation_dom @ SV580 ) ) )
= $true )
| ( ( relation @ SV580 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4380]) ).
thf(4554,plain,
! [SV581: $i,SV759: $i] :
( ( ( relation @ SV759 )
= $false )
| ( ( ~ ( subset @ ( relation_dom @ SV581 ) @ ( relation_rng @ SV759 ) )
| ( ( relation_rng @ ( relation_composition @ SV759 @ SV581 ) )
= ( relation_rng @ SV581 ) ) )
= $true )
| ( ( relation @ SV581 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4381]) ).
thf(4555,plain,
! [SV588: $i] :
( ( ( ~ ( one_to_one @ SV588 ) )
= $true )
| ( ( ( function_inverse @ SV588 )
= ( relation_inverse @ SV588 ) )
= $true )
| ( ( function @ SV588 )
= $false )
| ( ( relation @ SV588 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4382]) ).
thf(4556,plain,
! [SV590: $i,SV698: $i] :
( ( ( relation @ SV698 )
= $false )
| ( ( relation @ SV590 )
= $false )
| ( ( relation @ ( relation_composition @ SV590 @ SV698 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4383]) ).
thf(4557,plain,
! [SV594: $i,SV700: $i] :
( ( ( relation @ SV700 )
= $false )
| ( ( relation @ SV594 )
= $false )
| ( ( relation @ ( set_intersection2 @ SV594 @ SV700 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4384]) ).
thf(4558,plain,
! [SV595: $i,SV701: $i] :
( ( ( relation @ SV701 )
= $false )
| ( ( relation @ SV595 )
= $false )
| ( ( relation @ ( set_union2 @ SV595 @ SV701 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4385]) ).
thf(4559,plain,
! [SV761: $i,SV748: $i,SV704: $i,SV602: $i] :
( ( ( ~ ( subset @ SV602 @ SV704 ) )
= $true )
| ( ( ~ ( subset @ SV748 @ SV761 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV602 @ SV748 ) @ ( cartesian_product2 @ SV704 @ SV761 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4388]) ).
thf(4560,plain,
! [SV706: $i,SV604: $i] :
( ( ( SV604 = empty_set )
= $true )
| ( ( ~ ( subset @ SV604 @ ( relation_rng @ SV706 ) ) )
= $true )
| ( ( ( ( relation_inverse_image @ SV706 @ SV604 )
!= empty_set ) )
= $true )
| ( ( relation @ SV706 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4389]) ).
thf(4561,plain,
! [SV749: $i,SV708: $i,SV606: $i] :
( ( ( subset @ SV606 @ SV708 )
= $false )
| ( ( ~ ( subset @ SV606 @ SV749 ) )
= $true )
| ( ( subset @ SV606 @ ( set_intersection2 @ SV708 @ SV749 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4390]) ).
thf(4562,plain,
! [SV750: $i,SV709: $i,SV607: $i] :
( ( ( subset @ SV607 @ SV709 )
= $false )
| ( ( ~ ( subset @ SV709 @ SV750 ) )
= $true )
| ( ( subset @ SV607 @ SV750 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4391]) ).
thf(4563,plain,
! [SV608: $i,SV710: $i] :
( ( ( relation @ SV710 )
= $false )
| ( ( function @ SV710 )
= $false )
| ( ( ! [SY1352: $i] :
( ~ ( function @ SY1352 )
| ~ ( relation @ SY1352 )
| ~ ( in @ SV608 @ ( relation_dom @ ( relation_composition @ SY1352 @ SV710 ) ) )
| ( ( apply @ ( relation_composition @ SY1352 @ SV710 ) @ SV608 )
= ( apply @ SV710 @ ( apply @ SY1352 @ SV608 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4392]) ).
thf(4564,plain,
! [SV609: $i,SV711: $i] :
( ( ( relation @ SV711 )
= $false )
| ( ( function @ SV711 )
= $false )
| ( ( ! [SY1353: $i] :
( ~ ( function @ SY1353 )
| ~ ( relation @ SY1353 )
| ~ ( in @ SV609 @ ( relation_dom @ SV711 ) )
| ( ( apply @ ( relation_composition @ SV711 @ SY1353 ) @ SV609 )
= ( apply @ SY1353 @ ( apply @ SV711 @ SV609 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4393]) ).
thf(4565,plain,
! [SV624: $i,SV751: $i,SV723: $i] :
( ( ( disjoint @ SV723 @ SV751 )
= $false )
| ( ( ~ ( subset @ SV624 @ SV723 ) )
= $true )
| ( ( disjoint @ SV624 @ SV751 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4397]) ).
thf(4566,plain,
! [SV752: $i,SV726: $i,SV627: $i] :
( ( ( subset @ SV627 @ SV726 )
= $false )
| ( ( ~ ( subset @ SV752 @ SV726 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV627 @ SV752 ) @ SV726 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4398]) ).
thf(4567,plain,
! [SV651: $i,SV738: $i] :
( ( ( empty @ SV738 )
= $false )
| ( ( SV651 = SV738 )
= $true )
| ( ( empty @ SV651 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4403]) ).
thf(4568,plain,
! [SV652: $i,SV825: $i,SV885: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV652 )
| ~ ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV825 )
| ~ ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV885 ) )
| ~ ~ ( ~ ( ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV652 )
| ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV885 ) )
| ~ ( ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV825 )
| ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV885 ) ) ) )
| ( SV885
= ( set_intersection2 @ SV652 @ SV825 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4404]) ).
thf(4569,plain,
! [SV826: $i,SV652: $i,SV886: $i] :
( ( ( SV886
!= ( set_intersection2 @ SV652 @ SV826 ) )
| ~ ( ~ ! [SY1517: $i] :
( ~ ( in @ SY1517 @ SV652 )
| ~ ( in @ SY1517 @ SV826 )
| ( in @ SY1517 @ SV886 ) )
| ~ ~ ( ~ ! [SY1518: $i] :
( ~ ( in @ SY1518 @ SV886 )
| ( in @ SY1518 @ SV652 ) )
| ~ ! [SY1519: $i] :
( ~ ( in @ SY1519 @ SV886 )
| ( in @ SY1519 @ SV826 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4405]) ).
thf(4570,plain,
! [SV762: $i] :
( ( ( relation @ SV762 )
= $false )
| ( ( ( ( relation_dom @ SV762 )
!= empty_set )
| ( ( relation_rng @ SV762 )
= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4406]) ).
thf(4571,plain,
! [SV763: $i] :
( ( ( relation @ SV763 )
= $false )
| ( ( ( ( relation_rng @ SV763 )
!= empty_set )
| ( ( relation_dom @ SV763 )
= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4407]) ).
thf(4572,plain,
! [SV653: $i] :
( ( ( ~ ( one_to_one @ SV653 ) )
= $true )
| ( ( ~ ( ~ ! [SY1140: $i] :
( ~ ( function @ SY1140 )
| ~ ( relation @ SY1140 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SY1140 @ SV653 )
= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ( ( sK70_C @ SY1140 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY1140 @ SV653 )
= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY1140 @ SV653 )
= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ( ( sK71_SY424 @ SY1140 @ SV653 )
!= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK70_C @ SY1140 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK71_SY424 @ SY1140 @ SV653 )
!= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY1140 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK70_C @ SY1140 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SY1140 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SY1140 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK71_SY424 @ SY1140 @ SV653 )
!= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ( ( relation_dom @ SY1140 )
!= ( relation_rng @ SV653 ) )
| ( SY1140
= ( function_inverse @ SV653 ) ) )
| ~ ~ ( ~ ! [SY1141: $i] :
( ~ ( function @ SY1141 )
| ~ ( relation @ SY1141 )
| ( SY1141
!= ( function_inverse @ SV653 ) )
| ~ ( ~ ~ ( ~ ! [SY1142: $i,SY1143: $i] :
( ( SY1143
!= ( apply @ SY1141 @ SY1142 ) )
| ~ ( in @ SY1142 @ ( relation_rng @ SV653 ) )
| ( SY1142
= ( apply @ SV653 @ SY1143 ) ) )
| ~ ! [SY1144: $i,SY1145: $i] :
( ( SY1145
!= ( apply @ SY1141 @ SY1144 ) )
| ~ ( in @ SY1144 @ ( relation_rng @ SV653 ) )
| ( in @ SY1145 @ ( relation_dom @ SV653 ) ) ) )
| ~ ~ ( ~ ! [SY1146: $i,SY1147: $i] :
( ( SY1146
!= ( apply @ SV653 @ SY1147 ) )
| ~ ( in @ SY1147 @ ( relation_dom @ SV653 ) )
| ( SY1147
= ( apply @ SY1141 @ SY1146 ) ) )
| ~ ! [SY1148: $i] :
( ! [SY1149: $i] :
( ( SY1148
!= ( apply @ SV653 @ SY1149 ) )
| ~ ( in @ SY1149 @ ( relation_dom @ SV653 ) ) )
| ( in @ SY1148 @ ( relation_rng @ SV653 ) ) ) ) ) )
| ~ ! [SY1150: $i] :
( ~ ( function @ SY1150 )
| ~ ( relation @ SY1150 )
| ( SY1150
!= ( function_inverse @ SV653 ) )
| ( ( relation_dom @ SY1150 )
= ( relation_rng @ SV653 ) ) ) ) ) )
= $true )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4408]) ).
thf(4573,plain,
( ( function @ sK54_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4409]) ).
thf(4574,plain,
( ( relation @ sK54_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4410]) ).
thf(4575,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4411]) ).
thf(4576,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4412]) ).
thf(4577,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4413]) ).
thf(4578,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4414]) ).
thf(4579,plain,
! [SV827: $i,SV764: $i] :
( ( ( ( ( set_intersection2 @ SV764 @ SV827 )
!= empty_set ) )
= $true )
| ( ( disjoint @ SV764 @ SV827 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4415]) ).
thf(4580,plain,
! [SV828: $i,SV765: $i] :
( ( ( ~ ( disjoint @ SV765 @ SV828 ) )
= $true )
| ( ( ( set_intersection2 @ SV765 @ SV828 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4416]) ).
thf(4581,plain,
! [SV829: $i,SV766: $i] :
( ( ( ~ ( subset @ SV766 @ ( singleton @ SV829 ) ) )
= $true )
| ( ( ( SV766 = empty_set )
| ( SV766
= ( singleton @ SV829 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4417]) ).
thf(4582,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4418]) ).
thf(4583,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4419]) ).
thf(4584,plain,
! [SV830: $i,SV769: $i] :
( ( ( ~ ( in @ SV769 @ SV830 ) )
= $true )
| ( ( subset @ ( singleton @ SV769 ) @ SV830 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4420]) ).
thf(4585,plain,
! [SV831: $i,SV770: $i] :
( ( ( ~ ( subset @ ( singleton @ SV770 ) @ SV831 ) )
= $true )
| ( ( in @ SV770 @ SV831 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4421]) ).
thf(4586,plain,
! [SV771: $i] :
( ( ( empty @ SV771 )
= $false )
| ( ( empty @ ( relation_dom @ SV771 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4422]) ).
thf(4587,plain,
! [SV772: $i] :
( ( ( empty @ SV772 )
= $false )
| ( ( relation @ ( relation_dom @ SV772 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4423]) ).
thf(4588,plain,
! [SV832: $i,SV773: $i] :
( ( ( ( ( set_difference @ SV773 @ SV832 )
!= empty_set ) )
= $true )
| ( ( subset @ SV773 @ SV832 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4424]) ).
thf(4589,plain,
! [SV833: $i,SV774: $i] :
( ( ( ~ ( subset @ SV774 @ SV833 ) )
= $true )
| ( ( ( set_difference @ SV774 @ SV833 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4425]) ).
thf(4590,plain,
! [SV739: $i,SV887: $i,SV654: $i] :
( ( ! [SY1520: $i] :
( ~ ( relation @ SY1520 )
| ~ ( in @ SV654 @ SV887 )
| ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ SY1520 )
| ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SV887 ) @ SY1520 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4426]) ).
thf(4591,plain,
! [SV739: $i,SV654: $i] :
( ( ~ ! [SY1360: $i,SY1361: $i] :
( ~ ( relation @ SY1361 )
| ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SY1360 ) @ SY1361 ) )
| ( in @ SV654 @ SY1360 ) )
| ~ ! [SY1362: $i,SY1363: $i] :
( ~ ( relation @ SY1363 )
| ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SY1362 ) @ SY1363 ) )
| ( in @ ( ordered_pair @ SV654 @ SV739 ) @ SY1363 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4427]) ).
thf(4592,plain,
! [SV655: $i,SV740: $i] :
( ( ( ~ ! [SY1364: $i] :
( ~ ( relation @ SY1364 )
| ~ ( ~ ( ~ ( in @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) @ SV655 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY1364 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) ) @ SV740 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY1364 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) ) @ SY1364 ) )
| ~ ~ ( ~ ( ( in @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) @ SV655 )
| ( in @ ( ordered_pair @ ( sK40_D @ SY1364 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) ) @ SY1364 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SY1364 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) ) @ SV740 )
| ( in @ ( ordered_pair @ ( sK40_D @ SY1364 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) ) @ SY1364 ) ) ) )
| ( SY1364
= ( relation_rng_restriction @ SV655 @ SV740 ) ) ) )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4428]) ).
thf(4593,plain,
! [SV740: $i,SV655: $i] :
( ( ( ~ ! [SY1365: $i] :
( ~ ( relation @ SY1365 )
| ( SY1365
!= ( relation_rng_restriction @ SV655 @ SV740 ) )
| ~ ( ~ ! [SY1366: $i,SY1367: $i] :
( ~ ( in @ SY1367 @ SV655 )
| ~ ( in @ ( ordered_pair @ SY1366 @ SY1367 ) @ SV740 )
| ( in @ ( ordered_pair @ SY1366 @ SY1367 ) @ SY1365 ) )
| ~ ~ ( ~ ! [SY1163: $i,SY1164: $i] :
( ~ ( in @ ( ordered_pair @ SY1163 @ SY1164 ) @ SY1365 )
| ( in @ SY1164 @ SV655 ) )
| ~ ! [SY1370: $i,SY1371: $i] :
( ~ ( in @ ( ordered_pair @ SY1370 @ SY1371 ) @ SY1365 )
| ( in @ ( ordered_pair @ SY1370 @ SY1371 ) @ SV740 ) ) ) ) ) )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4428]) ).
thf(4594,plain,
! [SV888: $i,SV741: $i,SV656: $i] :
( ( ! [SY1521: $i] :
( ( ordered_pair @ SV656 @ SV741 )
!= ( ordered_pair @ SV888 @ SY1521 ) )
| ( SV656 = SV888 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4429]) ).
thf(4595,plain,
! [SV889: $i,SV741: $i,SV656: $i] :
( ( ! [SY1522: $i] :
( ( ( ordered_pair @ SV656 @ SV741 )
!= ( ordered_pair @ SV889 @ SY1522 ) )
| ( SV741 = SY1522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4430]) ).
thf(4596,plain,
! [SV657: $i] :
( ( ( ! [SY1172: $i,SY1173: $i] :
( ~ ( ~ ( ! [SY1174: $i] :
( ~ ( in @ ( ordered_pair @ ( sK35_D @ SY1173 @ SY1172 @ SV657 ) @ SY1174 ) @ SV657 )
| ~ ( in @ SY1174 @ SY1172 ) )
| ~ ( in @ ( sK35_D @ SY1173 @ SY1172 @ SV657 ) @ SY1173 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SY1173 @ SY1172 @ SV657 ) @ ( sK36_SY409 @ SY1173 @ SY1172 @ SV657 ) ) @ SV657 )
| ~ ( in @ ( sK36_SY409 @ SY1173 @ SY1172 @ SV657 ) @ SY1172 ) )
| ( in @ ( sK35_D @ SY1173 @ SY1172 @ SV657 ) @ SY1173 ) ) )
| ( SY1173
= ( relation_inverse_image @ SV657 @ SY1172 ) ) ) )
= $true )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4431]) ).
thf(4597,plain,
! [SV657: $i] :
( ( ( ! [SY1175: $i,SY1176: $i] :
( ( SY1176
!= ( relation_inverse_image @ SV657 @ SY1175 ) )
| ~ ( ~ ! [SY1177: $i] :
( ! [SY1178: $i] :
( ~ ( in @ ( ordered_pair @ SY1177 @ SY1178 ) @ SV657 )
| ~ ( in @ SY1178 @ SY1175 ) )
| ( in @ SY1177 @ SY1176 ) )
| ~ ! [SY1179: $i] :
( ~ ( in @ SY1179 @ SY1176 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1179 @ ( sK34_E @ SY1179 @ SY1176 @ SY1175 @ SV657 ) ) @ SV657 )
| ~ ( in @ ( sK34_E @ SY1179 @ SY1176 @ SY1175 @ SV657 ) @ SY1175 ) ) ) ) ) )
= $true )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4432]) ).
thf(4598,plain,
! [SV658: $i] :
( ( ( ! [SY1180: $i,SY1181: $i] :
( ~ ( ~ ( ! [SY1182: $i] :
( ~ ( in @ ( ordered_pair @ SY1182 @ ( sK38_D @ SY1181 @ SY1180 @ SV658 ) ) @ SV658 )
| ~ ( in @ SY1182 @ SY1180 ) )
| ~ ( in @ ( sK38_D @ SY1181 @ SY1180 @ SV658 ) @ SY1181 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SY1181 @ SY1180 @ SV658 ) @ ( sK38_D @ SY1181 @ SY1180 @ SV658 ) ) @ SV658 )
| ~ ( in @ ( sK39_SY411 @ SY1181 @ SY1180 @ SV658 ) @ SY1180 ) )
| ( in @ ( sK38_D @ SY1181 @ SY1180 @ SV658 ) @ SY1181 ) ) )
| ( SY1181
= ( relation_image @ SV658 @ SY1180 ) ) ) )
= $true )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4433]) ).
thf(4599,plain,
! [SV658: $i] :
( ( ( ! [SY1183: $i,SY1184: $i] :
( ( SY1184
!= ( relation_image @ SV658 @ SY1183 ) )
| ~ ( ~ ! [SY1185: $i] :
( ! [SY1186: $i] :
( ~ ( in @ ( ordered_pair @ SY1186 @ SY1185 ) @ SV658 )
| ~ ( in @ SY1186 @ SY1183 ) )
| ( in @ SY1185 @ SY1184 ) )
| ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ SY1184 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SY1187 @ SY1184 @ SY1183 @ SV658 ) @ SY1187 ) @ SV658 )
| ~ ( in @ ( sK37_E @ SY1187 @ SY1184 @ SY1183 @ SV658 ) @ SY1183 ) ) ) ) ) )
= $true )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4434]) ).
thf(4600,plain,
! [SV834: $i,SV777: $i] :
( ( ( ( SV777 = SV834 )
| ~ ( subset @ SV777 @ SV834 ) )
= $true )
| ( ( proper_subset @ SV777 @ SV834 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4435]) ).
thf(4601,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4436]) ).
thf(4602,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4437]) ).
thf(4603,plain,
! [SV835: $i,SV778: $i] :
( ( ( ~ ( empty @ SV778 )
| ~ ( relation @ SV835 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV835 @ SV778 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4438]) ).
thf(4604,plain,
! [SV836: $i,SV779: $i] :
( ( ( ~ ( empty @ SV779 )
| ~ ( relation @ SV836 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV836 @ SV779 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4439]) ).
thf(4605,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4440]) ).
thf(4606,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4441]) ).
thf(4607,plain,
! [SV780: $i] :
( ( ( ~ ( empty @ SV780 )
| ~ ( relation @ SV780 ) )
= $true )
| ( ( ~ ( function @ SV780 ) )
= $true )
| ( ( one_to_one @ SV780 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4442]) ).
thf(4608,plain,
! [SV781: $i] :
( ( ( ~ ! [SY1402: $i,SY1403: $i] :
( ( sK69_B @ SV781 )
!= ( ordered_pair @ SY1402 @ SY1403 ) )
| ~ ( in @ ( sK69_B @ SV781 ) @ SV781 ) )
= $false )
| ( ( relation @ SV781 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4443]) ).
thf(4609,plain,
! [SV782: $i] :
( ( ( relation @ SV782 )
= $false )
| ( ( ! [SY1404: $i] :
( ( SY1404
= ( ordered_pair @ ( sK67_C @ SY1404 @ SV782 ) @ ( sK68_SY421 @ SY1404 @ SV782 ) ) )
| ~ ( in @ SY1404 @ SV782 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4444]) ).
thf(4610,plain,
! [SV837: $i,SV890: $i,SV659: $i] :
( ( ~ ( in @ SV659 @ SV890 )
| ~ ( in @ SV837 @ SV890 )
| ( subset @ ( unordered_pair @ SV659 @ SV837 ) @ SV890 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4445]) ).
thf(4611,plain,
! [SV659: $i] :
( ( ~ ! [SY1190: $i,SY1191: $i] :
( ~ ( subset @ ( unordered_pair @ SV659 @ SY1190 ) @ SY1191 )
| ( in @ SV659 @ SY1191 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4446]) ).
thf(4612,plain,
! [SV659: $i] :
( ( ~ ! [SY1192: $i,SY1193: $i] :
( ~ ( subset @ ( unordered_pair @ SV659 @ SY1192 ) @ SY1193 )
| ( in @ SY1192 @ SY1193 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4446]) ).
thf(4613,plain,
! [SV660: $i,SV783: $i] :
( ( ( relation @ SV783 )
= $false )
| ( ( ~ ( ~ ! [SY1405: $i] :
( ~ ( relation @ SY1405 )
| ~ ( ~ ( ! [SY1406: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY1405 @ SV783 @ SV660 ) @ SY1406 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1406 @ ( sK9_SY391 @ SY1405 @ SV783 @ SV660 ) ) @ SV783 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SY1405 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SY1405 @ SV783 @ SV660 ) ) @ SY1405 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY1405 @ SV783 @ SV660 ) @ ( sK10_SY395 @ SY1405 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SY1405 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SY1405 @ SV783 @ SV660 ) ) @ SV783 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SY1405 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SY1405 @ SV783 @ SV660 ) ) @ SY1405 ) ) )
| ( SY1405
= ( relation_composition @ SV660 @ SV783 ) ) )
| ~ ! [SY1407: $i] :
( ~ ( relation @ SY1407 )
| ( SY1407
!= ( relation_composition @ SV660 @ SV783 ) )
| ~ ( ~ ! [SY1408: $i,SY1409: $i] :
( ! [SY1410: $i] :
( ~ ( in @ ( ordered_pair @ SY1408 @ SY1410 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1410 @ SY1409 ) @ SV783 ) )
| ( in @ ( ordered_pair @ SY1408 @ SY1409 ) @ SY1407 ) )
| ~ ! [SY1411: $i,SY1412: $i] :
( ~ ( in @ ( ordered_pair @ SY1411 @ SY1412 ) @ SY1407 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1411 @ ( sK7_F @ SY1412 @ SY1411 @ SY1407 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY1412 @ SY1411 @ SY1407 @ SV783 @ SV660 ) @ SY1412 ) @ SV783 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4447]) ).
thf(4614,plain,
! [SV785: $i] :
( ( ( SV785 = empty_set )
= $false )
| ( ( ! [SY1413: $i] :
~ ( in @ SY1413 @ SV785 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4449]) ).
thf(4615,plain,
! [SV786: $i] :
( ( ( empty @ SV786 )
= $false )
| ( ( empty @ ( relation_rng @ SV786 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4450]) ).
thf(4616,plain,
! [SV787: $i] :
( ( ( empty @ SV787 )
= $false )
| ( ( relation @ ( relation_rng @ SV787 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4451]) ).
thf(4617,plain,
! [SV788: $i] :
( ( ( relation @ SV788 )
= $false )
| ( ( ( relation_rng @ SV788 )
= ( relation_dom @ ( relation_inverse @ SV788 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4452]) ).
thf(4618,plain,
! [SV789: $i] :
( ( ( relation @ SV789 )
= $false )
| ( ( ( relation_dom @ SV789 )
= ( relation_rng @ ( relation_inverse @ SV789 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4453]) ).
thf(4619,plain,
! [SV661: $i] :
( ( ( ! [SY1203: $i] :
( ~ ( ~ ( ! [SY1204: $i] :
~ ( in @ ( ordered_pair @ SY1204 @ ( sK60_C @ SY1203 @ SV661 ) ) @ SV661 )
| ~ ( in @ ( sK60_C @ SY1203 @ SV661 ) @ SY1203 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK61_SY417 @ SY1203 @ SV661 ) @ ( sK60_C @ SY1203 @ SV661 ) ) @ SV661 )
| ( in @ ( sK60_C @ SY1203 @ SV661 ) @ SY1203 ) ) )
| ( SY1203
= ( relation_rng @ SV661 ) ) ) )
= $true )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4454]) ).
thf(4620,plain,
! [SV661: $i] :
( ( ( ! [SY1205: $i] :
( ( SY1205
!= ( relation_rng @ SV661 ) )
| ~ ( ~ ! [SY1206: $i] :
( ! [SY1207: $i] :
~ ( in @ ( ordered_pair @ SY1207 @ SY1206 ) @ SV661 )
| ( in @ SY1206 @ SY1205 ) )
| ~ ! [SY1208: $i] :
( ~ ( in @ SY1208 @ SY1205 )
| ( in @ ( ordered_pair @ ( sK59_D @ SY1208 @ SY1205 @ SV661 ) @ SY1208 ) @ SV661 ) ) ) ) )
= $true )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4455]) ).
thf(4621,plain,
! [SV662: $i,SV838: $i,SV891: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV662 )
| ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV838 )
| ~ ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV891 ) )
| ~ ~ ( ~ ( ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV662 )
| ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV891 ) )
| ~ ( ~ ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV838 )
| ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV891 ) ) ) )
| ( SV891
= ( set_difference @ SV662 @ SV838 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4456]) ).
thf(4622,plain,
! [SV839: $i,SV662: $i,SV892: $i] :
( ( ( SV892
!= ( set_difference @ SV662 @ SV839 ) )
| ~ ( ~ ! [SY1523: $i] :
( ~ ( in @ SY1523 @ SV662 )
| ( in @ SY1523 @ SV839 )
| ( in @ SY1523 @ SV892 ) )
| ~ ~ ( ~ ! [SY1524: $i] :
( ~ ( in @ SY1524 @ SV892 )
| ( in @ SY1524 @ SV662 ) )
| ~ ! [SY1525: $i] :
( ~ ( in @ SY1525 @ SV892 )
| ~ ( in @ SY1525 @ SV839 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4457]) ).
thf(4623,plain,
! [SV840: $i,SV790: $i] :
( ( ( ~ ( function @ SV790 )
| ~ ( relation @ SV790 )
| ~ ( relation @ SV840 )
| ~ ( function @ SV840 ) )
= $true )
| ( ( function @ ( relation_composition @ SV790 @ SV840 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4458]) ).
thf(4624,plain,
! [SV841: $i,SV791: $i] :
( ( ( ~ ( function @ SV791 )
| ~ ( relation @ SV791 )
| ~ ( relation @ SV841 )
| ~ ( function @ SV841 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV791 @ SV841 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4459]) ).
thf(4625,plain,
! [SV842: $i,SV663: $i,SV893: $i] :
( ( ~ ( relation @ SV893 )
| ~ ( in @ SV663 @ SV842 )
| ~ ( in @ SV663 @ ( relation_rng @ SV893 ) )
| ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SV842 @ SV893 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4460]) ).
thf(4626,plain,
! [SV663: $i] :
( ( ~ ! [SY1218: $i,SY1219: $i] :
( ~ ( relation @ SY1219 )
| ~ ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SY1218 @ SY1219 ) ) )
| ( in @ SV663 @ SY1218 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4461]) ).
thf(4627,plain,
! [SV663: $i] :
( ( ~ ! [SY1220: $i,SY1221: $i] :
( ~ ( relation @ SY1221 )
| ~ ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SY1220 @ SY1221 ) ) )
| ( in @ SV663 @ ( relation_rng @ SY1221 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4461]) ).
thf(4628,plain,
! [SV664: $i] :
( ( ( ~ ~ ( ~ ! [SY1222: $i] :
( ~ ( in @ SY1222 @ ( relation_dom @ SV664 ) )
| ! [SY1223: $i] :
( ( SY1223
!= ( apply @ SV664 @ SY1222 ) )
| ( in @ ( ordered_pair @ SY1222 @ SY1223 ) @ SV664 ) ) )
| ~ ! [SY1224: $i] :
( ~ ( in @ SY1224 @ ( relation_dom @ SV664 ) )
| ! [SY1225: $i] :
( ~ ( in @ ( ordered_pair @ SY1224 @ SY1225 ) @ SV664 )
| ( SY1225
= ( apply @ SV664 @ SY1224 ) ) ) ) )
| ~ ~ ( ~ ! [SY1226: $i] :
( ( in @ SY1226 @ ( relation_dom @ SV664 ) )
| ! [SY1227: $i] :
( ( SY1227
!= ( apply @ SV664 @ SY1226 ) )
| ( SY1227 = empty_set ) ) )
| ~ ! [SY1228: $i] :
( ( in @ SY1228 @ ( relation_dom @ SV664 ) )
| ! [SY1229: $i] :
( ( SY1229 != empty_set )
| ( SY1229
= ( apply @ SV664 @ SY1228 ) ) ) ) ) )
= $false )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4462]) ).
thf(4629,plain,
! [SV665: $i] :
( ( ( ! [SY1230: $i] :
( ~ ( relation @ SY1230 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SY1230 @ SV665 ) @ ( sK20_SY399 @ SY1230 @ SV665 ) ) @ SV665 )
| ~ ~ ( in @ ( ordered_pair @ ( sK19_C @ SY1230 @ SV665 ) @ ( sK20_SY399 @ SY1230 @ SV665 ) ) @ SY1230 ) )
| ( subset @ SV665 @ SY1230 ) ) )
= $true )
| ( ( relation @ SV665 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4463]) ).
thf(4630,plain,
! [SV665: $i] :
( ( ( ! [SY1231: $i] :
( ~ ( relation @ SY1231 )
| ~ ( subset @ SV665 @ SY1231 )
| ! [SY1232: $i,SY1233: $i] :
( ~ ( in @ ( ordered_pair @ SY1232 @ SY1233 ) @ SV665 )
| ( in @ ( ordered_pair @ SY1232 @ SY1233 ) @ SY1231 ) ) ) )
= $true )
| ( ( relation @ SV665 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4464]) ).
thf(4631,plain,
! [SV666: $i,SV742: $i] :
( ( ( relation @ SV742 )
= $false )
| ( ( function @ SV742 )
= $false )
| ( ( ~ ( ~ ! [SY1376: $i] :
( ~ ( function @ SY1376 )
| ~ ( relation @ SY1376 )
| ~ ( in @ SV666 @ ( relation_dom @ SY1376 ) )
| ~ ( in @ ( apply @ SY1376 @ SV666 ) @ ( relation_dom @ SV742 ) )
| ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1376 @ SV742 ) ) ) )
| ~ ~ ( ~ ! [SY1377: $i] :
( ~ ( function @ SY1377 )
| ~ ( relation @ SY1377 )
| ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1377 @ SV742 ) ) )
| ( in @ SV666 @ ( relation_dom @ SY1377 ) ) )
| ~ ! [SY1378: $i] :
( ~ ( function @ SY1378 )
| ~ ( relation @ SY1378 )
| ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1378 @ SV742 ) ) )
| ( in @ ( apply @ SY1378 @ SV666 ) @ ( relation_dom @ SV742 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4465]) ).
thf(4632,plain,
! [SV843: $i,SV667: $i,SV894: $i] :
( ( ~ ( relation @ SV894 )
| ! [SY1526: $i] :
( ~ ( in @ SY1526 @ ( relation_rng @ SV894 ) )
| ~ ( in @ ( ordered_pair @ SV667 @ SY1526 ) @ SV894 )
| ~ ( in @ SY1526 @ SV843 ) )
| ( in @ SV667 @ ( relation_inverse_image @ SV894 @ SV843 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4466]) ).
thf(4633,plain,
! [SV844: $i,SV667: $i,SV895: $i] :
( ( ~ ( relation @ SV895 )
| ~ ( in @ SV667 @ ( relation_inverse_image @ SV895 @ SV844 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK51_D @ SV895 @ SV844 @ SV667 ) @ ( relation_rng @ SV895 ) )
| ~ ( in @ ( ordered_pair @ SV667 @ ( sK51_D @ SV895 @ SV844 @ SV667 ) ) @ SV895 ) )
| ~ ( in @ ( sK51_D @ SV895 @ SV844 @ SV667 ) @ SV844 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4467]) ).
thf(4634,plain,
! [SV845: $i,SV792: $i] :
( ( ( disjoint @ SV792 @ SV845 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK49_C @ SV845 @ SV792 ) @ SV792 )
| ~ ( in @ ( sK49_C @ SV845 @ SV792 ) @ SV845 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4468]) ).
thf(4635,plain,
! [SV846: $i,SV793: $i] :
( ( ( ! [SY1471: $i] :
( ~ ( in @ SY1471 @ SV793 )
| ~ ( in @ SY1471 @ SV846 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV793 @ SV846 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4469]) ).
thf(4636,plain,
! [SV794: $i] :
( ( ( empty @ SV794 )
= $false )
| ( ( empty @ ( relation_inverse @ SV794 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4470]) ).
thf(4637,plain,
! [SV795: $i] :
( ( ( empty @ SV795 )
= $false )
| ( ( relation @ ( relation_inverse @ SV795 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4471]) ).
thf(4638,plain,
! [SV847: $i,SV668: $i,SV896: $i] :
( ( ~ ( relation @ SV896 )
| ~ ( in @ SV668 @ SV847 )
| ~ ( in @ SV668 @ ( relation_dom @ SV896 ) )
| ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SV896 @ SV847 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4472]) ).
thf(4639,plain,
! [SV668: $i] :
( ( ~ ! [SY1245: $i,SY1246: $i] :
( ~ ( relation @ SY1246 )
| ~ ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SY1246 @ SY1245 ) ) )
| ( in @ SV668 @ SY1245 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4473]) ).
thf(4640,plain,
! [SV668: $i] :
( ( ~ ! [SY1247: $i,SY1248: $i] :
( ~ ( relation @ SY1248 )
| ~ ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SY1248 @ SY1247 ) ) )
| ( in @ SV668 @ ( relation_dom @ SY1248 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4473]) ).
thf(4641,plain,
! [SV669: $i,SV848: $i,SV897: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV897 )
| ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV669 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV897 )
| ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV848 ) ) )
| ~ ( ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV897 )
| ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV669 )
| ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV848 ) ) )
| ( SV897
= ( set_union2 @ SV669 @ SV848 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4474]) ).
thf(4642,plain,
! [SV849: $i,SV669: $i,SV898: $i] :
( ( ( SV898
!= ( set_union2 @ SV669 @ SV849 ) )
| ~ ( ~ ! [SY1527: $i] :
( ~ ( in @ SY1527 @ SV898 )
| ( in @ SY1527 @ SV669 )
| ( in @ SY1527 @ SV849 ) )
| ~ ~ ( ~ ! [SY1528: $i] :
( ~ ( in @ SY1528 @ SV669 )
| ( in @ SY1528 @ SV898 ) )
| ~ ! [SY1529: $i] :
( ~ ( in @ SY1529 @ SV849 )
| ( in @ SY1529 @ SV898 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4475]) ).
thf(4643,plain,
( ( ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY406 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ ( sK33_SY406 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4476]) ).
thf(4644,plain,
( ( ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK31_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)],[4477]) ).
thf(4645,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4478]) ).
thf(4646,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4479]) ).
thf(4647,plain,
! [SV899: $i,SV850: $i,SV670: $i] :
( ( ~ ( ~ ( ! [SY1530: $i,SY1531: $i] :
( ~ ( in @ SY1530 @ SV670 )
| ~ ( in @ SY1531 @ SV850 )
| ( ( sK23_D @ SV899 @ SV850 @ SV670 )
!= ( ordered_pair @ SY1530 @ SY1531 ) ) )
| ~ ( in @ ( sK23_D @ SV899 @ SV850 @ SV670 ) @ SV899 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY403 @ SV899 @ SV850 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK25_SY405 @ SV899 @ SV850 @ SV670 ) @ SV850 ) )
| ( ( sK23_D @ SV899 @ SV850 @ SV670 )
!= ( ordered_pair @ ( sK24_SY403 @ SV899 @ SV850 @ SV670 ) @ ( sK25_SY405 @ SV899 @ SV850 @ SV670 ) ) ) )
| ( in @ ( sK23_D @ SV899 @ SV850 @ SV670 ) @ SV899 ) ) )
| ( SV899
= ( cartesian_product2 @ SV670 @ SV850 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4480]) ).
thf(4648,plain,
! [SV851: $i,SV670: $i,SV900: $i] :
( ( ( SV900
!= ( cartesian_product2 @ SV670 @ SV851 ) )
| ~ ( ~ ! [SY1532: $i] :
( ! [SY1483: $i,SY1484: $i] :
( ~ ( in @ SY1483 @ SV670 )
| ~ ( in @ SY1484 @ SV851 )
| ( SY1532
!= ( ordered_pair @ SY1483 @ SY1484 ) ) )
| ( in @ SY1532 @ SV900 ) )
| ~ ! [SY1535: $i] :
( ~ ( in @ SY1535 @ SV900 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY1535 @ SV900 @ SV851 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK22_SY400 @ SY1535 @ SV900 @ SV851 @ SV670 ) @ SV851 ) )
| ( SY1535
!= ( ordered_pair @ ( sK21_E @ SY1535 @ SV900 @ SV851 @ SV670 ) @ ( sK22_SY400 @ SY1535 @ SV900 @ SV851 @ SV670 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4481]) ).
thf(4649,plain,
! [SV671: $i,SV852: $i,SV901: $i] :
( ( ~ ( function @ SV901 )
| ~ ( relation @ SV901 )
| ( SV852
!= ( apply @ SV901 @ SV671 ) )
| ~ ( in @ SV671 @ ( relation_dom @ SV901 ) )
| ( in @ ( ordered_pair @ SV671 @ SV852 ) @ SV901 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4482]) ).
thf(4650,plain,
! [SV671: $i] :
( ( ~ ! [SY1268: $i,SY1269: $i] :
( ~ ( function @ SY1269 )
| ~ ( relation @ SY1269 )
| ~ ( in @ ( ordered_pair @ SV671 @ SY1268 ) @ SY1269 )
| ( SY1268
= ( apply @ SY1269 @ SV671 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4483]) ).
thf(4651,plain,
! [SV671: $i] :
( ( ~ ! [SY1270: $i,SY1271: $i] :
( ~ ( function @ SY1271 )
| ~ ( relation @ SY1271 )
| ~ ( in @ ( ordered_pair @ SV671 @ SY1270 ) @ SY1271 )
| ( in @ SV671 @ ( relation_dom @ SY1271 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4483]) ).
thf(4652,plain,
! [SV672: $i] :
( ( ( ! [SY1272: $i] :
( ~ ( relation @ SY1272 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SY1272 @ SV672 ) @ ( sK12_SY396 @ SY1272 @ SV672 ) ) @ SY1272 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SY1272 @ SV672 ) @ ( sK11_C @ SY1272 @ SV672 ) ) @ SV672 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_C @ SY1272 @ SV672 ) @ ( sK12_SY396 @ SY1272 @ SV672 ) ) @ SY1272 )
| ( in @ ( ordered_pair @ ( sK12_SY396 @ SY1272 @ SV672 ) @ ( sK11_C @ SY1272 @ SV672 ) ) @ SV672 ) ) )
| ( SY1272
= ( relation_inverse @ SV672 ) ) ) )
= $true )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4484]) ).
thf(4653,plain,
! [SV672: $i] :
( ( ( ! [SY1273: $i] :
( ~ ( relation @ SY1273 )
| ( SY1273
!= ( relation_inverse @ SV672 ) )
| ~ ( ~ ! [SY1274: $i,SY1275: $i] :
( ~ ( in @ ( ordered_pair @ SY1274 @ SY1275 ) @ SY1273 )
| ( in @ ( ordered_pair @ SY1275 @ SY1274 ) @ SV672 ) )
| ~ ! [SY1276: $i,SY1277: $i] :
( ~ ( in @ ( ordered_pair @ SY1277 @ SY1276 ) @ SV672 )
| ( in @ ( ordered_pair @ SY1276 @ SY1277 ) @ SY1273 ) ) ) ) )
= $true )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4485]) ).
thf(4654,plain,
! [SV853: $i,SV796: $i] :
( ( ( ( ( set_difference @ SV796 @ SV853 )
!= empty_set ) )
= $true )
| ( ( subset @ SV796 @ SV853 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4486]) ).
thf(4655,plain,
! [SV854: $i,SV797: $i] :
( ( ( ~ ( subset @ SV797 @ SV854 ) )
= $true )
| ( ( ( set_difference @ SV797 @ SV854 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4487]) ).
thf(4656,plain,
! [SV798: $i] :
( ( ( ~ ( function @ SV798 )
| ~ ( relation @ SV798 ) )
= $true )
| ( ( ~ ( one_to_one @ SV798 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV798 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4488]) ).
thf(4657,plain,
! [SV799: $i] :
( ( ( ~ ( function @ SV799 )
| ~ ( relation @ SV799 ) )
= $true )
| ( ( ~ ( one_to_one @ SV799 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV799 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4489]) ).
thf(4658,plain,
! [SV855: $i,SV673: $i,SV902: $i] :
( ( ~ ( relation @ SV902 )
| ~ ( in @ ( ordered_pair @ SV673 @ SV855 ) @ SV902 )
| ( in @ SV673 @ ( relation_dom @ SV902 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4490]) ).
thf(4659,plain,
! [SV856: $i,SV673: $i,SV903: $i] :
( ( ~ ( relation @ SV903 )
| ~ ( in @ ( ordered_pair @ SV673 @ SV856 ) @ SV903 )
| ( in @ SV856 @ ( relation_rng @ SV903 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4491]) ).
thf(4660,plain,
! [SV743: $i,SV904: $i,SV674: $i] :
( ( ! [SY1536: $i] :
( ~ ( in @ SV674 @ SV904 )
| ~ ( in @ SV743 @ SY1536 )
| ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SV904 @ SY1536 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4492]) ).
thf(4661,plain,
! [SV743: $i,SV674: $i] :
( ( ~ ! [SY1381: $i] :
( ! [SY1382: $i] :
~ ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SY1381 @ SY1382 ) )
| ( in @ SV674 @ SY1381 ) )
| ~ ! [SY1383: $i,SY1384: $i] :
( ~ ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SY1383 @ SY1384 ) )
| ( in @ SV743 @ SY1384 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4493]) ).
thf(4662,plain,
! [SV675: $i,SV857: $i,SV905: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SV905 @ SV857 @ SV675 ) @ SV905 )
| ( ( sK27_D @ SV905 @ SV857 @ SV675 )
!= SV675 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV905 @ SV857 @ SV675 ) @ SV905 )
| ( ( sK27_D @ SV905 @ SV857 @ SV675 )
!= SV857 ) ) )
| ~ ( ( in @ ( sK27_D @ SV905 @ SV857 @ SV675 ) @ SV905 )
| ( ( sK27_D @ SV905 @ SV857 @ SV675 )
= SV675 )
| ( ( sK27_D @ SV905 @ SV857 @ SV675 )
= SV857 ) ) )
| ( SV905
= ( unordered_pair @ SV675 @ SV857 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4494]) ).
thf(4663,plain,
! [SV858: $i,SV675: $i,SV906: $i] :
( ( ( SV906
!= ( unordered_pair @ SV675 @ SV858 ) )
| ~ ( ~ ! [SY1537: $i] :
( ~ ( in @ SY1537 @ SV906 )
| ( SY1537 = SV675 )
| ( SY1537 = SV858 ) )
| ~ ~ ( ~ ! [SY1538: $i] :
( ( SY1538 != SV675 )
| ( in @ SY1538 @ SV906 ) )
| ~ ! [SY1539: $i] :
( ( SY1539 != SV858 )
| ( in @ SY1539 @ SV906 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4495]) ).
thf(4664,plain,
! [SV744: $i,SV907: $i,SV676: $i] :
( ( ! [SY1540: $i] :
( ~ ( in @ SV676 @ SV907 )
| ~ ( in @ SV744 @ SY1540 )
| ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SV907 @ SY1540 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4496]) ).
thf(4665,plain,
! [SV744: $i,SV676: $i] :
( ( ~ ! [SY1387: $i] :
( ! [SY1388: $i] :
~ ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SY1387 @ SY1388 ) )
| ( in @ SV676 @ SY1387 ) )
| ~ ! [SY1389: $i,SY1390: $i] :
( ~ ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SY1389 @ SY1390 ) )
| ( in @ SV744 @ SY1390 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4497]) ).
thf(4666,plain,
! [SV859: $i,SV800: $i] :
( ( ( disjoint @ SV800 @ SV859 )
= $true )
| ( ( in @ ( sK48_C @ SV859 @ SV800 ) @ ( set_intersection2 @ SV800 @ SV859 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4498]) ).
thf(4667,plain,
! [SV860: $i,SV801: $i] :
( ( ( ! [SY1494: $i] :
~ ( in @ SY1494 @ ( set_intersection2 @ SV801 @ SV860 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV801 @ SV860 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4499]) ).
thf(4668,plain,
! [SV802: $i] :
( ( ( ~ ( function @ SV802 ) )
= $true )
| ( ( ~ ( relation @ SV802 ) )
= $true )
| ( ( function @ ( function_inverse @ SV802 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4500]) ).
thf(4669,plain,
! [SV803: $i] :
( ( ( ~ ( function @ SV803 ) )
= $true )
| ( ( ~ ( relation @ SV803 ) )
= $true )
| ( ( relation @ ( function_inverse @ SV803 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4501]) ).
thf(4670,plain,
! [SV677: $i,SV745: $i] :
( ( ( ~ ( in @ ( sK4_C @ SV745 @ SV677 ) @ SV677 )
| ~ ( in @ ( sK4_C @ SV745 @ SV677 ) @ SV745 ) )
= $true )
| ( ( SV677 = SV745 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4502]) ).
thf(4671,plain,
! [SV677: $i,SV745: $i] :
( ( ( ( in @ ( sK4_C @ SV745 @ SV677 ) @ SV677 )
| ( in @ ( sK4_C @ SV745 @ SV677 ) @ SV745 ) )
= $true )
| ( ( SV677 = SV745 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4503]) ).
thf(4672,plain,
! [SV861: $i,SV678: $i] :
( ( ( ~ ( subset @ SV678 @ SV861 ) )
= $true )
| ( ( ! [SY1495: $i] : ( subset @ ( cartesian_product2 @ SV678 @ SY1495 ) @ ( cartesian_product2 @ SV861 @ SY1495 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4504]) ).
thf(4673,plain,
! [SV862: $i,SV678: $i] :
( ( ( ~ ( subset @ SV678 @ SV862 ) )
= $true )
| ( ( ! [SY1496: $i] : ( subset @ ( cartesian_product2 @ SY1496 @ SV678 ) @ ( cartesian_product2 @ SY1496 @ SV862 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4505]) ).
thf(4674,plain,
! [SV804: $i,SV863: $i] :
( ( ( ~ ( ~ ( ! [SY1497: $i] :
( ~ ( in @ ( sK15_C @ SV863 @ SV804 ) @ SY1497 )
| ~ ( in @ SY1497 @ SV804 ) )
| ~ ( in @ ( sK15_C @ SV863 @ SV804 ) @ SV863 ) )
| ~ ( ~ ( ~ ( in @ ( sK15_C @ SV863 @ SV804 ) @ ( sK16_SY398 @ SV863 @ SV804 ) )
| ~ ( in @ ( sK16_SY398 @ SV863 @ SV804 ) @ SV804 ) )
| ( in @ ( sK15_C @ SV863 @ SV804 ) @ SV863 ) ) ) )
= $true )
| ( ( SV863
= ( union @ SV804 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4506]) ).
thf(4675,plain,
! [SV805: $i,SV864: $i] :
( ( ( ( SV864
!= ( union @ SV805 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1498: $i] :
( ! [SY1428: $i] :
( ~ ( in @ SY1498 @ SY1428 )
| ~ ( in @ SY1428 @ SV805 ) )
| ( in @ SY1498 @ SV864 ) )
| ~ ! [SY1500: $i] :
( ~ ( in @ SY1500 @ SV864 )
| ~ ( ~ ( in @ SY1500 @ ( sK14_D @ SY1500 @ SV864 @ SV805 ) )
| ~ ( in @ ( sK14_D @ SY1500 @ SV864 @ SV805 ) @ SV805 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4507]) ).
thf(4676,plain,
! [SV679: $i] :
( ( ( ! [SY1308: $i] :
( ~ ( ~ ( ! [SY1309: $i] :
~ ( in @ ( ordered_pair @ ( sK63_C @ SY1308 @ SV679 ) @ SY1309 ) @ SV679 )
| ~ ( in @ ( sK63_C @ SY1308 @ SV679 ) @ SY1308 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_C @ SY1308 @ SV679 ) @ ( sK64_SY419 @ SY1308 @ SV679 ) ) @ SV679 )
| ( in @ ( sK63_C @ SY1308 @ SV679 ) @ SY1308 ) ) )
| ( SY1308
= ( relation_dom @ SV679 ) ) ) )
= $true )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4508]) ).
thf(4677,plain,
! [SV679: $i] :
( ( ( ! [SY1310: $i] :
( ( SY1310
!= ( relation_dom @ SV679 ) )
| ~ ( ~ ! [SY1311: $i] :
( ! [SY1312: $i] :
~ ( in @ ( ordered_pair @ SY1311 @ SY1312 ) @ SV679 )
| ( in @ SY1311 @ SY1310 ) )
| ~ ! [SY1313: $i] :
( ~ ( in @ SY1313 @ SY1310 )
| ( in @ ( ordered_pair @ SY1313 @ ( sK62_D @ SY1313 @ SY1310 @ SV679 ) ) @ SV679 ) ) ) ) )
= $true )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4509]) ).
thf(4678,plain,
! [SV865: $i,SV680: $i,SV908: $i] :
( ( ~ ( relation @ SV908 )
| ~ ( in @ ( ordered_pair @ SV680 @ SV865 ) @ SV908 )
| ( in @ SV680 @ ( relation_field @ SV908 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4510]) ).
thf(4679,plain,
! [SV866: $i,SV680: $i,SV909: $i] :
( ( ~ ( relation @ SV909 )
| ~ ( in @ ( ordered_pair @ SV680 @ SV866 ) @ SV909 )
| ( in @ SV866 @ ( relation_field @ SV909 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4511]) ).
thf(4680,plain,
! [SV806: $i,SV867: $i] :
( ( ( ~ ( relation @ SV867 ) )
= $true )
| ( ( ~ ( ~ ( ( ( sK44_C @ SV867 @ SV806 )
!= ( sK45_SY414 @ SV867 @ SV806 ) )
| ~ ( in @ ( sK44_C @ SV867 @ SV806 ) @ SV806 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 ) )
| ~ ~ ( ~ ( ( ( sK44_C @ SV867 @ SV806 )
= ( sK45_SY414 @ SV867 @ SV806 ) )
| ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 ) )
| ~ ( ( in @ ( sK44_C @ SV867 @ SV806 ) @ SV806 )
| ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 ) ) ) )
| ( SV867
= ( identity_relation @ SV806 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4512]) ).
thf(4681,plain,
! [SV807: $i,SV868: $i] :
( ( ( ~ ( relation @ SV868 ) )
= $true )
| ( ( ( SV868
!= ( identity_relation @ SV807 ) )
| ~ ( ~ ! [SY1503: $i,SY1504: $i] :
( ( SY1503 != SY1504 )
| ~ ( in @ SY1503 @ SV807 )
| ( in @ ( ordered_pair @ SY1503 @ SY1504 ) @ SV868 ) )
| ~ ~ ( ~ ! [SY1505: $i,SY1506: $i] :
( ~ ( in @ ( ordered_pair @ SY1505 @ SY1506 ) @ SV868 )
| ( SY1505 = SY1506 ) )
| ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
~ ( in @ ( ordered_pair @ SY1507 @ SY1508 ) @ SV868 )
| ( in @ SY1507 @ SV807 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4513]) ).
thf(4682,plain,
! [SV681: $i] :
( ( ( ! [SY1318: $i,SY1319: $i] :
( ~ ( relation @ SY1319 )
| ~ ( ~ ( ~ ( in @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ SY1318 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ ( sK43_SY413 @ SY1319 @ SY1318 @ SV681 ) ) @ SV681 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ ( sK43_SY413 @ SY1319 @ SY1318 @ SV681 ) ) @ SY1319 ) )
| ~ ~ ( ~ ( ( in @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ SY1318 )
| ( in @ ( ordered_pair @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ ( sK43_SY413 @ SY1319 @ SY1318 @ SV681 ) ) @ SY1319 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ ( sK43_SY413 @ SY1319 @ SY1318 @ SV681 ) ) @ SV681 )
| ( in @ ( ordered_pair @ ( sK42_D @ SY1319 @ SY1318 @ SV681 ) @ ( sK43_SY413 @ SY1319 @ SY1318 @ SV681 ) ) @ SY1319 ) ) ) )
| ( SY1319
= ( relation_dom_restriction @ SV681 @ SY1318 ) ) ) )
= $true )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4514]) ).
thf(4683,plain,
! [SV681: $i] :
( ( ( ! [SY1320: $i,SY1321: $i] :
( ~ ( relation @ SY1321 )
| ( SY1321
!= ( relation_dom_restriction @ SV681 @ SY1320 ) )
| ~ ( ~ ! [SY1322: $i,SY1323: $i] :
( ~ ( in @ SY1322 @ SY1320 )
| ~ ( in @ ( ordered_pair @ SY1322 @ SY1323 ) @ SV681 )
| ( in @ ( ordered_pair @ SY1322 @ SY1323 ) @ SY1321 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY1321 )
| ( in @ SX3 @ SY1320 ) )
| ~ ! [SY1326: $i,SY1327: $i] :
( ~ ( in @ ( ordered_pair @ SY1326 @ SY1327 ) @ SY1321 )
| ( in @ ( ordered_pair @ SY1326 @ SY1327 ) @ SV681 ) ) ) ) ) )
= $true )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4515]) ).
thf(4684,plain,
! [SV808: $i,SV869: $i] :
( ( ( ~ ( ~ ( ( ( sK30_C @ SV869 @ SV808 )
!= SV808 )
| ~ ( in @ ( sK30_C @ SV869 @ SV808 ) @ SV869 ) )
| ~ ( ( ( sK30_C @ SV869 @ SV808 )
= SV808 )
| ( in @ ( sK30_C @ SV869 @ SV808 ) @ SV869 ) ) ) )
= $true )
| ( ( SV869
= ( singleton @ SV808 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4516]) ).
thf(4685,plain,
! [SV809: $i,SV870: $i] :
( ( ( ( SV870
!= ( singleton @ SV809 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1509: $i] :
( ( SY1509 != SV809 )
| ( in @ SY1509 @ SV870 ) )
| ~ ! [SY1510: $i] :
( ~ ( in @ SY1510 @ SV870 )
| ( SY1510 = SV809 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4517]) ).
thf(4686,plain,
! [SV871: $i,SV682: $i,SV910: $i] :
( ( ~ ( relation @ SV910 )
| ! [SY1541: $i] :
( ~ ( in @ SY1541 @ ( relation_dom @ SV910 ) )
| ~ ( in @ ( ordered_pair @ SY1541 @ SV682 ) @ SV910 )
| ~ ( in @ SY1541 @ SV871 ) )
| ( in @ SV682 @ ( relation_image @ SV910 @ SV871 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4518]) ).
thf(4687,plain,
! [SV872: $i,SV682: $i,SV911: $i] :
( ( ~ ( relation @ SV911 )
| ~ ( in @ SV682 @ ( relation_image @ SV911 @ SV872 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK52_D @ SV911 @ SV872 @ SV682 ) @ ( relation_dom @ SV911 ) )
| ~ ( in @ ( ordered_pair @ ( sK52_D @ SV911 @ SV872 @ SV682 ) @ SV682 ) @ SV911 ) )
| ~ ( in @ ( sK52_D @ SV911 @ SV872 @ SV682 ) @ SV872 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4519]) ).
thf(4688,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4520]) ).
thf(4689,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4521]) ).
thf(4690,plain,
! [SV683: $i] :
( ( ( ! [SY1333: $i] :
( ~ ( relation @ SY1333 )
| ~ ( subset @ SV683 @ SY1333 )
| ( subset @ ( relation_dom @ SV683 ) @ ( relation_dom @ SY1333 ) ) ) )
= $true )
| ( ( relation @ SV683 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4522]) ).
thf(4691,plain,
! [SV683: $i] :
( ( ( ! [SY1334: $i] :
( ~ ( relation @ SY1334 )
| ~ ( subset @ SV683 @ SY1334 )
| ( subset @ ( relation_rng @ SV683 ) @ ( relation_rng @ SY1334 ) ) ) )
= $true )
| ( ( relation @ SV683 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4523]) ).
thf(4692,plain,
! [SV873: $i,SV810: $i] :
( ( ( ~ ( empty @ SV810 )
| ~ ( relation @ SV873 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV810 @ SV873 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4524]) ).
thf(4693,plain,
! [SV874: $i,SV811: $i] :
( ( ( ~ ( empty @ SV811 )
| ~ ( relation @ SV874 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV811 @ SV874 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4525]) ).
thf(4694,plain,
! [SV684: $i] :
( ( ( ! [SY1335: $i] :
( ~ ( relation @ SY1335 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SY1335 @ SV684 ) @ ( sK66_SY420 @ SY1335 @ SV684 ) ) @ SV684 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SY1335 @ SV684 ) @ ( sK66_SY420 @ SY1335 @ SV684 ) ) @ SY1335 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_C @ SY1335 @ SV684 ) @ ( sK66_SY420 @ SY1335 @ SV684 ) ) @ SV684 )
| ( in @ ( ordered_pair @ ( sK65_C @ SY1335 @ SV684 ) @ ( sK66_SY420 @ SY1335 @ SV684 ) ) @ SY1335 ) ) )
| ( SV684 = SY1335 ) ) )
= $true )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4526]) ).
thf(4695,plain,
! [SV684: $i] :
( ( ( ! [SY1336: $i] :
( ~ ( relation @ SY1336 )
| ( SV684 != SY1336 )
| ~ ( ~ ! [SY1337: $i,SY1338: $i] :
( ~ ( in @ ( ordered_pair @ SY1337 @ SY1338 ) @ SV684 )
| ( in @ ( ordered_pair @ SY1337 @ SY1338 ) @ SY1336 ) )
| ~ ! [SY1339: $i,SY1340: $i] :
( ~ ( in @ ( ordered_pair @ SY1339 @ SY1340 ) @ SY1336 )
| ( in @ ( ordered_pair @ SY1339 @ SY1340 ) @ SV684 ) ) ) ) )
= $true )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4527]) ).
thf(4696,plain,
! [SV685: $i,SV875: $i] :
( ( ( ~ ( subset @ SV875 @ ( sK2_B @ SV685 ) )
| ( are_equipotent @ SV875 @ ( sK2_B @ SV685 ) ) )
= $true )
| ( ( in @ SV875 @ ( sK2_B @ SV685 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4528]) ).
thf(4697,plain,
! [SV685: $i] :
( ( ~ ! [SY1342: $i] :
( ~ ( ~ ! [SY1343: $i] :
( ~ ( subset @ SY1343 @ SY1342 )
| ( in @ SY1343 @ ( sK3_SY386 @ SY1342 @ SV685 ) ) )
| ~ ( in @ ( sK3_SY386 @ SY1342 @ SV685 ) @ ( sK2_B @ SV685 ) ) )
| ~ ( in @ SY1342 @ ( sK2_B @ SV685 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4529]) ).
thf(4698,plain,
! [SV685: $i] :
( ( ~ ~ ( ~ ! [SY1344: $i,SY1345: $i] :
( ~ ( in @ SY1344 @ ( sK2_B @ SV685 ) )
| ~ ( subset @ SY1345 @ SY1344 )
| ( in @ SY1345 @ ( sK2_B @ SV685 ) ) )
| ~ ( in @ SV685 @ ( sK2_B @ SV685 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4529]) ).
thf(4699,plain,
! [SV876: $i,SV812: $i] :
( ( ( ~ ( subset @ SV812 @ SV876 )
| ~ ( subset @ SV876 @ SV812 ) )
= $true )
| ( ( SV812 = SV876 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4530]) ).
thf(4700,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4531]) ).
thf(4701,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4532]) ).
thf(4702,plain,
! [SV813: $i,SV877: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK28_C @ SV877 @ SV813 ) @ SV877 )
| ~ ( subset @ ( sK28_C @ SV877 @ SV813 ) @ SV813 ) )
| ~ ( ( in @ ( sK28_C @ SV877 @ SV813 ) @ SV877 )
| ( subset @ ( sK28_C @ SV877 @ SV813 ) @ SV813 ) ) ) )
= $true )
| ( ( SV877
= ( powerset @ SV813 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4533]) ).
thf(4703,plain,
! [SV814: $i,SV878: $i] :
( ( ( ( SV878
!= ( powerset @ SV814 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1514: $i] :
( ~ ( in @ SY1514 @ SV878 )
| ( subset @ SY1514 @ SV814 ) )
| ~ ! [SY1515: $i] :
( ~ ( subset @ SY1515 @ SV814 )
| ( in @ SY1515 @ SV878 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4534]) ).
thf(4704,plain,
! [SV879: $i,SV815: $i] :
( ( ( ~ ( subset @ SV815 @ ( singleton @ SV879 ) ) )
= $true )
| ( ( ( SV815 = empty_set )
| ( SV815
= ( singleton @ SV879 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4535]) ).
thf(4705,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4536]) ).
thf(4706,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4537]) ).
thf(4707,plain,
! [SV816: $i] :
( ( ( relation @ SV816 )
= $false )
| ( ( ( ( relation_dom @ SV816 )
!= empty_set )
| ( SV816 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4538]) ).
thf(4708,plain,
! [SV817: $i] :
( ( ( relation @ SV817 )
= $false )
| ( ( ( ( relation_rng @ SV817 )
!= empty_set )
| ( SV817 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4539]) ).
thf(4709,plain,
( ( empty @ sK56_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4540]) ).
thf(4710,plain,
( ( relation @ sK56_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4541]) ).
thf(4711,plain,
! [SV818: $i,SV880: $i] :
( ( ( ~ ( function @ SV880 )
| ~ ( relation @ SV880 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK50_C @ SV880 @ SV818 ) @ SV818 )
| ~ ( ( ( apply @ SV880 @ ( sK50_C @ SV880 @ SV818 ) )
!= ( sK50_C @ SV880 @ SV818 ) ) ) )
| ( ( relation_dom @ SV880 )
!= SV818 )
| ( SV880
= ( identity_relation @ SV818 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4542]) ).
thf(4712,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)],[4543]) ).
thf(4713,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4544]) ).
thf(4714,plain,
! [SV881: $i,SV819: $i] :
( ( ( ~ ( in @ SV819 @ SV881 ) )
= $true )
| ( ( subset @ ( singleton @ SV819 ) @ SV881 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4545]) ).
thf(4715,plain,
! [SV882: $i,SV820: $i] :
( ( ( ~ ( subset @ ( singleton @ SV820 ) @ SV882 ) )
= $true )
| ( ( in @ SV820 @ SV882 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4546]) ).
thf(4716,plain,
! [SV821: $i,SV883: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_C @ SV883 @ SV821 ) @ SV821 )
| ~ ~ ( in @ ( sK18_C @ SV883 @ SV821 ) @ SV883 ) ) )
= $true )
| ( ( subset @ SV821 @ SV883 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4547]) ).
thf(4717,plain,
! [SV884: $i,SV822: $i] :
( ( ( ~ ( subset @ SV822 @ SV884 ) )
= $true )
| ( ( ! [SY1516: $i] :
( ~ ( in @ SY1516 @ SV822 )
| ( in @ SY1516 @ SV884 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4548]) ).
thf(4718,plain,
! [SV747: $i,SV694: $i,SV576: $i] :
( ( ( subset @ SV576 @ SV694 )
= $false )
| ( ( subset @ ( relation_inverse_image @ SV747 @ SV576 ) @ ( relation_inverse_image @ SV747 @ SV694 ) )
= $true )
| ( ( relation @ SV747 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4550]) ).
thf(4719,plain,
! [SV758: $i,SV580: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV580 ) @ ( relation_dom @ SV758 ) ) )
= $true )
| ( ( ( relation_dom @ ( relation_composition @ SV580 @ SV758 ) )
= ( relation_dom @ SV580 ) )
= $true )
| ( ( relation @ SV758 )
= $false )
| ( ( relation @ SV580 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4553]) ).
thf(4720,plain,
! [SV759: $i,SV581: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV581 ) @ ( relation_rng @ SV759 ) ) )
= $true )
| ( ( ( relation_rng @ ( relation_composition @ SV759 @ SV581 ) )
= ( relation_rng @ SV581 ) )
= $true )
| ( ( relation @ SV759 )
= $false )
| ( ( relation @ SV581 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4554]) ).
thf(4721,plain,
! [SV588: $i] :
( ( ( one_to_one @ SV588 )
= $false )
| ( ( ( function_inverse @ SV588 )
= ( relation_inverse @ SV588 ) )
= $true )
| ( ( function @ SV588 )
= $false )
| ( ( relation @ SV588 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4555]) ).
thf(4722,plain,
! [SV761: $i,SV748: $i,SV704: $i,SV602: $i] :
( ( ( subset @ SV602 @ SV704 )
= $false )
| ( ( ~ ( subset @ SV748 @ SV761 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV602 @ SV748 ) @ ( cartesian_product2 @ SV704 @ SV761 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4559]) ).
thf(4723,plain,
! [SV706: $i,SV604: $i] :
( ( ( subset @ SV604 @ ( relation_rng @ SV706 ) )
= $false )
| ( ( SV604 = empty_set )
= $true )
| ( ( ( ( relation_inverse_image @ SV706 @ SV604 )
!= empty_set ) )
= $true )
| ( ( relation @ SV706 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4560]) ).
thf(4724,plain,
! [SV708: $i,SV749: $i,SV606: $i] :
( ( ( subset @ SV606 @ SV749 )
= $false )
| ( ( subset @ SV606 @ SV708 )
= $false )
| ( ( subset @ SV606 @ ( set_intersection2 @ SV708 @ SV749 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4561]) ).
thf(4725,plain,
! [SV607: $i,SV750: $i,SV709: $i] :
( ( ( subset @ SV709 @ SV750 )
= $false )
| ( ( subset @ SV607 @ SV709 )
= $false )
| ( ( subset @ SV607 @ SV750 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4562]) ).
thf(4726,plain,
! [SV710: $i,SV608: $i,SV912: $i] :
( ( ( ~ ( function @ SV912 )
| ~ ( relation @ SV912 )
| ~ ( in @ SV608 @ ( relation_dom @ ( relation_composition @ SV912 @ SV710 ) ) )
| ( ( apply @ ( relation_composition @ SV912 @ SV710 ) @ SV608 )
= ( apply @ SV710 @ ( apply @ SV912 @ SV608 ) ) ) )
= $true )
| ( ( function @ SV710 )
= $false )
| ( ( relation @ SV710 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4563]) ).
thf(4727,plain,
! [SV711: $i,SV609: $i,SV913: $i] :
( ( ( ~ ( function @ SV913 )
| ~ ( relation @ SV913 )
| ~ ( in @ SV609 @ ( relation_dom @ SV711 ) )
| ( ( apply @ ( relation_composition @ SV711 @ SV913 ) @ SV609 )
= ( apply @ SV913 @ ( apply @ SV711 @ SV609 ) ) ) )
= $true )
| ( ( function @ SV711 )
= $false )
| ( ( relation @ SV711 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4564]) ).
thf(4728,plain,
! [SV751: $i,SV723: $i,SV624: $i] :
( ( ( subset @ SV624 @ SV723 )
= $false )
| ( ( disjoint @ SV723 @ SV751 )
= $false )
| ( ( disjoint @ SV624 @ SV751 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4565]) ).
thf(4729,plain,
! [SV627: $i,SV726: $i,SV752: $i] :
( ( ( subset @ SV752 @ SV726 )
= $false )
| ( ( subset @ SV627 @ SV726 )
= $false )
| ( ( subset @ ( set_union2 @ SV627 @ SV752 ) @ SV726 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4566]) ).
thf(4730,plain,
! [SV652: $i,SV825: $i,SV885: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV652 )
| ~ ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV825 )
| ~ ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV885 ) )
| ~ ~ ( ~ ( ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV652 )
| ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV885 ) )
| ~ ( ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV825 )
| ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV885 ) ) ) ) )
= $true )
| ( ( SV885
= ( set_intersection2 @ SV652 @ SV825 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4568]) ).
thf(4731,plain,
! [SV826: $i,SV652: $i,SV886: $i] :
( ( ( ( SV886
!= ( set_intersection2 @ SV652 @ SV826 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1517: $i] :
( ~ ( in @ SY1517 @ SV652 )
| ~ ( in @ SY1517 @ SV826 )
| ( in @ SY1517 @ SV886 ) )
| ~ ~ ( ~ ! [SY1518: $i] :
( ~ ( in @ SY1518 @ SV886 )
| ( in @ SY1518 @ SV652 ) )
| ~ ! [SY1519: $i] :
( ~ ( in @ SY1519 @ SV886 )
| ( in @ SY1519 @ SV826 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4569]) ).
thf(4732,plain,
! [SV762: $i] :
( ( ( ( ( relation_dom @ SV762 )
!= empty_set ) )
= $true )
| ( ( ( relation_rng @ SV762 )
= empty_set )
= $true )
| ( ( relation @ SV762 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4570]) ).
thf(4733,plain,
! [SV763: $i] :
( ( ( ( ( relation_rng @ SV763 )
!= empty_set ) )
= $true )
| ( ( ( relation_dom @ SV763 )
= empty_set )
= $true )
| ( ( relation @ SV763 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4571]) ).
thf(4734,plain,
! [SV653: $i] :
( ( ( one_to_one @ SV653 )
= $false )
| ( ( ~ ( ~ ! [SY1140: $i] :
( ~ ( function @ SY1140 )
| ~ ( relation @ SY1140 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SY1140 @ SV653 )
= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ( ( sK70_C @ SY1140 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY1140 @ SV653 )
= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY1140 @ SV653 )
= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ( ( sK71_SY424 @ SY1140 @ SV653 )
!= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK70_C @ SY1140 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK71_SY424 @ SY1140 @ SV653 )
!= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY1140 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK70_C @ SY1140 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SY1140 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SY1140 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK71_SY424 @ SY1140 @ SV653 )
!= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ( ( relation_dom @ SY1140 )
!= ( relation_rng @ SV653 ) )
| ( SY1140
= ( function_inverse @ SV653 ) ) )
| ~ ~ ( ~ ! [SY1141: $i] :
( ~ ( function @ SY1141 )
| ~ ( relation @ SY1141 )
| ( SY1141
!= ( function_inverse @ SV653 ) )
| ~ ( ~ ~ ( ~ ! [SY1142: $i,SY1143: $i] :
( ( SY1143
!= ( apply @ SY1141 @ SY1142 ) )
| ~ ( in @ SY1142 @ ( relation_rng @ SV653 ) )
| ( SY1142
= ( apply @ SV653 @ SY1143 ) ) )
| ~ ! [SY1144: $i,SY1145: $i] :
( ( SY1145
!= ( apply @ SY1141 @ SY1144 ) )
| ~ ( in @ SY1144 @ ( relation_rng @ SV653 ) )
| ( in @ SY1145 @ ( relation_dom @ SV653 ) ) ) )
| ~ ~ ( ~ ! [SY1146: $i,SY1147: $i] :
( ( SY1146
!= ( apply @ SV653 @ SY1147 ) )
| ~ ( in @ SY1147 @ ( relation_dom @ SV653 ) )
| ( SY1147
= ( apply @ SY1141 @ SY1146 ) ) )
| ~ ! [SY1148: $i] :
( ! [SY1149: $i] :
( ( SY1148
!= ( apply @ SV653 @ SY1149 ) )
| ~ ( in @ SY1149 @ ( relation_dom @ SV653 ) ) )
| ( in @ SY1148 @ ( relation_rng @ SV653 ) ) ) ) ) )
| ~ ! [SY1150: $i] :
( ~ ( function @ SY1150 )
| ~ ( relation @ SY1150 )
| ( SY1150
!= ( function_inverse @ SV653 ) )
| ( ( relation_dom @ SY1150 )
= ( relation_rng @ SV653 ) ) ) ) ) )
= $true )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4572]) ).
thf(4735,plain,
! [SV914: $i] :
( ( ( empty @ SV914 )
| ! [SY1542: $i] :
( ~ ( element @ SY1542 @ SV914 )
| ( in @ SY1542 @ SV914 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4575]) ).
thf(4736,plain,
! [SV915: $i] :
( ( ( empty @ SV915 )
| ! [SY1543: $i] :
( ~ ( in @ SY1543 @ SV915 )
| ( element @ SY1543 @ SV915 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4576]) ).
thf(4737,plain,
! [SV916: $i] :
( ( ~ ( empty @ SV916 )
| ! [SY1544: $i] :
( ~ ( element @ SY1544 @ SV916 )
| ( empty @ SY1544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4577]) ).
thf(4738,plain,
! [SV917: $i] :
( ( ~ ( empty @ SV917 )
| ! [SY1545: $i] :
( ~ ( empty @ SY1545 )
| ( element @ SY1545 @ SV917 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4578]) ).
thf(4739,plain,
! [SV827: $i,SV764: $i] :
( ( ( ( set_intersection2 @ SV764 @ SV827 )
= empty_set )
= $false )
| ( ( disjoint @ SV764 @ SV827 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4579]) ).
thf(4740,plain,
! [SV828: $i,SV765: $i] :
( ( ( disjoint @ SV765 @ SV828 )
= $false )
| ( ( ( set_intersection2 @ SV765 @ SV828 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4580]) ).
thf(4741,plain,
! [SV829: $i,SV766: $i] :
( ( ( subset @ SV766 @ ( singleton @ SV829 ) )
= $false )
| ( ( ( SV766 = empty_set )
| ( SV766
= ( singleton @ SV829 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4581]) ).
thf(4742,plain,
! [SV918: $i] :
( ( ( SV918 != empty_set )
| ! [SY1546: $i] : ( subset @ SV918 @ ( singleton @ SY1546 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4582]) ).
thf(4743,plain,
! [SV919: $i] :
( ( ! [SY1547: $i] :
( ( SV919
!= ( singleton @ SY1547 ) )
| ( subset @ SV919 @ ( singleton @ SY1547 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4583]) ).
thf(4744,plain,
! [SV830: $i,SV769: $i] :
( ( ( in @ SV769 @ SV830 )
= $false )
| ( ( subset @ ( singleton @ SV769 ) @ SV830 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4584]) ).
thf(4745,plain,
! [SV831: $i,SV770: $i] :
( ( ( subset @ ( singleton @ SV770 ) @ SV831 )
= $false )
| ( ( in @ SV770 @ SV831 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4585]) ).
thf(4746,plain,
! [SV832: $i,SV773: $i] :
( ( ( ( set_difference @ SV773 @ SV832 )
= empty_set )
= $false )
| ( ( subset @ SV773 @ SV832 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4588]) ).
thf(4747,plain,
! [SV833: $i,SV774: $i] :
( ( ( subset @ SV774 @ SV833 )
= $false )
| ( ( ( set_difference @ SV774 @ SV833 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4589]) ).
thf(4748,plain,
! [SV739: $i,SV887: $i,SV654: $i,SV920: $i] :
( ( ~ ( relation @ SV920 )
| ~ ( in @ SV654 @ SV887 )
| ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ SV920 )
| ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SV887 ) @ SV920 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4590]) ).
thf(4749,plain,
! [SV739: $i,SV654: $i] :
( ( ~ ! [SY1360: $i,SY1361: $i] :
( ~ ( relation @ SY1361 )
| ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SY1360 ) @ SY1361 ) )
| ( in @ SV654 @ SY1360 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4591]) ).
thf(4750,plain,
! [SV739: $i,SV654: $i] :
( ( ~ ! [SY1362: $i,SY1363: $i] :
( ~ ( relation @ SY1363 )
| ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SY1362 ) @ SY1363 ) )
| ( in @ ( ordered_pair @ SV654 @ SV739 ) @ SY1363 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4591]) ).
thf(4751,plain,
! [SV655: $i,SV740: $i] :
( ( ( ! [SY1364: $i] :
( ~ ( relation @ SY1364 )
| ~ ( ~ ( ~ ( in @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) @ SV655 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY1364 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) ) @ SV740 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY1364 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) ) @ SY1364 ) )
| ~ ~ ( ~ ( ( in @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) @ SV655 )
| ( in @ ( ordered_pair @ ( sK40_D @ SY1364 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) ) @ SY1364 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SY1364 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) ) @ SV740 )
| ( in @ ( ordered_pair @ ( sK40_D @ SY1364 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SY1364 @ SV740 @ SV655 ) ) @ SY1364 ) ) ) )
| ( SY1364
= ( relation_rng_restriction @ SV655 @ SV740 ) ) ) )
= $true )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4592]) ).
thf(4752,plain,
! [SV740: $i,SV655: $i] :
( ( ( ! [SY1365: $i] :
( ~ ( relation @ SY1365 )
| ( SY1365
!= ( relation_rng_restriction @ SV655 @ SV740 ) )
| ~ ( ~ ! [SY1366: $i,SY1367: $i] :
( ~ ( in @ SY1367 @ SV655 )
| ~ ( in @ ( ordered_pair @ SY1366 @ SY1367 ) @ SV740 )
| ( in @ ( ordered_pair @ SY1366 @ SY1367 ) @ SY1365 ) )
| ~ ~ ( ~ ! [SY1163: $i,SY1164: $i] :
( ~ ( in @ ( ordered_pair @ SY1163 @ SY1164 ) @ SY1365 )
| ( in @ SY1164 @ SV655 ) )
| ~ ! [SY1370: $i,SY1371: $i] :
( ~ ( in @ ( ordered_pair @ SY1370 @ SY1371 ) @ SY1365 )
| ( in @ ( ordered_pair @ SY1370 @ SY1371 ) @ SV740 ) ) ) ) ) )
= $true )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4593]) ).
thf(4753,plain,
! [SV888: $i,SV741: $i,SV656: $i] :
( ( ( ! [SY1521: $i] :
( ( ordered_pair @ SV656 @ SV741 )
!= ( ordered_pair @ SV888 @ SY1521 ) ) )
= $true )
| ( ( SV656 = SV888 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4594]) ).
thf(4754,plain,
! [SV921: $i,SV889: $i,SV741: $i,SV656: $i] :
( ( ( ( ordered_pair @ SV656 @ SV741 )
!= ( ordered_pair @ SV889 @ SV921 ) )
| ( SV741 = SV921 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4595]) ).
thf(4755,plain,
! [SV657: $i,SV922: $i] :
( ( ( ! [SY1548: $i] :
( ~ ( ~ ( ! [SY1549: $i] :
( ~ ( in @ ( ordered_pair @ ( sK35_D @ SY1548 @ SV922 @ SV657 ) @ SY1549 ) @ SV657 )
| ~ ( in @ SY1549 @ SV922 ) )
| ~ ( in @ ( sK35_D @ SY1548 @ SV922 @ SV657 ) @ SY1548 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SY1548 @ SV922 @ SV657 ) @ ( sK36_SY409 @ SY1548 @ SV922 @ SV657 ) ) @ SV657 )
| ~ ( in @ ( sK36_SY409 @ SY1548 @ SV922 @ SV657 ) @ SV922 ) )
| ( in @ ( sK35_D @ SY1548 @ SV922 @ SV657 ) @ SY1548 ) ) )
| ( SY1548
= ( relation_inverse_image @ SV657 @ SV922 ) ) ) )
= $true )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4596]) ).
thf(4756,plain,
! [SV923: $i,SV657: $i] :
( ( ( ! [SY1550: $i] :
( ( SY1550
!= ( relation_inverse_image @ SV657 @ SV923 ) )
| ~ ( ~ ! [SY1551: $i] :
( ! [SY1552: $i] :
( ~ ( in @ ( ordered_pair @ SY1551 @ SY1552 ) @ SV657 )
| ~ ( in @ SY1552 @ SV923 ) )
| ( in @ SY1551 @ SY1550 ) )
| ~ ! [SY1553: $i] :
( ~ ( in @ SY1553 @ SY1550 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1553 @ ( sK34_E @ SY1553 @ SY1550 @ SV923 @ SV657 ) ) @ SV657 )
| ~ ( in @ ( sK34_E @ SY1553 @ SY1550 @ SV923 @ SV657 ) @ SV923 ) ) ) ) ) )
= $true )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4597]) ).
thf(4757,plain,
! [SV658: $i,SV924: $i] :
( ( ( ! [SY1554: $i] :
( ~ ( ~ ( ! [SY1555: $i] :
( ~ ( in @ ( ordered_pair @ SY1555 @ ( sK38_D @ SY1554 @ SV924 @ SV658 ) ) @ SV658 )
| ~ ( in @ SY1555 @ SV924 ) )
| ~ ( in @ ( sK38_D @ SY1554 @ SV924 @ SV658 ) @ SY1554 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SY1554 @ SV924 @ SV658 ) @ ( sK38_D @ SY1554 @ SV924 @ SV658 ) ) @ SV658 )
| ~ ( in @ ( sK39_SY411 @ SY1554 @ SV924 @ SV658 ) @ SV924 ) )
| ( in @ ( sK38_D @ SY1554 @ SV924 @ SV658 ) @ SY1554 ) ) )
| ( SY1554
= ( relation_image @ SV658 @ SV924 ) ) ) )
= $true )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4598]) ).
thf(4758,plain,
! [SV925: $i,SV658: $i] :
( ( ( ! [SY1556: $i] :
( ( SY1556
!= ( relation_image @ SV658 @ SV925 ) )
| ~ ( ~ ! [SY1557: $i] :
( ! [SY1558: $i] :
( ~ ( in @ ( ordered_pair @ SY1558 @ SY1557 ) @ SV658 )
| ~ ( in @ SY1558 @ SV925 ) )
| ( in @ SY1557 @ SY1556 ) )
| ~ ! [SY1559: $i] :
( ~ ( in @ SY1559 @ SY1556 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SY1559 @ SY1556 @ SV925 @ SV658 ) @ SY1559 ) @ SV658 )
| ~ ( in @ ( sK37_E @ SY1559 @ SY1556 @ SV925 @ SV658 ) @ SV925 ) ) ) ) ) )
= $true )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4599]) ).
thf(4759,plain,
! [SV834: $i,SV777: $i] :
( ( ( SV777 = SV834 )
= $true )
| ( ( ~ ( subset @ SV777 @ SV834 ) )
= $true )
| ( ( proper_subset @ SV777 @ SV834 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4600]) ).
thf(4760,plain,
! [SV926: $i] :
( ( ! [SY1560: $i] :
( ~ ( proper_subset @ SV926 @ SY1560 )
| ( SV926 != SY1560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4601]) ).
thf(4761,plain,
! [SV927: $i] :
( ( ! [SY1561: $i] :
( ~ ( proper_subset @ SV927 @ SY1561 )
| ( subset @ SV927 @ SY1561 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4602]) ).
thf(4762,plain,
! [SV835: $i,SV778: $i] :
( ( ( ~ ( empty @ SV778 ) )
= $true )
| ( ( ~ ( relation @ SV835 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV835 @ SV778 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4603]) ).
thf(4763,plain,
! [SV836: $i,SV779: $i] :
( ( ( ~ ( empty @ SV779 ) )
= $true )
| ( ( ~ ( relation @ SV836 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV836 @ SV779 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4604]) ).
thf(4764,plain,
! [SV928: $i] :
( ( ~ ( empty @ SV928 )
| ~ ( relation @ SV928 )
| ~ ( function @ SV928 )
| ( function @ SV928 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4605]) ).
thf(4765,plain,
! [SV929: $i] :
( ( ~ ( empty @ SV929 )
| ~ ( relation @ SV929 )
| ~ ( function @ SV929 )
| ( relation @ SV929 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4606]) ).
thf(4766,plain,
! [SV780: $i] :
( ( ( ~ ( empty @ SV780 ) )
= $true )
| ( ( ~ ( relation @ SV780 ) )
= $true )
| ( ( ~ ( function @ SV780 ) )
= $true )
| ( ( one_to_one @ SV780 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4607]) ).
thf(4767,plain,
! [SV781: $i] :
( ( ( ~ ! [SY1402: $i,SY1403: $i] :
( ( sK69_B @ SV781 )
!= ( ordered_pair @ SY1402 @ SY1403 ) ) )
= $false )
| ( ( relation @ SV781 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4608]) ).
thf(4768,plain,
! [SV781: $i] :
( ( ( ~ ( in @ ( sK69_B @ SV781 ) @ SV781 ) )
= $false )
| ( ( relation @ SV781 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4608]) ).
thf(4769,plain,
! [SV782: $i,SV930: $i] :
( ( ( ( SV930
= ( ordered_pair @ ( sK67_C @ SV930 @ SV782 ) @ ( sK68_SY421 @ SV930 @ SV782 ) ) )
| ~ ( in @ SV930 @ SV782 ) )
= $true )
| ( ( relation @ SV782 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4609]) ).
thf(4770,plain,
! [SV837: $i,SV890: $i,SV659: $i] :
( ( ( ~ ( in @ SV659 @ SV890 )
| ~ ( in @ SV837 @ SV890 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV659 @ SV837 ) @ SV890 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4610]) ).
thf(4771,plain,
! [SV659: $i] :
( ( ! [SY1190: $i,SY1191: $i] :
( ~ ( subset @ ( unordered_pair @ SV659 @ SY1190 ) @ SY1191 )
| ( in @ SV659 @ SY1191 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4611]) ).
thf(4772,plain,
! [SV659: $i] :
( ( ! [SY1192: $i,SY1193: $i] :
( ~ ( subset @ ( unordered_pair @ SV659 @ SY1192 ) @ SY1193 )
| ( in @ SY1192 @ SY1193 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4612]) ).
thf(4773,plain,
! [SV660: $i,SV783: $i] :
( ( ( ~ ! [SY1405: $i] :
( ~ ( relation @ SY1405 )
| ~ ( ~ ( ! [SY1406: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY1405 @ SV783 @ SV660 ) @ SY1406 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1406 @ ( sK9_SY391 @ SY1405 @ SV783 @ SV660 ) ) @ SV783 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SY1405 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SY1405 @ SV783 @ SV660 ) ) @ SY1405 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY1405 @ SV783 @ SV660 ) @ ( sK10_SY395 @ SY1405 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SY1405 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SY1405 @ SV783 @ SV660 ) ) @ SV783 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SY1405 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SY1405 @ SV783 @ SV660 ) ) @ SY1405 ) ) )
| ( SY1405
= ( relation_composition @ SV660 @ SV783 ) ) )
| ~ ! [SY1407: $i] :
( ~ ( relation @ SY1407 )
| ( SY1407
!= ( relation_composition @ SV660 @ SV783 ) )
| ~ ( ~ ! [SY1408: $i,SY1409: $i] :
( ! [SY1410: $i] :
( ~ ( in @ ( ordered_pair @ SY1408 @ SY1410 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1410 @ SY1409 ) @ SV783 ) )
| ( in @ ( ordered_pair @ SY1408 @ SY1409 ) @ SY1407 ) )
| ~ ! [SY1411: $i,SY1412: $i] :
( ~ ( in @ ( ordered_pair @ SY1411 @ SY1412 ) @ SY1407 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1411 @ ( sK7_F @ SY1412 @ SY1411 @ SY1407 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY1412 @ SY1411 @ SY1407 @ SV783 @ SV660 ) @ SY1412 ) @ SV783 ) ) ) ) ) )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4613]) ).
thf(4774,plain,
! [SV785: $i,SV931: $i] :
( ( ( ~ ( in @ SV931 @ SV785 ) )
= $true )
| ( ( SV785 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4614]) ).
thf(4775,plain,
! [SV661: $i,SV932: $i] :
( ( ( ~ ( ~ ( ! [SY1562: $i] :
~ ( in @ ( ordered_pair @ SY1562 @ ( sK60_C @ SV932 @ SV661 ) ) @ SV661 )
| ~ ( in @ ( sK60_C @ SV932 @ SV661 ) @ SV932 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK61_SY417 @ SV932 @ SV661 ) @ ( sK60_C @ SV932 @ SV661 ) ) @ SV661 )
| ( in @ ( sK60_C @ SV932 @ SV661 ) @ SV932 ) ) )
| ( SV932
= ( relation_rng @ SV661 ) ) )
= $true )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4619]) ).
thf(4776,plain,
! [SV661: $i,SV933: $i] :
( ( ( ( SV933
!= ( relation_rng @ SV661 ) )
| ~ ( ~ ! [SY1563: $i] :
( ! [SY1207: $i] :
~ ( in @ ( ordered_pair @ SY1207 @ SY1563 ) @ SV661 )
| ( in @ SY1563 @ SV933 ) )
| ~ ! [SY1565: $i] :
( ~ ( in @ SY1565 @ SV933 )
| ( in @ ( ordered_pair @ ( sK59_D @ SY1565 @ SV933 @ SV661 ) @ SY1565 ) @ SV661 ) ) ) )
= $true )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4620]) ).
thf(4777,plain,
! [SV662: $i,SV838: $i,SV891: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV662 )
| ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV838 )
| ~ ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV891 ) )
| ~ ~ ( ~ ( ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV662 )
| ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV891 ) )
| ~ ( ~ ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV838 )
| ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV891 ) ) ) ) )
= $true )
| ( ( SV891
= ( set_difference @ SV662 @ SV838 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4621]) ).
thf(4778,plain,
! [SV839: $i,SV662: $i,SV892: $i] :
( ( ( ( SV892
!= ( set_difference @ SV662 @ SV839 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1523: $i] :
( ~ ( in @ SY1523 @ SV662 )
| ( in @ SY1523 @ SV839 )
| ( in @ SY1523 @ SV892 ) )
| ~ ~ ( ~ ! [SY1524: $i] :
( ~ ( in @ SY1524 @ SV892 )
| ( in @ SY1524 @ SV662 ) )
| ~ ! [SY1525: $i] :
( ~ ( in @ SY1525 @ SV892 )
| ~ ( in @ SY1525 @ SV839 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4622]) ).
thf(4779,plain,
! [SV840: $i,SV790: $i] :
( ( ( ~ ( function @ SV790 )
| ~ ( relation @ SV790 )
| ~ ( relation @ SV840 ) )
= $true )
| ( ( ~ ( function @ SV840 ) )
= $true )
| ( ( function @ ( relation_composition @ SV790 @ SV840 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4623]) ).
thf(4780,plain,
! [SV841: $i,SV791: $i] :
( ( ( ~ ( function @ SV791 )
| ~ ( relation @ SV791 )
| ~ ( relation @ SV841 ) )
= $true )
| ( ( ~ ( function @ SV841 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV791 @ SV841 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4624]) ).
thf(4781,plain,
! [SV842: $i,SV663: $i,SV893: $i] :
( ( ( ~ ( relation @ SV893 ) )
= $true )
| ( ( ~ ( in @ SV663 @ SV842 )
| ~ ( in @ SV663 @ ( relation_rng @ SV893 ) )
| ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SV842 @ SV893 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4625]) ).
thf(4782,plain,
! [SV663: $i] :
( ( ! [SY1218: $i,SY1219: $i] :
( ~ ( relation @ SY1219 )
| ~ ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SY1218 @ SY1219 ) ) )
| ( in @ SV663 @ SY1218 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4626]) ).
thf(4783,plain,
! [SV663: $i] :
( ( ! [SY1220: $i,SY1221: $i] :
( ~ ( relation @ SY1221 )
| ~ ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SY1220 @ SY1221 ) ) )
| ( in @ SV663 @ ( relation_rng @ SY1221 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4627]) ).
thf(4784,plain,
! [SV664: $i] :
( ( ( ~ ~ ( ~ ! [SY1222: $i] :
( ~ ( in @ SY1222 @ ( relation_dom @ SV664 ) )
| ! [SY1223: $i] :
( ( SY1223
!= ( apply @ SV664 @ SY1222 ) )
| ( in @ ( ordered_pair @ SY1222 @ SY1223 ) @ SV664 ) ) )
| ~ ! [SY1224: $i] :
( ~ ( in @ SY1224 @ ( relation_dom @ SV664 ) )
| ! [SY1225: $i] :
( ~ ( in @ ( ordered_pair @ SY1224 @ SY1225 ) @ SV664 )
| ( SY1225
= ( apply @ SV664 @ SY1224 ) ) ) ) ) )
= $false )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4628]) ).
thf(4785,plain,
! [SV664: $i] :
( ( ( ~ ~ ( ~ ! [SY1226: $i] :
( ( in @ SY1226 @ ( relation_dom @ SV664 ) )
| ! [SY1227: $i] :
( ( SY1227
!= ( apply @ SV664 @ SY1226 ) )
| ( SY1227 = empty_set ) ) )
| ~ ! [SY1228: $i] :
( ( in @ SY1228 @ ( relation_dom @ SV664 ) )
| ! [SY1229: $i] :
( ( SY1229 != empty_set )
| ( SY1229
= ( apply @ SV664 @ SY1228 ) ) ) ) ) )
= $false )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4628]) ).
thf(4786,plain,
! [SV665: $i,SV934: $i] :
( ( ( ~ ( relation @ SV934 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV934 @ SV665 ) @ ( sK20_SY399 @ SV934 @ SV665 ) ) @ SV665 )
| ~ ~ ( in @ ( ordered_pair @ ( sK19_C @ SV934 @ SV665 ) @ ( sK20_SY399 @ SV934 @ SV665 ) ) @ SV934 ) )
| ( subset @ SV665 @ SV934 ) )
= $true )
| ( ( relation @ SV665 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4629]) ).
thf(4787,plain,
! [SV665: $i,SV935: $i] :
( ( ( ~ ( relation @ SV935 )
| ~ ( subset @ SV665 @ SV935 )
| ! [SY1566: $i,SY1567: $i] :
( ~ ( in @ ( ordered_pair @ SY1566 @ SY1567 ) @ SV665 )
| ( in @ ( ordered_pair @ SY1566 @ SY1567 ) @ SV935 ) ) )
= $true )
| ( ( relation @ SV665 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4630]) ).
thf(4788,plain,
! [SV742: $i,SV666: $i] :
( ( ( ~ ! [SY1376: $i] :
( ~ ( function @ SY1376 )
| ~ ( relation @ SY1376 )
| ~ ( in @ SV666 @ ( relation_dom @ SY1376 ) )
| ~ ( in @ ( apply @ SY1376 @ SV666 ) @ ( relation_dom @ SV742 ) )
| ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1376 @ SV742 ) ) ) )
| ~ ~ ( ~ ! [SY1377: $i] :
( ~ ( function @ SY1377 )
| ~ ( relation @ SY1377 )
| ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1377 @ SV742 ) ) )
| ( in @ SV666 @ ( relation_dom @ SY1377 ) ) )
| ~ ! [SY1378: $i] :
( ~ ( function @ SY1378 )
| ~ ( relation @ SY1378 )
| ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1378 @ SV742 ) ) )
| ( in @ ( apply @ SY1378 @ SV666 ) @ ( relation_dom @ SV742 ) ) ) ) )
= $false )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4631]) ).
thf(4789,plain,
! [SV843: $i,SV667: $i,SV894: $i] :
( ( ( ~ ( relation @ SV894 ) )
= $true )
| ( ( ! [SY1526: $i] :
( ~ ( in @ SY1526 @ ( relation_rng @ SV894 ) )
| ~ ( in @ ( ordered_pair @ SV667 @ SY1526 ) @ SV894 )
| ~ ( in @ SY1526 @ SV843 ) )
| ( in @ SV667 @ ( relation_inverse_image @ SV894 @ SV843 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4632]) ).
thf(4790,plain,
! [SV844: $i,SV667: $i,SV895: $i] :
( ( ( ~ ( relation @ SV895 ) )
= $true )
| ( ( ~ ( in @ SV667 @ ( relation_inverse_image @ SV895 @ SV844 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK51_D @ SV895 @ SV844 @ SV667 ) @ ( relation_rng @ SV895 ) )
| ~ ( in @ ( ordered_pair @ SV667 @ ( sK51_D @ SV895 @ SV844 @ SV667 ) ) @ SV895 ) )
| ~ ( in @ ( sK51_D @ SV895 @ SV844 @ SV667 ) @ SV844 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4633]) ).
thf(4791,plain,
! [SV792: $i,SV845: $i] :
( ( ( ~ ( in @ ( sK49_C @ SV845 @ SV792 ) @ SV792 )
| ~ ( in @ ( sK49_C @ SV845 @ SV792 ) @ SV845 ) )
= $false )
| ( ( disjoint @ SV792 @ SV845 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4634]) ).
thf(4792,plain,
! [SV846: $i,SV793: $i,SV936: $i] :
( ( ( ~ ( in @ SV936 @ SV793 )
| ~ ( in @ SV936 @ SV846 ) )
= $true )
| ( ( ~ ( disjoint @ SV793 @ SV846 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4635]) ).
thf(4793,plain,
! [SV847: $i,SV668: $i,SV896: $i] :
( ( ( ~ ( relation @ SV896 ) )
= $true )
| ( ( ~ ( in @ SV668 @ SV847 )
| ~ ( in @ SV668 @ ( relation_dom @ SV896 ) )
| ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SV896 @ SV847 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4638]) ).
thf(4794,plain,
! [SV668: $i] :
( ( ! [SY1245: $i,SY1246: $i] :
( ~ ( relation @ SY1246 )
| ~ ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SY1246 @ SY1245 ) ) )
| ( in @ SV668 @ SY1245 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4639]) ).
thf(4795,plain,
! [SV668: $i] :
( ( ! [SY1247: $i,SY1248: $i] :
( ~ ( relation @ SY1248 )
| ~ ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SY1248 @ SY1247 ) ) )
| ( in @ SV668 @ ( relation_dom @ SY1248 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4640]) ).
thf(4796,plain,
! [SV669: $i,SV848: $i,SV897: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV897 )
| ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV669 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV897 )
| ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV848 ) ) )
| ~ ( ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV897 )
| ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV669 )
| ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV848 ) ) ) )
= $true )
| ( ( SV897
= ( set_union2 @ SV669 @ SV848 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4641]) ).
thf(4797,plain,
! [SV849: $i,SV669: $i,SV898: $i] :
( ( ( ( SV898
!= ( set_union2 @ SV669 @ SV849 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1527: $i] :
( ~ ( in @ SY1527 @ SV898 )
| ( in @ SY1527 @ SV669 )
| ( in @ SY1527 @ SV849 ) )
| ~ ~ ( ~ ! [SY1528: $i] :
( ~ ( in @ SY1528 @ SV669 )
| ( in @ SY1528 @ SV898 ) )
| ~ ! [SY1529: $i] :
( ~ ( in @ SY1529 @ SV849 )
| ( in @ SY1529 @ SV898 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4642]) ).
thf(4798,plain,
! [SV937: $i] :
( ( ( SV937 = empty_set )
| ! [SY1568: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY406 @ SY1568 @ SV937 ) @ SV937 )
| ~ ~ ( in @ ( sK32_C @ SY1568 @ SV937 ) @ ( sK33_SY406 @ SY1568 @ SV937 ) ) )
| ~ ( in @ ( sK32_C @ SY1568 @ SV937 ) @ SY1568 ) )
| ~ ( ! [SY1569: $i] :
( ~ ( in @ SY1569 @ SV937 )
| ( in @ ( sK32_C @ SY1568 @ SV937 ) @ SY1569 ) )
| ( in @ ( sK32_C @ SY1568 @ SV937 ) @ SY1568 ) ) )
| ( SY1568
= ( set_meet @ SV937 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4643]) ).
thf(4799,plain,
! [SV938: $i] :
( ( ( SV938 = empty_set )
| ! [SY1570: $i] :
( ( SY1570
!= ( set_meet @ SV938 ) )
| ~ ( ~ ! [SY1571: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY1571 @ SY1570 @ SV938 ) @ SV938 )
| ~ ~ ( in @ SY1571 @ ( sK31_D @ SY1571 @ SY1570 @ SV938 ) ) )
| ( in @ SY1571 @ SY1570 ) )
| ~ ! [SY1572: $i] :
( ~ ( in @ SY1572 @ SY1570 )
| ! [SY1573: $i] :
( ~ ( in @ SY1573 @ SV938 )
| ( in @ SY1572 @ SY1573 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4644]) ).
thf(4800,plain,
! [SV939: $i] :
( ( ( SV939 != empty_set )
| ! [SY1574: $i] :
( ( SY1574
!= ( set_meet @ SV939 ) )
| ( SY1574 = empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4645]) ).
thf(4801,plain,
! [SV940: $i] :
( ( ( SV940 != empty_set )
| ! [SY1575: $i] :
( ( SY1575 != empty_set )
| ( SY1575
= ( set_meet @ SV940 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4646]) ).
thf(4802,plain,
! [SV899: $i,SV850: $i,SV670: $i] :
( ( ( ~ ( ~ ( ! [SY1530: $i,SY1531: $i] :
( ~ ( in @ SY1530 @ SV670 )
| ~ ( in @ SY1531 @ SV850 )
| ( ( sK23_D @ SV899 @ SV850 @ SV670 )
!= ( ordered_pair @ SY1530 @ SY1531 ) ) )
| ~ ( in @ ( sK23_D @ SV899 @ SV850 @ SV670 ) @ SV899 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY403 @ SV899 @ SV850 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK25_SY405 @ SV899 @ SV850 @ SV670 ) @ SV850 ) )
| ( ( sK23_D @ SV899 @ SV850 @ SV670 )
!= ( ordered_pair @ ( sK24_SY403 @ SV899 @ SV850 @ SV670 ) @ ( sK25_SY405 @ SV899 @ SV850 @ SV670 ) ) ) )
| ( in @ ( sK23_D @ SV899 @ SV850 @ SV670 ) @ SV899 ) ) ) )
= $true )
| ( ( SV899
= ( cartesian_product2 @ SV670 @ SV850 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4647]) ).
thf(4803,plain,
! [SV851: $i,SV670: $i,SV900: $i] :
( ( ( ( SV900
!= ( cartesian_product2 @ SV670 @ SV851 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1532: $i] :
( ! [SY1483: $i,SY1484: $i] :
( ~ ( in @ SY1483 @ SV670 )
| ~ ( in @ SY1484 @ SV851 )
| ( SY1532
!= ( ordered_pair @ SY1483 @ SY1484 ) ) )
| ( in @ SY1532 @ SV900 ) )
| ~ ! [SY1535: $i] :
( ~ ( in @ SY1535 @ SV900 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY1535 @ SV900 @ SV851 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK22_SY400 @ SY1535 @ SV900 @ SV851 @ SV670 ) @ SV851 ) )
| ( SY1535
!= ( ordered_pair @ ( sK21_E @ SY1535 @ SV900 @ SV851 @ SV670 ) @ ( sK22_SY400 @ SY1535 @ SV900 @ SV851 @ SV670 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4648]) ).
thf(4804,plain,
! [SV671: $i,SV852: $i,SV901: $i] :
( ( ( ~ ( function @ SV901 )
| ~ ( relation @ SV901 ) )
= $true )
| ( ( ( SV852
!= ( apply @ SV901 @ SV671 ) )
| ~ ( in @ SV671 @ ( relation_dom @ SV901 ) )
| ( in @ ( ordered_pair @ SV671 @ SV852 ) @ SV901 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4649]) ).
thf(4805,plain,
! [SV671: $i] :
( ( ! [SY1268: $i,SY1269: $i] :
( ~ ( function @ SY1269 )
| ~ ( relation @ SY1269 )
| ~ ( in @ ( ordered_pair @ SV671 @ SY1268 ) @ SY1269 )
| ( SY1268
= ( apply @ SY1269 @ SV671 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4650]) ).
thf(4806,plain,
! [SV671: $i] :
( ( ! [SY1270: $i,SY1271: $i] :
( ~ ( function @ SY1271 )
| ~ ( relation @ SY1271 )
| ~ ( in @ ( ordered_pair @ SV671 @ SY1270 ) @ SY1271 )
| ( in @ SV671 @ ( relation_dom @ SY1271 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4651]) ).
thf(4807,plain,
! [SV672: $i,SV941: $i] :
( ( ( ~ ( relation @ SV941 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SV941 @ SV672 ) @ ( sK12_SY396 @ SV941 @ SV672 ) ) @ SV941 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SV941 @ SV672 ) @ ( sK11_C @ SV941 @ SV672 ) ) @ SV672 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_C @ SV941 @ SV672 ) @ ( sK12_SY396 @ SV941 @ SV672 ) ) @ SV941 )
| ( in @ ( ordered_pair @ ( sK12_SY396 @ SV941 @ SV672 ) @ ( sK11_C @ SV941 @ SV672 ) ) @ SV672 ) ) )
| ( SV941
= ( relation_inverse @ SV672 ) ) )
= $true )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4652]) ).
thf(4808,plain,
! [SV672: $i,SV942: $i] :
( ( ( ~ ( relation @ SV942 )
| ( SV942
!= ( relation_inverse @ SV672 ) )
| ~ ( ~ ! [SY1576: $i,SY1577: $i] :
( ~ ( in @ ( ordered_pair @ SY1576 @ SY1577 ) @ SV942 )
| ( in @ ( ordered_pair @ SY1577 @ SY1576 ) @ SV672 ) )
| ~ ! [SY1578: $i,SY1579: $i] :
( ~ ( in @ ( ordered_pair @ SY1579 @ SY1578 ) @ SV672 )
| ( in @ ( ordered_pair @ SY1578 @ SY1579 ) @ SV942 ) ) ) )
= $true )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4653]) ).
thf(4809,plain,
! [SV853: $i,SV796: $i] :
( ( ( ( set_difference @ SV796 @ SV853 )
= empty_set )
= $false )
| ( ( subset @ SV796 @ SV853 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4654]) ).
thf(4810,plain,
! [SV854: $i,SV797: $i] :
( ( ( subset @ SV797 @ SV854 )
= $false )
| ( ( ( set_difference @ SV797 @ SV854 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4655]) ).
thf(4811,plain,
! [SV798: $i] :
( ( ( ~ ( function @ SV798 ) )
= $true )
| ( ( ~ ( relation @ SV798 ) )
= $true )
| ( ( ~ ( one_to_one @ SV798 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV798 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4656]) ).
thf(4812,plain,
! [SV799: $i] :
( ( ( ~ ( function @ SV799 ) )
= $true )
| ( ( ~ ( relation @ SV799 ) )
= $true )
| ( ( ~ ( one_to_one @ SV799 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV799 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4657]) ).
thf(4813,plain,
! [SV855: $i,SV673: $i,SV902: $i] :
( ( ( ~ ( relation @ SV902 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV673 @ SV855 ) @ SV902 )
| ( in @ SV673 @ ( relation_dom @ SV902 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4658]) ).
thf(4814,plain,
! [SV856: $i,SV673: $i,SV903: $i] :
( ( ( ~ ( relation @ SV903 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV673 @ SV856 ) @ SV903 )
| ( in @ SV856 @ ( relation_rng @ SV903 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4659]) ).
thf(4815,plain,
! [SV943: $i,SV743: $i,SV904: $i,SV674: $i] :
( ( ~ ( in @ SV674 @ SV904 )
| ~ ( in @ SV743 @ SV943 )
| ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SV904 @ SV943 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4660]) ).
thf(4816,plain,
! [SV743: $i,SV674: $i] :
( ( ~ ! [SY1381: $i] :
( ! [SY1382: $i] :
~ ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SY1381 @ SY1382 ) )
| ( in @ SV674 @ SY1381 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4661]) ).
thf(4817,plain,
! [SV743: $i,SV674: $i] :
( ( ~ ! [SY1383: $i,SY1384: $i] :
( ~ ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SY1383 @ SY1384 ) )
| ( in @ SV743 @ SY1384 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4661]) ).
thf(4818,plain,
! [SV675: $i,SV857: $i,SV905: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SV905 @ SV857 @ SV675 ) @ SV905 )
| ( ( sK27_D @ SV905 @ SV857 @ SV675 )
!= SV675 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV905 @ SV857 @ SV675 ) @ SV905 )
| ( ( sK27_D @ SV905 @ SV857 @ SV675 )
!= SV857 ) ) )
| ~ ( ( in @ ( sK27_D @ SV905 @ SV857 @ SV675 ) @ SV905 )
| ( ( sK27_D @ SV905 @ SV857 @ SV675 )
= SV675 )
| ( ( sK27_D @ SV905 @ SV857 @ SV675 )
= SV857 ) ) ) )
= $true )
| ( ( SV905
= ( unordered_pair @ SV675 @ SV857 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4662]) ).
thf(4819,plain,
! [SV858: $i,SV675: $i,SV906: $i] :
( ( ( ( SV906
!= ( unordered_pair @ SV675 @ SV858 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1537: $i] :
( ~ ( in @ SY1537 @ SV906 )
| ( SY1537 = SV675 )
| ( SY1537 = SV858 ) )
| ~ ~ ( ~ ! [SY1538: $i] :
( ( SY1538 != SV675 )
| ( in @ SY1538 @ SV906 ) )
| ~ ! [SY1539: $i] :
( ( SY1539 != SV858 )
| ( in @ SY1539 @ SV906 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4663]) ).
thf(4820,plain,
! [SV944: $i,SV744: $i,SV907: $i,SV676: $i] :
( ( ~ ( in @ SV676 @ SV907 )
| ~ ( in @ SV744 @ SV944 )
| ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SV907 @ SV944 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4664]) ).
thf(4821,plain,
! [SV744: $i,SV676: $i] :
( ( ~ ! [SY1387: $i] :
( ! [SY1388: $i] :
~ ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SY1387 @ SY1388 ) )
| ( in @ SV676 @ SY1387 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4665]) ).
thf(4822,plain,
! [SV744: $i,SV676: $i] :
( ( ~ ! [SY1389: $i,SY1390: $i] :
( ~ ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SY1389 @ SY1390 ) )
| ( in @ SV744 @ SY1390 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4665]) ).
thf(4823,plain,
! [SV860: $i,SV801: $i,SV945: $i] :
( ( ( ~ ( in @ SV945 @ ( set_intersection2 @ SV801 @ SV860 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV801 @ SV860 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4667]) ).
thf(4824,plain,
! [SV802: $i] :
( ( ( function @ SV802 )
= $false )
| ( ( ~ ( relation @ SV802 ) )
= $true )
| ( ( function @ ( function_inverse @ SV802 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4668]) ).
thf(4825,plain,
! [SV803: $i] :
( ( ( function @ SV803 )
= $false )
| ( ( ~ ( relation @ SV803 ) )
= $true )
| ( ( relation @ ( function_inverse @ SV803 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4669]) ).
thf(4826,plain,
! [SV677: $i,SV745: $i] :
( ( ( ~ ( in @ ( sK4_C @ SV745 @ SV677 ) @ SV677 ) )
= $true )
| ( ( ~ ( in @ ( sK4_C @ SV745 @ SV677 ) @ SV745 ) )
= $true )
| ( ( SV677 = SV745 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4670]) ).
thf(4827,plain,
! [SV677: $i,SV745: $i] :
( ( ( in @ ( sK4_C @ SV745 @ SV677 ) @ SV677 )
= $true )
| ( ( in @ ( sK4_C @ SV745 @ SV677 ) @ SV745 )
= $true )
| ( ( SV677 = SV745 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4671]) ).
thf(4828,plain,
! [SV861: $i,SV678: $i] :
( ( ( subset @ SV678 @ SV861 )
= $false )
| ( ( ! [SY1495: $i] : ( subset @ ( cartesian_product2 @ SV678 @ SY1495 ) @ ( cartesian_product2 @ SV861 @ SY1495 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4672]) ).
thf(4829,plain,
! [SV862: $i,SV678: $i] :
( ( ( subset @ SV678 @ SV862 )
= $false )
| ( ( ! [SY1496: $i] : ( subset @ ( cartesian_product2 @ SY1496 @ SV678 ) @ ( cartesian_product2 @ SY1496 @ SV862 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4673]) ).
thf(4830,plain,
! [SV804: $i,SV863: $i] :
( ( ( ~ ( ! [SY1497: $i] :
( ~ ( in @ ( sK15_C @ SV863 @ SV804 ) @ SY1497 )
| ~ ( in @ SY1497 @ SV804 ) )
| ~ ( in @ ( sK15_C @ SV863 @ SV804 ) @ SV863 ) )
| ~ ( ~ ( ~ ( in @ ( sK15_C @ SV863 @ SV804 ) @ ( sK16_SY398 @ SV863 @ SV804 ) )
| ~ ( in @ ( sK16_SY398 @ SV863 @ SV804 ) @ SV804 ) )
| ( in @ ( sK15_C @ SV863 @ SV804 ) @ SV863 ) ) )
= $false )
| ( ( SV863
= ( union @ SV804 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4674]) ).
thf(4831,plain,
! [SV805: $i,SV864: $i] :
( ( ( SV864
= ( union @ SV805 ) )
= $false )
| ( ( ~ ( ~ ! [SY1498: $i] :
( ! [SY1428: $i] :
( ~ ( in @ SY1498 @ SY1428 )
| ~ ( in @ SY1428 @ SV805 ) )
| ( in @ SY1498 @ SV864 ) )
| ~ ! [SY1500: $i] :
( ~ ( in @ SY1500 @ SV864 )
| ~ ( ~ ( in @ SY1500 @ ( sK14_D @ SY1500 @ SV864 @ SV805 ) )
| ~ ( in @ ( sK14_D @ SY1500 @ SV864 @ SV805 ) @ SV805 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4675]) ).
thf(4832,plain,
! [SV679: $i,SV946: $i] :
( ( ( ~ ( ~ ( ! [SY1580: $i] :
~ ( in @ ( ordered_pair @ ( sK63_C @ SV946 @ SV679 ) @ SY1580 ) @ SV679 )
| ~ ( in @ ( sK63_C @ SV946 @ SV679 ) @ SV946 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_C @ SV946 @ SV679 ) @ ( sK64_SY419 @ SV946 @ SV679 ) ) @ SV679 )
| ( in @ ( sK63_C @ SV946 @ SV679 ) @ SV946 ) ) )
| ( SV946
= ( relation_dom @ SV679 ) ) )
= $true )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4676]) ).
thf(4833,plain,
! [SV679: $i,SV947: $i] :
( ( ( ( SV947
!= ( relation_dom @ SV679 ) )
| ~ ( ~ ! [SY1581: $i] :
( ! [SY1312: $i] :
~ ( in @ ( ordered_pair @ SY1581 @ SY1312 ) @ SV679 )
| ( in @ SY1581 @ SV947 ) )
| ~ ! [SY1583: $i] :
( ~ ( in @ SY1583 @ SV947 )
| ( in @ ( ordered_pair @ SY1583 @ ( sK62_D @ SY1583 @ SV947 @ SV679 ) ) @ SV679 ) ) ) )
= $true )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4677]) ).
thf(4834,plain,
! [SV865: $i,SV680: $i,SV908: $i] :
( ( ( ~ ( relation @ SV908 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV680 @ SV865 ) @ SV908 )
| ( in @ SV680 @ ( relation_field @ SV908 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4678]) ).
thf(4835,plain,
! [SV866: $i,SV680: $i,SV909: $i] :
( ( ( ~ ( relation @ SV909 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV680 @ SV866 ) @ SV909 )
| ( in @ SV866 @ ( relation_field @ SV909 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4679]) ).
thf(4836,plain,
! [SV806: $i,SV867: $i] :
( ( ( relation @ SV867 )
= $false )
| ( ( ~ ( ~ ( ( ( sK44_C @ SV867 @ SV806 )
!= ( sK45_SY414 @ SV867 @ SV806 ) )
| ~ ( in @ ( sK44_C @ SV867 @ SV806 ) @ SV806 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 ) )
| ~ ~ ( ~ ( ( ( sK44_C @ SV867 @ SV806 )
= ( sK45_SY414 @ SV867 @ SV806 ) )
| ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 ) )
| ~ ( ( in @ ( sK44_C @ SV867 @ SV806 ) @ SV806 )
| ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 ) ) ) )
| ( SV867
= ( identity_relation @ SV806 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4680]) ).
thf(4837,plain,
! [SV807: $i,SV868: $i] :
( ( ( relation @ SV868 )
= $false )
| ( ( ( SV868
!= ( identity_relation @ SV807 ) )
| ~ ( ~ ! [SY1503: $i,SY1504: $i] :
( ( SY1503 != SY1504 )
| ~ ( in @ SY1503 @ SV807 )
| ( in @ ( ordered_pair @ SY1503 @ SY1504 ) @ SV868 ) )
| ~ ~ ( ~ ! [SY1505: $i,SY1506: $i] :
( ~ ( in @ ( ordered_pair @ SY1505 @ SY1506 ) @ SV868 )
| ( SY1505 = SY1506 ) )
| ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
~ ( in @ ( ordered_pair @ SY1507 @ SY1508 ) @ SV868 )
| ( in @ SY1507 @ SV807 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4681]) ).
thf(4838,plain,
! [SV681: $i,SV948: $i] :
( ( ( ! [SY1584: $i] :
( ~ ( relation @ SY1584 )
| ~ ( ~ ( ~ ( in @ ( sK42_D @ SY1584 @ SV948 @ SV681 ) @ SV948 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SY1584 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SY1584 @ SV948 @ SV681 ) ) @ SV681 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SY1584 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SY1584 @ SV948 @ SV681 ) ) @ SY1584 ) )
| ~ ~ ( ~ ( ( in @ ( sK42_D @ SY1584 @ SV948 @ SV681 ) @ SV948 )
| ( in @ ( ordered_pair @ ( sK42_D @ SY1584 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SY1584 @ SV948 @ SV681 ) ) @ SY1584 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SY1584 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SY1584 @ SV948 @ SV681 ) ) @ SV681 )
| ( in @ ( ordered_pair @ ( sK42_D @ SY1584 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SY1584 @ SV948 @ SV681 ) ) @ SY1584 ) ) ) )
| ( SY1584
= ( relation_dom_restriction @ SV681 @ SV948 ) ) ) )
= $true )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4682]) ).
thf(4839,plain,
! [SV949: $i,SV681: $i] :
( ( ( ! [SY1585: $i] :
( ~ ( relation @ SY1585 )
| ( SY1585
!= ( relation_dom_restriction @ SV681 @ SV949 ) )
| ~ ( ~ ! [SY1586: $i,SY1587: $i] :
( ~ ( in @ SY1586 @ SV949 )
| ~ ( in @ ( ordered_pair @ SY1586 @ SY1587 ) @ SV681 )
| ( in @ ( ordered_pair @ SY1586 @ SY1587 ) @ SY1585 ) )
| ~ ~ ( ~ ! [SY1588: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SY1588 @ SX4 ) @ SY1585 )
| ( in @ SY1588 @ SV949 ) )
| ~ ! [SY1326: $i,SY1327: $i] :
( ~ ( in @ ( ordered_pair @ SY1326 @ SY1327 ) @ SY1585 )
| ( in @ ( ordered_pair @ SY1326 @ SY1327 ) @ SV681 ) ) ) ) ) )
= $true )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4683]) ).
thf(4840,plain,
! [SV808: $i,SV869: $i] :
( ( ( ~ ( ( ( sK30_C @ SV869 @ SV808 )
!= SV808 )
| ~ ( in @ ( sK30_C @ SV869 @ SV808 ) @ SV869 ) )
| ~ ( ( ( sK30_C @ SV869 @ SV808 )
= SV808 )
| ( in @ ( sK30_C @ SV869 @ SV808 ) @ SV869 ) ) )
= $false )
| ( ( SV869
= ( singleton @ SV808 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4684]) ).
thf(4841,plain,
! [SV809: $i,SV870: $i] :
( ( ( SV870
= ( singleton @ SV809 ) )
= $false )
| ( ( ~ ( ~ ! [SY1509: $i] :
( ( SY1509 != SV809 )
| ( in @ SY1509 @ SV870 ) )
| ~ ! [SY1510: $i] :
( ~ ( in @ SY1510 @ SV870 )
| ( SY1510 = SV809 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4685]) ).
thf(4842,plain,
! [SV871: $i,SV682: $i,SV910: $i] :
( ( ( ~ ( relation @ SV910 ) )
= $true )
| ( ( ! [SY1541: $i] :
( ~ ( in @ SY1541 @ ( relation_dom @ SV910 ) )
| ~ ( in @ ( ordered_pair @ SY1541 @ SV682 ) @ SV910 )
| ~ ( in @ SY1541 @ SV871 ) )
| ( in @ SV682 @ ( relation_image @ SV910 @ SV871 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4686]) ).
thf(4843,plain,
! [SV872: $i,SV682: $i,SV911: $i] :
( ( ( ~ ( relation @ SV911 ) )
= $true )
| ( ( ~ ( in @ SV682 @ ( relation_image @ SV911 @ SV872 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK52_D @ SV911 @ SV872 @ SV682 ) @ ( relation_dom @ SV911 ) )
| ~ ( in @ ( ordered_pair @ ( sK52_D @ SV911 @ SV872 @ SV682 ) @ SV682 ) @ SV911 ) )
| ~ ( in @ ( sK52_D @ SV911 @ SV872 @ SV682 ) @ SV872 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4687]) ).
thf(4844,plain,
! [SV683: $i,SV950: $i] :
( ( ( ~ ( relation @ SV950 )
| ~ ( subset @ SV683 @ SV950 )
| ( subset @ ( relation_dom @ SV683 ) @ ( relation_dom @ SV950 ) ) )
= $true )
| ( ( relation @ SV683 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4690]) ).
thf(4845,plain,
! [SV683: $i,SV951: $i] :
( ( ( ~ ( relation @ SV951 )
| ~ ( subset @ SV683 @ SV951 )
| ( subset @ ( relation_rng @ SV683 ) @ ( relation_rng @ SV951 ) ) )
= $true )
| ( ( relation @ SV683 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4691]) ).
thf(4846,plain,
! [SV873: $i,SV810: $i] :
( ( ( ~ ( empty @ SV810 ) )
= $true )
| ( ( ~ ( relation @ SV873 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV810 @ SV873 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4692]) ).
thf(4847,plain,
! [SV874: $i,SV811: $i] :
( ( ( ~ ( empty @ SV811 ) )
= $true )
| ( ( ~ ( relation @ SV874 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV811 @ SV874 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4693]) ).
thf(4848,plain,
! [SV684: $i,SV952: $i] :
( ( ( ~ ( relation @ SV952 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV684 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV952 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV684 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV952 ) ) )
| ( SV684 = SV952 ) )
= $true )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4694]) ).
thf(4849,plain,
! [SV684: $i,SV953: $i] :
( ( ( ~ ( relation @ SV953 )
| ( SV684 != SV953 )
| ~ ( ~ ! [SY1592: $i,SY1593: $i] :
( ~ ( in @ ( ordered_pair @ SY1592 @ SY1593 ) @ SV684 )
| ( in @ ( ordered_pair @ SY1592 @ SY1593 ) @ SV953 ) )
| ~ ! [SY1594: $i,SY1595: $i] :
( ~ ( in @ ( ordered_pair @ SY1594 @ SY1595 ) @ SV953 )
| ( in @ ( ordered_pair @ SY1594 @ SY1595 ) @ SV684 ) ) ) )
= $true )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4695]) ).
thf(4850,plain,
! [SV685: $i,SV875: $i] :
( ( ( ~ ( subset @ SV875 @ ( sK2_B @ SV685 ) ) )
= $true )
| ( ( are_equipotent @ SV875 @ ( sK2_B @ SV685 ) )
= $true )
| ( ( in @ SV875 @ ( sK2_B @ SV685 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4696]) ).
thf(4851,plain,
! [SV685: $i] :
( ( ! [SY1342: $i] :
( ~ ( ~ ! [SY1343: $i] :
( ~ ( subset @ SY1343 @ SY1342 )
| ( in @ SY1343 @ ( sK3_SY386 @ SY1342 @ SV685 ) ) )
| ~ ( in @ ( sK3_SY386 @ SY1342 @ SV685 ) @ ( sK2_B @ SV685 ) ) )
| ~ ( in @ SY1342 @ ( sK2_B @ SV685 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4697]) ).
thf(4852,plain,
! [SV685: $i] :
( ( ~ ( ~ ! [SY1344: $i,SY1345: $i] :
( ~ ( in @ SY1344 @ ( sK2_B @ SV685 ) )
| ~ ( subset @ SY1345 @ SY1344 )
| ( in @ SY1345 @ ( sK2_B @ SV685 ) ) )
| ~ ( in @ SV685 @ ( sK2_B @ SV685 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4698]) ).
thf(4853,plain,
! [SV876: $i,SV812: $i] :
( ( ( ~ ( subset @ SV812 @ SV876 ) )
= $true )
| ( ( ~ ( subset @ SV876 @ SV812 ) )
= $true )
| ( ( SV812 = SV876 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4699]) ).
thf(4854,plain,
! [SV954: $i] :
( ( ! [SY1596: $i] :
( ( SV954 != SY1596 )
| ( subset @ SV954 @ SY1596 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4700]) ).
thf(4855,plain,
! [SV955: $i] :
( ( ! [SY1597: $i] :
( ( SV955 != SY1597 )
| ( subset @ SY1597 @ SV955 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4701]) ).
thf(4856,plain,
! [SV813: $i,SV877: $i] :
( ( ( ~ ( ~ ( in @ ( sK28_C @ SV877 @ SV813 ) @ SV877 )
| ~ ( subset @ ( sK28_C @ SV877 @ SV813 ) @ SV813 ) )
| ~ ( ( in @ ( sK28_C @ SV877 @ SV813 ) @ SV877 )
| ( subset @ ( sK28_C @ SV877 @ SV813 ) @ SV813 ) ) )
= $false )
| ( ( SV877
= ( powerset @ SV813 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4702]) ).
thf(4857,plain,
! [SV814: $i,SV878: $i] :
( ( ( SV878
= ( powerset @ SV814 ) )
= $false )
| ( ( ~ ( ~ ! [SY1514: $i] :
( ~ ( in @ SY1514 @ SV878 )
| ( subset @ SY1514 @ SV814 ) )
| ~ ! [SY1515: $i] :
( ~ ( subset @ SY1515 @ SV814 )
| ( in @ SY1515 @ SV878 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4703]) ).
thf(4858,plain,
! [SV879: $i,SV815: $i] :
( ( ( subset @ SV815 @ ( singleton @ SV879 ) )
= $false )
| ( ( ( SV815 = empty_set )
| ( SV815
= ( singleton @ SV879 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4704]) ).
thf(4859,plain,
! [SV956: $i] :
( ( ( SV956 != empty_set )
| ! [SY1598: $i] : ( subset @ SV956 @ ( singleton @ SY1598 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4705]) ).
thf(4860,plain,
! [SV957: $i] :
( ( ! [SY1599: $i] :
( ( SV957
!= ( singleton @ SY1599 ) )
| ( subset @ SV957 @ ( singleton @ SY1599 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4706]) ).
thf(4861,plain,
! [SV816: $i] :
( ( ( ( ( relation_dom @ SV816 )
!= empty_set ) )
= $true )
| ( ( SV816 = empty_set )
= $true )
| ( ( relation @ SV816 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4707]) ).
thf(4862,plain,
! [SV817: $i] :
( ( ( ( ( relation_rng @ SV817 )
!= empty_set ) )
= $true )
| ( ( SV817 = empty_set )
= $true )
| ( ( relation @ SV817 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4708]) ).
thf(4863,plain,
! [SV818: $i,SV880: $i] :
( ( ( ~ ( function @ SV880 ) )
= $true )
| ( ( ~ ( relation @ SV880 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK50_C @ SV880 @ SV818 ) @ SV818 )
| ~ ( ( ( apply @ SV880 @ ( sK50_C @ SV880 @ SV818 ) )
!= ( sK50_C @ SV880 @ SV818 ) ) ) )
| ( ( relation_dom @ SV880 )
!= SV818 )
| ( SV880
= ( identity_relation @ SV818 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4711]) ).
thf(4864,plain,
! [SV958: $i] :
( ( ! [SY1600: $i] :
( ~ ( function @ SY1600 )
| ~ ( relation @ SY1600 )
| ( SY1600
!= ( identity_relation @ SV958 ) )
| ! [SY1601: $i] :
( ~ ( in @ SY1601 @ SV958 )
| ( ( apply @ SY1600 @ SY1601 )
= SY1601 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4712]) ).
thf(4865,plain,
! [SV959: $i] :
( ( ! [SY1602: $i] :
( ~ ( function @ SY1602 )
| ~ ( relation @ SY1602 )
| ( SY1602
!= ( identity_relation @ SV959 ) )
| ( ( relation_dom @ SY1602 )
= SV959 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4713]) ).
thf(4866,plain,
! [SV881: $i,SV819: $i] :
( ( ( in @ SV819 @ SV881 )
= $false )
| ( ( subset @ ( singleton @ SV819 ) @ SV881 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4714]) ).
thf(4867,plain,
! [SV882: $i,SV820: $i] :
( ( ( subset @ ( singleton @ SV820 ) @ SV882 )
= $false )
| ( ( in @ SV820 @ SV882 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4715]) ).
thf(4868,plain,
! [SV821: $i,SV883: $i] :
( ( ( ~ ( in @ ( sK18_C @ SV883 @ SV821 ) @ SV821 )
| ~ ~ ( in @ ( sK18_C @ SV883 @ SV821 ) @ SV883 ) )
= $false )
| ( ( subset @ SV821 @ SV883 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4716]) ).
thf(4869,plain,
! [SV884: $i,SV822: $i] :
( ( ( subset @ SV822 @ SV884 )
= $false )
| ( ( ! [SY1516: $i] :
( ~ ( in @ SY1516 @ SV822 )
| ( in @ SY1516 @ SV884 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4717]) ).
thf(4870,plain,
! [SV758: $i,SV580: $i] :
( ( ( subset @ ( relation_rng @ SV580 ) @ ( relation_dom @ SV758 ) )
= $false )
| ( ( ( relation_dom @ ( relation_composition @ SV580 @ SV758 ) )
= ( relation_dom @ SV580 ) )
= $true )
| ( ( relation @ SV758 )
= $false )
| ( ( relation @ SV580 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4719]) ).
thf(4871,plain,
! [SV759: $i,SV581: $i] :
( ( ( subset @ ( relation_dom @ SV581 ) @ ( relation_rng @ SV759 ) )
= $false )
| ( ( ( relation_rng @ ( relation_composition @ SV759 @ SV581 ) )
= ( relation_rng @ SV581 ) )
= $true )
| ( ( relation @ SV759 )
= $false )
| ( ( relation @ SV581 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4720]) ).
thf(4872,plain,
! [SV704: $i,SV602: $i,SV761: $i,SV748: $i] :
( ( ( subset @ SV748 @ SV761 )
= $false )
| ( ( subset @ SV602 @ SV704 )
= $false )
| ( ( subset @ ( cartesian_product2 @ SV602 @ SV748 ) @ ( cartesian_product2 @ SV704 @ SV761 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4722]) ).
thf(4873,plain,
! [SV604: $i,SV706: $i] :
( ( ( ( relation_inverse_image @ SV706 @ SV604 )
= empty_set )
= $false )
| ( ( SV604 = empty_set )
= $true )
| ( ( subset @ SV604 @ ( relation_rng @ SV706 ) )
= $false )
| ( ( relation @ SV706 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4723]) ).
thf(4874,plain,
! [SV710: $i,SV608: $i,SV912: $i] :
( ( ( ~ ( function @ SV912 )
| ~ ( relation @ SV912 ) )
= $true )
| ( ( ~ ( in @ SV608 @ ( relation_dom @ ( relation_composition @ SV912 @ SV710 ) ) )
| ( ( apply @ ( relation_composition @ SV912 @ SV710 ) @ SV608 )
= ( apply @ SV710 @ ( apply @ SV912 @ SV608 ) ) ) )
= $true )
| ( ( function @ SV710 )
= $false )
| ( ( relation @ SV710 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4726]) ).
thf(4875,plain,
! [SV711: $i,SV609: $i,SV913: $i] :
( ( ( ~ ( function @ SV913 )
| ~ ( relation @ SV913 ) )
= $true )
| ( ( ~ ( in @ SV609 @ ( relation_dom @ SV711 ) )
| ( ( apply @ ( relation_composition @ SV711 @ SV913 ) @ SV609 )
= ( apply @ SV913 @ ( apply @ SV711 @ SV609 ) ) ) )
= $true )
| ( ( function @ SV711 )
= $false )
| ( ( relation @ SV711 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4727]) ).
thf(4876,plain,
! [SV652: $i,SV825: $i,SV885: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV652 )
| ~ ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV825 )
| ~ ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV885 ) )
| ~ ~ ( ~ ( ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV652 )
| ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV885 ) )
| ~ ( ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV825 )
| ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV885 ) ) ) )
= $false )
| ( ( SV885
= ( set_intersection2 @ SV652 @ SV825 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4730]) ).
thf(4877,plain,
! [SV826: $i,SV652: $i,SV886: $i] :
( ( ( SV886
= ( set_intersection2 @ SV652 @ SV826 ) )
= $false )
| ( ( ~ ( ~ ! [SY1517: $i] :
( ~ ( in @ SY1517 @ SV652 )
| ~ ( in @ SY1517 @ SV826 )
| ( in @ SY1517 @ SV886 ) )
| ~ ~ ( ~ ! [SY1518: $i] :
( ~ ( in @ SY1518 @ SV886 )
| ( in @ SY1518 @ SV652 ) )
| ~ ! [SY1519: $i] :
( ~ ( in @ SY1519 @ SV886 )
| ( in @ SY1519 @ SV826 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4731]) ).
thf(4878,plain,
! [SV762: $i] :
( ( ( ( relation_dom @ SV762 )
= empty_set )
= $false )
| ( ( ( relation_rng @ SV762 )
= empty_set )
= $true )
| ( ( relation @ SV762 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4732]) ).
thf(4879,plain,
! [SV763: $i] :
( ( ( ( relation_rng @ SV763 )
= empty_set )
= $false )
| ( ( ( relation_dom @ SV763 )
= empty_set )
= $true )
| ( ( relation @ SV763 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4733]) ).
thf(4880,plain,
! [SV653: $i] :
( ( ( ~ ! [SY1140: $i] :
( ~ ( function @ SY1140 )
| ~ ( relation @ SY1140 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SY1140 @ SV653 )
= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ( ( sK70_C @ SY1140 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY1140 @ SV653 )
= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY1140 @ SV653 )
= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ( ( sK71_SY424 @ SY1140 @ SV653 )
!= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK70_C @ SY1140 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK71_SY424 @ SY1140 @ SV653 )
!= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY1140 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK70_C @ SY1140 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SY1140 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SY1140 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK71_SY424 @ SY1140 @ SV653 )
!= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ( ( relation_dom @ SY1140 )
!= ( relation_rng @ SV653 ) )
| ( SY1140
= ( function_inverse @ SV653 ) ) )
| ~ ~ ( ~ ! [SY1141: $i] :
( ~ ( function @ SY1141 )
| ~ ( relation @ SY1141 )
| ( SY1141
!= ( function_inverse @ SV653 ) )
| ~ ( ~ ~ ( ~ ! [SY1142: $i,SY1143: $i] :
( ( SY1143
!= ( apply @ SY1141 @ SY1142 ) )
| ~ ( in @ SY1142 @ ( relation_rng @ SV653 ) )
| ( SY1142
= ( apply @ SV653 @ SY1143 ) ) )
| ~ ! [SY1144: $i,SY1145: $i] :
( ( SY1145
!= ( apply @ SY1141 @ SY1144 ) )
| ~ ( in @ SY1144 @ ( relation_rng @ SV653 ) )
| ( in @ SY1145 @ ( relation_dom @ SV653 ) ) ) )
| ~ ~ ( ~ ! [SY1146: $i,SY1147: $i] :
( ( SY1146
!= ( apply @ SV653 @ SY1147 ) )
| ~ ( in @ SY1147 @ ( relation_dom @ SV653 ) )
| ( SY1147
= ( apply @ SY1141 @ SY1146 ) ) )
| ~ ! [SY1148: $i] :
( ! [SY1149: $i] :
( ( SY1148
!= ( apply @ SV653 @ SY1149 ) )
| ~ ( in @ SY1149 @ ( relation_dom @ SV653 ) ) )
| ( in @ SY1148 @ ( relation_rng @ SV653 ) ) ) ) ) )
| ~ ! [SY1150: $i] :
( ~ ( function @ SY1150 )
| ~ ( relation @ SY1150 )
| ( SY1150
!= ( function_inverse @ SV653 ) )
| ( ( relation_dom @ SY1150 )
= ( relation_rng @ SV653 ) ) ) ) )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4734]) ).
thf(4881,plain,
! [SV914: $i] :
( ( ( empty @ SV914 )
= $true )
| ( ( ! [SY1542: $i] :
( ~ ( element @ SY1542 @ SV914 )
| ( in @ SY1542 @ SV914 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4735]) ).
thf(4882,plain,
! [SV915: $i] :
( ( ( empty @ SV915 )
= $true )
| ( ( ! [SY1543: $i] :
( ~ ( in @ SY1543 @ SV915 )
| ( element @ SY1543 @ SV915 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4736]) ).
thf(4883,plain,
! [SV916: $i] :
( ( ( ~ ( empty @ SV916 ) )
= $true )
| ( ( ! [SY1544: $i] :
( ~ ( element @ SY1544 @ SV916 )
| ( empty @ SY1544 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4737]) ).
thf(4884,plain,
! [SV917: $i] :
( ( ( ~ ( empty @ SV917 ) )
= $true )
| ( ( ! [SY1545: $i] :
( ~ ( empty @ SY1545 )
| ( element @ SY1545 @ SV917 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4738]) ).
thf(4885,plain,
! [SV829: $i,SV766: $i] :
( ( ( SV766 = empty_set )
= $true )
| ( ( SV766
= ( singleton @ SV829 ) )
= $true )
| ( ( subset @ SV766 @ ( singleton @ SV829 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4741]) ).
thf(4886,plain,
! [SV918: $i] :
( ( ( ( SV918 != empty_set ) )
= $true )
| ( ( ! [SY1546: $i] : ( subset @ SV918 @ ( singleton @ SY1546 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4742]) ).
thf(4887,plain,
! [SV960: $i,SV919: $i] :
( ( ( SV919
!= ( singleton @ SV960 ) )
| ( subset @ SV919 @ ( singleton @ SV960 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4743]) ).
thf(4888,plain,
! [SV739: $i,SV887: $i,SV654: $i,SV920: $i] :
( ( ( ~ ( relation @ SV920 ) )
= $true )
| ( ( ~ ( in @ SV654 @ SV887 )
| ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ SV920 )
| ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SV887 ) @ SV920 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4748]) ).
thf(4889,plain,
! [SV739: $i,SV654: $i] :
( ( ! [SY1360: $i,SY1361: $i] :
( ~ ( relation @ SY1361 )
| ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SY1360 ) @ SY1361 ) )
| ( in @ SV654 @ SY1360 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4749]) ).
thf(4890,plain,
! [SV739: $i,SV654: $i] :
( ( ! [SY1362: $i,SY1363: $i] :
( ~ ( relation @ SY1363 )
| ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SY1362 ) @ SY1363 ) )
| ( in @ ( ordered_pair @ SV654 @ SV739 ) @ SY1363 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4750]) ).
thf(4891,plain,
! [SV655: $i,SV740: $i,SV961: $i] :
( ( ( ~ ( relation @ SV961 )
| ~ ( ~ ( ~ ( in @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) @ SV655 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV740 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 ) )
| ~ ~ ( ~ ( ( in @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) @ SV655 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV740 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 ) ) ) )
| ( SV961
= ( relation_rng_restriction @ SV655 @ SV740 ) ) )
= $true )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4751]) ).
thf(4892,plain,
! [SV740: $i,SV655: $i,SV962: $i] :
( ( ( ~ ( relation @ SV962 )
| ( SV962
!= ( relation_rng_restriction @ SV655 @ SV740 ) )
| ~ ( ~ ! [SY1603: $i,SY1604: $i] :
( ~ ( in @ SY1604 @ SV655 )
| ~ ( in @ ( ordered_pair @ SY1603 @ SY1604 ) @ SV740 )
| ( in @ ( ordered_pair @ SY1603 @ SY1604 ) @ SV962 ) )
| ~ ~ ( ~ ! [SY1605: $i,SY1606: $i] :
( ~ ( in @ ( ordered_pair @ SY1605 @ SY1606 ) @ SV962 )
| ( in @ SY1606 @ SV655 ) )
| ~ ! [SY1607: $i,SY1608: $i] :
( ~ ( in @ ( ordered_pair @ SY1607 @ SY1608 ) @ SV962 )
| ( in @ ( ordered_pair @ SY1607 @ SY1608 ) @ SV740 ) ) ) ) )
= $true )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4752]) ).
thf(4893,plain,
! [SV963: $i,SV888: $i,SV741: $i,SV656: $i] :
( ( ( ( ( ordered_pair @ SV656 @ SV741 )
!= ( ordered_pair @ SV888 @ SV963 ) ) )
= $true )
| ( ( SV656 = SV888 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4753]) ).
thf(4894,plain,
! [SV921: $i,SV889: $i,SV741: $i,SV656: $i] :
( ( ( ( ( ordered_pair @ SV656 @ SV741 )
!= ( ordered_pair @ SV889 @ SV921 ) ) )
= $true )
| ( ( SV741 = SV921 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4754]) ).
thf(4895,plain,
! [SV657: $i,SV922: $i,SV964: $i] :
( ( ( ~ ( ~ ( ! [SY1609: $i] :
( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SY1609 ) @ SV657 )
| ~ ( in @ SY1609 @ SV922 ) )
| ~ ( in @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SV964 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ ( sK36_SY409 @ SV964 @ SV922 @ SV657 ) ) @ SV657 )
| ~ ( in @ ( sK36_SY409 @ SV964 @ SV922 @ SV657 ) @ SV922 ) )
| ( in @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SV964 ) ) )
| ( SV964
= ( relation_inverse_image @ SV657 @ SV922 ) ) )
= $true )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4755]) ).
thf(4896,plain,
! [SV923: $i,SV657: $i,SV965: $i] :
( ( ( ( SV965
!= ( relation_inverse_image @ SV657 @ SV923 ) )
| ~ ( ~ ! [SY1610: $i] :
( ! [SY1552: $i] :
( ~ ( in @ ( ordered_pair @ SY1610 @ SY1552 ) @ SV657 )
| ~ ( in @ SY1552 @ SV923 ) )
| ( in @ SY1610 @ SV965 ) )
| ~ ! [SY1612: $i] :
( ~ ( in @ SY1612 @ SV965 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1612 @ ( sK34_E @ SY1612 @ SV965 @ SV923 @ SV657 ) ) @ SV657 )
| ~ ( in @ ( sK34_E @ SY1612 @ SV965 @ SV923 @ SV657 ) @ SV923 ) ) ) ) )
= $true )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4756]) ).
thf(4897,plain,
! [SV658: $i,SV924: $i,SV966: $i] :
( ( ( ~ ( ~ ( ! [SY1613: $i] :
( ~ ( in @ ( ordered_pair @ SY1613 @ ( sK38_D @ SV966 @ SV924 @ SV658 ) ) @ SV658 )
| ~ ( in @ SY1613 @ SV924 ) )
| ~ ( in @ ( sK38_D @ SV966 @ SV924 @ SV658 ) @ SV966 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SV966 @ SV924 @ SV658 ) @ ( sK38_D @ SV966 @ SV924 @ SV658 ) ) @ SV658 )
| ~ ( in @ ( sK39_SY411 @ SV966 @ SV924 @ SV658 ) @ SV924 ) )
| ( in @ ( sK38_D @ SV966 @ SV924 @ SV658 ) @ SV966 ) ) )
| ( SV966
= ( relation_image @ SV658 @ SV924 ) ) )
= $true )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4757]) ).
thf(4898,plain,
! [SV925: $i,SV658: $i,SV967: $i] :
( ( ( ( SV967
!= ( relation_image @ SV658 @ SV925 ) )
| ~ ( ~ ! [SY1614: $i] :
( ! [SY1558: $i] :
( ~ ( in @ ( ordered_pair @ SY1558 @ SY1614 ) @ SV658 )
| ~ ( in @ SY1558 @ SV925 ) )
| ( in @ SY1614 @ SV967 ) )
| ~ ! [SY1616: $i] :
( ~ ( in @ SY1616 @ SV967 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SY1616 @ SV967 @ SV925 @ SV658 ) @ SY1616 ) @ SV658 )
| ~ ( in @ ( sK37_E @ SY1616 @ SV967 @ SV925 @ SV658 ) @ SV925 ) ) ) ) )
= $true )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4758]) ).
thf(4899,plain,
! [SV834: $i,SV777: $i] :
( ( ( subset @ SV777 @ SV834 )
= $false )
| ( ( SV777 = SV834 )
= $true )
| ( ( proper_subset @ SV777 @ SV834 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4759]) ).
thf(4900,plain,
! [SV968: $i,SV926: $i] :
( ( ~ ( proper_subset @ SV926 @ SV968 )
| ( SV926 != SV968 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4760]) ).
thf(4901,plain,
! [SV969: $i,SV927: $i] :
( ( ~ ( proper_subset @ SV927 @ SV969 )
| ( subset @ SV927 @ SV969 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4761]) ).
thf(4902,plain,
! [SV835: $i,SV778: $i] :
( ( ( empty @ SV778 )
= $false )
| ( ( ~ ( relation @ SV835 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV835 @ SV778 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4762]) ).
thf(4903,plain,
! [SV836: $i,SV779: $i] :
( ( ( empty @ SV779 )
= $false )
| ( ( ~ ( relation @ SV836 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV836 @ SV779 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4763]) ).
thf(4904,plain,
! [SV928: $i] :
( ( ( ~ ( empty @ SV928 )
| ~ ( relation @ SV928 )
| ~ ( function @ SV928 ) )
= $true )
| ( ( function @ SV928 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4764]) ).
thf(4905,plain,
! [SV929: $i] :
( ( ( ~ ( empty @ SV929 )
| ~ ( relation @ SV929 )
| ~ ( function @ SV929 ) )
= $true )
| ( ( relation @ SV929 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4765]) ).
thf(4906,plain,
! [SV780: $i] :
( ( ( empty @ SV780 )
= $false )
| ( ( ~ ( relation @ SV780 ) )
= $true )
| ( ( ~ ( function @ SV780 ) )
= $true )
| ( ( one_to_one @ SV780 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4766]) ).
thf(4907,plain,
! [SV781: $i] :
( ( ( ! [SY1402: $i,SY1403: $i] :
( ( sK69_B @ SV781 )
!= ( ordered_pair @ SY1402 @ SY1403 ) ) )
= $true )
| ( ( relation @ SV781 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4767]) ).
thf(4908,plain,
! [SV781: $i] :
( ( ( in @ ( sK69_B @ SV781 ) @ SV781 )
= $true )
| ( ( relation @ SV781 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4768]) ).
thf(4909,plain,
! [SV782: $i,SV930: $i] :
( ( ( SV930
= ( ordered_pair @ ( sK67_C @ SV930 @ SV782 ) @ ( sK68_SY421 @ SV930 @ SV782 ) ) )
= $true )
| ( ( ~ ( in @ SV930 @ SV782 ) )
= $true )
| ( ( relation @ SV782 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4769]) ).
thf(4910,plain,
! [SV837: $i,SV890: $i,SV659: $i] :
( ( ( ~ ( in @ SV659 @ SV890 ) )
= $true )
| ( ( ~ ( in @ SV837 @ SV890 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV659 @ SV837 ) @ SV890 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4770]) ).
thf(4911,plain,
! [SV970: $i,SV659: $i] :
( ( ! [SY1617: $i] :
( ~ ( subset @ ( unordered_pair @ SV659 @ SV970 ) @ SY1617 )
| ( in @ SV659 @ SY1617 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4771]) ).
thf(4912,plain,
! [SV971: $i,SV659: $i] :
( ( ! [SY1618: $i] :
( ~ ( subset @ ( unordered_pair @ SV659 @ SV971 ) @ SY1618 )
| ( in @ SV971 @ SY1618 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4772]) ).
thf(4913,plain,
! [SV660: $i,SV783: $i] :
( ( ( ~ ! [SY1405: $i] :
( ~ ( relation @ SY1405 )
| ~ ( ~ ( ! [SY1406: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY1405 @ SV783 @ SV660 ) @ SY1406 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1406 @ ( sK9_SY391 @ SY1405 @ SV783 @ SV660 ) ) @ SV783 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SY1405 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SY1405 @ SV783 @ SV660 ) ) @ SY1405 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY1405 @ SV783 @ SV660 ) @ ( sK10_SY395 @ SY1405 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SY1405 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SY1405 @ SV783 @ SV660 ) ) @ SV783 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SY1405 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SY1405 @ SV783 @ SV660 ) ) @ SY1405 ) ) )
| ( SY1405
= ( relation_composition @ SV660 @ SV783 ) ) ) )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4773]) ).
thf(4914,plain,
! [SV783: $i,SV660: $i] :
( ( ( ~ ! [SY1407: $i] :
( ~ ( relation @ SY1407 )
| ( SY1407
!= ( relation_composition @ SV660 @ SV783 ) )
| ~ ( ~ ! [SY1408: $i,SY1409: $i] :
( ! [SY1410: $i] :
( ~ ( in @ ( ordered_pair @ SY1408 @ SY1410 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1410 @ SY1409 ) @ SV783 ) )
| ( in @ ( ordered_pair @ SY1408 @ SY1409 ) @ SY1407 ) )
| ~ ! [SY1411: $i,SY1412: $i] :
( ~ ( in @ ( ordered_pair @ SY1411 @ SY1412 ) @ SY1407 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1411 @ ( sK7_F @ SY1412 @ SY1411 @ SY1407 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY1412 @ SY1411 @ SY1407 @ SV783 @ SV660 ) @ SY1412 ) @ SV783 ) ) ) ) ) )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4773]) ).
thf(4915,plain,
! [SV785: $i,SV931: $i] :
( ( ( in @ SV931 @ SV785 )
= $false )
| ( ( SV785 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4774]) ).
thf(4916,plain,
! [SV661: $i,SV932: $i] :
( ( ( ~ ( ~ ( ! [SY1562: $i] :
~ ( in @ ( ordered_pair @ SY1562 @ ( sK60_C @ SV932 @ SV661 ) ) @ SV661 )
| ~ ( in @ ( sK60_C @ SV932 @ SV661 ) @ SV932 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK61_SY417 @ SV932 @ SV661 ) @ ( sK60_C @ SV932 @ SV661 ) ) @ SV661 )
| ( in @ ( sK60_C @ SV932 @ SV661 ) @ SV932 ) ) ) )
= $true )
| ( ( SV932
= ( relation_rng @ SV661 ) )
= $true )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4775]) ).
thf(4917,plain,
! [SV661: $i,SV933: $i] :
( ( ( ( SV933
!= ( relation_rng @ SV661 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1563: $i] :
( ! [SY1207: $i] :
~ ( in @ ( ordered_pair @ SY1207 @ SY1563 ) @ SV661 )
| ( in @ SY1563 @ SV933 ) )
| ~ ! [SY1565: $i] :
( ~ ( in @ SY1565 @ SV933 )
| ( in @ ( ordered_pair @ ( sK59_D @ SY1565 @ SV933 @ SV661 ) @ SY1565 ) @ SV661 ) ) ) )
= $true )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4776]) ).
thf(4918,plain,
! [SV662: $i,SV838: $i,SV891: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV662 )
| ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV838 )
| ~ ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV891 ) )
| ~ ~ ( ~ ( ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV662 )
| ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV891 ) )
| ~ ( ~ ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV838 )
| ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV891 ) ) ) )
= $false )
| ( ( SV891
= ( set_difference @ SV662 @ SV838 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4777]) ).
thf(4919,plain,
! [SV839: $i,SV662: $i,SV892: $i] :
( ( ( SV892
= ( set_difference @ SV662 @ SV839 ) )
= $false )
| ( ( ~ ( ~ ! [SY1523: $i] :
( ~ ( in @ SY1523 @ SV662 )
| ( in @ SY1523 @ SV839 )
| ( in @ SY1523 @ SV892 ) )
| ~ ~ ( ~ ! [SY1524: $i] :
( ~ ( in @ SY1524 @ SV892 )
| ( in @ SY1524 @ SV662 ) )
| ~ ! [SY1525: $i] :
( ~ ( in @ SY1525 @ SV892 )
| ~ ( in @ SY1525 @ SV839 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4778]) ).
thf(4920,plain,
! [SV840: $i,SV790: $i] :
( ( ( ~ ( function @ SV790 )
| ~ ( relation @ SV790 ) )
= $true )
| ( ( ~ ( relation @ SV840 ) )
= $true )
| ( ( ~ ( function @ SV840 ) )
= $true )
| ( ( function @ ( relation_composition @ SV790 @ SV840 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4779]) ).
thf(4921,plain,
! [SV841: $i,SV791: $i] :
( ( ( ~ ( function @ SV791 )
| ~ ( relation @ SV791 ) )
= $true )
| ( ( ~ ( relation @ SV841 ) )
= $true )
| ( ( ~ ( function @ SV841 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV791 @ SV841 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4780]) ).
thf(4922,plain,
! [SV842: $i,SV663: $i,SV893: $i] :
( ( ( relation @ SV893 )
= $false )
| ( ( ~ ( in @ SV663 @ SV842 )
| ~ ( in @ SV663 @ ( relation_rng @ SV893 ) )
| ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SV842 @ SV893 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4781]) ).
thf(4923,plain,
! [SV972: $i,SV663: $i] :
( ( ! [SY1619: $i] :
( ~ ( relation @ SY1619 )
| ~ ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SV972 @ SY1619 ) ) )
| ( in @ SV663 @ SV972 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4782]) ).
thf(4924,plain,
! [SV973: $i,SV663: $i] :
( ( ! [SY1620: $i] :
( ~ ( relation @ SY1620 )
| ~ ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SV973 @ SY1620 ) ) )
| ( in @ SV663 @ ( relation_rng @ SY1620 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4783]) ).
thf(4925,plain,
! [SV664: $i] :
( ( ( ~ ( ~ ! [SY1222: $i] :
( ~ ( in @ SY1222 @ ( relation_dom @ SV664 ) )
| ! [SY1223: $i] :
( ( SY1223
!= ( apply @ SV664 @ SY1222 ) )
| ( in @ ( ordered_pair @ SY1222 @ SY1223 ) @ SV664 ) ) )
| ~ ! [SY1224: $i] :
( ~ ( in @ SY1224 @ ( relation_dom @ SV664 ) )
| ! [SY1225: $i] :
( ~ ( in @ ( ordered_pair @ SY1224 @ SY1225 ) @ SV664 )
| ( SY1225
= ( apply @ SV664 @ SY1224 ) ) ) ) ) )
= $true )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4784]) ).
thf(4926,plain,
! [SV664: $i] :
( ( ( ~ ( ~ ! [SY1226: $i] :
( ( in @ SY1226 @ ( relation_dom @ SV664 ) )
| ! [SY1227: $i] :
( ( SY1227
!= ( apply @ SV664 @ SY1226 ) )
| ( SY1227 = empty_set ) ) )
| ~ ! [SY1228: $i] :
( ( in @ SY1228 @ ( relation_dom @ SV664 ) )
| ! [SY1229: $i] :
( ( SY1229 != empty_set )
| ( SY1229
= ( apply @ SV664 @ SY1228 ) ) ) ) ) )
= $true )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4785]) ).
thf(4927,plain,
! [SV665: $i,SV934: $i] :
( ( ( ~ ( relation @ SV934 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV934 @ SV665 ) @ ( sK20_SY399 @ SV934 @ SV665 ) ) @ SV665 )
| ~ ~ ( in @ ( ordered_pair @ ( sK19_C @ SV934 @ SV665 ) @ ( sK20_SY399 @ SV934 @ SV665 ) ) @ SV934 ) )
| ( subset @ SV665 @ SV934 ) )
= $true )
| ( ( relation @ SV665 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4786]) ).
thf(4928,plain,
! [SV665: $i,SV935: $i] :
( ( ( ~ ( relation @ SV935 ) )
= $true )
| ( ( ~ ( subset @ SV665 @ SV935 )
| ! [SY1566: $i,SY1567: $i] :
( ~ ( in @ ( ordered_pair @ SY1566 @ SY1567 ) @ SV665 )
| ( in @ ( ordered_pair @ SY1566 @ SY1567 ) @ SV935 ) ) )
= $true )
| ( ( relation @ SV665 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4787]) ).
thf(4929,plain,
! [SV742: $i,SV666: $i] :
( ( ( ~ ! [SY1376: $i] :
( ~ ( function @ SY1376 )
| ~ ( relation @ SY1376 )
| ~ ( in @ SV666 @ ( relation_dom @ SY1376 ) )
| ~ ( in @ ( apply @ SY1376 @ SV666 ) @ ( relation_dom @ SV742 ) )
| ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1376 @ SV742 ) ) ) ) )
= $false )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4788]) ).
thf(4930,plain,
! [SV742: $i,SV666: $i] :
( ( ( ~ ~ ( ~ ! [SY1377: $i] :
( ~ ( function @ SY1377 )
| ~ ( relation @ SY1377 )
| ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1377 @ SV742 ) ) )
| ( in @ SV666 @ ( relation_dom @ SY1377 ) ) )
| ~ ! [SY1378: $i] :
( ~ ( function @ SY1378 )
| ~ ( relation @ SY1378 )
| ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1378 @ SV742 ) ) )
| ( in @ ( apply @ SY1378 @ SV666 ) @ ( relation_dom @ SV742 ) ) ) ) )
= $false )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4788]) ).
thf(4931,plain,
! [SV843: $i,SV667: $i,SV894: $i] :
( ( ( relation @ SV894 )
= $false )
| ( ( ! [SY1526: $i] :
( ~ ( in @ SY1526 @ ( relation_rng @ SV894 ) )
| ~ ( in @ ( ordered_pair @ SV667 @ SY1526 ) @ SV894 )
| ~ ( in @ SY1526 @ SV843 ) )
| ( in @ SV667 @ ( relation_inverse_image @ SV894 @ SV843 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4789]) ).
thf(4932,plain,
! [SV844: $i,SV667: $i,SV895: $i] :
( ( ( relation @ SV895 )
= $false )
| ( ( ~ ( in @ SV667 @ ( relation_inverse_image @ SV895 @ SV844 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK51_D @ SV895 @ SV844 @ SV667 ) @ ( relation_rng @ SV895 ) )
| ~ ( in @ ( ordered_pair @ SV667 @ ( sK51_D @ SV895 @ SV844 @ SV667 ) ) @ SV895 ) )
| ~ ( in @ ( sK51_D @ SV895 @ SV844 @ SV667 ) @ SV844 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4790]) ).
thf(4933,plain,
! [SV792: $i,SV845: $i] :
( ( ( ~ ( in @ ( sK49_C @ SV845 @ SV792 ) @ SV792 ) )
= $false )
| ( ( disjoint @ SV792 @ SV845 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4791]) ).
thf(4934,plain,
! [SV792: $i,SV845: $i] :
( ( ( ~ ( in @ ( sK49_C @ SV845 @ SV792 ) @ SV845 ) )
= $false )
| ( ( disjoint @ SV792 @ SV845 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4791]) ).
thf(4935,plain,
! [SV846: $i,SV793: $i,SV936: $i] :
( ( ( ~ ( in @ SV936 @ SV793 ) )
= $true )
| ( ( ~ ( in @ SV936 @ SV846 ) )
= $true )
| ( ( ~ ( disjoint @ SV793 @ SV846 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4792]) ).
thf(4936,plain,
! [SV847: $i,SV668: $i,SV896: $i] :
( ( ( relation @ SV896 )
= $false )
| ( ( ~ ( in @ SV668 @ SV847 )
| ~ ( in @ SV668 @ ( relation_dom @ SV896 ) )
| ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SV896 @ SV847 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4793]) ).
thf(4937,plain,
! [SV974: $i,SV668: $i] :
( ( ! [SY1621: $i] :
( ~ ( relation @ SY1621 )
| ~ ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SY1621 @ SV974 ) ) )
| ( in @ SV668 @ SV974 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4794]) ).
thf(4938,plain,
! [SV975: $i,SV668: $i] :
( ( ! [SY1622: $i] :
( ~ ( relation @ SY1622 )
| ~ ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SY1622 @ SV975 ) ) )
| ( in @ SV668 @ ( relation_dom @ SY1622 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4795]) ).
thf(4939,plain,
! [SV669: $i,SV848: $i,SV897: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV897 )
| ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV669 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV897 )
| ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV848 ) ) )
| ~ ( ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV897 )
| ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV669 )
| ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV848 ) ) )
= $false )
| ( ( SV897
= ( set_union2 @ SV669 @ SV848 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4796]) ).
thf(4940,plain,
! [SV849: $i,SV669: $i,SV898: $i] :
( ( ( SV898
= ( set_union2 @ SV669 @ SV849 ) )
= $false )
| ( ( ~ ( ~ ! [SY1527: $i] :
( ~ ( in @ SY1527 @ SV898 )
| ( in @ SY1527 @ SV669 )
| ( in @ SY1527 @ SV849 ) )
| ~ ~ ( ~ ! [SY1528: $i] :
( ~ ( in @ SY1528 @ SV669 )
| ( in @ SY1528 @ SV898 ) )
| ~ ! [SY1529: $i] :
( ~ ( in @ SY1529 @ SV849 )
| ( in @ SY1529 @ SV898 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4797]) ).
thf(4941,plain,
! [SV937: $i] :
( ( ( SV937 = empty_set )
= $true )
| ( ( ! [SY1568: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY406 @ SY1568 @ SV937 ) @ SV937 )
| ~ ~ ( in @ ( sK32_C @ SY1568 @ SV937 ) @ ( sK33_SY406 @ SY1568 @ SV937 ) ) )
| ~ ( in @ ( sK32_C @ SY1568 @ SV937 ) @ SY1568 ) )
| ~ ( ! [SY1569: $i] :
( ~ ( in @ SY1569 @ SV937 )
| ( in @ ( sK32_C @ SY1568 @ SV937 ) @ SY1569 ) )
| ( in @ ( sK32_C @ SY1568 @ SV937 ) @ SY1568 ) ) )
| ( SY1568
= ( set_meet @ SV937 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4798]) ).
thf(4942,plain,
! [SV938: $i] :
( ( ( SV938 = empty_set )
= $true )
| ( ( ! [SY1570: $i] :
( ( SY1570
!= ( set_meet @ SV938 ) )
| ~ ( ~ ! [SY1571: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY1571 @ SY1570 @ SV938 ) @ SV938 )
| ~ ~ ( in @ SY1571 @ ( sK31_D @ SY1571 @ SY1570 @ SV938 ) ) )
| ( in @ SY1571 @ SY1570 ) )
| ~ ! [SY1572: $i] :
( ~ ( in @ SY1572 @ SY1570 )
| ! [SY1573: $i] :
( ~ ( in @ SY1573 @ SV938 )
| ( in @ SY1572 @ SY1573 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4799]) ).
thf(4943,plain,
! [SV939: $i] :
( ( ( ( SV939 != empty_set ) )
= $true )
| ( ( ! [SY1574: $i] :
( ( SY1574
!= ( set_meet @ SV939 ) )
| ( SY1574 = empty_set ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4800]) ).
thf(4944,plain,
! [SV940: $i] :
( ( ( ( SV940 != empty_set ) )
= $true )
| ( ( ! [SY1575: $i] :
( ( SY1575 != empty_set )
| ( SY1575
= ( set_meet @ SV940 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4801]) ).
thf(4945,plain,
! [SV899: $i,SV850: $i,SV670: $i] :
( ( ( ~ ( ! [SY1530: $i,SY1531: $i] :
( ~ ( in @ SY1530 @ SV670 )
| ~ ( in @ SY1531 @ SV850 )
| ( ( sK23_D @ SV899 @ SV850 @ SV670 )
!= ( ordered_pair @ SY1530 @ SY1531 ) ) )
| ~ ( in @ ( sK23_D @ SV899 @ SV850 @ SV670 ) @ SV899 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY403 @ SV899 @ SV850 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK25_SY405 @ SV899 @ SV850 @ SV670 ) @ SV850 ) )
| ( ( sK23_D @ SV899 @ SV850 @ SV670 )
!= ( ordered_pair @ ( sK24_SY403 @ SV899 @ SV850 @ SV670 ) @ ( sK25_SY405 @ SV899 @ SV850 @ SV670 ) ) ) )
| ( in @ ( sK23_D @ SV899 @ SV850 @ SV670 ) @ SV899 ) ) )
= $false )
| ( ( SV899
= ( cartesian_product2 @ SV670 @ SV850 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4802]) ).
thf(4946,plain,
! [SV851: $i,SV670: $i,SV900: $i] :
( ( ( SV900
= ( cartesian_product2 @ SV670 @ SV851 ) )
= $false )
| ( ( ~ ( ~ ! [SY1532: $i] :
( ! [SY1483: $i,SY1484: $i] :
( ~ ( in @ SY1483 @ SV670 )
| ~ ( in @ SY1484 @ SV851 )
| ( SY1532
!= ( ordered_pair @ SY1483 @ SY1484 ) ) )
| ( in @ SY1532 @ SV900 ) )
| ~ ! [SY1535: $i] :
( ~ ( in @ SY1535 @ SV900 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY1535 @ SV900 @ SV851 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK22_SY400 @ SY1535 @ SV900 @ SV851 @ SV670 ) @ SV851 ) )
| ( SY1535
!= ( ordered_pair @ ( sK21_E @ SY1535 @ SV900 @ SV851 @ SV670 ) @ ( sK22_SY400 @ SY1535 @ SV900 @ SV851 @ SV670 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4803]) ).
thf(4947,plain,
! [SV671: $i,SV852: $i,SV901: $i] :
( ( ( ~ ( function @ SV901 ) )
= $true )
| ( ( ~ ( relation @ SV901 ) )
= $true )
| ( ( ( SV852
!= ( apply @ SV901 @ SV671 ) )
| ~ ( in @ SV671 @ ( relation_dom @ SV901 ) )
| ( in @ ( ordered_pair @ SV671 @ SV852 ) @ SV901 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4804]) ).
thf(4948,plain,
! [SV976: $i,SV671: $i] :
( ( ! [SY1623: $i] :
( ~ ( function @ SY1623 )
| ~ ( relation @ SY1623 )
| ~ ( in @ ( ordered_pair @ SV671 @ SV976 ) @ SY1623 )
| ( SV976
= ( apply @ SY1623 @ SV671 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4805]) ).
thf(4949,plain,
! [SV977: $i,SV671: $i] :
( ( ! [SY1624: $i] :
( ~ ( function @ SY1624 )
| ~ ( relation @ SY1624 )
| ~ ( in @ ( ordered_pair @ SV671 @ SV977 ) @ SY1624 )
| ( in @ SV671 @ ( relation_dom @ SY1624 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4806]) ).
thf(4950,plain,
! [SV672: $i,SV941: $i] :
( ( ( ~ ( relation @ SV941 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SV941 @ SV672 ) @ ( sK12_SY396 @ SV941 @ SV672 ) ) @ SV941 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SV941 @ SV672 ) @ ( sK11_C @ SV941 @ SV672 ) ) @ SV672 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_C @ SV941 @ SV672 ) @ ( sK12_SY396 @ SV941 @ SV672 ) ) @ SV941 )
| ( in @ ( ordered_pair @ ( sK12_SY396 @ SV941 @ SV672 ) @ ( sK11_C @ SV941 @ SV672 ) ) @ SV672 ) ) )
| ( SV941
= ( relation_inverse @ SV672 ) ) )
= $true )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4807]) ).
thf(4951,plain,
! [SV672: $i,SV942: $i] :
( ( ( ~ ( relation @ SV942 ) )
= $true )
| ( ( ( SV942
!= ( relation_inverse @ SV672 ) )
| ~ ( ~ ! [SY1576: $i,SY1577: $i] :
( ~ ( in @ ( ordered_pair @ SY1576 @ SY1577 ) @ SV942 )
| ( in @ ( ordered_pair @ SY1577 @ SY1576 ) @ SV672 ) )
| ~ ! [SY1578: $i,SY1579: $i] :
( ~ ( in @ ( ordered_pair @ SY1579 @ SY1578 ) @ SV672 )
| ( in @ ( ordered_pair @ SY1578 @ SY1579 ) @ SV942 ) ) ) )
= $true )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4808]) ).
thf(4952,plain,
! [SV798: $i] :
( ( ( function @ SV798 )
= $false )
| ( ( ~ ( relation @ SV798 ) )
= $true )
| ( ( ~ ( one_to_one @ SV798 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV798 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4811]) ).
thf(4953,plain,
! [SV799: $i] :
( ( ( function @ SV799 )
= $false )
| ( ( ~ ( relation @ SV799 ) )
= $true )
| ( ( ~ ( one_to_one @ SV799 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV799 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4812]) ).
thf(4954,plain,
! [SV855: $i,SV673: $i,SV902: $i] :
( ( ( relation @ SV902 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV673 @ SV855 ) @ SV902 )
| ( in @ SV673 @ ( relation_dom @ SV902 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4813]) ).
thf(4955,plain,
! [SV856: $i,SV673: $i,SV903: $i] :
( ( ( relation @ SV903 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV673 @ SV856 ) @ SV903 )
| ( in @ SV856 @ ( relation_rng @ SV903 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4814]) ).
thf(4956,plain,
! [SV943: $i,SV743: $i,SV904: $i,SV674: $i] :
( ( ( ~ ( in @ SV674 @ SV904 )
| ~ ( in @ SV743 @ SV943 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SV904 @ SV943 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4815]) ).
thf(4957,plain,
! [SV743: $i,SV674: $i] :
( ( ! [SY1381: $i] :
( ! [SY1382: $i] :
~ ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SY1381 @ SY1382 ) )
| ( in @ SV674 @ SY1381 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4816]) ).
thf(4958,plain,
! [SV743: $i,SV674: $i] :
( ( ! [SY1383: $i,SY1384: $i] :
( ~ ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SY1383 @ SY1384 ) )
| ( in @ SV743 @ SY1384 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4817]) ).
thf(4959,plain,
! [SV675: $i,SV857: $i,SV905: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SV905 @ SV857 @ SV675 ) @ SV905 )
| ( ( sK27_D @ SV905 @ SV857 @ SV675 )
!= SV675 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV905 @ SV857 @ SV675 ) @ SV905 )
| ( ( sK27_D @ SV905 @ SV857 @ SV675 )
!= SV857 ) ) )
| ~ ( ( in @ ( sK27_D @ SV905 @ SV857 @ SV675 ) @ SV905 )
| ( ( sK27_D @ SV905 @ SV857 @ SV675 )
= SV675 )
| ( ( sK27_D @ SV905 @ SV857 @ SV675 )
= SV857 ) ) )
= $false )
| ( ( SV905
= ( unordered_pair @ SV675 @ SV857 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4818]) ).
thf(4960,plain,
! [SV858: $i,SV675: $i,SV906: $i] :
( ( ( SV906
= ( unordered_pair @ SV675 @ SV858 ) )
= $false )
| ( ( ~ ( ~ ! [SY1537: $i] :
( ~ ( in @ SY1537 @ SV906 )
| ( SY1537 = SV675 )
| ( SY1537 = SV858 ) )
| ~ ~ ( ~ ! [SY1538: $i] :
( ( SY1538 != SV675 )
| ( in @ SY1538 @ SV906 ) )
| ~ ! [SY1539: $i] :
( ( SY1539 != SV858 )
| ( in @ SY1539 @ SV906 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4819]) ).
thf(4961,plain,
! [SV944: $i,SV744: $i,SV907: $i,SV676: $i] :
( ( ( ~ ( in @ SV676 @ SV907 )
| ~ ( in @ SV744 @ SV944 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SV907 @ SV944 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4820]) ).
thf(4962,plain,
! [SV744: $i,SV676: $i] :
( ( ! [SY1387: $i] :
( ! [SY1388: $i] :
~ ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SY1387 @ SY1388 ) )
| ( in @ SV676 @ SY1387 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4821]) ).
thf(4963,plain,
! [SV744: $i,SV676: $i] :
( ( ! [SY1389: $i,SY1390: $i] :
( ~ ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SY1389 @ SY1390 ) )
| ( in @ SV744 @ SY1390 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4822]) ).
thf(4964,plain,
! [SV860: $i,SV801: $i,SV945: $i] :
( ( ( in @ SV945 @ ( set_intersection2 @ SV801 @ SV860 ) )
= $false )
| ( ( ~ ( disjoint @ SV801 @ SV860 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4823]) ).
thf(4965,plain,
! [SV802: $i] :
( ( ( relation @ SV802 )
= $false )
| ( ( function @ SV802 )
= $false )
| ( ( function @ ( function_inverse @ SV802 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4824]) ).
thf(4966,plain,
! [SV803: $i] :
( ( ( relation @ SV803 )
= $false )
| ( ( function @ SV803 )
= $false )
| ( ( relation @ ( function_inverse @ SV803 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4825]) ).
thf(4967,plain,
! [SV677: $i,SV745: $i] :
( ( ( in @ ( sK4_C @ SV745 @ SV677 ) @ SV677 )
= $false )
| ( ( ~ ( in @ ( sK4_C @ SV745 @ SV677 ) @ SV745 ) )
= $true )
| ( ( SV677 = SV745 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4826]) ).
thf(4968,plain,
! [SV861: $i,SV978: $i,SV678: $i] :
( ( ( subset @ ( cartesian_product2 @ SV678 @ SV978 ) @ ( cartesian_product2 @ SV861 @ SV978 ) )
= $true )
| ( ( subset @ SV678 @ SV861 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4828]) ).
thf(4969,plain,
! [SV862: $i,SV678: $i,SV979: $i] :
( ( ( subset @ ( cartesian_product2 @ SV979 @ SV678 ) @ ( cartesian_product2 @ SV979 @ SV862 ) )
= $true )
| ( ( subset @ SV678 @ SV862 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4829]) ).
thf(4970,plain,
! [SV804: $i,SV863: $i] :
( ( ( ~ ( ! [SY1497: $i] :
( ~ ( in @ ( sK15_C @ SV863 @ SV804 ) @ SY1497 )
| ~ ( in @ SY1497 @ SV804 ) )
| ~ ( in @ ( sK15_C @ SV863 @ SV804 ) @ SV863 ) ) )
= $false )
| ( ( SV863
= ( union @ SV804 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4830]) ).
thf(4971,plain,
! [SV804: $i,SV863: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK15_C @ SV863 @ SV804 ) @ ( sK16_SY398 @ SV863 @ SV804 ) )
| ~ ( in @ ( sK16_SY398 @ SV863 @ SV804 ) @ SV804 ) )
| ( in @ ( sK15_C @ SV863 @ SV804 ) @ SV863 ) ) )
= $false )
| ( ( SV863
= ( union @ SV804 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4830]) ).
thf(4972,plain,
! [SV864: $i,SV805: $i] :
( ( ( ~ ! [SY1498: $i] :
( ! [SY1428: $i] :
( ~ ( in @ SY1498 @ SY1428 )
| ~ ( in @ SY1428 @ SV805 ) )
| ( in @ SY1498 @ SV864 ) )
| ~ ! [SY1500: $i] :
( ~ ( in @ SY1500 @ SV864 )
| ~ ( ~ ( in @ SY1500 @ ( sK14_D @ SY1500 @ SV864 @ SV805 ) )
| ~ ( in @ ( sK14_D @ SY1500 @ SV864 @ SV805 ) @ SV805 ) ) ) )
= $false )
| ( ( SV864
= ( union @ SV805 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4831]) ).
thf(4973,plain,
! [SV679: $i,SV946: $i] :
( ( ( ~ ( ~ ( ! [SY1580: $i] :
~ ( in @ ( ordered_pair @ ( sK63_C @ SV946 @ SV679 ) @ SY1580 ) @ SV679 )
| ~ ( in @ ( sK63_C @ SV946 @ SV679 ) @ SV946 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_C @ SV946 @ SV679 ) @ ( sK64_SY419 @ SV946 @ SV679 ) ) @ SV679 )
| ( in @ ( sK63_C @ SV946 @ SV679 ) @ SV946 ) ) ) )
= $true )
| ( ( SV946
= ( relation_dom @ SV679 ) )
= $true )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4832]) ).
thf(4974,plain,
! [SV679: $i,SV947: $i] :
( ( ( ( SV947
!= ( relation_dom @ SV679 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1581: $i] :
( ! [SY1312: $i] :
~ ( in @ ( ordered_pair @ SY1581 @ SY1312 ) @ SV679 )
| ( in @ SY1581 @ SV947 ) )
| ~ ! [SY1583: $i] :
( ~ ( in @ SY1583 @ SV947 )
| ( in @ ( ordered_pair @ SY1583 @ ( sK62_D @ SY1583 @ SV947 @ SV679 ) ) @ SV679 ) ) ) )
= $true )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4833]) ).
thf(4975,plain,
! [SV865: $i,SV680: $i,SV908: $i] :
( ( ( relation @ SV908 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV680 @ SV865 ) @ SV908 )
| ( in @ SV680 @ ( relation_field @ SV908 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4834]) ).
thf(4976,plain,
! [SV866: $i,SV680: $i,SV909: $i] :
( ( ( relation @ SV909 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV680 @ SV866 ) @ SV909 )
| ( in @ SV866 @ ( relation_field @ SV909 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4835]) ).
thf(4977,plain,
! [SV806: $i,SV867: $i] :
( ( ( ~ ( ~ ( ( ( sK44_C @ SV867 @ SV806 )
!= ( sK45_SY414 @ SV867 @ SV806 ) )
| ~ ( in @ ( sK44_C @ SV867 @ SV806 ) @ SV806 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 ) )
| ~ ~ ( ~ ( ( ( sK44_C @ SV867 @ SV806 )
= ( sK45_SY414 @ SV867 @ SV806 ) )
| ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 ) )
| ~ ( ( in @ ( sK44_C @ SV867 @ SV806 ) @ SV806 )
| ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 ) ) ) ) )
= $true )
| ( ( SV867
= ( identity_relation @ SV806 ) )
= $true )
| ( ( relation @ SV867 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4836]) ).
thf(4978,plain,
! [SV807: $i,SV868: $i] :
( ( ( ( SV868
!= ( identity_relation @ SV807 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1503: $i,SY1504: $i] :
( ( SY1503 != SY1504 )
| ~ ( in @ SY1503 @ SV807 )
| ( in @ ( ordered_pair @ SY1503 @ SY1504 ) @ SV868 ) )
| ~ ~ ( ~ ! [SY1505: $i,SY1506: $i] :
( ~ ( in @ ( ordered_pair @ SY1505 @ SY1506 ) @ SV868 )
| ( SY1505 = SY1506 ) )
| ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
~ ( in @ ( ordered_pair @ SY1507 @ SY1508 ) @ SV868 )
| ( in @ SY1507 @ SV807 ) ) ) ) )
= $true )
| ( ( relation @ SV868 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4837]) ).
thf(4979,plain,
! [SV681: $i,SV948: $i,SV980: $i] :
( ( ( ~ ( relation @ SV980 )
| ~ ( ~ ( ~ ( in @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ SV948 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV681 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 ) )
| ~ ~ ( ~ ( ( in @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ SV948 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV681 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 ) ) ) )
| ( SV980
= ( relation_dom_restriction @ SV681 @ SV948 ) ) )
= $true )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4838]) ).
thf(4980,plain,
! [SV949: $i,SV681: $i,SV981: $i] :
( ( ( ~ ( relation @ SV981 )
| ( SV981
!= ( relation_dom_restriction @ SV681 @ SV949 ) )
| ~ ( ~ ! [SY1625: $i,SY1626: $i] :
( ~ ( in @ SY1625 @ SV949 )
| ~ ( in @ ( ordered_pair @ SY1625 @ SY1626 ) @ SV681 )
| ( in @ ( ordered_pair @ SY1625 @ SY1626 ) @ SV981 ) )
| ~ ~ ( ~ ! [SY1627: $i] :
( ! [SY1628: $i] :
~ ( in @ ( ordered_pair @ SY1627 @ SY1628 ) @ SV981 )
| ( in @ SY1627 @ SV949 ) )
| ~ ! [SY1629: $i,SY1630: $i] :
( ~ ( in @ ( ordered_pair @ SY1629 @ SY1630 ) @ SV981 )
| ( in @ ( ordered_pair @ SY1629 @ SY1630 ) @ SV681 ) ) ) ) )
= $true )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4839]) ).
thf(4981,plain,
! [SV808: $i,SV869: $i] :
( ( ( ~ ( ( ( sK30_C @ SV869 @ SV808 )
!= SV808 )
| ~ ( in @ ( sK30_C @ SV869 @ SV808 ) @ SV869 ) ) )
= $false )
| ( ( SV869
= ( singleton @ SV808 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4840]) ).
thf(4982,plain,
! [SV808: $i,SV869: $i] :
( ( ( ~ ( ( ( sK30_C @ SV869 @ SV808 )
= SV808 )
| ( in @ ( sK30_C @ SV869 @ SV808 ) @ SV869 ) ) )
= $false )
| ( ( SV869
= ( singleton @ SV808 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4840]) ).
thf(4983,plain,
! [SV870: $i,SV809: $i] :
( ( ( ~ ! [SY1509: $i] :
( ( SY1509 != SV809 )
| ( in @ SY1509 @ SV870 ) )
| ~ ! [SY1510: $i] :
( ~ ( in @ SY1510 @ SV870 )
| ( SY1510 = SV809 ) ) )
= $false )
| ( ( SV870
= ( singleton @ SV809 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4841]) ).
thf(4984,plain,
! [SV871: $i,SV682: $i,SV910: $i] :
( ( ( relation @ SV910 )
= $false )
| ( ( ! [SY1541: $i] :
( ~ ( in @ SY1541 @ ( relation_dom @ SV910 ) )
| ~ ( in @ ( ordered_pair @ SY1541 @ SV682 ) @ SV910 )
| ~ ( in @ SY1541 @ SV871 ) )
| ( in @ SV682 @ ( relation_image @ SV910 @ SV871 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4842]) ).
thf(4985,plain,
! [SV872: $i,SV682: $i,SV911: $i] :
( ( ( relation @ SV911 )
= $false )
| ( ( ~ ( in @ SV682 @ ( relation_image @ SV911 @ SV872 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK52_D @ SV911 @ SV872 @ SV682 ) @ ( relation_dom @ SV911 ) )
| ~ ( in @ ( ordered_pair @ ( sK52_D @ SV911 @ SV872 @ SV682 ) @ SV682 ) @ SV911 ) )
| ~ ( in @ ( sK52_D @ SV911 @ SV872 @ SV682 ) @ SV872 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4843]) ).
thf(4986,plain,
! [SV683: $i,SV950: $i] :
( ( ( ~ ( relation @ SV950 ) )
= $true )
| ( ( ~ ( subset @ SV683 @ SV950 )
| ( subset @ ( relation_dom @ SV683 ) @ ( relation_dom @ SV950 ) ) )
= $true )
| ( ( relation @ SV683 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4844]) ).
thf(4987,plain,
! [SV683: $i,SV951: $i] :
( ( ( ~ ( relation @ SV951 ) )
= $true )
| ( ( ~ ( subset @ SV683 @ SV951 )
| ( subset @ ( relation_rng @ SV683 ) @ ( relation_rng @ SV951 ) ) )
= $true )
| ( ( relation @ SV683 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4845]) ).
thf(4988,plain,
! [SV873: $i,SV810: $i] :
( ( ( empty @ SV810 )
= $false )
| ( ( ~ ( relation @ SV873 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV810 @ SV873 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4846]) ).
thf(4989,plain,
! [SV874: $i,SV811: $i] :
( ( ( empty @ SV811 )
= $false )
| ( ( ~ ( relation @ SV874 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV811 @ SV874 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4847]) ).
thf(4990,plain,
! [SV684: $i,SV952: $i] :
( ( ( ~ ( relation @ SV952 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV684 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV952 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV684 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV952 ) ) )
| ( SV684 = SV952 ) )
= $true )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4848]) ).
thf(4991,plain,
! [SV684: $i,SV953: $i] :
( ( ( ~ ( relation @ SV953 ) )
= $true )
| ( ( ( SV684 != SV953 )
| ~ ( ~ ! [SY1592: $i,SY1593: $i] :
( ~ ( in @ ( ordered_pair @ SY1592 @ SY1593 ) @ SV684 )
| ( in @ ( ordered_pair @ SY1592 @ SY1593 ) @ SV953 ) )
| ~ ! [SY1594: $i,SY1595: $i] :
( ~ ( in @ ( ordered_pair @ SY1594 @ SY1595 ) @ SV953 )
| ( in @ ( ordered_pair @ SY1594 @ SY1595 ) @ SV684 ) ) ) )
= $true )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4849]) ).
thf(4992,plain,
! [SV685: $i,SV875: $i] :
( ( ( subset @ SV875 @ ( sK2_B @ SV685 ) )
= $false )
| ( ( are_equipotent @ SV875 @ ( sK2_B @ SV685 ) )
= $true )
| ( ( in @ SV875 @ ( sK2_B @ SV685 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4850]) ).
thf(4993,plain,
! [SV685: $i,SV982: $i] :
( ( ~ ( ~ ! [SY1631: $i] :
( ~ ( subset @ SY1631 @ SV982 )
| ( in @ SY1631 @ ( sK3_SY386 @ SV982 @ SV685 ) ) )
| ~ ( in @ ( sK3_SY386 @ SV982 @ SV685 ) @ ( sK2_B @ SV685 ) ) )
| ~ ( in @ SV982 @ ( sK2_B @ SV685 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4851]) ).
thf(4994,plain,
! [SV685: $i] :
( ( ~ ! [SY1344: $i,SY1345: $i] :
( ~ ( in @ SY1344 @ ( sK2_B @ SV685 ) )
| ~ ( subset @ SY1345 @ SY1344 )
| ( in @ SY1345 @ ( sK2_B @ SV685 ) ) )
| ~ ( in @ SV685 @ ( sK2_B @ SV685 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4852]) ).
thf(4995,plain,
! [SV876: $i,SV812: $i] :
( ( ( subset @ SV812 @ SV876 )
= $false )
| ( ( ~ ( subset @ SV876 @ SV812 ) )
= $true )
| ( ( SV812 = SV876 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4853]) ).
thf(4996,plain,
! [SV983: $i,SV954: $i] :
( ( ( SV954 != SV983 )
| ( subset @ SV954 @ SV983 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4854]) ).
thf(4997,plain,
! [SV984: $i,SV955: $i] :
( ( ( SV955 != SV984 )
| ( subset @ SV984 @ SV955 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4855]) ).
thf(4998,plain,
! [SV813: $i,SV877: $i] :
( ( ( ~ ( ~ ( in @ ( sK28_C @ SV877 @ SV813 ) @ SV877 )
| ~ ( subset @ ( sK28_C @ SV877 @ SV813 ) @ SV813 ) ) )
= $false )
| ( ( SV877
= ( powerset @ SV813 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4856]) ).
thf(4999,plain,
! [SV813: $i,SV877: $i] :
( ( ( ~ ( ( in @ ( sK28_C @ SV877 @ SV813 ) @ SV877 )
| ( subset @ ( sK28_C @ SV877 @ SV813 ) @ SV813 ) ) )
= $false )
| ( ( SV877
= ( powerset @ SV813 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4856]) ).
thf(5000,plain,
! [SV814: $i,SV878: $i] :
( ( ( ~ ! [SY1514: $i] :
( ~ ( in @ SY1514 @ SV878 )
| ( subset @ SY1514 @ SV814 ) )
| ~ ! [SY1515: $i] :
( ~ ( subset @ SY1515 @ SV814 )
| ( in @ SY1515 @ SV878 ) ) )
= $false )
| ( ( SV878
= ( powerset @ SV814 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4857]) ).
thf(5001,plain,
! [SV879: $i,SV815: $i] :
( ( ( SV815 = empty_set )
= $true )
| ( ( SV815
= ( singleton @ SV879 ) )
= $true )
| ( ( subset @ SV815 @ ( singleton @ SV879 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4858]) ).
thf(5002,plain,
! [SV956: $i] :
( ( ( ( SV956 != empty_set ) )
= $true )
| ( ( ! [SY1598: $i] : ( subset @ SV956 @ ( singleton @ SY1598 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4859]) ).
thf(5003,plain,
! [SV985: $i,SV957: $i] :
( ( ( SV957
!= ( singleton @ SV985 ) )
| ( subset @ SV957 @ ( singleton @ SV985 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4860]) ).
thf(5004,plain,
! [SV816: $i] :
( ( ( ( relation_dom @ SV816 )
= empty_set )
= $false )
| ( ( SV816 = empty_set )
= $true )
| ( ( relation @ SV816 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4861]) ).
thf(5005,plain,
! [SV817: $i] :
( ( ( ( relation_rng @ SV817 )
= empty_set )
= $false )
| ( ( SV817 = empty_set )
= $true )
| ( ( relation @ SV817 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4862]) ).
thf(5006,plain,
! [SV818: $i,SV880: $i] :
( ( ( function @ SV880 )
= $false )
| ( ( ~ ( relation @ SV880 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK50_C @ SV880 @ SV818 ) @ SV818 )
| ~ ( ( ( apply @ SV880 @ ( sK50_C @ SV880 @ SV818 ) )
!= ( sK50_C @ SV880 @ SV818 ) ) ) )
| ( ( relation_dom @ SV880 )
!= SV818 )
| ( SV880
= ( identity_relation @ SV818 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4863]) ).
thf(5007,plain,
! [SV958: $i,SV986: $i] :
( ( ~ ( function @ SV986 )
| ~ ( relation @ SV986 )
| ( SV986
!= ( identity_relation @ SV958 ) )
| ! [SY1632: $i] :
( ~ ( in @ SY1632 @ SV958 )
| ( ( apply @ SV986 @ SY1632 )
= SY1632 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4864]) ).
thf(5008,plain,
! [SV959: $i,SV987: $i] :
( ( ~ ( function @ SV987 )
| ~ ( relation @ SV987 )
| ( SV987
!= ( identity_relation @ SV959 ) )
| ( ( relation_dom @ SV987 )
= SV959 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4865]) ).
thf(5009,plain,
! [SV821: $i,SV883: $i] :
( ( ( ~ ( in @ ( sK18_C @ SV883 @ SV821 ) @ SV821 ) )
= $false )
| ( ( subset @ SV821 @ SV883 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4868]) ).
thf(5010,plain,
! [SV821: $i,SV883: $i] :
( ( ( ~ ~ ( in @ ( sK18_C @ SV883 @ SV821 ) @ SV883 ) )
= $false )
| ( ( subset @ SV821 @ SV883 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4868]) ).
thf(5011,plain,
! [SV884: $i,SV822: $i,SV988: $i] :
( ( ( ~ ( in @ SV988 @ SV822 )
| ( in @ SV988 @ SV884 ) )
= $true )
| ( ( subset @ SV822 @ SV884 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4869]) ).
thf(5012,plain,
! [SV710: $i,SV608: $i,SV912: $i] :
( ( ( ~ ( function @ SV912 ) )
= $true )
| ( ( ~ ( relation @ SV912 ) )
= $true )
| ( ( ~ ( in @ SV608 @ ( relation_dom @ ( relation_composition @ SV912 @ SV710 ) ) )
| ( ( apply @ ( relation_composition @ SV912 @ SV710 ) @ SV608 )
= ( apply @ SV710 @ ( apply @ SV912 @ SV608 ) ) ) )
= $true )
| ( ( function @ SV710 )
= $false )
| ( ( relation @ SV710 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4874]) ).
thf(5013,plain,
! [SV711: $i,SV609: $i,SV913: $i] :
( ( ( ~ ( function @ SV913 ) )
= $true )
| ( ( ~ ( relation @ SV913 ) )
= $true )
| ( ( ~ ( in @ SV609 @ ( relation_dom @ SV711 ) )
| ( ( apply @ ( relation_composition @ SV711 @ SV913 ) @ SV609 )
= ( apply @ SV913 @ ( apply @ SV711 @ SV609 ) ) ) )
= $true )
| ( ( function @ SV711 )
= $false )
| ( ( relation @ SV711 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4875]) ).
thf(5014,plain,
! [SV652: $i,SV825: $i,SV885: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV652 )
| ~ ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV825 )
| ~ ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV885 ) ) )
= $false )
| ( ( SV885
= ( set_intersection2 @ SV652 @ SV825 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4876]) ).
thf(5015,plain,
! [SV652: $i,SV825: $i,SV885: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV652 )
| ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV885 ) )
| ~ ( ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV825 )
| ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV885 ) ) ) )
= $false )
| ( ( SV885
= ( set_intersection2 @ SV652 @ SV825 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4876]) ).
thf(5016,plain,
! [SV886: $i,SV826: $i,SV652: $i] :
( ( ( ~ ! [SY1517: $i] :
( ~ ( in @ SY1517 @ SV652 )
| ~ ( in @ SY1517 @ SV826 )
| ( in @ SY1517 @ SV886 ) )
| ~ ~ ( ~ ! [SY1518: $i] :
( ~ ( in @ SY1518 @ SV886 )
| ( in @ SY1518 @ SV652 ) )
| ~ ! [SY1519: $i] :
( ~ ( in @ SY1519 @ SV886 )
| ( in @ SY1519 @ SV826 ) ) ) )
= $false )
| ( ( SV886
= ( set_intersection2 @ SV652 @ SV826 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4877]) ).
thf(5017,plain,
! [SV653: $i] :
( ( ( ~ ! [SY1140: $i] :
( ~ ( function @ SY1140 )
| ~ ( relation @ SY1140 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SY1140 @ SV653 )
= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ( ( sK70_C @ SY1140 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY1140 @ SV653 )
= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY1140 @ SV653 )
= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ( ( sK71_SY424 @ SY1140 @ SV653 )
!= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK70_C @ SY1140 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK71_SY424 @ SY1140 @ SV653 )
!= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY1140 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK70_C @ SY1140 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SY1140 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SY1140 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK71_SY424 @ SY1140 @ SV653 )
!= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ( ( relation_dom @ SY1140 )
!= ( relation_rng @ SV653 ) )
| ( SY1140
= ( function_inverse @ SV653 ) ) ) )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4880]) ).
thf(5018,plain,
! [SV653: $i] :
( ( ( ~ ~ ( ~ ! [SY1141: $i] :
( ~ ( function @ SY1141 )
| ~ ( relation @ SY1141 )
| ( SY1141
!= ( function_inverse @ SV653 ) )
| ~ ( ~ ~ ( ~ ! [SY1142: $i,SY1143: $i] :
( ( SY1143
!= ( apply @ SY1141 @ SY1142 ) )
| ~ ( in @ SY1142 @ ( relation_rng @ SV653 ) )
| ( SY1142
= ( apply @ SV653 @ SY1143 ) ) )
| ~ ! [SY1144: $i,SY1145: $i] :
( ( SY1145
!= ( apply @ SY1141 @ SY1144 ) )
| ~ ( in @ SY1144 @ ( relation_rng @ SV653 ) )
| ( in @ SY1145 @ ( relation_dom @ SV653 ) ) ) )
| ~ ~ ( ~ ! [SY1146: $i,SY1147: $i] :
( ( SY1146
!= ( apply @ SV653 @ SY1147 ) )
| ~ ( in @ SY1147 @ ( relation_dom @ SV653 ) )
| ( SY1147
= ( apply @ SY1141 @ SY1146 ) ) )
| ~ ! [SY1148: $i] :
( ! [SY1149: $i] :
( ( SY1148
!= ( apply @ SV653 @ SY1149 ) )
| ~ ( in @ SY1149 @ ( relation_dom @ SV653 ) ) )
| ( in @ SY1148 @ ( relation_rng @ SV653 ) ) ) ) ) )
| ~ ! [SY1150: $i] :
( ~ ( function @ SY1150 )
| ~ ( relation @ SY1150 )
| ( SY1150
!= ( function_inverse @ SV653 ) )
| ( ( relation_dom @ SY1150 )
= ( relation_rng @ SV653 ) ) ) ) )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4880]) ).
thf(5019,plain,
! [SV914: $i,SV989: $i] :
( ( ( ~ ( element @ SV989 @ SV914 )
| ( in @ SV989 @ SV914 ) )
= $true )
| ( ( empty @ SV914 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4881]) ).
thf(5020,plain,
! [SV915: $i,SV990: $i] :
( ( ( ~ ( in @ SV990 @ SV915 )
| ( element @ SV990 @ SV915 ) )
= $true )
| ( ( empty @ SV915 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4882]) ).
thf(5021,plain,
! [SV916: $i] :
( ( ( empty @ SV916 )
= $false )
| ( ( ! [SY1544: $i] :
( ~ ( element @ SY1544 @ SV916 )
| ( empty @ SY1544 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4883]) ).
thf(5022,plain,
! [SV917: $i] :
( ( ( empty @ SV917 )
= $false )
| ( ( ! [SY1545: $i] :
( ~ ( empty @ SY1545 )
| ( element @ SY1545 @ SV917 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4884]) ).
thf(5023,plain,
! [SV918: $i] :
( ( ( SV918 = empty_set )
= $false )
| ( ( ! [SY1546: $i] : ( subset @ SV918 @ ( singleton @ SY1546 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4886]) ).
thf(5024,plain,
! [SV960: $i,SV919: $i] :
( ( ( ( SV919
!= ( singleton @ SV960 ) ) )
= $true )
| ( ( subset @ SV919 @ ( singleton @ SV960 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4887]) ).
thf(5025,plain,
! [SV739: $i,SV887: $i,SV654: $i,SV920: $i] :
( ( ( relation @ SV920 )
= $false )
| ( ( ~ ( in @ SV654 @ SV887 )
| ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ SV920 )
| ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SV887 ) @ SV920 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4888]) ).
thf(5026,plain,
! [SV991: $i,SV739: $i,SV654: $i] :
( ( ! [SY1633: $i] :
( ~ ( relation @ SY1633 )
| ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SV991 ) @ SY1633 ) )
| ( in @ SV654 @ SV991 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4889]) ).
thf(5027,plain,
! [SV992: $i,SV739: $i,SV654: $i] :
( ( ! [SY1634: $i] :
( ~ ( relation @ SY1634 )
| ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SV992 ) @ SY1634 ) )
| ( in @ ( ordered_pair @ SV654 @ SV739 ) @ SY1634 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4890]) ).
thf(5028,plain,
! [SV655: $i,SV740: $i,SV961: $i] :
( ( ( ~ ( relation @ SV961 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) @ SV655 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV740 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 ) )
| ~ ~ ( ~ ( ( in @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) @ SV655 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV740 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 ) ) ) )
| ( SV961
= ( relation_rng_restriction @ SV655 @ SV740 ) ) )
= $true )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4891]) ).
thf(5029,plain,
! [SV740: $i,SV655: $i,SV962: $i] :
( ( ( ~ ( relation @ SV962 ) )
= $true )
| ( ( ( SV962
!= ( relation_rng_restriction @ SV655 @ SV740 ) )
| ~ ( ~ ! [SY1603: $i,SY1604: $i] :
( ~ ( in @ SY1604 @ SV655 )
| ~ ( in @ ( ordered_pair @ SY1603 @ SY1604 ) @ SV740 )
| ( in @ ( ordered_pair @ SY1603 @ SY1604 ) @ SV962 ) )
| ~ ~ ( ~ ! [SY1605: $i,SY1606: $i] :
( ~ ( in @ ( ordered_pair @ SY1605 @ SY1606 ) @ SV962 )
| ( in @ SY1606 @ SV655 ) )
| ~ ! [SY1607: $i,SY1608: $i] :
( ~ ( in @ ( ordered_pair @ SY1607 @ SY1608 ) @ SV962 )
| ( in @ ( ordered_pair @ SY1607 @ SY1608 ) @ SV740 ) ) ) ) )
= $true )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4892]) ).
thf(5030,plain,
! [SV963: $i,SV888: $i,SV741: $i,SV656: $i] :
( ( ( ( ordered_pair @ SV656 @ SV741 )
= ( ordered_pair @ SV888 @ SV963 ) )
= $false )
| ( ( SV656 = SV888 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4893]) ).
thf(5031,plain,
! [SV921: $i,SV889: $i,SV741: $i,SV656: $i] :
( ( ( ( ordered_pair @ SV656 @ SV741 )
= ( ordered_pair @ SV889 @ SV921 ) )
= $false )
| ( ( SV741 = SV921 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4894]) ).
thf(5032,plain,
! [SV657: $i,SV922: $i,SV964: $i] :
( ( ( ~ ( ~ ( ! [SY1609: $i] :
( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SY1609 ) @ SV657 )
| ~ ( in @ SY1609 @ SV922 ) )
| ~ ( in @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SV964 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ ( sK36_SY409 @ SV964 @ SV922 @ SV657 ) ) @ SV657 )
| ~ ( in @ ( sK36_SY409 @ SV964 @ SV922 @ SV657 ) @ SV922 ) )
| ( in @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SV964 ) ) ) )
= $true )
| ( ( SV964
= ( relation_inverse_image @ SV657 @ SV922 ) )
= $true )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4895]) ).
thf(5033,plain,
! [SV923: $i,SV657: $i,SV965: $i] :
( ( ( ( SV965
!= ( relation_inverse_image @ SV657 @ SV923 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1610: $i] :
( ! [SY1552: $i] :
( ~ ( in @ ( ordered_pair @ SY1610 @ SY1552 ) @ SV657 )
| ~ ( in @ SY1552 @ SV923 ) )
| ( in @ SY1610 @ SV965 ) )
| ~ ! [SY1612: $i] :
( ~ ( in @ SY1612 @ SV965 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1612 @ ( sK34_E @ SY1612 @ SV965 @ SV923 @ SV657 ) ) @ SV657 )
| ~ ( in @ ( sK34_E @ SY1612 @ SV965 @ SV923 @ SV657 ) @ SV923 ) ) ) ) )
= $true )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4896]) ).
thf(5034,plain,
! [SV658: $i,SV924: $i,SV966: $i] :
( ( ( ~ ( ~ ( ! [SY1613: $i] :
( ~ ( in @ ( ordered_pair @ SY1613 @ ( sK38_D @ SV966 @ SV924 @ SV658 ) ) @ SV658 )
| ~ ( in @ SY1613 @ SV924 ) )
| ~ ( in @ ( sK38_D @ SV966 @ SV924 @ SV658 ) @ SV966 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SV966 @ SV924 @ SV658 ) @ ( sK38_D @ SV966 @ SV924 @ SV658 ) ) @ SV658 )
| ~ ( in @ ( sK39_SY411 @ SV966 @ SV924 @ SV658 ) @ SV924 ) )
| ( in @ ( sK38_D @ SV966 @ SV924 @ SV658 ) @ SV966 ) ) ) )
= $true )
| ( ( SV966
= ( relation_image @ SV658 @ SV924 ) )
= $true )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4897]) ).
thf(5035,plain,
! [SV925: $i,SV658: $i,SV967: $i] :
( ( ( ( SV967
!= ( relation_image @ SV658 @ SV925 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1614: $i] :
( ! [SY1558: $i] :
( ~ ( in @ ( ordered_pair @ SY1558 @ SY1614 ) @ SV658 )
| ~ ( in @ SY1558 @ SV925 ) )
| ( in @ SY1614 @ SV967 ) )
| ~ ! [SY1616: $i] :
( ~ ( in @ SY1616 @ SV967 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SY1616 @ SV967 @ SV925 @ SV658 ) @ SY1616 ) @ SV658 )
| ~ ( in @ ( sK37_E @ SY1616 @ SV967 @ SV925 @ SV658 ) @ SV925 ) ) ) ) )
= $true )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4898]) ).
thf(5036,plain,
! [SV968: $i,SV926: $i] :
( ( ( ~ ( proper_subset @ SV926 @ SV968 ) )
= $true )
| ( ( ( SV926 != SV968 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4900]) ).
thf(5037,plain,
! [SV969: $i,SV927: $i] :
( ( ( ~ ( proper_subset @ SV927 @ SV969 ) )
= $true )
| ( ( subset @ SV927 @ SV969 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4901]) ).
thf(5038,plain,
! [SV778: $i,SV835: $i] :
( ( ( relation @ SV835 )
= $false )
| ( ( empty @ SV778 )
= $false )
| ( ( empty @ ( relation_composition @ SV835 @ SV778 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4902]) ).
thf(5039,plain,
! [SV779: $i,SV836: $i] :
( ( ( relation @ SV836 )
= $false )
| ( ( empty @ SV779 )
= $false )
| ( ( relation @ ( relation_composition @ SV836 @ SV779 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4903]) ).
thf(5040,plain,
! [SV928: $i] :
( ( ( ~ ( empty @ SV928 )
| ~ ( relation @ SV928 ) )
= $true )
| ( ( ~ ( function @ SV928 ) )
= $true )
| ( ( function @ SV928 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4904]) ).
thf(5041,plain,
! [SV929: $i] :
( ( ( ~ ( empty @ SV929 )
| ~ ( relation @ SV929 ) )
= $true )
| ( ( ~ ( function @ SV929 ) )
= $true )
| ( ( relation @ SV929 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4905]) ).
thf(5042,plain,
! [SV780: $i] :
( ( ( relation @ SV780 )
= $false )
| ( ( empty @ SV780 )
= $false )
| ( ( ~ ( function @ SV780 ) )
= $true )
| ( ( one_to_one @ SV780 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4906]) ).
thf(5043,plain,
! [SV993: $i,SV781: $i] :
( ( ( ! [SY1635: $i] :
( ( sK69_B @ SV781 )
!= ( ordered_pair @ SV993 @ SY1635 ) ) )
= $true )
| ( ( relation @ SV781 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4907]) ).
thf(5044,plain,
! [SV782: $i,SV930: $i] :
( ( ( in @ SV930 @ SV782 )
= $false )
| ( ( SV930
= ( ordered_pair @ ( sK67_C @ SV930 @ SV782 ) @ ( sK68_SY421 @ SV930 @ SV782 ) ) )
= $true )
| ( ( relation @ SV782 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4909]) ).
thf(5045,plain,
! [SV837: $i,SV890: $i,SV659: $i] :
( ( ( in @ SV659 @ SV890 )
= $false )
| ( ( ~ ( in @ SV837 @ SV890 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV659 @ SV837 ) @ SV890 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4910]) ).
thf(5046,plain,
! [SV994: $i,SV970: $i,SV659: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV659 @ SV970 ) @ SV994 )
| ( in @ SV659 @ SV994 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4911]) ).
thf(5047,plain,
! [SV995: $i,SV971: $i,SV659: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV659 @ SV971 ) @ SV995 )
| ( in @ SV971 @ SV995 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4912]) ).
thf(5048,plain,
! [SV660: $i,SV783: $i] :
( ( ( ! [SY1405: $i] :
( ~ ( relation @ SY1405 )
| ~ ( ~ ( ! [SY1406: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY1405 @ SV783 @ SV660 ) @ SY1406 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1406 @ ( sK9_SY391 @ SY1405 @ SV783 @ SV660 ) ) @ SV783 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SY1405 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SY1405 @ SV783 @ SV660 ) ) @ SY1405 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY1405 @ SV783 @ SV660 ) @ ( sK10_SY395 @ SY1405 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SY1405 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SY1405 @ SV783 @ SV660 ) ) @ SV783 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SY1405 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SY1405 @ SV783 @ SV660 ) ) @ SY1405 ) ) )
| ( SY1405
= ( relation_composition @ SV660 @ SV783 ) ) ) )
= $true )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4913]) ).
thf(5049,plain,
! [SV783: $i,SV660: $i] :
( ( ( ! [SY1407: $i] :
( ~ ( relation @ SY1407 )
| ( SY1407
!= ( relation_composition @ SV660 @ SV783 ) )
| ~ ( ~ ! [SY1408: $i,SY1409: $i] :
( ! [SY1410: $i] :
( ~ ( in @ ( ordered_pair @ SY1408 @ SY1410 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1410 @ SY1409 ) @ SV783 ) )
| ( in @ ( ordered_pair @ SY1408 @ SY1409 ) @ SY1407 ) )
| ~ ! [SY1411: $i,SY1412: $i] :
( ~ ( in @ ( ordered_pair @ SY1411 @ SY1412 ) @ SY1407 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1411 @ ( sK7_F @ SY1412 @ SY1411 @ SY1407 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY1412 @ SY1411 @ SY1407 @ SV783 @ SV660 ) @ SY1412 ) @ SV783 ) ) ) ) ) )
= $true )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4914]) ).
thf(5050,plain,
! [SV661: $i,SV932: $i] :
( ( ( ~ ( ! [SY1562: $i] :
~ ( in @ ( ordered_pair @ SY1562 @ ( sK60_C @ SV932 @ SV661 ) ) @ SV661 )
| ~ ( in @ ( sK60_C @ SV932 @ SV661 ) @ SV932 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK61_SY417 @ SV932 @ SV661 ) @ ( sK60_C @ SV932 @ SV661 ) ) @ SV661 )
| ( in @ ( sK60_C @ SV932 @ SV661 ) @ SV932 ) ) )
= $false )
| ( ( SV932
= ( relation_rng @ SV661 ) )
= $true )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4916]) ).
thf(5051,plain,
! [SV661: $i,SV933: $i] :
( ( ( SV933
= ( relation_rng @ SV661 ) )
= $false )
| ( ( ~ ( ~ ! [SY1563: $i] :
( ! [SY1207: $i] :
~ ( in @ ( ordered_pair @ SY1207 @ SY1563 ) @ SV661 )
| ( in @ SY1563 @ SV933 ) )
| ~ ! [SY1565: $i] :
( ~ ( in @ SY1565 @ SV933 )
| ( in @ ( ordered_pair @ ( sK59_D @ SY1565 @ SV933 @ SV661 ) @ SY1565 ) @ SV661 ) ) ) )
= $true )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4917]) ).
thf(5052,plain,
! [SV662: $i,SV838: $i,SV891: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV662 )
| ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV838 )
| ~ ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV891 ) ) )
= $false )
| ( ( SV891
= ( set_difference @ SV662 @ SV838 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4918]) ).
thf(5053,plain,
! [SV662: $i,SV838: $i,SV891: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV662 )
| ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV891 ) )
| ~ ( ~ ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV838 )
| ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV891 ) ) ) )
= $false )
| ( ( SV891
= ( set_difference @ SV662 @ SV838 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4918]) ).
thf(5054,plain,
! [SV892: $i,SV839: $i,SV662: $i] :
( ( ( ~ ! [SY1523: $i] :
( ~ ( in @ SY1523 @ SV662 )
| ( in @ SY1523 @ SV839 )
| ( in @ SY1523 @ SV892 ) )
| ~ ~ ( ~ ! [SY1524: $i] :
( ~ ( in @ SY1524 @ SV892 )
| ( in @ SY1524 @ SV662 ) )
| ~ ! [SY1525: $i] :
( ~ ( in @ SY1525 @ SV892 )
| ~ ( in @ SY1525 @ SV839 ) ) ) )
= $false )
| ( ( SV892
= ( set_difference @ SV662 @ SV839 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4919]) ).
thf(5055,plain,
! [SV840: $i,SV790: $i] :
( ( ( ~ ( function @ SV790 ) )
= $true )
| ( ( ~ ( relation @ SV790 ) )
= $true )
| ( ( ~ ( relation @ SV840 ) )
= $true )
| ( ( ~ ( function @ SV840 ) )
= $true )
| ( ( function @ ( relation_composition @ SV790 @ SV840 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4920]) ).
thf(5056,plain,
! [SV841: $i,SV791: $i] :
( ( ( ~ ( function @ SV791 ) )
= $true )
| ( ( ~ ( relation @ SV791 ) )
= $true )
| ( ( ~ ( relation @ SV841 ) )
= $true )
| ( ( ~ ( function @ SV841 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV791 @ SV841 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4921]) ).
thf(5057,plain,
! [SV893: $i,SV842: $i,SV663: $i] :
( ( ( ~ ( in @ SV663 @ SV842 )
| ~ ( in @ SV663 @ ( relation_rng @ SV893 ) ) )
= $true )
| ( ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SV842 @ SV893 ) ) )
= $true )
| ( ( relation @ SV893 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4922]) ).
thf(5058,plain,
! [SV972: $i,SV663: $i,SV996: $i] :
( ( ~ ( relation @ SV996 )
| ~ ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SV972 @ SV996 ) ) )
| ( in @ SV663 @ SV972 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4923]) ).
thf(5059,plain,
! [SV973: $i,SV663: $i,SV997: $i] :
( ( ~ ( relation @ SV997 )
| ~ ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SV973 @ SV997 ) ) )
| ( in @ SV663 @ ( relation_rng @ SV997 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4924]) ).
thf(5060,plain,
! [SV664: $i] :
( ( ( ~ ! [SY1222: $i] :
( ~ ( in @ SY1222 @ ( relation_dom @ SV664 ) )
| ! [SY1223: $i] :
( ( SY1223
!= ( apply @ SV664 @ SY1222 ) )
| ( in @ ( ordered_pair @ SY1222 @ SY1223 ) @ SV664 ) ) )
| ~ ! [SY1224: $i] :
( ~ ( in @ SY1224 @ ( relation_dom @ SV664 ) )
| ! [SY1225: $i] :
( ~ ( in @ ( ordered_pair @ SY1224 @ SY1225 ) @ SV664 )
| ( SY1225
= ( apply @ SV664 @ SY1224 ) ) ) ) )
= $false )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4925]) ).
thf(5061,plain,
! [SV664: $i] :
( ( ( ~ ! [SY1226: $i] :
( ( in @ SY1226 @ ( relation_dom @ SV664 ) )
| ! [SY1227: $i] :
( ( SY1227
!= ( apply @ SV664 @ SY1226 ) )
| ( SY1227 = empty_set ) ) )
| ~ ! [SY1228: $i] :
( ( in @ SY1228 @ ( relation_dom @ SV664 ) )
| ! [SY1229: $i] :
( ( SY1229 != empty_set )
| ( SY1229
= ( apply @ SV664 @ SY1228 ) ) ) ) )
= $false )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4926]) ).
thf(5062,plain,
! [SV665: $i,SV934: $i] :
( ( ( relation @ SV934 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV934 @ SV665 ) @ ( sK20_SY399 @ SV934 @ SV665 ) ) @ SV665 )
| ~ ~ ( in @ ( ordered_pair @ ( sK19_C @ SV934 @ SV665 ) @ ( sK20_SY399 @ SV934 @ SV665 ) ) @ SV934 ) )
| ( subset @ SV665 @ SV934 ) )
= $true )
| ( ( relation @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4927]) ).
thf(5063,plain,
! [SV665: $i,SV935: $i] :
( ( ( relation @ SV935 )
= $false )
| ( ( ~ ( subset @ SV665 @ SV935 )
| ! [SY1566: $i,SY1567: $i] :
( ~ ( in @ ( ordered_pair @ SY1566 @ SY1567 ) @ SV665 )
| ( in @ ( ordered_pair @ SY1566 @ SY1567 ) @ SV935 ) ) )
= $true )
| ( ( relation @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4928]) ).
thf(5064,plain,
! [SV742: $i,SV666: $i] :
( ( ( ! [SY1376: $i] :
( ~ ( function @ SY1376 )
| ~ ( relation @ SY1376 )
| ~ ( in @ SV666 @ ( relation_dom @ SY1376 ) )
| ~ ( in @ ( apply @ SY1376 @ SV666 ) @ ( relation_dom @ SV742 ) )
| ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1376 @ SV742 ) ) ) ) )
= $true )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4929]) ).
thf(5065,plain,
! [SV742: $i,SV666: $i] :
( ( ( ~ ( ~ ! [SY1377: $i] :
( ~ ( function @ SY1377 )
| ~ ( relation @ SY1377 )
| ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1377 @ SV742 ) ) )
| ( in @ SV666 @ ( relation_dom @ SY1377 ) ) )
| ~ ! [SY1378: $i] :
( ~ ( function @ SY1378 )
| ~ ( relation @ SY1378 )
| ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1378 @ SV742 ) ) )
| ( in @ ( apply @ SY1378 @ SV666 ) @ ( relation_dom @ SV742 ) ) ) ) )
= $true )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4930]) ).
thf(5066,plain,
! [SV843: $i,SV667: $i,SV894: $i] :
( ( ( ! [SY1526: $i] :
( ~ ( in @ SY1526 @ ( relation_rng @ SV894 ) )
| ~ ( in @ ( ordered_pair @ SV667 @ SY1526 ) @ SV894 )
| ~ ( in @ SY1526 @ SV843 ) ) )
= $true )
| ( ( in @ SV667 @ ( relation_inverse_image @ SV894 @ SV843 ) )
= $true )
| ( ( relation @ SV894 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4931]) ).
thf(5067,plain,
! [SV844: $i,SV895: $i,SV667: $i] :
( ( ( ~ ( in @ SV667 @ ( relation_inverse_image @ SV895 @ SV844 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK51_D @ SV895 @ SV844 @ SV667 ) @ ( relation_rng @ SV895 ) )
| ~ ( in @ ( ordered_pair @ SV667 @ ( sK51_D @ SV895 @ SV844 @ SV667 ) ) @ SV895 ) )
| ~ ( in @ ( sK51_D @ SV895 @ SV844 @ SV667 ) @ SV844 ) ) )
= $true )
| ( ( relation @ SV895 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4932]) ).
thf(5068,plain,
! [SV792: $i,SV845: $i] :
( ( ( in @ ( sK49_C @ SV845 @ SV792 ) @ SV792 )
= $true )
| ( ( disjoint @ SV792 @ SV845 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4933]) ).
thf(5069,plain,
! [SV792: $i,SV845: $i] :
( ( ( in @ ( sK49_C @ SV845 @ SV792 ) @ SV845 )
= $true )
| ( ( disjoint @ SV792 @ SV845 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4934]) ).
thf(5070,plain,
! [SV846: $i,SV793: $i,SV936: $i] :
( ( ( in @ SV936 @ SV793 )
= $false )
| ( ( ~ ( in @ SV936 @ SV846 ) )
= $true )
| ( ( ~ ( disjoint @ SV793 @ SV846 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4935]) ).
thf(5071,plain,
! [SV896: $i,SV847: $i,SV668: $i] :
( ( ( ~ ( in @ SV668 @ SV847 )
| ~ ( in @ SV668 @ ( relation_dom @ SV896 ) ) )
= $true )
| ( ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SV896 @ SV847 ) ) )
= $true )
| ( ( relation @ SV896 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4936]) ).
thf(5072,plain,
! [SV974: $i,SV668: $i,SV998: $i] :
( ( ~ ( relation @ SV998 )
| ~ ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SV998 @ SV974 ) ) )
| ( in @ SV668 @ SV974 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4937]) ).
thf(5073,plain,
! [SV975: $i,SV668: $i,SV999: $i] :
( ( ~ ( relation @ SV999 )
| ~ ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SV999 @ SV975 ) ) )
| ( in @ SV668 @ ( relation_dom @ SV999 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4938]) ).
thf(5074,plain,
! [SV669: $i,SV848: $i,SV897: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV897 )
| ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV669 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV897 )
| ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV848 ) ) ) )
= $false )
| ( ( SV897
= ( set_union2 @ SV669 @ SV848 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4939]) ).
thf(5075,plain,
! [SV669: $i,SV848: $i,SV897: $i] :
( ( ( ~ ( ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV897 )
| ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV669 )
| ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV848 ) ) )
= $false )
| ( ( SV897
= ( set_union2 @ SV669 @ SV848 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4939]) ).
thf(5076,plain,
! [SV849: $i,SV669: $i,SV898: $i] :
( ( ( ~ ! [SY1527: $i] :
( ~ ( in @ SY1527 @ SV898 )
| ( in @ SY1527 @ SV669 )
| ( in @ SY1527 @ SV849 ) )
| ~ ~ ( ~ ! [SY1528: $i] :
( ~ ( in @ SY1528 @ SV669 )
| ( in @ SY1528 @ SV898 ) )
| ~ ! [SY1529: $i] :
( ~ ( in @ SY1529 @ SV849 )
| ( in @ SY1529 @ SV898 ) ) ) )
= $false )
| ( ( SV898
= ( set_union2 @ SV669 @ SV849 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4940]) ).
thf(5077,plain,
! [SV937: $i,SV1000: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY406 @ SV1000 @ SV937 ) @ SV937 )
| ~ ~ ( in @ ( sK32_C @ SV1000 @ SV937 ) @ ( sK33_SY406 @ SV1000 @ SV937 ) ) )
| ~ ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SV1000 ) )
| ~ ( ! [SY1636: $i] :
( ~ ( in @ SY1636 @ SV937 )
| ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SY1636 ) )
| ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SV1000 ) ) )
| ( SV1000
= ( set_meet @ SV937 ) ) )
= $true )
| ( ( SV937 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4941]) ).
thf(5078,plain,
! [SV938: $i,SV1001: $i] :
( ( ( ( SV1001
!= ( set_meet @ SV938 ) )
| ~ ( ~ ! [SY1637: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY1637 @ SV1001 @ SV938 ) @ SV938 )
| ~ ~ ( in @ SY1637 @ ( sK31_D @ SY1637 @ SV1001 @ SV938 ) ) )
| ( in @ SY1637 @ SV1001 ) )
| ~ ! [SY1638: $i] :
( ~ ( in @ SY1638 @ SV1001 )
| ! [SY1573: $i] :
( ~ ( in @ SY1573 @ SV938 )
| ( in @ SY1638 @ SY1573 ) ) ) ) )
= $true )
| ( ( SV938 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4942]) ).
thf(5079,plain,
! [SV939: $i] :
( ( ( SV939 = empty_set )
= $false )
| ( ( ! [SY1574: $i] :
( ( SY1574
!= ( set_meet @ SV939 ) )
| ( SY1574 = empty_set ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4943]) ).
thf(5080,plain,
! [SV940: $i] :
( ( ( SV940 = empty_set )
= $false )
| ( ( ! [SY1575: $i] :
( ( SY1575 != empty_set )
| ( SY1575
= ( set_meet @ SV940 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4944]) ).
thf(5081,plain,
! [SV899: $i,SV850: $i,SV670: $i] :
( ( ( ~ ( ! [SY1530: $i,SY1531: $i] :
( ~ ( in @ SY1530 @ SV670 )
| ~ ( in @ SY1531 @ SV850 )
| ( ( sK23_D @ SV899 @ SV850 @ SV670 )
!= ( ordered_pair @ SY1530 @ SY1531 ) ) )
| ~ ( in @ ( sK23_D @ SV899 @ SV850 @ SV670 ) @ SV899 ) ) )
= $false )
| ( ( SV899
= ( cartesian_product2 @ SV670 @ SV850 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4945]) ).
thf(5082,plain,
! [SV670: $i,SV850: $i,SV899: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY403 @ SV899 @ SV850 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK25_SY405 @ SV899 @ SV850 @ SV670 ) @ SV850 ) )
| ( ( sK23_D @ SV899 @ SV850 @ SV670 )
!= ( ordered_pair @ ( sK24_SY403 @ SV899 @ SV850 @ SV670 ) @ ( sK25_SY405 @ SV899 @ SV850 @ SV670 ) ) ) )
| ( in @ ( sK23_D @ SV899 @ SV850 @ SV670 ) @ SV899 ) ) )
= $false )
| ( ( SV899
= ( cartesian_product2 @ SV670 @ SV850 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4945]) ).
thf(5083,plain,
! [SV900: $i,SV851: $i,SV670: $i] :
( ( ( ~ ! [SY1532: $i] :
( ! [SY1483: $i,SY1484: $i] :
( ~ ( in @ SY1483 @ SV670 )
| ~ ( in @ SY1484 @ SV851 )
| ( SY1532
!= ( ordered_pair @ SY1483 @ SY1484 ) ) )
| ( in @ SY1532 @ SV900 ) )
| ~ ! [SY1535: $i] :
( ~ ( in @ SY1535 @ SV900 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY1535 @ SV900 @ SV851 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK22_SY400 @ SY1535 @ SV900 @ SV851 @ SV670 ) @ SV851 ) )
| ( SY1535
!= ( ordered_pair @ ( sK21_E @ SY1535 @ SV900 @ SV851 @ SV670 ) @ ( sK22_SY400 @ SY1535 @ SV900 @ SV851 @ SV670 ) ) ) ) ) )
= $false )
| ( ( SV900
= ( cartesian_product2 @ SV670 @ SV851 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4946]) ).
thf(5084,plain,
! [SV671: $i,SV852: $i,SV901: $i] :
( ( ( function @ SV901 )
= $false )
| ( ( ~ ( relation @ SV901 ) )
= $true )
| ( ( ( SV852
!= ( apply @ SV901 @ SV671 ) )
| ~ ( in @ SV671 @ ( relation_dom @ SV901 ) )
| ( in @ ( ordered_pair @ SV671 @ SV852 ) @ SV901 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4947]) ).
thf(5085,plain,
! [SV976: $i,SV671: $i,SV1002: $i] :
( ( ~ ( function @ SV1002 )
| ~ ( relation @ SV1002 )
| ~ ( in @ ( ordered_pair @ SV671 @ SV976 ) @ SV1002 )
| ( SV976
= ( apply @ SV1002 @ SV671 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4948]) ).
thf(5086,plain,
! [SV977: $i,SV671: $i,SV1003: $i] :
( ( ~ ( function @ SV1003 )
| ~ ( relation @ SV1003 )
| ~ ( in @ ( ordered_pair @ SV671 @ SV977 ) @ SV1003 )
| ( in @ SV671 @ ( relation_dom @ SV1003 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4949]) ).
thf(5087,plain,
! [SV672: $i,SV941: $i] :
( ( ( relation @ SV941 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SV941 @ SV672 ) @ ( sK12_SY396 @ SV941 @ SV672 ) ) @ SV941 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SV941 @ SV672 ) @ ( sK11_C @ SV941 @ SV672 ) ) @ SV672 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_C @ SV941 @ SV672 ) @ ( sK12_SY396 @ SV941 @ SV672 ) ) @ SV941 )
| ( in @ ( ordered_pair @ ( sK12_SY396 @ SV941 @ SV672 ) @ ( sK11_C @ SV941 @ SV672 ) ) @ SV672 ) ) )
| ( SV941
= ( relation_inverse @ SV672 ) ) )
= $true )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4950]) ).
thf(5088,plain,
! [SV672: $i,SV942: $i] :
( ( ( relation @ SV942 )
= $false )
| ( ( ( SV942
!= ( relation_inverse @ SV672 ) )
| ~ ( ~ ! [SY1576: $i,SY1577: $i] :
( ~ ( in @ ( ordered_pair @ SY1576 @ SY1577 ) @ SV942 )
| ( in @ ( ordered_pair @ SY1577 @ SY1576 ) @ SV672 ) )
| ~ ! [SY1578: $i,SY1579: $i] :
( ~ ( in @ ( ordered_pair @ SY1579 @ SY1578 ) @ SV672 )
| ( in @ ( ordered_pair @ SY1578 @ SY1579 ) @ SV942 ) ) ) )
= $true )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4951]) ).
thf(5089,plain,
! [SV798: $i] :
( ( ( relation @ SV798 )
= $false )
| ( ( function @ SV798 )
= $false )
| ( ( ~ ( one_to_one @ SV798 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV798 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4952]) ).
thf(5090,plain,
! [SV799: $i] :
( ( ( relation @ SV799 )
= $false )
| ( ( function @ SV799 )
= $false )
| ( ( ~ ( one_to_one @ SV799 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV799 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4953]) ).
thf(5091,plain,
! [SV902: $i,SV855: $i,SV673: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV673 @ SV855 ) @ SV902 ) )
= $true )
| ( ( in @ SV673 @ ( relation_dom @ SV902 ) )
= $true )
| ( ( relation @ SV902 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4954]) ).
thf(5092,plain,
! [SV903: $i,SV856: $i,SV673: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV673 @ SV856 ) @ SV903 ) )
= $true )
| ( ( in @ SV856 @ ( relation_rng @ SV903 ) )
= $true )
| ( ( relation @ SV903 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4955]) ).
thf(5093,plain,
! [SV943: $i,SV743: $i,SV904: $i,SV674: $i] :
( ( ( ~ ( in @ SV674 @ SV904 ) )
= $true )
| ( ( ~ ( in @ SV743 @ SV943 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SV904 @ SV943 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4956]) ).
thf(5094,plain,
! [SV1004: $i,SV743: $i,SV674: $i] :
( ( ! [SY1640: $i] :
~ ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SV1004 @ SY1640 ) )
| ( in @ SV674 @ SV1004 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4957]) ).
thf(5095,plain,
! [SV1005: $i,SV743: $i,SV674: $i] :
( ( ! [SY1641: $i] :
( ~ ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SV1005 @ SY1641 ) )
| ( in @ SV743 @ SY1641 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4958]) ).
thf(5096,plain,
! [SV675: $i,SV857: $i,SV905: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK27_D @ SV905 @ SV857 @ SV675 ) @ SV905 )
| ( ( sK27_D @ SV905 @ SV857 @ SV675 )
!= SV675 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV905 @ SV857 @ SV675 ) @ SV905 )
| ( ( sK27_D @ SV905 @ SV857 @ SV675 )
!= SV857 ) ) ) )
= $false )
| ( ( SV905
= ( unordered_pair @ SV675 @ SV857 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4959]) ).
thf(5097,plain,
! [SV675: $i,SV857: $i,SV905: $i] :
( ( ( ~ ( ( in @ ( sK27_D @ SV905 @ SV857 @ SV675 ) @ SV905 )
| ( ( sK27_D @ SV905 @ SV857 @ SV675 )
= SV675 )
| ( ( sK27_D @ SV905 @ SV857 @ SV675 )
= SV857 ) ) )
= $false )
| ( ( SV905
= ( unordered_pair @ SV675 @ SV857 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4959]) ).
thf(5098,plain,
! [SV858: $i,SV675: $i,SV906: $i] :
( ( ( ~ ! [SY1537: $i] :
( ~ ( in @ SY1537 @ SV906 )
| ( SY1537 = SV675 )
| ( SY1537 = SV858 ) )
| ~ ~ ( ~ ! [SY1538: $i] :
( ( SY1538 != SV675 )
| ( in @ SY1538 @ SV906 ) )
| ~ ! [SY1539: $i] :
( ( SY1539 != SV858 )
| ( in @ SY1539 @ SV906 ) ) ) )
= $false )
| ( ( SV906
= ( unordered_pair @ SV675 @ SV858 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4960]) ).
thf(5099,plain,
! [SV944: $i,SV744: $i,SV907: $i,SV676: $i] :
( ( ( ~ ( in @ SV676 @ SV907 ) )
= $true )
| ( ( ~ ( in @ SV744 @ SV944 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SV907 @ SV944 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4961]) ).
thf(5100,plain,
! [SV1006: $i,SV744: $i,SV676: $i] :
( ( ! [SY1642: $i] :
~ ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SV1006 @ SY1642 ) )
| ( in @ SV676 @ SV1006 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4962]) ).
thf(5101,plain,
! [SV1007: $i,SV744: $i,SV676: $i] :
( ( ! [SY1643: $i] :
( ~ ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SV1007 @ SY1643 ) )
| ( in @ SV744 @ SY1643 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4963]) ).
thf(5102,plain,
! [SV945: $i,SV860: $i,SV801: $i] :
( ( ( disjoint @ SV801 @ SV860 )
= $false )
| ( ( in @ SV945 @ ( set_intersection2 @ SV801 @ SV860 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4964]) ).
thf(5103,plain,
! [SV677: $i,SV745: $i] :
( ( ( in @ ( sK4_C @ SV745 @ SV677 ) @ SV745 )
= $false )
| ( ( in @ ( sK4_C @ SV745 @ SV677 ) @ SV677 )
= $false )
| ( ( SV677 = SV745 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4967]) ).
thf(5104,plain,
! [SV804: $i,SV863: $i] :
( ( ( ! [SY1497: $i] :
( ~ ( in @ ( sK15_C @ SV863 @ SV804 ) @ SY1497 )
| ~ ( in @ SY1497 @ SV804 ) )
| ~ ( in @ ( sK15_C @ SV863 @ SV804 ) @ SV863 ) )
= $true )
| ( ( SV863
= ( union @ SV804 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4970]) ).
thf(5105,plain,
! [SV804: $i,SV863: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_C @ SV863 @ SV804 ) @ ( sK16_SY398 @ SV863 @ SV804 ) )
| ~ ( in @ ( sK16_SY398 @ SV863 @ SV804 ) @ SV804 ) )
| ( in @ ( sK15_C @ SV863 @ SV804 ) @ SV863 ) )
= $true )
| ( ( SV863
= ( union @ SV804 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4971]) ).
thf(5106,plain,
! [SV864: $i,SV805: $i] :
( ( ( ~ ! [SY1498: $i] :
( ! [SY1428: $i] :
( ~ ( in @ SY1498 @ SY1428 )
| ~ ( in @ SY1428 @ SV805 ) )
| ( in @ SY1498 @ SV864 ) ) )
= $false )
| ( ( SV864
= ( union @ SV805 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4972]) ).
thf(5107,plain,
! [SV805: $i,SV864: $i] :
( ( ( ~ ! [SY1500: $i] :
( ~ ( in @ SY1500 @ SV864 )
| ~ ( ~ ( in @ SY1500 @ ( sK14_D @ SY1500 @ SV864 @ SV805 ) )
| ~ ( in @ ( sK14_D @ SY1500 @ SV864 @ SV805 ) @ SV805 ) ) ) )
= $false )
| ( ( SV864
= ( union @ SV805 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4972]) ).
thf(5108,plain,
! [SV679: $i,SV946: $i] :
( ( ( ~ ( ! [SY1580: $i] :
~ ( in @ ( ordered_pair @ ( sK63_C @ SV946 @ SV679 ) @ SY1580 ) @ SV679 )
| ~ ( in @ ( sK63_C @ SV946 @ SV679 ) @ SV946 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_C @ SV946 @ SV679 ) @ ( sK64_SY419 @ SV946 @ SV679 ) ) @ SV679 )
| ( in @ ( sK63_C @ SV946 @ SV679 ) @ SV946 ) ) )
= $false )
| ( ( SV946
= ( relation_dom @ SV679 ) )
= $true )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4973]) ).
thf(5109,plain,
! [SV679: $i,SV947: $i] :
( ( ( SV947
= ( relation_dom @ SV679 ) )
= $false )
| ( ( ~ ( ~ ! [SY1581: $i] :
( ! [SY1312: $i] :
~ ( in @ ( ordered_pair @ SY1581 @ SY1312 ) @ SV679 )
| ( in @ SY1581 @ SV947 ) )
| ~ ! [SY1583: $i] :
( ~ ( in @ SY1583 @ SV947 )
| ( in @ ( ordered_pair @ SY1583 @ ( sK62_D @ SY1583 @ SV947 @ SV679 ) ) @ SV679 ) ) ) )
= $true )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4974]) ).
thf(5110,plain,
! [SV908: $i,SV865: $i,SV680: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV680 @ SV865 ) @ SV908 ) )
= $true )
| ( ( in @ SV680 @ ( relation_field @ SV908 ) )
= $true )
| ( ( relation @ SV908 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4975]) ).
thf(5111,plain,
! [SV909: $i,SV866: $i,SV680: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV680 @ SV866 ) @ SV909 ) )
= $true )
| ( ( in @ SV866 @ ( relation_field @ SV909 ) )
= $true )
| ( ( relation @ SV909 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4976]) ).
thf(5112,plain,
! [SV806: $i,SV867: $i] :
( ( ( ~ ( ( ( sK44_C @ SV867 @ SV806 )
!= ( sK45_SY414 @ SV867 @ SV806 ) )
| ~ ( in @ ( sK44_C @ SV867 @ SV806 ) @ SV806 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 ) )
| ~ ~ ( ~ ( ( ( sK44_C @ SV867 @ SV806 )
= ( sK45_SY414 @ SV867 @ SV806 ) )
| ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 ) )
| ~ ( ( in @ ( sK44_C @ SV867 @ SV806 ) @ SV806 )
| ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 ) ) ) )
= $false )
| ( ( SV867
= ( identity_relation @ SV806 ) )
= $true )
| ( ( relation @ SV867 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4977]) ).
thf(5113,plain,
! [SV807: $i,SV868: $i] :
( ( ( SV868
= ( identity_relation @ SV807 ) )
= $false )
| ( ( ~ ( ~ ! [SY1503: $i,SY1504: $i] :
( ( SY1503 != SY1504 )
| ~ ( in @ SY1503 @ SV807 )
| ( in @ ( ordered_pair @ SY1503 @ SY1504 ) @ SV868 ) )
| ~ ~ ( ~ ! [SY1505: $i,SY1506: $i] :
( ~ ( in @ ( ordered_pair @ SY1505 @ SY1506 ) @ SV868 )
| ( SY1505 = SY1506 ) )
| ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
~ ( in @ ( ordered_pair @ SY1507 @ SY1508 ) @ SV868 )
| ( in @ SY1507 @ SV807 ) ) ) ) )
= $true )
| ( ( relation @ SV868 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4978]) ).
thf(5114,plain,
! [SV681: $i,SV948: $i,SV980: $i] :
( ( ( ~ ( relation @ SV980 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ SV948 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV681 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 ) )
| ~ ~ ( ~ ( ( in @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ SV948 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV681 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 ) ) ) )
| ( SV980
= ( relation_dom_restriction @ SV681 @ SV948 ) ) )
= $true )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4979]) ).
thf(5115,plain,
! [SV949: $i,SV681: $i,SV981: $i] :
( ( ( ~ ( relation @ SV981 ) )
= $true )
| ( ( ( SV981
!= ( relation_dom_restriction @ SV681 @ SV949 ) )
| ~ ( ~ ! [SY1625: $i,SY1626: $i] :
( ~ ( in @ SY1625 @ SV949 )
| ~ ( in @ ( ordered_pair @ SY1625 @ SY1626 ) @ SV681 )
| ( in @ ( ordered_pair @ SY1625 @ SY1626 ) @ SV981 ) )
| ~ ~ ( ~ ! [SY1627: $i] :
( ! [SY1628: $i] :
~ ( in @ ( ordered_pair @ SY1627 @ SY1628 ) @ SV981 )
| ( in @ SY1627 @ SV949 ) )
| ~ ! [SY1629: $i,SY1630: $i] :
( ~ ( in @ ( ordered_pair @ SY1629 @ SY1630 ) @ SV981 )
| ( in @ ( ordered_pair @ SY1629 @ SY1630 ) @ SV681 ) ) ) ) )
= $true )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4980]) ).
thf(5116,plain,
! [SV808: $i,SV869: $i] :
( ( ( ( ( sK30_C @ SV869 @ SV808 )
!= SV808 )
| ~ ( in @ ( sK30_C @ SV869 @ SV808 ) @ SV869 ) )
= $true )
| ( ( SV869
= ( singleton @ SV808 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4981]) ).
thf(5117,plain,
! [SV808: $i,SV869: $i] :
( ( ( ( ( sK30_C @ SV869 @ SV808 )
= SV808 )
| ( in @ ( sK30_C @ SV869 @ SV808 ) @ SV869 ) )
= $true )
| ( ( SV869
= ( singleton @ SV808 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4982]) ).
thf(5118,plain,
! [SV870: $i,SV809: $i] :
( ( ( ~ ! [SY1509: $i] :
( ( SY1509 != SV809 )
| ( in @ SY1509 @ SV870 ) ) )
= $false )
| ( ( SV870
= ( singleton @ SV809 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4983]) ).
thf(5119,plain,
! [SV809: $i,SV870: $i] :
( ( ( ~ ! [SY1510: $i] :
( ~ ( in @ SY1510 @ SV870 )
| ( SY1510 = SV809 ) ) )
= $false )
| ( ( SV870
= ( singleton @ SV809 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4983]) ).
thf(5120,plain,
! [SV871: $i,SV682: $i,SV910: $i] :
( ( ( ! [SY1541: $i] :
( ~ ( in @ SY1541 @ ( relation_dom @ SV910 ) )
| ~ ( in @ ( ordered_pair @ SY1541 @ SV682 ) @ SV910 )
| ~ ( in @ SY1541 @ SV871 ) ) )
= $true )
| ( ( in @ SV682 @ ( relation_image @ SV910 @ SV871 ) )
= $true )
| ( ( relation @ SV910 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4984]) ).
thf(5121,plain,
! [SV872: $i,SV911: $i,SV682: $i] :
( ( ( ~ ( in @ SV682 @ ( relation_image @ SV911 @ SV872 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK52_D @ SV911 @ SV872 @ SV682 ) @ ( relation_dom @ SV911 ) )
| ~ ( in @ ( ordered_pair @ ( sK52_D @ SV911 @ SV872 @ SV682 ) @ SV682 ) @ SV911 ) )
| ~ ( in @ ( sK52_D @ SV911 @ SV872 @ SV682 ) @ SV872 ) ) )
= $true )
| ( ( relation @ SV911 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4985]) ).
thf(5122,plain,
! [SV683: $i,SV950: $i] :
( ( ( relation @ SV950 )
= $false )
| ( ( ~ ( subset @ SV683 @ SV950 )
| ( subset @ ( relation_dom @ SV683 ) @ ( relation_dom @ SV950 ) ) )
= $true )
| ( ( relation @ SV683 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4986]) ).
thf(5123,plain,
! [SV683: $i,SV951: $i] :
( ( ( relation @ SV951 )
= $false )
| ( ( ~ ( subset @ SV683 @ SV951 )
| ( subset @ ( relation_rng @ SV683 ) @ ( relation_rng @ SV951 ) ) )
= $true )
| ( ( relation @ SV683 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4987]) ).
thf(5124,plain,
! [SV810: $i,SV873: $i] :
( ( ( relation @ SV873 )
= $false )
| ( ( empty @ SV810 )
= $false )
| ( ( empty @ ( relation_composition @ SV810 @ SV873 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4988]) ).
thf(5125,plain,
! [SV811: $i,SV874: $i] :
( ( ( relation @ SV874 )
= $false )
| ( ( empty @ SV811 )
= $false )
| ( ( relation @ ( relation_composition @ SV811 @ SV874 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4989]) ).
thf(5126,plain,
! [SV684: $i,SV952: $i] :
( ( ( relation @ SV952 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV684 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV952 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV684 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV952 ) ) )
| ( SV684 = SV952 ) )
= $true )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4990]) ).
thf(5127,plain,
! [SV684: $i,SV953: $i] :
( ( ( relation @ SV953 )
= $false )
| ( ( ( SV684 != SV953 )
| ~ ( ~ ! [SY1592: $i,SY1593: $i] :
( ~ ( in @ ( ordered_pair @ SY1592 @ SY1593 ) @ SV684 )
| ( in @ ( ordered_pair @ SY1592 @ SY1593 ) @ SV953 ) )
| ~ ! [SY1594: $i,SY1595: $i] :
( ~ ( in @ ( ordered_pair @ SY1594 @ SY1595 ) @ SV953 )
| ( in @ ( ordered_pair @ SY1594 @ SY1595 ) @ SV684 ) ) ) )
= $true )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4991]) ).
thf(5128,plain,
! [SV685: $i,SV982: $i] :
( ( ( ~ ( ~ ! [SY1631: $i] :
( ~ ( subset @ SY1631 @ SV982 )
| ( in @ SY1631 @ ( sK3_SY386 @ SV982 @ SV685 ) ) )
| ~ ( in @ ( sK3_SY386 @ SV982 @ SV685 ) @ ( sK2_B @ SV685 ) ) ) )
= $true )
| ( ( ~ ( in @ SV982 @ ( sK2_B @ SV685 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4993]) ).
thf(5129,plain,
! [SV685: $i] :
( ( ~ ! [SY1344: $i,SY1345: $i] :
( ~ ( in @ SY1344 @ ( sK2_B @ SV685 ) )
| ~ ( subset @ SY1345 @ SY1344 )
| ( in @ SY1345 @ ( sK2_B @ SV685 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4994]) ).
thf(5130,plain,
! [SV685: $i] :
( ( ~ ( in @ SV685 @ ( sK2_B @ SV685 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4994]) ).
thf(5131,plain,
! [SV812: $i,SV876: $i] :
( ( ( subset @ SV876 @ SV812 )
= $false )
| ( ( subset @ SV812 @ SV876 )
= $false )
| ( ( SV812 = SV876 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4995]) ).
thf(5132,plain,
! [SV983: $i,SV954: $i] :
( ( ( ( SV954 != SV983 ) )
= $true )
| ( ( subset @ SV954 @ SV983 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4996]) ).
thf(5133,plain,
! [SV984: $i,SV955: $i] :
( ( ( ( SV955 != SV984 ) )
= $true )
| ( ( subset @ SV984 @ SV955 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4997]) ).
thf(5134,plain,
! [SV813: $i,SV877: $i] :
( ( ( ~ ( in @ ( sK28_C @ SV877 @ SV813 ) @ SV877 )
| ~ ( subset @ ( sK28_C @ SV877 @ SV813 ) @ SV813 ) )
= $true )
| ( ( SV877
= ( powerset @ SV813 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4998]) ).
thf(5135,plain,
! [SV813: $i,SV877: $i] :
( ( ( ( in @ ( sK28_C @ SV877 @ SV813 ) @ SV877 )
| ( subset @ ( sK28_C @ SV877 @ SV813 ) @ SV813 ) )
= $true )
| ( ( SV877
= ( powerset @ SV813 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4999]) ).
thf(5136,plain,
! [SV814: $i,SV878: $i] :
( ( ( ~ ! [SY1514: $i] :
( ~ ( in @ SY1514 @ SV878 )
| ( subset @ SY1514 @ SV814 ) ) )
= $false )
| ( ( SV878
= ( powerset @ SV814 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5000]) ).
thf(5137,plain,
! [SV878: $i,SV814: $i] :
( ( ( ~ ! [SY1515: $i] :
( ~ ( subset @ SY1515 @ SV814 )
| ( in @ SY1515 @ SV878 ) ) )
= $false )
| ( ( SV878
= ( powerset @ SV814 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5000]) ).
thf(5138,plain,
! [SV956: $i] :
( ( ( SV956 = empty_set )
= $false )
| ( ( ! [SY1598: $i] : ( subset @ SV956 @ ( singleton @ SY1598 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5002]) ).
thf(5139,plain,
! [SV985: $i,SV957: $i] :
( ( ( ( SV957
!= ( singleton @ SV985 ) ) )
= $true )
| ( ( subset @ SV957 @ ( singleton @ SV985 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5003]) ).
thf(5140,plain,
! [SV818: $i,SV880: $i] :
( ( ( relation @ SV880 )
= $false )
| ( ( function @ SV880 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK50_C @ SV880 @ SV818 ) @ SV818 )
| ~ ( ( ( apply @ SV880 @ ( sK50_C @ SV880 @ SV818 ) )
!= ( sK50_C @ SV880 @ SV818 ) ) ) )
| ( ( relation_dom @ SV880 )
!= SV818 )
| ( SV880
= ( identity_relation @ SV818 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5006]) ).
thf(5141,plain,
! [SV958: $i,SV986: $i] :
( ( ( ~ ( function @ SV986 )
| ~ ( relation @ SV986 ) )
= $true )
| ( ( ( SV986
!= ( identity_relation @ SV958 ) )
| ! [SY1632: $i] :
( ~ ( in @ SY1632 @ SV958 )
| ( ( apply @ SV986 @ SY1632 )
= SY1632 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5007]) ).
thf(5142,plain,
! [SV959: $i,SV987: $i] :
( ( ( ~ ( function @ SV987 )
| ~ ( relation @ SV987 ) )
= $true )
| ( ( ( SV987
!= ( identity_relation @ SV959 ) )
| ( ( relation_dom @ SV987 )
= SV959 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5008]) ).
thf(5143,plain,
! [SV821: $i,SV883: $i] :
( ( ( in @ ( sK18_C @ SV883 @ SV821 ) @ SV821 )
= $true )
| ( ( subset @ SV821 @ SV883 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5009]) ).
thf(5144,plain,
! [SV821: $i,SV883: $i] :
( ( ( ~ ( in @ ( sK18_C @ SV883 @ SV821 ) @ SV883 ) )
= $true )
| ( ( subset @ SV821 @ SV883 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5010]) ).
thf(5145,plain,
! [SV884: $i,SV822: $i,SV988: $i] :
( ( ( ~ ( in @ SV988 @ SV822 ) )
= $true )
| ( ( in @ SV988 @ SV884 )
= $true )
| ( ( subset @ SV822 @ SV884 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5011]) ).
thf(5146,plain,
! [SV710: $i,SV608: $i,SV912: $i] :
( ( ( function @ SV912 )
= $false )
| ( ( ~ ( relation @ SV912 ) )
= $true )
| ( ( ~ ( in @ SV608 @ ( relation_dom @ ( relation_composition @ SV912 @ SV710 ) ) )
| ( ( apply @ ( relation_composition @ SV912 @ SV710 ) @ SV608 )
= ( apply @ SV710 @ ( apply @ SV912 @ SV608 ) ) ) )
= $true )
| ( ( function @ SV710 )
= $false )
| ( ( relation @ SV710 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5012]) ).
thf(5147,plain,
! [SV711: $i,SV609: $i,SV913: $i] :
( ( ( function @ SV913 )
= $false )
| ( ( ~ ( relation @ SV913 ) )
= $true )
| ( ( ~ ( in @ SV609 @ ( relation_dom @ SV711 ) )
| ( ( apply @ ( relation_composition @ SV711 @ SV913 ) @ SV609 )
= ( apply @ SV913 @ ( apply @ SV711 @ SV609 ) ) ) )
= $true )
| ( ( function @ SV711 )
= $false )
| ( ( relation @ SV711 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5013]) ).
thf(5148,plain,
! [SV652: $i,SV825: $i,SV885: $i] :
( ( ( ~ ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV652 )
| ~ ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV825 )
| ~ ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV885 ) )
= $true )
| ( ( SV885
= ( set_intersection2 @ SV652 @ SV825 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5014]) ).
thf(5149,plain,
! [SV652: $i,SV825: $i,SV885: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV652 )
| ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV885 ) )
| ~ ( ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV825 )
| ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV885 ) ) ) )
= $true )
| ( ( SV885
= ( set_intersection2 @ SV652 @ SV825 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5015]) ).
thf(5150,plain,
! [SV886: $i,SV826: $i,SV652: $i] :
( ( ( ~ ! [SY1517: $i] :
( ~ ( in @ SY1517 @ SV652 )
| ~ ( in @ SY1517 @ SV826 )
| ( in @ SY1517 @ SV886 ) ) )
= $false )
| ( ( SV886
= ( set_intersection2 @ SV652 @ SV826 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5016]) ).
thf(5151,plain,
! [SV826: $i,SV652: $i,SV886: $i] :
( ( ( ~ ~ ( ~ ! [SY1518: $i] :
( ~ ( in @ SY1518 @ SV886 )
| ( in @ SY1518 @ SV652 ) )
| ~ ! [SY1519: $i] :
( ~ ( in @ SY1519 @ SV886 )
| ( in @ SY1519 @ SV826 ) ) ) )
= $false )
| ( ( SV886
= ( set_intersection2 @ SV652 @ SV826 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5016]) ).
thf(5152,plain,
! [SV653: $i] :
( ( ( ! [SY1140: $i] :
( ~ ( function @ SY1140 )
| ~ ( relation @ SY1140 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SY1140 @ SV653 )
= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ( ( sK70_C @ SY1140 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY1140 @ SV653 )
= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SY1140 @ SV653 )
= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ( ( sK71_SY424 @ SY1140 @ SV653 )
!= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK70_C @ SY1140 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK71_SY424 @ SY1140 @ SV653 )
!= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY1140 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK70_C @ SY1140 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SY1140 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SY1140 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SY1140 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK71_SY424 @ SY1140 @ SV653 )
!= ( apply @ SY1140 @ ( sK70_C @ SY1140 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SY1140 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ( ( relation_dom @ SY1140 )
!= ( relation_rng @ SV653 ) )
| ( SY1140
= ( function_inverse @ SV653 ) ) ) )
= $true )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5017]) ).
thf(5153,plain,
! [SV653: $i] :
( ( ( ~ ( ~ ! [SY1141: $i] :
( ~ ( function @ SY1141 )
| ~ ( relation @ SY1141 )
| ( SY1141
!= ( function_inverse @ SV653 ) )
| ~ ( ~ ~ ( ~ ! [SY1142: $i,SY1143: $i] :
( ( SY1143
!= ( apply @ SY1141 @ SY1142 ) )
| ~ ( in @ SY1142 @ ( relation_rng @ SV653 ) )
| ( SY1142
= ( apply @ SV653 @ SY1143 ) ) )
| ~ ! [SY1144: $i,SY1145: $i] :
( ( SY1145
!= ( apply @ SY1141 @ SY1144 ) )
| ~ ( in @ SY1144 @ ( relation_rng @ SV653 ) )
| ( in @ SY1145 @ ( relation_dom @ SV653 ) ) ) )
| ~ ~ ( ~ ! [SY1146: $i,SY1147: $i] :
( ( SY1146
!= ( apply @ SV653 @ SY1147 ) )
| ~ ( in @ SY1147 @ ( relation_dom @ SV653 ) )
| ( SY1147
= ( apply @ SY1141 @ SY1146 ) ) )
| ~ ! [SY1148: $i] :
( ! [SY1149: $i] :
( ( SY1148
!= ( apply @ SV653 @ SY1149 ) )
| ~ ( in @ SY1149 @ ( relation_dom @ SV653 ) ) )
| ( in @ SY1148 @ ( relation_rng @ SV653 ) ) ) ) ) )
| ~ ! [SY1150: $i] :
( ~ ( function @ SY1150 )
| ~ ( relation @ SY1150 )
| ( SY1150
!= ( function_inverse @ SV653 ) )
| ( ( relation_dom @ SY1150 )
= ( relation_rng @ SV653 ) ) ) ) )
= $true )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5018]) ).
thf(5154,plain,
! [SV914: $i,SV989: $i] :
( ( ( ~ ( element @ SV989 @ SV914 ) )
= $true )
| ( ( in @ SV989 @ SV914 )
= $true )
| ( ( empty @ SV914 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5019]) ).
thf(5155,plain,
! [SV915: $i,SV990: $i] :
( ( ( ~ ( in @ SV990 @ SV915 ) )
= $true )
| ( ( element @ SV990 @ SV915 )
= $true )
| ( ( empty @ SV915 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5020]) ).
thf(5156,plain,
! [SV916: $i,SV1008: $i] :
( ( ( ~ ( element @ SV1008 @ SV916 )
| ( empty @ SV1008 ) )
= $true )
| ( ( empty @ SV916 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5021]) ).
thf(5157,plain,
! [SV917: $i,SV1009: $i] :
( ( ( ~ ( empty @ SV1009 )
| ( element @ SV1009 @ SV917 ) )
= $true )
| ( ( empty @ SV917 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5022]) ).
thf(5158,plain,
! [SV1010: $i,SV918: $i] :
( ( ( subset @ SV918 @ ( singleton @ SV1010 ) )
= $true )
| ( ( SV918 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5023]) ).
thf(5159,plain,
! [SV960: $i,SV919: $i] :
( ( ( SV919
= ( singleton @ SV960 ) )
= $false )
| ( ( subset @ SV919 @ ( singleton @ SV960 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5024]) ).
thf(5160,plain,
! [SV920: $i,SV739: $i,SV887: $i,SV654: $i] :
( ( ( ~ ( in @ SV654 @ SV887 )
| ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ SV920 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SV887 ) @ SV920 ) )
= $true )
| ( ( relation @ SV920 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5025]) ).
thf(5161,plain,
! [SV991: $i,SV739: $i,SV654: $i,SV1011: $i] :
( ( ~ ( relation @ SV1011 )
| ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SV991 ) @ SV1011 ) )
| ( in @ SV654 @ SV991 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5026]) ).
thf(5162,plain,
! [SV992: $i,SV739: $i,SV654: $i,SV1012: $i] :
( ( ~ ( relation @ SV1012 )
| ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SV992 ) @ SV1012 ) )
| ( in @ ( ordered_pair @ SV654 @ SV739 ) @ SV1012 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5027]) ).
thf(5163,plain,
! [SV655: $i,SV740: $i,SV961: $i] :
( ( ( relation @ SV961 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) @ SV655 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV740 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 ) )
| ~ ~ ( ~ ( ( in @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) @ SV655 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV740 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 ) ) ) )
| ( SV961
= ( relation_rng_restriction @ SV655 @ SV740 ) ) )
= $true )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5028]) ).
thf(5164,plain,
! [SV740: $i,SV655: $i,SV962: $i] :
( ( ( relation @ SV962 )
= $false )
| ( ( ( SV962
!= ( relation_rng_restriction @ SV655 @ SV740 ) )
| ~ ( ~ ! [SY1603: $i,SY1604: $i] :
( ~ ( in @ SY1604 @ SV655 )
| ~ ( in @ ( ordered_pair @ SY1603 @ SY1604 ) @ SV740 )
| ( in @ ( ordered_pair @ SY1603 @ SY1604 ) @ SV962 ) )
| ~ ~ ( ~ ! [SY1605: $i,SY1606: $i] :
( ~ ( in @ ( ordered_pair @ SY1605 @ SY1606 ) @ SV962 )
| ( in @ SY1606 @ SV655 ) )
| ~ ! [SY1607: $i,SY1608: $i] :
( ~ ( in @ ( ordered_pair @ SY1607 @ SY1608 ) @ SV962 )
| ( in @ ( ordered_pair @ SY1607 @ SY1608 ) @ SV740 ) ) ) ) )
= $true )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5029]) ).
thf(5165,plain,
! [SV657: $i,SV922: $i,SV964: $i] :
( ( ( ~ ( ! [SY1609: $i] :
( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SY1609 ) @ SV657 )
| ~ ( in @ SY1609 @ SV922 ) )
| ~ ( in @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SV964 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ ( sK36_SY409 @ SV964 @ SV922 @ SV657 ) ) @ SV657 )
| ~ ( in @ ( sK36_SY409 @ SV964 @ SV922 @ SV657 ) @ SV922 ) )
| ( in @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SV964 ) ) )
= $false )
| ( ( SV964
= ( relation_inverse_image @ SV657 @ SV922 ) )
= $true )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5032]) ).
thf(5166,plain,
! [SV923: $i,SV657: $i,SV965: $i] :
( ( ( SV965
= ( relation_inverse_image @ SV657 @ SV923 ) )
= $false )
| ( ( ~ ( ~ ! [SY1610: $i] :
( ! [SY1552: $i] :
( ~ ( in @ ( ordered_pair @ SY1610 @ SY1552 ) @ SV657 )
| ~ ( in @ SY1552 @ SV923 ) )
| ( in @ SY1610 @ SV965 ) )
| ~ ! [SY1612: $i] :
( ~ ( in @ SY1612 @ SV965 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1612 @ ( sK34_E @ SY1612 @ SV965 @ SV923 @ SV657 ) ) @ SV657 )
| ~ ( in @ ( sK34_E @ SY1612 @ SV965 @ SV923 @ SV657 ) @ SV923 ) ) ) ) )
= $true )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5033]) ).
thf(5167,plain,
! [SV658: $i,SV924: $i,SV966: $i] :
( ( ( ~ ( ! [SY1613: $i] :
( ~ ( in @ ( ordered_pair @ SY1613 @ ( sK38_D @ SV966 @ SV924 @ SV658 ) ) @ SV658 )
| ~ ( in @ SY1613 @ SV924 ) )
| ~ ( in @ ( sK38_D @ SV966 @ SV924 @ SV658 ) @ SV966 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SV966 @ SV924 @ SV658 ) @ ( sK38_D @ SV966 @ SV924 @ SV658 ) ) @ SV658 )
| ~ ( in @ ( sK39_SY411 @ SV966 @ SV924 @ SV658 ) @ SV924 ) )
| ( in @ ( sK38_D @ SV966 @ SV924 @ SV658 ) @ SV966 ) ) )
= $false )
| ( ( SV966
= ( relation_image @ SV658 @ SV924 ) )
= $true )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5034]) ).
thf(5168,plain,
! [SV925: $i,SV658: $i,SV967: $i] :
( ( ( SV967
= ( relation_image @ SV658 @ SV925 ) )
= $false )
| ( ( ~ ( ~ ! [SY1614: $i] :
( ! [SY1558: $i] :
( ~ ( in @ ( ordered_pair @ SY1558 @ SY1614 ) @ SV658 )
| ~ ( in @ SY1558 @ SV925 ) )
| ( in @ SY1614 @ SV967 ) )
| ~ ! [SY1616: $i] :
( ~ ( in @ SY1616 @ SV967 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SY1616 @ SV967 @ SV925 @ SV658 ) @ SY1616 ) @ SV658 )
| ~ ( in @ ( sK37_E @ SY1616 @ SV967 @ SV925 @ SV658 ) @ SV925 ) ) ) ) )
= $true )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5035]) ).
thf(5169,plain,
! [SV968: $i,SV926: $i] :
( ( ( proper_subset @ SV926 @ SV968 )
= $false )
| ( ( ( SV926 != SV968 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5036]) ).
thf(5170,plain,
! [SV969: $i,SV927: $i] :
( ( ( proper_subset @ SV927 @ SV969 )
= $false )
| ( ( subset @ SV927 @ SV969 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5037]) ).
thf(5171,plain,
! [SV928: $i] :
( ( ( ~ ( empty @ SV928 ) )
= $true )
| ( ( ~ ( relation @ SV928 ) )
= $true )
| ( ( ~ ( function @ SV928 ) )
= $true )
| ( ( function @ SV928 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5040]) ).
thf(5172,plain,
! [SV929: $i] :
( ( ( ~ ( empty @ SV929 ) )
= $true )
| ( ( ~ ( relation @ SV929 ) )
= $true )
| ( ( ~ ( function @ SV929 ) )
= $true )
| ( ( relation @ SV929 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5041]) ).
thf(5173,plain,
! [SV780: $i] :
( ( ( function @ SV780 )
= $false )
| ( ( empty @ SV780 )
= $false )
| ( ( relation @ SV780 )
= $false )
| ( ( one_to_one @ SV780 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5042]) ).
thf(5174,plain,
! [SV1013: $i,SV993: $i,SV781: $i] :
( ( ( ( ( sK69_B @ SV781 )
!= ( ordered_pair @ SV993 @ SV1013 ) ) )
= $true )
| ( ( relation @ SV781 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5043]) ).
thf(5175,plain,
! [SV659: $i,SV890: $i,SV837: $i] :
( ( ( in @ SV837 @ SV890 )
= $false )
| ( ( in @ SV659 @ SV890 )
= $false )
| ( ( subset @ ( unordered_pair @ SV659 @ SV837 ) @ SV890 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5045]) ).
thf(5176,plain,
! [SV994: $i,SV970: $i,SV659: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV659 @ SV970 ) @ SV994 ) )
= $true )
| ( ( in @ SV659 @ SV994 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5046]) ).
thf(5177,plain,
! [SV995: $i,SV971: $i,SV659: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV659 @ SV971 ) @ SV995 ) )
= $true )
| ( ( in @ SV971 @ SV995 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5047]) ).
thf(5178,plain,
! [SV660: $i,SV783: $i,SV1014: $i] :
( ( ( ~ ( relation @ SV1014 )
| ~ ( ~ ( ! [SY1644: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ SY1644 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1644 @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV783 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV1014 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK10_SY395 @ SV1014 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV783 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV1014 ) ) )
| ( SV1014
= ( relation_composition @ SV660 @ SV783 ) ) )
= $true )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5048]) ).
thf(5179,plain,
! [SV783: $i,SV660: $i,SV1015: $i] :
( ( ( ~ ( relation @ SV1015 )
| ( SV1015
!= ( relation_composition @ SV660 @ SV783 ) )
| ~ ( ~ ! [SY1645: $i,SY1646: $i] :
( ! [SY1410: $i] :
( ~ ( in @ ( ordered_pair @ SY1645 @ SY1410 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1410 @ SY1646 ) @ SV783 ) )
| ( in @ ( ordered_pair @ SY1645 @ SY1646 ) @ SV1015 ) )
| ~ ! [SY1648: $i,SY1649: $i] :
( ~ ( in @ ( ordered_pair @ SY1648 @ SY1649 ) @ SV1015 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1648 @ ( sK7_F @ SY1649 @ SY1648 @ SV1015 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY1649 @ SY1648 @ SV1015 @ SV783 @ SV660 ) @ SY1649 ) @ SV783 ) ) ) ) )
= $true )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5049]) ).
thf(5180,plain,
! [SV661: $i,SV932: $i] :
( ( ( ~ ( ! [SY1562: $i] :
~ ( in @ ( ordered_pair @ SY1562 @ ( sK60_C @ SV932 @ SV661 ) ) @ SV661 )
| ~ ( in @ ( sK60_C @ SV932 @ SV661 ) @ SV932 ) ) )
= $false )
| ( ( SV932
= ( relation_rng @ SV661 ) )
= $true )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5050]) ).
thf(5181,plain,
! [SV661: $i,SV932: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK61_SY417 @ SV932 @ SV661 ) @ ( sK60_C @ SV932 @ SV661 ) ) @ SV661 )
| ( in @ ( sK60_C @ SV932 @ SV661 ) @ SV932 ) ) )
= $false )
| ( ( SV932
= ( relation_rng @ SV661 ) )
= $true )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5050]) ).
thf(5182,plain,
! [SV933: $i,SV661: $i] :
( ( ( ~ ! [SY1563: $i] :
( ! [SY1207: $i] :
~ ( in @ ( ordered_pair @ SY1207 @ SY1563 ) @ SV661 )
| ( in @ SY1563 @ SV933 ) )
| ~ ! [SY1565: $i] :
( ~ ( in @ SY1565 @ SV933 )
| ( in @ ( ordered_pair @ ( sK59_D @ SY1565 @ SV933 @ SV661 ) @ SY1565 ) @ SV661 ) ) )
= $false )
| ( ( SV933
= ( relation_rng @ SV661 ) )
= $false )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5051]) ).
thf(5183,plain,
! [SV662: $i,SV838: $i,SV891: $i] :
( ( ( ~ ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV662 )
| ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV838 )
| ~ ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV891 ) )
= $true )
| ( ( SV891
= ( set_difference @ SV662 @ SV838 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5052]) ).
thf(5184,plain,
! [SV662: $i,SV838: $i,SV891: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV662 )
| ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV891 ) )
| ~ ( ~ ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV838 )
| ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV891 ) ) ) )
= $true )
| ( ( SV891
= ( set_difference @ SV662 @ SV838 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5053]) ).
thf(5185,plain,
! [SV892: $i,SV839: $i,SV662: $i] :
( ( ( ~ ! [SY1523: $i] :
( ~ ( in @ SY1523 @ SV662 )
| ( in @ SY1523 @ SV839 )
| ( in @ SY1523 @ SV892 ) ) )
= $false )
| ( ( SV892
= ( set_difference @ SV662 @ SV839 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5054]) ).
thf(5186,plain,
! [SV839: $i,SV662: $i,SV892: $i] :
( ( ( ~ ~ ( ~ ! [SY1524: $i] :
( ~ ( in @ SY1524 @ SV892 )
| ( in @ SY1524 @ SV662 ) )
| ~ ! [SY1525: $i] :
( ~ ( in @ SY1525 @ SV892 )
| ~ ( in @ SY1525 @ SV839 ) ) ) )
= $false )
| ( ( SV892
= ( set_difference @ SV662 @ SV839 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5054]) ).
thf(5187,plain,
! [SV840: $i,SV790: $i] :
( ( ( function @ SV790 )
= $false )
| ( ( ~ ( relation @ SV790 ) )
= $true )
| ( ( ~ ( relation @ SV840 ) )
= $true )
| ( ( ~ ( function @ SV840 ) )
= $true )
| ( ( function @ ( relation_composition @ SV790 @ SV840 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5055]) ).
thf(5188,plain,
! [SV841: $i,SV791: $i] :
( ( ( function @ SV791 )
= $false )
| ( ( ~ ( relation @ SV791 ) )
= $true )
| ( ( ~ ( relation @ SV841 ) )
= $true )
| ( ( ~ ( function @ SV841 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV791 @ SV841 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5056]) ).
thf(5189,plain,
! [SV893: $i,SV842: $i,SV663: $i] :
( ( ( ~ ( in @ SV663 @ SV842 ) )
= $true )
| ( ( ~ ( in @ SV663 @ ( relation_rng @ SV893 ) ) )
= $true )
| ( ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SV842 @ SV893 ) ) )
= $true )
| ( ( relation @ SV893 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5057]) ).
thf(5190,plain,
! [SV972: $i,SV663: $i,SV996: $i] :
( ( ( ~ ( relation @ SV996 ) )
= $true )
| ( ( ~ ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SV972 @ SV996 ) ) )
| ( in @ SV663 @ SV972 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5058]) ).
thf(5191,plain,
! [SV973: $i,SV663: $i,SV997: $i] :
( ( ( ~ ( relation @ SV997 ) )
= $true )
| ( ( ~ ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SV973 @ SV997 ) ) )
| ( in @ SV663 @ ( relation_rng @ SV997 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5059]) ).
thf(5192,plain,
! [SV664: $i] :
( ( ( ~ ! [SY1222: $i] :
( ~ ( in @ SY1222 @ ( relation_dom @ SV664 ) )
| ! [SY1223: $i] :
( ( SY1223
!= ( apply @ SV664 @ SY1222 ) )
| ( in @ ( ordered_pair @ SY1222 @ SY1223 ) @ SV664 ) ) ) )
= $false )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5060]) ).
thf(5193,plain,
! [SV664: $i] :
( ( ( ~ ! [SY1224: $i] :
( ~ ( in @ SY1224 @ ( relation_dom @ SV664 ) )
| ! [SY1225: $i] :
( ~ ( in @ ( ordered_pair @ SY1224 @ SY1225 ) @ SV664 )
| ( SY1225
= ( apply @ SV664 @ SY1224 ) ) ) ) )
= $false )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5060]) ).
thf(5194,plain,
! [SV664: $i] :
( ( ( ~ ! [SY1226: $i] :
( ( in @ SY1226 @ ( relation_dom @ SV664 ) )
| ! [SY1227: $i] :
( ( SY1227
!= ( apply @ SV664 @ SY1226 ) )
| ( SY1227 = empty_set ) ) ) )
= $false )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5061]) ).
thf(5195,plain,
! [SV664: $i] :
( ( ( ~ ! [SY1228: $i] :
( ( in @ SY1228 @ ( relation_dom @ SV664 ) )
| ! [SY1229: $i] :
( ( SY1229 != empty_set )
| ( SY1229
= ( apply @ SV664 @ SY1228 ) ) ) ) )
= $false )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5061]) ).
thf(5196,plain,
! [SV665: $i,SV934: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV934 @ SV665 ) @ ( sK20_SY399 @ SV934 @ SV665 ) ) @ SV665 )
| ~ ~ ( in @ ( ordered_pair @ ( sK19_C @ SV934 @ SV665 ) @ ( sK20_SY399 @ SV934 @ SV665 ) ) @ SV934 ) ) )
= $true )
| ( ( subset @ SV665 @ SV934 )
= $true )
| ( ( relation @ SV934 )
= $false )
| ( ( relation @ SV665 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5062]) ).
thf(5197,plain,
! [SV935: $i,SV665: $i] :
( ( ( ~ ( subset @ SV665 @ SV935 ) )
= $true )
| ( ( ! [SY1566: $i,SY1567: $i] :
( ~ ( in @ ( ordered_pair @ SY1566 @ SY1567 ) @ SV665 )
| ( in @ ( ordered_pair @ SY1566 @ SY1567 ) @ SV935 ) ) )
= $true )
| ( ( relation @ SV935 )
= $false )
| ( ( relation @ SV665 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5063]) ).
thf(5198,plain,
! [SV742: $i,SV666: $i,SV1016: $i] :
( ( ( ~ ( function @ SV1016 )
| ~ ( relation @ SV1016 )
| ~ ( in @ SV666 @ ( relation_dom @ SV1016 ) )
| ~ ( in @ ( apply @ SV1016 @ SV666 ) @ ( relation_dom @ SV742 ) )
| ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SV1016 @ SV742 ) ) ) )
= $true )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5064]) ).
thf(5199,plain,
! [SV742: $i,SV666: $i] :
( ( ( ~ ! [SY1377: $i] :
( ~ ( function @ SY1377 )
| ~ ( relation @ SY1377 )
| ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1377 @ SV742 ) ) )
| ( in @ SV666 @ ( relation_dom @ SY1377 ) ) )
| ~ ! [SY1378: $i] :
( ~ ( function @ SY1378 )
| ~ ( relation @ SY1378 )
| ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1378 @ SV742 ) ) )
| ( in @ ( apply @ SY1378 @ SV666 ) @ ( relation_dom @ SV742 ) ) ) )
= $false )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5065]) ).
thf(5200,plain,
! [SV843: $i,SV667: $i,SV894: $i,SV1017: $i] :
( ( ( ~ ( in @ SV1017 @ ( relation_rng @ SV894 ) )
| ~ ( in @ ( ordered_pair @ SV667 @ SV1017 ) @ SV894 )
| ~ ( in @ SV1017 @ SV843 ) )
= $true )
| ( ( in @ SV667 @ ( relation_inverse_image @ SV894 @ SV843 ) )
= $true )
| ( ( relation @ SV894 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5066]) ).
thf(5201,plain,
! [SV844: $i,SV895: $i,SV667: $i] :
( ( ( in @ SV667 @ ( relation_inverse_image @ SV895 @ SV844 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK51_D @ SV895 @ SV844 @ SV667 ) @ ( relation_rng @ SV895 ) )
| ~ ( in @ ( ordered_pair @ SV667 @ ( sK51_D @ SV895 @ SV844 @ SV667 ) ) @ SV895 ) )
| ~ ( in @ ( sK51_D @ SV895 @ SV844 @ SV667 ) @ SV844 ) ) )
= $true )
| ( ( relation @ SV895 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5067]) ).
thf(5202,plain,
! [SV793: $i,SV846: $i,SV936: $i] :
( ( ( in @ SV936 @ SV846 )
= $false )
| ( ( in @ SV936 @ SV793 )
= $false )
| ( ( ~ ( disjoint @ SV793 @ SV846 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5070]) ).
thf(5203,plain,
! [SV896: $i,SV847: $i,SV668: $i] :
( ( ( ~ ( in @ SV668 @ SV847 ) )
= $true )
| ( ( ~ ( in @ SV668 @ ( relation_dom @ SV896 ) ) )
= $true )
| ( ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SV896 @ SV847 ) ) )
= $true )
| ( ( relation @ SV896 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5071]) ).
thf(5204,plain,
! [SV974: $i,SV668: $i,SV998: $i] :
( ( ( ~ ( relation @ SV998 ) )
= $true )
| ( ( ~ ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SV998 @ SV974 ) ) )
| ( in @ SV668 @ SV974 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5072]) ).
thf(5205,plain,
! [SV975: $i,SV668: $i,SV999: $i] :
( ( ( ~ ( relation @ SV999 ) )
= $true )
| ( ( ~ ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SV999 @ SV975 ) ) )
| ( in @ SV668 @ ( relation_dom @ SV999 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5073]) ).
thf(5206,plain,
! [SV669: $i,SV848: $i,SV897: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV897 )
| ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV669 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV897 )
| ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV848 ) ) ) )
= $true )
| ( ( SV897
= ( set_union2 @ SV669 @ SV848 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5074]) ).
thf(5207,plain,
! [SV669: $i,SV848: $i,SV897: $i] :
( ( ( ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV897 )
| ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV669 )
| ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV848 ) )
= $true )
| ( ( SV897
= ( set_union2 @ SV669 @ SV848 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5075]) ).
thf(5208,plain,
! [SV849: $i,SV669: $i,SV898: $i] :
( ( ( ~ ! [SY1527: $i] :
( ~ ( in @ SY1527 @ SV898 )
| ( in @ SY1527 @ SV669 )
| ( in @ SY1527 @ SV849 ) ) )
= $false )
| ( ( SV898
= ( set_union2 @ SV669 @ SV849 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5076]) ).
thf(5209,plain,
! [SV849: $i,SV898: $i,SV669: $i] :
( ( ( ~ ~ ( ~ ! [SY1528: $i] :
( ~ ( in @ SY1528 @ SV669 )
| ( in @ SY1528 @ SV898 ) )
| ~ ! [SY1529: $i] :
( ~ ( in @ SY1529 @ SV849 )
| ( in @ SY1529 @ SV898 ) ) ) )
= $false )
| ( ( SV898
= ( set_union2 @ SV669 @ SV849 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5076]) ).
thf(5210,plain,
! [SV937: $i,SV1000: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( in @ ( sK33_SY406 @ SV1000 @ SV937 ) @ SV937 )
| ~ ~ ( in @ ( sK32_C @ SV1000 @ SV937 ) @ ( sK33_SY406 @ SV1000 @ SV937 ) ) )
| ~ ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SV1000 ) )
| ~ ( ! [SY1636: $i] :
( ~ ( in @ SY1636 @ SV937 )
| ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SY1636 ) )
| ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SV1000 ) ) ) )
= $true )
| ( ( SV1000
= ( set_meet @ SV937 ) )
= $true )
| ( ( SV937 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5077]) ).
thf(5211,plain,
! [SV938: $i,SV1001: $i] :
( ( ( ( SV1001
!= ( set_meet @ SV938 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1637: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY1637 @ SV1001 @ SV938 ) @ SV938 )
| ~ ~ ( in @ SY1637 @ ( sK31_D @ SY1637 @ SV1001 @ SV938 ) ) )
| ( in @ SY1637 @ SV1001 ) )
| ~ ! [SY1638: $i] :
( ~ ( in @ SY1638 @ SV1001 )
| ! [SY1573: $i] :
( ~ ( in @ SY1573 @ SV938 )
| ( in @ SY1638 @ SY1573 ) ) ) ) )
= $true )
| ( ( SV938 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5078]) ).
thf(5212,plain,
! [SV939: $i,SV1018: $i] :
( ( ( ( SV1018
!= ( set_meet @ SV939 ) )
| ( SV1018 = empty_set ) )
= $true )
| ( ( SV939 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5079]) ).
thf(5213,plain,
! [SV940: $i,SV1019: $i] :
( ( ( ( SV1019 != empty_set )
| ( SV1019
= ( set_meet @ SV940 ) ) )
= $true )
| ( ( SV940 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5080]) ).
thf(5214,plain,
! [SV899: $i,SV850: $i,SV670: $i] :
( ( ( ! [SY1530: $i,SY1531: $i] :
( ~ ( in @ SY1530 @ SV670 )
| ~ ( in @ SY1531 @ SV850 )
| ( ( sK23_D @ SV899 @ SV850 @ SV670 )
!= ( ordered_pair @ SY1530 @ SY1531 ) ) )
| ~ ( in @ ( sK23_D @ SV899 @ SV850 @ SV670 ) @ SV899 ) )
= $true )
| ( ( SV899
= ( cartesian_product2 @ SV670 @ SV850 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5081]) ).
thf(5215,plain,
! [SV670: $i,SV850: $i,SV899: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY403 @ SV899 @ SV850 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK25_SY405 @ SV899 @ SV850 @ SV670 ) @ SV850 ) )
| ( ( sK23_D @ SV899 @ SV850 @ SV670 )
!= ( ordered_pair @ ( sK24_SY403 @ SV899 @ SV850 @ SV670 ) @ ( sK25_SY405 @ SV899 @ SV850 @ SV670 ) ) ) )
| ( in @ ( sK23_D @ SV899 @ SV850 @ SV670 ) @ SV899 ) )
= $true )
| ( ( SV899
= ( cartesian_product2 @ SV670 @ SV850 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5082]) ).
thf(5216,plain,
! [SV900: $i,SV851: $i,SV670: $i] :
( ( ( ~ ! [SY1532: $i] :
( ! [SY1483: $i,SY1484: $i] :
( ~ ( in @ SY1483 @ SV670 )
| ~ ( in @ SY1484 @ SV851 )
| ( SY1532
!= ( ordered_pair @ SY1483 @ SY1484 ) ) )
| ( in @ SY1532 @ SV900 ) ) )
= $false )
| ( ( SV900
= ( cartesian_product2 @ SV670 @ SV851 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5083]) ).
thf(5217,plain,
! [SV670: $i,SV851: $i,SV900: $i] :
( ( ( ~ ! [SY1535: $i] :
( ~ ( in @ SY1535 @ SV900 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY1535 @ SV900 @ SV851 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK22_SY400 @ SY1535 @ SV900 @ SV851 @ SV670 ) @ SV851 ) )
| ( SY1535
!= ( ordered_pair @ ( sK21_E @ SY1535 @ SV900 @ SV851 @ SV670 ) @ ( sK22_SY400 @ SY1535 @ SV900 @ SV851 @ SV670 ) ) ) ) ) )
= $false )
| ( ( SV900
= ( cartesian_product2 @ SV670 @ SV851 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5083]) ).
thf(5218,plain,
! [SV671: $i,SV852: $i,SV901: $i] :
( ( ( relation @ SV901 )
= $false )
| ( ( function @ SV901 )
= $false )
| ( ( ( SV852
!= ( apply @ SV901 @ SV671 ) )
| ~ ( in @ SV671 @ ( relation_dom @ SV901 ) )
| ( in @ ( ordered_pair @ SV671 @ SV852 ) @ SV901 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5084]) ).
thf(5219,plain,
! [SV976: $i,SV671: $i,SV1002: $i] :
( ( ( ~ ( function @ SV1002 )
| ~ ( relation @ SV1002 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV671 @ SV976 ) @ SV1002 )
| ( SV976
= ( apply @ SV1002 @ SV671 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5085]) ).
thf(5220,plain,
! [SV977: $i,SV671: $i,SV1003: $i] :
( ( ( ~ ( function @ SV1003 )
| ~ ( relation @ SV1003 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV671 @ SV977 ) @ SV1003 )
| ( in @ SV671 @ ( relation_dom @ SV1003 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5086]) ).
thf(5221,plain,
! [SV672: $i,SV941: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SV941 @ SV672 ) @ ( sK12_SY396 @ SV941 @ SV672 ) ) @ SV941 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SV941 @ SV672 ) @ ( sK11_C @ SV941 @ SV672 ) ) @ SV672 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_C @ SV941 @ SV672 ) @ ( sK12_SY396 @ SV941 @ SV672 ) ) @ SV941 )
| ( in @ ( ordered_pair @ ( sK12_SY396 @ SV941 @ SV672 ) @ ( sK11_C @ SV941 @ SV672 ) ) @ SV672 ) ) ) )
= $true )
| ( ( SV941
= ( relation_inverse @ SV672 ) )
= $true )
| ( ( relation @ SV941 )
= $false )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5087]) ).
thf(5222,plain,
! [SV672: $i,SV942: $i] :
( ( ( ( SV942
!= ( relation_inverse @ SV672 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1576: $i,SY1577: $i] :
( ~ ( in @ ( ordered_pair @ SY1576 @ SY1577 ) @ SV942 )
| ( in @ ( ordered_pair @ SY1577 @ SY1576 ) @ SV672 ) )
| ~ ! [SY1578: $i,SY1579: $i] :
( ~ ( in @ ( ordered_pair @ SY1579 @ SY1578 ) @ SV672 )
| ( in @ ( ordered_pair @ SY1578 @ SY1579 ) @ SV942 ) ) ) )
= $true )
| ( ( relation @ SV942 )
= $false )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5088]) ).
thf(5223,plain,
! [SV798: $i] :
( ( ( one_to_one @ SV798 )
= $false )
| ( ( function @ SV798 )
= $false )
| ( ( relation @ SV798 )
= $false )
| ( ( function @ ( relation_inverse @ SV798 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5089]) ).
thf(5224,plain,
! [SV799: $i] :
( ( ( one_to_one @ SV799 )
= $false )
| ( ( function @ SV799 )
= $false )
| ( ( relation @ SV799 )
= $false )
| ( ( relation @ ( relation_inverse @ SV799 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5090]) ).
thf(5225,plain,
! [SV902: $i,SV855: $i,SV673: $i] :
( ( ( in @ ( ordered_pair @ SV673 @ SV855 ) @ SV902 )
= $false )
| ( ( in @ SV673 @ ( relation_dom @ SV902 ) )
= $true )
| ( ( relation @ SV902 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5091]) ).
thf(5226,plain,
! [SV903: $i,SV856: $i,SV673: $i] :
( ( ( in @ ( ordered_pair @ SV673 @ SV856 ) @ SV903 )
= $false )
| ( ( in @ SV856 @ ( relation_rng @ SV903 ) )
= $true )
| ( ( relation @ SV903 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5092]) ).
thf(5227,plain,
! [SV943: $i,SV743: $i,SV904: $i,SV674: $i] :
( ( ( in @ SV674 @ SV904 )
= $false )
| ( ( ~ ( in @ SV743 @ SV943 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SV904 @ SV943 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5093]) ).
thf(5228,plain,
! [SV1004: $i,SV743: $i,SV674: $i] :
( ( ( ! [SY1640: $i] :
~ ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SV1004 @ SY1640 ) ) )
= $true )
| ( ( in @ SV674 @ SV1004 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5094]) ).
thf(5229,plain,
! [SV1020: $i,SV1005: $i,SV743: $i,SV674: $i] :
( ( ~ ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SV1005 @ SV1020 ) )
| ( in @ SV743 @ SV1020 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5095]) ).
thf(5230,plain,
! [SV675: $i,SV857: $i,SV905: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK27_D @ SV905 @ SV857 @ SV675 ) @ SV905 )
| ( ( sK27_D @ SV905 @ SV857 @ SV675 )
!= SV675 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV905 @ SV857 @ SV675 ) @ SV905 )
| ( ( sK27_D @ SV905 @ SV857 @ SV675 )
!= SV857 ) ) ) )
= $true )
| ( ( SV905
= ( unordered_pair @ SV675 @ SV857 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5096]) ).
thf(5231,plain,
! [SV675: $i,SV857: $i,SV905: $i] :
( ( ( ( in @ ( sK27_D @ SV905 @ SV857 @ SV675 ) @ SV905 )
| ( ( sK27_D @ SV905 @ SV857 @ SV675 )
= SV675 )
| ( ( sK27_D @ SV905 @ SV857 @ SV675 )
= SV857 ) )
= $true )
| ( ( SV905
= ( unordered_pair @ SV675 @ SV857 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5097]) ).
thf(5232,plain,
! [SV858: $i,SV675: $i,SV906: $i] :
( ( ( ~ ! [SY1537: $i] :
( ~ ( in @ SY1537 @ SV906 )
| ( SY1537 = SV675 )
| ( SY1537 = SV858 ) ) )
= $false )
| ( ( SV906
= ( unordered_pair @ SV675 @ SV858 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5098]) ).
thf(5233,plain,
! [SV858: $i,SV906: $i,SV675: $i] :
( ( ( ~ ~ ( ~ ! [SY1538: $i] :
( ( SY1538 != SV675 )
| ( in @ SY1538 @ SV906 ) )
| ~ ! [SY1539: $i] :
( ( SY1539 != SV858 )
| ( in @ SY1539 @ SV906 ) ) ) )
= $false )
| ( ( SV906
= ( unordered_pair @ SV675 @ SV858 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5098]) ).
thf(5234,plain,
! [SV944: $i,SV744: $i,SV907: $i,SV676: $i] :
( ( ( in @ SV676 @ SV907 )
= $false )
| ( ( ~ ( in @ SV744 @ SV944 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SV907 @ SV944 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5099]) ).
thf(5235,plain,
! [SV1006: $i,SV744: $i,SV676: $i] :
( ( ( ! [SY1642: $i] :
~ ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SV1006 @ SY1642 ) ) )
= $true )
| ( ( in @ SV676 @ SV1006 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5100]) ).
thf(5236,plain,
! [SV1021: $i,SV1007: $i,SV744: $i,SV676: $i] :
( ( ~ ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SV1007 @ SV1021 ) )
| ( in @ SV744 @ SV1021 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5101]) ).
thf(5237,plain,
! [SV804: $i,SV863: $i] :
( ( ( ! [SY1497: $i] :
( ~ ( in @ ( sK15_C @ SV863 @ SV804 ) @ SY1497 )
| ~ ( in @ SY1497 @ SV804 ) ) )
= $true )
| ( ( ~ ( in @ ( sK15_C @ SV863 @ SV804 ) @ SV863 ) )
= $true )
| ( ( SV863
= ( union @ SV804 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5104]) ).
thf(5238,plain,
! [SV804: $i,SV863: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_C @ SV863 @ SV804 ) @ ( sK16_SY398 @ SV863 @ SV804 ) )
| ~ ( in @ ( sK16_SY398 @ SV863 @ SV804 ) @ SV804 ) ) )
= $true )
| ( ( in @ ( sK15_C @ SV863 @ SV804 ) @ SV863 )
= $true )
| ( ( SV863
= ( union @ SV804 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5105]) ).
thf(5239,plain,
! [SV864: $i,SV805: $i] :
( ( ( ! [SY1498: $i] :
( ! [SY1428: $i] :
( ~ ( in @ SY1498 @ SY1428 )
| ~ ( in @ SY1428 @ SV805 ) )
| ( in @ SY1498 @ SV864 ) ) )
= $true )
| ( ( SV864
= ( union @ SV805 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5106]) ).
thf(5240,plain,
! [SV805: $i,SV864: $i] :
( ( ( ! [SY1500: $i] :
( ~ ( in @ SY1500 @ SV864 )
| ~ ( ~ ( in @ SY1500 @ ( sK14_D @ SY1500 @ SV864 @ SV805 ) )
| ~ ( in @ ( sK14_D @ SY1500 @ SV864 @ SV805 ) @ SV805 ) ) ) )
= $true )
| ( ( SV864
= ( union @ SV805 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5107]) ).
thf(5241,plain,
! [SV679: $i,SV946: $i] :
( ( ( ~ ( ! [SY1580: $i] :
~ ( in @ ( ordered_pair @ ( sK63_C @ SV946 @ SV679 ) @ SY1580 ) @ SV679 )
| ~ ( in @ ( sK63_C @ SV946 @ SV679 ) @ SV946 ) ) )
= $false )
| ( ( SV946
= ( relation_dom @ SV679 ) )
= $true )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5108]) ).
thf(5242,plain,
! [SV679: $i,SV946: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK63_C @ SV946 @ SV679 ) @ ( sK64_SY419 @ SV946 @ SV679 ) ) @ SV679 )
| ( in @ ( sK63_C @ SV946 @ SV679 ) @ SV946 ) ) )
= $false )
| ( ( SV946
= ( relation_dom @ SV679 ) )
= $true )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5108]) ).
thf(5243,plain,
! [SV947: $i,SV679: $i] :
( ( ( ~ ! [SY1581: $i] :
( ! [SY1312: $i] :
~ ( in @ ( ordered_pair @ SY1581 @ SY1312 ) @ SV679 )
| ( in @ SY1581 @ SV947 ) )
| ~ ! [SY1583: $i] :
( ~ ( in @ SY1583 @ SV947 )
| ( in @ ( ordered_pair @ SY1583 @ ( sK62_D @ SY1583 @ SV947 @ SV679 ) ) @ SV679 ) ) )
= $false )
| ( ( SV947
= ( relation_dom @ SV679 ) )
= $false )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5109]) ).
thf(5244,plain,
! [SV908: $i,SV865: $i,SV680: $i] :
( ( ( in @ ( ordered_pair @ SV680 @ SV865 ) @ SV908 )
= $false )
| ( ( in @ SV680 @ ( relation_field @ SV908 ) )
= $true )
| ( ( relation @ SV908 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5110]) ).
thf(5245,plain,
! [SV909: $i,SV866: $i,SV680: $i] :
( ( ( in @ ( ordered_pair @ SV680 @ SV866 ) @ SV909 )
= $false )
| ( ( in @ SV866 @ ( relation_field @ SV909 ) )
= $true )
| ( ( relation @ SV909 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5111]) ).
thf(5246,plain,
! [SV806: $i,SV867: $i] :
( ( ( ~ ( ( ( sK44_C @ SV867 @ SV806 )
!= ( sK45_SY414 @ SV867 @ SV806 ) )
| ~ ( in @ ( sK44_C @ SV867 @ SV806 ) @ SV806 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 ) ) )
= $false )
| ( ( SV867
= ( identity_relation @ SV806 ) )
= $true )
| ( ( relation @ SV867 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5112]) ).
thf(5247,plain,
! [SV806: $i,SV867: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK44_C @ SV867 @ SV806 )
= ( sK45_SY414 @ SV867 @ SV806 ) )
| ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 ) )
| ~ ( ( in @ ( sK44_C @ SV867 @ SV806 ) @ SV806 )
| ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 ) ) ) )
= $false )
| ( ( SV867
= ( identity_relation @ SV806 ) )
= $true )
| ( ( relation @ SV867 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5112]) ).
thf(5248,plain,
! [SV868: $i,SV807: $i] :
( ( ( ~ ! [SY1503: $i,SY1504: $i] :
( ( SY1503 != SY1504 )
| ~ ( in @ SY1503 @ SV807 )
| ( in @ ( ordered_pair @ SY1503 @ SY1504 ) @ SV868 ) )
| ~ ~ ( ~ ! [SY1505: $i,SY1506: $i] :
( ~ ( in @ ( ordered_pair @ SY1505 @ SY1506 ) @ SV868 )
| ( SY1505 = SY1506 ) )
| ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
~ ( in @ ( ordered_pair @ SY1507 @ SY1508 ) @ SV868 )
| ( in @ SY1507 @ SV807 ) ) ) )
= $false )
| ( ( SV868
= ( identity_relation @ SV807 ) )
= $false )
| ( ( relation @ SV868 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5113]) ).
thf(5249,plain,
! [SV681: $i,SV948: $i,SV980: $i] :
( ( ( relation @ SV980 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ SV948 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV681 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 ) )
| ~ ~ ( ~ ( ( in @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ SV948 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV681 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 ) ) ) )
| ( SV980
= ( relation_dom_restriction @ SV681 @ SV948 ) ) )
= $true )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5114]) ).
thf(5250,plain,
! [SV949: $i,SV681: $i,SV981: $i] :
( ( ( relation @ SV981 )
= $false )
| ( ( ( SV981
!= ( relation_dom_restriction @ SV681 @ SV949 ) )
| ~ ( ~ ! [SY1625: $i,SY1626: $i] :
( ~ ( in @ SY1625 @ SV949 )
| ~ ( in @ ( ordered_pair @ SY1625 @ SY1626 ) @ SV681 )
| ( in @ ( ordered_pair @ SY1625 @ SY1626 ) @ SV981 ) )
| ~ ~ ( ~ ! [SY1627: $i] :
( ! [SY1628: $i] :
~ ( in @ ( ordered_pair @ SY1627 @ SY1628 ) @ SV981 )
| ( in @ SY1627 @ SV949 ) )
| ~ ! [SY1629: $i,SY1630: $i] :
( ~ ( in @ ( ordered_pair @ SY1629 @ SY1630 ) @ SV981 )
| ( in @ ( ordered_pair @ SY1629 @ SY1630 ) @ SV681 ) ) ) ) )
= $true )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5115]) ).
thf(5251,plain,
! [SV808: $i,SV869: $i] :
( ( ( ( ( sK30_C @ SV869 @ SV808 )
!= SV808 ) )
= $true )
| ( ( ~ ( in @ ( sK30_C @ SV869 @ SV808 ) @ SV869 ) )
= $true )
| ( ( SV869
= ( singleton @ SV808 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5116]) ).
thf(5252,plain,
! [SV808: $i,SV869: $i] :
( ( ( ( sK30_C @ SV869 @ SV808 )
= SV808 )
= $true )
| ( ( in @ ( sK30_C @ SV869 @ SV808 ) @ SV869 )
= $true )
| ( ( SV869
= ( singleton @ SV808 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5117]) ).
thf(5253,plain,
! [SV870: $i,SV809: $i] :
( ( ( ! [SY1509: $i] :
( ( SY1509 != SV809 )
| ( in @ SY1509 @ SV870 ) ) )
= $true )
| ( ( SV870
= ( singleton @ SV809 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5118]) ).
thf(5254,plain,
! [SV809: $i,SV870: $i] :
( ( ( ! [SY1510: $i] :
( ~ ( in @ SY1510 @ SV870 )
| ( SY1510 = SV809 ) ) )
= $true )
| ( ( SV870
= ( singleton @ SV809 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5119]) ).
thf(5255,plain,
! [SV871: $i,SV682: $i,SV910: $i,SV1022: $i] :
( ( ( ~ ( in @ SV1022 @ ( relation_dom @ SV910 ) )
| ~ ( in @ ( ordered_pair @ SV1022 @ SV682 ) @ SV910 )
| ~ ( in @ SV1022 @ SV871 ) )
= $true )
| ( ( in @ SV682 @ ( relation_image @ SV910 @ SV871 ) )
= $true )
| ( ( relation @ SV910 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5120]) ).
thf(5256,plain,
! [SV872: $i,SV911: $i,SV682: $i] :
( ( ( in @ SV682 @ ( relation_image @ SV911 @ SV872 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK52_D @ SV911 @ SV872 @ SV682 ) @ ( relation_dom @ SV911 ) )
| ~ ( in @ ( ordered_pair @ ( sK52_D @ SV911 @ SV872 @ SV682 ) @ SV682 ) @ SV911 ) )
| ~ ( in @ ( sK52_D @ SV911 @ SV872 @ SV682 ) @ SV872 ) ) )
= $true )
| ( ( relation @ SV911 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5121]) ).
thf(5257,plain,
! [SV950: $i,SV683: $i] :
( ( ( ~ ( subset @ SV683 @ SV950 ) )
= $true )
| ( ( subset @ ( relation_dom @ SV683 ) @ ( relation_dom @ SV950 ) )
= $true )
| ( ( relation @ SV950 )
= $false )
| ( ( relation @ SV683 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5122]) ).
thf(5258,plain,
! [SV951: $i,SV683: $i] :
( ( ( ~ ( subset @ SV683 @ SV951 ) )
= $true )
| ( ( subset @ ( relation_rng @ SV683 ) @ ( relation_rng @ SV951 ) )
= $true )
| ( ( relation @ SV951 )
= $false )
| ( ( relation @ SV683 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5123]) ).
thf(5259,plain,
! [SV684: $i,SV952: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV684 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV952 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV684 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV952 ) ) ) )
= $true )
| ( ( SV684 = SV952 )
= $true )
| ( ( relation @ SV952 )
= $false )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5126]) ).
thf(5260,plain,
! [SV953: $i,SV684: $i] :
( ( ( ( SV684 != SV953 ) )
= $true )
| ( ( ~ ( ~ ! [SY1592: $i,SY1593: $i] :
( ~ ( in @ ( ordered_pair @ SY1592 @ SY1593 ) @ SV684 )
| ( in @ ( ordered_pair @ SY1592 @ SY1593 ) @ SV953 ) )
| ~ ! [SY1594: $i,SY1595: $i] :
( ~ ( in @ ( ordered_pair @ SY1594 @ SY1595 ) @ SV953 )
| ( in @ ( ordered_pair @ SY1594 @ SY1595 ) @ SV684 ) ) ) )
= $true )
| ( ( relation @ SV953 )
= $false )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5127]) ).
thf(5261,plain,
! [SV685: $i,SV982: $i] :
( ( ( ~ ! [SY1631: $i] :
( ~ ( subset @ SY1631 @ SV982 )
| ( in @ SY1631 @ ( sK3_SY386 @ SV982 @ SV685 ) ) )
| ~ ( in @ ( sK3_SY386 @ SV982 @ SV685 ) @ ( sK2_B @ SV685 ) ) )
= $false )
| ( ( ~ ( in @ SV982 @ ( sK2_B @ SV685 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5128]) ).
thf(5262,plain,
! [SV685: $i] :
( ( ! [SY1344: $i,SY1345: $i] :
( ~ ( in @ SY1344 @ ( sK2_B @ SV685 ) )
| ~ ( subset @ SY1345 @ SY1344 )
| ( in @ SY1345 @ ( sK2_B @ SV685 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5129]) ).
thf(5263,plain,
! [SV685: $i] :
( ( in @ SV685 @ ( sK2_B @ SV685 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5130]) ).
thf(5264,plain,
! [SV983: $i,SV954: $i] :
( ( ( SV954 = SV983 )
= $false )
| ( ( subset @ SV954 @ SV983 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5132]) ).
thf(5265,plain,
! [SV984: $i,SV955: $i] :
( ( ( SV955 = SV984 )
= $false )
| ( ( subset @ SV984 @ SV955 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5133]) ).
thf(5266,plain,
! [SV813: $i,SV877: $i] :
( ( ( ~ ( in @ ( sK28_C @ SV877 @ SV813 ) @ SV877 ) )
= $true )
| ( ( ~ ( subset @ ( sK28_C @ SV877 @ SV813 ) @ SV813 ) )
= $true )
| ( ( SV877
= ( powerset @ SV813 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5134]) ).
thf(5267,plain,
! [SV813: $i,SV877: $i] :
( ( ( in @ ( sK28_C @ SV877 @ SV813 ) @ SV877 )
= $true )
| ( ( subset @ ( sK28_C @ SV877 @ SV813 ) @ SV813 )
= $true )
| ( ( SV877
= ( powerset @ SV813 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5135]) ).
thf(5268,plain,
! [SV814: $i,SV878: $i] :
( ( ( ! [SY1514: $i] :
( ~ ( in @ SY1514 @ SV878 )
| ( subset @ SY1514 @ SV814 ) ) )
= $true )
| ( ( SV878
= ( powerset @ SV814 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5136]) ).
thf(5269,plain,
! [SV878: $i,SV814: $i] :
( ( ( ! [SY1515: $i] :
( ~ ( subset @ SY1515 @ SV814 )
| ( in @ SY1515 @ SV878 ) ) )
= $true )
| ( ( SV878
= ( powerset @ SV814 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5137]) ).
thf(5270,plain,
! [SV1023: $i,SV956: $i] :
( ( ( subset @ SV956 @ ( singleton @ SV1023 ) )
= $true )
| ( ( SV956 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5138]) ).
thf(5271,plain,
! [SV985: $i,SV957: $i] :
( ( ( SV957
= ( singleton @ SV985 ) )
= $false )
| ( ( subset @ SV957 @ ( singleton @ SV985 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5139]) ).
thf(5272,plain,
! [SV818: $i,SV880: $i] :
( ( ( ~ ( ~ ( in @ ( sK50_C @ SV880 @ SV818 ) @ SV818 )
| ~ ( ( ( apply @ SV880 @ ( sK50_C @ SV880 @ SV818 ) )
!= ( sK50_C @ SV880 @ SV818 ) ) ) )
| ( ( relation_dom @ SV880 )
!= SV818 ) )
= $true )
| ( ( SV880
= ( identity_relation @ SV818 ) )
= $true )
| ( ( function @ SV880 )
= $false )
| ( ( relation @ SV880 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5140]) ).
thf(5273,plain,
! [SV958: $i,SV986: $i] :
( ( ( ~ ( function @ SV986 ) )
= $true )
| ( ( ~ ( relation @ SV986 ) )
= $true )
| ( ( ( SV986
!= ( identity_relation @ SV958 ) )
| ! [SY1632: $i] :
( ~ ( in @ SY1632 @ SV958 )
| ( ( apply @ SV986 @ SY1632 )
= SY1632 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5141]) ).
thf(5274,plain,
! [SV959: $i,SV987: $i] :
( ( ( ~ ( function @ SV987 ) )
= $true )
| ( ( ~ ( relation @ SV987 ) )
= $true )
| ( ( ( SV987
!= ( identity_relation @ SV959 ) )
| ( ( relation_dom @ SV987 )
= SV959 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5142]) ).
thf(5275,plain,
! [SV821: $i,SV883: $i] :
( ( ( in @ ( sK18_C @ SV883 @ SV821 ) @ SV883 )
= $false )
| ( ( subset @ SV821 @ SV883 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5144]) ).
thf(5276,plain,
! [SV884: $i,SV822: $i,SV988: $i] :
( ( ( in @ SV988 @ SV822 )
= $false )
| ( ( in @ SV988 @ SV884 )
= $true )
| ( ( subset @ SV822 @ SV884 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5145]) ).
thf(5277,plain,
! [SV710: $i,SV608: $i,SV912: $i] :
( ( ( relation @ SV912 )
= $false )
| ( ( function @ SV912 )
= $false )
| ( ( ~ ( in @ SV608 @ ( relation_dom @ ( relation_composition @ SV912 @ SV710 ) ) )
| ( ( apply @ ( relation_composition @ SV912 @ SV710 ) @ SV608 )
= ( apply @ SV710 @ ( apply @ SV912 @ SV608 ) ) ) )
= $true )
| ( ( function @ SV710 )
= $false )
| ( ( relation @ SV710 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5146]) ).
thf(5278,plain,
! [SV711: $i,SV609: $i,SV913: $i] :
( ( ( relation @ SV913 )
= $false )
| ( ( function @ SV913 )
= $false )
| ( ( ~ ( in @ SV609 @ ( relation_dom @ SV711 ) )
| ( ( apply @ ( relation_composition @ SV711 @ SV913 ) @ SV609 )
= ( apply @ SV913 @ ( apply @ SV711 @ SV609 ) ) ) )
= $true )
| ( ( function @ SV711 )
= $false )
| ( ( relation @ SV711 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5147]) ).
thf(5279,plain,
! [SV652: $i,SV825: $i,SV885: $i] :
( ( ( ~ ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV652 )
| ~ ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV825 ) )
= $true )
| ( ( ~ ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV885 ) )
= $true )
| ( ( SV885
= ( set_intersection2 @ SV652 @ SV825 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5148]) ).
thf(5280,plain,
! [SV652: $i,SV825: $i,SV885: $i] :
( ( ( ~ ( ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV652 )
| ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV885 ) )
| ~ ( ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV825 )
| ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV885 ) ) )
= $false )
| ( ( SV885
= ( set_intersection2 @ SV652 @ SV825 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5149]) ).
thf(5281,plain,
! [SV886: $i,SV826: $i,SV652: $i] :
( ( ( ! [SY1517: $i] :
( ~ ( in @ SY1517 @ SV652 )
| ~ ( in @ SY1517 @ SV826 )
| ( in @ SY1517 @ SV886 ) ) )
= $true )
| ( ( SV886
= ( set_intersection2 @ SV652 @ SV826 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5150]) ).
thf(5282,plain,
! [SV826: $i,SV652: $i,SV886: $i] :
( ( ( ~ ( ~ ! [SY1518: $i] :
( ~ ( in @ SY1518 @ SV886 )
| ( in @ SY1518 @ SV652 ) )
| ~ ! [SY1519: $i] :
( ~ ( in @ SY1519 @ SV886 )
| ( in @ SY1519 @ SV826 ) ) ) )
= $true )
| ( ( SV886
= ( set_intersection2 @ SV652 @ SV826 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5151]) ).
thf(5283,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ( function @ SV1024 )
| ~ ( relation @ SV1024 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) )
| ( SV1024
= ( function_inverse @ SV653 ) ) )
= $true )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5152]) ).
thf(5284,plain,
! [SV653: $i] :
( ( ( ~ ! [SY1141: $i] :
( ~ ( function @ SY1141 )
| ~ ( relation @ SY1141 )
| ( SY1141
!= ( function_inverse @ SV653 ) )
| ~ ( ~ ~ ( ~ ! [SY1142: $i,SY1143: $i] :
( ( SY1143
!= ( apply @ SY1141 @ SY1142 ) )
| ~ ( in @ SY1142 @ ( relation_rng @ SV653 ) )
| ( SY1142
= ( apply @ SV653 @ SY1143 ) ) )
| ~ ! [SY1144: $i,SY1145: $i] :
( ( SY1145
!= ( apply @ SY1141 @ SY1144 ) )
| ~ ( in @ SY1144 @ ( relation_rng @ SV653 ) )
| ( in @ SY1145 @ ( relation_dom @ SV653 ) ) ) )
| ~ ~ ( ~ ! [SY1146: $i,SY1147: $i] :
( ( SY1146
!= ( apply @ SV653 @ SY1147 ) )
| ~ ( in @ SY1147 @ ( relation_dom @ SV653 ) )
| ( SY1147
= ( apply @ SY1141 @ SY1146 ) ) )
| ~ ! [SY1148: $i] :
( ! [SY1149: $i] :
( ( SY1148
!= ( apply @ SV653 @ SY1149 ) )
| ~ ( in @ SY1149 @ ( relation_dom @ SV653 ) ) )
| ( in @ SY1148 @ ( relation_rng @ SV653 ) ) ) ) ) )
| ~ ! [SY1150: $i] :
( ~ ( function @ SY1150 )
| ~ ( relation @ SY1150 )
| ( SY1150
!= ( function_inverse @ SV653 ) )
| ( ( relation_dom @ SY1150 )
= ( relation_rng @ SV653 ) ) ) )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5153]) ).
thf(5285,plain,
! [SV914: $i,SV989: $i] :
( ( ( element @ SV989 @ SV914 )
= $false )
| ( ( in @ SV989 @ SV914 )
= $true )
| ( ( empty @ SV914 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5154]) ).
thf(5286,plain,
! [SV915: $i,SV990: $i] :
( ( ( in @ SV990 @ SV915 )
= $false )
| ( ( element @ SV990 @ SV915 )
= $true )
| ( ( empty @ SV915 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5155]) ).
thf(5287,plain,
! [SV916: $i,SV1008: $i] :
( ( ( ~ ( element @ SV1008 @ SV916 ) )
= $true )
| ( ( empty @ SV1008 )
= $true )
| ( ( empty @ SV916 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5156]) ).
thf(5288,plain,
! [SV917: $i,SV1009: $i] :
( ( ( ~ ( empty @ SV1009 ) )
= $true )
| ( ( element @ SV1009 @ SV917 )
= $true )
| ( ( empty @ SV917 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5157]) ).
thf(5289,plain,
! [SV920: $i,SV739: $i,SV887: $i,SV654: $i] :
( ( ( ~ ( in @ SV654 @ SV887 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ SV920 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SV887 ) @ SV920 ) )
= $true )
| ( ( relation @ SV920 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5160]) ).
thf(5290,plain,
! [SV991: $i,SV739: $i,SV654: $i,SV1011: $i] :
( ( ( ~ ( relation @ SV1011 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SV991 ) @ SV1011 ) )
| ( in @ SV654 @ SV991 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5161]) ).
thf(5291,plain,
! [SV992: $i,SV739: $i,SV654: $i,SV1012: $i] :
( ( ( ~ ( relation @ SV1012 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SV992 ) @ SV1012 ) )
| ( in @ ( ordered_pair @ SV654 @ SV739 ) @ SV1012 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5162]) ).
thf(5292,plain,
! [SV655: $i,SV740: $i,SV961: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) @ SV655 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV740 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 ) )
| ~ ~ ( ~ ( ( in @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) @ SV655 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV740 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 ) ) ) ) )
= $true )
| ( ( SV961
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $true )
| ( ( relation @ SV961 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5163]) ).
thf(5293,plain,
! [SV740: $i,SV655: $i,SV962: $i] :
( ( ( ( SV962
!= ( relation_rng_restriction @ SV655 @ SV740 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1603: $i,SY1604: $i] :
( ~ ( in @ SY1604 @ SV655 )
| ~ ( in @ ( ordered_pair @ SY1603 @ SY1604 ) @ SV740 )
| ( in @ ( ordered_pair @ SY1603 @ SY1604 ) @ SV962 ) )
| ~ ~ ( ~ ! [SY1605: $i,SY1606: $i] :
( ~ ( in @ ( ordered_pair @ SY1605 @ SY1606 ) @ SV962 )
| ( in @ SY1606 @ SV655 ) )
| ~ ! [SY1607: $i,SY1608: $i] :
( ~ ( in @ ( ordered_pair @ SY1607 @ SY1608 ) @ SV962 )
| ( in @ ( ordered_pair @ SY1607 @ SY1608 ) @ SV740 ) ) ) ) )
= $true )
| ( ( relation @ SV962 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5164]) ).
thf(5294,plain,
! [SV657: $i,SV922: $i,SV964: $i] :
( ( ( ~ ( ! [SY1609: $i] :
( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SY1609 ) @ SV657 )
| ~ ( in @ SY1609 @ SV922 ) )
| ~ ( in @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SV964 ) ) )
= $false )
| ( ( SV964
= ( relation_inverse_image @ SV657 @ SV922 ) )
= $true )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5165]) ).
thf(5295,plain,
! [SV657: $i,SV922: $i,SV964: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ ( sK36_SY409 @ SV964 @ SV922 @ SV657 ) ) @ SV657 )
| ~ ( in @ ( sK36_SY409 @ SV964 @ SV922 @ SV657 ) @ SV922 ) )
| ( in @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SV964 ) ) )
= $false )
| ( ( SV964
= ( relation_inverse_image @ SV657 @ SV922 ) )
= $true )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5165]) ).
thf(5296,plain,
! [SV965: $i,SV923: $i,SV657: $i] :
( ( ( ~ ! [SY1610: $i] :
( ! [SY1552: $i] :
( ~ ( in @ ( ordered_pair @ SY1610 @ SY1552 ) @ SV657 )
| ~ ( in @ SY1552 @ SV923 ) )
| ( in @ SY1610 @ SV965 ) )
| ~ ! [SY1612: $i] :
( ~ ( in @ SY1612 @ SV965 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1612 @ ( sK34_E @ SY1612 @ SV965 @ SV923 @ SV657 ) ) @ SV657 )
| ~ ( in @ ( sK34_E @ SY1612 @ SV965 @ SV923 @ SV657 ) @ SV923 ) ) ) )
= $false )
| ( ( SV965
= ( relation_inverse_image @ SV657 @ SV923 ) )
= $false )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5166]) ).
thf(5297,plain,
! [SV658: $i,SV924: $i,SV966: $i] :
( ( ( ~ ( ! [SY1613: $i] :
( ~ ( in @ ( ordered_pair @ SY1613 @ ( sK38_D @ SV966 @ SV924 @ SV658 ) ) @ SV658 )
| ~ ( in @ SY1613 @ SV924 ) )
| ~ ( in @ ( sK38_D @ SV966 @ SV924 @ SV658 ) @ SV966 ) ) )
= $false )
| ( ( SV966
= ( relation_image @ SV658 @ SV924 ) )
= $true )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5167]) ).
thf(5298,plain,
! [SV658: $i,SV924: $i,SV966: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SV966 @ SV924 @ SV658 ) @ ( sK38_D @ SV966 @ SV924 @ SV658 ) ) @ SV658 )
| ~ ( in @ ( sK39_SY411 @ SV966 @ SV924 @ SV658 ) @ SV924 ) )
| ( in @ ( sK38_D @ SV966 @ SV924 @ SV658 ) @ SV966 ) ) )
= $false )
| ( ( SV966
= ( relation_image @ SV658 @ SV924 ) )
= $true )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5167]) ).
thf(5299,plain,
! [SV967: $i,SV925: $i,SV658: $i] :
( ( ( ~ ! [SY1614: $i] :
( ! [SY1558: $i] :
( ~ ( in @ ( ordered_pair @ SY1558 @ SY1614 ) @ SV658 )
| ~ ( in @ SY1558 @ SV925 ) )
| ( in @ SY1614 @ SV967 ) )
| ~ ! [SY1616: $i] :
( ~ ( in @ SY1616 @ SV967 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SY1616 @ SV967 @ SV925 @ SV658 ) @ SY1616 ) @ SV658 )
| ~ ( in @ ( sK37_E @ SY1616 @ SV967 @ SV925 @ SV658 ) @ SV925 ) ) ) )
= $false )
| ( ( SV967
= ( relation_image @ SV658 @ SV925 ) )
= $false )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5168]) ).
thf(5300,plain,
! [SV968: $i,SV926: $i] :
( ( ( SV926 = SV968 )
= $false )
| ( ( proper_subset @ SV926 @ SV968 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5169]) ).
thf(5301,plain,
! [SV928: $i] :
( ( ( empty @ SV928 )
= $false )
| ( ( ~ ( relation @ SV928 ) )
= $true )
| ( ( ~ ( function @ SV928 ) )
= $true )
| ( ( function @ SV928 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5171]) ).
thf(5302,plain,
! [SV929: $i] :
( ( ( empty @ SV929 )
= $false )
| ( ( ~ ( relation @ SV929 ) )
= $true )
| ( ( ~ ( function @ SV929 ) )
= $true )
| ( ( relation @ SV929 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5172]) ).
thf(5303,plain,
! [SV1013: $i,SV993: $i,SV781: $i] :
( ( ( ( sK69_B @ SV781 )
= ( ordered_pair @ SV993 @ SV1013 ) )
= $false )
| ( ( relation @ SV781 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5174]) ).
thf(5304,plain,
! [SV994: $i,SV970: $i,SV659: $i] :
( ( ( subset @ ( unordered_pair @ SV659 @ SV970 ) @ SV994 )
= $false )
| ( ( in @ SV659 @ SV994 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5176]) ).
thf(5305,plain,
! [SV995: $i,SV971: $i,SV659: $i] :
( ( ( subset @ ( unordered_pair @ SV659 @ SV971 ) @ SV995 )
= $false )
| ( ( in @ SV971 @ SV995 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5177]) ).
thf(5306,plain,
! [SV660: $i,SV783: $i,SV1014: $i] :
( ( ( ~ ( relation @ SV1014 ) )
= $true )
| ( ( ~ ( ~ ( ! [SY1644: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ SY1644 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1644 @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV783 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV1014 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK10_SY395 @ SV1014 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV783 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV1014 ) ) )
| ( SV1014
= ( relation_composition @ SV660 @ SV783 ) ) )
= $true )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5178]) ).
thf(5307,plain,
! [SV783: $i,SV660: $i,SV1015: $i] :
( ( ( ~ ( relation @ SV1015 ) )
= $true )
| ( ( ( SV1015
!= ( relation_composition @ SV660 @ SV783 ) )
| ~ ( ~ ! [SY1645: $i,SY1646: $i] :
( ! [SY1410: $i] :
( ~ ( in @ ( ordered_pair @ SY1645 @ SY1410 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1410 @ SY1646 ) @ SV783 ) )
| ( in @ ( ordered_pair @ SY1645 @ SY1646 ) @ SV1015 ) )
| ~ ! [SY1648: $i,SY1649: $i] :
( ~ ( in @ ( ordered_pair @ SY1648 @ SY1649 ) @ SV1015 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1648 @ ( sK7_F @ SY1649 @ SY1648 @ SV1015 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY1649 @ SY1648 @ SV1015 @ SV783 @ SV660 ) @ SY1649 ) @ SV783 ) ) ) ) )
= $true )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5179]) ).
thf(5308,plain,
! [SV661: $i,SV932: $i] :
( ( ( ! [SY1562: $i] :
~ ( in @ ( ordered_pair @ SY1562 @ ( sK60_C @ SV932 @ SV661 ) ) @ SV661 )
| ~ ( in @ ( sK60_C @ SV932 @ SV661 ) @ SV932 ) )
= $true )
| ( ( SV932
= ( relation_rng @ SV661 ) )
= $true )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5180]) ).
thf(5309,plain,
! [SV661: $i,SV932: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK61_SY417 @ SV932 @ SV661 ) @ ( sK60_C @ SV932 @ SV661 ) ) @ SV661 )
| ( in @ ( sK60_C @ SV932 @ SV661 ) @ SV932 ) )
= $true )
| ( ( SV932
= ( relation_rng @ SV661 ) )
= $true )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5181]) ).
thf(5310,plain,
! [SV933: $i,SV661: $i] :
( ( ( ~ ! [SY1563: $i] :
( ! [SY1207: $i] :
~ ( in @ ( ordered_pair @ SY1207 @ SY1563 ) @ SV661 )
| ( in @ SY1563 @ SV933 ) ) )
= $false )
| ( ( SV933
= ( relation_rng @ SV661 ) )
= $false )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5182]) ).
thf(5311,plain,
! [SV661: $i,SV933: $i] :
( ( ( ~ ! [SY1565: $i] :
( ~ ( in @ SY1565 @ SV933 )
| ( in @ ( ordered_pair @ ( sK59_D @ SY1565 @ SV933 @ SV661 ) @ SY1565 ) @ SV661 ) ) )
= $false )
| ( ( SV933
= ( relation_rng @ SV661 ) )
= $false )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5182]) ).
thf(5312,plain,
! [SV662: $i,SV838: $i,SV891: $i] :
( ( ( ~ ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV662 )
| ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV838 ) )
= $true )
| ( ( ~ ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV891 ) )
= $true )
| ( ( SV891
= ( set_difference @ SV662 @ SV838 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5183]) ).
thf(5313,plain,
! [SV662: $i,SV838: $i,SV891: $i] :
( ( ( ~ ( ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV662 )
| ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV891 ) )
| ~ ( ~ ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV838 )
| ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV891 ) ) )
= $false )
| ( ( SV891
= ( set_difference @ SV662 @ SV838 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5184]) ).
thf(5314,plain,
! [SV892: $i,SV839: $i,SV662: $i] :
( ( ( ! [SY1523: $i] :
( ~ ( in @ SY1523 @ SV662 )
| ( in @ SY1523 @ SV839 )
| ( in @ SY1523 @ SV892 ) ) )
= $true )
| ( ( SV892
= ( set_difference @ SV662 @ SV839 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5185]) ).
thf(5315,plain,
! [SV839: $i,SV662: $i,SV892: $i] :
( ( ( ~ ( ~ ! [SY1524: $i] :
( ~ ( in @ SY1524 @ SV892 )
| ( in @ SY1524 @ SV662 ) )
| ~ ! [SY1525: $i] :
( ~ ( in @ SY1525 @ SV892 )
| ~ ( in @ SY1525 @ SV839 ) ) ) )
= $true )
| ( ( SV892
= ( set_difference @ SV662 @ SV839 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5186]) ).
thf(5316,plain,
! [SV840: $i,SV790: $i] :
( ( ( relation @ SV790 )
= $false )
| ( ( function @ SV790 )
= $false )
| ( ( ~ ( relation @ SV840 ) )
= $true )
| ( ( ~ ( function @ SV840 ) )
= $true )
| ( ( function @ ( relation_composition @ SV790 @ SV840 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5187]) ).
thf(5317,plain,
! [SV841: $i,SV791: $i] :
( ( ( relation @ SV791 )
= $false )
| ( ( function @ SV791 )
= $false )
| ( ( ~ ( relation @ SV841 ) )
= $true )
| ( ( ~ ( function @ SV841 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV791 @ SV841 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5188]) ).
thf(5318,plain,
! [SV893: $i,SV842: $i,SV663: $i] :
( ( ( in @ SV663 @ SV842 )
= $false )
| ( ( ~ ( in @ SV663 @ ( relation_rng @ SV893 ) ) )
= $true )
| ( ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SV842 @ SV893 ) ) )
= $true )
| ( ( relation @ SV893 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5189]) ).
thf(5319,plain,
! [SV972: $i,SV663: $i,SV996: $i] :
( ( ( relation @ SV996 )
= $false )
| ( ( ~ ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SV972 @ SV996 ) ) )
| ( in @ SV663 @ SV972 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5190]) ).
thf(5320,plain,
! [SV973: $i,SV663: $i,SV997: $i] :
( ( ( relation @ SV997 )
= $false )
| ( ( ~ ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SV973 @ SV997 ) ) )
| ( in @ SV663 @ ( relation_rng @ SV997 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5191]) ).
thf(5321,plain,
! [SV664: $i] :
( ( ( ! [SY1222: $i] :
( ~ ( in @ SY1222 @ ( relation_dom @ SV664 ) )
| ! [SY1223: $i] :
( ( SY1223
!= ( apply @ SV664 @ SY1222 ) )
| ( in @ ( ordered_pair @ SY1222 @ SY1223 ) @ SV664 ) ) ) )
= $true )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5192]) ).
thf(5322,plain,
! [SV664: $i] :
( ( ( ! [SY1224: $i] :
( ~ ( in @ SY1224 @ ( relation_dom @ SV664 ) )
| ! [SY1225: $i] :
( ~ ( in @ ( ordered_pair @ SY1224 @ SY1225 ) @ SV664 )
| ( SY1225
= ( apply @ SV664 @ SY1224 ) ) ) ) )
= $true )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5193]) ).
thf(5323,plain,
! [SV664: $i] :
( ( ( ! [SY1226: $i] :
( ( in @ SY1226 @ ( relation_dom @ SV664 ) )
| ! [SY1227: $i] :
( ( SY1227
!= ( apply @ SV664 @ SY1226 ) )
| ( SY1227 = empty_set ) ) ) )
= $true )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5194]) ).
thf(5324,plain,
! [SV664: $i] :
( ( ( ! [SY1228: $i] :
( ( in @ SY1228 @ ( relation_dom @ SV664 ) )
| ! [SY1229: $i] :
( ( SY1229 != empty_set )
| ( SY1229
= ( apply @ SV664 @ SY1228 ) ) ) ) )
= $true )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5195]) ).
thf(5325,plain,
! [SV665: $i,SV934: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV934 @ SV665 ) @ ( sK20_SY399 @ SV934 @ SV665 ) ) @ SV665 )
| ~ ~ ( in @ ( ordered_pair @ ( sK19_C @ SV934 @ SV665 ) @ ( sK20_SY399 @ SV934 @ SV665 ) ) @ SV934 ) )
= $false )
| ( ( subset @ SV665 @ SV934 )
= $true )
| ( ( relation @ SV934 )
= $false )
| ( ( relation @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5196]) ).
thf(5326,plain,
! [SV935: $i,SV665: $i] :
( ( ( subset @ SV665 @ SV935 )
= $false )
| ( ( ! [SY1566: $i,SY1567: $i] :
( ~ ( in @ ( ordered_pair @ SY1566 @ SY1567 ) @ SV665 )
| ( in @ ( ordered_pair @ SY1566 @ SY1567 ) @ SV935 ) ) )
= $true )
| ( ( relation @ SV935 )
= $false )
| ( ( relation @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5197]) ).
thf(5327,plain,
! [SV742: $i,SV666: $i,SV1016: $i] :
( ( ( ~ ( function @ SV1016 )
| ~ ( relation @ SV1016 ) )
= $true )
| ( ( ~ ( in @ SV666 @ ( relation_dom @ SV1016 ) )
| ~ ( in @ ( apply @ SV1016 @ SV666 ) @ ( relation_dom @ SV742 ) )
| ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SV1016 @ SV742 ) ) ) )
= $true )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5198]) ).
thf(5328,plain,
! [SV742: $i,SV666: $i] :
( ( ( ~ ! [SY1377: $i] :
( ~ ( function @ SY1377 )
| ~ ( relation @ SY1377 )
| ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1377 @ SV742 ) ) )
| ( in @ SV666 @ ( relation_dom @ SY1377 ) ) ) )
= $false )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5199]) ).
thf(5329,plain,
! [SV742: $i,SV666: $i] :
( ( ( ~ ! [SY1378: $i] :
( ~ ( function @ SY1378 )
| ~ ( relation @ SY1378 )
| ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1378 @ SV742 ) ) )
| ( in @ ( apply @ SY1378 @ SV666 ) @ ( relation_dom @ SV742 ) ) ) )
= $false )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5199]) ).
thf(5330,plain,
! [SV843: $i,SV667: $i,SV894: $i,SV1017: $i] :
( ( ( ~ ( in @ SV1017 @ ( relation_rng @ SV894 ) )
| ~ ( in @ ( ordered_pair @ SV667 @ SV1017 ) @ SV894 ) )
= $true )
| ( ( ~ ( in @ SV1017 @ SV843 ) )
= $true )
| ( ( in @ SV667 @ ( relation_inverse_image @ SV894 @ SV843 ) )
= $true )
| ( ( relation @ SV894 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5200]) ).
thf(5331,plain,
! [SV667: $i,SV844: $i,SV895: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK51_D @ SV895 @ SV844 @ SV667 ) @ ( relation_rng @ SV895 ) )
| ~ ( in @ ( ordered_pair @ SV667 @ ( sK51_D @ SV895 @ SV844 @ SV667 ) ) @ SV895 ) )
| ~ ( in @ ( sK51_D @ SV895 @ SV844 @ SV667 ) @ SV844 ) )
= $false )
| ( ( in @ SV667 @ ( relation_inverse_image @ SV895 @ SV844 ) )
= $false )
| ( ( relation @ SV895 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5201]) ).
thf(5332,plain,
! [SV936: $i,SV846: $i,SV793: $i] :
( ( ( disjoint @ SV793 @ SV846 )
= $false )
| ( ( in @ SV936 @ SV793 )
= $false )
| ( ( in @ SV936 @ SV846 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5202]) ).
thf(5333,plain,
! [SV896: $i,SV847: $i,SV668: $i] :
( ( ( in @ SV668 @ SV847 )
= $false )
| ( ( ~ ( in @ SV668 @ ( relation_dom @ SV896 ) ) )
= $true )
| ( ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SV896 @ SV847 ) ) )
= $true )
| ( ( relation @ SV896 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5203]) ).
thf(5334,plain,
! [SV974: $i,SV668: $i,SV998: $i] :
( ( ( relation @ SV998 )
= $false )
| ( ( ~ ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SV998 @ SV974 ) ) )
| ( in @ SV668 @ SV974 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5204]) ).
thf(5335,plain,
! [SV975: $i,SV668: $i,SV999: $i] :
( ( ( relation @ SV999 )
= $false )
| ( ( ~ ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SV999 @ SV975 ) ) )
| ( in @ SV668 @ ( relation_dom @ SV999 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5205]) ).
thf(5336,plain,
! [SV669: $i,SV848: $i,SV897: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV897 )
| ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV669 ) )
| ~ ( ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV897 )
| ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV848 ) ) )
= $false )
| ( ( SV897
= ( set_union2 @ SV669 @ SV848 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5206]) ).
thf(5337,plain,
! [SV669: $i,SV848: $i,SV897: $i] :
( ( ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV897 )
= $true )
| ( ( ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV669 )
| ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV848 ) )
= $true )
| ( ( SV897
= ( set_union2 @ SV669 @ SV848 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5207]) ).
thf(5338,plain,
! [SV849: $i,SV669: $i,SV898: $i] :
( ( ( ! [SY1527: $i] :
( ~ ( in @ SY1527 @ SV898 )
| ( in @ SY1527 @ SV669 )
| ( in @ SY1527 @ SV849 ) ) )
= $true )
| ( ( SV898
= ( set_union2 @ SV669 @ SV849 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5208]) ).
thf(5339,plain,
! [SV849: $i,SV898: $i,SV669: $i] :
( ( ( ~ ( ~ ! [SY1528: $i] :
( ~ ( in @ SY1528 @ SV669 )
| ( in @ SY1528 @ SV898 ) )
| ~ ! [SY1529: $i] :
( ~ ( in @ SY1529 @ SV849 )
| ( in @ SY1529 @ SV898 ) ) ) )
= $true )
| ( ( SV898
= ( set_union2 @ SV669 @ SV849 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5209]) ).
thf(5340,plain,
! [SV937: $i,SV1000: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK33_SY406 @ SV1000 @ SV937 ) @ SV937 )
| ~ ~ ( in @ ( sK32_C @ SV1000 @ SV937 ) @ ( sK33_SY406 @ SV1000 @ SV937 ) ) )
| ~ ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SV1000 ) )
| ~ ( ! [SY1636: $i] :
( ~ ( in @ SY1636 @ SV937 )
| ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SY1636 ) )
| ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SV1000 ) ) )
= $false )
| ( ( SV1000
= ( set_meet @ SV937 ) )
= $true )
| ( ( SV937 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5210]) ).
thf(5341,plain,
! [SV938: $i,SV1001: $i] :
( ( ( SV1001
= ( set_meet @ SV938 ) )
= $false )
| ( ( ~ ( ~ ! [SY1637: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY1637 @ SV1001 @ SV938 ) @ SV938 )
| ~ ~ ( in @ SY1637 @ ( sK31_D @ SY1637 @ SV1001 @ SV938 ) ) )
| ( in @ SY1637 @ SV1001 ) )
| ~ ! [SY1638: $i] :
( ~ ( in @ SY1638 @ SV1001 )
| ! [SY1573: $i] :
( ~ ( in @ SY1573 @ SV938 )
| ( in @ SY1638 @ SY1573 ) ) ) ) )
= $true )
| ( ( SV938 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5211]) ).
thf(5342,plain,
! [SV939: $i,SV1018: $i] :
( ( ( ( SV1018
!= ( set_meet @ SV939 ) ) )
= $true )
| ( ( SV1018 = empty_set )
= $true )
| ( ( SV939 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5212]) ).
thf(5343,plain,
! [SV940: $i,SV1019: $i] :
( ( ( ( SV1019 != empty_set ) )
= $true )
| ( ( SV1019
= ( set_meet @ SV940 ) )
= $true )
| ( ( SV940 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5213]) ).
thf(5344,plain,
! [SV899: $i,SV850: $i,SV670: $i] :
( ( ( ! [SY1530: $i,SY1531: $i] :
( ~ ( in @ SY1530 @ SV670 )
| ~ ( in @ SY1531 @ SV850 )
| ( ( sK23_D @ SV899 @ SV850 @ SV670 )
!= ( ordered_pair @ SY1530 @ SY1531 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV899 @ SV850 @ SV670 ) @ SV899 ) )
= $true )
| ( ( SV899
= ( cartesian_product2 @ SV670 @ SV850 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5214]) ).
thf(5345,plain,
! [SV670: $i,SV850: $i,SV899: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY403 @ SV899 @ SV850 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK25_SY405 @ SV899 @ SV850 @ SV670 ) @ SV850 ) )
| ( ( sK23_D @ SV899 @ SV850 @ SV670 )
!= ( ordered_pair @ ( sK24_SY403 @ SV899 @ SV850 @ SV670 ) @ ( sK25_SY405 @ SV899 @ SV850 @ SV670 ) ) ) ) )
= $true )
| ( ( in @ ( sK23_D @ SV899 @ SV850 @ SV670 ) @ SV899 )
= $true )
| ( ( SV899
= ( cartesian_product2 @ SV670 @ SV850 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5215]) ).
thf(5346,plain,
! [SV900: $i,SV851: $i,SV670: $i] :
( ( ( ! [SY1532: $i] :
( ! [SY1483: $i,SY1484: $i] :
( ~ ( in @ SY1483 @ SV670 )
| ~ ( in @ SY1484 @ SV851 )
| ( SY1532
!= ( ordered_pair @ SY1483 @ SY1484 ) ) )
| ( in @ SY1532 @ SV900 ) ) )
= $true )
| ( ( SV900
= ( cartesian_product2 @ SV670 @ SV851 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5216]) ).
thf(5347,plain,
! [SV670: $i,SV851: $i,SV900: $i] :
( ( ( ! [SY1535: $i] :
( ~ ( in @ SY1535 @ SV900 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SY1535 @ SV900 @ SV851 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK22_SY400 @ SY1535 @ SV900 @ SV851 @ SV670 ) @ SV851 ) )
| ( SY1535
!= ( ordered_pair @ ( sK21_E @ SY1535 @ SV900 @ SV851 @ SV670 ) @ ( sK22_SY400 @ SY1535 @ SV900 @ SV851 @ SV670 ) ) ) ) ) )
= $true )
| ( ( SV900
= ( cartesian_product2 @ SV670 @ SV851 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5217]) ).
thf(5348,plain,
! [SV671: $i,SV901: $i,SV852: $i] :
( ( ( ( SV852
!= ( apply @ SV901 @ SV671 ) )
| ~ ( in @ SV671 @ ( relation_dom @ SV901 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV671 @ SV852 ) @ SV901 )
= $true )
| ( ( function @ SV901 )
= $false )
| ( ( relation @ SV901 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5218]) ).
thf(5349,plain,
! [SV976: $i,SV671: $i,SV1002: $i] :
( ( ( ~ ( function @ SV1002 ) )
= $true )
| ( ( ~ ( relation @ SV1002 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV671 @ SV976 ) @ SV1002 )
| ( SV976
= ( apply @ SV1002 @ SV671 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5219]) ).
thf(5350,plain,
! [SV977: $i,SV671: $i,SV1003: $i] :
( ( ( ~ ( function @ SV1003 ) )
= $true )
| ( ( ~ ( relation @ SV1003 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV671 @ SV977 ) @ SV1003 )
| ( in @ SV671 @ ( relation_dom @ SV1003 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5220]) ).
thf(5351,plain,
! [SV672: $i,SV941: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SV941 @ SV672 ) @ ( sK12_SY396 @ SV941 @ SV672 ) ) @ SV941 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SV941 @ SV672 ) @ ( sK11_C @ SV941 @ SV672 ) ) @ SV672 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK11_C @ SV941 @ SV672 ) @ ( sK12_SY396 @ SV941 @ SV672 ) ) @ SV941 )
| ( in @ ( ordered_pair @ ( sK12_SY396 @ SV941 @ SV672 ) @ ( sK11_C @ SV941 @ SV672 ) ) @ SV672 ) ) )
= $false )
| ( ( SV941
= ( relation_inverse @ SV672 ) )
= $true )
| ( ( relation @ SV941 )
= $false )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5221]) ).
thf(5352,plain,
! [SV672: $i,SV942: $i] :
( ( ( SV942
= ( relation_inverse @ SV672 ) )
= $false )
| ( ( ~ ( ~ ! [SY1576: $i,SY1577: $i] :
( ~ ( in @ ( ordered_pair @ SY1576 @ SY1577 ) @ SV942 )
| ( in @ ( ordered_pair @ SY1577 @ SY1576 ) @ SV672 ) )
| ~ ! [SY1578: $i,SY1579: $i] :
( ~ ( in @ ( ordered_pair @ SY1579 @ SY1578 ) @ SV672 )
| ( in @ ( ordered_pair @ SY1578 @ SY1579 ) @ SV942 ) ) ) )
= $true )
| ( ( relation @ SV942 )
= $false )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5222]) ).
thf(5353,plain,
! [SV904: $i,SV674: $i,SV943: $i,SV743: $i] :
( ( ( in @ SV743 @ SV943 )
= $false )
| ( ( in @ SV674 @ SV904 )
= $false )
| ( ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SV904 @ SV943 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5227]) ).
thf(5354,plain,
! [SV1025: $i,SV1004: $i,SV743: $i,SV674: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SV1004 @ SV1025 ) ) )
= $true )
| ( ( in @ SV674 @ SV1004 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5228]) ).
thf(5355,plain,
! [SV1020: $i,SV1005: $i,SV743: $i,SV674: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SV1005 @ SV1020 ) ) )
= $true )
| ( ( in @ SV743 @ SV1020 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5229]) ).
thf(5356,plain,
! [SV675: $i,SV857: $i,SV905: $i] :
( ( ( ~ ( ~ ( in @ ( sK27_D @ SV905 @ SV857 @ SV675 ) @ SV905 )
| ( ( sK27_D @ SV905 @ SV857 @ SV675 )
!= SV675 ) )
| ~ ( ~ ( in @ ( sK27_D @ SV905 @ SV857 @ SV675 ) @ SV905 )
| ( ( sK27_D @ SV905 @ SV857 @ SV675 )
!= SV857 ) ) )
= $false )
| ( ( SV905
= ( unordered_pair @ SV675 @ SV857 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5230]) ).
thf(5357,plain,
! [SV675: $i,SV857: $i,SV905: $i] :
( ( ( in @ ( sK27_D @ SV905 @ SV857 @ SV675 ) @ SV905 )
= $true )
| ( ( ( ( sK27_D @ SV905 @ SV857 @ SV675 )
= SV675 )
| ( ( sK27_D @ SV905 @ SV857 @ SV675 )
= SV857 ) )
= $true )
| ( ( SV905
= ( unordered_pair @ SV675 @ SV857 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5231]) ).
thf(5358,plain,
! [SV858: $i,SV675: $i,SV906: $i] :
( ( ( ! [SY1537: $i] :
( ~ ( in @ SY1537 @ SV906 )
| ( SY1537 = SV675 )
| ( SY1537 = SV858 ) ) )
= $true )
| ( ( SV906
= ( unordered_pair @ SV675 @ SV858 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5232]) ).
thf(5359,plain,
! [SV858: $i,SV906: $i,SV675: $i] :
( ( ( ~ ( ~ ! [SY1538: $i] :
( ( SY1538 != SV675 )
| ( in @ SY1538 @ SV906 ) )
| ~ ! [SY1539: $i] :
( ( SY1539 != SV858 )
| ( in @ SY1539 @ SV906 ) ) ) )
= $true )
| ( ( SV906
= ( unordered_pair @ SV675 @ SV858 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5233]) ).
thf(5360,plain,
! [SV907: $i,SV676: $i,SV944: $i,SV744: $i] :
( ( ( in @ SV744 @ SV944 )
= $false )
| ( ( in @ SV676 @ SV907 )
= $false )
| ( ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SV907 @ SV944 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5234]) ).
thf(5361,plain,
! [SV1026: $i,SV1006: $i,SV744: $i,SV676: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SV1006 @ SV1026 ) ) )
= $true )
| ( ( in @ SV676 @ SV1006 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5235]) ).
thf(5362,plain,
! [SV1021: $i,SV1007: $i,SV744: $i,SV676: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SV1007 @ SV1021 ) ) )
= $true )
| ( ( in @ SV744 @ SV1021 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5236]) ).
thf(5363,plain,
! [SV1027: $i,SV804: $i,SV863: $i] :
( ( ( ~ ( in @ ( sK15_C @ SV863 @ SV804 ) @ SV1027 )
| ~ ( in @ SV1027 @ SV804 ) )
= $true )
| ( ( ~ ( in @ ( sK15_C @ SV863 @ SV804 ) @ SV863 ) )
= $true )
| ( ( SV863
= ( union @ SV804 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5237]) ).
thf(5364,plain,
! [SV804: $i,SV863: $i] :
( ( ( ~ ( in @ ( sK15_C @ SV863 @ SV804 ) @ ( sK16_SY398 @ SV863 @ SV804 ) )
| ~ ( in @ ( sK16_SY398 @ SV863 @ SV804 ) @ SV804 ) )
= $false )
| ( ( in @ ( sK15_C @ SV863 @ SV804 ) @ SV863 )
= $true )
| ( ( SV863
= ( union @ SV804 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5238]) ).
thf(5365,plain,
! [SV864: $i,SV805: $i,SV1028: $i] :
( ( ( ! [SY1650: $i] :
( ~ ( in @ SV1028 @ SY1650 )
| ~ ( in @ SY1650 @ SV805 ) )
| ( in @ SV1028 @ SV864 ) )
= $true )
| ( ( SV864
= ( union @ SV805 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5239]) ).
thf(5366,plain,
! [SV805: $i,SV864: $i,SV1029: $i] :
( ( ( ~ ( in @ SV1029 @ SV864 )
| ~ ( ~ ( in @ SV1029 @ ( sK14_D @ SV1029 @ SV864 @ SV805 ) )
| ~ ( in @ ( sK14_D @ SV1029 @ SV864 @ SV805 ) @ SV805 ) ) )
= $true )
| ( ( SV864
= ( union @ SV805 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5240]) ).
thf(5367,plain,
! [SV679: $i,SV946: $i] :
( ( ( ! [SY1580: $i] :
~ ( in @ ( ordered_pair @ ( sK63_C @ SV946 @ SV679 ) @ SY1580 ) @ SV679 )
| ~ ( in @ ( sK63_C @ SV946 @ SV679 ) @ SV946 ) )
= $true )
| ( ( SV946
= ( relation_dom @ SV679 ) )
= $true )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5241]) ).
thf(5368,plain,
! [SV679: $i,SV946: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK63_C @ SV946 @ SV679 ) @ ( sK64_SY419 @ SV946 @ SV679 ) ) @ SV679 )
| ( in @ ( sK63_C @ SV946 @ SV679 ) @ SV946 ) )
= $true )
| ( ( SV946
= ( relation_dom @ SV679 ) )
= $true )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5242]) ).
thf(5369,plain,
! [SV947: $i,SV679: $i] :
( ( ( ~ ! [SY1581: $i] :
( ! [SY1312: $i] :
~ ( in @ ( ordered_pair @ SY1581 @ SY1312 ) @ SV679 )
| ( in @ SY1581 @ SV947 ) ) )
= $false )
| ( ( SV947
= ( relation_dom @ SV679 ) )
= $false )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5243]) ).
thf(5370,plain,
! [SV679: $i,SV947: $i] :
( ( ( ~ ! [SY1583: $i] :
( ~ ( in @ SY1583 @ SV947 )
| ( in @ ( ordered_pair @ SY1583 @ ( sK62_D @ SY1583 @ SV947 @ SV679 ) ) @ SV679 ) ) )
= $false )
| ( ( SV947
= ( relation_dom @ SV679 ) )
= $false )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5243]) ).
thf(5371,plain,
! [SV806: $i,SV867: $i] :
( ( ( ( ( sK44_C @ SV867 @ SV806 )
!= ( sK45_SY414 @ SV867 @ SV806 ) )
| ~ ( in @ ( sK44_C @ SV867 @ SV806 ) @ SV806 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 ) )
= $true )
| ( ( SV867
= ( identity_relation @ SV806 ) )
= $true )
| ( ( relation @ SV867 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5246]) ).
thf(5372,plain,
! [SV806: $i,SV867: $i] :
( ( ( ~ ( ~ ( ( ( sK44_C @ SV867 @ SV806 )
= ( sK45_SY414 @ SV867 @ SV806 ) )
| ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 ) )
| ~ ( ( in @ ( sK44_C @ SV867 @ SV806 ) @ SV806 )
| ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 ) ) ) )
= $true )
| ( ( SV867
= ( identity_relation @ SV806 ) )
= $true )
| ( ( relation @ SV867 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5247]) ).
thf(5373,plain,
! [SV868: $i,SV807: $i] :
( ( ( ~ ! [SY1503: $i,SY1504: $i] :
( ( SY1503 != SY1504 )
| ~ ( in @ SY1503 @ SV807 )
| ( in @ ( ordered_pair @ SY1503 @ SY1504 ) @ SV868 ) ) )
= $false )
| ( ( SV868
= ( identity_relation @ SV807 ) )
= $false )
| ( ( relation @ SV868 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5248]) ).
thf(5374,plain,
! [SV807: $i,SV868: $i] :
( ( ( ~ ~ ( ~ ! [SY1505: $i,SY1506: $i] :
( ~ ( in @ ( ordered_pair @ SY1505 @ SY1506 ) @ SV868 )
| ( SY1505 = SY1506 ) )
| ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
~ ( in @ ( ordered_pair @ SY1507 @ SY1508 ) @ SV868 )
| ( in @ SY1507 @ SV807 ) ) ) )
= $false )
| ( ( SV868
= ( identity_relation @ SV807 ) )
= $false )
| ( ( relation @ SV868 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5248]) ).
thf(5375,plain,
! [SV681: $i,SV948: $i,SV980: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ SV948 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV681 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 ) )
| ~ ~ ( ~ ( ( in @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ SV948 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV681 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 ) ) ) ) )
= $true )
| ( ( SV980
= ( relation_dom_restriction @ SV681 @ SV948 ) )
= $true )
| ( ( relation @ SV980 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5249]) ).
thf(5376,plain,
! [SV949: $i,SV681: $i,SV981: $i] :
( ( ( ( SV981
!= ( relation_dom_restriction @ SV681 @ SV949 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1625: $i,SY1626: $i] :
( ~ ( in @ SY1625 @ SV949 )
| ~ ( in @ ( ordered_pair @ SY1625 @ SY1626 ) @ SV681 )
| ( in @ ( ordered_pair @ SY1625 @ SY1626 ) @ SV981 ) )
| ~ ~ ( ~ ! [SY1627: $i] :
( ! [SY1628: $i] :
~ ( in @ ( ordered_pair @ SY1627 @ SY1628 ) @ SV981 )
| ( in @ SY1627 @ SV949 ) )
| ~ ! [SY1629: $i,SY1630: $i] :
( ~ ( in @ ( ordered_pair @ SY1629 @ SY1630 ) @ SV981 )
| ( in @ ( ordered_pair @ SY1629 @ SY1630 ) @ SV681 ) ) ) ) )
= $true )
| ( ( relation @ SV981 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5250]) ).
thf(5377,plain,
! [SV808: $i,SV869: $i] :
( ( ( ( sK30_C @ SV869 @ SV808 )
= SV808 )
= $false )
| ( ( ~ ( in @ ( sK30_C @ SV869 @ SV808 ) @ SV869 ) )
= $true )
| ( ( SV869
= ( singleton @ SV808 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5251]) ).
thf(5378,plain,
! [SV870: $i,SV809: $i,SV1030: $i] :
( ( ( ( SV1030 != SV809 )
| ( in @ SV1030 @ SV870 ) )
= $true )
| ( ( SV870
= ( singleton @ SV809 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5253]) ).
thf(5379,plain,
! [SV809: $i,SV870: $i,SV1031: $i] :
( ( ( ~ ( in @ SV1031 @ SV870 )
| ( SV1031 = SV809 ) )
= $true )
| ( ( SV870
= ( singleton @ SV809 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5254]) ).
thf(5380,plain,
! [SV871: $i,SV682: $i,SV910: $i,SV1022: $i] :
( ( ( ~ ( in @ SV1022 @ ( relation_dom @ SV910 ) )
| ~ ( in @ ( ordered_pair @ SV1022 @ SV682 ) @ SV910 ) )
= $true )
| ( ( ~ ( in @ SV1022 @ SV871 ) )
= $true )
| ( ( in @ SV682 @ ( relation_image @ SV910 @ SV871 ) )
= $true )
| ( ( relation @ SV910 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5255]) ).
thf(5381,plain,
! [SV682: $i,SV872: $i,SV911: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK52_D @ SV911 @ SV872 @ SV682 ) @ ( relation_dom @ SV911 ) )
| ~ ( in @ ( ordered_pair @ ( sK52_D @ SV911 @ SV872 @ SV682 ) @ SV682 ) @ SV911 ) )
| ~ ( in @ ( sK52_D @ SV911 @ SV872 @ SV682 ) @ SV872 ) )
= $false )
| ( ( in @ SV682 @ ( relation_image @ SV911 @ SV872 ) )
= $false )
| ( ( relation @ SV911 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5256]) ).
thf(5382,plain,
! [SV950: $i,SV683: $i] :
( ( ( subset @ SV683 @ SV950 )
= $false )
| ( ( subset @ ( relation_dom @ SV683 ) @ ( relation_dom @ SV950 ) )
= $true )
| ( ( relation @ SV950 )
= $false )
| ( ( relation @ SV683 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5257]) ).
thf(5383,plain,
! [SV951: $i,SV683: $i] :
( ( ( subset @ SV683 @ SV951 )
= $false )
| ( ( subset @ ( relation_rng @ SV683 ) @ ( relation_rng @ SV951 ) )
= $true )
| ( ( relation @ SV951 )
= $false )
| ( ( relation @ SV683 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5258]) ).
thf(5384,plain,
! [SV684: $i,SV952: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV684 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV952 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV684 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV952 ) ) )
= $false )
| ( ( SV684 = SV952 )
= $true )
| ( ( relation @ SV952 )
= $false )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5259]) ).
thf(5385,plain,
! [SV953: $i,SV684: $i] :
( ( ( SV684 = SV953 )
= $false )
| ( ( ~ ( ~ ! [SY1592: $i,SY1593: $i] :
( ~ ( in @ ( ordered_pair @ SY1592 @ SY1593 ) @ SV684 )
| ( in @ ( ordered_pair @ SY1592 @ SY1593 ) @ SV953 ) )
| ~ ! [SY1594: $i,SY1595: $i] :
( ~ ( in @ ( ordered_pair @ SY1594 @ SY1595 ) @ SV953 )
| ( in @ ( ordered_pair @ SY1594 @ SY1595 ) @ SV684 ) ) ) )
= $true )
| ( ( relation @ SV953 )
= $false )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5260]) ).
thf(5386,plain,
! [SV685: $i,SV982: $i] :
( ( ( ~ ! [SY1631: $i] :
( ~ ( subset @ SY1631 @ SV982 )
| ( in @ SY1631 @ ( sK3_SY386 @ SV982 @ SV685 ) ) ) )
= $false )
| ( ( ~ ( in @ SV982 @ ( sK2_B @ SV685 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5261]) ).
thf(5387,plain,
! [SV685: $i,SV982: $i] :
( ( ( ~ ( in @ ( sK3_SY386 @ SV982 @ SV685 ) @ ( sK2_B @ SV685 ) ) )
= $false )
| ( ( ~ ( in @ SV982 @ ( sK2_B @ SV685 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5261]) ).
thf(5388,plain,
! [SV685: $i,SV1032: $i] :
( ( ! [SY1651: $i] :
( ~ ( in @ SV1032 @ ( sK2_B @ SV685 ) )
| ~ ( subset @ SY1651 @ SV1032 )
| ( in @ SY1651 @ ( sK2_B @ SV685 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5262]) ).
thf(5389,plain,
! [SV813: $i,SV877: $i] :
( ( ( in @ ( sK28_C @ SV877 @ SV813 ) @ SV877 )
= $false )
| ( ( ~ ( subset @ ( sK28_C @ SV877 @ SV813 ) @ SV813 ) )
= $true )
| ( ( SV877
= ( powerset @ SV813 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5266]) ).
thf(5390,plain,
! [SV814: $i,SV878: $i,SV1033: $i] :
( ( ( ~ ( in @ SV1033 @ SV878 )
| ( subset @ SV1033 @ SV814 ) )
= $true )
| ( ( SV878
= ( powerset @ SV814 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5268]) ).
thf(5391,plain,
! [SV878: $i,SV814: $i,SV1034: $i] :
( ( ( ~ ( subset @ SV1034 @ SV814 )
| ( in @ SV1034 @ SV878 ) )
= $true )
| ( ( SV878
= ( powerset @ SV814 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5269]) ).
thf(5392,plain,
! [SV818: $i,SV880: $i] :
( ( ( ~ ( ~ ( in @ ( sK50_C @ SV880 @ SV818 ) @ SV818 )
| ~ ( ( ( apply @ SV880 @ ( sK50_C @ SV880 @ SV818 ) )
!= ( sK50_C @ SV880 @ SV818 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV880 )
!= SV818 ) )
= $true )
| ( ( SV880
= ( identity_relation @ SV818 ) )
= $true )
| ( ( function @ SV880 )
= $false )
| ( ( relation @ SV880 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5272]) ).
thf(5393,plain,
! [SV958: $i,SV986: $i] :
( ( ( function @ SV986 )
= $false )
| ( ( ~ ( relation @ SV986 ) )
= $true )
| ( ( ( SV986
!= ( identity_relation @ SV958 ) )
| ! [SY1632: $i] :
( ~ ( in @ SY1632 @ SV958 )
| ( ( apply @ SV986 @ SY1632 )
= SY1632 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5273]) ).
thf(5394,plain,
! [SV959: $i,SV987: $i] :
( ( ( function @ SV987 )
= $false )
| ( ( ~ ( relation @ SV987 ) )
= $true )
| ( ( ( SV987
!= ( identity_relation @ SV959 ) )
| ( ( relation_dom @ SV987 )
= SV959 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5274]) ).
thf(5395,plain,
! [SV710: $i,SV912: $i,SV608: $i] :
( ( ( ~ ( in @ SV608 @ ( relation_dom @ ( relation_composition @ SV912 @ SV710 ) ) ) )
= $true )
| ( ( ( apply @ ( relation_composition @ SV912 @ SV710 ) @ SV608 )
= ( apply @ SV710 @ ( apply @ SV912 @ SV608 ) ) )
= $true )
| ( ( function @ SV912 )
= $false )
| ( ( relation @ SV912 )
= $false )
| ( ( function @ SV710 )
= $false )
| ( ( relation @ SV710 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5277]) ).
thf(5396,plain,
! [SV913: $i,SV711: $i,SV609: $i] :
( ( ( ~ ( in @ SV609 @ ( relation_dom @ SV711 ) ) )
= $true )
| ( ( ( apply @ ( relation_composition @ SV711 @ SV913 ) @ SV609 )
= ( apply @ SV913 @ ( apply @ SV711 @ SV609 ) ) )
= $true )
| ( ( function @ SV913 )
= $false )
| ( ( relation @ SV913 )
= $false )
| ( ( function @ SV711 )
= $false )
| ( ( relation @ SV711 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5278]) ).
thf(5397,plain,
! [SV652: $i,SV825: $i,SV885: $i] :
( ( ( ~ ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV652 ) )
= $true )
| ( ( ~ ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV825 ) )
= $true )
| ( ( ~ ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV885 ) )
= $true )
| ( ( SV885
= ( set_intersection2 @ SV652 @ SV825 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5279]) ).
thf(5398,plain,
! [SV652: $i,SV825: $i,SV885: $i] :
( ( ( ~ ( ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV652 )
| ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV885 ) ) )
= $false )
| ( ( SV885
= ( set_intersection2 @ SV652 @ SV825 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5280]) ).
thf(5399,plain,
! [SV652: $i,SV825: $i,SV885: $i] :
( ( ( ~ ( ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV825 )
| ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV885 ) ) )
= $false )
| ( ( SV885
= ( set_intersection2 @ SV652 @ SV825 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5280]) ).
thf(5400,plain,
! [SV886: $i,SV826: $i,SV652: $i,SV1035: $i] :
( ( ( ~ ( in @ SV1035 @ SV652 )
| ~ ( in @ SV1035 @ SV826 )
| ( in @ SV1035 @ SV886 ) )
= $true )
| ( ( SV886
= ( set_intersection2 @ SV652 @ SV826 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5281]) ).
thf(5401,plain,
! [SV826: $i,SV652: $i,SV886: $i] :
( ( ( ~ ! [SY1518: $i] :
( ~ ( in @ SY1518 @ SV886 )
| ( in @ SY1518 @ SV652 ) )
| ~ ! [SY1519: $i] :
( ~ ( in @ SY1519 @ SV886 )
| ( in @ SY1519 @ SV826 ) ) )
= $false )
| ( ( SV886
= ( set_intersection2 @ SV652 @ SV826 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5282]) ).
thf(5402,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ( function @ SV1024 )
| ~ ( relation @ SV1024 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) )
| ( SV1024
= ( function_inverse @ SV653 ) ) )
= $true )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5283]) ).
thf(5403,plain,
! [SV653: $i] :
( ( ( ~ ! [SY1141: $i] :
( ~ ( function @ SY1141 )
| ~ ( relation @ SY1141 )
| ( SY1141
!= ( function_inverse @ SV653 ) )
| ~ ( ~ ~ ( ~ ! [SY1142: $i,SY1143: $i] :
( ( SY1143
!= ( apply @ SY1141 @ SY1142 ) )
| ~ ( in @ SY1142 @ ( relation_rng @ SV653 ) )
| ( SY1142
= ( apply @ SV653 @ SY1143 ) ) )
| ~ ! [SY1144: $i,SY1145: $i] :
( ( SY1145
!= ( apply @ SY1141 @ SY1144 ) )
| ~ ( in @ SY1144 @ ( relation_rng @ SV653 ) )
| ( in @ SY1145 @ ( relation_dom @ SV653 ) ) ) )
| ~ ~ ( ~ ! [SY1146: $i,SY1147: $i] :
( ( SY1146
!= ( apply @ SV653 @ SY1147 ) )
| ~ ( in @ SY1147 @ ( relation_dom @ SV653 ) )
| ( SY1147
= ( apply @ SY1141 @ SY1146 ) ) )
| ~ ! [SY1148: $i] :
( ! [SY1149: $i] :
( ( SY1148
!= ( apply @ SV653 @ SY1149 ) )
| ~ ( in @ SY1149 @ ( relation_dom @ SV653 ) ) )
| ( in @ SY1148 @ ( relation_rng @ SV653 ) ) ) ) ) ) )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5284]) ).
thf(5404,plain,
! [SV653: $i] :
( ( ( ~ ! [SY1150: $i] :
( ~ ( function @ SY1150 )
| ~ ( relation @ SY1150 )
| ( SY1150
!= ( function_inverse @ SV653 ) )
| ( ( relation_dom @ SY1150 )
= ( relation_rng @ SV653 ) ) ) )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5284]) ).
thf(5405,plain,
! [SV916: $i,SV1008: $i] :
( ( ( element @ SV1008 @ SV916 )
= $false )
| ( ( empty @ SV1008 )
= $true )
| ( ( empty @ SV916 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5287]) ).
thf(5406,plain,
! [SV917: $i,SV1009: $i] :
( ( ( empty @ SV1009 )
= $false )
| ( ( element @ SV1009 @ SV917 )
= $true )
| ( ( empty @ SV917 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5288]) ).
thf(5407,plain,
! [SV920: $i,SV739: $i,SV887: $i,SV654: $i] :
( ( ( in @ SV654 @ SV887 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ SV920 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SV887 ) @ SV920 ) )
= $true )
| ( ( relation @ SV920 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5289]) ).
thf(5408,plain,
! [SV991: $i,SV739: $i,SV654: $i,SV1011: $i] :
( ( ( relation @ SV1011 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SV991 ) @ SV1011 ) )
| ( in @ SV654 @ SV991 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5290]) ).
thf(5409,plain,
! [SV992: $i,SV739: $i,SV654: $i,SV1012: $i] :
( ( ( relation @ SV1012 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SV992 ) @ SV1012 ) )
| ( in @ ( ordered_pair @ SV654 @ SV739 ) @ SV1012 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5291]) ).
thf(5410,plain,
! [SV655: $i,SV740: $i,SV961: $i] :
( ( ( ~ ( ~ ( in @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) @ SV655 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV740 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 ) )
| ~ ~ ( ~ ( ( in @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) @ SV655 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV740 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 ) ) ) )
= $false )
| ( ( SV961
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $true )
| ( ( relation @ SV961 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5292]) ).
thf(5411,plain,
! [SV740: $i,SV655: $i,SV962: $i] :
( ( ( SV962
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $false )
| ( ( ~ ( ~ ! [SY1603: $i,SY1604: $i] :
( ~ ( in @ SY1604 @ SV655 )
| ~ ( in @ ( ordered_pair @ SY1603 @ SY1604 ) @ SV740 )
| ( in @ ( ordered_pair @ SY1603 @ SY1604 ) @ SV962 ) )
| ~ ~ ( ~ ! [SY1605: $i,SY1606: $i] :
( ~ ( in @ ( ordered_pair @ SY1605 @ SY1606 ) @ SV962 )
| ( in @ SY1606 @ SV655 ) )
| ~ ! [SY1607: $i,SY1608: $i] :
( ~ ( in @ ( ordered_pair @ SY1607 @ SY1608 ) @ SV962 )
| ( in @ ( ordered_pair @ SY1607 @ SY1608 ) @ SV740 ) ) ) ) )
= $true )
| ( ( relation @ SV962 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5293]) ).
thf(5412,plain,
! [SV657: $i,SV922: $i,SV964: $i] :
( ( ( ! [SY1609: $i] :
( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SY1609 ) @ SV657 )
| ~ ( in @ SY1609 @ SV922 ) )
| ~ ( in @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SV964 ) )
= $true )
| ( ( SV964
= ( relation_inverse_image @ SV657 @ SV922 ) )
= $true )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5294]) ).
thf(5413,plain,
! [SV657: $i,SV922: $i,SV964: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ ( sK36_SY409 @ SV964 @ SV922 @ SV657 ) ) @ SV657 )
| ~ ( in @ ( sK36_SY409 @ SV964 @ SV922 @ SV657 ) @ SV922 ) )
| ( in @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SV964 ) )
= $true )
| ( ( SV964
= ( relation_inverse_image @ SV657 @ SV922 ) )
= $true )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5295]) ).
thf(5414,plain,
! [SV965: $i,SV923: $i,SV657: $i] :
( ( ( ~ ! [SY1610: $i] :
( ! [SY1552: $i] :
( ~ ( in @ ( ordered_pair @ SY1610 @ SY1552 ) @ SV657 )
| ~ ( in @ SY1552 @ SV923 ) )
| ( in @ SY1610 @ SV965 ) ) )
= $false )
| ( ( SV965
= ( relation_inverse_image @ SV657 @ SV923 ) )
= $false )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5296]) ).
thf(5415,plain,
! [SV657: $i,SV923: $i,SV965: $i] :
( ( ( ~ ! [SY1612: $i] :
( ~ ( in @ SY1612 @ SV965 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1612 @ ( sK34_E @ SY1612 @ SV965 @ SV923 @ SV657 ) ) @ SV657 )
| ~ ( in @ ( sK34_E @ SY1612 @ SV965 @ SV923 @ SV657 ) @ SV923 ) ) ) )
= $false )
| ( ( SV965
= ( relation_inverse_image @ SV657 @ SV923 ) )
= $false )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5296]) ).
thf(5416,plain,
! [SV658: $i,SV924: $i,SV966: $i] :
( ( ( ! [SY1613: $i] :
( ~ ( in @ ( ordered_pair @ SY1613 @ ( sK38_D @ SV966 @ SV924 @ SV658 ) ) @ SV658 )
| ~ ( in @ SY1613 @ SV924 ) )
| ~ ( in @ ( sK38_D @ SV966 @ SV924 @ SV658 ) @ SV966 ) )
= $true )
| ( ( SV966
= ( relation_image @ SV658 @ SV924 ) )
= $true )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5297]) ).
thf(5417,plain,
! [SV658: $i,SV924: $i,SV966: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SV966 @ SV924 @ SV658 ) @ ( sK38_D @ SV966 @ SV924 @ SV658 ) ) @ SV658 )
| ~ ( in @ ( sK39_SY411 @ SV966 @ SV924 @ SV658 ) @ SV924 ) )
| ( in @ ( sK38_D @ SV966 @ SV924 @ SV658 ) @ SV966 ) )
= $true )
| ( ( SV966
= ( relation_image @ SV658 @ SV924 ) )
= $true )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5298]) ).
thf(5418,plain,
! [SV967: $i,SV925: $i,SV658: $i] :
( ( ( ~ ! [SY1614: $i] :
( ! [SY1558: $i] :
( ~ ( in @ ( ordered_pair @ SY1558 @ SY1614 ) @ SV658 )
| ~ ( in @ SY1558 @ SV925 ) )
| ( in @ SY1614 @ SV967 ) ) )
= $false )
| ( ( SV967
= ( relation_image @ SV658 @ SV925 ) )
= $false )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5299]) ).
thf(5419,plain,
! [SV658: $i,SV925: $i,SV967: $i] :
( ( ( ~ ! [SY1616: $i] :
( ~ ( in @ SY1616 @ SV967 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SY1616 @ SV967 @ SV925 @ SV658 ) @ SY1616 ) @ SV658 )
| ~ ( in @ ( sK37_E @ SY1616 @ SV967 @ SV925 @ SV658 ) @ SV925 ) ) ) )
= $false )
| ( ( SV967
= ( relation_image @ SV658 @ SV925 ) )
= $false )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5299]) ).
thf(5420,plain,
! [SV928: $i] :
( ( ( relation @ SV928 )
= $false )
| ( ( empty @ SV928 )
= $false )
| ( ( ~ ( function @ SV928 ) )
= $true )
| ( ( function @ SV928 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5301]) ).
thf(5421,plain,
! [SV929: $i] :
( ( ( relation @ SV929 )
= $false )
| ( ( empty @ SV929 )
= $false )
| ( ( ~ ( function @ SV929 ) )
= $true )
| ( ( relation @ SV929 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5302]) ).
thf(5422,plain,
! [SV660: $i,SV783: $i,SV1014: $i] :
( ( ( relation @ SV1014 )
= $false )
| ( ( ~ ( ~ ( ! [SY1644: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ SY1644 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1644 @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV783 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV1014 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK10_SY395 @ SV1014 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV783 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV1014 ) ) )
| ( SV1014
= ( relation_composition @ SV660 @ SV783 ) ) )
= $true )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5306]) ).
thf(5423,plain,
! [SV783: $i,SV660: $i,SV1015: $i] :
( ( ( relation @ SV1015 )
= $false )
| ( ( ( SV1015
!= ( relation_composition @ SV660 @ SV783 ) )
| ~ ( ~ ! [SY1645: $i,SY1646: $i] :
( ! [SY1410: $i] :
( ~ ( in @ ( ordered_pair @ SY1645 @ SY1410 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1410 @ SY1646 ) @ SV783 ) )
| ( in @ ( ordered_pair @ SY1645 @ SY1646 ) @ SV1015 ) )
| ~ ! [SY1648: $i,SY1649: $i] :
( ~ ( in @ ( ordered_pair @ SY1648 @ SY1649 ) @ SV1015 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1648 @ ( sK7_F @ SY1649 @ SY1648 @ SV1015 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY1649 @ SY1648 @ SV1015 @ SV783 @ SV660 ) @ SY1649 ) @ SV783 ) ) ) ) )
= $true )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5307]) ).
thf(5424,plain,
! [SV661: $i,SV932: $i] :
( ( ( ! [SY1562: $i] :
~ ( in @ ( ordered_pair @ SY1562 @ ( sK60_C @ SV932 @ SV661 ) ) @ SV661 ) )
= $true )
| ( ( ~ ( in @ ( sK60_C @ SV932 @ SV661 ) @ SV932 ) )
= $true )
| ( ( SV932
= ( relation_rng @ SV661 ) )
= $true )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5308]) ).
thf(5425,plain,
! [SV661: $i,SV932: $i] :
( ( ( in @ ( ordered_pair @ ( sK61_SY417 @ SV932 @ SV661 ) @ ( sK60_C @ SV932 @ SV661 ) ) @ SV661 )
= $true )
| ( ( in @ ( sK60_C @ SV932 @ SV661 ) @ SV932 )
= $true )
| ( ( SV932
= ( relation_rng @ SV661 ) )
= $true )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5309]) ).
thf(5426,plain,
! [SV933: $i,SV661: $i] :
( ( ( ! [SY1563: $i] :
( ! [SY1207: $i] :
~ ( in @ ( ordered_pair @ SY1207 @ SY1563 ) @ SV661 )
| ( in @ SY1563 @ SV933 ) ) )
= $true )
| ( ( SV933
= ( relation_rng @ SV661 ) )
= $false )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5310]) ).
thf(5427,plain,
! [SV661: $i,SV933: $i] :
( ( ( ! [SY1565: $i] :
( ~ ( in @ SY1565 @ SV933 )
| ( in @ ( ordered_pair @ ( sK59_D @ SY1565 @ SV933 @ SV661 ) @ SY1565 ) @ SV661 ) ) )
= $true )
| ( ( SV933
= ( relation_rng @ SV661 ) )
= $false )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5311]) ).
thf(5428,plain,
! [SV662: $i,SV838: $i,SV891: $i] :
( ( ( ~ ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV662 ) )
= $true )
| ( ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV838 )
= $true )
| ( ( ~ ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV891 ) )
= $true )
| ( ( SV891
= ( set_difference @ SV662 @ SV838 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5312]) ).
thf(5429,plain,
! [SV662: $i,SV838: $i,SV891: $i] :
( ( ( ~ ( ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV662 )
| ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV891 ) ) )
= $false )
| ( ( SV891
= ( set_difference @ SV662 @ SV838 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5313]) ).
thf(5430,plain,
! [SV662: $i,SV838: $i,SV891: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV838 )
| ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV891 ) ) )
= $false )
| ( ( SV891
= ( set_difference @ SV662 @ SV838 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5313]) ).
thf(5431,plain,
! [SV892: $i,SV839: $i,SV662: $i,SV1036: $i] :
( ( ( ~ ( in @ SV1036 @ SV662 )
| ( in @ SV1036 @ SV839 )
| ( in @ SV1036 @ SV892 ) )
= $true )
| ( ( SV892
= ( set_difference @ SV662 @ SV839 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5314]) ).
thf(5432,plain,
! [SV839: $i,SV662: $i,SV892: $i] :
( ( ( ~ ! [SY1524: $i] :
( ~ ( in @ SY1524 @ SV892 )
| ( in @ SY1524 @ SV662 ) )
| ~ ! [SY1525: $i] :
( ~ ( in @ SY1525 @ SV892 )
| ~ ( in @ SY1525 @ SV839 ) ) )
= $false )
| ( ( SV892
= ( set_difference @ SV662 @ SV839 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5315]) ).
thf(5433,plain,
! [SV790: $i,SV840: $i] :
( ( ( relation @ SV840 )
= $false )
| ( ( function @ SV790 )
= $false )
| ( ( relation @ SV790 )
= $false )
| ( ( ~ ( function @ SV840 ) )
= $true )
| ( ( function @ ( relation_composition @ SV790 @ SV840 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5316]) ).
thf(5434,plain,
! [SV791: $i,SV841: $i] :
( ( ( relation @ SV841 )
= $false )
| ( ( function @ SV791 )
= $false )
| ( ( relation @ SV791 )
= $false )
| ( ( ~ ( function @ SV841 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV791 @ SV841 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5317]) ).
thf(5435,plain,
! [SV842: $i,SV893: $i,SV663: $i] :
( ( ( in @ SV663 @ ( relation_rng @ SV893 ) )
= $false )
| ( ( in @ SV663 @ SV842 )
= $false )
| ( ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SV842 @ SV893 ) ) )
= $true )
| ( ( relation @ SV893 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5318]) ).
thf(5436,plain,
! [SV996: $i,SV972: $i,SV663: $i] :
( ( ( ~ ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SV972 @ SV996 ) ) ) )
= $true )
| ( ( in @ SV663 @ SV972 )
= $true )
| ( ( relation @ SV996 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5319]) ).
thf(5437,plain,
! [SV997: $i,SV973: $i,SV663: $i] :
( ( ( ~ ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SV973 @ SV997 ) ) ) )
= $true )
| ( ( in @ SV663 @ ( relation_rng @ SV997 ) )
= $true )
| ( ( relation @ SV997 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5320]) ).
thf(5438,plain,
! [SV664: $i,SV1037: $i] :
( ( ( ~ ( in @ SV1037 @ ( relation_dom @ SV664 ) )
| ! [SY1652: $i] :
( ( SY1652
!= ( apply @ SV664 @ SV1037 ) )
| ( in @ ( ordered_pair @ SV1037 @ SY1652 ) @ SV664 ) ) )
= $true )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5321]) ).
thf(5439,plain,
! [SV664: $i,SV1038: $i] :
( ( ( ~ ( in @ SV1038 @ ( relation_dom @ SV664 ) )
| ! [SY1653: $i] :
( ~ ( in @ ( ordered_pair @ SV1038 @ SY1653 ) @ SV664 )
| ( SY1653
= ( apply @ SV664 @ SV1038 ) ) ) )
= $true )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5322]) ).
thf(5440,plain,
! [SV664: $i,SV1039: $i] :
( ( ( ( in @ SV1039 @ ( relation_dom @ SV664 ) )
| ! [SY1654: $i] :
( ( SY1654
!= ( apply @ SV664 @ SV1039 ) )
| ( SY1654 = empty_set ) ) )
= $true )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5323]) ).
thf(5441,plain,
! [SV664: $i,SV1040: $i] :
( ( ( ( in @ SV1040 @ ( relation_dom @ SV664 ) )
| ! [SY1655: $i] :
( ( SY1655 != empty_set )
| ( SY1655
= ( apply @ SV664 @ SV1040 ) ) ) )
= $true )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5324]) ).
thf(5442,plain,
! [SV665: $i,SV934: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV934 @ SV665 ) @ ( sK20_SY399 @ SV934 @ SV665 ) ) @ SV665 ) )
= $false )
| ( ( subset @ SV665 @ SV934 )
= $true )
| ( ( relation @ SV934 )
= $false )
| ( ( relation @ SV665 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5325]) ).
thf(5443,plain,
! [SV665: $i,SV934: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK19_C @ SV934 @ SV665 ) @ ( sK20_SY399 @ SV934 @ SV665 ) ) @ SV934 ) )
= $false )
| ( ( subset @ SV665 @ SV934 )
= $true )
| ( ( relation @ SV934 )
= $false )
| ( ( relation @ SV665 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5325]) ).
thf(5444,plain,
! [SV935: $i,SV665: $i,SV1041: $i] :
( ( ( ! [SY1656: $i] :
( ~ ( in @ ( ordered_pair @ SV1041 @ SY1656 ) @ SV665 )
| ( in @ ( ordered_pair @ SV1041 @ SY1656 ) @ SV935 ) ) )
= $true )
| ( ( subset @ SV665 @ SV935 )
= $false )
| ( ( relation @ SV935 )
= $false )
| ( ( relation @ SV665 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5326]) ).
thf(5445,plain,
! [SV742: $i,SV666: $i,SV1016: $i] :
( ( ( ~ ( function @ SV1016 ) )
= $true )
| ( ( ~ ( relation @ SV1016 ) )
= $true )
| ( ( ~ ( in @ SV666 @ ( relation_dom @ SV1016 ) )
| ~ ( in @ ( apply @ SV1016 @ SV666 ) @ ( relation_dom @ SV742 ) )
| ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SV1016 @ SV742 ) ) ) )
= $true )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5327]) ).
thf(5446,plain,
! [SV742: $i,SV666: $i] :
( ( ( ! [SY1377: $i] :
( ~ ( function @ SY1377 )
| ~ ( relation @ SY1377 )
| ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1377 @ SV742 ) ) )
| ( in @ SV666 @ ( relation_dom @ SY1377 ) ) ) )
= $true )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5328]) ).
thf(5447,plain,
! [SV742: $i,SV666: $i] :
( ( ( ! [SY1378: $i] :
( ~ ( function @ SY1378 )
| ~ ( relation @ SY1378 )
| ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SY1378 @ SV742 ) ) )
| ( in @ ( apply @ SY1378 @ SV666 ) @ ( relation_dom @ SV742 ) ) ) )
= $true )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5329]) ).
thf(5448,plain,
! [SV843: $i,SV667: $i,SV894: $i,SV1017: $i] :
( ( ( ~ ( in @ SV1017 @ ( relation_rng @ SV894 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV667 @ SV1017 ) @ SV894 ) )
= $true )
| ( ( ~ ( in @ SV1017 @ SV843 ) )
= $true )
| ( ( in @ SV667 @ ( relation_inverse_image @ SV894 @ SV843 ) )
= $true )
| ( ( relation @ SV894 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5330]) ).
thf(5449,plain,
! [SV667: $i,SV844: $i,SV895: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK51_D @ SV895 @ SV844 @ SV667 ) @ ( relation_rng @ SV895 ) )
| ~ ( in @ ( ordered_pair @ SV667 @ ( sK51_D @ SV895 @ SV844 @ SV667 ) ) @ SV895 ) ) )
= $false )
| ( ( in @ SV667 @ ( relation_inverse_image @ SV895 @ SV844 ) )
= $false )
| ( ( relation @ SV895 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5331]) ).
thf(5450,plain,
! [SV667: $i,SV844: $i,SV895: $i] :
( ( ( ~ ( in @ ( sK51_D @ SV895 @ SV844 @ SV667 ) @ SV844 ) )
= $false )
| ( ( in @ SV667 @ ( relation_inverse_image @ SV895 @ SV844 ) )
= $false )
| ( ( relation @ SV895 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5331]) ).
thf(5451,plain,
! [SV847: $i,SV896: $i,SV668: $i] :
( ( ( in @ SV668 @ ( relation_dom @ SV896 ) )
= $false )
| ( ( in @ SV668 @ SV847 )
= $false )
| ( ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SV896 @ SV847 ) ) )
= $true )
| ( ( relation @ SV896 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5333]) ).
thf(5452,plain,
! [SV974: $i,SV998: $i,SV668: $i] :
( ( ( ~ ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SV998 @ SV974 ) ) ) )
= $true )
| ( ( in @ SV668 @ SV974 )
= $true )
| ( ( relation @ SV998 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5334]) ).
thf(5453,plain,
! [SV975: $i,SV999: $i,SV668: $i] :
( ( ( ~ ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SV999 @ SV975 ) ) ) )
= $true )
| ( ( in @ SV668 @ ( relation_dom @ SV999 ) )
= $true )
| ( ( relation @ SV999 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5335]) ).
thf(5454,plain,
! [SV669: $i,SV848: $i,SV897: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV897 )
| ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV669 ) ) )
= $false )
| ( ( SV897
= ( set_union2 @ SV669 @ SV848 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5336]) ).
thf(5455,plain,
! [SV669: $i,SV848: $i,SV897: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV897 )
| ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV848 ) ) )
= $false )
| ( ( SV897
= ( set_union2 @ SV669 @ SV848 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5336]) ).
thf(5456,plain,
! [SV669: $i,SV848: $i,SV897: $i] :
( ( ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV669 )
= $true )
| ( ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV848 )
= $true )
| ( ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV897 )
= $true )
| ( ( SV897
= ( set_union2 @ SV669 @ SV848 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5337]) ).
thf(5457,plain,
! [SV849: $i,SV669: $i,SV898: $i,SV1042: $i] :
( ( ( ~ ( in @ SV1042 @ SV898 )
| ( in @ SV1042 @ SV669 )
| ( in @ SV1042 @ SV849 ) )
= $true )
| ( ( SV898
= ( set_union2 @ SV669 @ SV849 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5338]) ).
thf(5458,plain,
! [SV849: $i,SV898: $i,SV669: $i] :
( ( ( ~ ! [SY1528: $i] :
( ~ ( in @ SY1528 @ SV669 )
| ( in @ SY1528 @ SV898 ) )
| ~ ! [SY1529: $i] :
( ~ ( in @ SY1529 @ SV849 )
| ( in @ SY1529 @ SV898 ) ) )
= $false )
| ( ( SV898
= ( set_union2 @ SV669 @ SV849 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5339]) ).
thf(5459,plain,
! [SV937: $i,SV1000: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK33_SY406 @ SV1000 @ SV937 ) @ SV937 )
| ~ ~ ( in @ ( sK32_C @ SV1000 @ SV937 ) @ ( sK33_SY406 @ SV1000 @ SV937 ) ) )
| ~ ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SV1000 ) ) )
= $false )
| ( ( SV1000
= ( set_meet @ SV937 ) )
= $true )
| ( ( SV937 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5340]) ).
thf(5460,plain,
! [SV1000: $i,SV937: $i] :
( ( ( ~ ( ! [SY1636: $i] :
( ~ ( in @ SY1636 @ SV937 )
| ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SY1636 ) )
| ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SV1000 ) ) )
= $false )
| ( ( SV1000
= ( set_meet @ SV937 ) )
= $true )
| ( ( SV937 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5340]) ).
thf(5461,plain,
! [SV938: $i,SV1001: $i] :
( ( ( ~ ! [SY1637: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY1637 @ SV1001 @ SV938 ) @ SV938 )
| ~ ~ ( in @ SY1637 @ ( sK31_D @ SY1637 @ SV1001 @ SV938 ) ) )
| ( in @ SY1637 @ SV1001 ) )
| ~ ! [SY1638: $i] :
( ~ ( in @ SY1638 @ SV1001 )
| ! [SY1573: $i] :
( ~ ( in @ SY1573 @ SV938 )
| ( in @ SY1638 @ SY1573 ) ) ) )
= $false )
| ( ( SV1001
= ( set_meet @ SV938 ) )
= $false )
| ( ( SV938 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5341]) ).
thf(5462,plain,
! [SV939: $i,SV1018: $i] :
( ( ( SV1018
= ( set_meet @ SV939 ) )
= $false )
| ( ( SV1018 = empty_set )
= $true )
| ( ( SV939 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5342]) ).
thf(5463,plain,
! [SV940: $i,SV1019: $i] :
( ( ( SV1019 = empty_set )
= $false )
| ( ( SV1019
= ( set_meet @ SV940 ) )
= $true )
| ( ( SV940 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5343]) ).
thf(5464,plain,
! [SV899: $i,SV850: $i,SV670: $i,SV1043: $i] :
( ( ( ! [SY1657: $i] :
( ~ ( in @ SV1043 @ SV670 )
| ~ ( in @ SY1657 @ SV850 )
| ( ( sK23_D @ SV899 @ SV850 @ SV670 )
!= ( ordered_pair @ SV1043 @ SY1657 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV899 @ SV850 @ SV670 ) @ SV899 ) )
= $true )
| ( ( SV899
= ( cartesian_product2 @ SV670 @ SV850 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5344]) ).
thf(5465,plain,
! [SV670: $i,SV850: $i,SV899: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK24_SY403 @ SV899 @ SV850 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK25_SY405 @ SV899 @ SV850 @ SV670 ) @ SV850 ) )
| ( ( sK23_D @ SV899 @ SV850 @ SV670 )
!= ( ordered_pair @ ( sK24_SY403 @ SV899 @ SV850 @ SV670 ) @ ( sK25_SY405 @ SV899 @ SV850 @ SV670 ) ) ) )
= $false )
| ( ( in @ ( sK23_D @ SV899 @ SV850 @ SV670 ) @ SV899 )
= $true )
| ( ( SV899
= ( cartesian_product2 @ SV670 @ SV850 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5345]) ).
thf(5466,plain,
! [SV900: $i,SV1044: $i,SV851: $i,SV670: $i] :
( ( ( ! [SY1658: $i,SY1659: $i] :
( ~ ( in @ SY1658 @ SV670 )
| ~ ( in @ SY1659 @ SV851 )
| ( SV1044
!= ( ordered_pair @ SY1658 @ SY1659 ) ) )
| ( in @ SV1044 @ SV900 ) )
= $true )
| ( ( SV900
= ( cartesian_product2 @ SV670 @ SV851 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5346]) ).
thf(5467,plain,
! [SV670: $i,SV851: $i,SV900: $i,SV1045: $i] :
( ( ( ~ ( in @ SV1045 @ SV900 )
| ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SV1045 @ SV900 @ SV851 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK22_SY400 @ SV1045 @ SV900 @ SV851 @ SV670 ) @ SV851 ) )
| ( SV1045
!= ( ordered_pair @ ( sK21_E @ SV1045 @ SV900 @ SV851 @ SV670 ) @ ( sK22_SY400 @ SV1045 @ SV900 @ SV851 @ SV670 ) ) ) ) )
= $true )
| ( ( SV900
= ( cartesian_product2 @ SV670 @ SV851 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5347]) ).
thf(5468,plain,
! [SV671: $i,SV901: $i,SV852: $i] :
( ( ( ( SV852
!= ( apply @ SV901 @ SV671 ) ) )
= $true )
| ( ( ~ ( in @ SV671 @ ( relation_dom @ SV901 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV671 @ SV852 ) @ SV901 )
= $true )
| ( ( function @ SV901 )
= $false )
| ( ( relation @ SV901 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5348]) ).
thf(5469,plain,
! [SV976: $i,SV671: $i,SV1002: $i] :
( ( ( function @ SV1002 )
= $false )
| ( ( ~ ( relation @ SV1002 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV671 @ SV976 ) @ SV1002 )
| ( SV976
= ( apply @ SV1002 @ SV671 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5349]) ).
thf(5470,plain,
! [SV977: $i,SV671: $i,SV1003: $i] :
( ( ( function @ SV1003 )
= $false )
| ( ( ~ ( relation @ SV1003 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV671 @ SV977 ) @ SV1003 )
| ( in @ SV671 @ ( relation_dom @ SV1003 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5350]) ).
thf(5471,plain,
! [SV672: $i,SV941: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SV941 @ SV672 ) @ ( sK12_SY396 @ SV941 @ SV672 ) ) @ SV941 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SV941 @ SV672 ) @ ( sK11_C @ SV941 @ SV672 ) ) @ SV672 ) ) )
= $false )
| ( ( SV941
= ( relation_inverse @ SV672 ) )
= $true )
| ( ( relation @ SV941 )
= $false )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5351]) ).
thf(5472,plain,
! [SV672: $i,SV941: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK11_C @ SV941 @ SV672 ) @ ( sK12_SY396 @ SV941 @ SV672 ) ) @ SV941 )
| ( in @ ( ordered_pair @ ( sK12_SY396 @ SV941 @ SV672 ) @ ( sK11_C @ SV941 @ SV672 ) ) @ SV672 ) ) )
= $false )
| ( ( SV941
= ( relation_inverse @ SV672 ) )
= $true )
| ( ( relation @ SV941 )
= $false )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5351]) ).
thf(5473,plain,
! [SV672: $i,SV942: $i] :
( ( ( ~ ! [SY1576: $i,SY1577: $i] :
( ~ ( in @ ( ordered_pair @ SY1576 @ SY1577 ) @ SV942 )
| ( in @ ( ordered_pair @ SY1577 @ SY1576 ) @ SV672 ) )
| ~ ! [SY1578: $i,SY1579: $i] :
( ~ ( in @ ( ordered_pair @ SY1579 @ SY1578 ) @ SV672 )
| ( in @ ( ordered_pair @ SY1578 @ SY1579 ) @ SV942 ) ) )
= $false )
| ( ( SV942
= ( relation_inverse @ SV672 ) )
= $false )
| ( ( relation @ SV942 )
= $false )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5352]) ).
thf(5474,plain,
! [SV1025: $i,SV1004: $i,SV743: $i,SV674: $i] :
( ( ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SV1004 @ SV1025 ) )
= $false )
| ( ( in @ SV674 @ SV1004 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5354]) ).
thf(5475,plain,
! [SV1020: $i,SV1005: $i,SV743: $i,SV674: $i] :
( ( ( in @ ( ordered_pair @ SV674 @ SV743 ) @ ( cartesian_product2 @ SV1005 @ SV1020 ) )
= $false )
| ( ( in @ SV743 @ SV1020 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5355]) ).
thf(5476,plain,
! [SV675: $i,SV857: $i,SV905: $i] :
( ( ( ~ ( ~ ( in @ ( sK27_D @ SV905 @ SV857 @ SV675 ) @ SV905 )
| ( ( sK27_D @ SV905 @ SV857 @ SV675 )
!= SV675 ) ) )
= $false )
| ( ( SV905
= ( unordered_pair @ SV675 @ SV857 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5356]) ).
thf(5477,plain,
! [SV675: $i,SV857: $i,SV905: $i] :
( ( ( ~ ( ~ ( in @ ( sK27_D @ SV905 @ SV857 @ SV675 ) @ SV905 )
| ( ( sK27_D @ SV905 @ SV857 @ SV675 )
!= SV857 ) ) )
= $false )
| ( ( SV905
= ( unordered_pair @ SV675 @ SV857 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5356]) ).
thf(5478,plain,
! [SV675: $i,SV857: $i,SV905: $i] :
( ( ( ( sK27_D @ SV905 @ SV857 @ SV675 )
= SV675 )
= $true )
| ( ( ( sK27_D @ SV905 @ SV857 @ SV675 )
= SV857 )
= $true )
| ( ( in @ ( sK27_D @ SV905 @ SV857 @ SV675 ) @ SV905 )
= $true )
| ( ( SV905
= ( unordered_pair @ SV675 @ SV857 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5357]) ).
thf(5479,plain,
! [SV858: $i,SV675: $i,SV906: $i,SV1046: $i] :
( ( ( ~ ( in @ SV1046 @ SV906 )
| ( SV1046 = SV675 )
| ( SV1046 = SV858 ) )
= $true )
| ( ( SV906
= ( unordered_pair @ SV675 @ SV858 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5358]) ).
thf(5480,plain,
! [SV858: $i,SV906: $i,SV675: $i] :
( ( ( ~ ! [SY1538: $i] :
( ( SY1538 != SV675 )
| ( in @ SY1538 @ SV906 ) )
| ~ ! [SY1539: $i] :
( ( SY1539 != SV858 )
| ( in @ SY1539 @ SV906 ) ) )
= $false )
| ( ( SV906
= ( unordered_pair @ SV675 @ SV858 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5359]) ).
thf(5481,plain,
! [SV1026: $i,SV1006: $i,SV744: $i,SV676: $i] :
( ( ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SV1006 @ SV1026 ) )
= $false )
| ( ( in @ SV676 @ SV1006 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5361]) ).
thf(5482,plain,
! [SV1021: $i,SV1007: $i,SV744: $i,SV676: $i] :
( ( ( in @ ( ordered_pair @ SV676 @ SV744 ) @ ( cartesian_product2 @ SV1007 @ SV1021 ) )
= $false )
| ( ( in @ SV744 @ SV1021 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5362]) ).
thf(5483,plain,
! [SV1027: $i,SV804: $i,SV863: $i] :
( ( ( ~ ( in @ ( sK15_C @ SV863 @ SV804 ) @ SV1027 ) )
= $true )
| ( ( ~ ( in @ SV1027 @ SV804 ) )
= $true )
| ( ( ~ ( in @ ( sK15_C @ SV863 @ SV804 ) @ SV863 ) )
= $true )
| ( ( SV863
= ( union @ SV804 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5363]) ).
thf(5484,plain,
! [SV804: $i,SV863: $i] :
( ( ( ~ ( in @ ( sK15_C @ SV863 @ SV804 ) @ ( sK16_SY398 @ SV863 @ SV804 ) ) )
= $false )
| ( ( in @ ( sK15_C @ SV863 @ SV804 ) @ SV863 )
= $true )
| ( ( SV863
= ( union @ SV804 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5364]) ).
thf(5485,plain,
! [SV804: $i,SV863: $i] :
( ( ( ~ ( in @ ( sK16_SY398 @ SV863 @ SV804 ) @ SV804 ) )
= $false )
| ( ( in @ ( sK15_C @ SV863 @ SV804 ) @ SV863 )
= $true )
| ( ( SV863
= ( union @ SV804 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5364]) ).
thf(5486,plain,
! [SV864: $i,SV805: $i,SV1028: $i] :
( ( ( ! [SY1650: $i] :
( ~ ( in @ SV1028 @ SY1650 )
| ~ ( in @ SY1650 @ SV805 ) ) )
= $true )
| ( ( in @ SV1028 @ SV864 )
= $true )
| ( ( SV864
= ( union @ SV805 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5365]) ).
thf(5487,plain,
! [SV805: $i,SV864: $i,SV1029: $i] :
( ( ( ~ ( in @ SV1029 @ SV864 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV1029 @ ( sK14_D @ SV1029 @ SV864 @ SV805 ) )
| ~ ( in @ ( sK14_D @ SV1029 @ SV864 @ SV805 ) @ SV805 ) ) )
= $true )
| ( ( SV864
= ( union @ SV805 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5366]) ).
thf(5488,plain,
! [SV679: $i,SV946: $i] :
( ( ( ! [SY1580: $i] :
~ ( in @ ( ordered_pair @ ( sK63_C @ SV946 @ SV679 ) @ SY1580 ) @ SV679 ) )
= $true )
| ( ( ~ ( in @ ( sK63_C @ SV946 @ SV679 ) @ SV946 ) )
= $true )
| ( ( SV946
= ( relation_dom @ SV679 ) )
= $true )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5367]) ).
thf(5489,plain,
! [SV679: $i,SV946: $i] :
( ( ( in @ ( ordered_pair @ ( sK63_C @ SV946 @ SV679 ) @ ( sK64_SY419 @ SV946 @ SV679 ) ) @ SV679 )
= $true )
| ( ( in @ ( sK63_C @ SV946 @ SV679 ) @ SV946 )
= $true )
| ( ( SV946
= ( relation_dom @ SV679 ) )
= $true )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5368]) ).
thf(5490,plain,
! [SV947: $i,SV679: $i] :
( ( ( ! [SY1581: $i] :
( ! [SY1312: $i] :
~ ( in @ ( ordered_pair @ SY1581 @ SY1312 ) @ SV679 )
| ( in @ SY1581 @ SV947 ) ) )
= $true )
| ( ( SV947
= ( relation_dom @ SV679 ) )
= $false )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5369]) ).
thf(5491,plain,
! [SV679: $i,SV947: $i] :
( ( ( ! [SY1583: $i] :
( ~ ( in @ SY1583 @ SV947 )
| ( in @ ( ordered_pair @ SY1583 @ ( sK62_D @ SY1583 @ SV947 @ SV679 ) ) @ SV679 ) ) )
= $true )
| ( ( SV947
= ( relation_dom @ SV679 ) )
= $false )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5370]) ).
thf(5492,plain,
! [SV806: $i,SV867: $i] :
( ( ( ( ( sK44_C @ SV867 @ SV806 )
!= ( sK45_SY414 @ SV867 @ SV806 ) )
| ~ ( in @ ( sK44_C @ SV867 @ SV806 ) @ SV806 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 ) )
= $true )
| ( ( SV867
= ( identity_relation @ SV806 ) )
= $true )
| ( ( relation @ SV867 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5371]) ).
thf(5493,plain,
! [SV806: $i,SV867: $i] :
( ( ( ~ ( ( ( sK44_C @ SV867 @ SV806 )
= ( sK45_SY414 @ SV867 @ SV806 ) )
| ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 ) )
| ~ ( ( in @ ( sK44_C @ SV867 @ SV806 ) @ SV806 )
| ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 ) ) )
= $false )
| ( ( SV867
= ( identity_relation @ SV806 ) )
= $true )
| ( ( relation @ SV867 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5372]) ).
thf(5494,plain,
! [SV868: $i,SV807: $i] :
( ( ( ! [SY1503: $i,SY1504: $i] :
( ( SY1503 != SY1504 )
| ~ ( in @ SY1503 @ SV807 )
| ( in @ ( ordered_pair @ SY1503 @ SY1504 ) @ SV868 ) ) )
= $true )
| ( ( SV868
= ( identity_relation @ SV807 ) )
= $false )
| ( ( relation @ SV868 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5373]) ).
thf(5495,plain,
! [SV807: $i,SV868: $i] :
( ( ( ~ ( ~ ! [SY1505: $i,SY1506: $i] :
( ~ ( in @ ( ordered_pair @ SY1505 @ SY1506 ) @ SV868 )
| ( SY1505 = SY1506 ) )
| ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
~ ( in @ ( ordered_pair @ SY1507 @ SY1508 ) @ SV868 )
| ( in @ SY1507 @ SV807 ) ) ) )
= $true )
| ( ( SV868
= ( identity_relation @ SV807 ) )
= $false )
| ( ( relation @ SV868 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5374]) ).
thf(5496,plain,
! [SV681: $i,SV948: $i,SV980: $i] :
( ( ( ~ ( ~ ( in @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ SV948 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV681 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 ) )
| ~ ~ ( ~ ( ( in @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ SV948 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV681 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 ) ) ) )
= $false )
| ( ( SV980
= ( relation_dom_restriction @ SV681 @ SV948 ) )
= $true )
| ( ( relation @ SV980 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5375]) ).
thf(5497,plain,
! [SV949: $i,SV681: $i,SV981: $i] :
( ( ( SV981
= ( relation_dom_restriction @ SV681 @ SV949 ) )
= $false )
| ( ( ~ ( ~ ! [SY1625: $i,SY1626: $i] :
( ~ ( in @ SY1625 @ SV949 )
| ~ ( in @ ( ordered_pair @ SY1625 @ SY1626 ) @ SV681 )
| ( in @ ( ordered_pair @ SY1625 @ SY1626 ) @ SV981 ) )
| ~ ~ ( ~ ! [SY1627: $i] :
( ! [SY1628: $i] :
~ ( in @ ( ordered_pair @ SY1627 @ SY1628 ) @ SV981 )
| ( in @ SY1627 @ SV949 ) )
| ~ ! [SY1629: $i,SY1630: $i] :
( ~ ( in @ ( ordered_pair @ SY1629 @ SY1630 ) @ SV981 )
| ( in @ ( ordered_pair @ SY1629 @ SY1630 ) @ SV681 ) ) ) ) )
= $true )
| ( ( relation @ SV981 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5376]) ).
thf(5498,plain,
! [SV808: $i,SV869: $i] :
( ( ( in @ ( sK30_C @ SV869 @ SV808 ) @ SV869 )
= $false )
| ( ( ( sK30_C @ SV869 @ SV808 )
= SV808 )
= $false )
| ( ( SV869
= ( singleton @ SV808 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5377]) ).
thf(5499,plain,
! [SV870: $i,SV809: $i,SV1030: $i] :
( ( ( ( SV1030 != SV809 ) )
= $true )
| ( ( in @ SV1030 @ SV870 )
= $true )
| ( ( SV870
= ( singleton @ SV809 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5378]) ).
thf(5500,plain,
! [SV809: $i,SV870: $i,SV1031: $i] :
( ( ( ~ ( in @ SV1031 @ SV870 ) )
= $true )
| ( ( SV1031 = SV809 )
= $true )
| ( ( SV870
= ( singleton @ SV809 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5379]) ).
thf(5501,plain,
! [SV871: $i,SV682: $i,SV910: $i,SV1022: $i] :
( ( ( ~ ( in @ SV1022 @ ( relation_dom @ SV910 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV1022 @ SV682 ) @ SV910 ) )
= $true )
| ( ( ~ ( in @ SV1022 @ SV871 ) )
= $true )
| ( ( in @ SV682 @ ( relation_image @ SV910 @ SV871 ) )
= $true )
| ( ( relation @ SV910 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5380]) ).
thf(5502,plain,
! [SV682: $i,SV872: $i,SV911: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK52_D @ SV911 @ SV872 @ SV682 ) @ ( relation_dom @ SV911 ) )
| ~ ( in @ ( ordered_pair @ ( sK52_D @ SV911 @ SV872 @ SV682 ) @ SV682 ) @ SV911 ) ) )
= $false )
| ( ( in @ SV682 @ ( relation_image @ SV911 @ SV872 ) )
= $false )
| ( ( relation @ SV911 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5381]) ).
thf(5503,plain,
! [SV682: $i,SV872: $i,SV911: $i] :
( ( ( ~ ( in @ ( sK52_D @ SV911 @ SV872 @ SV682 ) @ SV872 ) )
= $false )
| ( ( in @ SV682 @ ( relation_image @ SV911 @ SV872 ) )
= $false )
| ( ( relation @ SV911 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5381]) ).
thf(5504,plain,
! [SV684: $i,SV952: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV684 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV952 ) ) )
= $false )
| ( ( SV684 = SV952 )
= $true )
| ( ( relation @ SV952 )
= $false )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5384]) ).
thf(5505,plain,
! [SV684: $i,SV952: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV684 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV952 ) ) )
= $false )
| ( ( SV684 = SV952 )
= $true )
| ( ( relation @ SV952 )
= $false )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5384]) ).
thf(5506,plain,
! [SV953: $i,SV684: $i] :
( ( ( ~ ! [SY1592: $i,SY1593: $i] :
( ~ ( in @ ( ordered_pair @ SY1592 @ SY1593 ) @ SV684 )
| ( in @ ( ordered_pair @ SY1592 @ SY1593 ) @ SV953 ) )
| ~ ! [SY1594: $i,SY1595: $i] :
( ~ ( in @ ( ordered_pair @ SY1594 @ SY1595 ) @ SV953 )
| ( in @ ( ordered_pair @ SY1594 @ SY1595 ) @ SV684 ) ) )
= $false )
| ( ( SV684 = SV953 )
= $false )
| ( ( relation @ SV953 )
= $false )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5385]) ).
thf(5507,plain,
! [SV685: $i,SV982: $i] :
( ( ( ! [SY1631: $i] :
( ~ ( subset @ SY1631 @ SV982 )
| ( in @ SY1631 @ ( sK3_SY386 @ SV982 @ SV685 ) ) ) )
= $true )
| ( ( ~ ( in @ SV982 @ ( sK2_B @ SV685 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5386]) ).
thf(5508,plain,
! [SV685: $i,SV982: $i] :
( ( ( in @ ( sK3_SY386 @ SV982 @ SV685 ) @ ( sK2_B @ SV685 ) )
= $true )
| ( ( ~ ( in @ SV982 @ ( sK2_B @ SV685 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5387]) ).
thf(5509,plain,
! [SV1047: $i,SV685: $i,SV1032: $i] :
( ( ~ ( in @ SV1032 @ ( sK2_B @ SV685 ) )
| ~ ( subset @ SV1047 @ SV1032 )
| ( in @ SV1047 @ ( sK2_B @ SV685 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5388]) ).
thf(5510,plain,
! [SV813: $i,SV877: $i] :
( ( ( subset @ ( sK28_C @ SV877 @ SV813 ) @ SV813 )
= $false )
| ( ( in @ ( sK28_C @ SV877 @ SV813 ) @ SV877 )
= $false )
| ( ( SV877
= ( powerset @ SV813 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5389]) ).
thf(5511,plain,
! [SV814: $i,SV878: $i,SV1033: $i] :
( ( ( ~ ( in @ SV1033 @ SV878 ) )
= $true )
| ( ( subset @ SV1033 @ SV814 )
= $true )
| ( ( SV878
= ( powerset @ SV814 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5390]) ).
thf(5512,plain,
! [SV878: $i,SV814: $i,SV1034: $i] :
( ( ( ~ ( subset @ SV1034 @ SV814 ) )
= $true )
| ( ( in @ SV1034 @ SV878 )
= $true )
| ( ( SV878
= ( powerset @ SV814 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5391]) ).
thf(5513,plain,
! [SV818: $i,SV880: $i] :
( ( ( ~ ( in @ ( sK50_C @ SV880 @ SV818 ) @ SV818 )
| ~ ( ( ( apply @ SV880 @ ( sK50_C @ SV880 @ SV818 ) )
!= ( sK50_C @ SV880 @ SV818 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV880 )
!= SV818 ) )
= $true )
| ( ( SV880
= ( identity_relation @ SV818 ) )
= $true )
| ( ( function @ SV880 )
= $false )
| ( ( relation @ SV880 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5392]) ).
thf(5514,plain,
! [SV958: $i,SV986: $i] :
( ( ( relation @ SV986 )
= $false )
| ( ( function @ SV986 )
= $false )
| ( ( ( SV986
!= ( identity_relation @ SV958 ) )
| ! [SY1632: $i] :
( ~ ( in @ SY1632 @ SV958 )
| ( ( apply @ SV986 @ SY1632 )
= SY1632 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5393]) ).
thf(5515,plain,
! [SV959: $i,SV987: $i] :
( ( ( relation @ SV987 )
= $false )
| ( ( function @ SV987 )
= $false )
| ( ( ( SV987
!= ( identity_relation @ SV959 ) )
| ( ( relation_dom @ SV987 )
= SV959 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5394]) ).
thf(5516,plain,
! [SV710: $i,SV912: $i,SV608: $i] :
( ( ( in @ SV608 @ ( relation_dom @ ( relation_composition @ SV912 @ SV710 ) ) )
= $false )
| ( ( ( apply @ ( relation_composition @ SV912 @ SV710 ) @ SV608 )
= ( apply @ SV710 @ ( apply @ SV912 @ SV608 ) ) )
= $true )
| ( ( function @ SV912 )
= $false )
| ( ( relation @ SV912 )
= $false )
| ( ( function @ SV710 )
= $false )
| ( ( relation @ SV710 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5395]) ).
thf(5517,plain,
! [SV913: $i,SV711: $i,SV609: $i] :
( ( ( in @ SV609 @ ( relation_dom @ SV711 ) )
= $false )
| ( ( ( apply @ ( relation_composition @ SV711 @ SV913 ) @ SV609 )
= ( apply @ SV913 @ ( apply @ SV711 @ SV609 ) ) )
= $true )
| ( ( function @ SV913 )
= $false )
| ( ( relation @ SV913 )
= $false )
| ( ( function @ SV711 )
= $false )
| ( ( relation @ SV711 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5396]) ).
thf(5518,plain,
! [SV652: $i,SV825: $i,SV885: $i] :
( ( ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV652 )
= $false )
| ( ( ~ ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV825 ) )
= $true )
| ( ( ~ ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV885 ) )
= $true )
| ( ( SV885
= ( set_intersection2 @ SV652 @ SV825 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5397]) ).
thf(5519,plain,
! [SV652: $i,SV825: $i,SV885: $i] :
( ( ( ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV652 )
| ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV885 ) )
= $true )
| ( ( SV885
= ( set_intersection2 @ SV652 @ SV825 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5398]) ).
thf(5520,plain,
! [SV652: $i,SV825: $i,SV885: $i] :
( ( ( ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV825 )
| ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV885 ) )
= $true )
| ( ( SV885
= ( set_intersection2 @ SV652 @ SV825 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5399]) ).
thf(5521,plain,
! [SV886: $i,SV826: $i,SV652: $i,SV1035: $i] :
( ( ( ~ ( in @ SV1035 @ SV652 )
| ~ ( in @ SV1035 @ SV826 ) )
= $true )
| ( ( in @ SV1035 @ SV886 )
= $true )
| ( ( SV886
= ( set_intersection2 @ SV652 @ SV826 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5400]) ).
thf(5522,plain,
! [SV826: $i,SV652: $i,SV886: $i] :
( ( ( ~ ! [SY1518: $i] :
( ~ ( in @ SY1518 @ SV886 )
| ( in @ SY1518 @ SV652 ) ) )
= $false )
| ( ( SV886
= ( set_intersection2 @ SV652 @ SV826 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5401]) ).
thf(5523,plain,
! [SV652: $i,SV826: $i,SV886: $i] :
( ( ( ~ ! [SY1519: $i] :
( ~ ( in @ SY1519 @ SV886 )
| ( in @ SY1519 @ SV826 ) ) )
= $false )
| ( ( SV886
= ( set_intersection2 @ SV652 @ SV826 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5401]) ).
thf(5524,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ( function @ SV1024 ) )
= $true )
| ( ( ~ ( relation @ SV1024 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) )
| ( SV1024
= ( function_inverse @ SV653 ) ) )
= $true )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5402]) ).
thf(5525,plain,
! [SV653: $i] :
( ( ( ! [SY1141: $i] :
( ~ ( function @ SY1141 )
| ~ ( relation @ SY1141 )
| ( SY1141
!= ( function_inverse @ SV653 ) )
| ~ ( ~ ~ ( ~ ! [SY1142: $i,SY1143: $i] :
( ( SY1143
!= ( apply @ SY1141 @ SY1142 ) )
| ~ ( in @ SY1142 @ ( relation_rng @ SV653 ) )
| ( SY1142
= ( apply @ SV653 @ SY1143 ) ) )
| ~ ! [SY1144: $i,SY1145: $i] :
( ( SY1145
!= ( apply @ SY1141 @ SY1144 ) )
| ~ ( in @ SY1144 @ ( relation_rng @ SV653 ) )
| ( in @ SY1145 @ ( relation_dom @ SV653 ) ) ) )
| ~ ~ ( ~ ! [SY1146: $i,SY1147: $i] :
( ( SY1146
!= ( apply @ SV653 @ SY1147 ) )
| ~ ( in @ SY1147 @ ( relation_dom @ SV653 ) )
| ( SY1147
= ( apply @ SY1141 @ SY1146 ) ) )
| ~ ! [SY1148: $i] :
( ! [SY1149: $i] :
( ( SY1148
!= ( apply @ SV653 @ SY1149 ) )
| ~ ( in @ SY1149 @ ( relation_dom @ SV653 ) ) )
| ( in @ SY1148 @ ( relation_rng @ SV653 ) ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5403]) ).
thf(5526,plain,
! [SV653: $i] :
( ( ( ! [SY1150: $i] :
( ~ ( function @ SY1150 )
| ~ ( relation @ SY1150 )
| ( SY1150
!= ( function_inverse @ SV653 ) )
| ( ( relation_dom @ SY1150 )
= ( relation_rng @ SV653 ) ) ) )
= $true )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5404]) ).
thf(5527,plain,
! [SV887: $i,SV920: $i,SV739: $i,SV654: $i] :
( ( ( in @ ( ordered_pair @ SV654 @ SV739 ) @ SV920 )
= $false )
| ( ( in @ SV654 @ SV887 )
= $false )
| ( ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SV887 ) @ SV920 ) )
= $true )
| ( ( relation @ SV920 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5407]) ).
thf(5528,plain,
! [SV1011: $i,SV991: $i,SV739: $i,SV654: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SV991 ) @ SV1011 ) ) )
= $true )
| ( ( in @ SV654 @ SV991 )
= $true )
| ( ( relation @ SV1011 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5408]) ).
thf(5529,plain,
! [SV1012: $i,SV992: $i,SV739: $i,SV654: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SV992 ) @ SV1012 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV654 @ SV739 ) @ SV1012 )
= $true )
| ( ( relation @ SV1012 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5409]) ).
thf(5530,plain,
! [SV655: $i,SV740: $i,SV961: $i] :
( ( ( ~ ( ~ ( in @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) @ SV655 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV740 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 ) ) )
= $false )
| ( ( SV961
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $true )
| ( ( relation @ SV961 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5410]) ).
thf(5531,plain,
! [SV655: $i,SV740: $i,SV961: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) @ SV655 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV740 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 ) ) ) )
= $false )
| ( ( SV961
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $true )
| ( ( relation @ SV961 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5410]) ).
thf(5532,plain,
! [SV962: $i,SV740: $i,SV655: $i] :
( ( ( ~ ! [SY1603: $i,SY1604: $i] :
( ~ ( in @ SY1604 @ SV655 )
| ~ ( in @ ( ordered_pair @ SY1603 @ SY1604 ) @ SV740 )
| ( in @ ( ordered_pair @ SY1603 @ SY1604 ) @ SV962 ) )
| ~ ~ ( ~ ! [SY1605: $i,SY1606: $i] :
( ~ ( in @ ( ordered_pair @ SY1605 @ SY1606 ) @ SV962 )
| ( in @ SY1606 @ SV655 ) )
| ~ ! [SY1607: $i,SY1608: $i] :
( ~ ( in @ ( ordered_pair @ SY1607 @ SY1608 ) @ SV962 )
| ( in @ ( ordered_pair @ SY1607 @ SY1608 ) @ SV740 ) ) ) )
= $false )
| ( ( SV962
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $false )
| ( ( relation @ SV962 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5411]) ).
thf(5533,plain,
! [SV657: $i,SV922: $i,SV964: $i] :
( ( ( ! [SY1609: $i] :
( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SY1609 ) @ SV657 )
| ~ ( in @ SY1609 @ SV922 ) ) )
= $true )
| ( ( ~ ( in @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SV964 ) )
= $true )
| ( ( SV964
= ( relation_inverse_image @ SV657 @ SV922 ) )
= $true )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5412]) ).
thf(5534,plain,
! [SV657: $i,SV922: $i,SV964: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ ( sK36_SY409 @ SV964 @ SV922 @ SV657 ) ) @ SV657 )
| ~ ( in @ ( sK36_SY409 @ SV964 @ SV922 @ SV657 ) @ SV922 ) ) )
= $true )
| ( ( in @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SV964 )
= $true )
| ( ( SV964
= ( relation_inverse_image @ SV657 @ SV922 ) )
= $true )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5413]) ).
thf(5535,plain,
! [SV965: $i,SV923: $i,SV657: $i] :
( ( ( ! [SY1610: $i] :
( ! [SY1552: $i] :
( ~ ( in @ ( ordered_pair @ SY1610 @ SY1552 ) @ SV657 )
| ~ ( in @ SY1552 @ SV923 ) )
| ( in @ SY1610 @ SV965 ) ) )
= $true )
| ( ( SV965
= ( relation_inverse_image @ SV657 @ SV923 ) )
= $false )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5414]) ).
thf(5536,plain,
! [SV657: $i,SV923: $i,SV965: $i] :
( ( ( ! [SY1612: $i] :
( ~ ( in @ SY1612 @ SV965 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1612 @ ( sK34_E @ SY1612 @ SV965 @ SV923 @ SV657 ) ) @ SV657 )
| ~ ( in @ ( sK34_E @ SY1612 @ SV965 @ SV923 @ SV657 ) @ SV923 ) ) ) )
= $true )
| ( ( SV965
= ( relation_inverse_image @ SV657 @ SV923 ) )
= $false )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5415]) ).
thf(5537,plain,
! [SV658: $i,SV924: $i,SV966: $i] :
( ( ( ! [SY1613: $i] :
( ~ ( in @ ( ordered_pair @ SY1613 @ ( sK38_D @ SV966 @ SV924 @ SV658 ) ) @ SV658 )
| ~ ( in @ SY1613 @ SV924 ) ) )
= $true )
| ( ( ~ ( in @ ( sK38_D @ SV966 @ SV924 @ SV658 ) @ SV966 ) )
= $true )
| ( ( SV966
= ( relation_image @ SV658 @ SV924 ) )
= $true )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5416]) ).
thf(5538,plain,
! [SV658: $i,SV924: $i,SV966: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SV966 @ SV924 @ SV658 ) @ ( sK38_D @ SV966 @ SV924 @ SV658 ) ) @ SV658 )
| ~ ( in @ ( sK39_SY411 @ SV966 @ SV924 @ SV658 ) @ SV924 ) ) )
= $true )
| ( ( in @ ( sK38_D @ SV966 @ SV924 @ SV658 ) @ SV966 )
= $true )
| ( ( SV966
= ( relation_image @ SV658 @ SV924 ) )
= $true )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5417]) ).
thf(5539,plain,
! [SV967: $i,SV925: $i,SV658: $i] :
( ( ( ! [SY1614: $i] :
( ! [SY1558: $i] :
( ~ ( in @ ( ordered_pair @ SY1558 @ SY1614 ) @ SV658 )
| ~ ( in @ SY1558 @ SV925 ) )
| ( in @ SY1614 @ SV967 ) ) )
= $true )
| ( ( SV967
= ( relation_image @ SV658 @ SV925 ) )
= $false )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5418]) ).
thf(5540,plain,
! [SV658: $i,SV925: $i,SV967: $i] :
( ( ( ! [SY1616: $i] :
( ~ ( in @ SY1616 @ SV967 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SY1616 @ SV967 @ SV925 @ SV658 ) @ SY1616 ) @ SV658 )
| ~ ( in @ ( sK37_E @ SY1616 @ SV967 @ SV925 @ SV658 ) @ SV925 ) ) ) )
= $true )
| ( ( SV967
= ( relation_image @ SV658 @ SV925 ) )
= $false )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5419]) ).
thf(5541,plain,
! [SV928: $i] :
( ( ( function @ SV928 )
= $false )
| ( ( empty @ SV928 )
= $false )
| ( ( relation @ SV928 )
= $false )
| ( ( function @ SV928 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5420]) ).
thf(5542,plain,
! [SV929: $i] :
( ( ( function @ SV929 )
= $false )
| ( ( empty @ SV929 )
= $false )
| ( ( relation @ SV929 )
= $false )
| ( ( relation @ SV929 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5421]) ).
thf(5543,plain,
! [SV660: $i,SV783: $i,SV1014: $i] :
( ( ( ~ ( ~ ( ! [SY1644: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ SY1644 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1644 @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV783 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV1014 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK10_SY395 @ SV1014 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV783 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV1014 ) ) ) )
= $true )
| ( ( SV1014
= ( relation_composition @ SV660 @ SV783 ) )
= $true )
| ( ( relation @ SV1014 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5422]) ).
thf(5544,plain,
! [SV783: $i,SV660: $i,SV1015: $i] :
( ( ( ( SV1015
!= ( relation_composition @ SV660 @ SV783 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1645: $i,SY1646: $i] :
( ! [SY1410: $i] :
( ~ ( in @ ( ordered_pair @ SY1645 @ SY1410 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1410 @ SY1646 ) @ SV783 ) )
| ( in @ ( ordered_pair @ SY1645 @ SY1646 ) @ SV1015 ) )
| ~ ! [SY1648: $i,SY1649: $i] :
( ~ ( in @ ( ordered_pair @ SY1648 @ SY1649 ) @ SV1015 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1648 @ ( sK7_F @ SY1649 @ SY1648 @ SV1015 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY1649 @ SY1648 @ SV1015 @ SV783 @ SV660 ) @ SY1649 ) @ SV783 ) ) ) ) )
= $true )
| ( ( relation @ SV1015 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5423]) ).
thf(5545,plain,
! [SV661: $i,SV932: $i,SV1048: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1048 @ ( sK60_C @ SV932 @ SV661 ) ) @ SV661 ) )
= $true )
| ( ( ~ ( in @ ( sK60_C @ SV932 @ SV661 ) @ SV932 ) )
= $true )
| ( ( SV932
= ( relation_rng @ SV661 ) )
= $true )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5424]) ).
thf(5546,plain,
! [SV933: $i,SV661: $i,SV1049: $i] :
( ( ( ! [SY1660: $i] :
~ ( in @ ( ordered_pair @ SY1660 @ SV1049 ) @ SV661 )
| ( in @ SV1049 @ SV933 ) )
= $true )
| ( ( SV933
= ( relation_rng @ SV661 ) )
= $false )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5426]) ).
thf(5547,plain,
! [SV661: $i,SV933: $i,SV1050: $i] :
( ( ( ~ ( in @ SV1050 @ SV933 )
| ( in @ ( ordered_pair @ ( sK59_D @ SV1050 @ SV933 @ SV661 ) @ SV1050 ) @ SV661 ) )
= $true )
| ( ( SV933
= ( relation_rng @ SV661 ) )
= $false )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5427]) ).
thf(5548,plain,
! [SV662: $i,SV838: $i,SV891: $i] :
( ( ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV662 )
= $false )
| ( ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV838 )
= $true )
| ( ( ~ ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV891 ) )
= $true )
| ( ( SV891
= ( set_difference @ SV662 @ SV838 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5428]) ).
thf(5549,plain,
! [SV662: $i,SV838: $i,SV891: $i] :
( ( ( ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV662 )
| ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV891 ) )
= $true )
| ( ( SV891
= ( set_difference @ SV662 @ SV838 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5429]) ).
thf(5550,plain,
! [SV662: $i,SV838: $i,SV891: $i] :
( ( ( ~ ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV838 )
| ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV891 ) )
= $true )
| ( ( SV891
= ( set_difference @ SV662 @ SV838 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5430]) ).
thf(5551,plain,
! [SV892: $i,SV839: $i,SV662: $i,SV1036: $i] :
( ( ( ~ ( in @ SV1036 @ SV662 )
| ( in @ SV1036 @ SV839 ) )
= $true )
| ( ( in @ SV1036 @ SV892 )
= $true )
| ( ( SV892
= ( set_difference @ SV662 @ SV839 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5431]) ).
thf(5552,plain,
! [SV839: $i,SV662: $i,SV892: $i] :
( ( ( ~ ! [SY1524: $i] :
( ~ ( in @ SY1524 @ SV892 )
| ( in @ SY1524 @ SV662 ) ) )
= $false )
| ( ( SV892
= ( set_difference @ SV662 @ SV839 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5432]) ).
thf(5553,plain,
! [SV662: $i,SV839: $i,SV892: $i] :
( ( ( ~ ! [SY1525: $i] :
( ~ ( in @ SY1525 @ SV892 )
| ~ ( in @ SY1525 @ SV839 ) ) )
= $false )
| ( ( SV892
= ( set_difference @ SV662 @ SV839 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5432]) ).
thf(5554,plain,
! [SV790: $i,SV840: $i] :
( ( ( function @ SV840 )
= $false )
| ( ( relation @ SV790 )
= $false )
| ( ( function @ SV790 )
= $false )
| ( ( relation @ SV840 )
= $false )
| ( ( function @ ( relation_composition @ SV790 @ SV840 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5433]) ).
thf(5555,plain,
! [SV791: $i,SV841: $i] :
( ( ( function @ SV841 )
= $false )
| ( ( relation @ SV791 )
= $false )
| ( ( function @ SV791 )
= $false )
| ( ( relation @ SV841 )
= $false )
| ( ( relation @ ( relation_composition @ SV791 @ SV841 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5434]) ).
thf(5556,plain,
! [SV996: $i,SV972: $i,SV663: $i] :
( ( ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SV972 @ SV996 ) ) )
= $false )
| ( ( in @ SV663 @ SV972 )
= $true )
| ( ( relation @ SV996 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5436]) ).
thf(5557,plain,
! [SV997: $i,SV973: $i,SV663: $i] :
( ( ( in @ SV663 @ ( relation_rng @ ( relation_rng_restriction @ SV973 @ SV997 ) ) )
= $false )
| ( ( in @ SV663 @ ( relation_rng @ SV997 ) )
= $true )
| ( ( relation @ SV997 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5437]) ).
thf(5558,plain,
! [SV664: $i,SV1037: $i] :
( ( ( ~ ( in @ SV1037 @ ( relation_dom @ SV664 ) ) )
= $true )
| ( ( ! [SY1652: $i] :
( ( SY1652
!= ( apply @ SV664 @ SV1037 ) )
| ( in @ ( ordered_pair @ SV1037 @ SY1652 ) @ SV664 ) ) )
= $true )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5438]) ).
thf(5559,plain,
! [SV664: $i,SV1038: $i] :
( ( ( ~ ( in @ SV1038 @ ( relation_dom @ SV664 ) ) )
= $true )
| ( ( ! [SY1653: $i] :
( ~ ( in @ ( ordered_pair @ SV1038 @ SY1653 ) @ SV664 )
| ( SY1653
= ( apply @ SV664 @ SV1038 ) ) ) )
= $true )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5439]) ).
thf(5560,plain,
! [SV664: $i,SV1039: $i] :
( ( ( in @ SV1039 @ ( relation_dom @ SV664 ) )
= $true )
| ( ( ! [SY1654: $i] :
( ( SY1654
!= ( apply @ SV664 @ SV1039 ) )
| ( SY1654 = empty_set ) ) )
= $true )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5440]) ).
thf(5561,plain,
! [SV664: $i,SV1040: $i] :
( ( ( in @ SV1040 @ ( relation_dom @ SV664 ) )
= $true )
| ( ( ! [SY1655: $i] :
( ( SY1655 != empty_set )
| ( SY1655
= ( apply @ SV664 @ SV1040 ) ) ) )
= $true )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5441]) ).
thf(5562,plain,
! [SV665: $i,SV934: $i] :
( ( ( in @ ( ordered_pair @ ( sK19_C @ SV934 @ SV665 ) @ ( sK20_SY399 @ SV934 @ SV665 ) ) @ SV665 )
= $true )
| ( ( subset @ SV665 @ SV934 )
= $true )
| ( ( relation @ SV934 )
= $false )
| ( ( relation @ SV665 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5442]) ).
thf(5563,plain,
! [SV665: $i,SV934: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV934 @ SV665 ) @ ( sK20_SY399 @ SV934 @ SV665 ) ) @ SV934 ) )
= $true )
| ( ( subset @ SV665 @ SV934 )
= $true )
| ( ( relation @ SV934 )
= $false )
| ( ( relation @ SV665 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5443]) ).
thf(5564,plain,
! [SV935: $i,SV665: $i,SV1051: $i,SV1041: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1041 @ SV1051 ) @ SV665 )
| ( in @ ( ordered_pair @ SV1041 @ SV1051 ) @ SV935 ) )
= $true )
| ( ( subset @ SV665 @ SV935 )
= $false )
| ( ( relation @ SV935 )
= $false )
| ( ( relation @ SV665 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5444]) ).
thf(5565,plain,
! [SV742: $i,SV666: $i,SV1016: $i] :
( ( ( function @ SV1016 )
= $false )
| ( ( ~ ( relation @ SV1016 ) )
= $true )
| ( ( ~ ( in @ SV666 @ ( relation_dom @ SV1016 ) )
| ~ ( in @ ( apply @ SV1016 @ SV666 ) @ ( relation_dom @ SV742 ) )
| ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SV1016 @ SV742 ) ) ) )
= $true )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5445]) ).
thf(5566,plain,
! [SV742: $i,SV666: $i,SV1052: $i] :
( ( ( ~ ( function @ SV1052 )
| ~ ( relation @ SV1052 )
| ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SV1052 @ SV742 ) ) )
| ( in @ SV666 @ ( relation_dom @ SV1052 ) ) )
= $true )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5446]) ).
thf(5567,plain,
! [SV742: $i,SV666: $i,SV1053: $i] :
( ( ( ~ ( function @ SV1053 )
| ~ ( relation @ SV1053 )
| ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SV1053 @ SV742 ) ) )
| ( in @ ( apply @ SV1053 @ SV666 ) @ ( relation_dom @ SV742 ) ) )
= $true )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5447]) ).
thf(5568,plain,
! [SV843: $i,SV667: $i,SV894: $i,SV1017: $i] :
( ( ( in @ SV1017 @ ( relation_rng @ SV894 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV667 @ SV1017 ) @ SV894 ) )
= $true )
| ( ( ~ ( in @ SV1017 @ SV843 ) )
= $true )
| ( ( in @ SV667 @ ( relation_inverse_image @ SV894 @ SV843 ) )
= $true )
| ( ( relation @ SV894 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5448]) ).
thf(5569,plain,
! [SV667: $i,SV844: $i,SV895: $i] :
( ( ( ~ ( ~ ( in @ ( sK51_D @ SV895 @ SV844 @ SV667 ) @ ( relation_rng @ SV895 ) )
| ~ ( in @ ( ordered_pair @ SV667 @ ( sK51_D @ SV895 @ SV844 @ SV667 ) ) @ SV895 ) ) )
= $true )
| ( ( in @ SV667 @ ( relation_inverse_image @ SV895 @ SV844 ) )
= $false )
| ( ( relation @ SV895 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5449]) ).
thf(5570,plain,
! [SV667: $i,SV844: $i,SV895: $i] :
( ( ( in @ ( sK51_D @ SV895 @ SV844 @ SV667 ) @ SV844 )
= $true )
| ( ( in @ SV667 @ ( relation_inverse_image @ SV895 @ SV844 ) )
= $false )
| ( ( relation @ SV895 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5450]) ).
thf(5571,plain,
! [SV974: $i,SV998: $i,SV668: $i] :
( ( ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SV998 @ SV974 ) ) )
= $false )
| ( ( in @ SV668 @ SV974 )
= $true )
| ( ( relation @ SV998 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5452]) ).
thf(5572,plain,
! [SV975: $i,SV999: $i,SV668: $i] :
( ( ( in @ SV668 @ ( relation_dom @ ( relation_dom_restriction @ SV999 @ SV975 ) ) )
= $false )
| ( ( in @ SV668 @ ( relation_dom @ SV999 ) )
= $true )
| ( ( relation @ SV999 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5453]) ).
thf(5573,plain,
! [SV669: $i,SV848: $i,SV897: $i] :
( ( ( ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV897 )
| ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV669 ) )
= $true )
| ( ( SV897
= ( set_union2 @ SV669 @ SV848 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5454]) ).
thf(5574,plain,
! [SV669: $i,SV848: $i,SV897: $i] :
( ( ( ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV897 )
| ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV848 ) )
= $true )
| ( ( SV897
= ( set_union2 @ SV669 @ SV848 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5455]) ).
thf(5575,plain,
! [SV849: $i,SV669: $i,SV898: $i,SV1042: $i] :
( ( ( ~ ( in @ SV1042 @ SV898 ) )
= $true )
| ( ( ( in @ SV1042 @ SV669 )
| ( in @ SV1042 @ SV849 ) )
= $true )
| ( ( SV898
= ( set_union2 @ SV669 @ SV849 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5457]) ).
thf(5576,plain,
! [SV849: $i,SV898: $i,SV669: $i] :
( ( ( ~ ! [SY1528: $i] :
( ~ ( in @ SY1528 @ SV669 )
| ( in @ SY1528 @ SV898 ) ) )
= $false )
| ( ( SV898
= ( set_union2 @ SV669 @ SV849 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5458]) ).
thf(5577,plain,
! [SV669: $i,SV898: $i,SV849: $i] :
( ( ( ~ ! [SY1529: $i] :
( ~ ( in @ SY1529 @ SV849 )
| ( in @ SY1529 @ SV898 ) ) )
= $false )
| ( ( SV898
= ( set_union2 @ SV669 @ SV849 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5458]) ).
thf(5578,plain,
! [SV937: $i,SV1000: $i] :
( ( ( ~ ( ~ ( in @ ( sK33_SY406 @ SV1000 @ SV937 ) @ SV937 )
| ~ ~ ( in @ ( sK32_C @ SV1000 @ SV937 ) @ ( sK33_SY406 @ SV1000 @ SV937 ) ) )
| ~ ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SV1000 ) )
= $true )
| ( ( SV1000
= ( set_meet @ SV937 ) )
= $true )
| ( ( SV937 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5459]) ).
thf(5579,plain,
! [SV1000: $i,SV937: $i] :
( ( ( ! [SY1636: $i] :
( ~ ( in @ SY1636 @ SV937 )
| ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SY1636 ) )
| ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SV1000 ) )
= $true )
| ( ( SV1000
= ( set_meet @ SV937 ) )
= $true )
| ( ( SV937 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5460]) ).
thf(5580,plain,
! [SV938: $i,SV1001: $i] :
( ( ( ~ ! [SY1637: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY1637 @ SV1001 @ SV938 ) @ SV938 )
| ~ ~ ( in @ SY1637 @ ( sK31_D @ SY1637 @ SV1001 @ SV938 ) ) )
| ( in @ SY1637 @ SV1001 ) ) )
= $false )
| ( ( SV1001
= ( set_meet @ SV938 ) )
= $false )
| ( ( SV938 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5461]) ).
thf(5581,plain,
! [SV938: $i,SV1001: $i] :
( ( ( ~ ! [SY1638: $i] :
( ~ ( in @ SY1638 @ SV1001 )
| ! [SY1573: $i] :
( ~ ( in @ SY1573 @ SV938 )
| ( in @ SY1638 @ SY1573 ) ) ) )
= $false )
| ( ( SV1001
= ( set_meet @ SV938 ) )
= $false )
| ( ( SV938 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5461]) ).
thf(5582,plain,
! [SV899: $i,SV850: $i,SV1054: $i,SV670: $i,SV1043: $i] :
( ( ( ~ ( in @ SV1043 @ SV670 )
| ~ ( in @ SV1054 @ SV850 )
| ( ( sK23_D @ SV899 @ SV850 @ SV670 )
!= ( ordered_pair @ SV1043 @ SV1054 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV899 @ SV850 @ SV670 ) @ SV899 ) )
= $true )
| ( ( SV899
= ( cartesian_product2 @ SV670 @ SV850 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5464]) ).
thf(5583,plain,
! [SV670: $i,SV850: $i,SV899: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK24_SY403 @ SV899 @ SV850 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK25_SY405 @ SV899 @ SV850 @ SV670 ) @ SV850 ) ) )
= $false )
| ( ( in @ ( sK23_D @ SV899 @ SV850 @ SV670 ) @ SV899 )
= $true )
| ( ( SV899
= ( cartesian_product2 @ SV670 @ SV850 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5465]) ).
thf(5584,plain,
! [SV670: $i,SV850: $i,SV899: $i] :
( ( ( ( ( sK23_D @ SV899 @ SV850 @ SV670 )
!= ( ordered_pair @ ( sK24_SY403 @ SV899 @ SV850 @ SV670 ) @ ( sK25_SY405 @ SV899 @ SV850 @ SV670 ) ) ) )
= $false )
| ( ( in @ ( sK23_D @ SV899 @ SV850 @ SV670 ) @ SV899 )
= $true )
| ( ( SV899
= ( cartesian_product2 @ SV670 @ SV850 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5465]) ).
thf(5585,plain,
! [SV900: $i,SV1044: $i,SV851: $i,SV670: $i] :
( ( ( ! [SY1658: $i,SY1659: $i] :
( ~ ( in @ SY1658 @ SV670 )
| ~ ( in @ SY1659 @ SV851 )
| ( SV1044
!= ( ordered_pair @ SY1658 @ SY1659 ) ) ) )
= $true )
| ( ( in @ SV1044 @ SV900 )
= $true )
| ( ( SV900
= ( cartesian_product2 @ SV670 @ SV851 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5466]) ).
thf(5586,plain,
! [SV670: $i,SV851: $i,SV900: $i,SV1045: $i] :
( ( ( ~ ( in @ SV1045 @ SV900 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SV1045 @ SV900 @ SV851 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK22_SY400 @ SV1045 @ SV900 @ SV851 @ SV670 ) @ SV851 ) )
| ( SV1045
!= ( ordered_pair @ ( sK21_E @ SV1045 @ SV900 @ SV851 @ SV670 ) @ ( sK22_SY400 @ SV1045 @ SV900 @ SV851 @ SV670 ) ) ) ) )
= $true )
| ( ( SV900
= ( cartesian_product2 @ SV670 @ SV851 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5467]) ).
thf(5587,plain,
! [SV671: $i,SV901: $i,SV852: $i] :
( ( ( SV852
= ( apply @ SV901 @ SV671 ) )
= $false )
| ( ( ~ ( in @ SV671 @ ( relation_dom @ SV901 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV671 @ SV852 ) @ SV901 )
= $true )
| ( ( function @ SV901 )
= $false )
| ( ( relation @ SV901 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5468]) ).
thf(5588,plain,
! [SV976: $i,SV671: $i,SV1002: $i] :
( ( ( relation @ SV1002 )
= $false )
| ( ( function @ SV1002 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV671 @ SV976 ) @ SV1002 )
| ( SV976
= ( apply @ SV1002 @ SV671 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5469]) ).
thf(5589,plain,
! [SV977: $i,SV671: $i,SV1003: $i] :
( ( ( relation @ SV1003 )
= $false )
| ( ( function @ SV1003 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV671 @ SV977 ) @ SV1003 )
| ( in @ SV671 @ ( relation_dom @ SV1003 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5470]) ).
thf(5590,plain,
! [SV672: $i,SV941: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SV941 @ SV672 ) @ ( sK12_SY396 @ SV941 @ SV672 ) ) @ SV941 )
| ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SV941 @ SV672 ) @ ( sK11_C @ SV941 @ SV672 ) ) @ SV672 ) )
= $true )
| ( ( SV941
= ( relation_inverse @ SV672 ) )
= $true )
| ( ( relation @ SV941 )
= $false )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5471]) ).
thf(5591,plain,
! [SV672: $i,SV941: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK11_C @ SV941 @ SV672 ) @ ( sK12_SY396 @ SV941 @ SV672 ) ) @ SV941 )
| ( in @ ( ordered_pair @ ( sK12_SY396 @ SV941 @ SV672 ) @ ( sK11_C @ SV941 @ SV672 ) ) @ SV672 ) )
= $true )
| ( ( SV941
= ( relation_inverse @ SV672 ) )
= $true )
| ( ( relation @ SV941 )
= $false )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5472]) ).
thf(5592,plain,
! [SV672: $i,SV942: $i] :
( ( ( ~ ! [SY1576: $i,SY1577: $i] :
( ~ ( in @ ( ordered_pair @ SY1576 @ SY1577 ) @ SV942 )
| ( in @ ( ordered_pair @ SY1577 @ SY1576 ) @ SV672 ) ) )
= $false )
| ( ( SV942
= ( relation_inverse @ SV672 ) )
= $false )
| ( ( relation @ SV942 )
= $false )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5473]) ).
thf(5593,plain,
! [SV942: $i,SV672: $i] :
( ( ( ~ ! [SY1578: $i,SY1579: $i] :
( ~ ( in @ ( ordered_pair @ SY1579 @ SY1578 ) @ SV672 )
| ( in @ ( ordered_pair @ SY1578 @ SY1579 ) @ SV942 ) ) )
= $false )
| ( ( SV942
= ( relation_inverse @ SV672 ) )
= $false )
| ( ( relation @ SV942 )
= $false )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5473]) ).
thf(5594,plain,
! [SV675: $i,SV857: $i,SV905: $i] :
( ( ( ~ ( in @ ( sK27_D @ SV905 @ SV857 @ SV675 ) @ SV905 )
| ( ( sK27_D @ SV905 @ SV857 @ SV675 )
!= SV675 ) )
= $true )
| ( ( SV905
= ( unordered_pair @ SV675 @ SV857 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5476]) ).
thf(5595,plain,
! [SV675: $i,SV857: $i,SV905: $i] :
( ( ( ~ ( in @ ( sK27_D @ SV905 @ SV857 @ SV675 ) @ SV905 )
| ( ( sK27_D @ SV905 @ SV857 @ SV675 )
!= SV857 ) )
= $true )
| ( ( SV905
= ( unordered_pair @ SV675 @ SV857 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5477]) ).
thf(5596,plain,
! [SV858: $i,SV675: $i,SV906: $i,SV1046: $i] :
( ( ( ~ ( in @ SV1046 @ SV906 ) )
= $true )
| ( ( ( SV1046 = SV675 )
| ( SV1046 = SV858 ) )
= $true )
| ( ( SV906
= ( unordered_pair @ SV675 @ SV858 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5479]) ).
thf(5597,plain,
! [SV858: $i,SV906: $i,SV675: $i] :
( ( ( ~ ! [SY1538: $i] :
( ( SY1538 != SV675 )
| ( in @ SY1538 @ SV906 ) ) )
= $false )
| ( ( SV906
= ( unordered_pair @ SV675 @ SV858 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5480]) ).
thf(5598,plain,
! [SV675: $i,SV906: $i,SV858: $i] :
( ( ( ~ ! [SY1539: $i] :
( ( SY1539 != SV858 )
| ( in @ SY1539 @ SV906 ) ) )
= $false )
| ( ( SV906
= ( unordered_pair @ SV675 @ SV858 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5480]) ).
thf(5599,plain,
! [SV1027: $i,SV804: $i,SV863: $i] :
( ( ( in @ ( sK15_C @ SV863 @ SV804 ) @ SV1027 )
= $false )
| ( ( ~ ( in @ SV1027 @ SV804 ) )
= $true )
| ( ( ~ ( in @ ( sK15_C @ SV863 @ SV804 ) @ SV863 ) )
= $true )
| ( ( SV863
= ( union @ SV804 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5483]) ).
thf(5600,plain,
! [SV804: $i,SV863: $i] :
( ( ( in @ ( sK15_C @ SV863 @ SV804 ) @ ( sK16_SY398 @ SV863 @ SV804 ) )
= $true )
| ( ( in @ ( sK15_C @ SV863 @ SV804 ) @ SV863 )
= $true )
| ( ( SV863
= ( union @ SV804 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5484]) ).
thf(5601,plain,
! [SV804: $i,SV863: $i] :
( ( ( in @ ( sK16_SY398 @ SV863 @ SV804 ) @ SV804 )
= $true )
| ( ( in @ ( sK15_C @ SV863 @ SV804 ) @ SV863 )
= $true )
| ( ( SV863
= ( union @ SV804 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5485]) ).
thf(5602,plain,
! [SV864: $i,SV805: $i,SV1055: $i,SV1028: $i] :
( ( ( ~ ( in @ SV1028 @ SV1055 )
| ~ ( in @ SV1055 @ SV805 ) )
= $true )
| ( ( in @ SV1028 @ SV864 )
= $true )
| ( ( SV864
= ( union @ SV805 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5486]) ).
thf(5603,plain,
! [SV805: $i,SV864: $i,SV1029: $i] :
( ( ( in @ SV1029 @ SV864 )
= $false )
| ( ( ~ ( ~ ( in @ SV1029 @ ( sK14_D @ SV1029 @ SV864 @ SV805 ) )
| ~ ( in @ ( sK14_D @ SV1029 @ SV864 @ SV805 ) @ SV805 ) ) )
= $true )
| ( ( SV864
= ( union @ SV805 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5487]) ).
thf(5604,plain,
! [SV1056: $i,SV679: $i,SV946: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK63_C @ SV946 @ SV679 ) @ SV1056 ) @ SV679 ) )
= $true )
| ( ( ~ ( in @ ( sK63_C @ SV946 @ SV679 ) @ SV946 ) )
= $true )
| ( ( SV946
= ( relation_dom @ SV679 ) )
= $true )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5488]) ).
thf(5605,plain,
! [SV947: $i,SV679: $i,SV1057: $i] :
( ( ( ! [SY1661: $i] :
~ ( in @ ( ordered_pair @ SV1057 @ SY1661 ) @ SV679 )
| ( in @ SV1057 @ SV947 ) )
= $true )
| ( ( SV947
= ( relation_dom @ SV679 ) )
= $false )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5490]) ).
thf(5606,plain,
! [SV679: $i,SV947: $i,SV1058: $i] :
( ( ( ~ ( in @ SV1058 @ SV947 )
| ( in @ ( ordered_pair @ SV1058 @ ( sK62_D @ SV1058 @ SV947 @ SV679 ) ) @ SV679 ) )
= $true )
| ( ( SV947
= ( relation_dom @ SV679 ) )
= $false )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5491]) ).
thf(5607,plain,
! [SV806: $i,SV867: $i] :
( ( ( ( ( sK44_C @ SV867 @ SV806 )
!= ( sK45_SY414 @ SV867 @ SV806 ) ) )
= $true )
| ( ( ~ ( in @ ( sK44_C @ SV867 @ SV806 ) @ SV806 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 ) )
= $true )
| ( ( SV867
= ( identity_relation @ SV806 ) )
= $true )
| ( ( relation @ SV867 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5492]) ).
thf(5608,plain,
! [SV806: $i,SV867: $i] :
( ( ( ~ ( ( ( sK44_C @ SV867 @ SV806 )
= ( sK45_SY414 @ SV867 @ SV806 ) )
| ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 ) ) )
= $false )
| ( ( SV867
= ( identity_relation @ SV806 ) )
= $true )
| ( ( relation @ SV867 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5493]) ).
thf(5609,plain,
! [SV806: $i,SV867: $i] :
( ( ( ~ ( ( in @ ( sK44_C @ SV867 @ SV806 ) @ SV806 )
| ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 ) ) )
= $false )
| ( ( SV867
= ( identity_relation @ SV806 ) )
= $true )
| ( ( relation @ SV867 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5493]) ).
thf(5610,plain,
! [SV868: $i,SV807: $i,SV1059: $i] :
( ( ( ! [SY1662: $i] :
( ( SV1059 != SY1662 )
| ~ ( in @ SV1059 @ SV807 )
| ( in @ ( ordered_pair @ SV1059 @ SY1662 ) @ SV868 ) ) )
= $true )
| ( ( SV868
= ( identity_relation @ SV807 ) )
= $false )
| ( ( relation @ SV868 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5494]) ).
thf(5611,plain,
! [SV807: $i,SV868: $i] :
( ( ( ~ ! [SY1505: $i,SY1506: $i] :
( ~ ( in @ ( ordered_pair @ SY1505 @ SY1506 ) @ SV868 )
| ( SY1505 = SY1506 ) )
| ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
~ ( in @ ( ordered_pair @ SY1507 @ SY1508 ) @ SV868 )
| ( in @ SY1507 @ SV807 ) ) )
= $false )
| ( ( SV868
= ( identity_relation @ SV807 ) )
= $false )
| ( ( relation @ SV868 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5495]) ).
thf(5612,plain,
! [SV681: $i,SV948: $i,SV980: $i] :
( ( ( ~ ( ~ ( in @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ SV948 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV681 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 ) ) )
= $false )
| ( ( SV980
= ( relation_dom_restriction @ SV681 @ SV948 ) )
= $true )
| ( ( relation @ SV980 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5496]) ).
thf(5613,plain,
! [SV681: $i,SV948: $i,SV980: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ SV948 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV681 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 ) ) ) )
= $false )
| ( ( SV980
= ( relation_dom_restriction @ SV681 @ SV948 ) )
= $true )
| ( ( relation @ SV980 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5496]) ).
thf(5614,plain,
! [SV981: $i,SV681: $i,SV949: $i] :
( ( ( ~ ! [SY1625: $i,SY1626: $i] :
( ~ ( in @ SY1625 @ SV949 )
| ~ ( in @ ( ordered_pair @ SY1625 @ SY1626 ) @ SV681 )
| ( in @ ( ordered_pair @ SY1625 @ SY1626 ) @ SV981 ) )
| ~ ~ ( ~ ! [SY1627: $i] :
( ! [SY1628: $i] :
~ ( in @ ( ordered_pair @ SY1627 @ SY1628 ) @ SV981 )
| ( in @ SY1627 @ SV949 ) )
| ~ ! [SY1629: $i,SY1630: $i] :
( ~ ( in @ ( ordered_pair @ SY1629 @ SY1630 ) @ SV981 )
| ( in @ ( ordered_pair @ SY1629 @ SY1630 ) @ SV681 ) ) ) )
= $false )
| ( ( SV981
= ( relation_dom_restriction @ SV681 @ SV949 ) )
= $false )
| ( ( relation @ SV981 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5497]) ).
thf(5615,plain,
! [SV870: $i,SV809: $i,SV1030: $i] :
( ( ( SV1030 = SV809 )
= $false )
| ( ( in @ SV1030 @ SV870 )
= $true )
| ( ( SV870
= ( singleton @ SV809 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5499]) ).
thf(5616,plain,
! [SV809: $i,SV870: $i,SV1031: $i] :
( ( ( in @ SV1031 @ SV870 )
= $false )
| ( ( SV1031 = SV809 )
= $true )
| ( ( SV870
= ( singleton @ SV809 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5500]) ).
thf(5617,plain,
! [SV871: $i,SV682: $i,SV910: $i,SV1022: $i] :
( ( ( in @ SV1022 @ ( relation_dom @ SV910 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV1022 @ SV682 ) @ SV910 ) )
= $true )
| ( ( ~ ( in @ SV1022 @ SV871 ) )
= $true )
| ( ( in @ SV682 @ ( relation_image @ SV910 @ SV871 ) )
= $true )
| ( ( relation @ SV910 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5501]) ).
thf(5618,plain,
! [SV682: $i,SV872: $i,SV911: $i] :
( ( ( ~ ( ~ ( in @ ( sK52_D @ SV911 @ SV872 @ SV682 ) @ ( relation_dom @ SV911 ) )
| ~ ( in @ ( ordered_pair @ ( sK52_D @ SV911 @ SV872 @ SV682 ) @ SV682 ) @ SV911 ) ) )
= $true )
| ( ( in @ SV682 @ ( relation_image @ SV911 @ SV872 ) )
= $false )
| ( ( relation @ SV911 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5502]) ).
thf(5619,plain,
! [SV682: $i,SV872: $i,SV911: $i] :
( ( ( in @ ( sK52_D @ SV911 @ SV872 @ SV682 ) @ SV872 )
= $true )
| ( ( in @ SV682 @ ( relation_image @ SV911 @ SV872 ) )
= $false )
| ( ( relation @ SV911 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5503]) ).
thf(5620,plain,
! [SV684: $i,SV952: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV684 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV952 ) )
= $true )
| ( ( SV684 = SV952 )
= $true )
| ( ( relation @ SV952 )
= $false )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5504]) ).
thf(5621,plain,
! [SV684: $i,SV952: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV684 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV952 ) )
= $true )
| ( ( SV684 = SV952 )
= $true )
| ( ( relation @ SV952 )
= $false )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5505]) ).
thf(5622,plain,
! [SV953: $i,SV684: $i] :
( ( ( ~ ! [SY1592: $i,SY1593: $i] :
( ~ ( in @ ( ordered_pair @ SY1592 @ SY1593 ) @ SV684 )
| ( in @ ( ordered_pair @ SY1592 @ SY1593 ) @ SV953 ) ) )
= $false )
| ( ( SV684 = SV953 )
= $false )
| ( ( relation @ SV953 )
= $false )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5506]) ).
thf(5623,plain,
! [SV684: $i,SV953: $i] :
( ( ( ~ ! [SY1594: $i,SY1595: $i] :
( ~ ( in @ ( ordered_pair @ SY1594 @ SY1595 ) @ SV953 )
| ( in @ ( ordered_pair @ SY1594 @ SY1595 ) @ SV684 ) ) )
= $false )
| ( ( SV684 = SV953 )
= $false )
| ( ( relation @ SV953 )
= $false )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5506]) ).
thf(5624,plain,
! [SV685: $i,SV982: $i,SV1060: $i] :
( ( ( ~ ( subset @ SV1060 @ SV982 )
| ( in @ SV1060 @ ( sK3_SY386 @ SV982 @ SV685 ) ) )
= $true )
| ( ( ~ ( in @ SV982 @ ( sK2_B @ SV685 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5507]) ).
thf(5625,plain,
! [SV685: $i,SV982: $i] :
( ( ( in @ SV982 @ ( sK2_B @ SV685 ) )
= $false )
| ( ( in @ ( sK3_SY386 @ SV982 @ SV685 ) @ ( sK2_B @ SV685 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5508]) ).
thf(5626,plain,
! [SV1047: $i,SV685: $i,SV1032: $i] :
( ( ( ~ ( in @ SV1032 @ ( sK2_B @ SV685 ) )
| ~ ( subset @ SV1047 @ SV1032 ) )
= $true )
| ( ( in @ SV1047 @ ( sK2_B @ SV685 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5509]) ).
thf(5627,plain,
! [SV814: $i,SV878: $i,SV1033: $i] :
( ( ( in @ SV1033 @ SV878 )
= $false )
| ( ( subset @ SV1033 @ SV814 )
= $true )
| ( ( SV878
= ( powerset @ SV814 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5511]) ).
thf(5628,plain,
! [SV878: $i,SV814: $i,SV1034: $i] :
( ( ( subset @ SV1034 @ SV814 )
= $false )
| ( ( in @ SV1034 @ SV878 )
= $true )
| ( ( SV878
= ( powerset @ SV814 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5512]) ).
thf(5629,plain,
! [SV818: $i,SV880: $i] :
( ( ( ~ ( in @ ( sK50_C @ SV880 @ SV818 ) @ SV818 ) )
= $false )
| ( ( ( ( relation_dom @ SV880 )
!= SV818 ) )
= $true )
| ( ( SV880
= ( identity_relation @ SV818 ) )
= $true )
| ( ( function @ SV880 )
= $false )
| ( ( relation @ SV880 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5513]) ).
thf(5630,plain,
! [SV818: $i,SV880: $i] :
( ( ( ~ ( ( ( apply @ SV880 @ ( sK50_C @ SV880 @ SV818 ) )
!= ( sK50_C @ SV880 @ SV818 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV880 )
!= SV818 ) )
= $true )
| ( ( SV880
= ( identity_relation @ SV818 ) )
= $true )
| ( ( function @ SV880 )
= $false )
| ( ( relation @ SV880 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5513]) ).
thf(5631,plain,
! [SV958: $i,SV986: $i] :
( ( ( ( SV986
!= ( identity_relation @ SV958 ) ) )
= $true )
| ( ( ! [SY1632: $i] :
( ~ ( in @ SY1632 @ SV958 )
| ( ( apply @ SV986 @ SY1632 )
= SY1632 ) ) )
= $true )
| ( ( function @ SV986 )
= $false )
| ( ( relation @ SV986 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5514]) ).
thf(5632,plain,
! [SV959: $i,SV987: $i] :
( ( ( ( SV987
!= ( identity_relation @ SV959 ) ) )
= $true )
| ( ( ( relation_dom @ SV987 )
= SV959 )
= $true )
| ( ( function @ SV987 )
= $false )
| ( ( relation @ SV987 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5515]) ).
thf(5633,plain,
! [SV652: $i,SV825: $i,SV885: $i] :
( ( ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV825 )
= $false )
| ( ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV652 )
= $false )
| ( ( ~ ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV885 ) )
= $true )
| ( ( SV885
= ( set_intersection2 @ SV652 @ SV825 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5518]) ).
thf(5634,plain,
! [SV652: $i,SV825: $i,SV885: $i] :
( ( ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV652 )
= $true )
| ( ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV885 )
= $true )
| ( ( SV885
= ( set_intersection2 @ SV652 @ SV825 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5519]) ).
thf(5635,plain,
! [SV652: $i,SV825: $i,SV885: $i] :
( ( ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV825 )
= $true )
| ( ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV885 )
= $true )
| ( ( SV885
= ( set_intersection2 @ SV652 @ SV825 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5520]) ).
thf(5636,plain,
! [SV886: $i,SV826: $i,SV652: $i,SV1035: $i] :
( ( ( ~ ( in @ SV1035 @ SV652 ) )
= $true )
| ( ( ~ ( in @ SV1035 @ SV826 ) )
= $true )
| ( ( in @ SV1035 @ SV886 )
= $true )
| ( ( SV886
= ( set_intersection2 @ SV652 @ SV826 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5521]) ).
thf(5637,plain,
! [SV826: $i,SV652: $i,SV886: $i] :
( ( ( ! [SY1518: $i] :
( ~ ( in @ SY1518 @ SV886 )
| ( in @ SY1518 @ SV652 ) ) )
= $true )
| ( ( SV886
= ( set_intersection2 @ SV652 @ SV826 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5522]) ).
thf(5638,plain,
! [SV652: $i,SV826: $i,SV886: $i] :
( ( ( ! [SY1519: $i] :
( ~ ( in @ SY1519 @ SV886 )
| ( in @ SY1519 @ SV826 ) ) )
= $true )
| ( ( SV886
= ( set_intersection2 @ SV652 @ SV826 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5523]) ).
thf(5639,plain,
! [SV653: $i,SV1024: $i] :
( ( ( function @ SV1024 )
= $false )
| ( ( ~ ( relation @ SV1024 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) )
| ( SV1024
= ( function_inverse @ SV653 ) ) )
= $true )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5524]) ).
thf(5640,plain,
! [SV653: $i,SV1061: $i] :
( ( ( ~ ( function @ SV1061 )
| ~ ( relation @ SV1061 )
| ( SV1061
!= ( function_inverse @ SV653 ) )
| ~ ( ~ ~ ( ~ ! [SY1663: $i,SY1664: $i] :
( ( SY1664
!= ( apply @ SV1061 @ SY1663 ) )
| ~ ( in @ SY1663 @ ( relation_rng @ SV653 ) )
| ( SY1663
= ( apply @ SV653 @ SY1664 ) ) )
| ~ ! [SY1665: $i,SY1666: $i] :
( ( SY1666
!= ( apply @ SV1061 @ SY1665 ) )
| ~ ( in @ SY1665 @ ( relation_rng @ SV653 ) )
| ( in @ SY1666 @ ( relation_dom @ SV653 ) ) ) )
| ~ ~ ( ~ ! [SY1667: $i,SY1668: $i] :
( ( SY1667
!= ( apply @ SV653 @ SY1668 ) )
| ~ ( in @ SY1668 @ ( relation_dom @ SV653 ) )
| ( SY1668
= ( apply @ SV1061 @ SY1667 ) ) )
| ~ ! [SY1148: $i] :
( ! [SY1149: $i] :
( ( SY1148
!= ( apply @ SV653 @ SY1149 ) )
| ~ ( in @ SY1149 @ ( relation_dom @ SV653 ) ) )
| ( in @ SY1148 @ ( relation_rng @ SV653 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5525]) ).
thf(5641,plain,
! [SV653: $i,SV1062: $i] :
( ( ( ~ ( function @ SV1062 )
| ~ ( relation @ SV1062 )
| ( SV1062
!= ( function_inverse @ SV653 ) )
| ( ( relation_dom @ SV1062 )
= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5526]) ).
thf(5642,plain,
! [SV1011: $i,SV991: $i,SV739: $i,SV654: $i] :
( ( ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SV991 ) @ SV1011 ) )
= $false )
| ( ( in @ SV654 @ SV991 )
= $true )
| ( ( relation @ SV1011 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5528]) ).
thf(5643,plain,
! [SV1012: $i,SV992: $i,SV739: $i,SV654: $i] :
( ( ( in @ ( ordered_pair @ SV654 @ SV739 ) @ ( relation_composition @ ( identity_relation @ SV992 ) @ SV1012 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV654 @ SV739 ) @ SV1012 )
= $true )
| ( ( relation @ SV1012 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5529]) ).
thf(5644,plain,
! [SV655: $i,SV740: $i,SV961: $i] :
( ( ( ~ ( in @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) @ SV655 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV740 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 ) )
= $true )
| ( ( SV961
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $true )
| ( ( relation @ SV961 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5530]) ).
thf(5645,plain,
! [SV655: $i,SV740: $i,SV961: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) @ SV655 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV740 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 ) ) ) )
= $true )
| ( ( SV961
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $true )
| ( ( relation @ SV961 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5531]) ).
thf(5646,plain,
! [SV962: $i,SV740: $i,SV655: $i] :
( ( ( ~ ! [SY1603: $i,SY1604: $i] :
( ~ ( in @ SY1604 @ SV655 )
| ~ ( in @ ( ordered_pair @ SY1603 @ SY1604 ) @ SV740 )
| ( in @ ( ordered_pair @ SY1603 @ SY1604 ) @ SV962 ) ) )
= $false )
| ( ( SV962
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $false )
| ( ( relation @ SV962 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5532]) ).
thf(5647,plain,
! [SV740: $i,SV655: $i,SV962: $i] :
( ( ( ~ ~ ( ~ ! [SY1605: $i,SY1606: $i] :
( ~ ( in @ ( ordered_pair @ SY1605 @ SY1606 ) @ SV962 )
| ( in @ SY1606 @ SV655 ) )
| ~ ! [SY1607: $i,SY1608: $i] :
( ~ ( in @ ( ordered_pair @ SY1607 @ SY1608 ) @ SV962 )
| ( in @ ( ordered_pair @ SY1607 @ SY1608 ) @ SV740 ) ) ) )
= $false )
| ( ( SV962
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $false )
| ( ( relation @ SV962 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5532]) ).
thf(5648,plain,
! [SV1063: $i,SV657: $i,SV922: $i,SV964: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SV1063 ) @ SV657 )
| ~ ( in @ SV1063 @ SV922 ) )
= $true )
| ( ( ~ ( in @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SV964 ) )
= $true )
| ( ( SV964
= ( relation_inverse_image @ SV657 @ SV922 ) )
= $true )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5533]) ).
thf(5649,plain,
! [SV657: $i,SV922: $i,SV964: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ ( sK36_SY409 @ SV964 @ SV922 @ SV657 ) ) @ SV657 )
| ~ ( in @ ( sK36_SY409 @ SV964 @ SV922 @ SV657 ) @ SV922 ) )
= $false )
| ( ( in @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SV964 )
= $true )
| ( ( SV964
= ( relation_inverse_image @ SV657 @ SV922 ) )
= $true )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5534]) ).
thf(5650,plain,
! [SV965: $i,SV923: $i,SV657: $i,SV1064: $i] :
( ( ( ! [SY1671: $i] :
( ~ ( in @ ( ordered_pair @ SV1064 @ SY1671 ) @ SV657 )
| ~ ( in @ SY1671 @ SV923 ) )
| ( in @ SV1064 @ SV965 ) )
= $true )
| ( ( SV965
= ( relation_inverse_image @ SV657 @ SV923 ) )
= $false )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5535]) ).
thf(5651,plain,
! [SV657: $i,SV923: $i,SV965: $i,SV1065: $i] :
( ( ( ~ ( in @ SV1065 @ SV965 )
| ~ ( ~ ( in @ ( ordered_pair @ SV1065 @ ( sK34_E @ SV1065 @ SV965 @ SV923 @ SV657 ) ) @ SV657 )
| ~ ( in @ ( sK34_E @ SV1065 @ SV965 @ SV923 @ SV657 ) @ SV923 ) ) )
= $true )
| ( ( SV965
= ( relation_inverse_image @ SV657 @ SV923 ) )
= $false )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5536]) ).
thf(5652,plain,
! [SV658: $i,SV924: $i,SV966: $i,SV1066: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1066 @ ( sK38_D @ SV966 @ SV924 @ SV658 ) ) @ SV658 )
| ~ ( in @ SV1066 @ SV924 ) )
= $true )
| ( ( ~ ( in @ ( sK38_D @ SV966 @ SV924 @ SV658 ) @ SV966 ) )
= $true )
| ( ( SV966
= ( relation_image @ SV658 @ SV924 ) )
= $true )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5537]) ).
thf(5653,plain,
! [SV658: $i,SV924: $i,SV966: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SV966 @ SV924 @ SV658 ) @ ( sK38_D @ SV966 @ SV924 @ SV658 ) ) @ SV658 )
| ~ ( in @ ( sK39_SY411 @ SV966 @ SV924 @ SV658 ) @ SV924 ) )
= $false )
| ( ( in @ ( sK38_D @ SV966 @ SV924 @ SV658 ) @ SV966 )
= $true )
| ( ( SV966
= ( relation_image @ SV658 @ SV924 ) )
= $true )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5538]) ).
thf(5654,plain,
! [SV967: $i,SV925: $i,SV658: $i,SV1067: $i] :
( ( ( ! [SY1672: $i] :
( ~ ( in @ ( ordered_pair @ SY1672 @ SV1067 ) @ SV658 )
| ~ ( in @ SY1672 @ SV925 ) )
| ( in @ SV1067 @ SV967 ) )
= $true )
| ( ( SV967
= ( relation_image @ SV658 @ SV925 ) )
= $false )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5539]) ).
thf(5655,plain,
! [SV658: $i,SV925: $i,SV967: $i,SV1068: $i] :
( ( ( ~ ( in @ SV1068 @ SV967 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SV1068 @ SV967 @ SV925 @ SV658 ) @ SV1068 ) @ SV658 )
| ~ ( in @ ( sK37_E @ SV1068 @ SV967 @ SV925 @ SV658 ) @ SV925 ) ) )
= $true )
| ( ( SV967
= ( relation_image @ SV658 @ SV925 ) )
= $false )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5540]) ).
thf(5656,plain,
! [SV660: $i,SV783: $i,SV1014: $i] :
( ( ( ~ ( ! [SY1644: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ SY1644 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1644 @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV783 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV1014 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK10_SY395 @ SV1014 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV783 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV1014 ) ) )
= $false )
| ( ( SV1014
= ( relation_composition @ SV660 @ SV783 ) )
= $true )
| ( ( relation @ SV1014 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5543]) ).
thf(5657,plain,
! [SV783: $i,SV660: $i,SV1015: $i] :
( ( ( SV1015
= ( relation_composition @ SV660 @ SV783 ) )
= $false )
| ( ( ~ ( ~ ! [SY1645: $i,SY1646: $i] :
( ! [SY1410: $i] :
( ~ ( in @ ( ordered_pair @ SY1645 @ SY1410 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1410 @ SY1646 ) @ SV783 ) )
| ( in @ ( ordered_pair @ SY1645 @ SY1646 ) @ SV1015 ) )
| ~ ! [SY1648: $i,SY1649: $i] :
( ~ ( in @ ( ordered_pair @ SY1648 @ SY1649 ) @ SV1015 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1648 @ ( sK7_F @ SY1649 @ SY1648 @ SV1015 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY1649 @ SY1648 @ SV1015 @ SV783 @ SV660 ) @ SY1649 ) @ SV783 ) ) ) ) )
= $true )
| ( ( relation @ SV1015 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5544]) ).
thf(5658,plain,
! [SV661: $i,SV932: $i,SV1048: $i] :
( ( ( in @ ( ordered_pair @ SV1048 @ ( sK60_C @ SV932 @ SV661 ) ) @ SV661 )
= $false )
| ( ( ~ ( in @ ( sK60_C @ SV932 @ SV661 ) @ SV932 ) )
= $true )
| ( ( SV932
= ( relation_rng @ SV661 ) )
= $true )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5545]) ).
thf(5659,plain,
! [SV933: $i,SV661: $i,SV1049: $i] :
( ( ( ! [SY1660: $i] :
~ ( in @ ( ordered_pair @ SY1660 @ SV1049 ) @ SV661 ) )
= $true )
| ( ( in @ SV1049 @ SV933 )
= $true )
| ( ( SV933
= ( relation_rng @ SV661 ) )
= $false )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5546]) ).
thf(5660,plain,
! [SV661: $i,SV933: $i,SV1050: $i] :
( ( ( ~ ( in @ SV1050 @ SV933 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK59_D @ SV1050 @ SV933 @ SV661 ) @ SV1050 ) @ SV661 )
= $true )
| ( ( SV933
= ( relation_rng @ SV661 ) )
= $false )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5547]) ).
thf(5661,plain,
! [SV662: $i,SV838: $i,SV891: $i] :
( ( ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV891 )
= $false )
| ( ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV838 )
= $true )
| ( ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV662 )
= $false )
| ( ( SV891
= ( set_difference @ SV662 @ SV838 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5548]) ).
thf(5662,plain,
! [SV662: $i,SV838: $i,SV891: $i] :
( ( ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV662 )
= $true )
| ( ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV891 )
= $true )
| ( ( SV891
= ( set_difference @ SV662 @ SV838 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5549]) ).
thf(5663,plain,
! [SV662: $i,SV838: $i,SV891: $i] :
( ( ( ~ ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV838 ) )
= $true )
| ( ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV891 )
= $true )
| ( ( SV891
= ( set_difference @ SV662 @ SV838 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5550]) ).
thf(5664,plain,
! [SV892: $i,SV839: $i,SV662: $i,SV1036: $i] :
( ( ( ~ ( in @ SV1036 @ SV662 ) )
= $true )
| ( ( in @ SV1036 @ SV839 )
= $true )
| ( ( in @ SV1036 @ SV892 )
= $true )
| ( ( SV892
= ( set_difference @ SV662 @ SV839 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5551]) ).
thf(5665,plain,
! [SV839: $i,SV662: $i,SV892: $i] :
( ( ( ! [SY1524: $i] :
( ~ ( in @ SY1524 @ SV892 )
| ( in @ SY1524 @ SV662 ) ) )
= $true )
| ( ( SV892
= ( set_difference @ SV662 @ SV839 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5552]) ).
thf(5666,plain,
! [SV662: $i,SV839: $i,SV892: $i] :
( ( ( ! [SY1525: $i] :
( ~ ( in @ SY1525 @ SV892 )
| ~ ( in @ SY1525 @ SV839 ) ) )
= $true )
| ( ( SV892
= ( set_difference @ SV662 @ SV839 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5553]) ).
thf(5667,plain,
! [SV664: $i,SV1037: $i] :
( ( ( in @ SV1037 @ ( relation_dom @ SV664 ) )
= $false )
| ( ( ! [SY1652: $i] :
( ( SY1652
!= ( apply @ SV664 @ SV1037 ) )
| ( in @ ( ordered_pair @ SV1037 @ SY1652 ) @ SV664 ) ) )
= $true )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5558]) ).
thf(5668,plain,
! [SV664: $i,SV1038: $i] :
( ( ( in @ SV1038 @ ( relation_dom @ SV664 ) )
= $false )
| ( ( ! [SY1653: $i] :
( ~ ( in @ ( ordered_pair @ SV1038 @ SY1653 ) @ SV664 )
| ( SY1653
= ( apply @ SV664 @ SV1038 ) ) ) )
= $true )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5559]) ).
thf(5669,plain,
! [SV1039: $i,SV664: $i,SV1069: $i] :
( ( ( ( SV1069
!= ( apply @ SV664 @ SV1039 ) )
| ( SV1069 = empty_set ) )
= $true )
| ( ( in @ SV1039 @ ( relation_dom @ SV664 ) )
= $true )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5560]) ).
thf(5670,plain,
! [SV1040: $i,SV664: $i,SV1070: $i] :
( ( ( ( SV1070 != empty_set )
| ( SV1070
= ( apply @ SV664 @ SV1040 ) ) )
= $true )
| ( ( in @ SV1040 @ ( relation_dom @ SV664 ) )
= $true )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5561]) ).
thf(5671,plain,
! [SV665: $i,SV934: $i] :
( ( ( in @ ( ordered_pair @ ( sK19_C @ SV934 @ SV665 ) @ ( sK20_SY399 @ SV934 @ SV665 ) ) @ SV934 )
= $false )
| ( ( subset @ SV665 @ SV934 )
= $true )
| ( ( relation @ SV934 )
= $false )
| ( ( relation @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5563]) ).
thf(5672,plain,
! [SV935: $i,SV665: $i,SV1051: $i,SV1041: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1041 @ SV1051 ) @ SV665 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV1041 @ SV1051 ) @ SV935 )
= $true )
| ( ( subset @ SV665 @ SV935 )
= $false )
| ( ( relation @ SV935 )
= $false )
| ( ( relation @ SV665 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5564]) ).
thf(5673,plain,
! [SV742: $i,SV666: $i,SV1016: $i] :
( ( ( relation @ SV1016 )
= $false )
| ( ( function @ SV1016 )
= $false )
| ( ( ~ ( in @ SV666 @ ( relation_dom @ SV1016 ) )
| ~ ( in @ ( apply @ SV1016 @ SV666 ) @ ( relation_dom @ SV742 ) )
| ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SV1016 @ SV742 ) ) ) )
= $true )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5565]) ).
thf(5674,plain,
! [SV742: $i,SV666: $i,SV1052: $i] :
( ( ( ~ ( function @ SV1052 )
| ~ ( relation @ SV1052 ) )
= $true )
| ( ( ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SV1052 @ SV742 ) ) )
| ( in @ SV666 @ ( relation_dom @ SV1052 ) ) )
= $true )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5566]) ).
thf(5675,plain,
! [SV742: $i,SV666: $i,SV1053: $i] :
( ( ( ~ ( function @ SV1053 )
| ~ ( relation @ SV1053 ) )
= $true )
| ( ( ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SV1053 @ SV742 ) ) )
| ( in @ ( apply @ SV1053 @ SV666 ) @ ( relation_dom @ SV742 ) ) )
= $true )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5567]) ).
thf(5676,plain,
! [SV843: $i,SV894: $i,SV1017: $i,SV667: $i] :
( ( ( in @ ( ordered_pair @ SV667 @ SV1017 ) @ SV894 )
= $false )
| ( ( in @ SV1017 @ ( relation_rng @ SV894 ) )
= $false )
| ( ( ~ ( in @ SV1017 @ SV843 ) )
= $true )
| ( ( in @ SV667 @ ( relation_inverse_image @ SV894 @ SV843 ) )
= $true )
| ( ( relation @ SV894 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5568]) ).
thf(5677,plain,
! [SV667: $i,SV844: $i,SV895: $i] :
( ( ( ~ ( in @ ( sK51_D @ SV895 @ SV844 @ SV667 ) @ ( relation_rng @ SV895 ) )
| ~ ( in @ ( ordered_pair @ SV667 @ ( sK51_D @ SV895 @ SV844 @ SV667 ) ) @ SV895 ) )
= $false )
| ( ( in @ SV667 @ ( relation_inverse_image @ SV895 @ SV844 ) )
= $false )
| ( ( relation @ SV895 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5569]) ).
thf(5678,plain,
! [SV669: $i,SV848: $i,SV897: $i] :
( ( ( ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV897 ) )
= $true )
| ( ( ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV669 ) )
= $true )
| ( ( SV897
= ( set_union2 @ SV669 @ SV848 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5573]) ).
thf(5679,plain,
! [SV669: $i,SV848: $i,SV897: $i] :
( ( ( ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV897 ) )
= $true )
| ( ( ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV848 ) )
= $true )
| ( ( SV897
= ( set_union2 @ SV669 @ SV848 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5574]) ).
thf(5680,plain,
! [SV849: $i,SV669: $i,SV898: $i,SV1042: $i] :
( ( ( in @ SV1042 @ SV898 )
= $false )
| ( ( ( in @ SV1042 @ SV669 )
| ( in @ SV1042 @ SV849 ) )
= $true )
| ( ( SV898
= ( set_union2 @ SV669 @ SV849 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5575]) ).
thf(5681,plain,
! [SV849: $i,SV898: $i,SV669: $i] :
( ( ( ! [SY1528: $i] :
( ~ ( in @ SY1528 @ SV669 )
| ( in @ SY1528 @ SV898 ) ) )
= $true )
| ( ( SV898
= ( set_union2 @ SV669 @ SV849 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5576]) ).
thf(5682,plain,
! [SV669: $i,SV898: $i,SV849: $i] :
( ( ( ! [SY1529: $i] :
( ~ ( in @ SY1529 @ SV849 )
| ( in @ SY1529 @ SV898 ) ) )
= $true )
| ( ( SV898
= ( set_union2 @ SV669 @ SV849 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5577]) ).
thf(5683,plain,
! [SV937: $i,SV1000: $i] :
( ( ( ~ ( ~ ( in @ ( sK33_SY406 @ SV1000 @ SV937 ) @ SV937 )
| ~ ~ ( in @ ( sK32_C @ SV1000 @ SV937 ) @ ( sK33_SY406 @ SV1000 @ SV937 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SV1000 ) )
= $true )
| ( ( SV1000
= ( set_meet @ SV937 ) )
= $true )
| ( ( SV937 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5578]) ).
thf(5684,plain,
! [SV1000: $i,SV937: $i] :
( ( ( ! [SY1636: $i] :
( ~ ( in @ SY1636 @ SV937 )
| ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SY1636 ) ) )
= $true )
| ( ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SV1000 )
= $true )
| ( ( SV1000
= ( set_meet @ SV937 ) )
= $true )
| ( ( SV937 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5579]) ).
thf(5685,plain,
! [SV938: $i,SV1001: $i] :
( ( ( ! [SY1637: $i] :
( ~ ( ~ ( in @ ( sK31_D @ SY1637 @ SV1001 @ SV938 ) @ SV938 )
| ~ ~ ( in @ SY1637 @ ( sK31_D @ SY1637 @ SV1001 @ SV938 ) ) )
| ( in @ SY1637 @ SV1001 ) ) )
= $true )
| ( ( SV1001
= ( set_meet @ SV938 ) )
= $false )
| ( ( SV938 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5580]) ).
thf(5686,plain,
! [SV938: $i,SV1001: $i] :
( ( ( ! [SY1638: $i] :
( ~ ( in @ SY1638 @ SV1001 )
| ! [SY1573: $i] :
( ~ ( in @ SY1573 @ SV938 )
| ( in @ SY1638 @ SY1573 ) ) ) )
= $true )
| ( ( SV1001
= ( set_meet @ SV938 ) )
= $false )
| ( ( SV938 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5581]) ).
thf(5687,plain,
! [SV899: $i,SV850: $i,SV1054: $i,SV670: $i,SV1043: $i] :
( ( ( ~ ( in @ SV1043 @ SV670 )
| ~ ( in @ SV1054 @ SV850 ) )
= $true )
| ( ( ( ( sK23_D @ SV899 @ SV850 @ SV670 )
!= ( ordered_pair @ SV1043 @ SV1054 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV899 @ SV850 @ SV670 ) @ SV899 ) )
= $true )
| ( ( SV899
= ( cartesian_product2 @ SV670 @ SV850 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5582]) ).
thf(5688,plain,
! [SV670: $i,SV850: $i,SV899: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_SY403 @ SV899 @ SV850 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK25_SY405 @ SV899 @ SV850 @ SV670 ) @ SV850 ) ) )
= $true )
| ( ( in @ ( sK23_D @ SV899 @ SV850 @ SV670 ) @ SV899 )
= $true )
| ( ( SV899
= ( cartesian_product2 @ SV670 @ SV850 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5583]) ).
thf(5689,plain,
! [SV670: $i,SV850: $i,SV899: $i] :
( ( ( ( sK23_D @ SV899 @ SV850 @ SV670 )
= ( ordered_pair @ ( sK24_SY403 @ SV899 @ SV850 @ SV670 ) @ ( sK25_SY405 @ SV899 @ SV850 @ SV670 ) ) )
= $true )
| ( ( in @ ( sK23_D @ SV899 @ SV850 @ SV670 ) @ SV899 )
= $true )
| ( ( SV899
= ( cartesian_product2 @ SV670 @ SV850 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5584]) ).
thf(5690,plain,
! [SV900: $i,SV1044: $i,SV851: $i,SV670: $i,SV1071: $i] :
( ( ( ! [SY1673: $i] :
( ~ ( in @ SV1071 @ SV670 )
| ~ ( in @ SY1673 @ SV851 )
| ( SV1044
!= ( ordered_pair @ SV1071 @ SY1673 ) ) ) )
= $true )
| ( ( in @ SV1044 @ SV900 )
= $true )
| ( ( SV900
= ( cartesian_product2 @ SV670 @ SV851 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5585]) ).
thf(5691,plain,
! [SV670: $i,SV851: $i,SV900: $i,SV1045: $i] :
( ( ( in @ SV1045 @ SV900 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK21_E @ SV1045 @ SV900 @ SV851 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK22_SY400 @ SV1045 @ SV900 @ SV851 @ SV670 ) @ SV851 ) )
| ( SV1045
!= ( ordered_pair @ ( sK21_E @ SV1045 @ SV900 @ SV851 @ SV670 ) @ ( sK22_SY400 @ SV1045 @ SV900 @ SV851 @ SV670 ) ) ) ) )
= $true )
| ( ( SV900
= ( cartesian_product2 @ SV670 @ SV851 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5586]) ).
thf(5692,plain,
! [SV852: $i,SV901: $i,SV671: $i] :
( ( ( in @ SV671 @ ( relation_dom @ SV901 ) )
= $false )
| ( ( SV852
= ( apply @ SV901 @ SV671 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV671 @ SV852 ) @ SV901 )
= $true )
| ( ( function @ SV901 )
= $false )
| ( ( relation @ SV901 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5587]) ).
thf(5693,plain,
! [SV1002: $i,SV976: $i,SV671: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV671 @ SV976 ) @ SV1002 ) )
= $true )
| ( ( SV976
= ( apply @ SV1002 @ SV671 ) )
= $true )
| ( ( function @ SV1002 )
= $false )
| ( ( relation @ SV1002 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5588]) ).
thf(5694,plain,
! [SV1003: $i,SV977: $i,SV671: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV671 @ SV977 ) @ SV1003 ) )
= $true )
| ( ( in @ SV671 @ ( relation_dom @ SV1003 ) )
= $true )
| ( ( function @ SV1003 )
= $false )
| ( ( relation @ SV1003 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5589]) ).
thf(5695,plain,
! [SV672: $i,SV941: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SV941 @ SV672 ) @ ( sK12_SY396 @ SV941 @ SV672 ) ) @ SV941 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SV941 @ SV672 ) @ ( sK11_C @ SV941 @ SV672 ) ) @ SV672 ) )
= $true )
| ( ( SV941
= ( relation_inverse @ SV672 ) )
= $true )
| ( ( relation @ SV941 )
= $false )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5590]) ).
thf(5696,plain,
! [SV672: $i,SV941: $i] :
( ( ( in @ ( ordered_pair @ ( sK11_C @ SV941 @ SV672 ) @ ( sK12_SY396 @ SV941 @ SV672 ) ) @ SV941 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK12_SY396 @ SV941 @ SV672 ) @ ( sK11_C @ SV941 @ SV672 ) ) @ SV672 )
= $true )
| ( ( SV941
= ( relation_inverse @ SV672 ) )
= $true )
| ( ( relation @ SV941 )
= $false )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5591]) ).
thf(5697,plain,
! [SV672: $i,SV942: $i] :
( ( ( ! [SY1576: $i,SY1577: $i] :
( ~ ( in @ ( ordered_pair @ SY1576 @ SY1577 ) @ SV942 )
| ( in @ ( ordered_pair @ SY1577 @ SY1576 ) @ SV672 ) ) )
= $true )
| ( ( SV942
= ( relation_inverse @ SV672 ) )
= $false )
| ( ( relation @ SV942 )
= $false )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5592]) ).
thf(5698,plain,
! [SV942: $i,SV672: $i] :
( ( ( ! [SY1578: $i,SY1579: $i] :
( ~ ( in @ ( ordered_pair @ SY1579 @ SY1578 ) @ SV672 )
| ( in @ ( ordered_pair @ SY1578 @ SY1579 ) @ SV942 ) ) )
= $true )
| ( ( SV942
= ( relation_inverse @ SV672 ) )
= $false )
| ( ( relation @ SV942 )
= $false )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5593]) ).
thf(5699,plain,
! [SV675: $i,SV857: $i,SV905: $i] :
( ( ( ~ ( in @ ( sK27_D @ SV905 @ SV857 @ SV675 ) @ SV905 ) )
= $true )
| ( ( ( ( sK27_D @ SV905 @ SV857 @ SV675 )
!= SV675 ) )
= $true )
| ( ( SV905
= ( unordered_pair @ SV675 @ SV857 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5594]) ).
thf(5700,plain,
! [SV675: $i,SV857: $i,SV905: $i] :
( ( ( ~ ( in @ ( sK27_D @ SV905 @ SV857 @ SV675 ) @ SV905 ) )
= $true )
| ( ( ( ( sK27_D @ SV905 @ SV857 @ SV675 )
!= SV857 ) )
= $true )
| ( ( SV905
= ( unordered_pair @ SV675 @ SV857 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5595]) ).
thf(5701,plain,
! [SV858: $i,SV675: $i,SV906: $i,SV1046: $i] :
( ( ( in @ SV1046 @ SV906 )
= $false )
| ( ( ( SV1046 = SV675 )
| ( SV1046 = SV858 ) )
= $true )
| ( ( SV906
= ( unordered_pair @ SV675 @ SV858 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5596]) ).
thf(5702,plain,
! [SV858: $i,SV906: $i,SV675: $i] :
( ( ( ! [SY1538: $i] :
( ( SY1538 != SV675 )
| ( in @ SY1538 @ SV906 ) ) )
= $true )
| ( ( SV906
= ( unordered_pair @ SV675 @ SV858 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5597]) ).
thf(5703,plain,
! [SV675: $i,SV906: $i,SV858: $i] :
( ( ( ! [SY1539: $i] :
( ( SY1539 != SV858 )
| ( in @ SY1539 @ SV906 ) ) )
= $true )
| ( ( SV906
= ( unordered_pair @ SV675 @ SV858 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5598]) ).
thf(5704,plain,
! [SV863: $i,SV804: $i,SV1027: $i] :
( ( ( in @ SV1027 @ SV804 )
= $false )
| ( ( in @ ( sK15_C @ SV863 @ SV804 ) @ SV1027 )
= $false )
| ( ( ~ ( in @ ( sK15_C @ SV863 @ SV804 ) @ SV863 ) )
= $true )
| ( ( SV863
= ( union @ SV804 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5599]) ).
thf(5705,plain,
! [SV864: $i,SV805: $i,SV1055: $i,SV1028: $i] :
( ( ( ~ ( in @ SV1028 @ SV1055 ) )
= $true )
| ( ( ~ ( in @ SV1055 @ SV805 ) )
= $true )
| ( ( in @ SV1028 @ SV864 )
= $true )
| ( ( SV864
= ( union @ SV805 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5602]) ).
thf(5706,plain,
! [SV805: $i,SV864: $i,SV1029: $i] :
( ( ( ~ ( in @ SV1029 @ ( sK14_D @ SV1029 @ SV864 @ SV805 ) )
| ~ ( in @ ( sK14_D @ SV1029 @ SV864 @ SV805 ) @ SV805 ) )
= $false )
| ( ( in @ SV1029 @ SV864 )
= $false )
| ( ( SV864
= ( union @ SV805 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5603]) ).
thf(5707,plain,
! [SV1056: $i,SV679: $i,SV946: $i] :
( ( ( in @ ( ordered_pair @ ( sK63_C @ SV946 @ SV679 ) @ SV1056 ) @ SV679 )
= $false )
| ( ( ~ ( in @ ( sK63_C @ SV946 @ SV679 ) @ SV946 ) )
= $true )
| ( ( SV946
= ( relation_dom @ SV679 ) )
= $true )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5604]) ).
thf(5708,plain,
! [SV947: $i,SV679: $i,SV1057: $i] :
( ( ( ! [SY1661: $i] :
~ ( in @ ( ordered_pair @ SV1057 @ SY1661 ) @ SV679 ) )
= $true )
| ( ( in @ SV1057 @ SV947 )
= $true )
| ( ( SV947
= ( relation_dom @ SV679 ) )
= $false )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5605]) ).
thf(5709,plain,
! [SV679: $i,SV947: $i,SV1058: $i] :
( ( ( ~ ( in @ SV1058 @ SV947 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV1058 @ ( sK62_D @ SV1058 @ SV947 @ SV679 ) ) @ SV679 )
= $true )
| ( ( SV947
= ( relation_dom @ SV679 ) )
= $false )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5606]) ).
thf(5710,plain,
! [SV806: $i,SV867: $i] :
( ( ( ( sK44_C @ SV867 @ SV806 )
= ( sK45_SY414 @ SV867 @ SV806 ) )
= $false )
| ( ( ~ ( in @ ( sK44_C @ SV867 @ SV806 ) @ SV806 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 ) )
= $true )
| ( ( SV867
= ( identity_relation @ SV806 ) )
= $true )
| ( ( relation @ SV867 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5607]) ).
thf(5711,plain,
! [SV806: $i,SV867: $i] :
( ( ( ( ( sK44_C @ SV867 @ SV806 )
= ( sK45_SY414 @ SV867 @ SV806 ) )
| ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 ) )
= $true )
| ( ( SV867
= ( identity_relation @ SV806 ) )
= $true )
| ( ( relation @ SV867 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5608]) ).
thf(5712,plain,
! [SV806: $i,SV867: $i] :
( ( ( ( in @ ( sK44_C @ SV867 @ SV806 ) @ SV806 )
| ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 ) )
= $true )
| ( ( SV867
= ( identity_relation @ SV806 ) )
= $true )
| ( ( relation @ SV867 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5609]) ).
thf(5713,plain,
! [SV868: $i,SV807: $i,SV1072: $i,SV1059: $i] :
( ( ( ( SV1059 != SV1072 )
| ~ ( in @ SV1059 @ SV807 )
| ( in @ ( ordered_pair @ SV1059 @ SV1072 ) @ SV868 ) )
= $true )
| ( ( SV868
= ( identity_relation @ SV807 ) )
= $false )
| ( ( relation @ SV868 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5610]) ).
thf(5714,plain,
! [SV807: $i,SV868: $i] :
( ( ( ~ ! [SY1505: $i,SY1506: $i] :
( ~ ( in @ ( ordered_pair @ SY1505 @ SY1506 ) @ SV868 )
| ( SY1505 = SY1506 ) ) )
= $false )
| ( ( SV868
= ( identity_relation @ SV807 ) )
= $false )
| ( ( relation @ SV868 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5611]) ).
thf(5715,plain,
! [SV807: $i,SV868: $i] :
( ( ( ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
~ ( in @ ( ordered_pair @ SY1507 @ SY1508 ) @ SV868 )
| ( in @ SY1507 @ SV807 ) ) )
= $false )
| ( ( SV868
= ( identity_relation @ SV807 ) )
= $false )
| ( ( relation @ SV868 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5611]) ).
thf(5716,plain,
! [SV681: $i,SV948: $i,SV980: $i] :
( ( ( ~ ( in @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ SV948 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV681 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 ) )
= $true )
| ( ( SV980
= ( relation_dom_restriction @ SV681 @ SV948 ) )
= $true )
| ( ( relation @ SV980 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5612]) ).
thf(5717,plain,
! [SV681: $i,SV948: $i,SV980: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ SV948 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV681 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 ) ) ) )
= $true )
| ( ( SV980
= ( relation_dom_restriction @ SV681 @ SV948 ) )
= $true )
| ( ( relation @ SV980 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5613]) ).
thf(5718,plain,
! [SV981: $i,SV681: $i,SV949: $i] :
( ( ( ~ ! [SY1625: $i,SY1626: $i] :
( ~ ( in @ SY1625 @ SV949 )
| ~ ( in @ ( ordered_pair @ SY1625 @ SY1626 ) @ SV681 )
| ( in @ ( ordered_pair @ SY1625 @ SY1626 ) @ SV981 ) ) )
= $false )
| ( ( SV981
= ( relation_dom_restriction @ SV681 @ SV949 ) )
= $false )
| ( ( relation @ SV981 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5614]) ).
thf(5719,plain,
! [SV681: $i,SV949: $i,SV981: $i] :
( ( ( ~ ~ ( ~ ! [SY1627: $i] :
( ! [SY1628: $i] :
~ ( in @ ( ordered_pair @ SY1627 @ SY1628 ) @ SV981 )
| ( in @ SY1627 @ SV949 ) )
| ~ ! [SY1629: $i,SY1630: $i] :
( ~ ( in @ ( ordered_pair @ SY1629 @ SY1630 ) @ SV981 )
| ( in @ ( ordered_pair @ SY1629 @ SY1630 ) @ SV681 ) ) ) )
= $false )
| ( ( SV981
= ( relation_dom_restriction @ SV681 @ SV949 ) )
= $false )
| ( ( relation @ SV981 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5614]) ).
thf(5720,plain,
! [SV871: $i,SV910: $i,SV682: $i,SV1022: $i] :
( ( ( in @ ( ordered_pair @ SV1022 @ SV682 ) @ SV910 )
= $false )
| ( ( in @ SV1022 @ ( relation_dom @ SV910 ) )
= $false )
| ( ( ~ ( in @ SV1022 @ SV871 ) )
= $true )
| ( ( in @ SV682 @ ( relation_image @ SV910 @ SV871 ) )
= $true )
| ( ( relation @ SV910 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5617]) ).
thf(5721,plain,
! [SV682: $i,SV872: $i,SV911: $i] :
( ( ( ~ ( in @ ( sK52_D @ SV911 @ SV872 @ SV682 ) @ ( relation_dom @ SV911 ) )
| ~ ( in @ ( ordered_pair @ ( sK52_D @ SV911 @ SV872 @ SV682 ) @ SV682 ) @ SV911 ) )
= $false )
| ( ( in @ SV682 @ ( relation_image @ SV911 @ SV872 ) )
= $false )
| ( ( relation @ SV911 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5618]) ).
thf(5722,plain,
! [SV684: $i,SV952: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV684 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV952 ) )
= $true )
| ( ( SV684 = SV952 )
= $true )
| ( ( relation @ SV952 )
= $false )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5620]) ).
thf(5723,plain,
! [SV684: $i,SV952: $i] :
( ( ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV684 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV952 )
= $true )
| ( ( SV684 = SV952 )
= $true )
| ( ( relation @ SV952 )
= $false )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5621]) ).
thf(5724,plain,
! [SV953: $i,SV684: $i] :
( ( ( ! [SY1592: $i,SY1593: $i] :
( ~ ( in @ ( ordered_pair @ SY1592 @ SY1593 ) @ SV684 )
| ( in @ ( ordered_pair @ SY1592 @ SY1593 ) @ SV953 ) ) )
= $true )
| ( ( SV684 = SV953 )
= $false )
| ( ( relation @ SV953 )
= $false )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5622]) ).
thf(5725,plain,
! [SV684: $i,SV953: $i] :
( ( ( ! [SY1594: $i,SY1595: $i] :
( ~ ( in @ ( ordered_pair @ SY1594 @ SY1595 ) @ SV953 )
| ( in @ ( ordered_pair @ SY1594 @ SY1595 ) @ SV684 ) ) )
= $true )
| ( ( SV684 = SV953 )
= $false )
| ( ( relation @ SV953 )
= $false )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5623]) ).
thf(5726,plain,
! [SV685: $i,SV982: $i,SV1060: $i] :
( ( ( ~ ( subset @ SV1060 @ SV982 ) )
= $true )
| ( ( in @ SV1060 @ ( sK3_SY386 @ SV982 @ SV685 ) )
= $true )
| ( ( ~ ( in @ SV982 @ ( sK2_B @ SV685 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5624]) ).
thf(5727,plain,
! [SV1047: $i,SV685: $i,SV1032: $i] :
( ( ( ~ ( in @ SV1032 @ ( sK2_B @ SV685 ) ) )
= $true )
| ( ( ~ ( subset @ SV1047 @ SV1032 ) )
= $true )
| ( ( in @ SV1047 @ ( sK2_B @ SV685 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5626]) ).
thf(5728,plain,
! [SV818: $i,SV880: $i] :
( ( ( in @ ( sK50_C @ SV880 @ SV818 ) @ SV818 )
= $true )
| ( ( ( ( relation_dom @ SV880 )
!= SV818 ) )
= $true )
| ( ( SV880
= ( identity_relation @ SV818 ) )
= $true )
| ( ( function @ SV880 )
= $false )
| ( ( relation @ SV880 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5629]) ).
thf(5729,plain,
! [SV818: $i,SV880: $i] :
( ( ( ( ( apply @ SV880 @ ( sK50_C @ SV880 @ SV818 ) )
!= ( sK50_C @ SV880 @ SV818 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV880 )
!= SV818 ) )
= $true )
| ( ( SV880
= ( identity_relation @ SV818 ) )
= $true )
| ( ( function @ SV880 )
= $false )
| ( ( relation @ SV880 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5630]) ).
thf(5730,plain,
! [SV958: $i,SV986: $i] :
( ( ( SV986
= ( identity_relation @ SV958 ) )
= $false )
| ( ( ! [SY1632: $i] :
( ~ ( in @ SY1632 @ SV958 )
| ( ( apply @ SV986 @ SY1632 )
= SY1632 ) ) )
= $true )
| ( ( function @ SV986 )
= $false )
| ( ( relation @ SV986 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5631]) ).
thf(5731,plain,
! [SV959: $i,SV987: $i] :
( ( ( SV987
= ( identity_relation @ SV959 ) )
= $false )
| ( ( ( relation_dom @ SV987 )
= SV959 )
= $true )
| ( ( function @ SV987 )
= $false )
| ( ( relation @ SV987 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5632]) ).
thf(5732,plain,
! [SV652: $i,SV825: $i,SV885: $i] :
( ( ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV885 )
= $false )
| ( ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV652 )
= $false )
| ( ( in @ ( sK17_D @ SV885 @ SV825 @ SV652 ) @ SV825 )
= $false )
| ( ( SV885
= ( set_intersection2 @ SV652 @ SV825 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5633]) ).
thf(5733,plain,
! [SV886: $i,SV826: $i,SV652: $i,SV1035: $i] :
( ( ( in @ SV1035 @ SV652 )
= $false )
| ( ( ~ ( in @ SV1035 @ SV826 ) )
= $true )
| ( ( in @ SV1035 @ SV886 )
= $true )
| ( ( SV886
= ( set_intersection2 @ SV652 @ SV826 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5636]) ).
thf(5734,plain,
! [SV826: $i,SV652: $i,SV886: $i,SV1073: $i] :
( ( ( ~ ( in @ SV1073 @ SV886 )
| ( in @ SV1073 @ SV652 ) )
= $true )
| ( ( SV886
= ( set_intersection2 @ SV652 @ SV826 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5637]) ).
thf(5735,plain,
! [SV652: $i,SV826: $i,SV886: $i,SV1074: $i] :
( ( ( ~ ( in @ SV1074 @ SV886 )
| ( in @ SV1074 @ SV826 ) )
= $true )
| ( ( SV886
= ( set_intersection2 @ SV652 @ SV826 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5638]) ).
thf(5736,plain,
! [SV653: $i,SV1024: $i] :
( ( ( relation @ SV1024 )
= $false )
| ( ( function @ SV1024 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) )
| ( SV1024
= ( function_inverse @ SV653 ) ) )
= $true )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5639]) ).
thf(5737,plain,
! [SV653: $i,SV1061: $i] :
( ( ( ~ ( function @ SV1061 )
| ~ ( relation @ SV1061 ) )
= $true )
| ( ( ( SV1061
!= ( function_inverse @ SV653 ) )
| ~ ( ~ ~ ( ~ ! [SY1663: $i,SY1664: $i] :
( ( SY1664
!= ( apply @ SV1061 @ SY1663 ) )
| ~ ( in @ SY1663 @ ( relation_rng @ SV653 ) )
| ( SY1663
= ( apply @ SV653 @ SY1664 ) ) )
| ~ ! [SY1665: $i,SY1666: $i] :
( ( SY1666
!= ( apply @ SV1061 @ SY1665 ) )
| ~ ( in @ SY1665 @ ( relation_rng @ SV653 ) )
| ( in @ SY1666 @ ( relation_dom @ SV653 ) ) ) )
| ~ ~ ( ~ ! [SY1667: $i,SY1668: $i] :
( ( SY1667
!= ( apply @ SV653 @ SY1668 ) )
| ~ ( in @ SY1668 @ ( relation_dom @ SV653 ) )
| ( SY1668
= ( apply @ SV1061 @ SY1667 ) ) )
| ~ ! [SY1148: $i] :
( ! [SY1149: $i] :
( ( SY1148
!= ( apply @ SV653 @ SY1149 ) )
| ~ ( in @ SY1149 @ ( relation_dom @ SV653 ) ) )
| ( in @ SY1148 @ ( relation_rng @ SV653 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5640]) ).
thf(5738,plain,
! [SV653: $i,SV1062: $i] :
( ( ( ~ ( function @ SV1062 )
| ~ ( relation @ SV1062 ) )
= $true )
| ( ( ( SV1062
!= ( function_inverse @ SV653 ) )
| ( ( relation_dom @ SV1062 )
= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5641]) ).
thf(5739,plain,
! [SV655: $i,SV740: $i,SV961: $i] :
( ( ( ~ ( in @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) @ SV655 )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV740 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 ) )
= $true )
| ( ( SV961
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $true )
| ( ( relation @ SV961 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5644]) ).
thf(5740,plain,
! [SV655: $i,SV740: $i,SV961: $i] :
( ( ( ~ ( ( in @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) @ SV655 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV740 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 ) ) )
= $false )
| ( ( SV961
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $true )
| ( ( relation @ SV961 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5645]) ).
thf(5741,plain,
! [SV962: $i,SV740: $i,SV655: $i] :
( ( ( ! [SY1603: $i,SY1604: $i] :
( ~ ( in @ SY1604 @ SV655 )
| ~ ( in @ ( ordered_pair @ SY1603 @ SY1604 ) @ SV740 )
| ( in @ ( ordered_pair @ SY1603 @ SY1604 ) @ SV962 ) ) )
= $true )
| ( ( SV962
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $false )
| ( ( relation @ SV962 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5646]) ).
thf(5742,plain,
! [SV740: $i,SV655: $i,SV962: $i] :
( ( ( ~ ( ~ ! [SY1605: $i,SY1606: $i] :
( ~ ( in @ ( ordered_pair @ SY1605 @ SY1606 ) @ SV962 )
| ( in @ SY1606 @ SV655 ) )
| ~ ! [SY1607: $i,SY1608: $i] :
( ~ ( in @ ( ordered_pair @ SY1607 @ SY1608 ) @ SV962 )
| ( in @ ( ordered_pair @ SY1607 @ SY1608 ) @ SV740 ) ) ) )
= $true )
| ( ( SV962
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $false )
| ( ( relation @ SV962 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5647]) ).
thf(5743,plain,
! [SV1063: $i,SV657: $i,SV922: $i,SV964: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SV1063 ) @ SV657 ) )
= $true )
| ( ( ~ ( in @ SV1063 @ SV922 ) )
= $true )
| ( ( ~ ( in @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SV964 ) )
= $true )
| ( ( SV964
= ( relation_inverse_image @ SV657 @ SV922 ) )
= $true )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5648]) ).
thf(5744,plain,
! [SV657: $i,SV922: $i,SV964: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ ( sK36_SY409 @ SV964 @ SV922 @ SV657 ) ) @ SV657 ) )
= $false )
| ( ( in @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SV964 )
= $true )
| ( ( SV964
= ( relation_inverse_image @ SV657 @ SV922 ) )
= $true )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5649]) ).
thf(5745,plain,
! [SV657: $i,SV922: $i,SV964: $i] :
( ( ( ~ ( in @ ( sK36_SY409 @ SV964 @ SV922 @ SV657 ) @ SV922 ) )
= $false )
| ( ( in @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SV964 )
= $true )
| ( ( SV964
= ( relation_inverse_image @ SV657 @ SV922 ) )
= $true )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5649]) ).
thf(5746,plain,
! [SV965: $i,SV923: $i,SV657: $i,SV1064: $i] :
( ( ( ! [SY1671: $i] :
( ~ ( in @ ( ordered_pair @ SV1064 @ SY1671 ) @ SV657 )
| ~ ( in @ SY1671 @ SV923 ) ) )
= $true )
| ( ( in @ SV1064 @ SV965 )
= $true )
| ( ( SV965
= ( relation_inverse_image @ SV657 @ SV923 ) )
= $false )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5650]) ).
thf(5747,plain,
! [SV657: $i,SV923: $i,SV965: $i,SV1065: $i] :
( ( ( ~ ( in @ SV1065 @ SV965 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV1065 @ ( sK34_E @ SV1065 @ SV965 @ SV923 @ SV657 ) ) @ SV657 )
| ~ ( in @ ( sK34_E @ SV1065 @ SV965 @ SV923 @ SV657 ) @ SV923 ) ) )
= $true )
| ( ( SV965
= ( relation_inverse_image @ SV657 @ SV923 ) )
= $false )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5651]) ).
thf(5748,plain,
! [SV658: $i,SV924: $i,SV966: $i,SV1066: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1066 @ ( sK38_D @ SV966 @ SV924 @ SV658 ) ) @ SV658 ) )
= $true )
| ( ( ~ ( in @ SV1066 @ SV924 ) )
= $true )
| ( ( ~ ( in @ ( sK38_D @ SV966 @ SV924 @ SV658 ) @ SV966 ) )
= $true )
| ( ( SV966
= ( relation_image @ SV658 @ SV924 ) )
= $true )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5652]) ).
thf(5749,plain,
! [SV658: $i,SV924: $i,SV966: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK39_SY411 @ SV966 @ SV924 @ SV658 ) @ ( sK38_D @ SV966 @ SV924 @ SV658 ) ) @ SV658 ) )
= $false )
| ( ( in @ ( sK38_D @ SV966 @ SV924 @ SV658 ) @ SV966 )
= $true )
| ( ( SV966
= ( relation_image @ SV658 @ SV924 ) )
= $true )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5653]) ).
thf(5750,plain,
! [SV658: $i,SV924: $i,SV966: $i] :
( ( ( ~ ( in @ ( sK39_SY411 @ SV966 @ SV924 @ SV658 ) @ SV924 ) )
= $false )
| ( ( in @ ( sK38_D @ SV966 @ SV924 @ SV658 ) @ SV966 )
= $true )
| ( ( SV966
= ( relation_image @ SV658 @ SV924 ) )
= $true )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5653]) ).
thf(5751,plain,
! [SV967: $i,SV925: $i,SV658: $i,SV1067: $i] :
( ( ( ! [SY1672: $i] :
( ~ ( in @ ( ordered_pair @ SY1672 @ SV1067 ) @ SV658 )
| ~ ( in @ SY1672 @ SV925 ) ) )
= $true )
| ( ( in @ SV1067 @ SV967 )
= $true )
| ( ( SV967
= ( relation_image @ SV658 @ SV925 ) )
= $false )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5654]) ).
thf(5752,plain,
! [SV658: $i,SV925: $i,SV967: $i,SV1068: $i] :
( ( ( ~ ( in @ SV1068 @ SV967 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SV1068 @ SV967 @ SV925 @ SV658 ) @ SV1068 ) @ SV658 )
| ~ ( in @ ( sK37_E @ SV1068 @ SV967 @ SV925 @ SV658 ) @ SV925 ) ) )
= $true )
| ( ( SV967
= ( relation_image @ SV658 @ SV925 ) )
= $false )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5655]) ).
thf(5753,plain,
! [SV660: $i,SV783: $i,SV1014: $i] :
( ( ( ~ ( ! [SY1644: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ SY1644 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1644 @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV783 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV1014 ) ) )
= $false )
| ( ( SV1014
= ( relation_composition @ SV660 @ SV783 ) )
= $true )
| ( ( relation @ SV1014 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5656]) ).
thf(5754,plain,
! [SV660: $i,SV783: $i,SV1014: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK10_SY395 @ SV1014 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV783 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV1014 ) ) )
= $false )
| ( ( SV1014
= ( relation_composition @ SV660 @ SV783 ) )
= $true )
| ( ( relation @ SV1014 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5656]) ).
thf(5755,plain,
! [SV1015: $i,SV783: $i,SV660: $i] :
( ( ( ~ ! [SY1645: $i,SY1646: $i] :
( ! [SY1410: $i] :
( ~ ( in @ ( ordered_pair @ SY1645 @ SY1410 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1410 @ SY1646 ) @ SV783 ) )
| ( in @ ( ordered_pair @ SY1645 @ SY1646 ) @ SV1015 ) )
| ~ ! [SY1648: $i,SY1649: $i] :
( ~ ( in @ ( ordered_pair @ SY1648 @ SY1649 ) @ SV1015 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1648 @ ( sK7_F @ SY1649 @ SY1648 @ SV1015 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY1649 @ SY1648 @ SV1015 @ SV783 @ SV660 ) @ SY1649 ) @ SV783 ) ) ) )
= $false )
| ( ( SV1015
= ( relation_composition @ SV660 @ SV783 ) )
= $false )
| ( ( relation @ SV1015 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5657]) ).
thf(5756,plain,
! [SV1048: $i,SV661: $i,SV932: $i] :
( ( ( in @ ( sK60_C @ SV932 @ SV661 ) @ SV932 )
= $false )
| ( ( in @ ( ordered_pair @ SV1048 @ ( sK60_C @ SV932 @ SV661 ) ) @ SV661 )
= $false )
| ( ( SV932
= ( relation_rng @ SV661 ) )
= $true )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5658]) ).
thf(5757,plain,
! [SV933: $i,SV661: $i,SV1049: $i,SV1075: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1075 @ SV1049 ) @ SV661 ) )
= $true )
| ( ( in @ SV1049 @ SV933 )
= $true )
| ( ( SV933
= ( relation_rng @ SV661 ) )
= $false )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5659]) ).
thf(5758,plain,
! [SV661: $i,SV933: $i,SV1050: $i] :
( ( ( in @ SV1050 @ SV933 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK59_D @ SV1050 @ SV933 @ SV661 ) @ SV1050 ) @ SV661 )
= $true )
| ( ( SV933
= ( relation_rng @ SV661 ) )
= $false )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5660]) ).
thf(5759,plain,
! [SV662: $i,SV838: $i,SV891: $i] :
( ( ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV838 )
= $false )
| ( ( in @ ( sK13_D @ SV891 @ SV838 @ SV662 ) @ SV891 )
= $true )
| ( ( SV891
= ( set_difference @ SV662 @ SV838 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5663]) ).
thf(5760,plain,
! [SV892: $i,SV839: $i,SV662: $i,SV1036: $i] :
( ( ( in @ SV1036 @ SV662 )
= $false )
| ( ( in @ SV1036 @ SV839 )
= $true )
| ( ( in @ SV1036 @ SV892 )
= $true )
| ( ( SV892
= ( set_difference @ SV662 @ SV839 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5664]) ).
thf(5761,plain,
! [SV839: $i,SV662: $i,SV892: $i,SV1076: $i] :
( ( ( ~ ( in @ SV1076 @ SV892 )
| ( in @ SV1076 @ SV662 ) )
= $true )
| ( ( SV892
= ( set_difference @ SV662 @ SV839 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5665]) ).
thf(5762,plain,
! [SV662: $i,SV839: $i,SV892: $i,SV1077: $i] :
( ( ( ~ ( in @ SV1077 @ SV892 )
| ~ ( in @ SV1077 @ SV839 ) )
= $true )
| ( ( SV892
= ( set_difference @ SV662 @ SV839 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5666]) ).
thf(5763,plain,
! [SV1037: $i,SV664: $i,SV1078: $i] :
( ( ( ( SV1078
!= ( apply @ SV664 @ SV1037 ) )
| ( in @ ( ordered_pair @ SV1037 @ SV1078 ) @ SV664 ) )
= $true )
| ( ( in @ SV1037 @ ( relation_dom @ SV664 ) )
= $false )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5667]) ).
thf(5764,plain,
! [SV664: $i,SV1079: $i,SV1038: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1038 @ SV1079 ) @ SV664 )
| ( SV1079
= ( apply @ SV664 @ SV1038 ) ) )
= $true )
| ( ( in @ SV1038 @ ( relation_dom @ SV664 ) )
= $false )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5668]) ).
thf(5765,plain,
! [SV1039: $i,SV664: $i,SV1069: $i] :
( ( ( ( SV1069
!= ( apply @ SV664 @ SV1039 ) ) )
= $true )
| ( ( SV1069 = empty_set )
= $true )
| ( ( in @ SV1039 @ ( relation_dom @ SV664 ) )
= $true )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5669]) ).
thf(5766,plain,
! [SV1040: $i,SV664: $i,SV1070: $i] :
( ( ( ( SV1070 != empty_set ) )
= $true )
| ( ( SV1070
= ( apply @ SV664 @ SV1040 ) )
= $true )
| ( ( in @ SV1040 @ ( relation_dom @ SV664 ) )
= $true )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5670]) ).
thf(5767,plain,
! [SV935: $i,SV665: $i,SV1051: $i,SV1041: $i] :
( ( ( in @ ( ordered_pair @ SV1041 @ SV1051 ) @ SV665 )
= $false )
| ( ( in @ ( ordered_pair @ SV1041 @ SV1051 ) @ SV935 )
= $true )
| ( ( subset @ SV665 @ SV935 )
= $false )
| ( ( relation @ SV935 )
= $false )
| ( ( relation @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5672]) ).
thf(5768,plain,
! [SV742: $i,SV1016: $i,SV666: $i] :
( ( ( ~ ( in @ SV666 @ ( relation_dom @ SV1016 ) )
| ~ ( in @ ( apply @ SV1016 @ SV666 ) @ ( relation_dom @ SV742 ) ) )
= $true )
| ( ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SV1016 @ SV742 ) ) )
= $true )
| ( ( function @ SV1016 )
= $false )
| ( ( relation @ SV1016 )
= $false )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5673]) ).
thf(5769,plain,
! [SV742: $i,SV666: $i,SV1052: $i] :
( ( ( ~ ( function @ SV1052 ) )
= $true )
| ( ( ~ ( relation @ SV1052 ) )
= $true )
| ( ( ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SV1052 @ SV742 ) ) )
| ( in @ SV666 @ ( relation_dom @ SV1052 ) ) )
= $true )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5674]) ).
thf(5770,plain,
! [SV742: $i,SV666: $i,SV1053: $i] :
( ( ( ~ ( function @ SV1053 ) )
= $true )
| ( ( ~ ( relation @ SV1053 ) )
= $true )
| ( ( ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SV1053 @ SV742 ) ) )
| ( in @ ( apply @ SV1053 @ SV666 ) @ ( relation_dom @ SV742 ) ) )
= $true )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5675]) ).
thf(5771,plain,
! [SV667: $i,SV894: $i,SV843: $i,SV1017: $i] :
( ( ( in @ SV1017 @ SV843 )
= $false )
| ( ( in @ SV1017 @ ( relation_rng @ SV894 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV667 @ SV1017 ) @ SV894 )
= $false )
| ( ( in @ SV667 @ ( relation_inverse_image @ SV894 @ SV843 ) )
= $true )
| ( ( relation @ SV894 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5676]) ).
thf(5772,plain,
! [SV667: $i,SV844: $i,SV895: $i] :
( ( ( ~ ( in @ ( sK51_D @ SV895 @ SV844 @ SV667 ) @ ( relation_rng @ SV895 ) ) )
= $false )
| ( ( in @ SV667 @ ( relation_inverse_image @ SV895 @ SV844 ) )
= $false )
| ( ( relation @ SV895 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5677]) ).
thf(5773,plain,
! [SV844: $i,SV895: $i,SV667: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV667 @ ( sK51_D @ SV895 @ SV844 @ SV667 ) ) @ SV895 ) )
= $false )
| ( ( in @ SV667 @ ( relation_inverse_image @ SV895 @ SV844 ) )
= $false )
| ( ( relation @ SV895 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5677]) ).
thf(5774,plain,
! [SV669: $i,SV848: $i,SV897: $i] :
( ( ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV897 )
= $false )
| ( ( ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV669 ) )
= $true )
| ( ( SV897
= ( set_union2 @ SV669 @ SV848 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5678]) ).
thf(5775,plain,
! [SV669: $i,SV848: $i,SV897: $i] :
( ( ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV897 )
= $false )
| ( ( ~ ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV848 ) )
= $true )
| ( ( SV897
= ( set_union2 @ SV669 @ SV848 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5679]) ).
thf(5776,plain,
! [SV898: $i,SV849: $i,SV669: $i,SV1042: $i] :
( ( ( in @ SV1042 @ SV669 )
= $true )
| ( ( in @ SV1042 @ SV849 )
= $true )
| ( ( in @ SV1042 @ SV898 )
= $false )
| ( ( SV898
= ( set_union2 @ SV669 @ SV849 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5680]) ).
thf(5777,plain,
! [SV849: $i,SV898: $i,SV669: $i,SV1080: $i] :
( ( ( ~ ( in @ SV1080 @ SV669 )
| ( in @ SV1080 @ SV898 ) )
= $true )
| ( ( SV898
= ( set_union2 @ SV669 @ SV849 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5681]) ).
thf(5778,plain,
! [SV669: $i,SV898: $i,SV849: $i,SV1081: $i] :
( ( ( ~ ( in @ SV1081 @ SV849 )
| ( in @ SV1081 @ SV898 ) )
= $true )
| ( ( SV898
= ( set_union2 @ SV669 @ SV849 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5682]) ).
thf(5779,plain,
! [SV937: $i,SV1000: $i] :
( ( ( ~ ( in @ ( sK33_SY406 @ SV1000 @ SV937 ) @ SV937 )
| ~ ~ ( in @ ( sK32_C @ SV1000 @ SV937 ) @ ( sK33_SY406 @ SV1000 @ SV937 ) ) )
= $false )
| ( ( ~ ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SV1000 ) )
= $true )
| ( ( SV1000
= ( set_meet @ SV937 ) )
= $true )
| ( ( SV937 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5683]) ).
thf(5780,plain,
! [SV1000: $i,SV937: $i,SV1082: $i] :
( ( ( ~ ( in @ SV1082 @ SV937 )
| ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SV1082 ) )
= $true )
| ( ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SV1000 )
= $true )
| ( ( SV1000
= ( set_meet @ SV937 ) )
= $true )
| ( ( SV937 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5684]) ).
thf(5781,plain,
! [SV938: $i,SV1001: $i,SV1083: $i] :
( ( ( ~ ( ~ ( in @ ( sK31_D @ SV1083 @ SV1001 @ SV938 ) @ SV938 )
| ~ ~ ( in @ SV1083 @ ( sK31_D @ SV1083 @ SV1001 @ SV938 ) ) )
| ( in @ SV1083 @ SV1001 ) )
= $true )
| ( ( SV1001
= ( set_meet @ SV938 ) )
= $false )
| ( ( SV938 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5685]) ).
thf(5782,plain,
! [SV938: $i,SV1001: $i,SV1084: $i] :
( ( ( ~ ( in @ SV1084 @ SV1001 )
| ! [SY1674: $i] :
( ~ ( in @ SY1674 @ SV938 )
| ( in @ SV1084 @ SY1674 ) ) )
= $true )
| ( ( SV1001
= ( set_meet @ SV938 ) )
= $false )
| ( ( SV938 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5686]) ).
thf(5783,plain,
! [SV899: $i,SV850: $i,SV1054: $i,SV670: $i,SV1043: $i] :
( ( ( ~ ( in @ SV1043 @ SV670 ) )
= $true )
| ( ( ~ ( in @ SV1054 @ SV850 ) )
= $true )
| ( ( ( ( sK23_D @ SV899 @ SV850 @ SV670 )
!= ( ordered_pair @ SV1043 @ SV1054 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV899 @ SV850 @ SV670 ) @ SV899 ) )
= $true )
| ( ( SV899
= ( cartesian_product2 @ SV670 @ SV850 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5687]) ).
thf(5784,plain,
! [SV670: $i,SV850: $i,SV899: $i] :
( ( ( ~ ( in @ ( sK24_SY403 @ SV899 @ SV850 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK25_SY405 @ SV899 @ SV850 @ SV670 ) @ SV850 ) )
= $false )
| ( ( in @ ( sK23_D @ SV899 @ SV850 @ SV670 ) @ SV899 )
= $true )
| ( ( SV899
= ( cartesian_product2 @ SV670 @ SV850 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5688]) ).
thf(5785,plain,
! [SV900: $i,SV1044: $i,SV851: $i,SV1085: $i,SV670: $i,SV1071: $i] :
( ( ( ~ ( in @ SV1071 @ SV670 )
| ~ ( in @ SV1085 @ SV851 )
| ( SV1044
!= ( ordered_pair @ SV1071 @ SV1085 ) ) )
= $true )
| ( ( in @ SV1044 @ SV900 )
= $true )
| ( ( SV900
= ( cartesian_product2 @ SV670 @ SV851 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5690]) ).
thf(5786,plain,
! [SV670: $i,SV851: $i,SV900: $i,SV1045: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK21_E @ SV1045 @ SV900 @ SV851 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK22_SY400 @ SV1045 @ SV900 @ SV851 @ SV670 ) @ SV851 ) )
| ( SV1045
!= ( ordered_pair @ ( sK21_E @ SV1045 @ SV900 @ SV851 @ SV670 ) @ ( sK22_SY400 @ SV1045 @ SV900 @ SV851 @ SV670 ) ) ) )
= $false )
| ( ( in @ SV1045 @ SV900 )
= $false )
| ( ( SV900
= ( cartesian_product2 @ SV670 @ SV851 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5691]) ).
thf(5787,plain,
! [SV1002: $i,SV976: $i,SV671: $i] :
( ( ( in @ ( ordered_pair @ SV671 @ SV976 ) @ SV1002 )
= $false )
| ( ( SV976
= ( apply @ SV1002 @ SV671 ) )
= $true )
| ( ( function @ SV1002 )
= $false )
| ( ( relation @ SV1002 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5693]) ).
thf(5788,plain,
! [SV1003: $i,SV977: $i,SV671: $i] :
( ( ( in @ ( ordered_pair @ SV671 @ SV977 ) @ SV1003 )
= $false )
| ( ( in @ SV671 @ ( relation_dom @ SV1003 ) )
= $true )
| ( ( function @ SV1003 )
= $false )
| ( ( relation @ SV1003 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5694]) ).
thf(5789,plain,
! [SV672: $i,SV941: $i] :
( ( ( in @ ( ordered_pair @ ( sK11_C @ SV941 @ SV672 ) @ ( sK12_SY396 @ SV941 @ SV672 ) ) @ SV941 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK12_SY396 @ SV941 @ SV672 ) @ ( sK11_C @ SV941 @ SV672 ) ) @ SV672 ) )
= $true )
| ( ( SV941
= ( relation_inverse @ SV672 ) )
= $true )
| ( ( relation @ SV941 )
= $false )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5695]) ).
thf(5790,plain,
! [SV672: $i,SV942: $i,SV1086: $i] :
( ( ( ! [SY1675: $i] :
( ~ ( in @ ( ordered_pair @ SV1086 @ SY1675 ) @ SV942 )
| ( in @ ( ordered_pair @ SY1675 @ SV1086 ) @ SV672 ) ) )
= $true )
| ( ( SV942
= ( relation_inverse @ SV672 ) )
= $false )
| ( ( relation @ SV942 )
= $false )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5697]) ).
thf(5791,plain,
! [SV942: $i,SV672: $i,SV1087: $i] :
( ( ( ! [SY1676: $i] :
( ~ ( in @ ( ordered_pair @ SY1676 @ SV1087 ) @ SV672 )
| ( in @ ( ordered_pair @ SV1087 @ SY1676 ) @ SV942 ) ) )
= $true )
| ( ( SV942
= ( relation_inverse @ SV672 ) )
= $false )
| ( ( relation @ SV942 )
= $false )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5698]) ).
thf(5792,plain,
! [SV675: $i,SV857: $i,SV905: $i] :
( ( ( in @ ( sK27_D @ SV905 @ SV857 @ SV675 ) @ SV905 )
= $false )
| ( ( ( ( sK27_D @ SV905 @ SV857 @ SV675 )
!= SV675 ) )
= $true )
| ( ( SV905
= ( unordered_pair @ SV675 @ SV857 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5699]) ).
thf(5793,plain,
! [SV675: $i,SV857: $i,SV905: $i] :
( ( ( in @ ( sK27_D @ SV905 @ SV857 @ SV675 ) @ SV905 )
= $false )
| ( ( ( ( sK27_D @ SV905 @ SV857 @ SV675 )
!= SV857 ) )
= $true )
| ( ( SV905
= ( unordered_pair @ SV675 @ SV857 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5700]) ).
thf(5794,plain,
! [SV906: $i,SV858: $i,SV675: $i,SV1046: $i] :
( ( ( SV1046 = SV675 )
= $true )
| ( ( SV1046 = SV858 )
= $true )
| ( ( in @ SV1046 @ SV906 )
= $false )
| ( ( SV906
= ( unordered_pair @ SV675 @ SV858 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5701]) ).
thf(5795,plain,
! [SV858: $i,SV906: $i,SV675: $i,SV1088: $i] :
( ( ( ( SV1088 != SV675 )
| ( in @ SV1088 @ SV906 ) )
= $true )
| ( ( SV906
= ( unordered_pair @ SV675 @ SV858 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5702]) ).
thf(5796,plain,
! [SV675: $i,SV906: $i,SV858: $i,SV1089: $i] :
( ( ( ( SV1089 != SV858 )
| ( in @ SV1089 @ SV906 ) )
= $true )
| ( ( SV906
= ( unordered_pair @ SV675 @ SV858 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5703]) ).
thf(5797,plain,
! [SV1027: $i,SV804: $i,SV863: $i] :
( ( ( in @ ( sK15_C @ SV863 @ SV804 ) @ SV863 )
= $false )
| ( ( in @ ( sK15_C @ SV863 @ SV804 ) @ SV1027 )
= $false )
| ( ( in @ SV1027 @ SV804 )
= $false )
| ( ( SV863
= ( union @ SV804 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5704]) ).
thf(5798,plain,
! [SV864: $i,SV805: $i,SV1055: $i,SV1028: $i] :
( ( ( in @ SV1028 @ SV1055 )
= $false )
| ( ( ~ ( in @ SV1055 @ SV805 ) )
= $true )
| ( ( in @ SV1028 @ SV864 )
= $true )
| ( ( SV864
= ( union @ SV805 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5705]) ).
thf(5799,plain,
! [SV805: $i,SV864: $i,SV1029: $i] :
( ( ( ~ ( in @ SV1029 @ ( sK14_D @ SV1029 @ SV864 @ SV805 ) ) )
= $false )
| ( ( in @ SV1029 @ SV864 )
= $false )
| ( ( SV864
= ( union @ SV805 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5706]) ).
thf(5800,plain,
! [SV805: $i,SV864: $i,SV1029: $i] :
( ( ( ~ ( in @ ( sK14_D @ SV1029 @ SV864 @ SV805 ) @ SV805 ) )
= $false )
| ( ( in @ SV1029 @ SV864 )
= $false )
| ( ( SV864
= ( union @ SV805 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5706]) ).
thf(5801,plain,
! [SV1056: $i,SV679: $i,SV946: $i] :
( ( ( in @ ( sK63_C @ SV946 @ SV679 ) @ SV946 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK63_C @ SV946 @ SV679 ) @ SV1056 ) @ SV679 )
= $false )
| ( ( SV946
= ( relation_dom @ SV679 ) )
= $true )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5707]) ).
thf(5802,plain,
! [SV947: $i,SV679: $i,SV1090: $i,SV1057: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1057 @ SV1090 ) @ SV679 ) )
= $true )
| ( ( in @ SV1057 @ SV947 )
= $true )
| ( ( SV947
= ( relation_dom @ SV679 ) )
= $false )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5708]) ).
thf(5803,plain,
! [SV679: $i,SV947: $i,SV1058: $i] :
( ( ( in @ SV1058 @ SV947 )
= $false )
| ( ( in @ ( ordered_pair @ SV1058 @ ( sK62_D @ SV1058 @ SV947 @ SV679 ) ) @ SV679 )
= $true )
| ( ( SV947
= ( relation_dom @ SV679 ) )
= $false )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5709]) ).
thf(5804,plain,
! [SV806: $i,SV867: $i] :
( ( ( in @ ( sK44_C @ SV867 @ SV806 ) @ SV806 )
= $false )
| ( ( ( sK44_C @ SV867 @ SV806 )
= ( sK45_SY414 @ SV867 @ SV806 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 ) )
= $true )
| ( ( SV867
= ( identity_relation @ SV806 ) )
= $true )
| ( ( relation @ SV867 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5710]) ).
thf(5805,plain,
! [SV806: $i,SV867: $i] :
( ( ( ( sK44_C @ SV867 @ SV806 )
= ( sK45_SY414 @ SV867 @ SV806 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 )
= $true )
| ( ( SV867
= ( identity_relation @ SV806 ) )
= $true )
| ( ( relation @ SV867 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5711]) ).
thf(5806,plain,
! [SV806: $i,SV867: $i] :
( ( ( in @ ( sK44_C @ SV867 @ SV806 ) @ SV806 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 )
= $true )
| ( ( SV867
= ( identity_relation @ SV806 ) )
= $true )
| ( ( relation @ SV867 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5712]) ).
thf(5807,plain,
! [SV868: $i,SV807: $i,SV1072: $i,SV1059: $i] :
( ( ( ( SV1059 != SV1072 )
| ~ ( in @ SV1059 @ SV807 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV1059 @ SV1072 ) @ SV868 )
= $true )
| ( ( SV868
= ( identity_relation @ SV807 ) )
= $false )
| ( ( relation @ SV868 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5713]) ).
thf(5808,plain,
! [SV807: $i,SV868: $i] :
( ( ( ! [SY1505: $i,SY1506: $i] :
( ~ ( in @ ( ordered_pair @ SY1505 @ SY1506 ) @ SV868 )
| ( SY1505 = SY1506 ) ) )
= $true )
| ( ( SV868
= ( identity_relation @ SV807 ) )
= $false )
| ( ( relation @ SV868 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5714]) ).
thf(5809,plain,
! [SV807: $i,SV868: $i] :
( ( ( ! [SY1507: $i] :
( ! [SY1508: $i] :
~ ( in @ ( ordered_pair @ SY1507 @ SY1508 ) @ SV868 )
| ( in @ SY1507 @ SV807 ) ) )
= $true )
| ( ( SV868
= ( identity_relation @ SV807 ) )
= $false )
| ( ( relation @ SV868 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5715]) ).
thf(5810,plain,
! [SV681: $i,SV948: $i,SV980: $i] :
( ( ( ~ ( in @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ SV948 )
| ~ ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV681 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 ) )
= $true )
| ( ( SV980
= ( relation_dom_restriction @ SV681 @ SV948 ) )
= $true )
| ( ( relation @ SV980 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5716]) ).
thf(5811,plain,
! [SV681: $i,SV948: $i,SV980: $i] :
( ( ( ~ ( ( in @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ SV948 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV681 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 ) ) )
= $false )
| ( ( SV980
= ( relation_dom_restriction @ SV681 @ SV948 ) )
= $true )
| ( ( relation @ SV980 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5717]) ).
thf(5812,plain,
! [SV981: $i,SV681: $i,SV949: $i] :
( ( ( ! [SY1625: $i,SY1626: $i] :
( ~ ( in @ SY1625 @ SV949 )
| ~ ( in @ ( ordered_pair @ SY1625 @ SY1626 ) @ SV681 )
| ( in @ ( ordered_pair @ SY1625 @ SY1626 ) @ SV981 ) ) )
= $true )
| ( ( SV981
= ( relation_dom_restriction @ SV681 @ SV949 ) )
= $false )
| ( ( relation @ SV981 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5718]) ).
thf(5813,plain,
! [SV681: $i,SV949: $i,SV981: $i] :
( ( ( ~ ( ~ ! [SY1627: $i] :
( ! [SY1628: $i] :
~ ( in @ ( ordered_pair @ SY1627 @ SY1628 ) @ SV981 )
| ( in @ SY1627 @ SV949 ) )
| ~ ! [SY1629: $i,SY1630: $i] :
( ~ ( in @ ( ordered_pair @ SY1629 @ SY1630 ) @ SV981 )
| ( in @ ( ordered_pair @ SY1629 @ SY1630 ) @ SV681 ) ) ) )
= $true )
| ( ( SV981
= ( relation_dom_restriction @ SV681 @ SV949 ) )
= $false )
| ( ( relation @ SV981 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5719]) ).
thf(5814,plain,
! [SV682: $i,SV910: $i,SV871: $i,SV1022: $i] :
( ( ( in @ SV1022 @ SV871 )
= $false )
| ( ( in @ SV1022 @ ( relation_dom @ SV910 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV1022 @ SV682 ) @ SV910 )
= $false )
| ( ( in @ SV682 @ ( relation_image @ SV910 @ SV871 ) )
= $true )
| ( ( relation @ SV910 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5720]) ).
thf(5815,plain,
! [SV682: $i,SV872: $i,SV911: $i] :
( ( ( ~ ( in @ ( sK52_D @ SV911 @ SV872 @ SV682 ) @ ( relation_dom @ SV911 ) ) )
= $false )
| ( ( in @ SV682 @ ( relation_image @ SV911 @ SV872 ) )
= $false )
| ( ( relation @ SV911 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5721]) ).
thf(5816,plain,
! [SV682: $i,SV872: $i,SV911: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV911 @ SV872 @ SV682 ) @ SV682 ) @ SV911 ) )
= $false )
| ( ( in @ SV682 @ ( relation_image @ SV911 @ SV872 ) )
= $false )
| ( ( relation @ SV911 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5721]) ).
thf(5817,plain,
! [SV684: $i,SV952: $i] :
( ( ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV684 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV952 ) )
= $true )
| ( ( SV684 = SV952 )
= $true )
| ( ( relation @ SV952 )
= $false )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5722]) ).
thf(5818,plain,
! [SV953: $i,SV684: $i,SV1091: $i] :
( ( ( ! [SY1677: $i] :
( ~ ( in @ ( ordered_pair @ SV1091 @ SY1677 ) @ SV684 )
| ( in @ ( ordered_pair @ SV1091 @ SY1677 ) @ SV953 ) ) )
= $true )
| ( ( SV684 = SV953 )
= $false )
| ( ( relation @ SV953 )
= $false )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5724]) ).
thf(5819,plain,
! [SV684: $i,SV953: $i,SV1092: $i] :
( ( ( ! [SY1678: $i] :
( ~ ( in @ ( ordered_pair @ SV1092 @ SY1678 ) @ SV953 )
| ( in @ ( ordered_pair @ SV1092 @ SY1678 ) @ SV684 ) ) )
= $true )
| ( ( SV684 = SV953 )
= $false )
| ( ( relation @ SV953 )
= $false )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5725]) ).
thf(5820,plain,
! [SV685: $i,SV982: $i,SV1060: $i] :
( ( ( subset @ SV1060 @ SV982 )
= $false )
| ( ( in @ SV1060 @ ( sK3_SY386 @ SV982 @ SV685 ) )
= $true )
| ( ( ~ ( in @ SV982 @ ( sK2_B @ SV685 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5726]) ).
thf(5821,plain,
! [SV1047: $i,SV685: $i,SV1032: $i] :
( ( ( in @ SV1032 @ ( sK2_B @ SV685 ) )
= $false )
| ( ( ~ ( subset @ SV1047 @ SV1032 ) )
= $true )
| ( ( in @ SV1047 @ ( sK2_B @ SV685 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5727]) ).
thf(5822,plain,
! [SV818: $i,SV880: $i] :
( ( ( ( relation_dom @ SV880 )
= SV818 )
= $false )
| ( ( in @ ( sK50_C @ SV880 @ SV818 ) @ SV818 )
= $true )
| ( ( SV880
= ( identity_relation @ SV818 ) )
= $true )
| ( ( function @ SV880 )
= $false )
| ( ( relation @ SV880 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5728]) ).
thf(5823,plain,
! [SV818: $i,SV880: $i] :
( ( ( ( apply @ SV880 @ ( sK50_C @ SV880 @ SV818 ) )
= ( sK50_C @ SV880 @ SV818 ) )
= $false )
| ( ( ( ( relation_dom @ SV880 )
!= SV818 ) )
= $true )
| ( ( SV880
= ( identity_relation @ SV818 ) )
= $true )
| ( ( function @ SV880 )
= $false )
| ( ( relation @ SV880 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5729]) ).
thf(5824,plain,
! [SV986: $i,SV958: $i,SV1093: $i] :
( ( ( ~ ( in @ SV1093 @ SV958 )
| ( ( apply @ SV986 @ SV1093 )
= SV1093 ) )
= $true )
| ( ( SV986
= ( identity_relation @ SV958 ) )
= $false )
| ( ( function @ SV986 )
= $false )
| ( ( relation @ SV986 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5730]) ).
thf(5825,plain,
! [SV886: $i,SV652: $i,SV826: $i,SV1035: $i] :
( ( ( in @ SV1035 @ SV826 )
= $false )
| ( ( in @ SV1035 @ SV652 )
= $false )
| ( ( in @ SV1035 @ SV886 )
= $true )
| ( ( SV886
= ( set_intersection2 @ SV652 @ SV826 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5733]) ).
thf(5826,plain,
! [SV826: $i,SV652: $i,SV886: $i,SV1073: $i] :
( ( ( ~ ( in @ SV1073 @ SV886 ) )
= $true )
| ( ( in @ SV1073 @ SV652 )
= $true )
| ( ( SV886
= ( set_intersection2 @ SV652 @ SV826 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5734]) ).
thf(5827,plain,
! [SV652: $i,SV826: $i,SV886: $i,SV1074: $i] :
( ( ( ~ ( in @ SV1074 @ SV886 ) )
= $true )
| ( ( in @ SV1074 @ SV826 )
= $true )
| ( ( SV886
= ( set_intersection2 @ SV652 @ SV826 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5735]) ).
thf(5828,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5736]) ).
thf(5829,plain,
! [SV653: $i,SV1061: $i] :
( ( ( ~ ( function @ SV1061 ) )
= $true )
| ( ( ~ ( relation @ SV1061 ) )
= $true )
| ( ( ( SV1061
!= ( function_inverse @ SV653 ) )
| ~ ( ~ ~ ( ~ ! [SY1663: $i,SY1664: $i] :
( ( SY1664
!= ( apply @ SV1061 @ SY1663 ) )
| ~ ( in @ SY1663 @ ( relation_rng @ SV653 ) )
| ( SY1663
= ( apply @ SV653 @ SY1664 ) ) )
| ~ ! [SY1665: $i,SY1666: $i] :
( ( SY1666
!= ( apply @ SV1061 @ SY1665 ) )
| ~ ( in @ SY1665 @ ( relation_rng @ SV653 ) )
| ( in @ SY1666 @ ( relation_dom @ SV653 ) ) ) )
| ~ ~ ( ~ ! [SY1667: $i,SY1668: $i] :
( ( SY1667
!= ( apply @ SV653 @ SY1668 ) )
| ~ ( in @ SY1668 @ ( relation_dom @ SV653 ) )
| ( SY1668
= ( apply @ SV1061 @ SY1667 ) ) )
| ~ ! [SY1148: $i] :
( ! [SY1149: $i] :
( ( SY1148
!= ( apply @ SV653 @ SY1149 ) )
| ~ ( in @ SY1149 @ ( relation_dom @ SV653 ) ) )
| ( in @ SY1148 @ ( relation_rng @ SV653 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5737]) ).
thf(5830,plain,
! [SV653: $i,SV1062: $i] :
( ( ( ~ ( function @ SV1062 ) )
= $true )
| ( ( ~ ( relation @ SV1062 ) )
= $true )
| ( ( ( SV1062
!= ( function_inverse @ SV653 ) )
| ( ( relation_dom @ SV1062 )
= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5738]) ).
thf(5831,plain,
! [SV655: $i,SV740: $i,SV961: $i] :
( ( ( ~ ( in @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) @ SV655 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV740 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 ) )
= $true )
| ( ( SV961
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $true )
| ( ( relation @ SV961 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5739]) ).
thf(5832,plain,
! [SV655: $i,SV740: $i,SV961: $i] :
( ( ( ~ ( ( in @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) @ SV655 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 ) ) )
= $false )
| ( ( SV961
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $true )
| ( ( relation @ SV961 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5740]) ).
thf(5833,plain,
! [SV655: $i,SV740: $i,SV961: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV740 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 ) ) )
= $false )
| ( ( SV961
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $true )
| ( ( relation @ SV961 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5740]) ).
thf(5834,plain,
! [SV962: $i,SV740: $i,SV1094: $i,SV655: $i] :
( ( ( ! [SY1679: $i] :
( ~ ( in @ SY1679 @ SV655 )
| ~ ( in @ ( ordered_pair @ SV1094 @ SY1679 ) @ SV740 )
| ( in @ ( ordered_pair @ SV1094 @ SY1679 ) @ SV962 ) ) )
= $true )
| ( ( SV962
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $false )
| ( ( relation @ SV962 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5741]) ).
thf(5835,plain,
! [SV740: $i,SV655: $i,SV962: $i] :
( ( ( ~ ! [SY1605: $i,SY1606: $i] :
( ~ ( in @ ( ordered_pair @ SY1605 @ SY1606 ) @ SV962 )
| ( in @ SY1606 @ SV655 ) )
| ~ ! [SY1607: $i,SY1608: $i] :
( ~ ( in @ ( ordered_pair @ SY1607 @ SY1608 ) @ SV962 )
| ( in @ ( ordered_pair @ SY1607 @ SY1608 ) @ SV740 ) ) )
= $false )
| ( ( SV962
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $false )
| ( ( relation @ SV962 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5742]) ).
thf(5836,plain,
! [SV1063: $i,SV657: $i,SV922: $i,SV964: $i] :
( ( ( in @ ( ordered_pair @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SV1063 ) @ SV657 )
= $false )
| ( ( ~ ( in @ SV1063 @ SV922 ) )
= $true )
| ( ( ~ ( in @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SV964 ) )
= $true )
| ( ( SV964
= ( relation_inverse_image @ SV657 @ SV922 ) )
= $true )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5743]) ).
thf(5837,plain,
! [SV657: $i,SV922: $i,SV964: $i] :
( ( ( in @ ( ordered_pair @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ ( sK36_SY409 @ SV964 @ SV922 @ SV657 ) ) @ SV657 )
= $true )
| ( ( in @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SV964 )
= $true )
| ( ( SV964
= ( relation_inverse_image @ SV657 @ SV922 ) )
= $true )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5744]) ).
thf(5838,plain,
! [SV657: $i,SV922: $i,SV964: $i] :
( ( ( in @ ( sK36_SY409 @ SV964 @ SV922 @ SV657 ) @ SV922 )
= $true )
| ( ( in @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SV964 )
= $true )
| ( ( SV964
= ( relation_inverse_image @ SV657 @ SV922 ) )
= $true )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5745]) ).
thf(5839,plain,
! [SV965: $i,SV923: $i,SV657: $i,SV1095: $i,SV1064: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1064 @ SV1095 ) @ SV657 )
| ~ ( in @ SV1095 @ SV923 ) )
= $true )
| ( ( in @ SV1064 @ SV965 )
= $true )
| ( ( SV965
= ( relation_inverse_image @ SV657 @ SV923 ) )
= $false )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5746]) ).
thf(5840,plain,
! [SV657: $i,SV923: $i,SV965: $i,SV1065: $i] :
( ( ( in @ SV1065 @ SV965 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV1065 @ ( sK34_E @ SV1065 @ SV965 @ SV923 @ SV657 ) ) @ SV657 )
| ~ ( in @ ( sK34_E @ SV1065 @ SV965 @ SV923 @ SV657 ) @ SV923 ) ) )
= $true )
| ( ( SV965
= ( relation_inverse_image @ SV657 @ SV923 ) )
= $false )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5747]) ).
thf(5841,plain,
! [SV658: $i,SV924: $i,SV966: $i,SV1066: $i] :
( ( ( in @ ( ordered_pair @ SV1066 @ ( sK38_D @ SV966 @ SV924 @ SV658 ) ) @ SV658 )
= $false )
| ( ( ~ ( in @ SV1066 @ SV924 ) )
= $true )
| ( ( ~ ( in @ ( sK38_D @ SV966 @ SV924 @ SV658 ) @ SV966 ) )
= $true )
| ( ( SV966
= ( relation_image @ SV658 @ SV924 ) )
= $true )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5748]) ).
thf(5842,plain,
! [SV658: $i,SV924: $i,SV966: $i] :
( ( ( in @ ( ordered_pair @ ( sK39_SY411 @ SV966 @ SV924 @ SV658 ) @ ( sK38_D @ SV966 @ SV924 @ SV658 ) ) @ SV658 )
= $true )
| ( ( in @ ( sK38_D @ SV966 @ SV924 @ SV658 ) @ SV966 )
= $true )
| ( ( SV966
= ( relation_image @ SV658 @ SV924 ) )
= $true )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5749]) ).
thf(5843,plain,
! [SV658: $i,SV924: $i,SV966: $i] :
( ( ( in @ ( sK39_SY411 @ SV966 @ SV924 @ SV658 ) @ SV924 )
= $true )
| ( ( in @ ( sK38_D @ SV966 @ SV924 @ SV658 ) @ SV966 )
= $true )
| ( ( SV966
= ( relation_image @ SV658 @ SV924 ) )
= $true )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5750]) ).
thf(5844,plain,
! [SV967: $i,SV925: $i,SV658: $i,SV1067: $i,SV1096: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1096 @ SV1067 ) @ SV658 )
| ~ ( in @ SV1096 @ SV925 ) )
= $true )
| ( ( in @ SV1067 @ SV967 )
= $true )
| ( ( SV967
= ( relation_image @ SV658 @ SV925 ) )
= $false )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5751]) ).
thf(5845,plain,
! [SV658: $i,SV925: $i,SV967: $i,SV1068: $i] :
( ( ( in @ SV1068 @ SV967 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SV1068 @ SV967 @ SV925 @ SV658 ) @ SV1068 ) @ SV658 )
| ~ ( in @ ( sK37_E @ SV1068 @ SV967 @ SV925 @ SV658 ) @ SV925 ) ) )
= $true )
| ( ( SV967
= ( relation_image @ SV658 @ SV925 ) )
= $false )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5752]) ).
thf(5846,plain,
! [SV660: $i,SV783: $i,SV1014: $i] :
( ( ( ! [SY1644: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ SY1644 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1644 @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV783 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV1014 ) )
= $true )
| ( ( SV1014
= ( relation_composition @ SV660 @ SV783 ) )
= $true )
| ( ( relation @ SV1014 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5753]) ).
thf(5847,plain,
! [SV660: $i,SV783: $i,SV1014: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK10_SY395 @ SV1014 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV783 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV1014 ) )
= $true )
| ( ( SV1014
= ( relation_composition @ SV660 @ SV783 ) )
= $true )
| ( ( relation @ SV1014 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5754]) ).
thf(5848,plain,
! [SV1015: $i,SV783: $i,SV660: $i] :
( ( ( ~ ! [SY1645: $i,SY1646: $i] :
( ! [SY1410: $i] :
( ~ ( in @ ( ordered_pair @ SY1645 @ SY1410 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1410 @ SY1646 ) @ SV783 ) )
| ( in @ ( ordered_pair @ SY1645 @ SY1646 ) @ SV1015 ) ) )
= $false )
| ( ( SV1015
= ( relation_composition @ SV660 @ SV783 ) )
= $false )
| ( ( relation @ SV1015 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5755]) ).
thf(5849,plain,
! [SV660: $i,SV783: $i,SV1015: $i] :
( ( ( ~ ! [SY1648: $i,SY1649: $i] :
( ~ ( in @ ( ordered_pair @ SY1648 @ SY1649 ) @ SV1015 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1648 @ ( sK7_F @ SY1649 @ SY1648 @ SV1015 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY1649 @ SY1648 @ SV1015 @ SV783 @ SV660 ) @ SY1649 ) @ SV783 ) ) ) )
= $false )
| ( ( SV1015
= ( relation_composition @ SV660 @ SV783 ) )
= $false )
| ( ( relation @ SV1015 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5755]) ).
thf(5850,plain,
! [SV933: $i,SV661: $i,SV1049: $i,SV1075: $i] :
( ( ( in @ ( ordered_pair @ SV1075 @ SV1049 ) @ SV661 )
= $false )
| ( ( in @ SV1049 @ SV933 )
= $true )
| ( ( SV933
= ( relation_rng @ SV661 ) )
= $false )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5757]) ).
thf(5851,plain,
! [SV839: $i,SV662: $i,SV892: $i,SV1076: $i] :
( ( ( ~ ( in @ SV1076 @ SV892 ) )
= $true )
| ( ( in @ SV1076 @ SV662 )
= $true )
| ( ( SV892
= ( set_difference @ SV662 @ SV839 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5761]) ).
thf(5852,plain,
! [SV662: $i,SV839: $i,SV892: $i,SV1077: $i] :
( ( ( ~ ( in @ SV1077 @ SV892 ) )
= $true )
| ( ( ~ ( in @ SV1077 @ SV839 ) )
= $true )
| ( ( SV892
= ( set_difference @ SV662 @ SV839 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5762]) ).
thf(5853,plain,
! [SV1037: $i,SV664: $i,SV1078: $i] :
( ( ( ( SV1078
!= ( apply @ SV664 @ SV1037 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV1037 @ SV1078 ) @ SV664 )
= $true )
| ( ( in @ SV1037 @ ( relation_dom @ SV664 ) )
= $false )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5763]) ).
thf(5854,plain,
! [SV664: $i,SV1079: $i,SV1038: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1038 @ SV1079 ) @ SV664 ) )
= $true )
| ( ( SV1079
= ( apply @ SV664 @ SV1038 ) )
= $true )
| ( ( in @ SV1038 @ ( relation_dom @ SV664 ) )
= $false )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5764]) ).
thf(5855,plain,
! [SV1039: $i,SV664: $i,SV1069: $i] :
( ( ( SV1069
= ( apply @ SV664 @ SV1039 ) )
= $false )
| ( ( SV1069 = empty_set )
= $true )
| ( ( in @ SV1039 @ ( relation_dom @ SV664 ) )
= $true )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5765]) ).
thf(5856,plain,
! [SV1040: $i,SV664: $i,SV1070: $i] :
( ( ( SV1070 = empty_set )
= $false )
| ( ( SV1070
= ( apply @ SV664 @ SV1040 ) )
= $true )
| ( ( in @ SV1040 @ ( relation_dom @ SV664 ) )
= $true )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5766]) ).
thf(5857,plain,
! [SV742: $i,SV1016: $i,SV666: $i] :
( ( ( ~ ( in @ SV666 @ ( relation_dom @ SV1016 ) ) )
= $true )
| ( ( ~ ( in @ ( apply @ SV1016 @ SV666 ) @ ( relation_dom @ SV742 ) ) )
= $true )
| ( ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SV1016 @ SV742 ) ) )
= $true )
| ( ( function @ SV1016 )
= $false )
| ( ( relation @ SV1016 )
= $false )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5768]) ).
thf(5858,plain,
! [SV742: $i,SV666: $i,SV1052: $i] :
( ( ( function @ SV1052 )
= $false )
| ( ( ~ ( relation @ SV1052 ) )
= $true )
| ( ( ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SV1052 @ SV742 ) ) )
| ( in @ SV666 @ ( relation_dom @ SV1052 ) ) )
= $true )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5769]) ).
thf(5859,plain,
! [SV742: $i,SV666: $i,SV1053: $i] :
( ( ( function @ SV1053 )
= $false )
| ( ( ~ ( relation @ SV1053 ) )
= $true )
| ( ( ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SV1053 @ SV742 ) ) )
| ( in @ ( apply @ SV1053 @ SV666 ) @ ( relation_dom @ SV742 ) ) )
= $true )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5770]) ).
thf(5860,plain,
! [SV667: $i,SV844: $i,SV895: $i] :
( ( ( in @ ( sK51_D @ SV895 @ SV844 @ SV667 ) @ ( relation_rng @ SV895 ) )
= $true )
| ( ( in @ SV667 @ ( relation_inverse_image @ SV895 @ SV844 ) )
= $false )
| ( ( relation @ SV895 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5772]) ).
thf(5861,plain,
! [SV844: $i,SV895: $i,SV667: $i] :
( ( ( in @ ( ordered_pair @ SV667 @ ( sK51_D @ SV895 @ SV844 @ SV667 ) ) @ SV895 )
= $true )
| ( ( in @ SV667 @ ( relation_inverse_image @ SV895 @ SV844 ) )
= $false )
| ( ( relation @ SV895 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5773]) ).
thf(5862,plain,
! [SV669: $i,SV848: $i,SV897: $i] :
( ( ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV669 )
= $false )
| ( ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV897 )
= $false )
| ( ( SV897
= ( set_union2 @ SV669 @ SV848 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5774]) ).
thf(5863,plain,
! [SV669: $i,SV848: $i,SV897: $i] :
( ( ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV848 )
= $false )
| ( ( in @ ( sK26_D @ SV897 @ SV848 @ SV669 ) @ SV897 )
= $false )
| ( ( SV897
= ( set_union2 @ SV669 @ SV848 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5775]) ).
thf(5864,plain,
! [SV849: $i,SV898: $i,SV669: $i,SV1080: $i] :
( ( ( ~ ( in @ SV1080 @ SV669 ) )
= $true )
| ( ( in @ SV1080 @ SV898 )
= $true )
| ( ( SV898
= ( set_union2 @ SV669 @ SV849 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5777]) ).
thf(5865,plain,
! [SV669: $i,SV898: $i,SV849: $i,SV1081: $i] :
( ( ( ~ ( in @ SV1081 @ SV849 ) )
= $true )
| ( ( in @ SV1081 @ SV898 )
= $true )
| ( ( SV898
= ( set_union2 @ SV669 @ SV849 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5778]) ).
thf(5866,plain,
! [SV937: $i,SV1000: $i] :
( ( ( ~ ( in @ ( sK33_SY406 @ SV1000 @ SV937 ) @ SV937 ) )
= $false )
| ( ( ~ ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SV1000 ) )
= $true )
| ( ( SV1000
= ( set_meet @ SV937 ) )
= $true )
| ( ( SV937 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5779]) ).
thf(5867,plain,
! [SV937: $i,SV1000: $i] :
( ( ( ~ ~ ( in @ ( sK32_C @ SV1000 @ SV937 ) @ ( sK33_SY406 @ SV1000 @ SV937 ) ) )
= $false )
| ( ( ~ ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SV1000 ) )
= $true )
| ( ( SV1000
= ( set_meet @ SV937 ) )
= $true )
| ( ( SV937 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5779]) ).
thf(5868,plain,
! [SV1000: $i,SV937: $i,SV1082: $i] :
( ( ( ~ ( in @ SV1082 @ SV937 ) )
= $true )
| ( ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SV1082 )
= $true )
| ( ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SV1000 )
= $true )
| ( ( SV1000
= ( set_meet @ SV937 ) )
= $true )
| ( ( SV937 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5780]) ).
thf(5869,plain,
! [SV938: $i,SV1001: $i,SV1083: $i] :
( ( ( ~ ( ~ ( in @ ( sK31_D @ SV1083 @ SV1001 @ SV938 ) @ SV938 )
| ~ ~ ( in @ SV1083 @ ( sK31_D @ SV1083 @ SV1001 @ SV938 ) ) ) )
= $true )
| ( ( in @ SV1083 @ SV1001 )
= $true )
| ( ( SV1001
= ( set_meet @ SV938 ) )
= $false )
| ( ( SV938 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5781]) ).
thf(5870,plain,
! [SV938: $i,SV1001: $i,SV1084: $i] :
( ( ( ~ ( in @ SV1084 @ SV1001 ) )
= $true )
| ( ( ! [SY1674: $i] :
( ~ ( in @ SY1674 @ SV938 )
| ( in @ SV1084 @ SY1674 ) ) )
= $true )
| ( ( SV1001
= ( set_meet @ SV938 ) )
= $false )
| ( ( SV938 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5782]) ).
thf(5871,plain,
! [SV899: $i,SV850: $i,SV1054: $i,SV670: $i,SV1043: $i] :
( ( ( in @ SV1043 @ SV670 )
= $false )
| ( ( ~ ( in @ SV1054 @ SV850 ) )
= $true )
| ( ( ( ( sK23_D @ SV899 @ SV850 @ SV670 )
!= ( ordered_pair @ SV1043 @ SV1054 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV899 @ SV850 @ SV670 ) @ SV899 ) )
= $true )
| ( ( SV899
= ( cartesian_product2 @ SV670 @ SV850 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5783]) ).
thf(5872,plain,
! [SV670: $i,SV850: $i,SV899: $i] :
( ( ( ~ ( in @ ( sK24_SY403 @ SV899 @ SV850 @ SV670 ) @ SV670 ) )
= $false )
| ( ( in @ ( sK23_D @ SV899 @ SV850 @ SV670 ) @ SV899 )
= $true )
| ( ( SV899
= ( cartesian_product2 @ SV670 @ SV850 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5784]) ).
thf(5873,plain,
! [SV670: $i,SV850: $i,SV899: $i] :
( ( ( ~ ( in @ ( sK25_SY405 @ SV899 @ SV850 @ SV670 ) @ SV850 ) )
= $false )
| ( ( in @ ( sK23_D @ SV899 @ SV850 @ SV670 ) @ SV899 )
= $true )
| ( ( SV899
= ( cartesian_product2 @ SV670 @ SV850 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5784]) ).
thf(5874,plain,
! [SV900: $i,SV1044: $i,SV851: $i,SV1085: $i,SV670: $i,SV1071: $i] :
( ( ( ~ ( in @ SV1071 @ SV670 )
| ~ ( in @ SV1085 @ SV851 ) )
= $true )
| ( ( ( SV1044
!= ( ordered_pair @ SV1071 @ SV1085 ) ) )
= $true )
| ( ( in @ SV1044 @ SV900 )
= $true )
| ( ( SV900
= ( cartesian_product2 @ SV670 @ SV851 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5785]) ).
thf(5875,plain,
! [SV670: $i,SV851: $i,SV900: $i,SV1045: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK21_E @ SV1045 @ SV900 @ SV851 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK22_SY400 @ SV1045 @ SV900 @ SV851 @ SV670 ) @ SV851 ) ) )
= $false )
| ( ( in @ SV1045 @ SV900 )
= $false )
| ( ( SV900
= ( cartesian_product2 @ SV670 @ SV851 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5786]) ).
thf(5876,plain,
! [SV670: $i,SV851: $i,SV900: $i,SV1045: $i] :
( ( ( ( SV1045
!= ( ordered_pair @ ( sK21_E @ SV1045 @ SV900 @ SV851 @ SV670 ) @ ( sK22_SY400 @ SV1045 @ SV900 @ SV851 @ SV670 ) ) ) )
= $false )
| ( ( in @ SV1045 @ SV900 )
= $false )
| ( ( SV900
= ( cartesian_product2 @ SV670 @ SV851 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5786]) ).
thf(5877,plain,
! [SV672: $i,SV941: $i] :
( ( ( in @ ( ordered_pair @ ( sK12_SY396 @ SV941 @ SV672 ) @ ( sK11_C @ SV941 @ SV672 ) ) @ SV672 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK11_C @ SV941 @ SV672 ) @ ( sK12_SY396 @ SV941 @ SV672 ) ) @ SV941 )
= $false )
| ( ( SV941
= ( relation_inverse @ SV672 ) )
= $true )
| ( ( relation @ SV941 )
= $false )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5789]) ).
thf(5878,plain,
! [SV672: $i,SV942: $i,SV1097: $i,SV1086: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1086 @ SV1097 ) @ SV942 )
| ( in @ ( ordered_pair @ SV1097 @ SV1086 ) @ SV672 ) )
= $true )
| ( ( SV942
= ( relation_inverse @ SV672 ) )
= $false )
| ( ( relation @ SV942 )
= $false )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5790]) ).
thf(5879,plain,
! [SV942: $i,SV672: $i,SV1087: $i,SV1098: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1098 @ SV1087 ) @ SV672 )
| ( in @ ( ordered_pair @ SV1087 @ SV1098 ) @ SV942 ) )
= $true )
| ( ( SV942
= ( relation_inverse @ SV672 ) )
= $false )
| ( ( relation @ SV942 )
= $false )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5791]) ).
thf(5880,plain,
! [SV675: $i,SV857: $i,SV905: $i] :
( ( ( ( sK27_D @ SV905 @ SV857 @ SV675 )
= SV675 )
= $false )
| ( ( in @ ( sK27_D @ SV905 @ SV857 @ SV675 ) @ SV905 )
= $false )
| ( ( SV905
= ( unordered_pair @ SV675 @ SV857 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5792]) ).
thf(5881,plain,
! [SV675: $i,SV857: $i,SV905: $i] :
( ( ( ( sK27_D @ SV905 @ SV857 @ SV675 )
= SV857 )
= $false )
| ( ( in @ ( sK27_D @ SV905 @ SV857 @ SV675 ) @ SV905 )
= $false )
| ( ( SV905
= ( unordered_pair @ SV675 @ SV857 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5793]) ).
thf(5882,plain,
! [SV858: $i,SV906: $i,SV675: $i,SV1088: $i] :
( ( ( ( SV1088 != SV675 ) )
= $true )
| ( ( in @ SV1088 @ SV906 )
= $true )
| ( ( SV906
= ( unordered_pair @ SV675 @ SV858 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5795]) ).
thf(5883,plain,
! [SV675: $i,SV906: $i,SV858: $i,SV1089: $i] :
( ( ( ( SV1089 != SV858 ) )
= $true )
| ( ( in @ SV1089 @ SV906 )
= $true )
| ( ( SV906
= ( unordered_pair @ SV675 @ SV858 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5796]) ).
thf(5884,plain,
! [SV864: $i,SV1028: $i,SV805: $i,SV1055: $i] :
( ( ( in @ SV1055 @ SV805 )
= $false )
| ( ( in @ SV1028 @ SV1055 )
= $false )
| ( ( in @ SV1028 @ SV864 )
= $true )
| ( ( SV864
= ( union @ SV805 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5798]) ).
thf(5885,plain,
! [SV805: $i,SV864: $i,SV1029: $i] :
( ( ( in @ SV1029 @ ( sK14_D @ SV1029 @ SV864 @ SV805 ) )
= $true )
| ( ( in @ SV1029 @ SV864 )
= $false )
| ( ( SV864
= ( union @ SV805 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5799]) ).
thf(5886,plain,
! [SV805: $i,SV864: $i,SV1029: $i] :
( ( ( in @ ( sK14_D @ SV1029 @ SV864 @ SV805 ) @ SV805 )
= $true )
| ( ( in @ SV1029 @ SV864 )
= $false )
| ( ( SV864
= ( union @ SV805 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5800]) ).
thf(5887,plain,
! [SV947: $i,SV679: $i,SV1090: $i,SV1057: $i] :
( ( ( in @ ( ordered_pair @ SV1057 @ SV1090 ) @ SV679 )
= $false )
| ( ( in @ SV1057 @ SV947 )
= $true )
| ( ( SV947
= ( relation_dom @ SV679 ) )
= $false )
| ( ( relation @ SV679 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5802]) ).
thf(5888,plain,
! [SV806: $i,SV867: $i] :
( ( ( in @ ( ordered_pair @ ( sK44_C @ SV867 @ SV806 ) @ ( sK45_SY414 @ SV867 @ SV806 ) ) @ SV867 )
= $false )
| ( ( ( sK44_C @ SV867 @ SV806 )
= ( sK45_SY414 @ SV867 @ SV806 ) )
= $false )
| ( ( in @ ( sK44_C @ SV867 @ SV806 ) @ SV806 )
= $false )
| ( ( SV867
= ( identity_relation @ SV806 ) )
= $true )
| ( ( relation @ SV867 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5804]) ).
thf(5889,plain,
! [SV868: $i,SV807: $i,SV1072: $i,SV1059: $i] :
( ( ( ( SV1059 != SV1072 ) )
= $true )
| ( ( ~ ( in @ SV1059 @ SV807 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV1059 @ SV1072 ) @ SV868 )
= $true )
| ( ( SV868
= ( identity_relation @ SV807 ) )
= $false )
| ( ( relation @ SV868 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5807]) ).
thf(5890,plain,
! [SV807: $i,SV868: $i,SV1099: $i] :
( ( ( ! [SY1680: $i] :
( ~ ( in @ ( ordered_pair @ SV1099 @ SY1680 ) @ SV868 )
| ( SV1099 = SY1680 ) ) )
= $true )
| ( ( SV868
= ( identity_relation @ SV807 ) )
= $false )
| ( ( relation @ SV868 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5808]) ).
thf(5891,plain,
! [SV807: $i,SV868: $i,SV1100: $i] :
( ( ( ! [SY1681: $i] :
~ ( in @ ( ordered_pair @ SV1100 @ SY1681 ) @ SV868 )
| ( in @ SV1100 @ SV807 ) )
= $true )
| ( ( SV868
= ( identity_relation @ SV807 ) )
= $false )
| ( ( relation @ SV868 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5809]) ).
thf(5892,plain,
! [SV681: $i,SV948: $i,SV980: $i] :
( ( ( ~ ( in @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ SV948 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV681 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 ) )
= $true )
| ( ( SV980
= ( relation_dom_restriction @ SV681 @ SV948 ) )
= $true )
| ( ( relation @ SV980 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5810]) ).
thf(5893,plain,
! [SV681: $i,SV948: $i,SV980: $i] :
( ( ( ~ ( ( in @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ SV948 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 ) ) )
= $false )
| ( ( SV980
= ( relation_dom_restriction @ SV681 @ SV948 ) )
= $true )
| ( ( relation @ SV980 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5811]) ).
thf(5894,plain,
! [SV681: $i,SV948: $i,SV980: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV681 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 ) ) )
= $false )
| ( ( SV980
= ( relation_dom_restriction @ SV681 @ SV948 ) )
= $true )
| ( ( relation @ SV980 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5811]) ).
thf(5895,plain,
! [SV981: $i,SV681: $i,SV949: $i,SV1101: $i] :
( ( ( ! [SY1682: $i] :
( ~ ( in @ SV1101 @ SV949 )
| ~ ( in @ ( ordered_pair @ SV1101 @ SY1682 ) @ SV681 )
| ( in @ ( ordered_pair @ SV1101 @ SY1682 ) @ SV981 ) ) )
= $true )
| ( ( SV981
= ( relation_dom_restriction @ SV681 @ SV949 ) )
= $false )
| ( ( relation @ SV981 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5812]) ).
thf(5896,plain,
! [SV681: $i,SV949: $i,SV981: $i] :
( ( ( ~ ! [SY1627: $i] :
( ! [SY1628: $i] :
~ ( in @ ( ordered_pair @ SY1627 @ SY1628 ) @ SV981 )
| ( in @ SY1627 @ SV949 ) )
| ~ ! [SY1629: $i,SY1630: $i] :
( ~ ( in @ ( ordered_pair @ SY1629 @ SY1630 ) @ SV981 )
| ( in @ ( ordered_pair @ SY1629 @ SY1630 ) @ SV681 ) ) )
= $false )
| ( ( SV981
= ( relation_dom_restriction @ SV681 @ SV949 ) )
= $false )
| ( ( relation @ SV981 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5813]) ).
thf(5897,plain,
! [SV682: $i,SV872: $i,SV911: $i] :
( ( ( in @ ( sK52_D @ SV911 @ SV872 @ SV682 ) @ ( relation_dom @ SV911 ) )
= $true )
| ( ( in @ SV682 @ ( relation_image @ SV911 @ SV872 ) )
= $false )
| ( ( relation @ SV911 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5815]) ).
thf(5898,plain,
! [SV682: $i,SV872: $i,SV911: $i] :
( ( ( in @ ( ordered_pair @ ( sK52_D @ SV911 @ SV872 @ SV682 ) @ SV682 ) @ SV911 )
= $true )
| ( ( in @ SV682 @ ( relation_image @ SV911 @ SV872 ) )
= $false )
| ( ( relation @ SV911 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5816]) ).
thf(5899,plain,
! [SV684: $i,SV952: $i] :
( ( ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV952 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK65_C @ SV952 @ SV684 ) @ ( sK66_SY420 @ SV952 @ SV684 ) ) @ SV684 )
= $false )
| ( ( SV684 = SV952 )
= $true )
| ( ( relation @ SV952 )
= $false )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5817]) ).
thf(5900,plain,
! [SV953: $i,SV684: $i,SV1102: $i,SV1091: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1091 @ SV1102 ) @ SV684 )
| ( in @ ( ordered_pair @ SV1091 @ SV1102 ) @ SV953 ) )
= $true )
| ( ( SV684 = SV953 )
= $false )
| ( ( relation @ SV953 )
= $false )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5818]) ).
thf(5901,plain,
! [SV684: $i,SV953: $i,SV1103: $i,SV1092: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1092 @ SV1103 ) @ SV953 )
| ( in @ ( ordered_pair @ SV1092 @ SV1103 ) @ SV684 ) )
= $true )
| ( ( SV684 = SV953 )
= $false )
| ( ( relation @ SV953 )
= $false )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5819]) ).
thf(5902,plain,
! [SV1060: $i,SV685: $i,SV982: $i] :
( ( ( in @ SV982 @ ( sK2_B @ SV685 ) )
= $false )
| ( ( in @ SV1060 @ ( sK3_SY386 @ SV982 @ SV685 ) )
= $true )
| ( ( subset @ SV1060 @ SV982 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5820]) ).
thf(5903,plain,
! [SV685: $i,SV1032: $i,SV1047: $i] :
( ( ( subset @ SV1047 @ SV1032 )
= $false )
| ( ( in @ SV1032 @ ( sK2_B @ SV685 ) )
= $false )
| ( ( in @ SV1047 @ ( sK2_B @ SV685 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5821]) ).
thf(5904,plain,
! [SV818: $i,SV880: $i] :
( ( ( ( relation_dom @ SV880 )
= SV818 )
= $false )
| ( ( ( apply @ SV880 @ ( sK50_C @ SV880 @ SV818 ) )
= ( sK50_C @ SV880 @ SV818 ) )
= $false )
| ( ( SV880
= ( identity_relation @ SV818 ) )
= $true )
| ( ( function @ SV880 )
= $false )
| ( ( relation @ SV880 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5823]) ).
thf(5905,plain,
! [SV986: $i,SV958: $i,SV1093: $i] :
( ( ( ~ ( in @ SV1093 @ SV958 ) )
= $true )
| ( ( ( apply @ SV986 @ SV1093 )
= SV1093 )
= $true )
| ( ( SV986
= ( identity_relation @ SV958 ) )
= $false )
| ( ( function @ SV986 )
= $false )
| ( ( relation @ SV986 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5824]) ).
thf(5906,plain,
! [SV826: $i,SV652: $i,SV886: $i,SV1073: $i] :
( ( ( in @ SV1073 @ SV886 )
= $false )
| ( ( in @ SV1073 @ SV652 )
= $true )
| ( ( SV886
= ( set_intersection2 @ SV652 @ SV826 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5826]) ).
thf(5907,plain,
! [SV652: $i,SV826: $i,SV886: $i,SV1074: $i] :
( ( ( in @ SV1074 @ SV886 )
= $false )
| ( ( in @ SV1074 @ SV826 )
= $true )
| ( ( SV886
= ( set_intersection2 @ SV652 @ SV826 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5827]) ).
thf(5908,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5828]) ).
thf(5909,plain,
! [SV653: $i,SV1061: $i] :
( ( ( function @ SV1061 )
= $false )
| ( ( ~ ( relation @ SV1061 ) )
= $true )
| ( ( ( SV1061
!= ( function_inverse @ SV653 ) )
| ~ ( ~ ~ ( ~ ! [SY1663: $i,SY1664: $i] :
( ( SY1664
!= ( apply @ SV1061 @ SY1663 ) )
| ~ ( in @ SY1663 @ ( relation_rng @ SV653 ) )
| ( SY1663
= ( apply @ SV653 @ SY1664 ) ) )
| ~ ! [SY1665: $i,SY1666: $i] :
( ( SY1666
!= ( apply @ SV1061 @ SY1665 ) )
| ~ ( in @ SY1665 @ ( relation_rng @ SV653 ) )
| ( in @ SY1666 @ ( relation_dom @ SV653 ) ) ) )
| ~ ~ ( ~ ! [SY1667: $i,SY1668: $i] :
( ( SY1667
!= ( apply @ SV653 @ SY1668 ) )
| ~ ( in @ SY1668 @ ( relation_dom @ SV653 ) )
| ( SY1668
= ( apply @ SV1061 @ SY1667 ) ) )
| ~ ! [SY1148: $i] :
( ! [SY1149: $i] :
( ( SY1148
!= ( apply @ SV653 @ SY1149 ) )
| ~ ( in @ SY1149 @ ( relation_dom @ SV653 ) ) )
| ( in @ SY1148 @ ( relation_rng @ SV653 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5829]) ).
thf(5910,plain,
! [SV653: $i,SV1062: $i] :
( ( ( function @ SV1062 )
= $false )
| ( ( ~ ( relation @ SV1062 ) )
= $true )
| ( ( ( SV1062
!= ( function_inverse @ SV653 ) )
| ( ( relation_dom @ SV1062 )
= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5830]) ).
thf(5911,plain,
! [SV655: $i,SV740: $i,SV961: $i] :
( ( ( in @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) @ SV655 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV740 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 ) )
= $true )
| ( ( SV961
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $true )
| ( ( relation @ SV961 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5831]) ).
thf(5912,plain,
! [SV655: $i,SV740: $i,SV961: $i] :
( ( ( ( in @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) @ SV655 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 ) )
= $true )
| ( ( SV961
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $true )
| ( ( relation @ SV961 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5832]) ).
thf(5913,plain,
! [SV655: $i,SV740: $i,SV961: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV740 )
| ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 ) )
= $true )
| ( ( SV961
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $true )
| ( ( relation @ SV961 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5833]) ).
thf(5914,plain,
! [SV962: $i,SV740: $i,SV1094: $i,SV655: $i,SV1104: $i] :
( ( ( ~ ( in @ SV1104 @ SV655 )
| ~ ( in @ ( ordered_pair @ SV1094 @ SV1104 ) @ SV740 )
| ( in @ ( ordered_pair @ SV1094 @ SV1104 ) @ SV962 ) )
= $true )
| ( ( SV962
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $false )
| ( ( relation @ SV962 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5834]) ).
thf(5915,plain,
! [SV740: $i,SV655: $i,SV962: $i] :
( ( ( ~ ! [SY1605: $i,SY1606: $i] :
( ~ ( in @ ( ordered_pair @ SY1605 @ SY1606 ) @ SV962 )
| ( in @ SY1606 @ SV655 ) ) )
= $false )
| ( ( SV962
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $false )
| ( ( relation @ SV962 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5835]) ).
thf(5916,plain,
! [SV655: $i,SV740: $i,SV962: $i] :
( ( ( ~ ! [SY1607: $i,SY1608: $i] :
( ~ ( in @ ( ordered_pair @ SY1607 @ SY1608 ) @ SV962 )
| ( in @ ( ordered_pair @ SY1607 @ SY1608 ) @ SV740 ) ) )
= $false )
| ( ( SV962
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $false )
| ( ( relation @ SV962 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5835]) ).
thf(5917,plain,
! [SV657: $i,SV964: $i,SV922: $i,SV1063: $i] :
( ( ( in @ SV1063 @ SV922 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SV1063 ) @ SV657 )
= $false )
| ( ( ~ ( in @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SV964 ) )
= $true )
| ( ( SV964
= ( relation_inverse_image @ SV657 @ SV922 ) )
= $true )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5836]) ).
thf(5918,plain,
! [SV965: $i,SV923: $i,SV657: $i,SV1095: $i,SV1064: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1064 @ SV1095 ) @ SV657 ) )
= $true )
| ( ( ~ ( in @ SV1095 @ SV923 ) )
= $true )
| ( ( in @ SV1064 @ SV965 )
= $true )
| ( ( SV965
= ( relation_inverse_image @ SV657 @ SV923 ) )
= $false )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5839]) ).
thf(5919,plain,
! [SV657: $i,SV923: $i,SV965: $i,SV1065: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1065 @ ( sK34_E @ SV1065 @ SV965 @ SV923 @ SV657 ) ) @ SV657 )
| ~ ( in @ ( sK34_E @ SV1065 @ SV965 @ SV923 @ SV657 ) @ SV923 ) )
= $false )
| ( ( in @ SV1065 @ SV965 )
= $false )
| ( ( SV965
= ( relation_inverse_image @ SV657 @ SV923 ) )
= $false )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5840]) ).
thf(5920,plain,
! [SV658: $i,SV966: $i,SV924: $i,SV1066: $i] :
( ( ( in @ SV1066 @ SV924 )
= $false )
| ( ( in @ ( ordered_pair @ SV1066 @ ( sK38_D @ SV966 @ SV924 @ SV658 ) ) @ SV658 )
= $false )
| ( ( ~ ( in @ ( sK38_D @ SV966 @ SV924 @ SV658 ) @ SV966 ) )
= $true )
| ( ( SV966
= ( relation_image @ SV658 @ SV924 ) )
= $true )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5841]) ).
thf(5921,plain,
! [SV967: $i,SV925: $i,SV658: $i,SV1067: $i,SV1096: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1096 @ SV1067 ) @ SV658 ) )
= $true )
| ( ( ~ ( in @ SV1096 @ SV925 ) )
= $true )
| ( ( in @ SV1067 @ SV967 )
= $true )
| ( ( SV967
= ( relation_image @ SV658 @ SV925 ) )
= $false )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5844]) ).
thf(5922,plain,
! [SV658: $i,SV925: $i,SV967: $i,SV1068: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SV1068 @ SV967 @ SV925 @ SV658 ) @ SV1068 ) @ SV658 )
| ~ ( in @ ( sK37_E @ SV1068 @ SV967 @ SV925 @ SV658 ) @ SV925 ) )
= $false )
| ( ( in @ SV1068 @ SV967 )
= $false )
| ( ( SV967
= ( relation_image @ SV658 @ SV925 ) )
= $false )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5845]) ).
thf(5923,plain,
! [SV660: $i,SV783: $i,SV1014: $i] :
( ( ( ! [SY1644: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ SY1644 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1644 @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV783 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV1014 ) )
= $true )
| ( ( SV1014
= ( relation_composition @ SV660 @ SV783 ) )
= $true )
| ( ( relation @ SV1014 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5846]) ).
thf(5924,plain,
! [SV660: $i,SV783: $i,SV1014: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK10_SY395 @ SV1014 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV783 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV1014 )
= $true )
| ( ( SV1014
= ( relation_composition @ SV660 @ SV783 ) )
= $true )
| ( ( relation @ SV1014 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5847]) ).
thf(5925,plain,
! [SV1015: $i,SV783: $i,SV660: $i] :
( ( ( ! [SY1645: $i,SY1646: $i] :
( ! [SY1410: $i] :
( ~ ( in @ ( ordered_pair @ SY1645 @ SY1410 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1410 @ SY1646 ) @ SV783 ) )
| ( in @ ( ordered_pair @ SY1645 @ SY1646 ) @ SV1015 ) ) )
= $true )
| ( ( SV1015
= ( relation_composition @ SV660 @ SV783 ) )
= $false )
| ( ( relation @ SV1015 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5848]) ).
thf(5926,plain,
! [SV660: $i,SV783: $i,SV1015: $i] :
( ( ( ! [SY1648: $i,SY1649: $i] :
( ~ ( in @ ( ordered_pair @ SY1648 @ SY1649 ) @ SV1015 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1648 @ ( sK7_F @ SY1649 @ SY1648 @ SV1015 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY1649 @ SY1648 @ SV1015 @ SV783 @ SV660 ) @ SY1649 ) @ SV783 ) ) ) )
= $true )
| ( ( SV1015
= ( relation_composition @ SV660 @ SV783 ) )
= $false )
| ( ( relation @ SV1015 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5849]) ).
thf(5927,plain,
! [SV839: $i,SV662: $i,SV892: $i,SV1076: $i] :
( ( ( in @ SV1076 @ SV892 )
= $false )
| ( ( in @ SV1076 @ SV662 )
= $true )
| ( ( SV892
= ( set_difference @ SV662 @ SV839 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5851]) ).
thf(5928,plain,
! [SV662: $i,SV839: $i,SV892: $i,SV1077: $i] :
( ( ( in @ SV1077 @ SV892 )
= $false )
| ( ( ~ ( in @ SV1077 @ SV839 ) )
= $true )
| ( ( SV892
= ( set_difference @ SV662 @ SV839 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5852]) ).
thf(5929,plain,
! [SV1037: $i,SV664: $i,SV1078: $i] :
( ( ( SV1078
= ( apply @ SV664 @ SV1037 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV1037 @ SV1078 ) @ SV664 )
= $true )
| ( ( in @ SV1037 @ ( relation_dom @ SV664 ) )
= $false )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5853]) ).
thf(5930,plain,
! [SV664: $i,SV1079: $i,SV1038: $i] :
( ( ( in @ ( ordered_pair @ SV1038 @ SV1079 ) @ SV664 )
= $false )
| ( ( SV1079
= ( apply @ SV664 @ SV1038 ) )
= $true )
| ( ( in @ SV1038 @ ( relation_dom @ SV664 ) )
= $false )
| ( ( function @ SV664 )
= $false )
| ( ( relation @ SV664 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5854]) ).
thf(5931,plain,
! [SV742: $i,SV1016: $i,SV666: $i] :
( ( ( in @ SV666 @ ( relation_dom @ SV1016 ) )
= $false )
| ( ( ~ ( in @ ( apply @ SV1016 @ SV666 ) @ ( relation_dom @ SV742 ) ) )
= $true )
| ( ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SV1016 @ SV742 ) ) )
= $true )
| ( ( function @ SV1016 )
= $false )
| ( ( relation @ SV1016 )
= $false )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5857]) ).
thf(5932,plain,
! [SV742: $i,SV666: $i,SV1052: $i] :
( ( ( relation @ SV1052 )
= $false )
| ( ( function @ SV1052 )
= $false )
| ( ( ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SV1052 @ SV742 ) ) )
| ( in @ SV666 @ ( relation_dom @ SV1052 ) ) )
= $true )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5858]) ).
thf(5933,plain,
! [SV742: $i,SV666: $i,SV1053: $i] :
( ( ( relation @ SV1053 )
= $false )
| ( ( function @ SV1053 )
= $false )
| ( ( ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SV1053 @ SV742 ) ) )
| ( in @ ( apply @ SV1053 @ SV666 ) @ ( relation_dom @ SV742 ) ) )
= $true )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5859]) ).
thf(5934,plain,
! [SV849: $i,SV898: $i,SV669: $i,SV1080: $i] :
( ( ( in @ SV1080 @ SV669 )
= $false )
| ( ( in @ SV1080 @ SV898 )
= $true )
| ( ( SV898
= ( set_union2 @ SV669 @ SV849 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5864]) ).
thf(5935,plain,
! [SV669: $i,SV898: $i,SV849: $i,SV1081: $i] :
( ( ( in @ SV1081 @ SV849 )
= $false )
| ( ( in @ SV1081 @ SV898 )
= $true )
| ( ( SV898
= ( set_union2 @ SV669 @ SV849 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5865]) ).
thf(5936,plain,
! [SV937: $i,SV1000: $i] :
( ( ( in @ ( sK33_SY406 @ SV1000 @ SV937 ) @ SV937 )
= $true )
| ( ( ~ ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SV1000 ) )
= $true )
| ( ( SV1000
= ( set_meet @ SV937 ) )
= $true )
| ( ( SV937 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5866]) ).
thf(5937,plain,
! [SV937: $i,SV1000: $i] :
( ( ( ~ ( in @ ( sK32_C @ SV1000 @ SV937 ) @ ( sK33_SY406 @ SV1000 @ SV937 ) ) )
= $true )
| ( ( ~ ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SV1000 ) )
= $true )
| ( ( SV1000
= ( set_meet @ SV937 ) )
= $true )
| ( ( SV937 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5867]) ).
thf(5938,plain,
! [SV1000: $i,SV937: $i,SV1082: $i] :
( ( ( in @ SV1082 @ SV937 )
= $false )
| ( ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SV1082 )
= $true )
| ( ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SV1000 )
= $true )
| ( ( SV1000
= ( set_meet @ SV937 ) )
= $true )
| ( ( SV937 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5868]) ).
thf(5939,plain,
! [SV938: $i,SV1001: $i,SV1083: $i] :
( ( ( ~ ( in @ ( sK31_D @ SV1083 @ SV1001 @ SV938 ) @ SV938 )
| ~ ~ ( in @ SV1083 @ ( sK31_D @ SV1083 @ SV1001 @ SV938 ) ) )
= $false )
| ( ( in @ SV1083 @ SV1001 )
= $true )
| ( ( SV1001
= ( set_meet @ SV938 ) )
= $false )
| ( ( SV938 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5869]) ).
thf(5940,plain,
! [SV938: $i,SV1001: $i,SV1084: $i] :
( ( ( in @ SV1084 @ SV1001 )
= $false )
| ( ( ! [SY1674: $i] :
( ~ ( in @ SY1674 @ SV938 )
| ( in @ SV1084 @ SY1674 ) ) )
= $true )
| ( ( SV1001
= ( set_meet @ SV938 ) )
= $false )
| ( ( SV938 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5870]) ).
thf(5941,plain,
! [SV899: $i,SV670: $i,SV1043: $i,SV850: $i,SV1054: $i] :
( ( ( in @ SV1054 @ SV850 )
= $false )
| ( ( in @ SV1043 @ SV670 )
= $false )
| ( ( ( ( sK23_D @ SV899 @ SV850 @ SV670 )
!= ( ordered_pair @ SV1043 @ SV1054 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_D @ SV899 @ SV850 @ SV670 ) @ SV899 ) )
= $true )
| ( ( SV899
= ( cartesian_product2 @ SV670 @ SV850 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5871]) ).
thf(5942,plain,
! [SV670: $i,SV850: $i,SV899: $i] :
( ( ( in @ ( sK24_SY403 @ SV899 @ SV850 @ SV670 ) @ SV670 )
= $true )
| ( ( in @ ( sK23_D @ SV899 @ SV850 @ SV670 ) @ SV899 )
= $true )
| ( ( SV899
= ( cartesian_product2 @ SV670 @ SV850 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5872]) ).
thf(5943,plain,
! [SV670: $i,SV850: $i,SV899: $i] :
( ( ( in @ ( sK25_SY405 @ SV899 @ SV850 @ SV670 ) @ SV850 )
= $true )
| ( ( in @ ( sK23_D @ SV899 @ SV850 @ SV670 ) @ SV899 )
= $true )
| ( ( SV899
= ( cartesian_product2 @ SV670 @ SV850 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5873]) ).
thf(5944,plain,
! [SV900: $i,SV1044: $i,SV851: $i,SV1085: $i,SV670: $i,SV1071: $i] :
( ( ( ~ ( in @ SV1071 @ SV670 ) )
= $true )
| ( ( ~ ( in @ SV1085 @ SV851 ) )
= $true )
| ( ( ( SV1044
!= ( ordered_pair @ SV1071 @ SV1085 ) ) )
= $true )
| ( ( in @ SV1044 @ SV900 )
= $true )
| ( ( SV900
= ( cartesian_product2 @ SV670 @ SV851 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5874]) ).
thf(5945,plain,
! [SV670: $i,SV851: $i,SV900: $i,SV1045: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_E @ SV1045 @ SV900 @ SV851 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK22_SY400 @ SV1045 @ SV900 @ SV851 @ SV670 ) @ SV851 ) ) )
= $true )
| ( ( in @ SV1045 @ SV900 )
= $false )
| ( ( SV900
= ( cartesian_product2 @ SV670 @ SV851 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5875]) ).
thf(5946,plain,
! [SV670: $i,SV851: $i,SV900: $i,SV1045: $i] :
( ( ( SV1045
= ( ordered_pair @ ( sK21_E @ SV1045 @ SV900 @ SV851 @ SV670 ) @ ( sK22_SY400 @ SV1045 @ SV900 @ SV851 @ SV670 ) ) )
= $true )
| ( ( in @ SV1045 @ SV900 )
= $false )
| ( ( SV900
= ( cartesian_product2 @ SV670 @ SV851 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5876]) ).
thf(5947,plain,
! [SV672: $i,SV942: $i,SV1097: $i,SV1086: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1086 @ SV1097 ) @ SV942 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV1097 @ SV1086 ) @ SV672 )
= $true )
| ( ( SV942
= ( relation_inverse @ SV672 ) )
= $false )
| ( ( relation @ SV942 )
= $false )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5878]) ).
thf(5948,plain,
! [SV942: $i,SV672: $i,SV1087: $i,SV1098: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1098 @ SV1087 ) @ SV672 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV1087 @ SV1098 ) @ SV942 )
= $true )
| ( ( SV942
= ( relation_inverse @ SV672 ) )
= $false )
| ( ( relation @ SV942 )
= $false )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5879]) ).
thf(5949,plain,
! [SV858: $i,SV906: $i,SV675: $i,SV1088: $i] :
( ( ( SV1088 = SV675 )
= $false )
| ( ( in @ SV1088 @ SV906 )
= $true )
| ( ( SV906
= ( unordered_pair @ SV675 @ SV858 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5882]) ).
thf(5950,plain,
! [SV675: $i,SV906: $i,SV858: $i,SV1089: $i] :
( ( ( SV1089 = SV858 )
= $false )
| ( ( in @ SV1089 @ SV906 )
= $true )
| ( ( SV906
= ( unordered_pair @ SV675 @ SV858 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5883]) ).
thf(5951,plain,
! [SV868: $i,SV807: $i,SV1072: $i,SV1059: $i] :
( ( ( SV1059 = SV1072 )
= $false )
| ( ( ~ ( in @ SV1059 @ SV807 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV1059 @ SV1072 ) @ SV868 )
= $true )
| ( ( SV868
= ( identity_relation @ SV807 ) )
= $false )
| ( ( relation @ SV868 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5889]) ).
thf(5952,plain,
! [SV807: $i,SV868: $i,SV1105: $i,SV1099: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1099 @ SV1105 ) @ SV868 )
| ( SV1099 = SV1105 ) )
= $true )
| ( ( SV868
= ( identity_relation @ SV807 ) )
= $false )
| ( ( relation @ SV868 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5890]) ).
thf(5953,plain,
! [SV807: $i,SV868: $i,SV1100: $i] :
( ( ( ! [SY1681: $i] :
~ ( in @ ( ordered_pair @ SV1100 @ SY1681 ) @ SV868 ) )
= $true )
| ( ( in @ SV1100 @ SV807 )
= $true )
| ( ( SV868
= ( identity_relation @ SV807 ) )
= $false )
| ( ( relation @ SV868 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5891]) ).
thf(5954,plain,
! [SV681: $i,SV948: $i,SV980: $i] :
( ( ( in @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ SV948 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV681 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 ) )
= $true )
| ( ( SV980
= ( relation_dom_restriction @ SV681 @ SV948 ) )
= $true )
| ( ( relation @ SV980 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5892]) ).
thf(5955,plain,
! [SV681: $i,SV948: $i,SV980: $i] :
( ( ( ( in @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ SV948 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 ) )
= $true )
| ( ( SV980
= ( relation_dom_restriction @ SV681 @ SV948 ) )
= $true )
| ( ( relation @ SV980 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5893]) ).
thf(5956,plain,
! [SV681: $i,SV948: $i,SV980: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV681 )
| ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 ) )
= $true )
| ( ( SV980
= ( relation_dom_restriction @ SV681 @ SV948 ) )
= $true )
| ( ( relation @ SV980 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5894]) ).
thf(5957,plain,
! [SV981: $i,SV681: $i,SV1106: $i,SV949: $i,SV1101: $i] :
( ( ( ~ ( in @ SV1101 @ SV949 )
| ~ ( in @ ( ordered_pair @ SV1101 @ SV1106 ) @ SV681 )
| ( in @ ( ordered_pair @ SV1101 @ SV1106 ) @ SV981 ) )
= $true )
| ( ( SV981
= ( relation_dom_restriction @ SV681 @ SV949 ) )
= $false )
| ( ( relation @ SV981 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5895]) ).
thf(5958,plain,
! [SV681: $i,SV949: $i,SV981: $i] :
( ( ( ~ ! [SY1627: $i] :
( ! [SY1628: $i] :
~ ( in @ ( ordered_pair @ SY1627 @ SY1628 ) @ SV981 )
| ( in @ SY1627 @ SV949 ) ) )
= $false )
| ( ( SV981
= ( relation_dom_restriction @ SV681 @ SV949 ) )
= $false )
| ( ( relation @ SV981 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5896]) ).
thf(5959,plain,
! [SV949: $i,SV681: $i,SV981: $i] :
( ( ( ~ ! [SY1629: $i,SY1630: $i] :
( ~ ( in @ ( ordered_pair @ SY1629 @ SY1630 ) @ SV981 )
| ( in @ ( ordered_pair @ SY1629 @ SY1630 ) @ SV681 ) ) )
= $false )
| ( ( SV981
= ( relation_dom_restriction @ SV681 @ SV949 ) )
= $false )
| ( ( relation @ SV981 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5896]) ).
thf(5960,plain,
! [SV953: $i,SV684: $i,SV1102: $i,SV1091: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1091 @ SV1102 ) @ SV684 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV1091 @ SV1102 ) @ SV953 )
= $true )
| ( ( SV684 = SV953 )
= $false )
| ( ( relation @ SV953 )
= $false )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5900]) ).
thf(5961,plain,
! [SV684: $i,SV953: $i,SV1103: $i,SV1092: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1092 @ SV1103 ) @ SV953 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV1092 @ SV1103 ) @ SV684 )
= $true )
| ( ( SV684 = SV953 )
= $false )
| ( ( relation @ SV953 )
= $false )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5901]) ).
thf(5962,plain,
! [SV986: $i,SV958: $i,SV1093: $i] :
( ( ( in @ SV1093 @ SV958 )
= $false )
| ( ( ( apply @ SV986 @ SV1093 )
= SV1093 )
= $true )
| ( ( SV986
= ( identity_relation @ SV958 ) )
= $false )
| ( ( function @ SV986 )
= $false )
| ( ( relation @ SV986 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5905]) ).
thf(5963,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5908]) ).
thf(5964,plain,
! [SV653: $i,SV1061: $i] :
( ( ( relation @ SV1061 )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( ( SV1061
!= ( function_inverse @ SV653 ) )
| ~ ( ~ ~ ( ~ ! [SY1663: $i,SY1664: $i] :
( ( SY1664
!= ( apply @ SV1061 @ SY1663 ) )
| ~ ( in @ SY1663 @ ( relation_rng @ SV653 ) )
| ( SY1663
= ( apply @ SV653 @ SY1664 ) ) )
| ~ ! [SY1665: $i,SY1666: $i] :
( ( SY1666
!= ( apply @ SV1061 @ SY1665 ) )
| ~ ( in @ SY1665 @ ( relation_rng @ SV653 ) )
| ( in @ SY1666 @ ( relation_dom @ SV653 ) ) ) )
| ~ ~ ( ~ ! [SY1667: $i,SY1668: $i] :
( ( SY1667
!= ( apply @ SV653 @ SY1668 ) )
| ~ ( in @ SY1668 @ ( relation_dom @ SV653 ) )
| ( SY1668
= ( apply @ SV1061 @ SY1667 ) ) )
| ~ ! [SY1148: $i] :
( ! [SY1149: $i] :
( ( SY1148
!= ( apply @ SV653 @ SY1149 ) )
| ~ ( in @ SY1149 @ ( relation_dom @ SV653 ) ) )
| ( in @ SY1148 @ ( relation_rng @ SV653 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5909]) ).
thf(5965,plain,
! [SV653: $i,SV1062: $i] :
( ( ( relation @ SV1062 )
= $false )
| ( ( function @ SV1062 )
= $false )
| ( ( ( SV1062
!= ( function_inverse @ SV653 ) )
| ( ( relation_dom @ SV1062 )
= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5910]) ).
thf(5966,plain,
! [SV655: $i,SV740: $i,SV961: $i] :
( ( ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV740 )
= $false )
| ( ( in @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) @ SV655 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 ) )
= $true )
| ( ( SV961
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $true )
| ( ( relation @ SV961 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5911]) ).
thf(5967,plain,
! [SV655: $i,SV740: $i,SV961: $i] :
( ( ( in @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) @ SV655 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 )
= $true )
| ( ( SV961
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $true )
| ( ( relation @ SV961 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5912]) ).
thf(5968,plain,
! [SV655: $i,SV740: $i,SV961: $i] :
( ( ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV740 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 )
= $true )
| ( ( SV961
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $true )
| ( ( relation @ SV961 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5913]) ).
thf(5969,plain,
! [SV962: $i,SV740: $i,SV1094: $i,SV655: $i,SV1104: $i] :
( ( ( ~ ( in @ SV1104 @ SV655 )
| ~ ( in @ ( ordered_pair @ SV1094 @ SV1104 ) @ SV740 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV1094 @ SV1104 ) @ SV962 )
= $true )
| ( ( SV962
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $false )
| ( ( relation @ SV962 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5914]) ).
thf(5970,plain,
! [SV740: $i,SV655: $i,SV962: $i] :
( ( ( ! [SY1605: $i,SY1606: $i] :
( ~ ( in @ ( ordered_pair @ SY1605 @ SY1606 ) @ SV962 )
| ( in @ SY1606 @ SV655 ) ) )
= $true )
| ( ( SV962
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $false )
| ( ( relation @ SV962 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5915]) ).
thf(5971,plain,
! [SV655: $i,SV740: $i,SV962: $i] :
( ( ( ! [SY1607: $i,SY1608: $i] :
( ~ ( in @ ( ordered_pair @ SY1607 @ SY1608 ) @ SV962 )
| ( in @ ( ordered_pair @ SY1607 @ SY1608 ) @ SV740 ) ) )
= $true )
| ( ( SV962
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $false )
| ( ( relation @ SV962 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5916]) ).
thf(5972,plain,
! [SV1063: $i,SV657: $i,SV922: $i,SV964: $i] :
( ( ( in @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SV964 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK35_D @ SV964 @ SV922 @ SV657 ) @ SV1063 ) @ SV657 )
= $false )
| ( ( in @ SV1063 @ SV922 )
= $false )
| ( ( SV964
= ( relation_inverse_image @ SV657 @ SV922 ) )
= $true )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5917]) ).
thf(5973,plain,
! [SV965: $i,SV923: $i,SV657: $i,SV1095: $i,SV1064: $i] :
( ( ( in @ ( ordered_pair @ SV1064 @ SV1095 ) @ SV657 )
= $false )
| ( ( ~ ( in @ SV1095 @ SV923 ) )
= $true )
| ( ( in @ SV1064 @ SV965 )
= $true )
| ( ( SV965
= ( relation_inverse_image @ SV657 @ SV923 ) )
= $false )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5918]) ).
thf(5974,plain,
! [SV657: $i,SV923: $i,SV965: $i,SV1065: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1065 @ ( sK34_E @ SV1065 @ SV965 @ SV923 @ SV657 ) ) @ SV657 ) )
= $false )
| ( ( in @ SV1065 @ SV965 )
= $false )
| ( ( SV965
= ( relation_inverse_image @ SV657 @ SV923 ) )
= $false )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5919]) ).
thf(5975,plain,
! [SV657: $i,SV923: $i,SV965: $i,SV1065: $i] :
( ( ( ~ ( in @ ( sK34_E @ SV1065 @ SV965 @ SV923 @ SV657 ) @ SV923 ) )
= $false )
| ( ( in @ SV1065 @ SV965 )
= $false )
| ( ( SV965
= ( relation_inverse_image @ SV657 @ SV923 ) )
= $false )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5919]) ).
thf(5976,plain,
! [SV1066: $i,SV658: $i,SV924: $i,SV966: $i] :
( ( ( in @ ( sK38_D @ SV966 @ SV924 @ SV658 ) @ SV966 )
= $false )
| ( ( in @ ( ordered_pair @ SV1066 @ ( sK38_D @ SV966 @ SV924 @ SV658 ) ) @ SV658 )
= $false )
| ( ( in @ SV1066 @ SV924 )
= $false )
| ( ( SV966
= ( relation_image @ SV658 @ SV924 ) )
= $true )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5920]) ).
thf(5977,plain,
! [SV967: $i,SV925: $i,SV658: $i,SV1067: $i,SV1096: $i] :
( ( ( in @ ( ordered_pair @ SV1096 @ SV1067 ) @ SV658 )
= $false )
| ( ( ~ ( in @ SV1096 @ SV925 ) )
= $true )
| ( ( in @ SV1067 @ SV967 )
= $true )
| ( ( SV967
= ( relation_image @ SV658 @ SV925 ) )
= $false )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5921]) ).
thf(5978,plain,
! [SV658: $i,SV925: $i,SV967: $i,SV1068: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK37_E @ SV1068 @ SV967 @ SV925 @ SV658 ) @ SV1068 ) @ SV658 ) )
= $false )
| ( ( in @ SV1068 @ SV967 )
= $false )
| ( ( SV967
= ( relation_image @ SV658 @ SV925 ) )
= $false )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5922]) ).
thf(5979,plain,
! [SV658: $i,SV925: $i,SV967: $i,SV1068: $i] :
( ( ( ~ ( in @ ( sK37_E @ SV1068 @ SV967 @ SV925 @ SV658 ) @ SV925 ) )
= $false )
| ( ( in @ SV1068 @ SV967 )
= $false )
| ( ( SV967
= ( relation_image @ SV658 @ SV925 ) )
= $false )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5922]) ).
thf(5980,plain,
! [SV1107: $i,SV660: $i,SV783: $i,SV1014: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ SV1107 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SV1107 @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV783 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV1014 ) )
= $true )
| ( ( SV1014
= ( relation_composition @ SV660 @ SV783 ) )
= $true )
| ( ( relation @ SV1014 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5923]) ).
thf(5981,plain,
! [SV660: $i,SV783: $i,SV1014: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK10_SY395 @ SV1014 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV783 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV1014 )
= $true )
| ( ( SV1014
= ( relation_composition @ SV660 @ SV783 ) )
= $true )
| ( ( relation @ SV1014 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5924]) ).
thf(5982,plain,
! [SV1015: $i,SV783: $i,SV660: $i,SV1108: $i] :
( ( ( ! [SY1683: $i] :
( ! [SY1684: $i] :
( ~ ( in @ ( ordered_pair @ SV1108 @ SY1684 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1684 @ SY1683 ) @ SV783 ) )
| ( in @ ( ordered_pair @ SV1108 @ SY1683 ) @ SV1015 ) ) )
= $true )
| ( ( SV1015
= ( relation_composition @ SV660 @ SV783 ) )
= $false )
| ( ( relation @ SV1015 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5925]) ).
thf(5983,plain,
! [SV660: $i,SV783: $i,SV1015: $i,SV1109: $i] :
( ( ( ! [SY1685: $i] :
( ~ ( in @ ( ordered_pair @ SV1109 @ SY1685 ) @ SV1015 )
| ~ ( ~ ( in @ ( ordered_pair @ SV1109 @ ( sK7_F @ SY1685 @ SV1109 @ SV1015 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY1685 @ SV1109 @ SV1015 @ SV783 @ SV660 ) @ SY1685 ) @ SV783 ) ) ) )
= $true )
| ( ( SV1015
= ( relation_composition @ SV660 @ SV783 ) )
= $false )
| ( ( relation @ SV1015 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5926]) ).
thf(5984,plain,
! [SV662: $i,SV892: $i,SV839: $i,SV1077: $i] :
( ( ( in @ SV1077 @ SV839 )
= $false )
| ( ( in @ SV1077 @ SV892 )
= $false )
| ( ( SV892
= ( set_difference @ SV662 @ SV839 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5928]) ).
thf(5985,plain,
! [SV742: $i,SV666: $i,SV1016: $i] :
( ( ( in @ ( apply @ SV1016 @ SV666 ) @ ( relation_dom @ SV742 ) )
= $false )
| ( ( in @ SV666 @ ( relation_dom @ SV1016 ) )
= $false )
| ( ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SV1016 @ SV742 ) ) )
= $true )
| ( ( function @ SV1016 )
= $false )
| ( ( relation @ SV1016 )
= $false )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5931]) ).
thf(5986,plain,
! [SV742: $i,SV1052: $i,SV666: $i] :
( ( ( ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SV1052 @ SV742 ) ) ) )
= $true )
| ( ( in @ SV666 @ ( relation_dom @ SV1052 ) )
= $true )
| ( ( function @ SV1052 )
= $false )
| ( ( relation @ SV1052 )
= $false )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5932]) ).
thf(5987,plain,
! [SV742: $i,SV1053: $i,SV666: $i] :
( ( ( ~ ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SV1053 @ SV742 ) ) ) )
= $true )
| ( ( in @ ( apply @ SV1053 @ SV666 ) @ ( relation_dom @ SV742 ) )
= $true )
| ( ( function @ SV1053 )
= $false )
| ( ( relation @ SV1053 )
= $false )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5933]) ).
thf(5988,plain,
! [SV937: $i,SV1000: $i] :
( ( ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SV1000 )
= $false )
| ( ( in @ ( sK33_SY406 @ SV1000 @ SV937 ) @ SV937 )
= $true )
| ( ( SV1000
= ( set_meet @ SV937 ) )
= $true )
| ( ( SV937 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5936]) ).
thf(5989,plain,
! [SV937: $i,SV1000: $i] :
( ( ( in @ ( sK32_C @ SV1000 @ SV937 ) @ ( sK33_SY406 @ SV1000 @ SV937 ) )
= $false )
| ( ( ~ ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SV1000 ) )
= $true )
| ( ( SV1000
= ( set_meet @ SV937 ) )
= $true )
| ( ( SV937 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5937]) ).
thf(5990,plain,
! [SV938: $i,SV1001: $i,SV1083: $i] :
( ( ( ~ ( in @ ( sK31_D @ SV1083 @ SV1001 @ SV938 ) @ SV938 ) )
= $false )
| ( ( in @ SV1083 @ SV1001 )
= $true )
| ( ( SV1001
= ( set_meet @ SV938 ) )
= $false )
| ( ( SV938 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5939]) ).
thf(5991,plain,
! [SV938: $i,SV1001: $i,SV1083: $i] :
( ( ( ~ ~ ( in @ SV1083 @ ( sK31_D @ SV1083 @ SV1001 @ SV938 ) ) )
= $false )
| ( ( in @ SV1083 @ SV1001 )
= $true )
| ( ( SV1001
= ( set_meet @ SV938 ) )
= $false )
| ( ( SV938 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5939]) ).
thf(5992,plain,
! [SV1001: $i,SV1084: $i,SV938: $i,SV1110: $i] :
( ( ( ~ ( in @ SV1110 @ SV938 )
| ( in @ SV1084 @ SV1110 ) )
= $true )
| ( ( in @ SV1084 @ SV1001 )
= $false )
| ( ( SV1001
= ( set_meet @ SV938 ) )
= $false )
| ( ( SV938 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5940]) ).
thf(5993,plain,
! [SV1054: $i,SV1043: $i,SV670: $i,SV850: $i,SV899: $i] :
( ( ( ( sK23_D @ SV899 @ SV850 @ SV670 )
= ( ordered_pair @ SV1043 @ SV1054 ) )
= $false )
| ( ( in @ SV1043 @ SV670 )
= $false )
| ( ( in @ SV1054 @ SV850 )
= $false )
| ( ( ~ ( in @ ( sK23_D @ SV899 @ SV850 @ SV670 ) @ SV899 ) )
= $true )
| ( ( SV899
= ( cartesian_product2 @ SV670 @ SV850 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5941]) ).
thf(5994,plain,
! [SV900: $i,SV1044: $i,SV851: $i,SV1085: $i,SV670: $i,SV1071: $i] :
( ( ( in @ SV1071 @ SV670 )
= $false )
| ( ( ~ ( in @ SV1085 @ SV851 ) )
= $true )
| ( ( ( SV1044
!= ( ordered_pair @ SV1071 @ SV1085 ) ) )
= $true )
| ( ( in @ SV1044 @ SV900 )
= $true )
| ( ( SV900
= ( cartesian_product2 @ SV670 @ SV851 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5944]) ).
thf(5995,plain,
! [SV670: $i,SV851: $i,SV900: $i,SV1045: $i] :
( ( ( ~ ( in @ ( sK21_E @ SV1045 @ SV900 @ SV851 @ SV670 ) @ SV670 )
| ~ ( in @ ( sK22_SY400 @ SV1045 @ SV900 @ SV851 @ SV670 ) @ SV851 ) )
= $false )
| ( ( in @ SV1045 @ SV900 )
= $false )
| ( ( SV900
= ( cartesian_product2 @ SV670 @ SV851 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5945]) ).
thf(5996,plain,
! [SV672: $i,SV942: $i,SV1097: $i,SV1086: $i] :
( ( ( in @ ( ordered_pair @ SV1086 @ SV1097 ) @ SV942 )
= $false )
| ( ( in @ ( ordered_pair @ SV1097 @ SV1086 ) @ SV672 )
= $true )
| ( ( SV942
= ( relation_inverse @ SV672 ) )
= $false )
| ( ( relation @ SV942 )
= $false )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5947]) ).
thf(5997,plain,
! [SV942: $i,SV672: $i,SV1087: $i,SV1098: $i] :
( ( ( in @ ( ordered_pair @ SV1098 @ SV1087 ) @ SV672 )
= $false )
| ( ( in @ ( ordered_pair @ SV1087 @ SV1098 ) @ SV942 )
= $true )
| ( ( SV942
= ( relation_inverse @ SV672 ) )
= $false )
| ( ( relation @ SV942 )
= $false )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5948]) ).
thf(5998,plain,
! [SV868: $i,SV1072: $i,SV807: $i,SV1059: $i] :
( ( ( in @ SV1059 @ SV807 )
= $false )
| ( ( SV1059 = SV1072 )
= $false )
| ( ( in @ ( ordered_pair @ SV1059 @ SV1072 ) @ SV868 )
= $true )
| ( ( SV868
= ( identity_relation @ SV807 ) )
= $false )
| ( ( relation @ SV868 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5951]) ).
thf(5999,plain,
! [SV807: $i,SV868: $i,SV1105: $i,SV1099: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1099 @ SV1105 ) @ SV868 ) )
= $true )
| ( ( SV1099 = SV1105 )
= $true )
| ( ( SV868
= ( identity_relation @ SV807 ) )
= $false )
| ( ( relation @ SV868 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5952]) ).
thf(6000,plain,
! [SV807: $i,SV868: $i,SV1111: $i,SV1100: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1100 @ SV1111 ) @ SV868 ) )
= $true )
| ( ( in @ SV1100 @ SV807 )
= $true )
| ( ( SV868
= ( identity_relation @ SV807 ) )
= $false )
| ( ( relation @ SV868 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5953]) ).
thf(6001,plain,
! [SV681: $i,SV948: $i,SV980: $i] :
( ( ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV681 )
= $false )
| ( ( in @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ SV948 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 ) )
= $true )
| ( ( SV980
= ( relation_dom_restriction @ SV681 @ SV948 ) )
= $true )
| ( ( relation @ SV980 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5954]) ).
thf(6002,plain,
! [SV681: $i,SV948: $i,SV980: $i] :
( ( ( in @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ SV948 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 )
= $true )
| ( ( SV980
= ( relation_dom_restriction @ SV681 @ SV948 ) )
= $true )
| ( ( relation @ SV980 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5955]) ).
thf(6003,plain,
! [SV681: $i,SV948: $i,SV980: $i] :
( ( ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV681 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 )
= $true )
| ( ( SV980
= ( relation_dom_restriction @ SV681 @ SV948 ) )
= $true )
| ( ( relation @ SV980 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5956]) ).
thf(6004,plain,
! [SV981: $i,SV681: $i,SV1106: $i,SV949: $i,SV1101: $i] :
( ( ( ~ ( in @ SV1101 @ SV949 )
| ~ ( in @ ( ordered_pair @ SV1101 @ SV1106 ) @ SV681 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV1101 @ SV1106 ) @ SV981 )
= $true )
| ( ( SV981
= ( relation_dom_restriction @ SV681 @ SV949 ) )
= $false )
| ( ( relation @ SV981 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5957]) ).
thf(6005,plain,
! [SV681: $i,SV949: $i,SV981: $i] :
( ( ( ! [SY1627: $i] :
( ! [SY1628: $i] :
~ ( in @ ( ordered_pair @ SY1627 @ SY1628 ) @ SV981 )
| ( in @ SY1627 @ SV949 ) ) )
= $true )
| ( ( SV981
= ( relation_dom_restriction @ SV681 @ SV949 ) )
= $false )
| ( ( relation @ SV981 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5958]) ).
thf(6006,plain,
! [SV949: $i,SV681: $i,SV981: $i] :
( ( ( ! [SY1629: $i,SY1630: $i] :
( ~ ( in @ ( ordered_pair @ SY1629 @ SY1630 ) @ SV981 )
| ( in @ ( ordered_pair @ SY1629 @ SY1630 ) @ SV681 ) ) )
= $true )
| ( ( SV981
= ( relation_dom_restriction @ SV681 @ SV949 ) )
= $false )
| ( ( relation @ SV981 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5959]) ).
thf(6007,plain,
! [SV953: $i,SV684: $i,SV1102: $i,SV1091: $i] :
( ( ( in @ ( ordered_pair @ SV1091 @ SV1102 ) @ SV684 )
= $false )
| ( ( in @ ( ordered_pair @ SV1091 @ SV1102 ) @ SV953 )
= $true )
| ( ( SV684 = SV953 )
= $false )
| ( ( relation @ SV953 )
= $false )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5960]) ).
thf(6008,plain,
! [SV684: $i,SV953: $i,SV1103: $i,SV1092: $i] :
( ( ( in @ ( ordered_pair @ SV1092 @ SV1103 ) @ SV953 )
= $false )
| ( ( in @ ( ordered_pair @ SV1092 @ SV1103 ) @ SV684 )
= $true )
| ( ( SV684 = SV953 )
= $false )
| ( ( relation @ SV953 )
= $false )
| ( ( relation @ SV684 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5961]) ).
thf(6009,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5963]) ).
thf(6010,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5963]) ).
thf(6011,plain,
! [SV653: $i,SV1061: $i] :
( ( ( ( SV1061
!= ( function_inverse @ SV653 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY1663: $i,SY1664: $i] :
( ( SY1664
!= ( apply @ SV1061 @ SY1663 ) )
| ~ ( in @ SY1663 @ ( relation_rng @ SV653 ) )
| ( SY1663
= ( apply @ SV653 @ SY1664 ) ) )
| ~ ! [SY1665: $i,SY1666: $i] :
( ( SY1666
!= ( apply @ SV1061 @ SY1665 ) )
| ~ ( in @ SY1665 @ ( relation_rng @ SV653 ) )
| ( in @ SY1666 @ ( relation_dom @ SV653 ) ) ) )
| ~ ~ ( ~ ! [SY1667: $i,SY1668: $i] :
( ( SY1667
!= ( apply @ SV653 @ SY1668 ) )
| ~ ( in @ SY1668 @ ( relation_dom @ SV653 ) )
| ( SY1668
= ( apply @ SV1061 @ SY1667 ) ) )
| ~ ! [SY1148: $i] :
( ! [SY1149: $i] :
( ( SY1148
!= ( apply @ SV653 @ SY1149 ) )
| ~ ( in @ SY1149 @ ( relation_dom @ SV653 ) ) )
| ( in @ SY1148 @ ( relation_rng @ SV653 ) ) ) ) ) )
= $true )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5964]) ).
thf(6012,plain,
! [SV653: $i,SV1062: $i] :
( ( ( ( SV1062
!= ( function_inverse @ SV653 ) ) )
= $true )
| ( ( ( relation_dom @ SV1062 )
= ( relation_rng @ SV653 ) )
= $true )
| ( ( function @ SV1062 )
= $false )
| ( ( relation @ SV1062 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5965]) ).
thf(6013,plain,
! [SV655: $i,SV740: $i,SV961: $i] :
( ( ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV961 )
= $false )
| ( ( in @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) @ SV655 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK40_D @ SV961 @ SV740 @ SV655 ) @ ( sK41_SY412 @ SV961 @ SV740 @ SV655 ) ) @ SV740 )
= $false )
| ( ( SV961
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $true )
| ( ( relation @ SV961 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5966]) ).
thf(6014,plain,
! [SV962: $i,SV740: $i,SV1094: $i,SV655: $i,SV1104: $i] :
( ( ( ~ ( in @ SV1104 @ SV655 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV1094 @ SV1104 ) @ SV740 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV1094 @ SV1104 ) @ SV962 )
= $true )
| ( ( SV962
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $false )
| ( ( relation @ SV962 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5969]) ).
thf(6015,plain,
! [SV740: $i,SV655: $i,SV962: $i,SV1112: $i] :
( ( ( ! [SY1686: $i] :
( ~ ( in @ ( ordered_pair @ SV1112 @ SY1686 ) @ SV962 )
| ( in @ SY1686 @ SV655 ) ) )
= $true )
| ( ( SV962
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $false )
| ( ( relation @ SV962 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5970]) ).
thf(6016,plain,
! [SV655: $i,SV740: $i,SV962: $i,SV1113: $i] :
( ( ( ! [SY1687: $i] :
( ~ ( in @ ( ordered_pair @ SV1113 @ SY1687 ) @ SV962 )
| ( in @ ( ordered_pair @ SV1113 @ SY1687 ) @ SV740 ) ) )
= $true )
| ( ( SV962
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $false )
| ( ( relation @ SV962 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5971]) ).
thf(6017,plain,
! [SV965: $i,SV657: $i,SV1064: $i,SV923: $i,SV1095: $i] :
( ( ( in @ SV1095 @ SV923 )
= $false )
| ( ( in @ ( ordered_pair @ SV1064 @ SV1095 ) @ SV657 )
= $false )
| ( ( in @ SV1064 @ SV965 )
= $true )
| ( ( SV965
= ( relation_inverse_image @ SV657 @ SV923 ) )
= $false )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5973]) ).
thf(6018,plain,
! [SV657: $i,SV923: $i,SV965: $i,SV1065: $i] :
( ( ( in @ ( ordered_pair @ SV1065 @ ( sK34_E @ SV1065 @ SV965 @ SV923 @ SV657 ) ) @ SV657 )
= $true )
| ( ( in @ SV1065 @ SV965 )
= $false )
| ( ( SV965
= ( relation_inverse_image @ SV657 @ SV923 ) )
= $false )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5974]) ).
thf(6019,plain,
! [SV657: $i,SV923: $i,SV965: $i,SV1065: $i] :
( ( ( in @ ( sK34_E @ SV1065 @ SV965 @ SV923 @ SV657 ) @ SV923 )
= $true )
| ( ( in @ SV1065 @ SV965 )
= $false )
| ( ( SV965
= ( relation_inverse_image @ SV657 @ SV923 ) )
= $false )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5975]) ).
thf(6020,plain,
! [SV967: $i,SV658: $i,SV1067: $i,SV925: $i,SV1096: $i] :
( ( ( in @ SV1096 @ SV925 )
= $false )
| ( ( in @ ( ordered_pair @ SV1096 @ SV1067 ) @ SV658 )
= $false )
| ( ( in @ SV1067 @ SV967 )
= $true )
| ( ( SV967
= ( relation_image @ SV658 @ SV925 ) )
= $false )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5977]) ).
thf(6021,plain,
! [SV658: $i,SV925: $i,SV967: $i,SV1068: $i] :
( ( ( in @ ( ordered_pair @ ( sK37_E @ SV1068 @ SV967 @ SV925 @ SV658 ) @ SV1068 ) @ SV658 )
= $true )
| ( ( in @ SV1068 @ SV967 )
= $false )
| ( ( SV967
= ( relation_image @ SV658 @ SV925 ) )
= $false )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5978]) ).
thf(6022,plain,
! [SV658: $i,SV925: $i,SV967: $i,SV1068: $i] :
( ( ( in @ ( sK37_E @ SV1068 @ SV967 @ SV925 @ SV658 ) @ SV925 )
= $true )
| ( ( in @ SV1068 @ SV967 )
= $false )
| ( ( SV967
= ( relation_image @ SV658 @ SV925 ) )
= $false )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5979]) ).
thf(6023,plain,
! [SV1107: $i,SV660: $i,SV783: $i,SV1014: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ SV1107 ) @ SV660 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV1107 @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV783 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV1014 ) )
= $true )
| ( ( SV1014
= ( relation_composition @ SV660 @ SV783 ) )
= $true )
| ( ( relation @ SV1014 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5980]) ).
thf(6024,plain,
! [SV660: $i,SV783: $i,SV1014: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK10_SY395 @ SV1014 @ SV783 @ SV660 ) ) @ SV660 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV1014 )
= $true )
| ( ( SV1014
= ( relation_composition @ SV660 @ SV783 ) )
= $true )
| ( ( relation @ SV1014 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5981]) ).
thf(6025,plain,
! [SV660: $i,SV783: $i,SV1014: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK10_SY395 @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV783 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV1014 )
= $true )
| ( ( SV1014
= ( relation_composition @ SV660 @ SV783 ) )
= $true )
| ( ( relation @ SV1014 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5981]) ).
thf(6026,plain,
! [SV1015: $i,SV783: $i,SV1114: $i,SV660: $i,SV1108: $i] :
( ( ( ! [SY1688: $i] :
( ~ ( in @ ( ordered_pair @ SV1108 @ SY1688 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1688 @ SV1114 ) @ SV783 ) )
| ( in @ ( ordered_pair @ SV1108 @ SV1114 ) @ SV1015 ) )
= $true )
| ( ( SV1015
= ( relation_composition @ SV660 @ SV783 ) )
= $false )
| ( ( relation @ SV1015 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5982]) ).
thf(6027,plain,
! [SV660: $i,SV783: $i,SV1015: $i,SV1115: $i,SV1109: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1109 @ SV1115 ) @ SV1015 )
| ~ ( ~ ( in @ ( ordered_pair @ SV1109 @ ( sK7_F @ SV1115 @ SV1109 @ SV1015 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SV1115 @ SV1109 @ SV1015 @ SV783 @ SV660 ) @ SV1115 ) @ SV783 ) ) )
= $true )
| ( ( SV1015
= ( relation_composition @ SV660 @ SV783 ) )
= $false )
| ( ( relation @ SV1015 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5983]) ).
thf(6028,plain,
! [SV742: $i,SV1052: $i,SV666: $i] :
( ( ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SV1052 @ SV742 ) ) )
= $false )
| ( ( in @ SV666 @ ( relation_dom @ SV1052 ) )
= $true )
| ( ( function @ SV1052 )
= $false )
| ( ( relation @ SV1052 )
= $false )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5986]) ).
thf(6029,plain,
! [SV742: $i,SV1053: $i,SV666: $i] :
( ( ( in @ SV666 @ ( relation_dom @ ( relation_composition @ SV1053 @ SV742 ) ) )
= $false )
| ( ( in @ ( apply @ SV1053 @ SV666 ) @ ( relation_dom @ SV742 ) )
= $true )
| ( ( function @ SV1053 )
= $false )
| ( ( relation @ SV1053 )
= $false )
| ( ( function @ SV742 )
= $false )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5987]) ).
thf(6030,plain,
! [SV937: $i,SV1000: $i] :
( ( ( in @ ( sK32_C @ SV1000 @ SV937 ) @ SV1000 )
= $false )
| ( ( in @ ( sK32_C @ SV1000 @ SV937 ) @ ( sK33_SY406 @ SV1000 @ SV937 ) )
= $false )
| ( ( SV1000
= ( set_meet @ SV937 ) )
= $true )
| ( ( SV937 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5989]) ).
thf(6031,plain,
! [SV938: $i,SV1001: $i,SV1083: $i] :
( ( ( in @ ( sK31_D @ SV1083 @ SV1001 @ SV938 ) @ SV938 )
= $true )
| ( ( in @ SV1083 @ SV1001 )
= $true )
| ( ( SV1001
= ( set_meet @ SV938 ) )
= $false )
| ( ( SV938 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5990]) ).
thf(6032,plain,
! [SV938: $i,SV1001: $i,SV1083: $i] :
( ( ( ~ ( in @ SV1083 @ ( sK31_D @ SV1083 @ SV1001 @ SV938 ) ) )
= $true )
| ( ( in @ SV1083 @ SV1001 )
= $true )
| ( ( SV1001
= ( set_meet @ SV938 ) )
= $false )
| ( ( SV938 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5991]) ).
thf(6033,plain,
! [SV1001: $i,SV1084: $i,SV938: $i,SV1110: $i] :
( ( ( ~ ( in @ SV1110 @ SV938 ) )
= $true )
| ( ( in @ SV1084 @ SV1110 )
= $true )
| ( ( in @ SV1084 @ SV1001 )
= $false )
| ( ( SV1001
= ( set_meet @ SV938 ) )
= $false )
| ( ( SV938 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5992]) ).
thf(6034,plain,
! [SV1043: $i,SV1054: $i,SV670: $i,SV850: $i,SV899: $i] :
( ( ( in @ ( sK23_D @ SV899 @ SV850 @ SV670 ) @ SV899 )
= $false )
| ( ( in @ SV1054 @ SV850 )
= $false )
| ( ( in @ SV1043 @ SV670 )
= $false )
| ( ( ( sK23_D @ SV899 @ SV850 @ SV670 )
= ( ordered_pair @ SV1043 @ SV1054 ) )
= $false )
| ( ( SV899
= ( cartesian_product2 @ SV670 @ SV850 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5993]) ).
thf(6035,plain,
! [SV900: $i,SV1044: $i,SV670: $i,SV1071: $i,SV851: $i,SV1085: $i] :
( ( ( in @ SV1085 @ SV851 )
= $false )
| ( ( in @ SV1071 @ SV670 )
= $false )
| ( ( ( SV1044
!= ( ordered_pair @ SV1071 @ SV1085 ) ) )
= $true )
| ( ( in @ SV1044 @ SV900 )
= $true )
| ( ( SV900
= ( cartesian_product2 @ SV670 @ SV851 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5994]) ).
thf(6036,plain,
! [SV670: $i,SV851: $i,SV900: $i,SV1045: $i] :
( ( ( ~ ( in @ ( sK21_E @ SV1045 @ SV900 @ SV851 @ SV670 ) @ SV670 ) )
= $false )
| ( ( in @ SV1045 @ SV900 )
= $false )
| ( ( SV900
= ( cartesian_product2 @ SV670 @ SV851 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5995]) ).
thf(6037,plain,
! [SV670: $i,SV851: $i,SV900: $i,SV1045: $i] :
( ( ( ~ ( in @ ( sK22_SY400 @ SV1045 @ SV900 @ SV851 @ SV670 ) @ SV851 ) )
= $false )
| ( ( in @ SV1045 @ SV900 )
= $false )
| ( ( SV900
= ( cartesian_product2 @ SV670 @ SV851 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5995]) ).
thf(6038,plain,
! [SV807: $i,SV868: $i,SV1105: $i,SV1099: $i] :
( ( ( in @ ( ordered_pair @ SV1099 @ SV1105 ) @ SV868 )
= $false )
| ( ( SV1099 = SV1105 )
= $true )
| ( ( SV868
= ( identity_relation @ SV807 ) )
= $false )
| ( ( relation @ SV868 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5999]) ).
thf(6039,plain,
! [SV807: $i,SV868: $i,SV1111: $i,SV1100: $i] :
( ( ( in @ ( ordered_pair @ SV1100 @ SV1111 ) @ SV868 )
= $false )
| ( ( in @ SV1100 @ SV807 )
= $true )
| ( ( SV868
= ( identity_relation @ SV807 ) )
= $false )
| ( ( relation @ SV868 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6000]) ).
thf(6040,plain,
! [SV681: $i,SV948: $i,SV980: $i] :
( ( ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV980 )
= $false )
| ( ( in @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ SV948 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_D @ SV980 @ SV948 @ SV681 ) @ ( sK43_SY413 @ SV980 @ SV948 @ SV681 ) ) @ SV681 )
= $false )
| ( ( SV980
= ( relation_dom_restriction @ SV681 @ SV948 ) )
= $true )
| ( ( relation @ SV980 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6001]) ).
thf(6041,plain,
! [SV981: $i,SV681: $i,SV1106: $i,SV949: $i,SV1101: $i] :
( ( ( ~ ( in @ SV1101 @ SV949 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV1101 @ SV1106 ) @ SV681 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV1101 @ SV1106 ) @ SV981 )
= $true )
| ( ( SV981
= ( relation_dom_restriction @ SV681 @ SV949 ) )
= $false )
| ( ( relation @ SV981 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6004]) ).
thf(6042,plain,
! [SV681: $i,SV949: $i,SV981: $i,SV1116: $i] :
( ( ( ! [SY1689: $i] :
~ ( in @ ( ordered_pair @ SV1116 @ SY1689 ) @ SV981 )
| ( in @ SV1116 @ SV949 ) )
= $true )
| ( ( SV981
= ( relation_dom_restriction @ SV681 @ SV949 ) )
= $false )
| ( ( relation @ SV981 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6005]) ).
thf(6043,plain,
! [SV949: $i,SV681: $i,SV981: $i,SV1117: $i] :
( ( ( ! [SY1690: $i] :
( ~ ( in @ ( ordered_pair @ SV1117 @ SY1690 ) @ SV981 )
| ( in @ ( ordered_pair @ SV1117 @ SY1690 ) @ SV681 ) ) )
= $true )
| ( ( SV981
= ( relation_dom_restriction @ SV681 @ SV949 ) )
= $false )
| ( ( relation @ SV981 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6006]) ).
thf(6044,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6009]) ).
thf(6045,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6010]) ).
thf(6046,plain,
! [SV653: $i,SV1061: $i] :
( ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY1663: $i,SY1664: $i] :
( ( SY1664
!= ( apply @ SV1061 @ SY1663 ) )
| ~ ( in @ SY1663 @ ( relation_rng @ SV653 ) )
| ( SY1663
= ( apply @ SV653 @ SY1664 ) ) )
| ~ ! [SY1665: $i,SY1666: $i] :
( ( SY1666
!= ( apply @ SV1061 @ SY1665 ) )
| ~ ( in @ SY1665 @ ( relation_rng @ SV653 ) )
| ( in @ SY1666 @ ( relation_dom @ SV653 ) ) ) )
| ~ ~ ( ~ ! [SY1667: $i,SY1668: $i] :
( ( SY1667
!= ( apply @ SV653 @ SY1668 ) )
| ~ ( in @ SY1668 @ ( relation_dom @ SV653 ) )
| ( SY1668
= ( apply @ SV1061 @ SY1667 ) ) )
| ~ ! [SY1148: $i] :
( ! [SY1149: $i] :
( ( SY1148
!= ( apply @ SV653 @ SY1149 ) )
| ~ ( in @ SY1149 @ ( relation_dom @ SV653 ) ) )
| ( in @ SY1148 @ ( relation_rng @ SV653 ) ) ) ) ) )
= $true )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6011]) ).
thf(6047,plain,
! [SV653: $i,SV1062: $i] :
( ( ( SV1062
= ( function_inverse @ SV653 ) )
= $false )
| ( ( ( relation_dom @ SV1062 )
= ( relation_rng @ SV653 ) )
= $true )
| ( ( function @ SV1062 )
= $false )
| ( ( relation @ SV1062 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6012]) ).
thf(6048,plain,
! [SV962: $i,SV740: $i,SV1094: $i,SV655: $i,SV1104: $i] :
( ( ( in @ SV1104 @ SV655 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV1094 @ SV1104 ) @ SV740 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV1094 @ SV1104 ) @ SV962 )
= $true )
| ( ( SV962
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $false )
| ( ( relation @ SV962 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6014]) ).
thf(6049,plain,
! [SV740: $i,SV655: $i,SV962: $i,SV1118: $i,SV1112: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1112 @ SV1118 ) @ SV962 )
| ( in @ SV1118 @ SV655 ) )
= $true )
| ( ( SV962
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $false )
| ( ( relation @ SV962 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6015]) ).
thf(6050,plain,
! [SV655: $i,SV740: $i,SV962: $i,SV1119: $i,SV1113: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1113 @ SV1119 ) @ SV962 )
| ( in @ ( ordered_pair @ SV1113 @ SV1119 ) @ SV740 ) )
= $true )
| ( ( SV962
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $false )
| ( ( relation @ SV962 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6016]) ).
thf(6051,plain,
! [SV1107: $i,SV660: $i,SV783: $i,SV1014: $i] :
( ( ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ SV1107 ) @ SV660 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV1107 @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV783 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV1014 ) )
= $true )
| ( ( SV1014
= ( relation_composition @ SV660 @ SV783 ) )
= $true )
| ( ( relation @ SV1014 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6023]) ).
thf(6052,plain,
! [SV660: $i,SV783: $i,SV1014: $i] :
( ( ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK10_SY395 @ SV1014 @ SV783 @ SV660 ) ) @ SV660 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV1014 )
= $true )
| ( ( SV1014
= ( relation_composition @ SV660 @ SV783 ) )
= $true )
| ( ( relation @ SV1014 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6024]) ).
thf(6053,plain,
! [SV660: $i,SV783: $i,SV1014: $i] :
( ( ( in @ ( ordered_pair @ ( sK10_SY395 @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV783 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV1014 )
= $true )
| ( ( SV1014
= ( relation_composition @ SV660 @ SV783 ) )
= $true )
| ( ( relation @ SV1014 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6025]) ).
thf(6054,plain,
! [SV1015: $i,SV783: $i,SV1114: $i,SV660: $i,SV1108: $i] :
( ( ( ! [SY1688: $i] :
( ~ ( in @ ( ordered_pair @ SV1108 @ SY1688 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SY1688 @ SV1114 ) @ SV783 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV1108 @ SV1114 ) @ SV1015 )
= $true )
| ( ( SV1015
= ( relation_composition @ SV660 @ SV783 ) )
= $false )
| ( ( relation @ SV1015 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6026]) ).
thf(6055,plain,
! [SV660: $i,SV783: $i,SV1015: $i,SV1115: $i,SV1109: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1109 @ SV1115 ) @ SV1015 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV1109 @ ( sK7_F @ SV1115 @ SV1109 @ SV1015 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SV1115 @ SV1109 @ SV1015 @ SV783 @ SV660 ) @ SV1115 ) @ SV783 ) ) )
= $true )
| ( ( SV1015
= ( relation_composition @ SV660 @ SV783 ) )
= $false )
| ( ( relation @ SV1015 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6027]) ).
thf(6056,plain,
! [SV938: $i,SV1001: $i,SV1083: $i] :
( ( ( in @ SV1083 @ ( sK31_D @ SV1083 @ SV1001 @ SV938 ) )
= $false )
| ( ( in @ SV1083 @ SV1001 )
= $true )
| ( ( SV1001
= ( set_meet @ SV938 ) )
= $false )
| ( ( SV938 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6032]) ).
thf(6057,plain,
! [SV1001: $i,SV1084: $i,SV938: $i,SV1110: $i] :
( ( ( in @ SV1110 @ SV938 )
= $false )
| ( ( in @ SV1084 @ SV1110 )
= $true )
| ( ( in @ SV1084 @ SV1001 )
= $false )
| ( ( SV1001
= ( set_meet @ SV938 ) )
= $false )
| ( ( SV938 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6033]) ).
thf(6058,plain,
! [SV900: $i,SV851: $i,SV670: $i,SV1085: $i,SV1071: $i,SV1044: $i] :
( ( ( SV1044
= ( ordered_pair @ SV1071 @ SV1085 ) )
= $false )
| ( ( in @ SV1071 @ SV670 )
= $false )
| ( ( in @ SV1085 @ SV851 )
= $false )
| ( ( in @ SV1044 @ SV900 )
= $true )
| ( ( SV900
= ( cartesian_product2 @ SV670 @ SV851 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6035]) ).
thf(6059,plain,
! [SV670: $i,SV851: $i,SV900: $i,SV1045: $i] :
( ( ( in @ ( sK21_E @ SV1045 @ SV900 @ SV851 @ SV670 ) @ SV670 )
= $true )
| ( ( in @ SV1045 @ SV900 )
= $false )
| ( ( SV900
= ( cartesian_product2 @ SV670 @ SV851 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6036]) ).
thf(6060,plain,
! [SV670: $i,SV851: $i,SV900: $i,SV1045: $i] :
( ( ( in @ ( sK22_SY400 @ SV1045 @ SV900 @ SV851 @ SV670 ) @ SV851 )
= $true )
| ( ( in @ SV1045 @ SV900 )
= $false )
| ( ( SV900
= ( cartesian_product2 @ SV670 @ SV851 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6037]) ).
thf(6061,plain,
! [SV981: $i,SV681: $i,SV1106: $i,SV949: $i,SV1101: $i] :
( ( ( in @ SV1101 @ SV949 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV1101 @ SV1106 ) @ SV681 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV1101 @ SV1106 ) @ SV981 )
= $true )
| ( ( SV981
= ( relation_dom_restriction @ SV681 @ SV949 ) )
= $false )
| ( ( relation @ SV981 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6041]) ).
thf(6062,plain,
! [SV681: $i,SV949: $i,SV981: $i,SV1116: $i] :
( ( ( ! [SY1689: $i] :
~ ( in @ ( ordered_pair @ SV1116 @ SY1689 ) @ SV981 ) )
= $true )
| ( ( in @ SV1116 @ SV949 )
= $true )
| ( ( SV981
= ( relation_dom_restriction @ SV681 @ SV949 ) )
= $false )
| ( ( relation @ SV981 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6042]) ).
thf(6063,plain,
! [SV949: $i,SV681: $i,SV981: $i,SV1120: $i,SV1117: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1117 @ SV1120 ) @ SV981 )
| ( in @ ( ordered_pair @ SV1117 @ SV1120 ) @ SV681 ) )
= $true )
| ( ( SV981
= ( relation_dom_restriction @ SV681 @ SV949 ) )
= $false )
| ( ( relation @ SV981 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6043]) ).
thf(6064,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6044]) ).
thf(6065,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6045]) ).
thf(6066,plain,
! [SV653: $i,SV1061: $i] :
( ( ( ~ ~ ( ~ ! [SY1663: $i,SY1664: $i] :
( ( SY1664
!= ( apply @ SV1061 @ SY1663 ) )
| ~ ( in @ SY1663 @ ( relation_rng @ SV653 ) )
| ( SY1663
= ( apply @ SV653 @ SY1664 ) ) )
| ~ ! [SY1665: $i,SY1666: $i] :
( ( SY1666
!= ( apply @ SV1061 @ SY1665 ) )
| ~ ( in @ SY1665 @ ( relation_rng @ SV653 ) )
| ( in @ SY1666 @ ( relation_dom @ SV653 ) ) ) )
| ~ ~ ( ~ ! [SY1667: $i,SY1668: $i] :
( ( SY1667
!= ( apply @ SV653 @ SY1668 ) )
| ~ ( in @ SY1668 @ ( relation_dom @ SV653 ) )
| ( SY1668
= ( apply @ SV1061 @ SY1667 ) ) )
| ~ ! [SY1148: $i] :
( ! [SY1149: $i] :
( ( SY1148
!= ( apply @ SV653 @ SY1149 ) )
| ~ ( in @ SY1149 @ ( relation_dom @ SV653 ) ) )
| ( in @ SY1148 @ ( relation_rng @ SV653 ) ) ) ) )
= $false )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6046]) ).
thf(6067,plain,
! [SV962: $i,SV655: $i,SV740: $i,SV1104: $i,SV1094: $i] :
( ( ( in @ ( ordered_pair @ SV1094 @ SV1104 ) @ SV740 )
= $false )
| ( ( in @ SV1104 @ SV655 )
= $false )
| ( ( in @ ( ordered_pair @ SV1094 @ SV1104 ) @ SV962 )
= $true )
| ( ( SV962
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $false )
| ( ( relation @ SV962 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6048]) ).
thf(6068,plain,
! [SV740: $i,SV655: $i,SV962: $i,SV1118: $i,SV1112: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1112 @ SV1118 ) @ SV962 ) )
= $true )
| ( ( in @ SV1118 @ SV655 )
= $true )
| ( ( SV962
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $false )
| ( ( relation @ SV962 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6049]) ).
thf(6069,plain,
! [SV655: $i,SV740: $i,SV962: $i,SV1119: $i,SV1113: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1113 @ SV1119 ) @ SV962 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV1113 @ SV1119 ) @ SV740 )
= $true )
| ( ( SV962
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $false )
| ( ( relation @ SV962 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6050]) ).
thf(6070,plain,
! [SV660: $i,SV783: $i,SV1014: $i,SV1107: $i] :
( ( ( in @ ( ordered_pair @ SV1107 @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV783 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ SV1107 ) @ SV660 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV1014 ) )
= $true )
| ( ( SV1014
= ( relation_composition @ SV660 @ SV783 ) )
= $true )
| ( ( relation @ SV1014 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6051]) ).
thf(6071,plain,
! [SV1015: $i,SV783: $i,SV1114: $i,SV660: $i,SV1121: $i,SV1108: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1108 @ SV1121 ) @ SV660 )
| ~ ( in @ ( ordered_pair @ SV1121 @ SV1114 ) @ SV783 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV1108 @ SV1114 ) @ SV1015 )
= $true )
| ( ( SV1015
= ( relation_composition @ SV660 @ SV783 ) )
= $false )
| ( ( relation @ SV1015 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6054]) ).
thf(6072,plain,
! [SV660: $i,SV783: $i,SV1015: $i,SV1115: $i,SV1109: $i] :
( ( ( in @ ( ordered_pair @ SV1109 @ SV1115 ) @ SV1015 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV1109 @ ( sK7_F @ SV1115 @ SV1109 @ SV1015 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SV1115 @ SV1109 @ SV1015 @ SV783 @ SV660 ) @ SV1115 ) @ SV783 ) ) )
= $true )
| ( ( SV1015
= ( relation_composition @ SV660 @ SV783 ) )
= $false )
| ( ( relation @ SV1015 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6055]) ).
thf(6073,plain,
! [SV981: $i,SV949: $i,SV681: $i,SV1106: $i,SV1101: $i] :
( ( ( in @ ( ordered_pair @ SV1101 @ SV1106 ) @ SV681 )
= $false )
| ( ( in @ SV1101 @ SV949 )
= $false )
| ( ( in @ ( ordered_pair @ SV1101 @ SV1106 ) @ SV981 )
= $true )
| ( ( SV981
= ( relation_dom_restriction @ SV681 @ SV949 ) )
= $false )
| ( ( relation @ SV981 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6061]) ).
thf(6074,plain,
! [SV681: $i,SV949: $i,SV981: $i,SV1122: $i,SV1116: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1116 @ SV1122 ) @ SV981 ) )
= $true )
| ( ( in @ SV1116 @ SV949 )
= $true )
| ( ( SV981
= ( relation_dom_restriction @ SV681 @ SV949 ) )
= $false )
| ( ( relation @ SV981 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6062]) ).
thf(6075,plain,
! [SV949: $i,SV681: $i,SV981: $i,SV1120: $i,SV1117: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1117 @ SV1120 ) @ SV981 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV1117 @ SV1120 ) @ SV681 )
= $true )
| ( ( SV981
= ( relation_dom_restriction @ SV681 @ SV949 ) )
= $false )
| ( ( relation @ SV981 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6063]) ).
thf(6076,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6064]) ).
thf(6077,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6064]) ).
thf(6078,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6065]) ).
thf(6079,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6065]) ).
thf(6080,plain,
! [SV653: $i,SV1061: $i] :
( ( ( ~ ~ ( ~ ! [SY1663: $i,SY1664: $i] :
( ( SY1664
!= ( apply @ SV1061 @ SY1663 ) )
| ~ ( in @ SY1663 @ ( relation_rng @ SV653 ) )
| ( SY1663
= ( apply @ SV653 @ SY1664 ) ) )
| ~ ! [SY1665: $i,SY1666: $i] :
( ( SY1666
!= ( apply @ SV1061 @ SY1665 ) )
| ~ ( in @ SY1665 @ ( relation_rng @ SV653 ) )
| ( in @ SY1666 @ ( relation_dom @ SV653 ) ) ) ) )
= $false )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6066]) ).
thf(6081,plain,
! [SV1061: $i,SV653: $i] :
( ( ( ~ ~ ( ~ ! [SY1667: $i,SY1668: $i] :
( ( SY1667
!= ( apply @ SV653 @ SY1668 ) )
| ~ ( in @ SY1668 @ ( relation_dom @ SV653 ) )
| ( SY1668
= ( apply @ SV1061 @ SY1667 ) ) )
| ~ ! [SY1148: $i] :
( ! [SY1149: $i] :
( ( SY1148
!= ( apply @ SV653 @ SY1149 ) )
| ~ ( in @ SY1149 @ ( relation_dom @ SV653 ) ) )
| ( in @ SY1148 @ ( relation_rng @ SV653 ) ) ) ) )
= $false )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6066]) ).
thf(6082,plain,
! [SV740: $i,SV655: $i,SV962: $i,SV1118: $i,SV1112: $i] :
( ( ( in @ ( ordered_pair @ SV1112 @ SV1118 ) @ SV962 )
= $false )
| ( ( in @ SV1118 @ SV655 )
= $true )
| ( ( SV962
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $false )
| ( ( relation @ SV962 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6068]) ).
thf(6083,plain,
! [SV655: $i,SV740: $i,SV962: $i,SV1119: $i,SV1113: $i] :
( ( ( in @ ( ordered_pair @ SV1113 @ SV1119 ) @ SV962 )
= $false )
| ( ( in @ ( ordered_pair @ SV1113 @ SV1119 ) @ SV740 )
= $true )
| ( ( SV962
= ( relation_rng_restriction @ SV655 @ SV740 ) )
= $false )
| ( ( relation @ SV962 )
= $false )
| ( ( relation @ SV740 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6069]) ).
thf(6084,plain,
! [SV1107: $i,SV660: $i,SV783: $i,SV1014: $i] :
( ( ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV1014 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_D @ SV1014 @ SV783 @ SV660 ) @ SV1107 ) @ SV660 )
= $false )
| ( ( in @ ( ordered_pair @ SV1107 @ ( sK9_SY391 @ SV1014 @ SV783 @ SV660 ) ) @ SV783 )
= $false )
| ( ( SV1014
= ( relation_composition @ SV660 @ SV783 ) )
= $true )
| ( ( relation @ SV1014 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6070]) ).
thf(6085,plain,
! [SV1015: $i,SV783: $i,SV1114: $i,SV660: $i,SV1121: $i,SV1108: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1108 @ SV1121 ) @ SV660 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV1121 @ SV1114 ) @ SV783 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV1108 @ SV1114 ) @ SV1015 )
= $true )
| ( ( SV1015
= ( relation_composition @ SV660 @ SV783 ) )
= $false )
| ( ( relation @ SV1015 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6071]) ).
thf(6086,plain,
! [SV660: $i,SV783: $i,SV1015: $i,SV1115: $i,SV1109: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1109 @ ( sK7_F @ SV1115 @ SV1109 @ SV1015 @ SV783 @ SV660 ) ) @ SV660 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SV1115 @ SV1109 @ SV1015 @ SV783 @ SV660 ) @ SV1115 ) @ SV783 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV1109 @ SV1115 ) @ SV1015 )
= $false )
| ( ( SV1015
= ( relation_composition @ SV660 @ SV783 ) )
= $false )
| ( ( relation @ SV1015 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6072]) ).
thf(6087,plain,
! [SV681: $i,SV949: $i,SV981: $i,SV1122: $i,SV1116: $i] :
( ( ( in @ ( ordered_pair @ SV1116 @ SV1122 ) @ SV981 )
= $false )
| ( ( in @ SV1116 @ SV949 )
= $true )
| ( ( SV981
= ( relation_dom_restriction @ SV681 @ SV949 ) )
= $false )
| ( ( relation @ SV981 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6074]) ).
thf(6088,plain,
! [SV949: $i,SV681: $i,SV981: $i,SV1120: $i,SV1117: $i] :
( ( ( in @ ( ordered_pair @ SV1117 @ SV1120 ) @ SV981 )
= $false )
| ( ( in @ ( ordered_pair @ SV1117 @ SV1120 ) @ SV681 )
= $true )
| ( ( SV981
= ( relation_dom_restriction @ SV681 @ SV949 ) )
= $false )
| ( ( relation @ SV981 )
= $false )
| ( ( relation @ SV681 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6075]) ).
thf(6089,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6076]) ).
thf(6090,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6077]) ).
thf(6091,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ( ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6078]) ).
thf(6092,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6079]) ).
thf(6093,plain,
! [SV653: $i,SV1061: $i] :
( ( ( ~ ( ~ ! [SY1663: $i,SY1664: $i] :
( ( SY1664
!= ( apply @ SV1061 @ SY1663 ) )
| ~ ( in @ SY1663 @ ( relation_rng @ SV653 ) )
| ( SY1663
= ( apply @ SV653 @ SY1664 ) ) )
| ~ ! [SY1665: $i,SY1666: $i] :
( ( SY1666
!= ( apply @ SV1061 @ SY1665 ) )
| ~ ( in @ SY1665 @ ( relation_rng @ SV653 ) )
| ( in @ SY1666 @ ( relation_dom @ SV653 ) ) ) ) )
= $true )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6080]) ).
thf(6094,plain,
! [SV1061: $i,SV653: $i] :
( ( ( ~ ( ~ ! [SY1667: $i,SY1668: $i] :
( ( SY1667
!= ( apply @ SV653 @ SY1668 ) )
| ~ ( in @ SY1668 @ ( relation_dom @ SV653 ) )
| ( SY1668
= ( apply @ SV1061 @ SY1667 ) ) )
| ~ ! [SY1148: $i] :
( ! [SY1149: $i] :
( ( SY1148
!= ( apply @ SV653 @ SY1149 ) )
| ~ ( in @ SY1149 @ ( relation_dom @ SV653 ) ) )
| ( in @ SY1148 @ ( relation_rng @ SV653 ) ) ) ) )
= $true )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6081]) ).
thf(6095,plain,
! [SV1015: $i,SV783: $i,SV1114: $i,SV660: $i,SV1121: $i,SV1108: $i] :
( ( ( in @ ( ordered_pair @ SV1108 @ SV1121 ) @ SV660 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV1121 @ SV1114 ) @ SV783 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV1108 @ SV1114 ) @ SV1015 )
= $true )
| ( ( SV1015
= ( relation_composition @ SV660 @ SV783 ) )
= $false )
| ( ( relation @ SV1015 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6085]) ).
thf(6096,plain,
! [SV660: $i,SV783: $i,SV1015: $i,SV1115: $i,SV1109: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV1109 @ ( sK7_F @ SV1115 @ SV1109 @ SV1015 @ SV783 @ SV660 ) ) @ SV660 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV1109 @ SV1115 ) @ SV1015 )
= $false )
| ( ( SV1015
= ( relation_composition @ SV660 @ SV783 ) )
= $false )
| ( ( relation @ SV1015 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6086]) ).
thf(6097,plain,
! [SV660: $i,SV783: $i,SV1015: $i,SV1109: $i,SV1115: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK7_F @ SV1115 @ SV1109 @ SV1015 @ SV783 @ SV660 ) @ SV1115 ) @ SV783 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV1109 @ SV1115 ) @ SV1015 )
= $false )
| ( ( SV1015
= ( relation_composition @ SV660 @ SV783 ) )
= $false )
| ( ( relation @ SV1015 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6086]) ).
thf(6098,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6089]) ).
thf(6099,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6090]) ).
thf(6100,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6091]) ).
thf(6101,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) )
= $true )
| ( ( ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6092]) ).
thf(6102,plain,
! [SV653: $i,SV1061: $i] :
( ( ( ~ ! [SY1663: $i,SY1664: $i] :
( ( SY1664
!= ( apply @ SV1061 @ SY1663 ) )
| ~ ( in @ SY1663 @ ( relation_rng @ SV653 ) )
| ( SY1663
= ( apply @ SV653 @ SY1664 ) ) )
| ~ ! [SY1665: $i,SY1666: $i] :
( ( SY1666
!= ( apply @ SV1061 @ SY1665 ) )
| ~ ( in @ SY1665 @ ( relation_rng @ SV653 ) )
| ( in @ SY1666 @ ( relation_dom @ SV653 ) ) ) )
= $false )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6093]) ).
thf(6103,plain,
! [SV1061: $i,SV653: $i] :
( ( ( ~ ! [SY1667: $i,SY1668: $i] :
( ( SY1667
!= ( apply @ SV653 @ SY1668 ) )
| ~ ( in @ SY1668 @ ( relation_dom @ SV653 ) )
| ( SY1668
= ( apply @ SV1061 @ SY1667 ) ) )
| ~ ! [SY1148: $i] :
( ! [SY1149: $i] :
( ( SY1148
!= ( apply @ SV653 @ SY1149 ) )
| ~ ( in @ SY1149 @ ( relation_dom @ SV653 ) ) )
| ( in @ SY1148 @ ( relation_rng @ SV653 ) ) ) )
= $false )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6094]) ).
thf(6104,plain,
! [SV1015: $i,SV660: $i,SV1108: $i,SV783: $i,SV1114: $i,SV1121: $i] :
( ( ( in @ ( ordered_pair @ SV1121 @ SV1114 ) @ SV783 )
= $false )
| ( ( in @ ( ordered_pair @ SV1108 @ SV1121 ) @ SV660 )
= $false )
| ( ( in @ ( ordered_pair @ SV1108 @ SV1114 ) @ SV1015 )
= $true )
| ( ( SV1015
= ( relation_composition @ SV660 @ SV783 ) )
= $false )
| ( ( relation @ SV1015 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6095]) ).
thf(6105,plain,
! [SV660: $i,SV783: $i,SV1015: $i,SV1115: $i,SV1109: $i] :
( ( ( in @ ( ordered_pair @ SV1109 @ ( sK7_F @ SV1115 @ SV1109 @ SV1015 @ SV783 @ SV660 ) ) @ SV660 )
= $true )
| ( ( in @ ( ordered_pair @ SV1109 @ SV1115 ) @ SV1015 )
= $false )
| ( ( SV1015
= ( relation_composition @ SV660 @ SV783 ) )
= $false )
| ( ( relation @ SV1015 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6096]) ).
thf(6106,plain,
! [SV660: $i,SV783: $i,SV1015: $i,SV1109: $i,SV1115: $i] :
( ( ( in @ ( ordered_pair @ ( sK7_F @ SV1115 @ SV1109 @ SV1015 @ SV783 @ SV660 ) @ SV1115 ) @ SV783 )
= $true )
| ( ( in @ ( ordered_pair @ SV1109 @ SV1115 ) @ SV1015 )
= $false )
| ( ( SV1015
= ( relation_composition @ SV660 @ SV783 ) )
= $false )
| ( ( relation @ SV1015 )
= $false )
| ( ( relation @ SV783 )
= $false )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6097]) ).
thf(6107,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6098]) ).
thf(6108,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6098]) ).
thf(6109,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6099]) ).
thf(6110,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6099]) ).
thf(6111,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6100]) ).
thf(6112,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6100]) ).
thf(6113,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) )
= $true )
| ( ( ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6101]) ).
thf(6114,plain,
! [SV653: $i,SV1061: $i] :
( ( ( ~ ! [SY1663: $i,SY1664: $i] :
( ( SY1664
!= ( apply @ SV1061 @ SY1663 ) )
| ~ ( in @ SY1663 @ ( relation_rng @ SV653 ) )
| ( SY1663
= ( apply @ SV653 @ SY1664 ) ) ) )
= $false )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6102]) ).
thf(6115,plain,
! [SV653: $i,SV1061: $i] :
( ( ( ~ ! [SY1665: $i,SY1666: $i] :
( ( SY1666
!= ( apply @ SV1061 @ SY1665 ) )
| ~ ( in @ SY1665 @ ( relation_rng @ SV653 ) )
| ( in @ SY1666 @ ( relation_dom @ SV653 ) ) ) )
= $false )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6102]) ).
thf(6116,plain,
! [SV1061: $i,SV653: $i] :
( ( ( ~ ! [SY1667: $i,SY1668: $i] :
( ( SY1667
!= ( apply @ SV653 @ SY1668 ) )
| ~ ( in @ SY1668 @ ( relation_dom @ SV653 ) )
| ( SY1668
= ( apply @ SV1061 @ SY1667 ) ) ) )
= $false )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6103]) ).
thf(6117,plain,
! [SV1061: $i,SV653: $i] :
( ( ( ~ ! [SY1148: $i] :
( ! [SY1149: $i] :
( ( SY1148
!= ( apply @ SV653 @ SY1149 ) )
| ~ ( in @ SY1149 @ ( relation_dom @ SV653 ) ) )
| ( in @ SY1148 @ ( relation_rng @ SV653 ) ) ) )
= $false )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6103]) ).
thf(6118,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ( ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6107]) ).
thf(6119,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6108]) ).
thf(6120,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6109]) ).
thf(6121,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6110]) ).
thf(6122,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6111]) ).
thf(6123,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6112]) ).
thf(6124,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
= $false )
| ( ( ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) )
= $true )
| ( ( ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6113]) ).
thf(6125,plain,
! [SV653: $i,SV1061: $i] :
( ( ( ! [SY1663: $i,SY1664: $i] :
( ( SY1664
!= ( apply @ SV1061 @ SY1663 ) )
| ~ ( in @ SY1663 @ ( relation_rng @ SV653 ) )
| ( SY1663
= ( apply @ SV653 @ SY1664 ) ) ) )
= $true )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6114]) ).
thf(6126,plain,
! [SV653: $i,SV1061: $i] :
( ( ( ! [SY1665: $i,SY1666: $i] :
( ( SY1666
!= ( apply @ SV1061 @ SY1665 ) )
| ~ ( in @ SY1665 @ ( relation_rng @ SV653 ) )
| ( in @ SY1666 @ ( relation_dom @ SV653 ) ) ) )
= $true )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6115]) ).
thf(6127,plain,
! [SV1061: $i,SV653: $i] :
( ( ( ! [SY1667: $i,SY1668: $i] :
( ( SY1667
!= ( apply @ SV653 @ SY1668 ) )
| ~ ( in @ SY1668 @ ( relation_dom @ SV653 ) )
| ( SY1668
= ( apply @ SV1061 @ SY1667 ) ) ) )
= $true )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6116]) ).
thf(6128,plain,
! [SV1061: $i,SV653: $i] :
( ( ( ! [SY1148: $i] :
( ! [SY1149: $i] :
( ( SY1148
!= ( apply @ SV653 @ SY1149 ) )
| ~ ( in @ SY1149 @ ( relation_dom @ SV653 ) ) )
| ( in @ SY1148 @ ( relation_rng @ SV653 ) ) ) )
= $true )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6117]) ).
thf(6129,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6118]) ).
thf(6130,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
= $true )
| ( ( ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6119]) ).
thf(6131,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6120]) ).
thf(6132,plain,
! [SV653: $i,SV1024: $i] :
( ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
= $true )
| ( ( ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6121]) ).
thf(6133,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) )
= $true )
| ( ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6122]) ).
thf(6134,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) )
= $true )
| ( ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6123]) ).
thf(6135,plain,
! [SV653: $i,SV1024: $i] :
( ( ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
= $false )
| ( ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
= $false )
| ( ( ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6124]) ).
thf(6136,plain,
! [SV653: $i,SV1123: $i,SV1061: $i] :
( ( ( ! [SY1691: $i] :
( ( SY1691
!= ( apply @ SV1061 @ SV1123 ) )
| ~ ( in @ SV1123 @ ( relation_rng @ SV653 ) )
| ( SV1123
= ( apply @ SV653 @ SY1691 ) ) ) )
= $true )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6125]) ).
thf(6137,plain,
! [SV653: $i,SV1124: $i,SV1061: $i] :
( ( ( ! [SY1692: $i] :
( ( SY1692
!= ( apply @ SV1061 @ SV1124 ) )
| ~ ( in @ SV1124 @ ( relation_rng @ SV653 ) )
| ( in @ SY1692 @ ( relation_dom @ SV653 ) ) ) )
= $true )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6126]) ).
thf(6138,plain,
! [SV1061: $i,SV653: $i,SV1125: $i] :
( ( ( ! [SY1693: $i] :
( ( SV1125
!= ( apply @ SV653 @ SY1693 ) )
| ~ ( in @ SY1693 @ ( relation_dom @ SV653 ) )
| ( SY1693
= ( apply @ SV1061 @ SV1125 ) ) ) )
= $true )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6127]) ).
thf(6139,plain,
! [SV1061: $i,SV653: $i,SV1126: $i] :
( ( ( ! [SY1694: $i] :
( ( SV1126
!= ( apply @ SV653 @ SY1694 ) )
| ~ ( in @ SY1694 @ ( relation_dom @ SV653 ) ) )
| ( in @ SV1126 @ ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6128]) ).
thf(6140,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6129]) ).
thf(6141,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6129]) ).
thf(6142,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) )
= $true )
| ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6130]) ).
thf(6143,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6131]) ).
thf(6144,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ~ ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6131]) ).
thf(6145,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) )
= $true )
| ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6132]) ).
thf(6146,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) )
= $true )
| ( ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6133]) ).
thf(6147,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( ( sK70_C @ SV1024 @ SV653 )
!= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) )
= $true )
| ( ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6134]) ).
thf(6148,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( ( sK71_SY424 @ SV1024 @ SV653 )
!= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) )
= $true )
| ( ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
= $false )
| ( ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
= $false )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6135]) ).
thf(6149,plain,
! [SV653: $i,SV1123: $i,SV1061: $i,SV1127: $i] :
( ( ( ( SV1127
!= ( apply @ SV1061 @ SV1123 ) )
| ~ ( in @ SV1123 @ ( relation_rng @ SV653 ) )
| ( SV1123
= ( apply @ SV653 @ SV1127 ) ) )
= $true )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6136]) ).
thf(6150,plain,
! [SV653: $i,SV1124: $i,SV1061: $i,SV1128: $i] :
( ( ( ( SV1128
!= ( apply @ SV1061 @ SV1124 ) )
| ~ ( in @ SV1124 @ ( relation_rng @ SV653 ) )
| ( in @ SV1128 @ ( relation_dom @ SV653 ) ) )
= $true )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6137]) ).
thf(6151,plain,
! [SV1061: $i,SV1129: $i,SV653: $i,SV1125: $i] :
( ( ( ( SV1125
!= ( apply @ SV653 @ SV1129 ) )
| ~ ( in @ SV1129 @ ( relation_dom @ SV653 ) )
| ( SV1129
= ( apply @ SV1061 @ SV1125 ) ) )
= $true )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6138]) ).
thf(6152,plain,
! [SV1061: $i,SV653: $i,SV1126: $i] :
( ( ( ! [SY1694: $i] :
( ( SV1126
!= ( apply @ SV653 @ SY1694 ) )
| ~ ( in @ SY1694 @ ( relation_dom @ SV653 ) ) ) )
= $true )
| ( ( in @ SV1126 @ ( relation_rng @ SV653 ) )
= $true )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6139]) ).
thf(6153,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6140]) ).
thf(6154,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6141]) ).
thf(6155,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
= $false )
| ( ( ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) )
= $true )
| ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6142]) ).
thf(6156,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6143]) ).
thf(6157,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
| ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6144]) ).
thf(6158,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
= $false )
| ( ( ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) )
= $true )
| ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6145]) ).
thf(6159,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
= $false )
| ( ( ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) )
= $true )
| ( ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6146]) ).
thf(6160,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
= $false )
| ( ( ~ ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) ) )
= $true )
| ( ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6147]) ).
thf(6161,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
= $false )
| ( ( ~ ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) ) )
= $true )
| ( ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
= $false )
| ( ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
= $false )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6148]) ).
thf(6162,plain,
! [SV653: $i,SV1123: $i,SV1061: $i,SV1127: $i] :
( ( ( ( SV1127
!= ( apply @ SV1061 @ SV1123 ) )
| ~ ( in @ SV1123 @ ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1123
= ( apply @ SV653 @ SV1127 ) )
= $true )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6149]) ).
thf(6163,plain,
! [SV653: $i,SV1124: $i,SV1061: $i,SV1128: $i] :
( ( ( ( SV1128
!= ( apply @ SV1061 @ SV1124 ) )
| ~ ( in @ SV1124 @ ( relation_rng @ SV653 ) ) )
= $true )
| ( ( in @ SV1128 @ ( relation_dom @ SV653 ) )
= $true )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6150]) ).
thf(6164,plain,
! [SV1061: $i,SV1129: $i,SV653: $i,SV1125: $i] :
( ( ( ( SV1125
!= ( apply @ SV653 @ SV1129 ) )
| ~ ( in @ SV1129 @ ( relation_dom @ SV653 ) ) )
= $true )
| ( ( SV1129
= ( apply @ SV1061 @ SV1125 ) )
= $true )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6151]) ).
thf(6165,plain,
! [SV1061: $i,SV1130: $i,SV653: $i,SV1126: $i] :
( ( ( ( SV1126
!= ( apply @ SV653 @ SV1130 ) )
| ~ ( in @ SV1130 @ ( relation_dom @ SV653 ) ) )
= $true )
| ( ( in @ SV1126 @ ( relation_rng @ SV653 ) )
= $true )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6152]) ).
thf(6166,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
= $true )
| ( ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6153]) ).
thf(6167,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
= $true )
| ( ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6154]) ).
thf(6168,plain,
! [SV653: $i,SV1024: $i] :
( ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
= $false )
| ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
= $false )
| ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6155]) ).
thf(6169,plain,
! [SV653: $i,SV1024: $i] :
( ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
= $true )
| ( ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6156]) ).
thf(6170,plain,
! [SV653: $i,SV1024: $i] :
( ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
= $true )
| ( ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6157]) ).
thf(6171,plain,
! [SV653: $i,SV1024: $i] :
( ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
= $false )
| ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
= $false )
| ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6158]) ).
thf(6172,plain,
! [SV653: $i,SV1024: $i] :
( ( ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
= $false )
| ( ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
= $false )
| ( ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6159]) ).
thf(6173,plain,
! [SV653: $i,SV1024: $i] :
( ( ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
= $false )
| ( ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
= $false )
| ( ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
= $true )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6160]) ).
thf(6174,plain,
! [SV653: $i,SV1024: $i] :
( ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
= $false )
| ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
= $false )
| ( ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
= $false )
| ( ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
= $false )
| ( ( ( ( relation_dom @ SV1024 )
!= ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6161]) ).
thf(6175,plain,
! [SV653: $i,SV1123: $i,SV1061: $i,SV1127: $i] :
( ( ( ( SV1127
!= ( apply @ SV1061 @ SV1123 ) ) )
= $true )
| ( ( ~ ( in @ SV1123 @ ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1123
= ( apply @ SV653 @ SV1127 ) )
= $true )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6162]) ).
thf(6176,plain,
! [SV653: $i,SV1124: $i,SV1061: $i,SV1128: $i] :
( ( ( ( SV1128
!= ( apply @ SV1061 @ SV1124 ) ) )
= $true )
| ( ( ~ ( in @ SV1124 @ ( relation_rng @ SV653 ) ) )
= $true )
| ( ( in @ SV1128 @ ( relation_dom @ SV653 ) )
= $true )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6163]) ).
thf(6177,plain,
! [SV1061: $i,SV1129: $i,SV653: $i,SV1125: $i] :
( ( ( ( SV1125
!= ( apply @ SV653 @ SV1129 ) ) )
= $true )
| ( ( ~ ( in @ SV1129 @ ( relation_dom @ SV653 ) ) )
= $true )
| ( ( SV1129
= ( apply @ SV1061 @ SV1125 ) )
= $true )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6164]) ).
thf(6178,plain,
! [SV1061: $i,SV1130: $i,SV653: $i,SV1126: $i] :
( ( ( ( SV1126
!= ( apply @ SV653 @ SV1130 ) ) )
= $true )
| ( ( ~ ( in @ SV1130 @ ( relation_dom @ SV653 ) ) )
= $true )
| ( ( in @ SV1126 @ ( relation_rng @ SV653 ) )
= $true )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6165]) ).
thf(6179,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( relation_dom @ SV1024 )
= ( relation_rng @ SV653 ) )
= $false )
| ( ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
= $true )
| ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6166]) ).
thf(6180,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( relation_dom @ SV1024 )
= ( relation_rng @ SV653 ) )
= $false )
| ( ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
= $true )
| ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6167]) ).
thf(6181,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( relation_dom @ SV1024 )
= ( relation_rng @ SV653 ) )
= $false )
| ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
= $true )
| ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
= $false )
| ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
= $false )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6168]) ).
thf(6182,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( relation_dom @ SV1024 )
= ( relation_rng @ SV653 ) )
= $false )
| ( ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
= $true )
| ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6169]) ).
thf(6183,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( relation_dom @ SV1024 )
= ( relation_rng @ SV653 ) )
= $false )
| ( ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
= $true )
| ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
= $true )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6170]) ).
thf(6184,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( relation_dom @ SV1024 )
= ( relation_rng @ SV653 ) )
= $false )
| ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
= $true )
| ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
= $false )
| ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
= $false )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6171]) ).
thf(6185,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( relation_dom @ SV1024 )
= ( relation_rng @ SV653 ) )
= $false )
| ( ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
= $true )
| ( ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
= $false )
| ( ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
= $false )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6172]) ).
thf(6186,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( relation_dom @ SV1024 )
= ( relation_rng @ SV653 ) )
= $false )
| ( ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
= $true )
| ( ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
= $false )
| ( ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
= $false )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6173]) ).
thf(6187,plain,
! [SV653: $i,SV1024: $i] :
( ( ( ( relation_dom @ SV1024 )
= ( relation_rng @ SV653 ) )
= $false )
| ( ( in @ ( sK71_SY424 @ SV1024 @ SV653 ) @ ( relation_dom @ SV653 ) )
= $false )
| ( ( ( sK70_C @ SV1024 @ SV653 )
= ( apply @ SV653 @ ( sK71_SY424 @ SV1024 @ SV653 ) ) )
= $false )
| ( ( ( sK71_SY424 @ SV1024 @ SV653 )
= ( apply @ SV1024 @ ( sK70_C @ SV1024 @ SV653 ) ) )
= $false )
| ( ( in @ ( sK70_C @ SV1024 @ SV653 ) @ ( relation_rng @ SV653 ) )
= $false )
| ( ( SV1024
= ( function_inverse @ SV653 ) )
= $true )
| ( ( function @ SV1024 )
= $false )
| ( ( relation @ SV1024 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6174]) ).
thf(6188,plain,
! [SV653: $i,SV1123: $i,SV1061: $i,SV1127: $i] :
( ( ( SV1127
= ( apply @ SV1061 @ SV1123 ) )
= $false )
| ( ( ~ ( in @ SV1123 @ ( relation_rng @ SV653 ) ) )
= $true )
| ( ( SV1123
= ( apply @ SV653 @ SV1127 ) )
= $true )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6175]) ).
thf(6189,plain,
! [SV653: $i,SV1124: $i,SV1061: $i,SV1128: $i] :
( ( ( SV1128
= ( apply @ SV1061 @ SV1124 ) )
= $false )
| ( ( ~ ( in @ SV1124 @ ( relation_rng @ SV653 ) ) )
= $true )
| ( ( in @ SV1128 @ ( relation_dom @ SV653 ) )
= $true )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6176]) ).
thf(6190,plain,
! [SV1061: $i,SV1129: $i,SV653: $i,SV1125: $i] :
( ( ( SV1125
= ( apply @ SV653 @ SV1129 ) )
= $false )
| ( ( ~ ( in @ SV1129 @ ( relation_dom @ SV653 ) ) )
= $true )
| ( ( SV1129
= ( apply @ SV1061 @ SV1125 ) )
= $true )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6177]) ).
thf(6191,plain,
! [SV1061: $i,SV1130: $i,SV653: $i,SV1126: $i] :
( ( ( SV1126
= ( apply @ SV653 @ SV1130 ) )
= $false )
| ( ( ~ ( in @ SV1130 @ ( relation_dom @ SV653 ) ) )
= $true )
| ( ( in @ SV1126 @ ( relation_rng @ SV653 ) )
= $true )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6178]) ).
thf(6192,plain,
! [SV1061: $i,SV1127: $i,SV653: $i,SV1123: $i] :
( ( ( in @ SV1123 @ ( relation_rng @ SV653 ) )
= $false )
| ( ( SV1127
= ( apply @ SV1061 @ SV1123 ) )
= $false )
| ( ( SV1123
= ( apply @ SV653 @ SV1127 ) )
= $true )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6188]) ).
thf(6193,plain,
! [SV1061: $i,SV1128: $i,SV653: $i,SV1124: $i] :
( ( ( in @ SV1124 @ ( relation_rng @ SV653 ) )
= $false )
| ( ( SV1128
= ( apply @ SV1061 @ SV1124 ) )
= $false )
| ( ( in @ SV1128 @ ( relation_dom @ SV653 ) )
= $true )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6189]) ).
thf(6194,plain,
! [SV1061: $i,SV1125: $i,SV653: $i,SV1129: $i] :
( ( ( in @ SV1129 @ ( relation_dom @ SV653 ) )
= $false )
| ( ( SV1125
= ( apply @ SV653 @ SV1129 ) )
= $false )
| ( ( SV1129
= ( apply @ SV1061 @ SV1125 ) )
= $true )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6190]) ).
thf(6195,plain,
! [SV1061: $i,SV1126: $i,SV653: $i,SV1130: $i] :
( ( ( in @ SV1130 @ ( relation_dom @ SV653 ) )
= $false )
| ( ( SV1126
= ( apply @ SV653 @ SV1130 ) )
= $false )
| ( ( in @ SV1126 @ ( relation_rng @ SV653 ) )
= $true )
| ( ( SV1061
= ( function_inverse @ SV653 ) )
= $false )
| ( ( function @ SV1061 )
= $false )
| ( ( relation @ SV1061 )
= $false )
| ( ( one_to_one @ SV653 )
= $false )
| ( ( function @ SV653 )
= $false )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6191]) ).
thf(6196,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[3520,6195,6194,6193,6192,6187,6186,6185,6184,6183,6182,6181,6180,6179,6106,6105,6104,6088,6087,6084,6083,6082,6073,6067,6060,6059,6058,6057,6056,6053,6052,6047,6040,6039,6038,6034,6031,6030,6029,6028,6022,6021,6020,6019,6018,6017,6013,6008,6007,6003,6002,5998,5997,5996,5988,5985,5984,5976,5972,5968,5967,5962,5950,5949,5946,5943,5942,5938,5935,5934,5930,5929,5927,5907,5906,5904,5903,5902,5899,5898,5897,5888,5887,5886,5885,5884,5881,5880,5877,5863,5862,5861,5860,5856,5855,5850,5843,5842,5838,5837,5825,5822,5814,5806,5805,5803,5801,5797,5794,5788,5787,5776,5771,5767,5760,5759,5758,5756,5732,5731,5723,5696,5692,5689,5671,5662,5661,5643,5642,5635,5634,5628,5627,5625,5619,5616,5615,5601,5600,5572,5571,5570,5562,5557,5556,5555,5554,5542,5541,5527,5517,5516,5510,5498,5489,5482,5481,5478,5475,5474,5463,5462,5456,5451,5435,5425,5406,5405,5383,5382,5360,5353,5332,5305,5304,5303,5300,5286,5285,5276,5275,5271,5270,5267,5265,5264,5263,5252,5245,5244,5226,5225,5224,5223,5175,5173,5170,5159,5158,5143,5131,5125,5124,5103,5102,5069,5068,5044,5039,5038,5031,5030,5005,5004,5001,4992,4969,4968,4966,4965,4915,4908,4899,4885,4879,4878,4873,4872,4871,4870,4867,4866,4827,4810,4809,4747,4746,4745,4744,4740,4739,4729,4728,4725,4724,4721,4718,4710,4709,4689,4688,4666,4637,4636,4618,4617,4616,4615,4587,4586,4574,4573,4567,4558,4557,4556,4552,4551,4549,4448,4402,4401,4400,4399,4396,4395,4394,4387,4386,4375,4273,4272,4262,4261,4254,4244,4242,4241,4239,4238,4236,4233,4232,4231,4230,4228,4221,4219,4218,4213,4212,4209,4208,4207,4201,4199,4198,4196,4195,4194,4193,4186,4176,4175,4168,4164,4163,4135,4134,4100,4099,4066,4064,4059,4058,4053,4048,4046,4035,4021,4013,4011,4010,4009,4001,3997,3858,3856,3855,3854,3849,3844,3841,3839,3838,3829,3823,3712,3708,3707,3705,3703,3702,3701,3700,3699,3671,3650,3545,3544,3543,3529]) ).
thf(6197,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[6196,3375]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU219+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 19 20:30:18 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.44 ......
% 0.19/0.51
% 0.19/0.51 No.of.Axioms: 230
% 0.19/0.51
% 0.19/0.51 Length.of.Defs: 0
% 0.19/0.51
% 0.19/0.51 Contains.Choice.Funs: false
% 0.37/0.57 ..............
% 0.46/0.64 (rf:2,axioms:167,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:232,loop_count:0,foatp_calls:0,translation:fof_full).......................................................................................................................................................................................................................................................................................................................................................................................................................................................
% 3.31/3.71
% 3.31/3.71 ********************************
% 3.31/3.71 * All subproblems solved! *
% 3.31/3.71 ********************************
% 3.31/3.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:170,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:6196,loop_count:0,foatp_calls:1,translation:fof_full)
% 16.18/16.40
% 16.18/16.40 %**** Beginning of derivation protocol ****
% 16.18/16.40 % SZS output start CNFRefutation
% See solution above
% 16.18/16.43
% 16.18/16.43 %**** End of derivation protocol ****
% 16.18/16.43 %**** no. of clauses in derivation: 6134 ****
% 16.18/16.43 %**** clause counter: 6196 ****
% 16.18/16.43
% 16.18/16.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:170,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:6196,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------