%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET764+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:41:00 AM UTC 2026
% Result : Theorem 7.17s 1.48s
% Output : CNFRefutation 7.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 29
% Syntax : Number of formulae : 1240 ( 317 unt; 0 typ; 0 def)
% Number of atoms : 13868 (3488 equ; 0 cnn)
% Maximal formula atoms : 11 ( 11 avg)
% Number of connectives : 42748 (9849 ~;5804 |; 150 &;26795 @)
% ( 90 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 80 ( 77 usr; 6 con; 0-8 aty)
% Number of variables : 6911 ( 0 ^;6884 !; 27 ?;6911 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_apply,type,
apply: $i > $i > $i > $o ).
thf(tp_compose_function,type,
compose_function: $i > $i > $i > $i > $i > $i ).
thf(tp_compose_predicate,type,
compose_predicate: $i > $i > $i > $i > $i > $i > $o ).
thf(tp_decreasing,type,
decreasing: $i > $i > $i > $i > $i > $o ).
thf(tp_difference,type,
difference: $i > $i > $i ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_equal_maps,type,
equal_maps: $i > $i > $i > $i > $o ).
thf(tp_equal_set,type,
equal_set: $i > $i > $o ).
thf(tp_identity,type,
identity: $i > $i > $o ).
thf(tp_image2,type,
image2: $i > $i > $i ).
thf(tp_image3,type,
image3: $i > $i > $i > $i ).
thf(tp_increasing,type,
increasing: $i > $i > $i > $i > $i > $o ).
thf(tp_injective,type,
injective: $i > $i > $i > $o ).
thf(tp_intersection,type,
intersection: $i > $i > $i ).
thf(tp_inverse_function,type,
inverse_function: $i > $i > $i > $i ).
thf(tp_inverse_image2,type,
inverse_image2: $i > $i > $i ).
thf(tp_inverse_image3,type,
inverse_image3: $i > $i > $i > $i ).
thf(tp_inverse_predicate,type,
inverse_predicate: $i > $i > $i > $i > $o ).
thf(tp_isomorphism,type,
isomorphism: $i > $i > $i > $i > $i > $o ).
thf(tp_maps,type,
maps: $i > $i > $i > $o ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_one_to_one,type,
one_to_one: $i > $i > $i > $o ).
thf(tp_power_set,type,
power_set: $i > $i ).
thf(tp_product,type,
product: $i > $i ).
thf(tp_sK10_SY443,type,
sK10_SY443: $i > $i > $i > $i ).
thf(tp_sK11_SY529,type,
sK11_SY529: $i > $i > $i > $i > $i ).
thf(tp_sK12_SY480,type,
sK12_SY480: $i > $i > $i > $i ).
thf(tp_sK13_SY606,type,
sK13_SY606: $i > $i > $i > $i ).
thf(tp_sK14_SY549,type,
sK14_SY549: $i > $i > $i > $i > $i ).
thf(tp_sK15_SY556,type,
sK15_SY556: $i > $i > $i > $i > $i > $i ).
thf(tp_sK16_SY572,type,
sK16_SY572: $i > $i > $i > $i > $i > $i ).
thf(tp_sK17_SY609,type,
sK17_SY609: $i > $i > $i > $i > $i ).
thf(tp_sK18_SY611,type,
sK18_SY611: $i > $i > $i > $i ).
thf(tp_sK19_SY614,type,
sK19_SY614: $i > $i > $i > $i > $i ).
thf(tp_sK1_F,type,
sK1_F: $i ).
thf(tp_sK20_SY619,type,
sK20_SY619: $i > $i > $i > $i > $i > $i ).
thf(tp_sK21_SY625,type,
sK21_SY625: $i > $i > $i > $i > $i > $i ).
thf(tp_sK22_SY458,type,
sK22_SY458: $i > $i > $i > $i ).
thf(tp_sK23_SY593,type,
sK23_SY593: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK24_SY629,type,
sK24_SY629: $i > $i > $i > $i > $i ).
thf(tp_sK25_SY602,type,
sK25_SY602: $i > $i > $i > $i > $i ).
thf(tp_sK26_SY632,type,
sK26_SY632: $i > $i > $i > $i > $i > $i ).
thf(tp_sK27_SY636,type,
sK27_SY636: $i > $i > $i > $i > $i > $i ).
thf(tp_sK28_SY645,type,
sK28_SY645: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK29_SY496,type,
sK29_SY496: $i > $i > $i > $i > $i ).
thf(tp_sK2_SY136,type,
sK2_SY136: $i ).
thf(tp_sK30_SY649,type,
sK30_SY649: $i > $i > $i > $i > $i > $i ).
thf(tp_sK31_SY651,type,
sK31_SY651: $i > $i > $i > $i > $i > $i ).
thf(tp_sK32_SY525,type,
sK32_SY525: $i > $i > $i > $i > $i ).
thf(tp_sK33_SY638,type,
sK33_SY638: $i > $i > $i > $i > $i ).
thf(tp_sK34_SY460,type,
sK34_SY460: $i > $i > $i > $i ).
thf(tp_sK35_SY663,type,
sK35_SY663: $i > $i > $i > $i ).
thf(tp_sK36_SY665,type,
sK36_SY665: $i > $i > $i > $i ).
thf(tp_sK37_SY564,type,
sK37_SY564: $i > $i > $i > $i > $i > $i ).
thf(tp_sK38_SY666,type,
sK38_SY666: $i > $i > $i > $i > $i > $i ).
thf(tp_sK39_SY600,type,
sK39_SY600: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK3_SY138,type,
sK3_SY138: $i ).
thf(tp_sK40_SY669,type,
sK40_SY669: $i > $i > $i > $i > $i > $i ).
thf(tp_sK41_SY671,type,
sK41_SY671: $i > $i > $i > $i > $i > $i ).
thf(tp_sK42_SY460,type,
sK42_SY460: $i > $i > $i > $i > $i ).
thf(tp_sK43_SY672,type,
sK43_SY672: $i > $i > $i > $i > $i ).
thf(tp_sK44_SY674,type,
sK44_SY674: $i > $i > $i > $i > $i ).
thf(tp_sK45_SY656,type,
sK45_SY656: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK46_SY653,type,
sK46_SY653: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK47_SY656,type,
sK47_SY656: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK4_SY298,type,
sK4_SY298: $i > $i > $i ).
thf(tp_sK5_SY351,type,
sK5_SY351: $i > $i > $i ).
thf(tp_sK6_SY365,type,
sK6_SY365: $i > $i > $i ).
thf(tp_sK7_SY411,type,
sK7_SY411: $i > $i > $i > $i ).
thf(tp_sK8_SY333,type,
sK8_SY333: $i > $i > $i ).
thf(tp_sK9_SY485,type,
sK9_SY485: $i > $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_sum,type,
sum: $i > $i ).
thf(tp_surjective,type,
surjective: $i > $i > $i > $o ).
thf(tp_union,type,
union: $i > $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [F: $i,A: $i,R: $i,B: $i,S: $i] :
( ( isomorphism @ F @ A @ R @ B @ S )
<=> ( ( maps @ F @ A @ B )
& ( one_to_one @ F @ A @ B )
& ! [X1: $i,Y1: $i,X2: $i,Y2: $i] :
( ( ( member @ X1 @ A )
& ( member @ Y1 @ B )
& ( member @ X2 @ A )
& ( member @ Y2 @ B )
& ( apply @ F @ X1 @ Y1 )
& ( apply @ F @ X2 @ Y2 ) )
=> ( ( apply @ R @ X1 @ X2 )
<=> ( apply @ S @ Y1 @ Y2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isomorphism) ).
thf(2,axiom,
! [F: $i,A: $i,R: $i,B: $i,S: $i] :
( ( decreasing @ F @ A @ R @ B @ S )
<=> ! [X1: $i,Y1: $i,X2: $i,Y2: $i] :
( ( ( member @ X1 @ A )
& ( member @ Y1 @ B )
& ( member @ X2 @ A )
& ( member @ Y2 @ B )
& ( apply @ R @ X1 @ X2 )
& ( apply @ F @ X1 @ Y1 )
& ( apply @ F @ X2 @ Y2 ) )
=> ( apply @ S @ Y2 @ Y1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',decreasing_function) ).
thf(3,axiom,
! [F: $i,A: $i,R: $i,B: $i,S: $i] :
( ( increasing @ F @ A @ R @ B @ S )
<=> ! [X1: $i,Y1: $i,X2: $i,Y2: $i] :
( ( ( member @ X1 @ A )
& ( member @ Y1 @ B )
& ( member @ X2 @ A )
& ( member @ Y2 @ B )
& ( apply @ R @ X1 @ X2 )
& ( apply @ F @ X1 @ Y1 )
& ( apply @ F @ X2 @ Y2 ) )
=> ( apply @ S @ Y1 @ Y2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',increasing_function) ).
thf(4,axiom,
! [F: $i,B: $i,A: $i,X: $i] :
( ( member @ X @ ( inverse_image3 @ F @ B @ A ) )
<=> ( ( member @ X @ A )
& ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_image3) ).
thf(5,axiom,
! [F: $i,B: $i,X: $i] :
( ( member @ X @ ( inverse_image2 @ F @ B ) )
<=> ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_image2) ).
thf(6,axiom,
! [F: $i,A: $i,B: $i,Y: $i] :
( ( member @ Y @ ( image3 @ F @ A @ B ) )
<=> ( ( member @ Y @ B )
& ? [X: $i] :
( ( member @ X @ A )
& ( apply @ F @ X @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image3) ).
thf(7,axiom,
! [F: $i,A: $i,Y: $i] :
( ( member @ Y @ ( image2 @ F @ A ) )
<=> ? [X: $i] :
( ( member @ X @ A )
& ( apply @ F @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image2) ).
thf(8,axiom,
! [F: $i,A: $i,B: $i,X: $i,Y: $i] :
( ( ( member @ X @ A )
& ( member @ Y @ B ) )
=> ( ( apply @ F @ X @ Y )
<=> ( apply @ ( inverse_function @ F @ A @ B ) @ Y @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_function) ).
thf(9,axiom,
! [G: $i,F: $i,A: $i,B: $i] :
( ( inverse_predicate @ G @ F @ A @ B )
<=> ! [X: $i,Y: $i] :
( ( ( member @ X @ A )
& ( member @ Y @ B ) )
=> ( ( apply @ F @ X @ Y )
<=> ( apply @ G @ Y @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_predicate) ).
thf(10,axiom,
! [F: $i,A: $i,B: $i] :
( ( one_to_one @ F @ A @ B )
<=> ( ( injective @ F @ A @ B )
& ( surjective @ F @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one) ).
thf(11,axiom,
! [F: $i,A: $i,B: $i] :
( ( surjective @ F @ A @ B )
<=> ! [Y: $i] :
( ( member @ Y @ B )
=> ? [E: $i] :
( ( member @ E @ A )
& ( apply @ F @ E @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjective) ).
thf(12,axiom,
! [F: $i,A: $i,B: $i] :
( ( injective @ F @ A @ B )
<=> ! [X1: $i,X2: $i,Y: $i] :
( ( ( member @ X1 @ A )
& ( member @ X2 @ A )
& ( member @ Y @ B ) )
=> ( ( ( apply @ F @ X1 @ Y )
& ( apply @ F @ X2 @ Y ) )
=> ( X1 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',injective) ).
thf(13,axiom,
! [F: $i,A: $i] :
( ( identity @ F @ A )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( apply @ F @ X @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
thf(14,axiom,
! [F: $i,G: $i,A: $i,B: $i] :
( ( equal_maps @ F @ G @ A @ B )
<=> ! [X: $i,Y1: $i,Y2: $i] :
( ( ( member @ X @ A )
& ( member @ Y1 @ B )
& ( member @ Y2 @ B ) )
=> ( ( ( apply @ F @ X @ Y1 )
& ( apply @ G @ X @ Y2 ) )
=> ( Y1 = Y2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_maps) ).
thf(15,axiom,
! [G: $i,F: $i,A: $i,B: $i,C: $i,X: $i,Z: $i] :
( ( ( member @ X @ A )
& ( member @ Z @ C ) )
=> ( ( apply @ ( compose_function @ G @ F @ A @ B @ C ) @ X @ Z )
<=> ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y )
& ( apply @ G @ Y @ Z ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_function) ).
thf(16,axiom,
! [H: $i,G: $i,F: $i,A: $i,B: $i,C: $i] :
( ( compose_predicate @ H @ G @ F @ A @ B @ C )
<=> ! [X: $i,Z: $i] :
( ( ( member @ X @ A )
& ( member @ Z @ C ) )
=> ( ( apply @ H @ X @ Z )
<=> ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y )
& ( apply @ G @ Y @ Z ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_predicate) ).
thf(17,axiom,
! [F: $i,A: $i,B: $i] :
( ( maps @ F @ A @ B )
<=> ( ! [X: $i] :
( ( member @ X @ A )
=> ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y ) ) )
& ! [X: $i,Y1: $i,Y2: $i] :
( ( ( member @ X @ A )
& ( member @ Y1 @ B )
& ( member @ Y2 @ B ) )
=> ( ( ( apply @ F @ X @ Y1 )
& ( apply @ F @ X @ Y2 ) )
=> ( Y1 = Y2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps) ).
thf(18,axiom,
! [X: $i,A: $i] :
( ( member @ X @ ( product @ A ) )
<=> ! [Y: $i] :
( ( member @ Y @ A )
=> ( member @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product) ).
thf(19,axiom,
! [X: $i,A: $i] :
( ( member @ X @ ( sum @ A ) )
<=> ? [Y: $i] :
( ( member @ Y @ A )
& ( member @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum) ).
thf(20,axiom,
! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( unordered_pair @ A @ B ) )
<=> ( ( X = A )
| ( X = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair) ).
thf(21,axiom,
! [X: $i,A: $i] :
( ( member @ X @ ( singleton @ A ) )
<=> ( X = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
thf(22,axiom,
! [B: $i,A: $i,E: $i] :
( ( member @ B @ ( difference @ E @ A ) )
<=> ( ( member @ B @ E )
& ~ ( member @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference) ).
thf(23,axiom,
! [X: $i] :
~ ( member @ X @ empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
thf(24,axiom,
! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( union @ A @ B ) )
<=> ( ( member @ X @ A )
| ( member @ X @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
thf(25,axiom,
! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( intersection @ A @ B ) )
<=> ( ( member @ X @ A )
& ( member @ X @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection) ).
thf(26,axiom,
! [X: $i,A: $i] :
( ( member @ X @ ( power_set @ A ) )
<=> ( subset @ X @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_set) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( equal_set @ A @ B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( member @ X @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
thf(29,conjecture,
! [F: $i,A: $i,B: $i] :
( ( maps @ F @ A @ B )
=> ( equal_set @ ( inverse_image2 @ F @ empty_set ) @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIIa14) ).
thf(30,negated_conjecture,
( ( ! [F: $i,A: $i,B: $i] :
( ( maps @ F @ A @ B )
=> ( equal_set @ ( inverse_image2 @ F @ empty_set ) @ empty_set ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[29]) ).
thf(31,plain,
( ( ! [F: $i,A: $i,B: $i] :
( ( maps @ F @ A @ B )
=> ( equal_set @ ( inverse_image2 @ F @ empty_set ) @ empty_set ) ) )
= $false ),
inference(unfold_def,[status(thm)],[30]) ).
thf(32,plain,
( ( ! [F: $i,A: $i,R: $i,B: $i,S: $i] :
( ( isomorphism @ F @ A @ R @ B @ S )
<=> ( ( maps @ F @ A @ B )
& ( one_to_one @ F @ A @ B )
& ! [X1: $i,Y1: $i,X2: $i,Y2: $i] :
( ( ( member @ X1 @ A )
& ( member @ Y1 @ B )
& ( member @ X2 @ A )
& ( member @ Y2 @ B )
& ( apply @ F @ X1 @ Y1 )
& ( apply @ F @ X2 @ Y2 ) )
=> ( ( apply @ R @ X1 @ X2 )
<=> ( apply @ S @ Y1 @ Y2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(33,plain,
( ( ! [F: $i,A: $i,R: $i,B: $i,S: $i] :
( ( decreasing @ F @ A @ R @ B @ S )
<=> ! [X1: $i,Y1: $i,X2: $i,Y2: $i] :
( ( ( member @ X1 @ A )
& ( member @ Y1 @ B )
& ( member @ X2 @ A )
& ( member @ Y2 @ B )
& ( apply @ R @ X1 @ X2 )
& ( apply @ F @ X1 @ Y1 )
& ( apply @ F @ X2 @ Y2 ) )
=> ( apply @ S @ Y2 @ Y1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(34,plain,
( ( ! [F: $i,A: $i,R: $i,B: $i,S: $i] :
( ( increasing @ F @ A @ R @ B @ S )
<=> ! [X1: $i,Y1: $i,X2: $i,Y2: $i] :
( ( ( member @ X1 @ A )
& ( member @ Y1 @ B )
& ( member @ X2 @ A )
& ( member @ Y2 @ B )
& ( apply @ R @ X1 @ X2 )
& ( apply @ F @ X1 @ Y1 )
& ( apply @ F @ X2 @ Y2 ) )
=> ( apply @ S @ Y1 @ Y2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(35,plain,
( ( ! [F: $i,B: $i,A: $i,X: $i] :
( ( member @ X @ ( inverse_image3 @ F @ B @ A ) )
<=> ( ( member @ X @ A )
& ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(36,plain,
( ( ! [F: $i,B: $i,X: $i] :
( ( member @ X @ ( inverse_image2 @ F @ B ) )
<=> ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(37,plain,
( ( ! [F: $i,A: $i,B: $i,Y: $i] :
( ( member @ Y @ ( image3 @ F @ A @ B ) )
<=> ( ( member @ Y @ B )
& ? [X: $i] :
( ( member @ X @ A )
& ( apply @ F @ X @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(38,plain,
( ( ! [F: $i,A: $i,Y: $i] :
( ( member @ Y @ ( image2 @ F @ A ) )
<=> ? [X: $i] :
( ( member @ X @ A )
& ( apply @ F @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(39,plain,
( ( ! [F: $i,A: $i,B: $i,X: $i,Y: $i] :
( ( ( member @ X @ A )
& ( member @ Y @ B ) )
=> ( ( apply @ F @ X @ Y )
<=> ( apply @ ( inverse_function @ F @ A @ B ) @ Y @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(40,plain,
( ( ! [G: $i,F: $i,A: $i,B: $i] :
( ( inverse_predicate @ G @ F @ A @ B )
<=> ! [X: $i,Y: $i] :
( ( ( member @ X @ A )
& ( member @ Y @ B ) )
=> ( ( apply @ F @ X @ Y )
<=> ( apply @ G @ Y @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(41,plain,
( ( ! [F: $i,A: $i,B: $i] :
( ( one_to_one @ F @ A @ B )
<=> ( ( injective @ F @ A @ B )
& ( surjective @ F @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(42,plain,
( ( ! [F: $i,A: $i,B: $i] :
( ( surjective @ F @ A @ B )
<=> ! [Y: $i] :
( ( member @ Y @ B )
=> ? [E: $i] :
( ( member @ E @ A )
& ( apply @ F @ E @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(43,plain,
( ( ! [F: $i,A: $i,B: $i] :
( ( injective @ F @ A @ B )
<=> ! [X1: $i,X2: $i,Y: $i] :
( ( ( member @ X1 @ A )
& ( member @ X2 @ A )
& ( member @ Y @ B ) )
=> ( ( ( apply @ F @ X1 @ Y )
& ( apply @ F @ X2 @ Y ) )
=> ( X1 = X2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(44,plain,
( ( ! [F: $i,A: $i] :
( ( identity @ F @ A )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( apply @ F @ X @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(45,plain,
( ( ! [F: $i,G: $i,A: $i,B: $i] :
( ( equal_maps @ F @ G @ A @ B )
<=> ! [X: $i,Y1: $i,Y2: $i] :
( ( ( member @ X @ A )
& ( member @ Y1 @ B )
& ( member @ Y2 @ B ) )
=> ( ( ( apply @ F @ X @ Y1 )
& ( apply @ G @ X @ Y2 ) )
=> ( Y1 = Y2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(46,plain,
( ( ! [G: $i,F: $i,A: $i,B: $i,C: $i,X: $i,Z: $i] :
( ( ( member @ X @ A )
& ( member @ Z @ C ) )
=> ( ( apply @ ( compose_function @ G @ F @ A @ B @ C ) @ X @ Z )
<=> ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y )
& ( apply @ G @ Y @ Z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(47,plain,
( ( ! [H: $i,G: $i,F: $i,A: $i,B: $i,C: $i] :
( ( compose_predicate @ H @ G @ F @ A @ B @ C )
<=> ! [X: $i,Z: $i] :
( ( ( member @ X @ A )
& ( member @ Z @ C ) )
=> ( ( apply @ H @ X @ Z )
<=> ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y )
& ( apply @ G @ Y @ Z ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(48,plain,
( ( ! [F: $i,A: $i,B: $i] :
( ( maps @ F @ A @ B )
<=> ( ! [X: $i] :
( ( member @ X @ A )
=> ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y ) ) )
& ! [X: $i,Y1: $i,Y2: $i] :
( ( ( member @ X @ A )
& ( member @ Y1 @ B )
& ( member @ Y2 @ B ) )
=> ( ( ( apply @ F @ X @ Y1 )
& ( apply @ F @ X @ Y2 ) )
=> ( Y1 = Y2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(49,plain,
( ( ! [X: $i,A: $i] :
( ( member @ X @ ( product @ A ) )
<=> ! [Y: $i] :
( ( member @ Y @ A )
=> ( member @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(50,plain,
( ( ! [X: $i,A: $i] :
( ( member @ X @ ( sum @ A ) )
<=> ? [Y: $i] :
( ( member @ Y @ A )
& ( member @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(51,plain,
( ( ! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( unordered_pair @ A @ B ) )
<=> ( ( X = A )
| ( X = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(52,plain,
( ( ! [X: $i,A: $i] :
( ( member @ X @ ( singleton @ A ) )
<=> ( X = A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(53,plain,
( ( ! [B: $i,A: $i,E: $i] :
( ( member @ B @ ( difference @ E @ A ) )
<=> ( ( member @ B @ E )
& ~ ( member @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(54,plain,
( ( ! [X: $i] :
~ ( member @ X @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(55,plain,
( ( ! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( union @ A @ B ) )
<=> ( ( member @ X @ A )
| ( member @ X @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(56,plain,
( ( ! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( intersection @ A @ B ) )
<=> ( ( member @ X @ A )
& ( member @ X @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(57,plain,
( ( ! [X: $i,A: $i] :
( ( member @ X @ ( power_set @ A ) )
<=> ( subset @ X @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(58,plain,
( ( ! [A: $i,B: $i] :
( ( equal_set @ A @ B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(59,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( member @ X @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(60,plain,
( ( ! [SY136: $i,SY137: $i] :
( ( maps @ sK1_F @ SY136 @ SY137 )
=> ( equal_set @ ( inverse_image2 @ sK1_F @ empty_set ) @ empty_set ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[31]) ).
thf(61,plain,
( ( ! [SY138: $i] :
( ( maps @ sK1_F @ sK2_SY136 @ SY138 )
=> ( equal_set @ ( inverse_image2 @ sK1_F @ empty_set ) @ empty_set ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[60]) ).
thf(62,plain,
( ( ( maps @ sK1_F @ sK2_SY136 @ sK3_SY138 )
=> ( equal_set @ ( inverse_image2 @ sK1_F @ empty_set ) @ empty_set ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[61]) ).
thf(63,plain,
( ( maps @ sK1_F @ sK2_SY136 @ sK3_SY138 )
= $true ),
inference(standard_cnf,[status(thm)],[62]) ).
thf(64,plain,
( ( equal_set @ ( inverse_image2 @ sK1_F @ empty_set ) @ empty_set )
= $false ),
inference(standard_cnf,[status(thm)],[62]) ).
thf(65,plain,
( ( ~ ( equal_set @ ( inverse_image2 @ sK1_F @ empty_set ) @ empty_set ) )
= $true ),
inference(polarity_switch,[status(thm)],[64]) ).
thf(66,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( member @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(67,plain,
( ( ! [A: $i,B: $i] :
( ( equal_set @ A @ B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(68,plain,
( ( ! [X: $i,A: $i] :
( ( member @ X @ ( power_set @ A ) )
<=> ( subset @ X @ A ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(69,plain,
( ( ! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( intersection @ A @ B ) )
<=> ( ( member @ X @ A )
& ( member @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(70,plain,
( ( ! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( union @ A @ B ) )
<=> ( ( member @ X @ A )
| ( member @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(71,plain,
( ( ! [X: $i] :
~ ( member @ X @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(72,plain,
( ( ! [B: $i,A: $i,E: $i] :
( ( member @ B @ ( difference @ E @ A ) )
<=> ( ( member @ B @ E )
& ~ ( member @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(73,plain,
( ( ! [X: $i,A: $i] :
( ( member @ X @ ( singleton @ A ) )
<=> ( X = A ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(74,plain,
( ( ! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( unordered_pair @ A @ B ) )
<=> ( ( X = A )
| ( X = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(75,plain,
( ( ! [X: $i,A: $i] :
( ( member @ X @ ( sum @ A ) )
<=> ? [Y: $i] :
( ( member @ Y @ A )
& ( member @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(76,plain,
( ( ! [X: $i,A: $i] :
( ( member @ X @ ( product @ A ) )
<=> ! [Y: $i] :
( ( member @ Y @ A )
=> ( member @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(77,plain,
( ( ! [F: $i,A: $i,B: $i] :
( ( maps @ F @ A @ B )
<=> ( ! [X: $i] :
( ( member @ X @ A )
=> ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y ) ) )
& ! [X: $i,Y1: $i,Y2: $i] :
( ( ( member @ X @ A )
& ( member @ Y1 @ B )
& ( member @ Y2 @ B ) )
=> ( ( ( apply @ F @ X @ Y1 )
& ( apply @ F @ X @ Y2 ) )
=> ( Y1 = Y2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(78,plain,
( ( ! [H: $i,G: $i,F: $i,A: $i,B: $i,C: $i] :
( ( compose_predicate @ H @ G @ F @ A @ B @ C )
<=> ! [X: $i,Z: $i] :
( ( ( member @ X @ A )
& ( member @ Z @ C ) )
=> ( ( apply @ H @ X @ Z )
<=> ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y )
& ( apply @ G @ Y @ Z ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(79,plain,
( ( ! [G: $i,F: $i,A: $i,B: $i,C: $i,X: $i,Z: $i] :
( ( ( member @ X @ A )
& ( member @ Z @ C ) )
=> ( ( apply @ ( compose_function @ G @ F @ A @ B @ C ) @ X @ Z )
<=> ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y )
& ( apply @ G @ Y @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(80,plain,
( ( ! [F: $i,G: $i,A: $i,B: $i] :
( ( equal_maps @ F @ G @ A @ B )
<=> ! [X: $i,Y1: $i,Y2: $i] :
( ( ( member @ X @ A )
& ( member @ Y1 @ B )
& ( member @ Y2 @ B ) )
=> ( ( ( apply @ F @ X @ Y1 )
& ( apply @ G @ X @ Y2 ) )
=> ( Y1 = Y2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(81,plain,
( ( ! [F: $i,A: $i] :
( ( identity @ F @ A )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( apply @ F @ X @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(82,plain,
( ( ! [F: $i,A: $i,B: $i] :
( ( injective @ F @ A @ B )
<=> ! [X1: $i,X2: $i,Y: $i] :
( ( ( member @ X1 @ A )
& ( member @ X2 @ A )
& ( member @ Y @ B ) )
=> ( ( ( apply @ F @ X1 @ Y )
& ( apply @ F @ X2 @ Y ) )
=> ( X1 = X2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(83,plain,
( ( ! [F: $i,A: $i,B: $i] :
( ( surjective @ F @ A @ B )
<=> ! [Y: $i] :
( ( member @ Y @ B )
=> ? [E: $i] :
( ( member @ E @ A )
& ( apply @ F @ E @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(84,plain,
( ( ! [F: $i,A: $i,B: $i] :
( ( one_to_one @ F @ A @ B )
<=> ( ( injective @ F @ A @ B )
& ( surjective @ F @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(85,plain,
( ( ! [G: $i,F: $i,A: $i,B: $i] :
( ( inverse_predicate @ G @ F @ A @ B )
<=> ! [X: $i,Y: $i] :
( ( ( member @ X @ A )
& ( member @ Y @ B ) )
=> ( ( apply @ F @ X @ Y )
<=> ( apply @ G @ Y @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(86,plain,
( ( ! [F: $i,A: $i,B: $i,X: $i,Y: $i] :
( ( ( member @ X @ A )
& ( member @ Y @ B ) )
=> ( ( apply @ F @ X @ Y )
<=> ( apply @ ( inverse_function @ F @ A @ B ) @ Y @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(87,plain,
( ( ! [F: $i,A: $i,Y: $i] :
( ( member @ Y @ ( image2 @ F @ A ) )
<=> ? [X: $i] :
( ( member @ X @ A )
& ( apply @ F @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(88,plain,
( ( ! [F: $i,A: $i,B: $i,Y: $i] :
( ( member @ Y @ ( image3 @ F @ A @ B ) )
<=> ( ( member @ Y @ B )
& ? [X: $i] :
( ( member @ X @ A )
& ( apply @ F @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(89,plain,
( ( ! [F: $i,B: $i,X: $i] :
( ( member @ X @ ( inverse_image2 @ F @ B ) )
<=> ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(90,plain,
( ( ! [F: $i,B: $i,A: $i,X: $i] :
( ( member @ X @ ( inverse_image3 @ F @ B @ A ) )
<=> ( ( member @ X @ A )
& ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(91,plain,
( ( ! [F: $i,A: $i,R: $i,B: $i,S: $i] :
( ( increasing @ F @ A @ R @ B @ S )
<=> ! [X1: $i,Y1: $i,X2: $i,Y2: $i] :
( ( ( member @ X1 @ A )
& ( member @ Y1 @ B )
& ( member @ X2 @ A )
& ( member @ Y2 @ B )
& ( apply @ R @ X1 @ X2 )
& ( apply @ F @ X1 @ Y1 )
& ( apply @ F @ X2 @ Y2 ) )
=> ( apply @ S @ Y1 @ Y2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(92,plain,
( ( ! [F: $i,A: $i,R: $i,B: $i,S: $i] :
( ( decreasing @ F @ A @ R @ B @ S )
<=> ! [X1: $i,Y1: $i,X2: $i,Y2: $i] :
( ( ( member @ X1 @ A )
& ( member @ Y1 @ B )
& ( member @ X2 @ A )
& ( member @ Y2 @ B )
& ( apply @ R @ X1 @ X2 )
& ( apply @ F @ X1 @ Y1 )
& ( apply @ F @ X2 @ Y2 ) )
=> ( apply @ S @ Y2 @ Y1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(93,plain,
( ( ! [F: $i,A: $i,R: $i,B: $i,S: $i] :
( ( isomorphism @ F @ A @ R @ B @ S )
<=> ( ( maps @ F @ A @ B )
& ( one_to_one @ F @ A @ B )
& ! [X1: $i,Y1: $i,X2: $i,Y2: $i] :
( ( ( member @ X1 @ A )
& ( member @ Y1 @ B )
& ( member @ X2 @ A )
& ( member @ Y2 @ B )
& ( apply @ F @ X1 @ Y1 )
& ( apply @ F @ X2 @ Y2 ) )
=> ( ( apply @ R @ X1 @ X2 )
<=> ( apply @ S @ Y1 @ Y2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(94,plain,
( ( maps @ sK1_F @ sK2_SY136 @ sK3_SY138 )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(95,plain,
( ( ~ ( equal_set @ ( inverse_image2 @ sK1_F @ empty_set ) @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(96,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ~ ( ~ ( member @ SX3 @ SX1 )
| ~ ( member @ SX4 @ SX2 ) )
| ~ ( ~ ( ~ ( apply @ SX0 @ SX3 @ SX4 )
| ( apply @ ( inverse_function @ SX0 @ SX1 @ SX2 ) @ SX4 @ SX3 ) )
| ~ ( ~ ( apply @ ( inverse_function @ SX0 @ SX1 @ SX2 ) @ SX4 @ SX3 )
| ( apply @ SX0 @ SX3 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(97,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( member @ SX3 @ ( image3 @ SX0 @ SX1 @ SX2 ) )
| ~ ( ~ ( member @ SX3 @ SX2 )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( member @ SX4 @ SX1 )
| ~ ( apply @ SX0 @ SX4 @ SX3 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX3 @ SX2 )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( member @ SX4 @ SX1 )
| ~ ( apply @ SX0 @ SX4 @ SX3 ) ) )
| ( member @ SX3 @ ( image3 @ SX0 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(98,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( surjective @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( member @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( member @ SX4 @ SX1 )
| ~ ( apply @ SX0 @ SX4 @ SX3 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( member @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( member @ SX4 @ SX1 )
| ~ ( apply @ SX0 @ SX4 @ SX3 ) ) )
| ( surjective @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(99,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(100,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( decreasing @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 )
| ! [SX5: $i,SX6: $i,SX7: $i,SX8: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SX5 @ SX1 )
| ~ ( member @ SX6 @ SX3 ) )
| ~ ( member @ SX7 @ SX1 ) )
| ~ ( member @ SX8 @ SX3 ) )
| ~ ( apply @ SX2 @ SX5 @ SX7 ) )
| ~ ( apply @ SX0 @ SX5 @ SX6 ) )
| ~ ( apply @ SX0 @ SX7 @ SX8 ) )
| ( apply @ SX4 @ SX8 @ SX6 ) ) )
| ~ ( ~ ! [SX5: $i,SX6: $i,SX7: $i,SX8: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SX5 @ SX1 )
| ~ ( member @ SX6 @ SX3 ) )
| ~ ( member @ SX7 @ SX1 ) )
| ~ ( member @ SX8 @ SX3 ) )
| ~ ( apply @ SX2 @ SX5 @ SX7 ) )
| ~ ( apply @ SX0 @ SX5 @ SX6 ) )
| ~ ( apply @ SX0 @ SX7 @ SX8 ) )
| ( apply @ SX4 @ SX8 @ SX6 ) )
| ( decreasing @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(101,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( isomorphism @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 )
| ~ ( ~ ~ ( ~ ( maps @ SX0 @ SX1 @ SX3 )
| ~ ( one_to_one @ SX0 @ SX1 @ SX3 ) )
| ~ ! [SX5: $i,SX6: $i,SX7: $i,SX8: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SX5 @ SX1 )
| ~ ( member @ SX6 @ SX3 ) )
| ~ ( member @ SX7 @ SX1 ) )
| ~ ( member @ SX8 @ SX3 ) )
| ~ ( apply @ SX0 @ SX5 @ SX6 ) )
| ~ ( apply @ SX0 @ SX7 @ SX8 ) )
| ~ ( ~ ( ~ ( apply @ SX2 @ SX5 @ SX7 )
| ( apply @ SX4 @ SX6 @ SX8 ) )
| ~ ( ~ ( apply @ SX4 @ SX6 @ SX8 )
| ( apply @ SX2 @ SX5 @ SX7 ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( maps @ SX0 @ SX1 @ SX3 )
| ~ ( one_to_one @ SX0 @ SX1 @ SX3 ) )
| ~ ! [SX5: $i,SX6: $i,SX7: $i,SX8: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SX5 @ SX1 )
| ~ ( member @ SX6 @ SX3 ) )
| ~ ( member @ SX7 @ SX1 ) )
| ~ ( member @ SX8 @ SX3 ) )
| ~ ( apply @ SX0 @ SX5 @ SX6 ) )
| ~ ( apply @ SX0 @ SX7 @ SX8 ) )
| ~ ( ~ ( ~ ( apply @ SX2 @ SX5 @ SX7 )
| ( apply @ SX4 @ SX6 @ SX8 ) )
| ~ ( ~ ( apply @ SX4 @ SX6 @ SX8 )
| ( apply @ SX2 @ SX5 @ SX7 ) ) ) ) )
| ( isomorphism @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(102,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( difference @ SX2 @ SX1 ) )
| ~ ( ~ ( member @ SX0 @ SX2 )
| ~ ~ ( member @ SX0 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX0 @ SX2 )
| ~ ~ ( member @ SX0 @ SX1 ) )
| ( member @ SX0 @ ( difference @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(103,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( increasing @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 )
| ! [SX5: $i,SX6: $i,SX7: $i,SX8: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SX5 @ SX1 )
| ~ ( member @ SX6 @ SX3 ) )
| ~ ( member @ SX7 @ SX1 ) )
| ~ ( member @ SX8 @ SX3 ) )
| ~ ( apply @ SX2 @ SX5 @ SX7 ) )
| ~ ( apply @ SX0 @ SX5 @ SX6 ) )
| ~ ( apply @ SX0 @ SX7 @ SX8 ) )
| ( apply @ SX4 @ SX6 @ SX8 ) ) )
| ~ ( ~ ! [SX5: $i,SX6: $i,SX7: $i,SX8: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SX5 @ SX1 )
| ~ ( member @ SX6 @ SX3 ) )
| ~ ( member @ SX7 @ SX1 ) )
| ~ ( member @ SX8 @ SX3 ) )
| ~ ( apply @ SX2 @ SX5 @ SX7 ) )
| ~ ( apply @ SX0 @ SX5 @ SX6 ) )
| ~ ( apply @ SX0 @ SX7 @ SX8 ) )
| ( apply @ SX4 @ SX6 @ SX8 ) )
| ( increasing @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(104,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ( ( SX0 != SX1 )
| ( member @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(105,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( sum @ SX1 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( sum @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(106,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) )
| ( SX0 = SX1 )
| ( SX0 = SX2 ) )
| ~ ( ~ ( ( SX0 = SX1 )
| ( SX0 = SX2 ) )
| ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(107,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( one_to_one @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ( injective @ SX0 @ SX1 @ SX2 )
| ~ ( surjective @ SX0 @ SX1 @ SX2 ) ) )
| ~ ( ~ ~ ( ~ ( injective @ SX0 @ SX1 @ SX2 )
| ~ ( surjective @ SX0 @ SX1 @ SX2 ) )
| ( one_to_one @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(108,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX2 @ ( image2 @ SX0 @ SX1 ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( member @ SX3 @ SX1 )
| ~ ( apply @ SX0 @ SX3 @ SX2 ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( member @ SX3 @ SX1 )
| ~ ( apply @ SX0 @ SX3 @ SX2 ) )
| ( member @ SX2 @ ( image2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(109,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( equal_set @ SX0 @ SX1 )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) )
| ( equal_set @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(110,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( member @ SX3 @ ( inverse_image3 @ SX0 @ SX1 @ SX2 ) )
| ~ ( ~ ( member @ SX3 @ SX2 )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( member @ SX4 @ SX1 )
| ~ ( apply @ SX0 @ SX3 @ SX4 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX3 @ SX2 )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( member @ SX4 @ SX1 )
| ~ ( apply @ SX0 @ SX3 @ SX4 ) ) )
| ( member @ SX3 @ ( inverse_image3 @ SX0 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(111,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( inverse_predicate @ SX0 @ SX1 @ SX2 @ SX3 )
| ! [SX4: $i,SX5: $i] :
( ~ ~ ( ~ ( member @ SX4 @ SX2 )
| ~ ( member @ SX5 @ SX3 ) )
| ~ ( ~ ( ~ ( apply @ SX1 @ SX4 @ SX5 )
| ( apply @ SX0 @ SX5 @ SX4 ) )
| ~ ( ~ ( apply @ SX0 @ SX5 @ SX4 )
| ( apply @ SX1 @ SX4 @ SX5 ) ) ) ) )
| ~ ( ~ ! [SX4: $i,SX5: $i] :
( ~ ~ ( ~ ( member @ SX4 @ SX2 )
| ~ ( member @ SX5 @ SX3 ) )
| ~ ( ~ ( ~ ( apply @ SX1 @ SX4 @ SX5 )
| ( apply @ SX0 @ SX5 @ SX4 ) )
| ~ ( ~ ( apply @ SX0 @ SX5 @ SX4 )
| ( apply @ SX1 @ SX4 @ SX5 ) ) ) )
| ( inverse_predicate @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(112,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( power_set @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( member @ SX0 @ ( power_set @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(113,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( product @ SX1 ) )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX0 @ SX2 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( product @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(114,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( union @ SX1 @ SX2 ) )
| ( member @ SX0 @ SX1 )
| ( member @ SX0 @ SX2 ) )
| ~ ( ~ ( ( member @ SX0 @ SX1 )
| ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( union @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(115,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( maps @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ! [SX3: $i] :
( ~ ( member @ SX3 @ SX1 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( member @ SX4 @ SX2 )
| ~ ( apply @ SX0 @ SX3 @ SX4 ) ) )
| ~ ! [SX3: $i,SX4: $i,SX5: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SX3 @ SX1 )
| ~ ( member @ SX4 @ SX2 ) )
| ~ ( member @ SX5 @ SX2 ) )
| ~ ~ ( ~ ( apply @ SX0 @ SX3 @ SX4 )
| ~ ( apply @ SX0 @ SX3 @ SX5 ) )
| ( SX4 = SX5 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SX3: $i] :
( ~ ( member @ SX3 @ SX1 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( member @ SX4 @ SX2 )
| ~ ( apply @ SX0 @ SX3 @ SX4 ) ) )
| ~ ! [SX3: $i,SX4: $i,SX5: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SX3 @ SX1 )
| ~ ( member @ SX4 @ SX2 ) )
| ~ ( member @ SX5 @ SX2 ) )
| ~ ~ ( ~ ( apply @ SX0 @ SX3 @ SX4 )
| ~ ( apply @ SX0 @ SX3 @ SX5 ) )
| ( SX4 = SX5 ) ) )
| ( maps @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(116,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( identity @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( apply @ SX0 @ SX2 @ SX2 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( apply @ SX0 @ SX2 @ SX2 ) )
| ( identity @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(117,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
~ ( ~ ( ~ ( compose_predicate @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 @ SX5 )
| ! [SX6: $i,SX7: $i] :
( ~ ~ ( ~ ( member @ SX6 @ SX3 )
| ~ ( member @ SX7 @ SX5 ) )
| ~ ( ~ ( ~ ( apply @ SX0 @ SX6 @ SX7 )
| ~ ! [SX8: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SX8 @ SX4 )
| ~ ( apply @ SX2 @ SX6 @ SX8 ) )
| ~ ( apply @ SX1 @ SX8 @ SX7 ) ) )
| ~ ( ~ ~ ! [SX8: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SX8 @ SX4 )
| ~ ( apply @ SX2 @ SX6 @ SX8 ) )
| ~ ( apply @ SX1 @ SX8 @ SX7 ) )
| ( apply @ SX0 @ SX6 @ SX7 ) ) ) ) )
| ~ ( ~ ! [SX6: $i,SX7: $i] :
( ~ ~ ( ~ ( member @ SX6 @ SX3 )
| ~ ( member @ SX7 @ SX5 ) )
| ~ ( ~ ( ~ ( apply @ SX0 @ SX6 @ SX7 )
| ~ ! [SX8: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SX8 @ SX4 )
| ~ ( apply @ SX2 @ SX6 @ SX8 ) )
| ~ ( apply @ SX1 @ SX8 @ SX7 ) ) )
| ~ ( ~ ~ ! [SX8: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SX8 @ SX4 )
| ~ ( apply @ SX2 @ SX6 @ SX8 ) )
| ~ ( apply @ SX1 @ SX8 @ SX7 ) )
| ( apply @ SX0 @ SX6 @ SX7 ) ) ) )
| ( compose_predicate @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 @ SX5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(118,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( intersection @ SX1 @ SX2 ) )
| ~ ( ~ ( member @ SX0 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX0 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( intersection @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(119,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( member @ SX5 @ SX2 )
| ~ ( member @ SX6 @ SX4 ) )
| ~ ( ~ ( ~ ( apply @ ( compose_function @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) @ SX5 @ SX6 )
| ~ ! [SX7: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SX7 @ SX3 )
| ~ ( apply @ SX1 @ SX5 @ SX7 ) )
| ~ ( apply @ SX0 @ SX7 @ SX6 ) ) )
| ~ ( ~ ~ ! [SX7: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SX7 @ SX3 )
| ~ ( apply @ SX1 @ SX5 @ SX7 ) )
| ~ ( apply @ SX0 @ SX7 @ SX6 ) )
| ( apply @ ( compose_function @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) @ SX5 @ SX6 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(120,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX2 @ ( inverse_image2 @ SX0 @ SX1 ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( member @ SX3 @ SX1 )
| ~ ( apply @ SX0 @ SX2 @ SX3 ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( member @ SX3 @ SX1 )
| ~ ( apply @ SX0 @ SX2 @ SX3 ) )
| ( member @ SX2 @ ( inverse_image2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(121,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( injective @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i,SX4: $i,SX5: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SX3 @ SX1 )
| ~ ( member @ SX4 @ SX1 ) )
| ~ ( member @ SX5 @ SX2 ) )
| ~ ~ ( ~ ( apply @ SX0 @ SX3 @ SX5 )
| ~ ( apply @ SX0 @ SX4 @ SX5 ) )
| ( SX3 = SX4 ) ) )
| ~ ( ~ ! [SX3: $i,SX4: $i,SX5: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SX3 @ SX1 )
| ~ ( member @ SX4 @ SX1 ) )
| ~ ( member @ SX5 @ SX2 ) )
| ~ ~ ( ~ ( apply @ SX0 @ SX3 @ SX5 )
| ~ ( apply @ SX0 @ SX4 @ SX5 ) )
| ( SX3 = SX4 ) )
| ( injective @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(122,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( equal_maps @ SX0 @ SX1 @ SX2 @ SX3 )
| ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SX4 @ SX2 )
| ~ ( member @ SX5 @ SX3 ) )
| ~ ( member @ SX6 @ SX3 ) )
| ~ ~ ( ~ ( apply @ SX0 @ SX4 @ SX5 )
| ~ ( apply @ SX1 @ SX4 @ SX6 ) )
| ( SX5 = SX6 ) ) )
| ~ ( ~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SX4 @ SX2 )
| ~ ( member @ SX5 @ SX3 ) )
| ~ ( member @ SX6 @ SX3 ) )
| ~ ~ ( ~ ( apply @ SX0 @ SX4 @ SX5 )
| ~ ( apply @ SX1 @ SX4 @ SX6 ) )
| ( SX5 = SX6 ) )
| ( equal_maps @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(123,plain,
! [SV1: $i] :
( ( ~ ( member @ SV1 @ empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(124,plain,
( ( equal_set @ ( inverse_image2 @ sK1_F @ empty_set ) @ empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(125,plain,
! [SV2: $i] :
( ( ! [SY139: $i,SY140: $i,SY141: $i,SY142: $i] :
( ~ ~ ( ~ ( member @ SY141 @ SY139 )
| ~ ( member @ SY142 @ SY140 ) )
| ~ ( ~ ( ~ ( apply @ SV2 @ SY141 @ SY142 )
| ( apply @ ( inverse_function @ SV2 @ SY139 @ SY140 ) @ SY142 @ SY141 ) )
| ~ ( ~ ( apply @ ( inverse_function @ SV2 @ SY139 @ SY140 ) @ SY142 @ SY141 )
| ( apply @ SV2 @ SY141 @ SY142 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(126,plain,
! [SV3: $i] :
( ( ! [SY143: $i,SY144: $i,SY145: $i] :
~ ( ~ ( ~ ( member @ SY145 @ ( image3 @ SV3 @ SY143 @ SY144 ) )
| ~ ( ~ ( member @ SY145 @ SY144 )
| ~ ~ ! [SY146: $i] :
~ ~ ( ~ ( member @ SY146 @ SY143 )
| ~ ( apply @ SV3 @ SY146 @ SY145 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY145 @ SY144 )
| ~ ~ ! [SY147: $i] :
~ ~ ( ~ ( member @ SY147 @ SY143 )
| ~ ( apply @ SV3 @ SY147 @ SY145 ) ) )
| ( member @ SY145 @ ( image3 @ SV3 @ SY143 @ SY144 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(127,plain,
! [SV4: $i] :
( ( ! [SY148: $i,SY149: $i] :
~ ( ~ ( ~ ( surjective @ SV4 @ SY148 @ SY149 )
| ! [SY150: $i] :
( ~ ( member @ SY150 @ SY149 )
| ~ ! [SY151: $i] :
~ ~ ( ~ ( member @ SY151 @ SY148 )
| ~ ( apply @ SV4 @ SY151 @ SY150 ) ) ) )
| ~ ( ~ ! [SY152: $i] :
( ~ ( member @ SY152 @ SY149 )
| ~ ! [SY153: $i] :
~ ~ ( ~ ( member @ SY153 @ SY148 )
| ~ ( apply @ SV4 @ SY153 @ SY152 ) ) )
| ( surjective @ SV4 @ SY148 @ SY149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(128,plain,
! [SV5: $i] :
( ( ! [SY154: $i] :
~ ( ~ ( ~ ( subset @ SV5 @ SY154 )
| ! [SY155: $i] :
( ~ ( member @ SY155 @ SV5 )
| ( member @ SY155 @ SY154 ) ) )
| ~ ( ~ ! [SY156: $i] :
( ~ ( member @ SY156 @ SV5 )
| ( member @ SY156 @ SY154 ) )
| ( subset @ SV5 @ SY154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(129,plain,
! [SV6: $i] :
( ( ! [SY157: $i,SY158: $i,SY159: $i,SY160: $i] :
~ ( ~ ( ~ ( decreasing @ SV6 @ SY157 @ SY158 @ SY159 @ SY160 )
| ! [SY161: $i,SY162: $i,SY163: $i,SY164: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY161 @ SY157 )
| ~ ( member @ SY162 @ SY159 ) )
| ~ ( member @ SY163 @ SY157 ) )
| ~ ( member @ SY164 @ SY159 ) )
| ~ ( apply @ SY158 @ SY161 @ SY163 ) )
| ~ ( apply @ SV6 @ SY161 @ SY162 ) )
| ~ ( apply @ SV6 @ SY163 @ SY164 ) )
| ( apply @ SY160 @ SY164 @ SY162 ) ) )
| ~ ( ~ ! [SY165: $i,SY166: $i,SY167: $i,SY168: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY165 @ SY157 )
| ~ ( member @ SY166 @ SY159 ) )
| ~ ( member @ SY167 @ SY157 ) )
| ~ ( member @ SY168 @ SY159 ) )
| ~ ( apply @ SY158 @ SY165 @ SY167 ) )
| ~ ( apply @ SV6 @ SY165 @ SY166 ) )
| ~ ( apply @ SV6 @ SY167 @ SY168 ) )
| ( apply @ SY160 @ SY168 @ SY166 ) )
| ( decreasing @ SV6 @ SY157 @ SY158 @ SY159 @ SY160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(130,plain,
! [SV7: $i] :
( ( ! [SY169: $i,SY170: $i,SY171: $i,SY172: $i] :
~ ( ~ ( ~ ( isomorphism @ SV7 @ SY169 @ SY170 @ SY171 @ SY172 )
| ~ ( ~ ~ ( ~ ( maps @ SV7 @ SY169 @ SY171 )
| ~ ( one_to_one @ SV7 @ SY169 @ SY171 ) )
| ~ ! [SY173: $i,SY174: $i,SY175: $i,SY176: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY173 @ SY169 )
| ~ ( member @ SY174 @ SY171 ) )
| ~ ( member @ SY175 @ SY169 ) )
| ~ ( member @ SY176 @ SY171 ) )
| ~ ( apply @ SV7 @ SY173 @ SY174 ) )
| ~ ( apply @ SV7 @ SY175 @ SY176 ) )
| ~ ( ~ ( ~ ( apply @ SY170 @ SY173 @ SY175 )
| ( apply @ SY172 @ SY174 @ SY176 ) )
| ~ ( ~ ( apply @ SY172 @ SY174 @ SY176 )
| ( apply @ SY170 @ SY173 @ SY175 ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( maps @ SV7 @ SY169 @ SY171 )
| ~ ( one_to_one @ SV7 @ SY169 @ SY171 ) )
| ~ ! [SY177: $i,SY178: $i,SY179: $i,SY180: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY177 @ SY169 )
| ~ ( member @ SY178 @ SY171 ) )
| ~ ( member @ SY179 @ SY169 ) )
| ~ ( member @ SY180 @ SY171 ) )
| ~ ( apply @ SV7 @ SY177 @ SY178 ) )
| ~ ( apply @ SV7 @ SY179 @ SY180 ) )
| ~ ( ~ ( ~ ( apply @ SY170 @ SY177 @ SY179 )
| ( apply @ SY172 @ SY178 @ SY180 ) )
| ~ ( ~ ( apply @ SY172 @ SY178 @ SY180 )
| ( apply @ SY170 @ SY177 @ SY179 ) ) ) ) )
| ( isomorphism @ SV7 @ SY169 @ SY170 @ SY171 @ SY172 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(131,plain,
! [SV8: $i] :
( ( ! [SY181: $i,SY182: $i] :
~ ( ~ ( ~ ( member @ SV8 @ ( difference @ SY182 @ SY181 ) )
| ~ ( ~ ( member @ SV8 @ SY182 )
| ~ ~ ( member @ SV8 @ SY181 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV8 @ SY182 )
| ~ ~ ( member @ SV8 @ SY181 ) )
| ( member @ SV8 @ ( difference @ SY182 @ SY181 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(132,plain,
! [SV9: $i] :
( ( ! [SY183: $i,SY184: $i,SY185: $i,SY186: $i] :
~ ( ~ ( ~ ( increasing @ SV9 @ SY183 @ SY184 @ SY185 @ SY186 )
| ! [SY187: $i,SY188: $i,SY189: $i,SY190: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY187 @ SY183 )
| ~ ( member @ SY188 @ SY185 ) )
| ~ ( member @ SY189 @ SY183 ) )
| ~ ( member @ SY190 @ SY185 ) )
| ~ ( apply @ SY184 @ SY187 @ SY189 ) )
| ~ ( apply @ SV9 @ SY187 @ SY188 ) )
| ~ ( apply @ SV9 @ SY189 @ SY190 ) )
| ( apply @ SY186 @ SY188 @ SY190 ) ) )
| ~ ( ~ ! [SY191: $i,SY192: $i,SY193: $i,SY194: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY191 @ SY183 )
| ~ ( member @ SY192 @ SY185 ) )
| ~ ( member @ SY193 @ SY183 ) )
| ~ ( member @ SY194 @ SY185 ) )
| ~ ( apply @ SY184 @ SY191 @ SY193 ) )
| ~ ( apply @ SV9 @ SY191 @ SY192 ) )
| ~ ( apply @ SV9 @ SY193 @ SY194 ) )
| ( apply @ SY186 @ SY192 @ SY194 ) )
| ( increasing @ SV9 @ SY183 @ SY184 @ SY185 @ SY186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(133,plain,
! [SV10: $i] :
( ( ! [SY195: $i] :
~ ( ~ ( ~ ( member @ SV10 @ ( singleton @ SY195 ) )
| ( SV10 = SY195 ) )
| ~ ( ( SV10 != SY195 )
| ( member @ SV10 @ ( singleton @ SY195 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(134,plain,
! [SV11: $i] :
( ( ! [SY196: $i] :
~ ( ~ ( ~ ( member @ SV11 @ ( sum @ SY196 ) )
| ~ ! [SY197: $i] :
~ ~ ( ~ ( member @ SY197 @ SY196 )
| ~ ( member @ SV11 @ SY197 ) ) )
| ~ ( ~ ~ ! [SY198: $i] :
~ ~ ( ~ ( member @ SY198 @ SY196 )
| ~ ( member @ SV11 @ SY198 ) )
| ( member @ SV11 @ ( sum @ SY196 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(135,plain,
! [SV12: $i] :
( ( ! [SY199: $i,SY200: $i] :
~ ( ~ ( ~ ( member @ SV12 @ ( unordered_pair @ SY199 @ SY200 ) )
| ( SV12 = SY199 )
| ( SV12 = SY200 ) )
| ~ ( ~ ( ( SV12 = SY199 )
| ( SV12 = SY200 ) )
| ( member @ SV12 @ ( unordered_pair @ SY199 @ SY200 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(136,plain,
! [SV13: $i] :
( ( ! [SY201: $i,SY202: $i] :
~ ( ~ ( ~ ( one_to_one @ SV13 @ SY201 @ SY202 )
| ~ ( ~ ( injective @ SV13 @ SY201 @ SY202 )
| ~ ( surjective @ SV13 @ SY201 @ SY202 ) ) )
| ~ ( ~ ~ ( ~ ( injective @ SV13 @ SY201 @ SY202 )
| ~ ( surjective @ SV13 @ SY201 @ SY202 ) )
| ( one_to_one @ SV13 @ SY201 @ SY202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(137,plain,
! [SV14: $i] :
( ( ! [SY203: $i,SY204: $i] :
~ ( ~ ( ~ ( member @ SY204 @ ( image2 @ SV14 @ SY203 ) )
| ~ ! [SY205: $i] :
~ ~ ( ~ ( member @ SY205 @ SY203 )
| ~ ( apply @ SV14 @ SY205 @ SY204 ) ) )
| ~ ( ~ ~ ! [SY206: $i] :
~ ~ ( ~ ( member @ SY206 @ SY203 )
| ~ ( apply @ SV14 @ SY206 @ SY204 ) )
| ( member @ SY204 @ ( image2 @ SV14 @ SY203 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(138,plain,
! [SV15: $i] :
( ( ! [SY207: $i] :
~ ( ~ ( ~ ( equal_set @ SV15 @ SY207 )
| ~ ( ~ ( subset @ SV15 @ SY207 )
| ~ ( subset @ SY207 @ SV15 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV15 @ SY207 )
| ~ ( subset @ SY207 @ SV15 ) )
| ( equal_set @ SV15 @ SY207 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(139,plain,
! [SV16: $i] :
( ( ! [SY208: $i,SY209: $i,SY210: $i] :
~ ( ~ ( ~ ( member @ SY210 @ ( inverse_image3 @ SV16 @ SY208 @ SY209 ) )
| ~ ( ~ ( member @ SY210 @ SY209 )
| ~ ~ ! [SY211: $i] :
~ ~ ( ~ ( member @ SY211 @ SY208 )
| ~ ( apply @ SV16 @ SY210 @ SY211 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY210 @ SY209 )
| ~ ~ ! [SY212: $i] :
~ ~ ( ~ ( member @ SY212 @ SY208 )
| ~ ( apply @ SV16 @ SY210 @ SY212 ) ) )
| ( member @ SY210 @ ( inverse_image3 @ SV16 @ SY208 @ SY209 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(140,plain,
! [SV17: $i] :
( ( ! [SY213: $i,SY214: $i,SY215: $i] :
~ ( ~ ( ~ ( inverse_predicate @ SV17 @ SY213 @ SY214 @ SY215 )
| ! [SY216: $i,SY217: $i] :
( ~ ~ ( ~ ( member @ SY216 @ SY214 )
| ~ ( member @ SY217 @ SY215 ) )
| ~ ( ~ ( ~ ( apply @ SY213 @ SY216 @ SY217 )
| ( apply @ SV17 @ SY217 @ SY216 ) )
| ~ ( ~ ( apply @ SV17 @ SY217 @ SY216 )
| ( apply @ SY213 @ SY216 @ SY217 ) ) ) ) )
| ~ ( ~ ! [SY218: $i,SY219: $i] :
( ~ ~ ( ~ ( member @ SY218 @ SY214 )
| ~ ( member @ SY219 @ SY215 ) )
| ~ ( ~ ( ~ ( apply @ SY213 @ SY218 @ SY219 )
| ( apply @ SV17 @ SY219 @ SY218 ) )
| ~ ( ~ ( apply @ SV17 @ SY219 @ SY218 )
| ( apply @ SY213 @ SY218 @ SY219 ) ) ) )
| ( inverse_predicate @ SV17 @ SY213 @ SY214 @ SY215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(141,plain,
! [SV18: $i] :
( ( ! [SY220: $i] :
~ ( ~ ( ~ ( member @ SV18 @ ( power_set @ SY220 ) )
| ( subset @ SV18 @ SY220 ) )
| ~ ( ~ ( subset @ SV18 @ SY220 )
| ( member @ SV18 @ ( power_set @ SY220 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(142,plain,
! [SV19: $i] :
( ( ! [SY221: $i] :
~ ( ~ ( ~ ( member @ SV19 @ ( product @ SY221 ) )
| ! [SY222: $i] :
( ~ ( member @ SY222 @ SY221 )
| ( member @ SV19 @ SY222 ) ) )
| ~ ( ~ ! [SY223: $i] :
( ~ ( member @ SY223 @ SY221 )
| ( member @ SV19 @ SY223 ) )
| ( member @ SV19 @ ( product @ SY221 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(143,plain,
! [SV20: $i] :
( ( ! [SY224: $i,SY225: $i] :
~ ( ~ ( ~ ( member @ SV20 @ ( union @ SY224 @ SY225 ) )
| ( member @ SV20 @ SY224 )
| ( member @ SV20 @ SY225 ) )
| ~ ( ~ ( ( member @ SV20 @ SY224 )
| ( member @ SV20 @ SY225 ) )
| ( member @ SV20 @ ( union @ SY224 @ SY225 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(144,plain,
! [SV21: $i] :
( ( ! [SY226: $i,SY227: $i] :
~ ( ~ ( ~ ( maps @ SV21 @ SY226 @ SY227 )
| ~ ( ~ ! [SY228: $i] :
( ~ ( member @ SY228 @ SY226 )
| ~ ! [SY229: $i] :
~ ~ ( ~ ( member @ SY229 @ SY227 )
| ~ ( apply @ SV21 @ SY228 @ SY229 ) ) )
| ~ ! [SY230: $i,SY231: $i,SY232: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY230 @ SY226 )
| ~ ( member @ SY231 @ SY227 ) )
| ~ ( member @ SY232 @ SY227 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY230 @ SY231 )
| ~ ( apply @ SV21 @ SY230 @ SY232 ) )
| ( SY231 = SY232 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SY233: $i] :
( ~ ( member @ SY233 @ SY226 )
| ~ ! [SY234: $i] :
~ ~ ( ~ ( member @ SY234 @ SY227 )
| ~ ( apply @ SV21 @ SY233 @ SY234 ) ) )
| ~ ! [SY235: $i,SY236: $i,SY237: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY235 @ SY226 )
| ~ ( member @ SY236 @ SY227 ) )
| ~ ( member @ SY237 @ SY227 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY235 @ SY236 )
| ~ ( apply @ SV21 @ SY235 @ SY237 ) )
| ( SY236 = SY237 ) ) )
| ( maps @ SV21 @ SY226 @ SY227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(145,plain,
! [SV22: $i] :
( ( ! [SY238: $i] :
~ ( ~ ( ~ ( identity @ SV22 @ SY238 )
| ! [SY239: $i] :
( ~ ( member @ SY239 @ SY238 )
| ( apply @ SV22 @ SY239 @ SY239 ) ) )
| ~ ( ~ ! [SY240: $i] :
( ~ ( member @ SY240 @ SY238 )
| ( apply @ SV22 @ SY240 @ SY240 ) )
| ( identity @ SV22 @ SY238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(146,plain,
! [SV23: $i] :
( ( ! [SY241: $i,SY242: $i,SY243: $i,SY244: $i,SY245: $i] :
~ ( ~ ( ~ ( compose_predicate @ SV23 @ SY241 @ SY242 @ SY243 @ SY244 @ SY245 )
| ! [SY246: $i,SY247: $i] :
( ~ ~ ( ~ ( member @ SY246 @ SY243 )
| ~ ( member @ SY247 @ SY245 ) )
| ~ ( ~ ( ~ ( apply @ SV23 @ SY246 @ SY247 )
| ~ ! [SX8: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SX8 @ SY244 )
| ~ ( apply @ SY242 @ SY246 @ SX8 ) )
| ~ ( apply @ SY241 @ SX8 @ SY247 ) ) )
| ~ ( ~ ~ ! [SX8: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SX8 @ SY244 )
| ~ ( apply @ SY242 @ SY246 @ SX8 ) )
| ~ ( apply @ SY241 @ SX8 @ SY247 ) )
| ( apply @ SV23 @ SY246 @ SY247 ) ) ) ) )
| ~ ( ~ ! [SY250: $i,SY251: $i] :
( ~ ~ ( ~ ( member @ SY250 @ SY243 )
| ~ ( member @ SY251 @ SY245 ) )
| ~ ( ~ ( ~ ( apply @ SV23 @ SY250 @ SY251 )
| ~ ! [SX8: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SX8 @ SY244 )
| ~ ( apply @ SY242 @ SY250 @ SX8 ) )
| ~ ( apply @ SY241 @ SX8 @ SY251 ) ) )
| ~ ( ~ ~ ! [SX8: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SX8 @ SY244 )
| ~ ( apply @ SY242 @ SY250 @ SX8 ) )
| ~ ( apply @ SY241 @ SX8 @ SY251 ) )
| ( apply @ SV23 @ SY250 @ SY251 ) ) ) )
| ( compose_predicate @ SV23 @ SY241 @ SY242 @ SY243 @ SY244 @ SY245 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(147,plain,
! [SV24: $i] :
( ( ! [SY254: $i,SY255: $i] :
~ ( ~ ( ~ ( member @ SV24 @ ( intersection @ SY254 @ SY255 ) )
| ~ ( ~ ( member @ SV24 @ SY254 )
| ~ ( member @ SV24 @ SY255 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV24 @ SY254 )
| ~ ( member @ SV24 @ SY255 ) )
| ( member @ SV24 @ ( intersection @ SY254 @ SY255 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(148,plain,
! [SV25: $i] :
( ( ! [SY256: $i,SY257: $i,SY258: $i,SY259: $i,SY260: $i,SY261: $i] :
( ~ ~ ( ~ ( member @ SY260 @ SY257 )
| ~ ( member @ SY261 @ SY259 ) )
| ~ ( ~ ( ~ ( apply @ ( compose_function @ SV25 @ SY256 @ SY257 @ SY258 @ SY259 ) @ SY260 @ SY261 )
| ~ ! [SY262: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY262 @ SY258 )
| ~ ( apply @ SY256 @ SY260 @ SY262 ) )
| ~ ( apply @ SV25 @ SY262 @ SY261 ) ) )
| ~ ( ~ ~ ! [SY263: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY263 @ SY258 )
| ~ ( apply @ SY256 @ SY260 @ SY263 ) )
| ~ ( apply @ SV25 @ SY263 @ SY261 ) )
| ( apply @ ( compose_function @ SV25 @ SY256 @ SY257 @ SY258 @ SY259 ) @ SY260 @ SY261 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(149,plain,
! [SV26: $i] :
( ( ! [SY264: $i,SY265: $i] :
~ ( ~ ( ~ ( member @ SY265 @ ( inverse_image2 @ SV26 @ SY264 ) )
| ~ ! [SY266: $i] :
~ ~ ( ~ ( member @ SY266 @ SY264 )
| ~ ( apply @ SV26 @ SY265 @ SY266 ) ) )
| ~ ( ~ ~ ! [SY267: $i] :
~ ~ ( ~ ( member @ SY267 @ SY264 )
| ~ ( apply @ SV26 @ SY265 @ SY267 ) )
| ( member @ SY265 @ ( inverse_image2 @ SV26 @ SY264 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(150,plain,
! [SV27: $i] :
( ( ! [SY268: $i,SY269: $i] :
~ ( ~ ( ~ ( injective @ SV27 @ SY268 @ SY269 )
| ! [SY270: $i,SY271: $i,SY272: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY270 @ SY268 )
| ~ ( member @ SY271 @ SY268 ) )
| ~ ( member @ SY272 @ SY269 ) )
| ~ ~ ( ~ ( apply @ SV27 @ SY270 @ SY272 )
| ~ ( apply @ SV27 @ SY271 @ SY272 ) )
| ( SY270 = SY271 ) ) )
| ~ ( ~ ! [SY273: $i,SY274: $i,SY275: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY273 @ SY268 )
| ~ ( member @ SY274 @ SY268 ) )
| ~ ( member @ SY275 @ SY269 ) )
| ~ ~ ( ~ ( apply @ SV27 @ SY273 @ SY275 )
| ~ ( apply @ SV27 @ SY274 @ SY275 ) )
| ( SY273 = SY274 ) )
| ( injective @ SV27 @ SY268 @ SY269 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(151,plain,
! [SV28: $i] :
( ( ! [SY276: $i,SY277: $i,SY278: $i] :
~ ( ~ ( ~ ( equal_maps @ SV28 @ SY276 @ SY277 @ SY278 )
| ! [SY279: $i,SY280: $i,SY281: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY279 @ SY277 )
| ~ ( member @ SY280 @ SY278 ) )
| ~ ( member @ SY281 @ SY278 ) )
| ~ ~ ( ~ ( apply @ SV28 @ SY279 @ SY280 )
| ~ ( apply @ SY276 @ SY279 @ SY281 ) )
| ( SY280 = SY281 ) ) )
| ~ ( ~ ! [SY282: $i,SY283: $i,SY284: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY282 @ SY277 )
| ~ ( member @ SY283 @ SY278 ) )
| ~ ( member @ SY284 @ SY278 ) )
| ~ ~ ( ~ ( apply @ SV28 @ SY282 @ SY283 )
| ~ ( apply @ SY276 @ SY282 @ SY284 ) )
| ( SY283 = SY284 ) )
| ( equal_maps @ SV28 @ SY276 @ SY277 @ SY278 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(152,plain,
! [SV1: $i] :
( ( member @ SV1 @ empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(153,plain,
! [SV2: $i,SV29: $i] :
( ( ! [SY285: $i,SY286: $i,SY287: $i] :
( ~ ~ ( ~ ( member @ SY286 @ SV29 )
| ~ ( member @ SY287 @ SY285 ) )
| ~ ( ~ ( ~ ( apply @ SV2 @ SY286 @ SY287 )
| ( apply @ ( inverse_function @ SV2 @ SV29 @ SY285 ) @ SY287 @ SY286 ) )
| ~ ( ~ ( apply @ ( inverse_function @ SV2 @ SV29 @ SY285 ) @ SY287 @ SY286 )
| ( apply @ SV2 @ SY286 @ SY287 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(154,plain,
! [SV30: $i,SV3: $i] :
( ( ! [SY288: $i,SY289: $i] :
~ ( ~ ( ~ ( member @ SY289 @ ( image3 @ SV3 @ SV30 @ SY288 ) )
| ~ ( ~ ( member @ SY289 @ SY288 )
| ~ ~ ! [SY290: $i] :
~ ~ ( ~ ( member @ SY290 @ SV30 )
| ~ ( apply @ SV3 @ SY290 @ SY289 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY289 @ SY288 )
| ~ ~ ! [SY291: $i] :
~ ~ ( ~ ( member @ SY291 @ SV30 )
| ~ ( apply @ SV3 @ SY291 @ SY289 ) ) )
| ( member @ SY289 @ ( image3 @ SV3 @ SV30 @ SY288 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(155,plain,
! [SV31: $i,SV4: $i] :
( ( ! [SY292: $i] :
~ ( ~ ( ~ ( surjective @ SV4 @ SV31 @ SY292 )
| ! [SY293: $i] :
( ~ ( member @ SY293 @ SY292 )
| ~ ! [SY294: $i] :
~ ~ ( ~ ( member @ SY294 @ SV31 )
| ~ ( apply @ SV4 @ SY294 @ SY293 ) ) ) )
| ~ ( ~ ! [SY295: $i] :
( ~ ( member @ SY295 @ SY292 )
| ~ ! [SY296: $i] :
~ ~ ( ~ ( member @ SY296 @ SV31 )
| ~ ( apply @ SV4 @ SY296 @ SY295 ) ) )
| ( surjective @ SV4 @ SV31 @ SY292 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(156,plain,
! [SV32: $i,SV5: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV5 @ SV32 )
| ! [SY297: $i] :
( ~ ( member @ SY297 @ SV5 )
| ( member @ SY297 @ SV32 ) ) )
| ~ ( ~ ! [SY298: $i] :
( ~ ( member @ SY298 @ SV5 )
| ( member @ SY298 @ SV32 ) )
| ( subset @ SV5 @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(157,plain,
! [SV33: $i,SV6: $i] :
( ( ! [SY299: $i,SY300: $i,SY301: $i] :
~ ( ~ ( ~ ( decreasing @ SV6 @ SV33 @ SY299 @ SY300 @ SY301 )
| ! [SY302: $i,SY303: $i,SY304: $i,SY305: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY302 @ SV33 )
| ~ ( member @ SY303 @ SY300 ) )
| ~ ( member @ SY304 @ SV33 ) )
| ~ ( member @ SY305 @ SY300 ) )
| ~ ( apply @ SY299 @ SY302 @ SY304 ) )
| ~ ( apply @ SV6 @ SY302 @ SY303 ) )
| ~ ( apply @ SV6 @ SY304 @ SY305 ) )
| ( apply @ SY301 @ SY305 @ SY303 ) ) )
| ~ ( ~ ! [SY306: $i,SY307: $i,SY308: $i,SY309: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY306 @ SV33 )
| ~ ( member @ SY307 @ SY300 ) )
| ~ ( member @ SY308 @ SV33 ) )
| ~ ( member @ SY309 @ SY300 ) )
| ~ ( apply @ SY299 @ SY306 @ SY308 ) )
| ~ ( apply @ SV6 @ SY306 @ SY307 ) )
| ~ ( apply @ SV6 @ SY308 @ SY309 ) )
| ( apply @ SY301 @ SY309 @ SY307 ) )
| ( decreasing @ SV6 @ SV33 @ SY299 @ SY300 @ SY301 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(158,plain,
! [SV34: $i,SV7: $i] :
( ( ! [SY310: $i,SY311: $i,SY312: $i] :
~ ( ~ ( ~ ( isomorphism @ SV7 @ SV34 @ SY310 @ SY311 @ SY312 )
| ~ ( ~ ~ ( ~ ( maps @ SV7 @ SV34 @ SY311 )
| ~ ( one_to_one @ SV7 @ SV34 @ SY311 ) )
| ~ ! [SY313: $i,SY314: $i,SY315: $i,SY316: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY313 @ SV34 )
| ~ ( member @ SY314 @ SY311 ) )
| ~ ( member @ SY315 @ SV34 ) )
| ~ ( member @ SY316 @ SY311 ) )
| ~ ( apply @ SV7 @ SY313 @ SY314 ) )
| ~ ( apply @ SV7 @ SY315 @ SY316 ) )
| ~ ( ~ ( ~ ( apply @ SY310 @ SY313 @ SY315 )
| ( apply @ SY312 @ SY314 @ SY316 ) )
| ~ ( ~ ( apply @ SY312 @ SY314 @ SY316 )
| ( apply @ SY310 @ SY313 @ SY315 ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( maps @ SV7 @ SV34 @ SY311 )
| ~ ( one_to_one @ SV7 @ SV34 @ SY311 ) )
| ~ ! [SY317: $i,SY318: $i,SY319: $i,SY320: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY317 @ SV34 )
| ~ ( member @ SY318 @ SY311 ) )
| ~ ( member @ SY319 @ SV34 ) )
| ~ ( member @ SY320 @ SY311 ) )
| ~ ( apply @ SV7 @ SY317 @ SY318 ) )
| ~ ( apply @ SV7 @ SY319 @ SY320 ) )
| ~ ( ~ ( ~ ( apply @ SY310 @ SY317 @ SY319 )
| ( apply @ SY312 @ SY318 @ SY320 ) )
| ~ ( ~ ( apply @ SY312 @ SY318 @ SY320 )
| ( apply @ SY310 @ SY317 @ SY319 ) ) ) ) )
| ( isomorphism @ SV7 @ SV34 @ SY310 @ SY311 @ SY312 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(159,plain,
! [SV35: $i,SV8: $i] :
( ( ! [SY321: $i] :
~ ( ~ ( ~ ( member @ SV8 @ ( difference @ SY321 @ SV35 ) )
| ~ ( ~ ( member @ SV8 @ SY321 )
| ~ ~ ( member @ SV8 @ SV35 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV8 @ SY321 )
| ~ ~ ( member @ SV8 @ SV35 ) )
| ( member @ SV8 @ ( difference @ SY321 @ SV35 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(160,plain,
! [SV36: $i,SV9: $i] :
( ( ! [SY322: $i,SY323: $i,SY324: $i] :
~ ( ~ ( ~ ( increasing @ SV9 @ SV36 @ SY322 @ SY323 @ SY324 )
| ! [SY325: $i,SY326: $i,SY327: $i,SY328: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY325 @ SV36 )
| ~ ( member @ SY326 @ SY323 ) )
| ~ ( member @ SY327 @ SV36 ) )
| ~ ( member @ SY328 @ SY323 ) )
| ~ ( apply @ SY322 @ SY325 @ SY327 ) )
| ~ ( apply @ SV9 @ SY325 @ SY326 ) )
| ~ ( apply @ SV9 @ SY327 @ SY328 ) )
| ( apply @ SY324 @ SY326 @ SY328 ) ) )
| ~ ( ~ ! [SY329: $i,SY330: $i,SY331: $i,SY332: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY329 @ SV36 )
| ~ ( member @ SY330 @ SY323 ) )
| ~ ( member @ SY331 @ SV36 ) )
| ~ ( member @ SY332 @ SY323 ) )
| ~ ( apply @ SY322 @ SY329 @ SY331 ) )
| ~ ( apply @ SV9 @ SY329 @ SY330 ) )
| ~ ( apply @ SV9 @ SY331 @ SY332 ) )
| ( apply @ SY324 @ SY330 @ SY332 ) )
| ( increasing @ SV9 @ SV36 @ SY322 @ SY323 @ SY324 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(161,plain,
! [SV37: $i,SV10: $i] :
( ( ~ ( ~ ( ~ ( member @ SV10 @ ( singleton @ SV37 ) )
| ( SV10 = SV37 ) )
| ~ ( ( SV10 != SV37 )
| ( member @ SV10 @ ( singleton @ SV37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(162,plain,
! [SV38: $i,SV11: $i] :
( ( ~ ( ~ ( ~ ( member @ SV11 @ ( sum @ SV38 ) )
| ~ ! [SY333: $i] :
~ ~ ( ~ ( member @ SY333 @ SV38 )
| ~ ( member @ SV11 @ SY333 ) ) )
| ~ ( ~ ~ ! [SY334: $i] :
~ ~ ( ~ ( member @ SY334 @ SV38 )
| ~ ( member @ SV11 @ SY334 ) )
| ( member @ SV11 @ ( sum @ SV38 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(163,plain,
! [SV39: $i,SV12: $i] :
( ( ! [SY335: $i] :
~ ( ~ ( ~ ( member @ SV12 @ ( unordered_pair @ SV39 @ SY335 ) )
| ( SV12 = SV39 )
| ( SV12 = SY335 ) )
| ~ ( ~ ( ( SV12 = SV39 )
| ( SV12 = SY335 ) )
| ( member @ SV12 @ ( unordered_pair @ SV39 @ SY335 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(164,plain,
! [SV40: $i,SV13: $i] :
( ( ! [SY336: $i] :
~ ( ~ ( ~ ( one_to_one @ SV13 @ SV40 @ SY336 )
| ~ ( ~ ( injective @ SV13 @ SV40 @ SY336 )
| ~ ( surjective @ SV13 @ SV40 @ SY336 ) ) )
| ~ ( ~ ~ ( ~ ( injective @ SV13 @ SV40 @ SY336 )
| ~ ( surjective @ SV13 @ SV40 @ SY336 ) )
| ( one_to_one @ SV13 @ SV40 @ SY336 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(165,plain,
! [SV41: $i,SV14: $i] :
( ( ! [SY337: $i] :
~ ( ~ ( ~ ( member @ SY337 @ ( image2 @ SV14 @ SV41 ) )
| ~ ! [SY338: $i] :
~ ~ ( ~ ( member @ SY338 @ SV41 )
| ~ ( apply @ SV14 @ SY338 @ SY337 ) ) )
| ~ ( ~ ~ ! [SY339: $i] :
~ ~ ( ~ ( member @ SY339 @ SV41 )
| ~ ( apply @ SV14 @ SY339 @ SY337 ) )
| ( member @ SY337 @ ( image2 @ SV14 @ SV41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(166,plain,
! [SV42: $i,SV15: $i] :
( ( ~ ( ~ ( ~ ( equal_set @ SV15 @ SV42 )
| ~ ( ~ ( subset @ SV15 @ SV42 )
| ~ ( subset @ SV42 @ SV15 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV15 @ SV42 )
| ~ ( subset @ SV42 @ SV15 ) )
| ( equal_set @ SV15 @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(167,plain,
! [SV43: $i,SV16: $i] :
( ( ! [SY340: $i,SY341: $i] :
~ ( ~ ( ~ ( member @ SY341 @ ( inverse_image3 @ SV16 @ SV43 @ SY340 ) )
| ~ ( ~ ( member @ SY341 @ SY340 )
| ~ ~ ! [SY342: $i] :
~ ~ ( ~ ( member @ SY342 @ SV43 )
| ~ ( apply @ SV16 @ SY341 @ SY342 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY341 @ SY340 )
| ~ ~ ! [SY343: $i] :
~ ~ ( ~ ( member @ SY343 @ SV43 )
| ~ ( apply @ SV16 @ SY341 @ SY343 ) ) )
| ( member @ SY341 @ ( inverse_image3 @ SV16 @ SV43 @ SY340 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(168,plain,
! [SV44: $i,SV17: $i] :
( ( ! [SY344: $i,SY345: $i] :
~ ( ~ ( ~ ( inverse_predicate @ SV17 @ SV44 @ SY344 @ SY345 )
| ! [SY346: $i,SY347: $i] :
( ~ ~ ( ~ ( member @ SY346 @ SY344 )
| ~ ( member @ SY347 @ SY345 ) )
| ~ ( ~ ( ~ ( apply @ SV44 @ SY346 @ SY347 )
| ( apply @ SV17 @ SY347 @ SY346 ) )
| ~ ( ~ ( apply @ SV17 @ SY347 @ SY346 )
| ( apply @ SV44 @ SY346 @ SY347 ) ) ) ) )
| ~ ( ~ ! [SY348: $i,SY349: $i] :
( ~ ~ ( ~ ( member @ SY348 @ SY344 )
| ~ ( member @ SY349 @ SY345 ) )
| ~ ( ~ ( ~ ( apply @ SV44 @ SY348 @ SY349 )
| ( apply @ SV17 @ SY349 @ SY348 ) )
| ~ ( ~ ( apply @ SV17 @ SY349 @ SY348 )
| ( apply @ SV44 @ SY348 @ SY349 ) ) ) )
| ( inverse_predicate @ SV17 @ SV44 @ SY344 @ SY345 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(169,plain,
! [SV45: $i,SV18: $i] :
( ( ~ ( ~ ( ~ ( member @ SV18 @ ( power_set @ SV45 ) )
| ( subset @ SV18 @ SV45 ) )
| ~ ( ~ ( subset @ SV18 @ SV45 )
| ( member @ SV18 @ ( power_set @ SV45 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(170,plain,
! [SV46: $i,SV19: $i] :
( ( ~ ( ~ ( ~ ( member @ SV19 @ ( product @ SV46 ) )
| ! [SY350: $i] :
( ~ ( member @ SY350 @ SV46 )
| ( member @ SV19 @ SY350 ) ) )
| ~ ( ~ ! [SY351: $i] :
( ~ ( member @ SY351 @ SV46 )
| ( member @ SV19 @ SY351 ) )
| ( member @ SV19 @ ( product @ SV46 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(171,plain,
! [SV47: $i,SV20: $i] :
( ( ! [SY352: $i] :
~ ( ~ ( ~ ( member @ SV20 @ ( union @ SV47 @ SY352 ) )
| ( member @ SV20 @ SV47 )
| ( member @ SV20 @ SY352 ) )
| ~ ( ~ ( ( member @ SV20 @ SV47 )
| ( member @ SV20 @ SY352 ) )
| ( member @ SV20 @ ( union @ SV47 @ SY352 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(172,plain,
! [SV48: $i,SV21: $i] :
( ( ! [SY353: $i] :
~ ( ~ ( ~ ( maps @ SV21 @ SV48 @ SY353 )
| ~ ( ~ ! [SY354: $i] :
( ~ ( member @ SY354 @ SV48 )
| ~ ! [SY229: $i] :
~ ~ ( ~ ( member @ SY229 @ SY353 )
| ~ ( apply @ SV21 @ SY354 @ SY229 ) ) )
| ~ ! [SY356: $i,SY357: $i,SY358: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY356 @ SV48 )
| ~ ( member @ SY357 @ SY353 ) )
| ~ ( member @ SY358 @ SY353 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY356 @ SY357 )
| ~ ( apply @ SV21 @ SY356 @ SY358 ) )
| ( SY357 = SY358 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SY359: $i] :
( ~ ( member @ SY359 @ SV48 )
| ~ ! [SY234: $i] :
~ ~ ( ~ ( member @ SY234 @ SY353 )
| ~ ( apply @ SV21 @ SY359 @ SY234 ) ) )
| ~ ! [SY361: $i,SY362: $i,SY363: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY361 @ SV48 )
| ~ ( member @ SY362 @ SY353 ) )
| ~ ( member @ SY363 @ SY353 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY361 @ SY362 )
| ~ ( apply @ SV21 @ SY361 @ SY363 ) )
| ( SY362 = SY363 ) ) )
| ( maps @ SV21 @ SV48 @ SY353 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(173,plain,
! [SV49: $i,SV22: $i] :
( ( ~ ( ~ ( ~ ( identity @ SV22 @ SV49 )
| ! [SY364: $i] :
( ~ ( member @ SY364 @ SV49 )
| ( apply @ SV22 @ SY364 @ SY364 ) ) )
| ~ ( ~ ! [SY365: $i] :
( ~ ( member @ SY365 @ SV49 )
| ( apply @ SV22 @ SY365 @ SY365 ) )
| ( identity @ SV22 @ SV49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(174,plain,
! [SV50: $i,SV23: $i] :
( ( ! [SY366: $i,SY367: $i,SY368: $i,SY369: $i] :
~ ( ~ ( ~ ( compose_predicate @ SV23 @ SV50 @ SY366 @ SY367 @ SY368 @ SY369 )
| ! [SY370: $i,SY371: $i] :
( ~ ~ ( ~ ( member @ SY370 @ SY367 )
| ~ ( member @ SY371 @ SY369 ) )
| ~ ( ~ ( ~ ( apply @ SV23 @ SY370 @ SY371 )
| ~ ! [SY372: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY372 @ SY368 )
| ~ ( apply @ SY366 @ SY370 @ SY372 ) )
| ~ ( apply @ SV50 @ SY372 @ SY371 ) ) )
| ~ ( ~ ~ ! [SY373: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY373 @ SY368 )
| ~ ( apply @ SY366 @ SY370 @ SY373 ) )
| ~ ( apply @ SV50 @ SY373 @ SY371 ) )
| ( apply @ SV23 @ SY370 @ SY371 ) ) ) ) )
| ~ ( ~ ! [SY374: $i,SY375: $i] :
( ~ ~ ( ~ ( member @ SY374 @ SY367 )
| ~ ( member @ SY375 @ SY369 ) )
| ~ ( ~ ( ~ ( apply @ SV23 @ SY374 @ SY375 )
| ~ ! [SY376: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY376 @ SY368 )
| ~ ( apply @ SY366 @ SY374 @ SY376 ) )
| ~ ( apply @ SV50 @ SY376 @ SY375 ) ) )
| ~ ( ~ ~ ! [SY377: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY377 @ SY368 )
| ~ ( apply @ SY366 @ SY374 @ SY377 ) )
| ~ ( apply @ SV50 @ SY377 @ SY375 ) )
| ( apply @ SV23 @ SY374 @ SY375 ) ) ) )
| ( compose_predicate @ SV23 @ SV50 @ SY366 @ SY367 @ SY368 @ SY369 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(175,plain,
! [SV51: $i,SV24: $i] :
( ( ! [SY378: $i] :
~ ( ~ ( ~ ( member @ SV24 @ ( intersection @ SV51 @ SY378 ) )
| ~ ( ~ ( member @ SV24 @ SV51 )
| ~ ( member @ SV24 @ SY378 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV24 @ SV51 )
| ~ ( member @ SV24 @ SY378 ) )
| ( member @ SV24 @ ( intersection @ SV51 @ SY378 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(176,plain,
! [SV52: $i,SV25: $i] :
( ( ! [SY379: $i,SY380: $i,SY381: $i,SY382: $i,SY383: $i] :
( ~ ~ ( ~ ( member @ SY382 @ SY379 )
| ~ ( member @ SY383 @ SY381 ) )
| ~ ( ~ ( ~ ( apply @ ( compose_function @ SV25 @ SV52 @ SY379 @ SY380 @ SY381 ) @ SY382 @ SY383 )
| ~ ! [SY384: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY384 @ SY380 )
| ~ ( apply @ SV52 @ SY382 @ SY384 ) )
| ~ ( apply @ SV25 @ SY384 @ SY383 ) ) )
| ~ ( ~ ~ ! [SY385: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY385 @ SY380 )
| ~ ( apply @ SV52 @ SY382 @ SY385 ) )
| ~ ( apply @ SV25 @ SY385 @ SY383 ) )
| ( apply @ ( compose_function @ SV25 @ SV52 @ SY379 @ SY380 @ SY381 ) @ SY382 @ SY383 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(177,plain,
! [SV53: $i,SV26: $i] :
( ( ! [SY386: $i] :
~ ( ~ ( ~ ( member @ SY386 @ ( inverse_image2 @ SV26 @ SV53 ) )
| ~ ! [SY387: $i] :
~ ~ ( ~ ( member @ SY387 @ SV53 )
| ~ ( apply @ SV26 @ SY386 @ SY387 ) ) )
| ~ ( ~ ~ ! [SY388: $i] :
~ ~ ( ~ ( member @ SY388 @ SV53 )
| ~ ( apply @ SV26 @ SY386 @ SY388 ) )
| ( member @ SY386 @ ( inverse_image2 @ SV26 @ SV53 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(178,plain,
! [SV54: $i,SV27: $i] :
( ( ! [SY389: $i] :
~ ( ~ ( ~ ( injective @ SV27 @ SV54 @ SY389 )
| ! [SY390: $i,SY391: $i,SY392: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY390 @ SV54 )
| ~ ( member @ SY391 @ SV54 ) )
| ~ ( member @ SY392 @ SY389 ) )
| ~ ~ ( ~ ( apply @ SV27 @ SY390 @ SY392 )
| ~ ( apply @ SV27 @ SY391 @ SY392 ) )
| ( SY390 = SY391 ) ) )
| ~ ( ~ ! [SY393: $i,SY394: $i,SY395: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY393 @ SV54 )
| ~ ( member @ SY394 @ SV54 ) )
| ~ ( member @ SY395 @ SY389 ) )
| ~ ~ ( ~ ( apply @ SV27 @ SY393 @ SY395 )
| ~ ( apply @ SV27 @ SY394 @ SY395 ) )
| ( SY393 = SY394 ) )
| ( injective @ SV27 @ SV54 @ SY389 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(179,plain,
! [SV55: $i,SV28: $i] :
( ( ! [SY396: $i,SY397: $i] :
~ ( ~ ( ~ ( equal_maps @ SV28 @ SV55 @ SY396 @ SY397 )
| ! [SY398: $i,SY399: $i,SY400: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY398 @ SY396 )
| ~ ( member @ SY399 @ SY397 ) )
| ~ ( member @ SY400 @ SY397 ) )
| ~ ~ ( ~ ( apply @ SV28 @ SY398 @ SY399 )
| ~ ( apply @ SV55 @ SY398 @ SY400 ) )
| ( SY399 = SY400 ) ) )
| ~ ( ~ ! [SY401: $i,SY402: $i,SY403: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY401 @ SY396 )
| ~ ( member @ SY402 @ SY397 ) )
| ~ ( member @ SY403 @ SY397 ) )
| ~ ~ ( ~ ( apply @ SV28 @ SY401 @ SY402 )
| ~ ( apply @ SV55 @ SY401 @ SY403 ) )
| ( SY402 = SY403 ) )
| ( equal_maps @ SV28 @ SV55 @ SY396 @ SY397 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(180,plain,
! [SV2: $i,SV56: $i,SV29: $i] :
( ( ! [SY404: $i,SY405: $i] :
( ~ ~ ( ~ ( member @ SY404 @ SV29 )
| ~ ( member @ SY405 @ SV56 ) )
| ~ ( ~ ( ~ ( apply @ SV2 @ SY404 @ SY405 )
| ( apply @ ( inverse_function @ SV2 @ SV29 @ SV56 ) @ SY405 @ SY404 ) )
| ~ ( ~ ( apply @ ( inverse_function @ SV2 @ SV29 @ SV56 ) @ SY405 @ SY404 )
| ( apply @ SV2 @ SY404 @ SY405 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(181,plain,
! [SV57: $i,SV30: $i,SV3: $i] :
( ( ! [SY406: $i] :
~ ( ~ ( ~ ( member @ SY406 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
| ~ ( ~ ( member @ SY406 @ SV57 )
| ~ ~ ! [SY290: $i] :
~ ~ ( ~ ( member @ SY290 @ SV30 )
| ~ ( apply @ SV3 @ SY290 @ SY406 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY406 @ SV57 )
| ~ ~ ! [SY291: $i] :
~ ~ ( ~ ( member @ SY291 @ SV30 )
| ~ ( apply @ SV3 @ SY291 @ SY406 ) ) )
| ( member @ SY406 @ ( image3 @ SV3 @ SV30 @ SV57 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(182,plain,
! [SV58: $i,SV31: $i,SV4: $i] :
( ( ~ ( ~ ( ~ ( surjective @ SV4 @ SV31 @ SV58 )
| ! [SY409: $i] :
( ~ ( member @ SY409 @ SV58 )
| ~ ! [SY294: $i] :
~ ~ ( ~ ( member @ SY294 @ SV31 )
| ~ ( apply @ SV4 @ SY294 @ SY409 ) ) ) )
| ~ ( ~ ! [SY411: $i] :
( ~ ( member @ SY411 @ SV58 )
| ~ ! [SY296: $i] :
~ ~ ( ~ ( member @ SY296 @ SV31 )
| ~ ( apply @ SV4 @ SY296 @ SY411 ) ) )
| ( surjective @ SV4 @ SV31 @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(183,plain,
! [SV32: $i,SV5: $i] :
( ( ~ ( ~ ( subset @ SV5 @ SV32 )
| ! [SY297: $i] :
( ~ ( member @ SY297 @ SV5 )
| ( member @ SY297 @ SV32 ) ) )
| ~ ( ~ ! [SY298: $i] :
( ~ ( member @ SY298 @ SV5 )
| ( member @ SY298 @ SV32 ) )
| ( subset @ SV5 @ SV32 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(184,plain,
! [SV59: $i,SV33: $i,SV6: $i] :
( ( ! [SY413: $i,SY414: $i] :
~ ( ~ ( ~ ( decreasing @ SV6 @ SV33 @ SV59 @ SY413 @ SY414 )
| ! [SY415: $i,SY416: $i,SY417: $i,SY418: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY415 @ SV33 )
| ~ ( member @ SY416 @ SY413 ) )
| ~ ( member @ SY417 @ SV33 ) )
| ~ ( member @ SY418 @ SY413 ) )
| ~ ( apply @ SV59 @ SY415 @ SY417 ) )
| ~ ( apply @ SV6 @ SY415 @ SY416 ) )
| ~ ( apply @ SV6 @ SY417 @ SY418 ) )
| ( apply @ SY414 @ SY418 @ SY416 ) ) )
| ~ ( ~ ! [SY419: $i,SY420: $i,SY421: $i,SY422: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY419 @ SV33 )
| ~ ( member @ SY420 @ SY413 ) )
| ~ ( member @ SY421 @ SV33 ) )
| ~ ( member @ SY422 @ SY413 ) )
| ~ ( apply @ SV59 @ SY419 @ SY421 ) )
| ~ ( apply @ SV6 @ SY419 @ SY420 ) )
| ~ ( apply @ SV6 @ SY421 @ SY422 ) )
| ( apply @ SY414 @ SY422 @ SY420 ) )
| ( decreasing @ SV6 @ SV33 @ SV59 @ SY413 @ SY414 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(185,plain,
! [SV60: $i,SV34: $i,SV7: $i] :
( ( ! [SY423: $i,SY424: $i] :
~ ( ~ ( ~ ( isomorphism @ SV7 @ SV34 @ SV60 @ SY423 @ SY424 )
| ~ ( ~ ~ ( ~ ( maps @ SV7 @ SV34 @ SY423 )
| ~ ( one_to_one @ SV7 @ SV34 @ SY423 ) )
| ~ ! [SY425: $i,SY426: $i,SY427: $i,SY428: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY425 @ SV34 )
| ~ ( member @ SY426 @ SY423 ) )
| ~ ( member @ SY427 @ SV34 ) )
| ~ ( member @ SY428 @ SY423 ) )
| ~ ( apply @ SV7 @ SY425 @ SY426 ) )
| ~ ( apply @ SV7 @ SY427 @ SY428 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ SY425 @ SY427 )
| ( apply @ SY424 @ SY426 @ SY428 ) )
| ~ ( ~ ( apply @ SY424 @ SY426 @ SY428 )
| ( apply @ SV60 @ SY425 @ SY427 ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( maps @ SV7 @ SV34 @ SY423 )
| ~ ( one_to_one @ SV7 @ SV34 @ SY423 ) )
| ~ ! [SY429: $i,SY430: $i,SY431: $i,SY432: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY429 @ SV34 )
| ~ ( member @ SY430 @ SY423 ) )
| ~ ( member @ SY431 @ SV34 ) )
| ~ ( member @ SY432 @ SY423 ) )
| ~ ( apply @ SV7 @ SY429 @ SY430 ) )
| ~ ( apply @ SV7 @ SY431 @ SY432 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ SY429 @ SY431 )
| ( apply @ SY424 @ SY430 @ SY432 ) )
| ~ ( ~ ( apply @ SY424 @ SY430 @ SY432 )
| ( apply @ SV60 @ SY429 @ SY431 ) ) ) ) )
| ( isomorphism @ SV7 @ SV34 @ SV60 @ SY423 @ SY424 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(186,plain,
! [SV35: $i,SV61: $i,SV8: $i] :
( ( ~ ( ~ ( ~ ( member @ SV8 @ ( difference @ SV61 @ SV35 ) )
| ~ ( ~ ( member @ SV8 @ SV61 )
| ~ ~ ( member @ SV8 @ SV35 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV8 @ SV61 )
| ~ ~ ( member @ SV8 @ SV35 ) )
| ( member @ SV8 @ ( difference @ SV61 @ SV35 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(187,plain,
! [SV62: $i,SV36: $i,SV9: $i] :
( ( ! [SY433: $i,SY434: $i] :
~ ( ~ ( ~ ( increasing @ SV9 @ SV36 @ SV62 @ SY433 @ SY434 )
| ! [SY435: $i,SY436: $i,SY437: $i,SY438: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY435 @ SV36 )
| ~ ( member @ SY436 @ SY433 ) )
| ~ ( member @ SY437 @ SV36 ) )
| ~ ( member @ SY438 @ SY433 ) )
| ~ ( apply @ SV62 @ SY435 @ SY437 ) )
| ~ ( apply @ SV9 @ SY435 @ SY436 ) )
| ~ ( apply @ SV9 @ SY437 @ SY438 ) )
| ( apply @ SY434 @ SY436 @ SY438 ) ) )
| ~ ( ~ ! [SY439: $i,SY440: $i,SY441: $i,SY442: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY439 @ SV36 )
| ~ ( member @ SY440 @ SY433 ) )
| ~ ( member @ SY441 @ SV36 ) )
| ~ ( member @ SY442 @ SY433 ) )
| ~ ( apply @ SV62 @ SY439 @ SY441 ) )
| ~ ( apply @ SV9 @ SY439 @ SY440 ) )
| ~ ( apply @ SV9 @ SY441 @ SY442 ) )
| ( apply @ SY434 @ SY440 @ SY442 ) )
| ( increasing @ SV9 @ SV36 @ SV62 @ SY433 @ SY434 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(188,plain,
! [SV37: $i,SV10: $i] :
( ( ~ ( ~ ( member @ SV10 @ ( singleton @ SV37 ) )
| ( SV10 = SV37 ) )
| ~ ( ( SV10 != SV37 )
| ( member @ SV10 @ ( singleton @ SV37 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(189,plain,
! [SV38: $i,SV11: $i] :
( ( ~ ( ~ ( member @ SV11 @ ( sum @ SV38 ) )
| ~ ! [SY333: $i] :
~ ~ ( ~ ( member @ SY333 @ SV38 )
| ~ ( member @ SV11 @ SY333 ) ) )
| ~ ( ~ ~ ! [SY334: $i] :
~ ~ ( ~ ( member @ SY334 @ SV38 )
| ~ ( member @ SV11 @ SY334 ) )
| ( member @ SV11 @ ( sum @ SV38 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(190,plain,
! [SV63: $i,SV39: $i,SV12: $i] :
( ( ~ ( ~ ( ~ ( member @ SV12 @ ( unordered_pair @ SV39 @ SV63 ) )
| ( SV12 = SV39 )
| ( SV12 = SV63 ) )
| ~ ( ~ ( ( SV12 = SV39 )
| ( SV12 = SV63 ) )
| ( member @ SV12 @ ( unordered_pair @ SV39 @ SV63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(191,plain,
! [SV64: $i,SV40: $i,SV13: $i] :
( ( ~ ( ~ ( ~ ( one_to_one @ SV13 @ SV40 @ SV64 )
| ~ ( ~ ( injective @ SV13 @ SV40 @ SV64 )
| ~ ( surjective @ SV13 @ SV40 @ SV64 ) ) )
| ~ ( ~ ~ ( ~ ( injective @ SV13 @ SV40 @ SV64 )
| ~ ( surjective @ SV13 @ SV40 @ SV64 ) )
| ( one_to_one @ SV13 @ SV40 @ SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(192,plain,
! [SV41: $i,SV14: $i,SV65: $i] :
( ( ~ ( ~ ( ~ ( member @ SV65 @ ( image2 @ SV14 @ SV41 ) )
| ~ ! [SY443: $i] :
~ ~ ( ~ ( member @ SY443 @ SV41 )
| ~ ( apply @ SV14 @ SY443 @ SV65 ) ) )
| ~ ( ~ ~ ! [SY444: $i] :
~ ~ ( ~ ( member @ SY444 @ SV41 )
| ~ ( apply @ SV14 @ SY444 @ SV65 ) )
| ( member @ SV65 @ ( image2 @ SV14 @ SV41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(193,plain,
! [SV42: $i,SV15: $i] :
( ( ~ ( ~ ( equal_set @ SV15 @ SV42 )
| ~ ( ~ ( subset @ SV15 @ SV42 )
| ~ ( subset @ SV42 @ SV15 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV15 @ SV42 )
| ~ ( subset @ SV42 @ SV15 ) )
| ( equal_set @ SV15 @ SV42 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(194,plain,
! [SV66: $i,SV43: $i,SV16: $i] :
( ( ! [SY445: $i] :
~ ( ~ ( ~ ( member @ SY445 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
| ~ ( ~ ( member @ SY445 @ SV66 )
| ~ ~ ! [SY342: $i] :
~ ~ ( ~ ( member @ SY342 @ SV43 )
| ~ ( apply @ SV16 @ SY445 @ SY342 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY445 @ SV66 )
| ~ ~ ! [SY343: $i] :
~ ~ ( ~ ( member @ SY343 @ SV43 )
| ~ ( apply @ SV16 @ SY445 @ SY343 ) ) )
| ( member @ SY445 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(195,plain,
! [SV67: $i,SV44: $i,SV17: $i] :
( ( ! [SY448: $i] :
~ ( ~ ( ~ ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SY448 )
| ! [SY449: $i,SY450: $i] :
( ~ ~ ( ~ ( member @ SY449 @ SV67 )
| ~ ( member @ SY450 @ SY448 ) )
| ~ ( ~ ( ~ ( apply @ SV44 @ SY449 @ SY450 )
| ( apply @ SV17 @ SY450 @ SY449 ) )
| ~ ( ~ ( apply @ SV17 @ SY450 @ SY449 )
| ( apply @ SV44 @ SY449 @ SY450 ) ) ) ) )
| ~ ( ~ ! [SY451: $i,SY452: $i] :
( ~ ~ ( ~ ( member @ SY451 @ SV67 )
| ~ ( member @ SY452 @ SY448 ) )
| ~ ( ~ ( ~ ( apply @ SV44 @ SY451 @ SY452 )
| ( apply @ SV17 @ SY452 @ SY451 ) )
| ~ ( ~ ( apply @ SV17 @ SY452 @ SY451 )
| ( apply @ SV44 @ SY451 @ SY452 ) ) ) )
| ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SY448 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(196,plain,
! [SV45: $i,SV18: $i] :
( ( ~ ( ~ ( member @ SV18 @ ( power_set @ SV45 ) )
| ( subset @ SV18 @ SV45 ) )
| ~ ( ~ ( subset @ SV18 @ SV45 )
| ( member @ SV18 @ ( power_set @ SV45 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(197,plain,
! [SV46: $i,SV19: $i] :
( ( ~ ( ~ ( member @ SV19 @ ( product @ SV46 ) )
| ! [SY350: $i] :
( ~ ( member @ SY350 @ SV46 )
| ( member @ SV19 @ SY350 ) ) )
| ~ ( ~ ! [SY351: $i] :
( ~ ( member @ SY351 @ SV46 )
| ( member @ SV19 @ SY351 ) )
| ( member @ SV19 @ ( product @ SV46 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(198,plain,
! [SV68: $i,SV47: $i,SV20: $i] :
( ( ~ ( ~ ( ~ ( member @ SV20 @ ( union @ SV47 @ SV68 ) )
| ( member @ SV20 @ SV47 )
| ( member @ SV20 @ SV68 ) )
| ~ ( ~ ( ( member @ SV20 @ SV47 )
| ( member @ SV20 @ SV68 ) )
| ( member @ SV20 @ ( union @ SV47 @ SV68 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(199,plain,
! [SV69: $i,SV48: $i,SV21: $i] :
( ( ~ ( ~ ( ~ ( maps @ SV21 @ SV48 @ SV69 )
| ~ ( ~ ! [SY453: $i] :
( ~ ( member @ SY453 @ SV48 )
| ~ ! [SY454: $i] :
~ ~ ( ~ ( member @ SY454 @ SV69 )
| ~ ( apply @ SV21 @ SY453 @ SY454 ) ) )
| ~ ! [SY455: $i,SY456: $i,SY457: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY455 @ SV48 )
| ~ ( member @ SY456 @ SV69 ) )
| ~ ( member @ SY457 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY455 @ SY456 )
| ~ ( apply @ SV21 @ SY455 @ SY457 ) )
| ( SY456 = SY457 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SY458: $i] :
( ~ ( member @ SY458 @ SV48 )
| ~ ! [SY459: $i] :
~ ~ ( ~ ( member @ SY459 @ SV69 )
| ~ ( apply @ SV21 @ SY458 @ SY459 ) ) )
| ~ ! [SY460: $i,SY461: $i,SY462: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY460 @ SV48 )
| ~ ( member @ SY461 @ SV69 ) )
| ~ ( member @ SY462 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY460 @ SY461 )
| ~ ( apply @ SV21 @ SY460 @ SY462 ) )
| ( SY461 = SY462 ) ) )
| ( maps @ SV21 @ SV48 @ SV69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(200,plain,
! [SV49: $i,SV22: $i] :
( ( ~ ( ~ ( identity @ SV22 @ SV49 )
| ! [SY364: $i] :
( ~ ( member @ SY364 @ SV49 )
| ( apply @ SV22 @ SY364 @ SY364 ) ) )
| ~ ( ~ ! [SY365: $i] :
( ~ ( member @ SY365 @ SV49 )
| ( apply @ SV22 @ SY365 @ SY365 ) )
| ( identity @ SV22 @ SV49 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(201,plain,
! [SV70: $i,SV50: $i,SV23: $i] :
( ( ! [SY463: $i,SY464: $i,SY465: $i] :
~ ( ~ ( ~ ( compose_predicate @ SV23 @ SV50 @ SV70 @ SY463 @ SY464 @ SY465 )
| ! [SY466: $i,SY467: $i] :
( ~ ~ ( ~ ( member @ SY466 @ SY463 )
| ~ ( member @ SY467 @ SY465 ) )
| ~ ( ~ ( ~ ( apply @ SV23 @ SY466 @ SY467 )
| ~ ! [SY468: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY468 @ SY464 )
| ~ ( apply @ SV70 @ SY466 @ SY468 ) )
| ~ ( apply @ SV50 @ SY468 @ SY467 ) ) )
| ~ ( ~ ~ ! [SY469: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY469 @ SY464 )
| ~ ( apply @ SV70 @ SY466 @ SY469 ) )
| ~ ( apply @ SV50 @ SY469 @ SY467 ) )
| ( apply @ SV23 @ SY466 @ SY467 ) ) ) ) )
| ~ ( ~ ! [SY470: $i,SY471: $i] :
( ~ ~ ( ~ ( member @ SY470 @ SY463 )
| ~ ( member @ SY471 @ SY465 ) )
| ~ ( ~ ( ~ ( apply @ SV23 @ SY470 @ SY471 )
| ~ ! [SY472: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY472 @ SY464 )
| ~ ( apply @ SV70 @ SY470 @ SY472 ) )
| ~ ( apply @ SV50 @ SY472 @ SY471 ) ) )
| ~ ( ~ ~ ! [SY473: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY473 @ SY464 )
| ~ ( apply @ SV70 @ SY470 @ SY473 ) )
| ~ ( apply @ SV50 @ SY473 @ SY471 ) )
| ( apply @ SV23 @ SY470 @ SY471 ) ) ) )
| ( compose_predicate @ SV23 @ SV50 @ SV70 @ SY463 @ SY464 @ SY465 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(202,plain,
! [SV71: $i,SV51: $i,SV24: $i] :
( ( ~ ( ~ ( ~ ( member @ SV24 @ ( intersection @ SV51 @ SV71 ) )
| ~ ( ~ ( member @ SV24 @ SV51 )
| ~ ( member @ SV24 @ SV71 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV24 @ SV51 )
| ~ ( member @ SV24 @ SV71 ) )
| ( member @ SV24 @ ( intersection @ SV51 @ SV71 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(203,plain,
! [SV52: $i,SV25: $i,SV72: $i] :
( ( ! [SY474: $i,SY475: $i,SY476: $i,SY477: $i] :
( ~ ~ ( ~ ( member @ SY476 @ SV72 )
| ~ ( member @ SY477 @ SY475 ) )
| ~ ( ~ ( ~ ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SY474 @ SY475 ) @ SY476 @ SY477 )
| ~ ! [SY384: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY384 @ SY474 )
| ~ ( apply @ SV52 @ SY476 @ SY384 ) )
| ~ ( apply @ SV25 @ SY384 @ SY477 ) ) )
| ~ ( ~ ~ ! [SY385: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY385 @ SY474 )
| ~ ( apply @ SV52 @ SY476 @ SY385 ) )
| ~ ( apply @ SV25 @ SY385 @ SY477 ) )
| ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SY474 @ SY475 ) @ SY476 @ SY477 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(204,plain,
! [SV53: $i,SV26: $i,SV73: $i] :
( ( ~ ( ~ ( ~ ( member @ SV73 @ ( inverse_image2 @ SV26 @ SV53 ) )
| ~ ! [SY480: $i] :
~ ~ ( ~ ( member @ SY480 @ SV53 )
| ~ ( apply @ SV26 @ SV73 @ SY480 ) ) )
| ~ ( ~ ~ ! [SY481: $i] :
~ ~ ( ~ ( member @ SY481 @ SV53 )
| ~ ( apply @ SV26 @ SV73 @ SY481 ) )
| ( member @ SV73 @ ( inverse_image2 @ SV26 @ SV53 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(205,plain,
! [SV74: $i,SV54: $i,SV27: $i] :
( ( ~ ( ~ ( ~ ( injective @ SV27 @ SV54 @ SV74 )
| ! [SY482: $i,SY483: $i,SY484: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY482 @ SV54 )
| ~ ( member @ SY483 @ SV54 ) )
| ~ ( member @ SY484 @ SV74 ) )
| ~ ~ ( ~ ( apply @ SV27 @ SY482 @ SY484 )
| ~ ( apply @ SV27 @ SY483 @ SY484 ) )
| ( SY482 = SY483 ) ) )
| ~ ( ~ ! [SY485: $i,SY486: $i,SY487: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY485 @ SV54 )
| ~ ( member @ SY486 @ SV54 ) )
| ~ ( member @ SY487 @ SV74 ) )
| ~ ~ ( ~ ( apply @ SV27 @ SY485 @ SY487 )
| ~ ( apply @ SV27 @ SY486 @ SY487 ) )
| ( SY485 = SY486 ) )
| ( injective @ SV27 @ SV54 @ SV74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(206,plain,
! [SV75: $i,SV55: $i,SV28: $i] :
( ( ! [SY488: $i] :
~ ( ~ ( ~ ( equal_maps @ SV28 @ SV55 @ SV75 @ SY488 )
| ! [SY489: $i,SY490: $i,SY491: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY489 @ SV75 )
| ~ ( member @ SY490 @ SY488 ) )
| ~ ( member @ SY491 @ SY488 ) )
| ~ ~ ( ~ ( apply @ SV28 @ SY489 @ SY490 )
| ~ ( apply @ SV55 @ SY489 @ SY491 ) )
| ( SY490 = SY491 ) ) )
| ~ ( ~ ! [SY492: $i,SY493: $i,SY494: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY492 @ SV75 )
| ~ ( member @ SY493 @ SY488 ) )
| ~ ( member @ SY494 @ SY488 ) )
| ~ ~ ( ~ ( apply @ SV28 @ SY492 @ SY493 )
| ~ ( apply @ SV55 @ SY492 @ SY494 ) )
| ( SY493 = SY494 ) )
| ( equal_maps @ SV28 @ SV55 @ SV75 @ SY488 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(207,plain,
! [SV2: $i,SV56: $i,SV29: $i,SV76: $i] :
( ( ! [SY495: $i] :
( ~ ~ ( ~ ( member @ SV76 @ SV29 )
| ~ ( member @ SY495 @ SV56 ) )
| ~ ( ~ ( ~ ( apply @ SV2 @ SV76 @ SY495 )
| ( apply @ ( inverse_function @ SV2 @ SV29 @ SV56 ) @ SY495 @ SV76 ) )
| ~ ( ~ ( apply @ ( inverse_function @ SV2 @ SV29 @ SV56 ) @ SY495 @ SV76 )
| ( apply @ SV2 @ SV76 @ SY495 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(208,plain,
! [SV57: $i,SV30: $i,SV3: $i,SV77: $i] :
( ( ~ ( ~ ( ~ ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
| ~ ( ~ ( member @ SV77 @ SV57 )
| ~ ~ ! [SY496: $i] :
~ ~ ( ~ ( member @ SY496 @ SV30 )
| ~ ( apply @ SV3 @ SY496 @ SV77 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV77 @ SV57 )
| ~ ~ ! [SY497: $i] :
~ ~ ( ~ ( member @ SY497 @ SV30 )
| ~ ( apply @ SV3 @ SY497 @ SV77 ) ) )
| ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(209,plain,
! [SV58: $i,SV31: $i,SV4: $i] :
( ( ~ ( ~ ( surjective @ SV4 @ SV31 @ SV58 )
| ! [SY409: $i] :
( ~ ( member @ SY409 @ SV58 )
| ~ ! [SY294: $i] :
~ ~ ( ~ ( member @ SY294 @ SV31 )
| ~ ( apply @ SV4 @ SY294 @ SY409 ) ) ) )
| ~ ( ~ ! [SY411: $i] :
( ~ ( member @ SY411 @ SV58 )
| ~ ! [SY296: $i] :
~ ~ ( ~ ( member @ SY296 @ SV31 )
| ~ ( apply @ SV4 @ SY296 @ SY411 ) ) )
| ( surjective @ SV4 @ SV31 @ SV58 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(210,plain,
! [SV32: $i,SV5: $i] :
( ( ~ ( ~ ( subset @ SV5 @ SV32 )
| ! [SY297: $i] :
( ~ ( member @ SY297 @ SV5 )
| ( member @ SY297 @ SV32 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(211,plain,
! [SV32: $i,SV5: $i] :
( ( ~ ( ~ ! [SY298: $i] :
( ~ ( member @ SY298 @ SV5 )
| ( member @ SY298 @ SV32 ) )
| ( subset @ SV5 @ SV32 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(212,plain,
! [SV78: $i,SV59: $i,SV33: $i,SV6: $i] :
( ( ! [SY498: $i] :
~ ( ~ ( ~ ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SY498 )
| ! [SY499: $i,SY500: $i,SY501: $i,SY502: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY499 @ SV33 )
| ~ ( member @ SY500 @ SV78 ) )
| ~ ( member @ SY501 @ SV33 ) )
| ~ ( member @ SY502 @ SV78 ) )
| ~ ( apply @ SV59 @ SY499 @ SY501 ) )
| ~ ( apply @ SV6 @ SY499 @ SY500 ) )
| ~ ( apply @ SV6 @ SY501 @ SY502 ) )
| ( apply @ SY498 @ SY502 @ SY500 ) ) )
| ~ ( ~ ! [SY503: $i,SY504: $i,SY505: $i,SY506: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY503 @ SV33 )
| ~ ( member @ SY504 @ SV78 ) )
| ~ ( member @ SY505 @ SV33 ) )
| ~ ( member @ SY506 @ SV78 ) )
| ~ ( apply @ SV59 @ SY503 @ SY505 ) )
| ~ ( apply @ SV6 @ SY503 @ SY504 ) )
| ~ ( apply @ SV6 @ SY505 @ SY506 ) )
| ( apply @ SY498 @ SY506 @ SY504 ) )
| ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SY498 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(213,plain,
! [SV79: $i,SV60: $i,SV34: $i,SV7: $i] :
( ( ! [SY507: $i] :
~ ( ~ ( ~ ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SY507 )
| ~ ( ~ ~ ( ~ ( maps @ SV7 @ SV34 @ SV79 )
| ~ ( one_to_one @ SV7 @ SV34 @ SV79 ) )
| ~ ! [SY508: $i,SY509: $i,SY510: $i,SY511: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY508 @ SV34 )
| ~ ( member @ SY509 @ SV79 ) )
| ~ ( member @ SY510 @ SV34 ) )
| ~ ( member @ SY511 @ SV79 ) )
| ~ ( apply @ SV7 @ SY508 @ SY509 ) )
| ~ ( apply @ SV7 @ SY510 @ SY511 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ SY508 @ SY510 )
| ( apply @ SY507 @ SY509 @ SY511 ) )
| ~ ( ~ ( apply @ SY507 @ SY509 @ SY511 )
| ( apply @ SV60 @ SY508 @ SY510 ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( maps @ SV7 @ SV34 @ SV79 )
| ~ ( one_to_one @ SV7 @ SV34 @ SV79 ) )
| ~ ! [SY512: $i,SY513: $i,SY514: $i,SY515: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY512 @ SV34 )
| ~ ( member @ SY513 @ SV79 ) )
| ~ ( member @ SY514 @ SV34 ) )
| ~ ( member @ SY515 @ SV79 ) )
| ~ ( apply @ SV7 @ SY512 @ SY513 ) )
| ~ ( apply @ SV7 @ SY514 @ SY515 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ SY512 @ SY514 )
| ( apply @ SY507 @ SY513 @ SY515 ) )
| ~ ( ~ ( apply @ SY507 @ SY513 @ SY515 )
| ( apply @ SV60 @ SY512 @ SY514 ) ) ) ) )
| ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SY507 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(214,plain,
! [SV35: $i,SV61: $i,SV8: $i] :
( ( ~ ( ~ ( member @ SV8 @ ( difference @ SV61 @ SV35 ) )
| ~ ( ~ ( member @ SV8 @ SV61 )
| ~ ~ ( member @ SV8 @ SV35 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV8 @ SV61 )
| ~ ~ ( member @ SV8 @ SV35 ) )
| ( member @ SV8 @ ( difference @ SV61 @ SV35 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(215,plain,
! [SV80: $i,SV62: $i,SV36: $i,SV9: $i] :
( ( ! [SY516: $i] :
~ ( ~ ( ~ ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SY516 )
| ! [SY517: $i,SY518: $i,SY519: $i,SY520: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY517 @ SV36 )
| ~ ( member @ SY518 @ SV80 ) )
| ~ ( member @ SY519 @ SV36 ) )
| ~ ( member @ SY520 @ SV80 ) )
| ~ ( apply @ SV62 @ SY517 @ SY519 ) )
| ~ ( apply @ SV9 @ SY517 @ SY518 ) )
| ~ ( apply @ SV9 @ SY519 @ SY520 ) )
| ( apply @ SY516 @ SY518 @ SY520 ) ) )
| ~ ( ~ ! [SY521: $i,SY522: $i,SY523: $i,SY524: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY521 @ SV36 )
| ~ ( member @ SY522 @ SV80 ) )
| ~ ( member @ SY523 @ SV36 ) )
| ~ ( member @ SY524 @ SV80 ) )
| ~ ( apply @ SV62 @ SY521 @ SY523 ) )
| ~ ( apply @ SV9 @ SY521 @ SY522 ) )
| ~ ( apply @ SV9 @ SY523 @ SY524 ) )
| ( apply @ SY516 @ SY522 @ SY524 ) )
| ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SY516 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(216,plain,
! [SV37: $i,SV10: $i] :
( ( ~ ( ~ ( member @ SV10 @ ( singleton @ SV37 ) )
| ( SV10 = SV37 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(217,plain,
! [SV37: $i,SV10: $i] :
( ( ~ ( ( SV10 != SV37 )
| ( member @ SV10 @ ( singleton @ SV37 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(218,plain,
! [SV38: $i,SV11: $i] :
( ( ~ ( ~ ( member @ SV11 @ ( sum @ SV38 ) )
| ~ ! [SY333: $i] :
~ ~ ( ~ ( member @ SY333 @ SV38 )
| ~ ( member @ SV11 @ SY333 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(219,plain,
! [SV11: $i,SV38: $i] :
( ( ~ ( ~ ~ ! [SY334: $i] :
~ ~ ( ~ ( member @ SY334 @ SV38 )
| ~ ( member @ SV11 @ SY334 ) )
| ( member @ SV11 @ ( sum @ SV38 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(220,plain,
! [SV63: $i,SV39: $i,SV12: $i] :
( ( ~ ( ~ ( member @ SV12 @ ( unordered_pair @ SV39 @ SV63 ) )
| ( SV12 = SV39 )
| ( SV12 = SV63 ) )
| ~ ( ~ ( ( SV12 = SV39 )
| ( SV12 = SV63 ) )
| ( member @ SV12 @ ( unordered_pair @ SV39 @ SV63 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(221,plain,
! [SV64: $i,SV40: $i,SV13: $i] :
( ( ~ ( ~ ( one_to_one @ SV13 @ SV40 @ SV64 )
| ~ ( ~ ( injective @ SV13 @ SV40 @ SV64 )
| ~ ( surjective @ SV13 @ SV40 @ SV64 ) ) )
| ~ ( ~ ~ ( ~ ( injective @ SV13 @ SV40 @ SV64 )
| ~ ( surjective @ SV13 @ SV40 @ SV64 ) )
| ( one_to_one @ SV13 @ SV40 @ SV64 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(222,plain,
! [SV41: $i,SV14: $i,SV65: $i] :
( ( ~ ( ~ ( member @ SV65 @ ( image2 @ SV14 @ SV41 ) )
| ~ ! [SY443: $i] :
~ ~ ( ~ ( member @ SY443 @ SV41 )
| ~ ( apply @ SV14 @ SY443 @ SV65 ) ) )
| ~ ( ~ ~ ! [SY444: $i] :
~ ~ ( ~ ( member @ SY444 @ SV41 )
| ~ ( apply @ SV14 @ SY444 @ SV65 ) )
| ( member @ SV65 @ ( image2 @ SV14 @ SV41 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(223,plain,
! [SV42: $i,SV15: $i] :
( ( ~ ( ~ ( equal_set @ SV15 @ SV42 )
| ~ ( ~ ( subset @ SV15 @ SV42 )
| ~ ( subset @ SV42 @ SV15 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(224,plain,
! [SV42: $i,SV15: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV15 @ SV42 )
| ~ ( subset @ SV42 @ SV15 ) )
| ( equal_set @ SV15 @ SV42 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(225,plain,
! [SV66: $i,SV43: $i,SV16: $i,SV81: $i] :
( ( ~ ( ~ ( ~ ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
| ~ ( ~ ( member @ SV81 @ SV66 )
| ~ ~ ! [SY525: $i] :
~ ~ ( ~ ( member @ SY525 @ SV43 )
| ~ ( apply @ SV16 @ SV81 @ SY525 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV81 @ SV66 )
| ~ ~ ! [SY526: $i] :
~ ~ ( ~ ( member @ SY526 @ SV43 )
| ~ ( apply @ SV16 @ SV81 @ SY526 ) ) )
| ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(226,plain,
! [SV82: $i,SV67: $i,SV44: $i,SV17: $i] :
( ( ~ ( ~ ( ~ ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
| ! [SY527: $i,SY528: $i] :
( ~ ~ ( ~ ( member @ SY527 @ SV67 )
| ~ ( member @ SY528 @ SV82 ) )
| ~ ( ~ ( ~ ( apply @ SV44 @ SY527 @ SY528 )
| ( apply @ SV17 @ SY528 @ SY527 ) )
| ~ ( ~ ( apply @ SV17 @ SY528 @ SY527 )
| ( apply @ SV44 @ SY527 @ SY528 ) ) ) ) )
| ~ ( ~ ! [SY529: $i,SY530: $i] :
( ~ ~ ( ~ ( member @ SY529 @ SV67 )
| ~ ( member @ SY530 @ SV82 ) )
| ~ ( ~ ( ~ ( apply @ SV44 @ SY529 @ SY530 )
| ( apply @ SV17 @ SY530 @ SY529 ) )
| ~ ( ~ ( apply @ SV17 @ SY530 @ SY529 )
| ( apply @ SV44 @ SY529 @ SY530 ) ) ) )
| ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(227,plain,
! [SV45: $i,SV18: $i] :
( ( ~ ( ~ ( member @ SV18 @ ( power_set @ SV45 ) )
| ( subset @ SV18 @ SV45 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(228,plain,
! [SV45: $i,SV18: $i] :
( ( ~ ( ~ ( subset @ SV18 @ SV45 )
| ( member @ SV18 @ ( power_set @ SV45 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(229,plain,
! [SV46: $i,SV19: $i] :
( ( ~ ( ~ ( member @ SV19 @ ( product @ SV46 ) )
| ! [SY350: $i] :
( ~ ( member @ SY350 @ SV46 )
| ( member @ SV19 @ SY350 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(230,plain,
! [SV19: $i,SV46: $i] :
( ( ~ ( ~ ! [SY351: $i] :
( ~ ( member @ SY351 @ SV46 )
| ( member @ SV19 @ SY351 ) )
| ( member @ SV19 @ ( product @ SV46 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(231,plain,
! [SV68: $i,SV47: $i,SV20: $i] :
( ( ~ ( ~ ( member @ SV20 @ ( union @ SV47 @ SV68 ) )
| ( member @ SV20 @ SV47 )
| ( member @ SV20 @ SV68 ) )
| ~ ( ~ ( ( member @ SV20 @ SV47 )
| ( member @ SV20 @ SV68 ) )
| ( member @ SV20 @ ( union @ SV47 @ SV68 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(232,plain,
! [SV69: $i,SV48: $i,SV21: $i] :
( ( ~ ( ~ ( maps @ SV21 @ SV48 @ SV69 )
| ~ ( ~ ! [SY453: $i] :
( ~ ( member @ SY453 @ SV48 )
| ~ ! [SY454: $i] :
~ ~ ( ~ ( member @ SY454 @ SV69 )
| ~ ( apply @ SV21 @ SY453 @ SY454 ) ) )
| ~ ! [SY455: $i,SY456: $i,SY457: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY455 @ SV48 )
| ~ ( member @ SY456 @ SV69 ) )
| ~ ( member @ SY457 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY455 @ SY456 )
| ~ ( apply @ SV21 @ SY455 @ SY457 ) )
| ( SY456 = SY457 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SY458: $i] :
( ~ ( member @ SY458 @ SV48 )
| ~ ! [SY459: $i] :
~ ~ ( ~ ( member @ SY459 @ SV69 )
| ~ ( apply @ SV21 @ SY458 @ SY459 ) ) )
| ~ ! [SY460: $i,SY461: $i,SY462: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY460 @ SV48 )
| ~ ( member @ SY461 @ SV69 ) )
| ~ ( member @ SY462 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY460 @ SY461 )
| ~ ( apply @ SV21 @ SY460 @ SY462 ) )
| ( SY461 = SY462 ) ) )
| ( maps @ SV21 @ SV48 @ SV69 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(233,plain,
! [SV49: $i,SV22: $i] :
( ( ~ ( ~ ( identity @ SV22 @ SV49 )
| ! [SY364: $i] :
( ~ ( member @ SY364 @ SV49 )
| ( apply @ SV22 @ SY364 @ SY364 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[200]) ).
thf(234,plain,
! [SV22: $i,SV49: $i] :
( ( ~ ( ~ ! [SY365: $i] :
( ~ ( member @ SY365 @ SV49 )
| ( apply @ SV22 @ SY365 @ SY365 ) )
| ( identity @ SV22 @ SV49 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[200]) ).
thf(235,plain,
! [SV83: $i,SV70: $i,SV50: $i,SV23: $i] :
( ( ! [SY531: $i,SY532: $i] :
~ ( ~ ( ~ ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SY531 @ SY532 )
| ! [SY533: $i,SY534: $i] :
( ~ ~ ( ~ ( member @ SY533 @ SV83 )
| ~ ( member @ SY534 @ SY532 ) )
| ~ ( ~ ( ~ ( apply @ SV23 @ SY533 @ SY534 )
| ~ ! [SY468: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY468 @ SY531 )
| ~ ( apply @ SV70 @ SY533 @ SY468 ) )
| ~ ( apply @ SV50 @ SY468 @ SY534 ) ) )
| ~ ( ~ ~ ! [SY469: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY469 @ SY531 )
| ~ ( apply @ SV70 @ SY533 @ SY469 ) )
| ~ ( apply @ SV50 @ SY469 @ SY534 ) )
| ( apply @ SV23 @ SY533 @ SY534 ) ) ) ) )
| ~ ( ~ ! [SY537: $i,SY538: $i] :
( ~ ~ ( ~ ( member @ SY537 @ SV83 )
| ~ ( member @ SY538 @ SY532 ) )
| ~ ( ~ ( ~ ( apply @ SV23 @ SY537 @ SY538 )
| ~ ! [SY472: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY472 @ SY531 )
| ~ ( apply @ SV70 @ SY537 @ SY472 ) )
| ~ ( apply @ SV50 @ SY472 @ SY538 ) ) )
| ~ ( ~ ~ ! [SY473: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY473 @ SY531 )
| ~ ( apply @ SV70 @ SY537 @ SY473 ) )
| ~ ( apply @ SV50 @ SY473 @ SY538 ) )
| ( apply @ SV23 @ SY537 @ SY538 ) ) ) )
| ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SY531 @ SY532 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(236,plain,
! [SV71: $i,SV51: $i,SV24: $i] :
( ( ~ ( ~ ( member @ SV24 @ ( intersection @ SV51 @ SV71 ) )
| ~ ( ~ ( member @ SV24 @ SV51 )
| ~ ( member @ SV24 @ SV71 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV24 @ SV51 )
| ~ ( member @ SV24 @ SV71 ) )
| ( member @ SV24 @ ( intersection @ SV51 @ SV71 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(237,plain,
! [SV84: $i,SV52: $i,SV25: $i,SV72: $i] :
( ( ! [SY541: $i,SY542: $i,SY543: $i] :
( ~ ~ ( ~ ( member @ SY542 @ SV72 )
| ~ ( member @ SY543 @ SY541 ) )
| ~ ( ~ ( ~ ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SY541 ) @ SY542 @ SY543 )
| ~ ! [SY544: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY544 @ SV84 )
| ~ ( apply @ SV52 @ SY542 @ SY544 ) )
| ~ ( apply @ SV25 @ SY544 @ SY543 ) ) )
| ~ ( ~ ~ ! [SY545: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY545 @ SV84 )
| ~ ( apply @ SV52 @ SY542 @ SY545 ) )
| ~ ( apply @ SV25 @ SY545 @ SY543 ) )
| ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SY541 ) @ SY542 @ SY543 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(238,plain,
! [SV53: $i,SV26: $i,SV73: $i] :
( ( ~ ( ~ ( member @ SV73 @ ( inverse_image2 @ SV26 @ SV53 ) )
| ~ ! [SY480: $i] :
~ ~ ( ~ ( member @ SY480 @ SV53 )
| ~ ( apply @ SV26 @ SV73 @ SY480 ) ) )
| ~ ( ~ ~ ! [SY481: $i] :
~ ~ ( ~ ( member @ SY481 @ SV53 )
| ~ ( apply @ SV26 @ SV73 @ SY481 ) )
| ( member @ SV73 @ ( inverse_image2 @ SV26 @ SV53 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(239,plain,
! [SV74: $i,SV54: $i,SV27: $i] :
( ( ~ ( ~ ( injective @ SV27 @ SV54 @ SV74 )
| ! [SY482: $i,SY483: $i,SY484: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY482 @ SV54 )
| ~ ( member @ SY483 @ SV54 ) )
| ~ ( member @ SY484 @ SV74 ) )
| ~ ~ ( ~ ( apply @ SV27 @ SY482 @ SY484 )
| ~ ( apply @ SV27 @ SY483 @ SY484 ) )
| ( SY482 = SY483 ) ) )
| ~ ( ~ ! [SY485: $i,SY486: $i,SY487: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY485 @ SV54 )
| ~ ( member @ SY486 @ SV54 ) )
| ~ ( member @ SY487 @ SV74 ) )
| ~ ~ ( ~ ( apply @ SV27 @ SY485 @ SY487 )
| ~ ( apply @ SV27 @ SY486 @ SY487 ) )
| ( SY485 = SY486 ) )
| ( injective @ SV27 @ SV54 @ SV74 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(240,plain,
! [SV85: $i,SV75: $i,SV55: $i,SV28: $i] :
( ( ~ ( ~ ( ~ ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
| ! [SY546: $i,SY547: $i,SY548: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY546 @ SV75 )
| ~ ( member @ SY547 @ SV85 ) )
| ~ ( member @ SY548 @ SV85 ) )
| ~ ~ ( ~ ( apply @ SV28 @ SY546 @ SY547 )
| ~ ( apply @ SV55 @ SY546 @ SY548 ) )
| ( SY547 = SY548 ) ) )
| ~ ( ~ ! [SY549: $i,SY550: $i,SY551: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY549 @ SV75 )
| ~ ( member @ SY550 @ SV85 ) )
| ~ ( member @ SY551 @ SV85 ) )
| ~ ~ ( ~ ( apply @ SV28 @ SY549 @ SY550 )
| ~ ( apply @ SV55 @ SY549 @ SY551 ) )
| ( SY550 = SY551 ) )
| ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(241,plain,
! [SV2: $i,SV56: $i,SV86: $i,SV29: $i,SV76: $i] :
( ( ~ ~ ( ~ ( member @ SV76 @ SV29 )
| ~ ( member @ SV86 @ SV56 ) )
| ~ ( ~ ( ~ ( apply @ SV2 @ SV76 @ SV86 )
| ( apply @ ( inverse_function @ SV2 @ SV29 @ SV56 ) @ SV86 @ SV76 ) )
| ~ ( ~ ( apply @ ( inverse_function @ SV2 @ SV29 @ SV56 ) @ SV86 @ SV76 )
| ( apply @ SV2 @ SV76 @ SV86 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(242,plain,
! [SV57: $i,SV30: $i,SV3: $i,SV77: $i] :
( ( ~ ( ~ ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
| ~ ( ~ ( member @ SV77 @ SV57 )
| ~ ~ ! [SY496: $i] :
~ ~ ( ~ ( member @ SY496 @ SV30 )
| ~ ( apply @ SV3 @ SY496 @ SV77 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV77 @ SV57 )
| ~ ~ ! [SY497: $i] :
~ ~ ( ~ ( member @ SY497 @ SV30 )
| ~ ( apply @ SV3 @ SY497 @ SV77 ) ) )
| ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(243,plain,
! [SV58: $i,SV31: $i,SV4: $i] :
( ( ~ ( ~ ( surjective @ SV4 @ SV31 @ SV58 )
| ! [SY409: $i] :
( ~ ( member @ SY409 @ SV58 )
| ~ ! [SY294: $i] :
~ ~ ( ~ ( member @ SY294 @ SV31 )
| ~ ( apply @ SV4 @ SY294 @ SY409 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(244,plain,
! [SV4: $i,SV31: $i,SV58: $i] :
( ( ~ ( ~ ! [SY411: $i] :
( ~ ( member @ SY411 @ SV58 )
| ~ ! [SY296: $i] :
~ ~ ( ~ ( member @ SY296 @ SV31 )
| ~ ( apply @ SV4 @ SY296 @ SY411 ) ) )
| ( surjective @ SV4 @ SV31 @ SV58 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(245,plain,
! [SV32: $i,SV5: $i] :
( ( ~ ( subset @ SV5 @ SV32 )
| ! [SY297: $i] :
( ~ ( member @ SY297 @ SV5 )
| ( member @ SY297 @ SV32 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(246,plain,
! [SV32: $i,SV5: $i] :
( ( ~ ! [SY298: $i] :
( ~ ( member @ SY298 @ SV5 )
| ( member @ SY298 @ SV32 ) )
| ( subset @ SV5 @ SV32 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(247,plain,
! [SV87: $i,SV78: $i,SV59: $i,SV33: $i,SV6: $i] :
( ( ~ ( ~ ( ~ ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
| ! [SY552: $i,SY553: $i,SY554: $i,SY555: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY552 @ SV33 )
| ~ ( member @ SY553 @ SV78 ) )
| ~ ( member @ SY554 @ SV33 ) )
| ~ ( member @ SY555 @ SV78 ) )
| ~ ( apply @ SV59 @ SY552 @ SY554 ) )
| ~ ( apply @ SV6 @ SY552 @ SY553 ) )
| ~ ( apply @ SV6 @ SY554 @ SY555 ) )
| ( apply @ SV87 @ SY555 @ SY553 ) ) )
| ~ ( ~ ! [SY556: $i,SY557: $i,SY558: $i,SY559: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY556 @ SV33 )
| ~ ( member @ SY557 @ SV78 ) )
| ~ ( member @ SY558 @ SV33 ) )
| ~ ( member @ SY559 @ SV78 ) )
| ~ ( apply @ SV59 @ SY556 @ SY558 ) )
| ~ ( apply @ SV6 @ SY556 @ SY557 ) )
| ~ ( apply @ SV6 @ SY558 @ SY559 ) )
| ( apply @ SV87 @ SY559 @ SY557 ) )
| ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(248,plain,
! [SV88: $i,SV79: $i,SV60: $i,SV34: $i,SV7: $i] :
( ( ~ ( ~ ( ~ ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
| ~ ( ~ ~ ( ~ ( maps @ SV7 @ SV34 @ SV79 )
| ~ ( one_to_one @ SV7 @ SV34 @ SV79 ) )
| ~ ! [SY560: $i,SY561: $i,SY562: $i,SY563: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY560 @ SV34 )
| ~ ( member @ SY561 @ SV79 ) )
| ~ ( member @ SY562 @ SV34 ) )
| ~ ( member @ SY563 @ SV79 ) )
| ~ ( apply @ SV7 @ SY560 @ SY561 ) )
| ~ ( apply @ SV7 @ SY562 @ SY563 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ SY560 @ SY562 )
| ( apply @ SV88 @ SY561 @ SY563 ) )
| ~ ( ~ ( apply @ SV88 @ SY561 @ SY563 )
| ( apply @ SV60 @ SY560 @ SY562 ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( maps @ SV7 @ SV34 @ SV79 )
| ~ ( one_to_one @ SV7 @ SV34 @ SV79 ) )
| ~ ! [SY564: $i,SY565: $i,SY566: $i,SY567: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY564 @ SV34 )
| ~ ( member @ SY565 @ SV79 ) )
| ~ ( member @ SY566 @ SV34 ) )
| ~ ( member @ SY567 @ SV79 ) )
| ~ ( apply @ SV7 @ SY564 @ SY565 ) )
| ~ ( apply @ SV7 @ SY566 @ SY567 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ SY564 @ SY566 )
| ( apply @ SV88 @ SY565 @ SY567 ) )
| ~ ( ~ ( apply @ SV88 @ SY565 @ SY567 )
| ( apply @ SV60 @ SY564 @ SY566 ) ) ) ) )
| ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(249,plain,
! [SV35: $i,SV61: $i,SV8: $i] :
( ( ~ ( ~ ( member @ SV8 @ ( difference @ SV61 @ SV35 ) )
| ~ ( ~ ( member @ SV8 @ SV61 )
| ~ ~ ( member @ SV8 @ SV35 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(250,plain,
! [SV35: $i,SV61: $i,SV8: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV8 @ SV61 )
| ~ ~ ( member @ SV8 @ SV35 ) )
| ( member @ SV8 @ ( difference @ SV61 @ SV35 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(251,plain,
! [SV89: $i,SV80: $i,SV62: $i,SV36: $i,SV9: $i] :
( ( ~ ( ~ ( ~ ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
| ! [SY568: $i,SY569: $i,SY570: $i,SY571: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY568 @ SV36 )
| ~ ( member @ SY569 @ SV80 ) )
| ~ ( member @ SY570 @ SV36 ) )
| ~ ( member @ SY571 @ SV80 ) )
| ~ ( apply @ SV62 @ SY568 @ SY570 ) )
| ~ ( apply @ SV9 @ SY568 @ SY569 ) )
| ~ ( apply @ SV9 @ SY570 @ SY571 ) )
| ( apply @ SV89 @ SY569 @ SY571 ) ) )
| ~ ( ~ ! [SY572: $i,SY573: $i,SY574: $i,SY575: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY572 @ SV36 )
| ~ ( member @ SY573 @ SV80 ) )
| ~ ( member @ SY574 @ SV36 ) )
| ~ ( member @ SY575 @ SV80 ) )
| ~ ( apply @ SV62 @ SY572 @ SY574 ) )
| ~ ( apply @ SV9 @ SY572 @ SY573 ) )
| ~ ( apply @ SV9 @ SY574 @ SY575 ) )
| ( apply @ SV89 @ SY573 @ SY575 ) )
| ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(252,plain,
! [SV37: $i,SV10: $i] :
( ( ~ ( member @ SV10 @ ( singleton @ SV37 ) )
| ( SV10 = SV37 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[216]) ).
thf(253,plain,
! [SV37: $i,SV10: $i] :
( ( ( SV10 != SV37 )
| ( member @ SV10 @ ( singleton @ SV37 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(254,plain,
! [SV38: $i,SV11: $i] :
( ( ~ ( member @ SV11 @ ( sum @ SV38 ) )
| ~ ! [SY333: $i] :
~ ~ ( ~ ( member @ SY333 @ SV38 )
| ~ ( member @ SV11 @ SY333 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(255,plain,
! [SV11: $i,SV38: $i] :
( ( ~ ~ ! [SY334: $i] :
~ ~ ( ~ ( member @ SY334 @ SV38 )
| ~ ( member @ SV11 @ SY334 ) )
| ( member @ SV11 @ ( sum @ SV38 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(256,plain,
! [SV63: $i,SV39: $i,SV12: $i] :
( ( ~ ( ~ ( member @ SV12 @ ( unordered_pair @ SV39 @ SV63 ) )
| ( SV12 = SV39 )
| ( SV12 = SV63 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[220]) ).
thf(257,plain,
! [SV63: $i,SV39: $i,SV12: $i] :
( ( ~ ( ~ ( ( SV12 = SV39 )
| ( SV12 = SV63 ) )
| ( member @ SV12 @ ( unordered_pair @ SV39 @ SV63 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[220]) ).
thf(258,plain,
! [SV64: $i,SV40: $i,SV13: $i] :
( ( ~ ( ~ ( one_to_one @ SV13 @ SV40 @ SV64 )
| ~ ( ~ ( injective @ SV13 @ SV40 @ SV64 )
| ~ ( surjective @ SV13 @ SV40 @ SV64 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(259,plain,
! [SV64: $i,SV40: $i,SV13: $i] :
( ( ~ ( ~ ~ ( ~ ( injective @ SV13 @ SV40 @ SV64 )
| ~ ( surjective @ SV13 @ SV40 @ SV64 ) )
| ( one_to_one @ SV13 @ SV40 @ SV64 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(260,plain,
! [SV41: $i,SV14: $i,SV65: $i] :
( ( ~ ( ~ ( member @ SV65 @ ( image2 @ SV14 @ SV41 ) )
| ~ ! [SY443: $i] :
~ ~ ( ~ ( member @ SY443 @ SV41 )
| ~ ( apply @ SV14 @ SY443 @ SV65 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(261,plain,
! [SV65: $i,SV14: $i,SV41: $i] :
( ( ~ ( ~ ~ ! [SY444: $i] :
~ ~ ( ~ ( member @ SY444 @ SV41 )
| ~ ( apply @ SV14 @ SY444 @ SV65 ) )
| ( member @ SV65 @ ( image2 @ SV14 @ SV41 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(262,plain,
! [SV42: $i,SV15: $i] :
( ( ~ ( equal_set @ SV15 @ SV42 )
| ~ ( ~ ( subset @ SV15 @ SV42 )
| ~ ( subset @ SV42 @ SV15 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(263,plain,
! [SV42: $i,SV15: $i] :
( ( ~ ~ ( ~ ( subset @ SV15 @ SV42 )
| ~ ( subset @ SV42 @ SV15 ) )
| ( equal_set @ SV15 @ SV42 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[224]) ).
thf(264,plain,
! [SV66: $i,SV43: $i,SV16: $i,SV81: $i] :
( ( ~ ( ~ ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
| ~ ( ~ ( member @ SV81 @ SV66 )
| ~ ~ ! [SY525: $i] :
~ ~ ( ~ ( member @ SY525 @ SV43 )
| ~ ( apply @ SV16 @ SV81 @ SY525 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV81 @ SV66 )
| ~ ~ ! [SY526: $i] :
~ ~ ( ~ ( member @ SY526 @ SV43 )
| ~ ( apply @ SV16 @ SV81 @ SY526 ) ) )
| ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(265,plain,
! [SV82: $i,SV67: $i,SV44: $i,SV17: $i] :
( ( ~ ( ~ ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
| ! [SY527: $i,SY528: $i] :
( ~ ~ ( ~ ( member @ SY527 @ SV67 )
| ~ ( member @ SY528 @ SV82 ) )
| ~ ( ~ ( ~ ( apply @ SV44 @ SY527 @ SY528 )
| ( apply @ SV17 @ SY528 @ SY527 ) )
| ~ ( ~ ( apply @ SV17 @ SY528 @ SY527 )
| ( apply @ SV44 @ SY527 @ SY528 ) ) ) ) )
| ~ ( ~ ! [SY529: $i,SY530: $i] :
( ~ ~ ( ~ ( member @ SY529 @ SV67 )
| ~ ( member @ SY530 @ SV82 ) )
| ~ ( ~ ( ~ ( apply @ SV44 @ SY529 @ SY530 )
| ( apply @ SV17 @ SY530 @ SY529 ) )
| ~ ( ~ ( apply @ SV17 @ SY530 @ SY529 )
| ( apply @ SV44 @ SY529 @ SY530 ) ) ) )
| ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(266,plain,
! [SV45: $i,SV18: $i] :
( ( ~ ( member @ SV18 @ ( power_set @ SV45 ) )
| ( subset @ SV18 @ SV45 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(267,plain,
! [SV45: $i,SV18: $i] :
( ( ~ ( subset @ SV18 @ SV45 )
| ( member @ SV18 @ ( power_set @ SV45 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(268,plain,
! [SV46: $i,SV19: $i] :
( ( ~ ( member @ SV19 @ ( product @ SV46 ) )
| ! [SY350: $i] :
( ~ ( member @ SY350 @ SV46 )
| ( member @ SV19 @ SY350 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(269,plain,
! [SV19: $i,SV46: $i] :
( ( ~ ! [SY351: $i] :
( ~ ( member @ SY351 @ SV46 )
| ( member @ SV19 @ SY351 ) )
| ( member @ SV19 @ ( product @ SV46 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(270,plain,
! [SV68: $i,SV47: $i,SV20: $i] :
( ( ~ ( ~ ( member @ SV20 @ ( union @ SV47 @ SV68 ) )
| ( member @ SV20 @ SV47 )
| ( member @ SV20 @ SV68 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[231]) ).
thf(271,plain,
! [SV68: $i,SV47: $i,SV20: $i] :
( ( ~ ( ~ ( ( member @ SV20 @ SV47 )
| ( member @ SV20 @ SV68 ) )
| ( member @ SV20 @ ( union @ SV47 @ SV68 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[231]) ).
thf(272,plain,
! [SV69: $i,SV48: $i,SV21: $i] :
( ( ~ ( ~ ( maps @ SV21 @ SV48 @ SV69 )
| ~ ( ~ ! [SY453: $i] :
( ~ ( member @ SY453 @ SV48 )
| ~ ! [SY454: $i] :
~ ~ ( ~ ( member @ SY454 @ SV69 )
| ~ ( apply @ SV21 @ SY453 @ SY454 ) ) )
| ~ ! [SY455: $i,SY456: $i,SY457: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY455 @ SV48 )
| ~ ( member @ SY456 @ SV69 ) )
| ~ ( member @ SY457 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY455 @ SY456 )
| ~ ( apply @ SV21 @ SY455 @ SY457 ) )
| ( SY456 = SY457 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[232]) ).
thf(273,plain,
! [SV21: $i,SV69: $i,SV48: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY458: $i] :
( ~ ( member @ SY458 @ SV48 )
| ~ ! [SY459: $i] :
~ ~ ( ~ ( member @ SY459 @ SV69 )
| ~ ( apply @ SV21 @ SY458 @ SY459 ) ) )
| ~ ! [SY460: $i,SY461: $i,SY462: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY460 @ SV48 )
| ~ ( member @ SY461 @ SV69 ) )
| ~ ( member @ SY462 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY460 @ SY461 )
| ~ ( apply @ SV21 @ SY460 @ SY462 ) )
| ( SY461 = SY462 ) ) )
| ( maps @ SV21 @ SV48 @ SV69 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[232]) ).
thf(274,plain,
! [SV49: $i,SV22: $i] :
( ( ~ ( identity @ SV22 @ SV49 )
| ! [SY364: $i] :
( ~ ( member @ SY364 @ SV49 )
| ( apply @ SV22 @ SY364 @ SY364 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(275,plain,
! [SV22: $i,SV49: $i] :
( ( ~ ! [SY365: $i] :
( ~ ( member @ SY365 @ SV49 )
| ( apply @ SV22 @ SY365 @ SY365 ) )
| ( identity @ SV22 @ SV49 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(276,plain,
! [SV90: $i,SV83: $i,SV70: $i,SV50: $i,SV23: $i] :
( ( ! [SY576: $i] :
~ ( ~ ( ~ ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SY576 )
| ! [SY577: $i,SY578: $i] :
( ~ ~ ( ~ ( member @ SY577 @ SV83 )
| ~ ( member @ SY578 @ SY576 ) )
| ~ ( ~ ( ~ ( apply @ SV23 @ SY577 @ SY578 )
| ~ ! [SY579: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY579 @ SV90 )
| ~ ( apply @ SV70 @ SY577 @ SY579 ) )
| ~ ( apply @ SV50 @ SY579 @ SY578 ) ) )
| ~ ( ~ ~ ! [SY580: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY580 @ SV90 )
| ~ ( apply @ SV70 @ SY577 @ SY580 ) )
| ~ ( apply @ SV50 @ SY580 @ SY578 ) )
| ( apply @ SV23 @ SY577 @ SY578 ) ) ) ) )
| ~ ( ~ ! [SY581: $i,SY582: $i] :
( ~ ~ ( ~ ( member @ SY581 @ SV83 )
| ~ ( member @ SY582 @ SY576 ) )
| ~ ( ~ ( ~ ( apply @ SV23 @ SY581 @ SY582 )
| ~ ! [SY583: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY583 @ SV90 )
| ~ ( apply @ SV70 @ SY581 @ SY583 ) )
| ~ ( apply @ SV50 @ SY583 @ SY582 ) ) )
| ~ ( ~ ~ ! [SY584: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY584 @ SV90 )
| ~ ( apply @ SV70 @ SY581 @ SY584 ) )
| ~ ( apply @ SV50 @ SY584 @ SY582 ) )
| ( apply @ SV23 @ SY581 @ SY582 ) ) ) )
| ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SY576 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(277,plain,
! [SV71: $i,SV51: $i,SV24: $i] :
( ( ~ ( ~ ( member @ SV24 @ ( intersection @ SV51 @ SV71 ) )
| ~ ( ~ ( member @ SV24 @ SV51 )
| ~ ( member @ SV24 @ SV71 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(278,plain,
! [SV71: $i,SV51: $i,SV24: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV24 @ SV51 )
| ~ ( member @ SV24 @ SV71 ) )
| ( member @ SV24 @ ( intersection @ SV51 @ SV71 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(279,plain,
! [SV84: $i,SV52: $i,SV25: $i,SV91: $i,SV72: $i] :
( ( ! [SY585: $i,SY586: $i] :
( ~ ~ ( ~ ( member @ SY585 @ SV72 )
| ~ ( member @ SY586 @ SV91 ) )
| ~ ( ~ ( ~ ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SY585 @ SY586 )
| ~ ! [SY544: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY544 @ SV84 )
| ~ ( apply @ SV52 @ SY585 @ SY544 ) )
| ~ ( apply @ SV25 @ SY544 @ SY586 ) ) )
| ~ ( ~ ~ ! [SY545: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY545 @ SV84 )
| ~ ( apply @ SV52 @ SY585 @ SY545 ) )
| ~ ( apply @ SV25 @ SY545 @ SY586 ) )
| ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SY585 @ SY586 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(280,plain,
! [SV53: $i,SV26: $i,SV73: $i] :
( ( ~ ( ~ ( member @ SV73 @ ( inverse_image2 @ SV26 @ SV53 ) )
| ~ ! [SY480: $i] :
~ ~ ( ~ ( member @ SY480 @ SV53 )
| ~ ( apply @ SV26 @ SV73 @ SY480 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[238]) ).
thf(281,plain,
! [SV73: $i,SV26: $i,SV53: $i] :
( ( ~ ( ~ ~ ! [SY481: $i] :
~ ~ ( ~ ( member @ SY481 @ SV53 )
| ~ ( apply @ SV26 @ SV73 @ SY481 ) )
| ( member @ SV73 @ ( inverse_image2 @ SV26 @ SV53 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[238]) ).
thf(282,plain,
! [SV74: $i,SV54: $i,SV27: $i] :
( ( ~ ( ~ ( injective @ SV27 @ SV54 @ SV74 )
| ! [SY482: $i,SY483: $i,SY484: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY482 @ SV54 )
| ~ ( member @ SY483 @ SV54 ) )
| ~ ( member @ SY484 @ SV74 ) )
| ~ ~ ( ~ ( apply @ SV27 @ SY482 @ SY484 )
| ~ ( apply @ SV27 @ SY483 @ SY484 ) )
| ( SY482 = SY483 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[239]) ).
thf(283,plain,
! [SV27: $i,SV74: $i,SV54: $i] :
( ( ~ ( ~ ! [SY485: $i,SY486: $i,SY487: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY485 @ SV54 )
| ~ ( member @ SY486 @ SV54 ) )
| ~ ( member @ SY487 @ SV74 ) )
| ~ ~ ( ~ ( apply @ SV27 @ SY485 @ SY487 )
| ~ ( apply @ SV27 @ SY486 @ SY487 ) )
| ( SY485 = SY486 ) )
| ( injective @ SV27 @ SV54 @ SV74 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[239]) ).
thf(284,plain,
! [SV85: $i,SV75: $i,SV55: $i,SV28: $i] :
( ( ~ ( ~ ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
| ! [SY546: $i,SY547: $i,SY548: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY546 @ SV75 )
| ~ ( member @ SY547 @ SV85 ) )
| ~ ( member @ SY548 @ SV85 ) )
| ~ ~ ( ~ ( apply @ SV28 @ SY546 @ SY547 )
| ~ ( apply @ SV55 @ SY546 @ SY548 ) )
| ( SY547 = SY548 ) ) )
| ~ ( ~ ! [SY549: $i,SY550: $i,SY551: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY549 @ SV75 )
| ~ ( member @ SY550 @ SV85 ) )
| ~ ( member @ SY551 @ SV85 ) )
| ~ ~ ( ~ ( apply @ SV28 @ SY549 @ SY550 )
| ~ ( apply @ SV55 @ SY549 @ SY551 ) )
| ( SY550 = SY551 ) )
| ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(285,plain,
! [SV2: $i,SV56: $i,SV86: $i,SV29: $i,SV76: $i] :
( ( ( ~ ~ ( ~ ( member @ SV76 @ SV29 )
| ~ ( member @ SV86 @ SV56 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV2 @ SV76 @ SV86 )
| ( apply @ ( inverse_function @ SV2 @ SV29 @ SV56 ) @ SV86 @ SV76 ) )
| ~ ( ~ ( apply @ ( inverse_function @ SV2 @ SV29 @ SV56 ) @ SV86 @ SV76 )
| ( apply @ SV2 @ SV76 @ SV86 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(286,plain,
! [SV57: $i,SV30: $i,SV3: $i,SV77: $i] :
( ( ~ ( ~ ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
| ~ ( ~ ( member @ SV77 @ SV57 )
| ~ ~ ! [SY496: $i] :
~ ~ ( ~ ( member @ SY496 @ SV30 )
| ~ ( apply @ SV3 @ SY496 @ SV77 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(287,plain,
! [SV3: $i,SV30: $i,SV57: $i,SV77: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV77 @ SV57 )
| ~ ~ ! [SY497: $i] :
~ ~ ( ~ ( member @ SY497 @ SV30 )
| ~ ( apply @ SV3 @ SY497 @ SV77 ) ) )
| ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(288,plain,
! [SV58: $i,SV31: $i,SV4: $i] :
( ( ~ ( surjective @ SV4 @ SV31 @ SV58 )
| ! [SY409: $i] :
( ~ ( member @ SY409 @ SV58 )
| ~ ! [SY294: $i] :
~ ~ ( ~ ( member @ SY294 @ SV31 )
| ~ ( apply @ SV4 @ SY294 @ SY409 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(289,plain,
! [SV4: $i,SV31: $i,SV58: $i] :
( ( ~ ! [SY411: $i] :
( ~ ( member @ SY411 @ SV58 )
| ~ ! [SY296: $i] :
~ ~ ( ~ ( member @ SY296 @ SV31 )
| ~ ( apply @ SV4 @ SY296 @ SY411 ) ) )
| ( surjective @ SV4 @ SV31 @ SV58 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(290,plain,
! [SV32: $i,SV5: $i] :
( ( ( ~ ( subset @ SV5 @ SV32 ) )
= $true )
| ( ( ! [SY297: $i] :
( ~ ( member @ SY297 @ SV5 )
| ( member @ SY297 @ SV32 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(291,plain,
! [SV32: $i,SV5: $i] :
( ( ( ~ ! [SY298: $i] :
( ~ ( member @ SY298 @ SV5 )
| ( member @ SY298 @ SV32 ) ) )
= $true )
| ( ( subset @ SV5 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(292,plain,
! [SV87: $i,SV78: $i,SV59: $i,SV33: $i,SV6: $i] :
( ( ~ ( ~ ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
| ! [SY552: $i,SY553: $i,SY554: $i,SY555: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY552 @ SV33 )
| ~ ( member @ SY553 @ SV78 ) )
| ~ ( member @ SY554 @ SV33 ) )
| ~ ( member @ SY555 @ SV78 ) )
| ~ ( apply @ SV59 @ SY552 @ SY554 ) )
| ~ ( apply @ SV6 @ SY552 @ SY553 ) )
| ~ ( apply @ SV6 @ SY554 @ SY555 ) )
| ( apply @ SV87 @ SY555 @ SY553 ) ) )
| ~ ( ~ ! [SY556: $i,SY557: $i,SY558: $i,SY559: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY556 @ SV33 )
| ~ ( member @ SY557 @ SV78 ) )
| ~ ( member @ SY558 @ SV33 ) )
| ~ ( member @ SY559 @ SV78 ) )
| ~ ( apply @ SV59 @ SY556 @ SY558 ) )
| ~ ( apply @ SV6 @ SY556 @ SY557 ) )
| ~ ( apply @ SV6 @ SY558 @ SY559 ) )
| ( apply @ SV87 @ SY559 @ SY557 ) )
| ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(293,plain,
! [SV88: $i,SV79: $i,SV60: $i,SV34: $i,SV7: $i] :
( ( ~ ( ~ ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
| ~ ( ~ ~ ( ~ ( maps @ SV7 @ SV34 @ SV79 )
| ~ ( one_to_one @ SV7 @ SV34 @ SV79 ) )
| ~ ! [SY560: $i,SY561: $i,SY562: $i,SY563: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY560 @ SV34 )
| ~ ( member @ SY561 @ SV79 ) )
| ~ ( member @ SY562 @ SV34 ) )
| ~ ( member @ SY563 @ SV79 ) )
| ~ ( apply @ SV7 @ SY560 @ SY561 ) )
| ~ ( apply @ SV7 @ SY562 @ SY563 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ SY560 @ SY562 )
| ( apply @ SV88 @ SY561 @ SY563 ) )
| ~ ( ~ ( apply @ SV88 @ SY561 @ SY563 )
| ( apply @ SV60 @ SY560 @ SY562 ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( maps @ SV7 @ SV34 @ SV79 )
| ~ ( one_to_one @ SV7 @ SV34 @ SV79 ) )
| ~ ! [SY564: $i,SY565: $i,SY566: $i,SY567: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY564 @ SV34 )
| ~ ( member @ SY565 @ SV79 ) )
| ~ ( member @ SY566 @ SV34 ) )
| ~ ( member @ SY567 @ SV79 ) )
| ~ ( apply @ SV7 @ SY564 @ SY565 ) )
| ~ ( apply @ SV7 @ SY566 @ SY567 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ SY564 @ SY566 )
| ( apply @ SV88 @ SY565 @ SY567 ) )
| ~ ( ~ ( apply @ SV88 @ SY565 @ SY567 )
| ( apply @ SV60 @ SY564 @ SY566 ) ) ) ) )
| ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(294,plain,
! [SV35: $i,SV61: $i,SV8: $i] :
( ( ~ ( member @ SV8 @ ( difference @ SV61 @ SV35 ) )
| ~ ( ~ ( member @ SV8 @ SV61 )
| ~ ~ ( member @ SV8 @ SV35 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(295,plain,
! [SV35: $i,SV61: $i,SV8: $i] :
( ( ~ ~ ( ~ ( member @ SV8 @ SV61 )
| ~ ~ ( member @ SV8 @ SV35 ) )
| ( member @ SV8 @ ( difference @ SV61 @ SV35 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(296,plain,
! [SV89: $i,SV80: $i,SV62: $i,SV36: $i,SV9: $i] :
( ( ~ ( ~ ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
| ! [SY568: $i,SY569: $i,SY570: $i,SY571: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY568 @ SV36 )
| ~ ( member @ SY569 @ SV80 ) )
| ~ ( member @ SY570 @ SV36 ) )
| ~ ( member @ SY571 @ SV80 ) )
| ~ ( apply @ SV62 @ SY568 @ SY570 ) )
| ~ ( apply @ SV9 @ SY568 @ SY569 ) )
| ~ ( apply @ SV9 @ SY570 @ SY571 ) )
| ( apply @ SV89 @ SY569 @ SY571 ) ) )
| ~ ( ~ ! [SY572: $i,SY573: $i,SY574: $i,SY575: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY572 @ SV36 )
| ~ ( member @ SY573 @ SV80 ) )
| ~ ( member @ SY574 @ SV36 ) )
| ~ ( member @ SY575 @ SV80 ) )
| ~ ( apply @ SV62 @ SY572 @ SY574 ) )
| ~ ( apply @ SV9 @ SY572 @ SY573 ) )
| ~ ( apply @ SV9 @ SY574 @ SY575 ) )
| ( apply @ SV89 @ SY573 @ SY575 ) )
| ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(297,plain,
! [SV37: $i,SV10: $i] :
( ( ( ~ ( member @ SV10 @ ( singleton @ SV37 ) ) )
= $true )
| ( ( SV10 = SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(298,plain,
! [SV37: $i,SV10: $i] :
( ( ( SV10 != SV37 )
= $true )
| ( ( member @ SV10 @ ( singleton @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(299,plain,
! [SV38: $i,SV11: $i] :
( ( ( ~ ( member @ SV11 @ ( sum @ SV38 ) ) )
= $true )
| ( ( ~ ! [SY333: $i] :
~ ~ ( ~ ( member @ SY333 @ SV38 )
| ~ ( member @ SV11 @ SY333 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(300,plain,
! [SV11: $i,SV38: $i] :
( ( ( ~ ~ ! [SY334: $i] :
~ ~ ( ~ ( member @ SY334 @ SV38 )
| ~ ( member @ SV11 @ SY334 ) ) )
= $true )
| ( ( member @ SV11 @ ( sum @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[255]) ).
thf(301,plain,
! [SV63: $i,SV39: $i,SV12: $i] :
( ( ~ ( member @ SV12 @ ( unordered_pair @ SV39 @ SV63 ) )
| ( SV12 = SV39 )
| ( SV12 = SV63 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[256]) ).
thf(302,plain,
! [SV63: $i,SV39: $i,SV12: $i] :
( ( ~ ( ( SV12 = SV39 )
| ( SV12 = SV63 ) )
| ( member @ SV12 @ ( unordered_pair @ SV39 @ SV63 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(303,plain,
! [SV64: $i,SV40: $i,SV13: $i] :
( ( ~ ( one_to_one @ SV13 @ SV40 @ SV64 )
| ~ ( ~ ( injective @ SV13 @ SV40 @ SV64 )
| ~ ( surjective @ SV13 @ SV40 @ SV64 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[258]) ).
thf(304,plain,
! [SV64: $i,SV40: $i,SV13: $i] :
( ( ~ ~ ( ~ ( injective @ SV13 @ SV40 @ SV64 )
| ~ ( surjective @ SV13 @ SV40 @ SV64 ) )
| ( one_to_one @ SV13 @ SV40 @ SV64 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[259]) ).
thf(305,plain,
! [SV41: $i,SV14: $i,SV65: $i] :
( ( ~ ( member @ SV65 @ ( image2 @ SV14 @ SV41 ) )
| ~ ! [SY443: $i] :
~ ~ ( ~ ( member @ SY443 @ SV41 )
| ~ ( apply @ SV14 @ SY443 @ SV65 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[260]) ).
thf(306,plain,
! [SV65: $i,SV14: $i,SV41: $i] :
( ( ~ ~ ! [SY444: $i] :
~ ~ ( ~ ( member @ SY444 @ SV41 )
| ~ ( apply @ SV14 @ SY444 @ SV65 ) )
| ( member @ SV65 @ ( image2 @ SV14 @ SV41 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(307,plain,
! [SV42: $i,SV15: $i] :
( ( ( ~ ( equal_set @ SV15 @ SV42 ) )
= $true )
| ( ( ~ ( ~ ( subset @ SV15 @ SV42 )
| ~ ( subset @ SV42 @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(308,plain,
! [SV42: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV15 @ SV42 )
| ~ ( subset @ SV42 @ SV15 ) ) )
= $true )
| ( ( equal_set @ SV15 @ SV42 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[263]) ).
thf(309,plain,
! [SV66: $i,SV43: $i,SV16: $i,SV81: $i] :
( ( ~ ( ~ ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
| ~ ( ~ ( member @ SV81 @ SV66 )
| ~ ~ ! [SY525: $i] :
~ ~ ( ~ ( member @ SY525 @ SV43 )
| ~ ( apply @ SV16 @ SV81 @ SY525 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[264]) ).
thf(310,plain,
! [SV16: $i,SV43: $i,SV66: $i,SV81: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV81 @ SV66 )
| ~ ~ ! [SY526: $i] :
~ ~ ( ~ ( member @ SY526 @ SV43 )
| ~ ( apply @ SV16 @ SV81 @ SY526 ) ) )
| ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[264]) ).
thf(311,plain,
! [SV82: $i,SV67: $i,SV44: $i,SV17: $i] :
( ( ~ ( ~ ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
| ! [SY527: $i,SY528: $i] :
( ~ ~ ( ~ ( member @ SY527 @ SV67 )
| ~ ( member @ SY528 @ SV82 ) )
| ~ ( ~ ( ~ ( apply @ SV44 @ SY527 @ SY528 )
| ( apply @ SV17 @ SY528 @ SY527 ) )
| ~ ( ~ ( apply @ SV17 @ SY528 @ SY527 )
| ( apply @ SV44 @ SY527 @ SY528 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[265]) ).
thf(312,plain,
! [SV17: $i,SV44: $i,SV82: $i,SV67: $i] :
( ( ~ ( ~ ! [SY529: $i,SY530: $i] :
( ~ ~ ( ~ ( member @ SY529 @ SV67 )
| ~ ( member @ SY530 @ SV82 ) )
| ~ ( ~ ( ~ ( apply @ SV44 @ SY529 @ SY530 )
| ( apply @ SV17 @ SY530 @ SY529 ) )
| ~ ( ~ ( apply @ SV17 @ SY530 @ SY529 )
| ( apply @ SV44 @ SY529 @ SY530 ) ) ) )
| ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[265]) ).
thf(313,plain,
! [SV45: $i,SV18: $i] :
( ( ( ~ ( member @ SV18 @ ( power_set @ SV45 ) ) )
= $true )
| ( ( subset @ SV18 @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(314,plain,
! [SV45: $i,SV18: $i] :
( ( ( ~ ( subset @ SV18 @ SV45 ) )
= $true )
| ( ( member @ SV18 @ ( power_set @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[267]) ).
thf(315,plain,
! [SV46: $i,SV19: $i] :
( ( ( ~ ( member @ SV19 @ ( product @ SV46 ) ) )
= $true )
| ( ( ! [SY350: $i] :
( ~ ( member @ SY350 @ SV46 )
| ( member @ SV19 @ SY350 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(316,plain,
! [SV19: $i,SV46: $i] :
( ( ( ~ ! [SY351: $i] :
( ~ ( member @ SY351 @ SV46 )
| ( member @ SV19 @ SY351 ) ) )
= $true )
| ( ( member @ SV19 @ ( product @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[269]) ).
thf(317,plain,
! [SV68: $i,SV47: $i,SV20: $i] :
( ( ~ ( member @ SV20 @ ( union @ SV47 @ SV68 ) )
| ( member @ SV20 @ SV47 )
| ( member @ SV20 @ SV68 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[270]) ).
thf(318,plain,
! [SV68: $i,SV47: $i,SV20: $i] :
( ( ~ ( ( member @ SV20 @ SV47 )
| ( member @ SV20 @ SV68 ) )
| ( member @ SV20 @ ( union @ SV47 @ SV68 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[271]) ).
thf(319,plain,
! [SV69: $i,SV48: $i,SV21: $i] :
( ( ~ ( maps @ SV21 @ SV48 @ SV69 )
| ~ ( ~ ! [SY453: $i] :
( ~ ( member @ SY453 @ SV48 )
| ~ ! [SY454: $i] :
~ ~ ( ~ ( member @ SY454 @ SV69 )
| ~ ( apply @ SV21 @ SY453 @ SY454 ) ) )
| ~ ! [SY455: $i,SY456: $i,SY457: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY455 @ SV48 )
| ~ ( member @ SY456 @ SV69 ) )
| ~ ( member @ SY457 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY455 @ SY456 )
| ~ ( apply @ SV21 @ SY455 @ SY457 ) )
| ( SY456 = SY457 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[272]) ).
thf(320,plain,
! [SV21: $i,SV69: $i,SV48: $i] :
( ( ~ ~ ( ~ ! [SY458: $i] :
( ~ ( member @ SY458 @ SV48 )
| ~ ! [SY459: $i] :
~ ~ ( ~ ( member @ SY459 @ SV69 )
| ~ ( apply @ SV21 @ SY458 @ SY459 ) ) )
| ~ ! [SY460: $i,SY461: $i,SY462: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY460 @ SV48 )
| ~ ( member @ SY461 @ SV69 ) )
| ~ ( member @ SY462 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY460 @ SY461 )
| ~ ( apply @ SV21 @ SY460 @ SY462 ) )
| ( SY461 = SY462 ) ) )
| ( maps @ SV21 @ SV48 @ SV69 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[273]) ).
thf(321,plain,
! [SV49: $i,SV22: $i] :
( ( ( ~ ( identity @ SV22 @ SV49 ) )
= $true )
| ( ( ! [SY364: $i] :
( ~ ( member @ SY364 @ SV49 )
| ( apply @ SV22 @ SY364 @ SY364 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(322,plain,
! [SV22: $i,SV49: $i] :
( ( ( ~ ! [SY365: $i] :
( ~ ( member @ SY365 @ SV49 )
| ( apply @ SV22 @ SY365 @ SY365 ) ) )
= $true )
| ( ( identity @ SV22 @ SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(323,plain,
! [SV92: $i,SV90: $i,SV83: $i,SV70: $i,SV50: $i,SV23: $i] :
( ( ~ ( ~ ( ~ ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
| ! [SY589: $i,SY590: $i] :
( ~ ~ ( ~ ( member @ SY589 @ SV83 )
| ~ ( member @ SY590 @ SV92 ) )
| ~ ( ~ ( ~ ( apply @ SV23 @ SY589 @ SY590 )
| ~ ! [SY579: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY579 @ SV90 )
| ~ ( apply @ SV70 @ SY589 @ SY579 ) )
| ~ ( apply @ SV50 @ SY579 @ SY590 ) ) )
| ~ ( ~ ~ ! [SY580: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY580 @ SV90 )
| ~ ( apply @ SV70 @ SY589 @ SY580 ) )
| ~ ( apply @ SV50 @ SY580 @ SY590 ) )
| ( apply @ SV23 @ SY589 @ SY590 ) ) ) ) )
| ~ ( ~ ! [SY593: $i,SY594: $i] :
( ~ ~ ( ~ ( member @ SY593 @ SV83 )
| ~ ( member @ SY594 @ SV92 ) )
| ~ ( ~ ( ~ ( apply @ SV23 @ SY593 @ SY594 )
| ~ ! [SY583: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY583 @ SV90 )
| ~ ( apply @ SV70 @ SY593 @ SY583 ) )
| ~ ( apply @ SV50 @ SY583 @ SY594 ) ) )
| ~ ( ~ ~ ! [SY584: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY584 @ SV90 )
| ~ ( apply @ SV70 @ SY593 @ SY584 ) )
| ~ ( apply @ SV50 @ SY584 @ SY594 ) )
| ( apply @ SV23 @ SY593 @ SY594 ) ) ) )
| ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(324,plain,
! [SV71: $i,SV51: $i,SV24: $i] :
( ( ~ ( member @ SV24 @ ( intersection @ SV51 @ SV71 ) )
| ~ ( ~ ( member @ SV24 @ SV51 )
| ~ ( member @ SV24 @ SV71 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[277]) ).
thf(325,plain,
! [SV71: $i,SV51: $i,SV24: $i] :
( ( ~ ~ ( ~ ( member @ SV24 @ SV51 )
| ~ ( member @ SV24 @ SV71 ) )
| ( member @ SV24 @ ( intersection @ SV51 @ SV71 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[278]) ).
thf(326,plain,
! [SV84: $i,SV52: $i,SV25: $i,SV91: $i,SV72: $i,SV93: $i] :
( ( ! [SY597: $i] :
( ~ ~ ( ~ ( member @ SV93 @ SV72 )
| ~ ( member @ SY597 @ SV91 ) )
| ~ ( ~ ( ~ ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SY597 )
| ~ ! [SY598: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY598 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SY598 ) )
| ~ ( apply @ SV25 @ SY598 @ SY597 ) ) )
| ~ ( ~ ~ ! [SY599: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY599 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SY599 ) )
| ~ ( apply @ SV25 @ SY599 @ SY597 ) )
| ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SY597 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(327,plain,
! [SV53: $i,SV26: $i,SV73: $i] :
( ( ~ ( member @ SV73 @ ( inverse_image2 @ SV26 @ SV53 ) )
| ~ ! [SY480: $i] :
~ ~ ( ~ ( member @ SY480 @ SV53 )
| ~ ( apply @ SV26 @ SV73 @ SY480 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[280]) ).
thf(328,plain,
! [SV73: $i,SV26: $i,SV53: $i] :
( ( ~ ~ ! [SY481: $i] :
~ ~ ( ~ ( member @ SY481 @ SV53 )
| ~ ( apply @ SV26 @ SV73 @ SY481 ) )
| ( member @ SV73 @ ( inverse_image2 @ SV26 @ SV53 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(329,plain,
! [SV74: $i,SV54: $i,SV27: $i] :
( ( ~ ( injective @ SV27 @ SV54 @ SV74 )
| ! [SY482: $i,SY483: $i,SY484: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY482 @ SV54 )
| ~ ( member @ SY483 @ SV54 ) )
| ~ ( member @ SY484 @ SV74 ) )
| ~ ~ ( ~ ( apply @ SV27 @ SY482 @ SY484 )
| ~ ( apply @ SV27 @ SY483 @ SY484 ) )
| ( SY482 = SY483 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[282]) ).
thf(330,plain,
! [SV27: $i,SV74: $i,SV54: $i] :
( ( ~ ! [SY485: $i,SY486: $i,SY487: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY485 @ SV54 )
| ~ ( member @ SY486 @ SV54 ) )
| ~ ( member @ SY487 @ SV74 ) )
| ~ ~ ( ~ ( apply @ SV27 @ SY485 @ SY487 )
| ~ ( apply @ SV27 @ SY486 @ SY487 ) )
| ( SY485 = SY486 ) )
| ( injective @ SV27 @ SV54 @ SV74 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[283]) ).
thf(331,plain,
! [SV85: $i,SV75: $i,SV55: $i,SV28: $i] :
( ( ~ ( ~ ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
| ! [SY546: $i,SY547: $i,SY548: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY546 @ SV75 )
| ~ ( member @ SY547 @ SV85 ) )
| ~ ( member @ SY548 @ SV85 ) )
| ~ ~ ( ~ ( apply @ SV28 @ SY546 @ SY547 )
| ~ ( apply @ SV55 @ SY546 @ SY548 ) )
| ( SY547 = SY548 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[284]) ).
thf(332,plain,
! [SV55: $i,SV28: $i,SV85: $i,SV75: $i] :
( ( ~ ( ~ ! [SY549: $i,SY550: $i,SY551: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY549 @ SV75 )
| ~ ( member @ SY550 @ SV85 ) )
| ~ ( member @ SY551 @ SV85 ) )
| ~ ~ ( ~ ( apply @ SV28 @ SY549 @ SY550 )
| ~ ( apply @ SV55 @ SY549 @ SY551 ) )
| ( SY550 = SY551 ) )
| ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[284]) ).
thf(333,plain,
! [SV2: $i,SV56: $i,SV86: $i,SV29: $i,SV76: $i] :
( ( ( ~ ( ~ ( member @ SV76 @ SV29 )
| ~ ( member @ SV86 @ SV56 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( apply @ SV2 @ SV76 @ SV86 )
| ( apply @ ( inverse_function @ SV2 @ SV29 @ SV56 ) @ SV86 @ SV76 ) )
| ~ ( ~ ( apply @ ( inverse_function @ SV2 @ SV29 @ SV56 ) @ SV86 @ SV76 )
| ( apply @ SV2 @ SV76 @ SV86 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(334,plain,
! [SV57: $i,SV30: $i,SV3: $i,SV77: $i] :
( ( ~ ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
| ~ ( ~ ( member @ SV77 @ SV57 )
| ~ ~ ! [SY496: $i] :
~ ~ ( ~ ( member @ SY496 @ SV30 )
| ~ ( apply @ SV3 @ SY496 @ SV77 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(335,plain,
! [SV3: $i,SV30: $i,SV57: $i,SV77: $i] :
( ( ~ ~ ( ~ ( member @ SV77 @ SV57 )
| ~ ~ ! [SY497: $i] :
~ ~ ( ~ ( member @ SY497 @ SV30 )
| ~ ( apply @ SV3 @ SY497 @ SV77 ) ) )
| ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[287]) ).
thf(336,plain,
! [SV58: $i,SV31: $i,SV4: $i] :
( ( ( ~ ( surjective @ SV4 @ SV31 @ SV58 ) )
= $true )
| ( ( ! [SY409: $i] :
( ~ ( member @ SY409 @ SV58 )
| ~ ! [SY294: $i] :
~ ~ ( ~ ( member @ SY294 @ SV31 )
| ~ ( apply @ SV4 @ SY294 @ SY409 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(337,plain,
! [SV4: $i,SV31: $i,SV58: $i] :
( ( ( ~ ! [SY411: $i] :
( ~ ( member @ SY411 @ SV58 )
| ~ ! [SY296: $i] :
~ ~ ( ~ ( member @ SY296 @ SV31 )
| ~ ( apply @ SV4 @ SY296 @ SY411 ) ) ) )
= $true )
| ( ( surjective @ SV4 @ SV31 @ SV58 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(338,plain,
! [SV32: $i,SV5: $i] :
( ( ( subset @ SV5 @ SV32 )
= $false )
| ( ( ! [SY297: $i] :
( ~ ( member @ SY297 @ SV5 )
| ( member @ SY297 @ SV32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(339,plain,
! [SV32: $i,SV5: $i] :
( ( ( ! [SY298: $i] :
( ~ ( member @ SY298 @ SV5 )
| ( member @ SY298 @ SV32 ) ) )
= $false )
| ( ( subset @ SV5 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(340,plain,
! [SV87: $i,SV78: $i,SV59: $i,SV33: $i,SV6: $i] :
( ( ~ ( ~ ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
| ! [SY552: $i,SY553: $i,SY554: $i,SY555: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY552 @ SV33 )
| ~ ( member @ SY553 @ SV78 ) )
| ~ ( member @ SY554 @ SV33 ) )
| ~ ( member @ SY555 @ SV78 ) )
| ~ ( apply @ SV59 @ SY552 @ SY554 ) )
| ~ ( apply @ SV6 @ SY552 @ SY553 ) )
| ~ ( apply @ SV6 @ SY554 @ SY555 ) )
| ( apply @ SV87 @ SY555 @ SY553 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[292]) ).
thf(341,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV78: $i,SV33: $i] :
( ( ~ ( ~ ! [SY556: $i,SY557: $i,SY558: $i,SY559: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY556 @ SV33 )
| ~ ( member @ SY557 @ SV78 ) )
| ~ ( member @ SY558 @ SV33 ) )
| ~ ( member @ SY559 @ SV78 ) )
| ~ ( apply @ SV59 @ SY556 @ SY558 ) )
| ~ ( apply @ SV6 @ SY556 @ SY557 ) )
| ~ ( apply @ SV6 @ SY558 @ SY559 ) )
| ( apply @ SV87 @ SY559 @ SY557 ) )
| ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[292]) ).
thf(342,plain,
! [SV88: $i,SV79: $i,SV60: $i,SV34: $i,SV7: $i] :
( ( ~ ( ~ ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
| ~ ( ~ ~ ( ~ ( maps @ SV7 @ SV34 @ SV79 )
| ~ ( one_to_one @ SV7 @ SV34 @ SV79 ) )
| ~ ! [SY560: $i,SY561: $i,SY562: $i,SY563: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY560 @ SV34 )
| ~ ( member @ SY561 @ SV79 ) )
| ~ ( member @ SY562 @ SV34 ) )
| ~ ( member @ SY563 @ SV79 ) )
| ~ ( apply @ SV7 @ SY560 @ SY561 ) )
| ~ ( apply @ SV7 @ SY562 @ SY563 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ SY560 @ SY562 )
| ( apply @ SV88 @ SY561 @ SY563 ) )
| ~ ( ~ ( apply @ SV88 @ SY561 @ SY563 )
| ( apply @ SV60 @ SY560 @ SY562 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[293]) ).
thf(343,plain,
! [SV88: $i,SV60: $i,SV79: $i,SV34: $i,SV7: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( maps @ SV7 @ SV34 @ SV79 )
| ~ ( one_to_one @ SV7 @ SV34 @ SV79 ) )
| ~ ! [SY564: $i,SY565: $i,SY566: $i,SY567: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY564 @ SV34 )
| ~ ( member @ SY565 @ SV79 ) )
| ~ ( member @ SY566 @ SV34 ) )
| ~ ( member @ SY567 @ SV79 ) )
| ~ ( apply @ SV7 @ SY564 @ SY565 ) )
| ~ ( apply @ SV7 @ SY566 @ SY567 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ SY564 @ SY566 )
| ( apply @ SV88 @ SY565 @ SY567 ) )
| ~ ( ~ ( apply @ SV88 @ SY565 @ SY567 )
| ( apply @ SV60 @ SY564 @ SY566 ) ) ) ) )
| ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[293]) ).
thf(344,plain,
! [SV35: $i,SV61: $i,SV8: $i] :
( ( ( ~ ( member @ SV8 @ ( difference @ SV61 @ SV35 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV8 @ SV61 )
| ~ ~ ( member @ SV8 @ SV35 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(345,plain,
! [SV35: $i,SV61: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( member @ SV8 @ SV61 )
| ~ ~ ( member @ SV8 @ SV35 ) ) )
= $true )
| ( ( member @ SV8 @ ( difference @ SV61 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(346,plain,
! [SV89: $i,SV80: $i,SV62: $i,SV36: $i,SV9: $i] :
( ( ~ ( ~ ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
| ! [SY568: $i,SY569: $i,SY570: $i,SY571: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY568 @ SV36 )
| ~ ( member @ SY569 @ SV80 ) )
| ~ ( member @ SY570 @ SV36 ) )
| ~ ( member @ SY571 @ SV80 ) )
| ~ ( apply @ SV62 @ SY568 @ SY570 ) )
| ~ ( apply @ SV9 @ SY568 @ SY569 ) )
| ~ ( apply @ SV9 @ SY570 @ SY571 ) )
| ( apply @ SV89 @ SY569 @ SY571 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(347,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV80: $i,SV36: $i] :
( ( ~ ( ~ ! [SY572: $i,SY573: $i,SY574: $i,SY575: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY572 @ SV36 )
| ~ ( member @ SY573 @ SV80 ) )
| ~ ( member @ SY574 @ SV36 ) )
| ~ ( member @ SY575 @ SV80 ) )
| ~ ( apply @ SV62 @ SY572 @ SY574 ) )
| ~ ( apply @ SV9 @ SY572 @ SY573 ) )
| ~ ( apply @ SV9 @ SY574 @ SY575 ) )
| ( apply @ SV89 @ SY573 @ SY575 ) )
| ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(348,plain,
! [SV37: $i,SV10: $i] :
( ( ( member @ SV10 @ ( singleton @ SV37 ) )
= $false )
| ( ( SV10 = SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(349,plain,
! [SV37: $i,SV10: $i] :
( ( ( SV10 = SV37 )
= $false )
| ( ( member @ SV10 @ ( singleton @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(350,plain,
! [SV38: $i,SV11: $i] :
( ( ( member @ SV11 @ ( sum @ SV38 ) )
= $false )
| ( ( ~ ! [SY333: $i] :
~ ~ ( ~ ( member @ SY333 @ SV38 )
| ~ ( member @ SV11 @ SY333 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(351,plain,
! [SV11: $i,SV38: $i] :
( ( ( ~ ! [SY334: $i] :
~ ~ ( ~ ( member @ SY334 @ SV38 )
| ~ ( member @ SV11 @ SY334 ) ) )
= $false )
| ( ( member @ SV11 @ ( sum @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(352,plain,
! [SV63: $i,SV39: $i,SV12: $i] :
( ( ( ~ ( member @ SV12 @ ( unordered_pair @ SV39 @ SV63 ) ) )
= $true )
| ( ( ( SV12 = SV39 )
| ( SV12 = SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(353,plain,
! [SV63: $i,SV39: $i,SV12: $i] :
( ( ( ~ ( ( SV12 = SV39 )
| ( SV12 = SV63 ) ) )
= $true )
| ( ( member @ SV12 @ ( unordered_pair @ SV39 @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(354,plain,
! [SV64: $i,SV40: $i,SV13: $i] :
( ( ( ~ ( one_to_one @ SV13 @ SV40 @ SV64 ) )
= $true )
| ( ( ~ ( ~ ( injective @ SV13 @ SV40 @ SV64 )
| ~ ( surjective @ SV13 @ SV40 @ SV64 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(355,plain,
! [SV64: $i,SV40: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( injective @ SV13 @ SV40 @ SV64 )
| ~ ( surjective @ SV13 @ SV40 @ SV64 ) ) )
= $true )
| ( ( one_to_one @ SV13 @ SV40 @ SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(356,plain,
! [SV41: $i,SV14: $i,SV65: $i] :
( ( ( ~ ( member @ SV65 @ ( image2 @ SV14 @ SV41 ) ) )
= $true )
| ( ( ~ ! [SY443: $i] :
~ ~ ( ~ ( member @ SY443 @ SV41 )
| ~ ( apply @ SV14 @ SY443 @ SV65 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[305]) ).
thf(357,plain,
! [SV65: $i,SV14: $i,SV41: $i] :
( ( ( ~ ~ ! [SY444: $i] :
~ ~ ( ~ ( member @ SY444 @ SV41 )
| ~ ( apply @ SV14 @ SY444 @ SV65 ) ) )
= $true )
| ( ( member @ SV65 @ ( image2 @ SV14 @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(358,plain,
! [SV42: $i,SV15: $i] :
( ( ( equal_set @ SV15 @ SV42 )
= $false )
| ( ( ~ ( ~ ( subset @ SV15 @ SV42 )
| ~ ( subset @ SV42 @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(359,plain,
! [SV42: $i,SV15: $i] :
( ( ( ~ ( ~ ( subset @ SV15 @ SV42 )
| ~ ( subset @ SV42 @ SV15 ) ) )
= $false )
| ( ( equal_set @ SV15 @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(360,plain,
! [SV66: $i,SV43: $i,SV16: $i,SV81: $i] :
( ( ~ ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
| ~ ( ~ ( member @ SV81 @ SV66 )
| ~ ~ ! [SY525: $i] :
~ ~ ( ~ ( member @ SY525 @ SV43 )
| ~ ( apply @ SV16 @ SV81 @ SY525 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(361,plain,
! [SV16: $i,SV43: $i,SV66: $i,SV81: $i] :
( ( ~ ~ ( ~ ( member @ SV81 @ SV66 )
| ~ ~ ! [SY526: $i] :
~ ~ ( ~ ( member @ SY526 @ SV43 )
| ~ ( apply @ SV16 @ SV81 @ SY526 ) ) )
| ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[310]) ).
thf(362,plain,
! [SV82: $i,SV67: $i,SV44: $i,SV17: $i] :
( ( ~ ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
| ! [SY527: $i,SY528: $i] :
( ~ ~ ( ~ ( member @ SY527 @ SV67 )
| ~ ( member @ SY528 @ SV82 ) )
| ~ ( ~ ( ~ ( apply @ SV44 @ SY527 @ SY528 )
| ( apply @ SV17 @ SY528 @ SY527 ) )
| ~ ( ~ ( apply @ SV17 @ SY528 @ SY527 )
| ( apply @ SV44 @ SY527 @ SY528 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[311]) ).
thf(363,plain,
! [SV17: $i,SV44: $i,SV82: $i,SV67: $i] :
( ( ~ ! [SY529: $i,SY530: $i] :
( ~ ~ ( ~ ( member @ SY529 @ SV67 )
| ~ ( member @ SY530 @ SV82 ) )
| ~ ( ~ ( ~ ( apply @ SV44 @ SY529 @ SY530 )
| ( apply @ SV17 @ SY530 @ SY529 ) )
| ~ ( ~ ( apply @ SV17 @ SY530 @ SY529 )
| ( apply @ SV44 @ SY529 @ SY530 ) ) ) )
| ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[312]) ).
thf(364,plain,
! [SV45: $i,SV18: $i] :
( ( ( member @ SV18 @ ( power_set @ SV45 ) )
= $false )
| ( ( subset @ SV18 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(365,plain,
! [SV45: $i,SV18: $i] :
( ( ( subset @ SV18 @ SV45 )
= $false )
| ( ( member @ SV18 @ ( power_set @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(366,plain,
! [SV46: $i,SV19: $i] :
( ( ( member @ SV19 @ ( product @ SV46 ) )
= $false )
| ( ( ! [SY350: $i] :
( ~ ( member @ SY350 @ SV46 )
| ( member @ SV19 @ SY350 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(367,plain,
! [SV19: $i,SV46: $i] :
( ( ( ! [SY351: $i] :
( ~ ( member @ SY351 @ SV46 )
| ( member @ SV19 @ SY351 ) ) )
= $false )
| ( ( member @ SV19 @ ( product @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(368,plain,
! [SV68: $i,SV47: $i,SV20: $i] :
( ( ( ~ ( member @ SV20 @ ( union @ SV47 @ SV68 ) ) )
= $true )
| ( ( ( member @ SV20 @ SV47 )
| ( member @ SV20 @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[317]) ).
thf(369,plain,
! [SV68: $i,SV47: $i,SV20: $i] :
( ( ( ~ ( ( member @ SV20 @ SV47 )
| ( member @ SV20 @ SV68 ) ) )
= $true )
| ( ( member @ SV20 @ ( union @ SV47 @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(370,plain,
! [SV69: $i,SV48: $i,SV21: $i] :
( ( ( ~ ( maps @ SV21 @ SV48 @ SV69 ) )
= $true )
| ( ( ~ ( ~ ! [SY453: $i] :
( ~ ( member @ SY453 @ SV48 )
| ~ ! [SY454: $i] :
~ ~ ( ~ ( member @ SY454 @ SV69 )
| ~ ( apply @ SV21 @ SY453 @ SY454 ) ) )
| ~ ! [SY455: $i,SY456: $i,SY457: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY455 @ SV48 )
| ~ ( member @ SY456 @ SV69 ) )
| ~ ( member @ SY457 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY455 @ SY456 )
| ~ ( apply @ SV21 @ SY455 @ SY457 ) )
| ( SY456 = SY457 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(371,plain,
! [SV21: $i,SV69: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ! [SY458: $i] :
( ~ ( member @ SY458 @ SV48 )
| ~ ! [SY459: $i] :
~ ~ ( ~ ( member @ SY459 @ SV69 )
| ~ ( apply @ SV21 @ SY458 @ SY459 ) ) )
| ~ ! [SY460: $i,SY461: $i,SY462: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY460 @ SV48 )
| ~ ( member @ SY461 @ SV69 ) )
| ~ ( member @ SY462 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY460 @ SY461 )
| ~ ( apply @ SV21 @ SY460 @ SY462 ) )
| ( SY461 = SY462 ) ) ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(372,plain,
! [SV49: $i,SV22: $i] :
( ( ( identity @ SV22 @ SV49 )
= $false )
| ( ( ! [SY364: $i] :
( ~ ( member @ SY364 @ SV49 )
| ( apply @ SV22 @ SY364 @ SY364 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(373,plain,
! [SV22: $i,SV49: $i] :
( ( ( ! [SY365: $i] :
( ~ ( member @ SY365 @ SV49 )
| ( apply @ SV22 @ SY365 @ SY365 ) ) )
= $false )
| ( ( identity @ SV22 @ SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(374,plain,
! [SV92: $i,SV90: $i,SV83: $i,SV70: $i,SV50: $i,SV23: $i] :
( ( ~ ( ~ ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
| ! [SY589: $i,SY590: $i] :
( ~ ~ ( ~ ( member @ SY589 @ SV83 )
| ~ ( member @ SY590 @ SV92 ) )
| ~ ( ~ ( ~ ( apply @ SV23 @ SY589 @ SY590 )
| ~ ! [SY579: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY579 @ SV90 )
| ~ ( apply @ SV70 @ SY589 @ SY579 ) )
| ~ ( apply @ SV50 @ SY579 @ SY590 ) ) )
| ~ ( ~ ~ ! [SY580: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY580 @ SV90 )
| ~ ( apply @ SV70 @ SY589 @ SY580 ) )
| ~ ( apply @ SV50 @ SY580 @ SY590 ) )
| ( apply @ SV23 @ SY589 @ SY590 ) ) ) ) )
| ~ ( ~ ! [SY593: $i,SY594: $i] :
( ~ ~ ( ~ ( member @ SY593 @ SV83 )
| ~ ( member @ SY594 @ SV92 ) )
| ~ ( ~ ( ~ ( apply @ SV23 @ SY593 @ SY594 )
| ~ ! [SY583: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY583 @ SV90 )
| ~ ( apply @ SV70 @ SY593 @ SY583 ) )
| ~ ( apply @ SV50 @ SY583 @ SY594 ) ) )
| ~ ( ~ ~ ! [SY584: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY584 @ SV90 )
| ~ ( apply @ SV70 @ SY593 @ SY584 ) )
| ~ ( apply @ SV50 @ SY584 @ SY594 ) )
| ( apply @ SV23 @ SY593 @ SY594 ) ) ) )
| ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(375,plain,
! [SV71: $i,SV51: $i,SV24: $i] :
( ( ( ~ ( member @ SV24 @ ( intersection @ SV51 @ SV71 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV24 @ SV51 )
| ~ ( member @ SV24 @ SV71 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[324]) ).
thf(376,plain,
! [SV71: $i,SV51: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( member @ SV24 @ SV51 )
| ~ ( member @ SV24 @ SV71 ) ) )
= $true )
| ( ( member @ SV24 @ ( intersection @ SV51 @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(377,plain,
! [SV84: $i,SV52: $i,SV25: $i,SV91: $i,SV94: $i,SV72: $i,SV93: $i] :
( ( ~ ~ ( ~ ( member @ SV93 @ SV72 )
| ~ ( member @ SV94 @ SV91 ) )
| ~ ( ~ ( ~ ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
| ~ ! [SY600: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY600 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SY600 ) )
| ~ ( apply @ SV25 @ SY600 @ SV94 ) ) )
| ~ ( ~ ~ ! [SY601: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY601 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SY601 ) )
| ~ ( apply @ SV25 @ SY601 @ SV94 ) )
| ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(378,plain,
! [SV53: $i,SV26: $i,SV73: $i] :
( ( ( ~ ( member @ SV73 @ ( inverse_image2 @ SV26 @ SV53 ) ) )
= $true )
| ( ( ~ ! [SY480: $i] :
~ ~ ( ~ ( member @ SY480 @ SV53 )
| ~ ( apply @ SV26 @ SV73 @ SY480 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(379,plain,
! [SV73: $i,SV26: $i,SV53: $i] :
( ( ( ~ ~ ! [SY481: $i] :
~ ~ ( ~ ( member @ SY481 @ SV53 )
| ~ ( apply @ SV26 @ SV73 @ SY481 ) ) )
= $true )
| ( ( member @ SV73 @ ( inverse_image2 @ SV26 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[328]) ).
thf(380,plain,
! [SV74: $i,SV54: $i,SV27: $i] :
( ( ( ~ ( injective @ SV27 @ SV54 @ SV74 ) )
= $true )
| ( ( ! [SY482: $i,SY483: $i,SY484: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY482 @ SV54 )
| ~ ( member @ SY483 @ SV54 ) )
| ~ ( member @ SY484 @ SV74 ) )
| ~ ~ ( ~ ( apply @ SV27 @ SY482 @ SY484 )
| ~ ( apply @ SV27 @ SY483 @ SY484 ) )
| ( SY482 = SY483 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(381,plain,
! [SV27: $i,SV74: $i,SV54: $i] :
( ( ( ~ ! [SY485: $i,SY486: $i,SY487: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY485 @ SV54 )
| ~ ( member @ SY486 @ SV54 ) )
| ~ ( member @ SY487 @ SV74 ) )
| ~ ~ ( ~ ( apply @ SV27 @ SY485 @ SY487 )
| ~ ( apply @ SV27 @ SY486 @ SY487 ) )
| ( SY485 = SY486 ) ) )
= $true )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[330]) ).
thf(382,plain,
! [SV85: $i,SV75: $i,SV55: $i,SV28: $i] :
( ( ~ ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
| ! [SY546: $i,SY547: $i,SY548: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY546 @ SV75 )
| ~ ( member @ SY547 @ SV85 ) )
| ~ ( member @ SY548 @ SV85 ) )
| ~ ~ ( ~ ( apply @ SV28 @ SY546 @ SY547 )
| ~ ( apply @ SV55 @ SY546 @ SY548 ) )
| ( SY547 = SY548 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[331]) ).
thf(383,plain,
! [SV55: $i,SV28: $i,SV85: $i,SV75: $i] :
( ( ~ ! [SY549: $i,SY550: $i,SY551: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY549 @ SV75 )
| ~ ( member @ SY550 @ SV85 ) )
| ~ ( member @ SY551 @ SV85 ) )
| ~ ~ ( ~ ( apply @ SV28 @ SY549 @ SY550 )
| ~ ( apply @ SV55 @ SY549 @ SY551 ) )
| ( SY550 = SY551 ) )
| ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[332]) ).
thf(384,plain,
! [SV2: $i,SV56: $i,SV86: $i,SV29: $i,SV76: $i] :
( ( ( ~ ( member @ SV76 @ SV29 )
| ~ ( member @ SV86 @ SV56 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV2 @ SV76 @ SV86 )
| ( apply @ ( inverse_function @ SV2 @ SV29 @ SV56 ) @ SV86 @ SV76 ) )
| ~ ( ~ ( apply @ ( inverse_function @ SV2 @ SV29 @ SV56 ) @ SV86 @ SV76 )
| ( apply @ SV2 @ SV76 @ SV86 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[333]) ).
thf(385,plain,
! [SV57: $i,SV30: $i,SV3: $i,SV77: $i] :
( ( ( ~ ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV77 @ SV57 )
| ~ ~ ! [SY496: $i] :
~ ~ ( ~ ( member @ SY496 @ SV30 )
| ~ ( apply @ SV3 @ SY496 @ SV77 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[334]) ).
thf(386,plain,
! [SV3: $i,SV30: $i,SV57: $i,SV77: $i] :
( ( ( ~ ~ ( ~ ( member @ SV77 @ SV57 )
| ~ ~ ! [SY497: $i] :
~ ~ ( ~ ( member @ SY497 @ SV30 )
| ~ ( apply @ SV3 @ SY497 @ SV77 ) ) ) )
= $true )
| ( ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(387,plain,
! [SV58: $i,SV31: $i,SV4: $i] :
( ( ( surjective @ SV4 @ SV31 @ SV58 )
= $false )
| ( ( ! [SY409: $i] :
( ~ ( member @ SY409 @ SV58 )
| ~ ! [SY294: $i] :
~ ~ ( ~ ( member @ SY294 @ SV31 )
| ~ ( apply @ SV4 @ SY294 @ SY409 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(388,plain,
! [SV4: $i,SV31: $i,SV58: $i] :
( ( ( ! [SY411: $i] :
( ~ ( member @ SY411 @ SV58 )
| ~ ! [SY296: $i] :
~ ~ ( ~ ( member @ SY296 @ SV31 )
| ~ ( apply @ SV4 @ SY296 @ SY411 ) ) ) )
= $false )
| ( ( surjective @ SV4 @ SV31 @ SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(389,plain,
! [SV32: $i,SV5: $i,SV95: $i] :
( ( ( ~ ( member @ SV95 @ SV5 )
| ( member @ SV95 @ SV32 ) )
= $true )
| ( ( subset @ SV5 @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(390,plain,
! [SV5: $i,SV32: $i] :
( ( ( ~ ( member @ ( sK4_SY298 @ SV32 @ SV5 ) @ SV5 )
| ( member @ ( sK4_SY298 @ SV32 @ SV5 ) @ SV32 ) )
= $false )
| ( ( subset @ SV5 @ SV32 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[339]) ).
thf(391,plain,
! [SV87: $i,SV78: $i,SV59: $i,SV33: $i,SV6: $i] :
( ( ~ ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
| ! [SY552: $i,SY553: $i,SY554: $i,SY555: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY552 @ SV33 )
| ~ ( member @ SY553 @ SV78 ) )
| ~ ( member @ SY554 @ SV33 ) )
| ~ ( member @ SY555 @ SV78 ) )
| ~ ( apply @ SV59 @ SY552 @ SY554 ) )
| ~ ( apply @ SV6 @ SY552 @ SY553 ) )
| ~ ( apply @ SV6 @ SY554 @ SY555 ) )
| ( apply @ SV87 @ SY555 @ SY553 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[340]) ).
thf(392,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV78: $i,SV33: $i] :
( ( ~ ! [SY556: $i,SY557: $i,SY558: $i,SY559: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY556 @ SV33 )
| ~ ( member @ SY557 @ SV78 ) )
| ~ ( member @ SY558 @ SV33 ) )
| ~ ( member @ SY559 @ SV78 ) )
| ~ ( apply @ SV59 @ SY556 @ SY558 ) )
| ~ ( apply @ SV6 @ SY556 @ SY557 ) )
| ~ ( apply @ SV6 @ SY558 @ SY559 ) )
| ( apply @ SV87 @ SY559 @ SY557 ) )
| ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[341]) ).
thf(393,plain,
! [SV88: $i,SV79: $i,SV60: $i,SV34: $i,SV7: $i] :
( ( ~ ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
| ~ ( ~ ~ ( ~ ( maps @ SV7 @ SV34 @ SV79 )
| ~ ( one_to_one @ SV7 @ SV34 @ SV79 ) )
| ~ ! [SY560: $i,SY561: $i,SY562: $i,SY563: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY560 @ SV34 )
| ~ ( member @ SY561 @ SV79 ) )
| ~ ( member @ SY562 @ SV34 ) )
| ~ ( member @ SY563 @ SV79 ) )
| ~ ( apply @ SV7 @ SY560 @ SY561 ) )
| ~ ( apply @ SV7 @ SY562 @ SY563 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ SY560 @ SY562 )
| ( apply @ SV88 @ SY561 @ SY563 ) )
| ~ ( ~ ( apply @ SV88 @ SY561 @ SY563 )
| ( apply @ SV60 @ SY560 @ SY562 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[342]) ).
thf(394,plain,
! [SV88: $i,SV60: $i,SV79: $i,SV34: $i,SV7: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( maps @ SV7 @ SV34 @ SV79 )
| ~ ( one_to_one @ SV7 @ SV34 @ SV79 ) )
| ~ ! [SY564: $i,SY565: $i,SY566: $i,SY567: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY564 @ SV34 )
| ~ ( member @ SY565 @ SV79 ) )
| ~ ( member @ SY566 @ SV34 ) )
| ~ ( member @ SY567 @ SV79 ) )
| ~ ( apply @ SV7 @ SY564 @ SY565 ) )
| ~ ( apply @ SV7 @ SY566 @ SY567 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ SY564 @ SY566 )
| ( apply @ SV88 @ SY565 @ SY567 ) )
| ~ ( ~ ( apply @ SV88 @ SY565 @ SY567 )
| ( apply @ SV60 @ SY564 @ SY566 ) ) ) ) )
| ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[343]) ).
thf(395,plain,
! [SV35: $i,SV61: $i,SV8: $i] :
( ( ( member @ SV8 @ ( difference @ SV61 @ SV35 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV8 @ SV61 )
| ~ ~ ( member @ SV8 @ SV35 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(396,plain,
! [SV35: $i,SV61: $i,SV8: $i] :
( ( ( ~ ( ~ ( member @ SV8 @ SV61 )
| ~ ~ ( member @ SV8 @ SV35 ) ) )
= $false )
| ( ( member @ SV8 @ ( difference @ SV61 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(397,plain,
! [SV89: $i,SV80: $i,SV62: $i,SV36: $i,SV9: $i] :
( ( ~ ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
| ! [SY568: $i,SY569: $i,SY570: $i,SY571: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY568 @ SV36 )
| ~ ( member @ SY569 @ SV80 ) )
| ~ ( member @ SY570 @ SV36 ) )
| ~ ( member @ SY571 @ SV80 ) )
| ~ ( apply @ SV62 @ SY568 @ SY570 ) )
| ~ ( apply @ SV9 @ SY568 @ SY569 ) )
| ~ ( apply @ SV9 @ SY570 @ SY571 ) )
| ( apply @ SV89 @ SY569 @ SY571 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[346]) ).
thf(398,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV80: $i,SV36: $i] :
( ( ~ ! [SY572: $i,SY573: $i,SY574: $i,SY575: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY572 @ SV36 )
| ~ ( member @ SY573 @ SV80 ) )
| ~ ( member @ SY574 @ SV36 ) )
| ~ ( member @ SY575 @ SV80 ) )
| ~ ( apply @ SV62 @ SY572 @ SY574 ) )
| ~ ( apply @ SV9 @ SY572 @ SY573 ) )
| ~ ( apply @ SV9 @ SY574 @ SY575 ) )
| ( apply @ SV89 @ SY573 @ SY575 ) )
| ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[347]) ).
thf(399,plain,
! [SV11: $i,SV38: $i] :
( ( ( ! [SY333: $i] :
~ ~ ( ~ ( member @ SY333 @ SV38 )
| ~ ( member @ SV11 @ SY333 ) ) )
= $false )
| ( ( member @ SV11 @ ( sum @ SV38 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(400,plain,
! [SV11: $i,SV38: $i] :
( ( ( ! [SY334: $i] :
~ ~ ( ~ ( member @ SY334 @ SV38 )
| ~ ( member @ SV11 @ SY334 ) ) )
= $true )
| ( ( member @ SV11 @ ( sum @ SV38 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[351]) ).
thf(401,plain,
! [SV63: $i,SV39: $i,SV12: $i] :
( ( ( member @ SV12 @ ( unordered_pair @ SV39 @ SV63 ) )
= $false )
| ( ( ( SV12 = SV39 )
| ( SV12 = SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(402,plain,
! [SV63: $i,SV39: $i,SV12: $i] :
( ( ( ( SV12 = SV39 )
| ( SV12 = SV63 ) )
= $false )
| ( ( member @ SV12 @ ( unordered_pair @ SV39 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(403,plain,
! [SV64: $i,SV40: $i,SV13: $i] :
( ( ( one_to_one @ SV13 @ SV40 @ SV64 )
= $false )
| ( ( ~ ( ~ ( injective @ SV13 @ SV40 @ SV64 )
| ~ ( surjective @ SV13 @ SV40 @ SV64 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(404,plain,
! [SV64: $i,SV40: $i,SV13: $i] :
( ( ( ~ ( ~ ( injective @ SV13 @ SV40 @ SV64 )
| ~ ( surjective @ SV13 @ SV40 @ SV64 ) ) )
= $false )
| ( ( one_to_one @ SV13 @ SV40 @ SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(405,plain,
! [SV41: $i,SV14: $i,SV65: $i] :
( ( ( member @ SV65 @ ( image2 @ SV14 @ SV41 ) )
= $false )
| ( ( ~ ! [SY443: $i] :
~ ~ ( ~ ( member @ SY443 @ SV41 )
| ~ ( apply @ SV14 @ SY443 @ SV65 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(406,plain,
! [SV65: $i,SV14: $i,SV41: $i] :
( ( ( ~ ! [SY444: $i] :
~ ~ ( ~ ( member @ SY444 @ SV41 )
| ~ ( apply @ SV14 @ SY444 @ SV65 ) ) )
= $false )
| ( ( member @ SV65 @ ( image2 @ SV14 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(407,plain,
! [SV42: $i,SV15: $i] :
( ( ( ~ ( subset @ SV15 @ SV42 )
| ~ ( subset @ SV42 @ SV15 ) )
= $false )
| ( ( equal_set @ SV15 @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(408,plain,
! [SV42: $i,SV15: $i] :
( ( ( ~ ( subset @ SV15 @ SV42 )
| ~ ( subset @ SV42 @ SV15 ) )
= $true )
| ( ( equal_set @ SV15 @ SV42 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[359]) ).
thf(409,plain,
! [SV66: $i,SV43: $i,SV16: $i,SV81: $i] :
( ( ( ~ ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV81 @ SV66 )
| ~ ~ ! [SY525: $i] :
~ ~ ( ~ ( member @ SY525 @ SV43 )
| ~ ( apply @ SV16 @ SV81 @ SY525 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[360]) ).
thf(410,plain,
! [SV16: $i,SV43: $i,SV66: $i,SV81: $i] :
( ( ( ~ ~ ( ~ ( member @ SV81 @ SV66 )
| ~ ~ ! [SY526: $i] :
~ ~ ( ~ ( member @ SY526 @ SV43 )
| ~ ( apply @ SV16 @ SV81 @ SY526 ) ) ) )
= $true )
| ( ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(411,plain,
! [SV82: $i,SV67: $i,SV44: $i,SV17: $i] :
( ( ( ~ ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 ) )
= $true )
| ( ( ! [SY527: $i,SY528: $i] :
( ~ ~ ( ~ ( member @ SY527 @ SV67 )
| ~ ( member @ SY528 @ SV82 ) )
| ~ ( ~ ( ~ ( apply @ SV44 @ SY527 @ SY528 )
| ( apply @ SV17 @ SY528 @ SY527 ) )
| ~ ( ~ ( apply @ SV17 @ SY528 @ SY527 )
| ( apply @ SV44 @ SY527 @ SY528 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[362]) ).
thf(412,plain,
! [SV17: $i,SV44: $i,SV82: $i,SV67: $i] :
( ( ( ~ ! [SY529: $i,SY530: $i] :
( ~ ~ ( ~ ( member @ SY529 @ SV67 )
| ~ ( member @ SY530 @ SV82 ) )
| ~ ( ~ ( ~ ( apply @ SV44 @ SY529 @ SY530 )
| ( apply @ SV17 @ SY530 @ SY529 ) )
| ~ ( ~ ( apply @ SV17 @ SY530 @ SY529 )
| ( apply @ SV44 @ SY529 @ SY530 ) ) ) ) )
= $true )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[363]) ).
thf(413,plain,
! [SV19: $i,SV46: $i,SV96: $i] :
( ( ( ~ ( member @ SV96 @ SV46 )
| ( member @ SV19 @ SV96 ) )
= $true )
| ( ( member @ SV19 @ ( product @ SV46 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(414,plain,
! [SV46: $i,SV19: $i] :
( ( ( ~ ( member @ ( sK5_SY351 @ SV19 @ SV46 ) @ SV46 )
| ( member @ SV19 @ ( sK5_SY351 @ SV19 @ SV46 ) ) )
= $false )
| ( ( member @ SV19 @ ( product @ SV46 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[367]) ).
thf(415,plain,
! [SV68: $i,SV47: $i,SV20: $i] :
( ( ( member @ SV20 @ ( union @ SV47 @ SV68 ) )
= $false )
| ( ( ( member @ SV20 @ SV47 )
| ( member @ SV20 @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(416,plain,
! [SV68: $i,SV47: $i,SV20: $i] :
( ( ( ( member @ SV20 @ SV47 )
| ( member @ SV20 @ SV68 ) )
= $false )
| ( ( member @ SV20 @ ( union @ SV47 @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(417,plain,
! [SV69: $i,SV48: $i,SV21: $i] :
( ( ( maps @ SV21 @ SV48 @ SV69 )
= $false )
| ( ( ~ ( ~ ! [SY453: $i] :
( ~ ( member @ SY453 @ SV48 )
| ~ ! [SY454: $i] :
~ ~ ( ~ ( member @ SY454 @ SV69 )
| ~ ( apply @ SV21 @ SY453 @ SY454 ) ) )
| ~ ! [SY455: $i,SY456: $i,SY457: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY455 @ SV48 )
| ~ ( member @ SY456 @ SV69 ) )
| ~ ( member @ SY457 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY455 @ SY456 )
| ~ ( apply @ SV21 @ SY455 @ SY457 ) )
| ( SY456 = SY457 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(418,plain,
! [SV21: $i,SV69: $i,SV48: $i] :
( ( ( ~ ( ~ ! [SY458: $i] :
( ~ ( member @ SY458 @ SV48 )
| ~ ! [SY459: $i] :
~ ~ ( ~ ( member @ SY459 @ SV69 )
| ~ ( apply @ SV21 @ SY458 @ SY459 ) ) )
| ~ ! [SY460: $i,SY461: $i,SY462: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY460 @ SV48 )
| ~ ( member @ SY461 @ SV69 ) )
| ~ ( member @ SY462 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY460 @ SY461 )
| ~ ( apply @ SV21 @ SY460 @ SY462 ) )
| ( SY461 = SY462 ) ) ) )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(419,plain,
! [SV22: $i,SV49: $i,SV97: $i] :
( ( ( ~ ( member @ SV97 @ SV49 )
| ( apply @ SV22 @ SV97 @ SV97 ) )
= $true )
| ( ( identity @ SV22 @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(420,plain,
! [SV49: $i,SV22: $i] :
( ( ( ~ ( member @ ( sK6_SY365 @ SV22 @ SV49 ) @ SV49 )
| ( apply @ SV22 @ ( sK6_SY365 @ SV22 @ SV49 ) @ ( sK6_SY365 @ SV22 @ SV49 ) ) )
= $false )
| ( ( identity @ SV22 @ SV49 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[373]) ).
thf(421,plain,
! [SV92: $i,SV90: $i,SV83: $i,SV70: $i,SV50: $i,SV23: $i] :
( ( ~ ( ~ ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
| ! [SY589: $i,SY590: $i] :
( ~ ~ ( ~ ( member @ SY589 @ SV83 )
| ~ ( member @ SY590 @ SV92 ) )
| ~ ( ~ ( ~ ( apply @ SV23 @ SY589 @ SY590 )
| ~ ! [SY579: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY579 @ SV90 )
| ~ ( apply @ SV70 @ SY589 @ SY579 ) )
| ~ ( apply @ SV50 @ SY579 @ SY590 ) ) )
| ~ ( ~ ~ ! [SY580: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY580 @ SV90 )
| ~ ( apply @ SV70 @ SY589 @ SY580 ) )
| ~ ( apply @ SV50 @ SY580 @ SY590 ) )
| ( apply @ SV23 @ SY589 @ SY590 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[374]) ).
thf(422,plain,
! [SV50: $i,SV70: $i,SV90: $i,SV23: $i,SV92: $i,SV83: $i] :
( ( ~ ( ~ ! [SY593: $i,SY594: $i] :
( ~ ~ ( ~ ( member @ SY593 @ SV83 )
| ~ ( member @ SY594 @ SV92 ) )
| ~ ( ~ ( ~ ( apply @ SV23 @ SY593 @ SY594 )
| ~ ! [SY583: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY583 @ SV90 )
| ~ ( apply @ SV70 @ SY593 @ SY583 ) )
| ~ ( apply @ SV50 @ SY583 @ SY594 ) ) )
| ~ ( ~ ~ ! [SY584: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY584 @ SV90 )
| ~ ( apply @ SV70 @ SY593 @ SY584 ) )
| ~ ( apply @ SV50 @ SY584 @ SY594 ) )
| ( apply @ SV23 @ SY593 @ SY594 ) ) ) )
| ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[374]) ).
thf(423,plain,
! [SV71: $i,SV51: $i,SV24: $i] :
( ( ( member @ SV24 @ ( intersection @ SV51 @ SV71 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV24 @ SV51 )
| ~ ( member @ SV24 @ SV71 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(424,plain,
! [SV71: $i,SV51: $i,SV24: $i] :
( ( ( ~ ( ~ ( member @ SV24 @ SV51 )
| ~ ( member @ SV24 @ SV71 ) ) )
= $false )
| ( ( member @ SV24 @ ( intersection @ SV51 @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(425,plain,
! [SV84: $i,SV52: $i,SV25: $i,SV91: $i,SV94: $i,SV72: $i,SV93: $i] :
( ( ( ~ ~ ( ~ ( member @ SV93 @ SV72 )
| ~ ( member @ SV94 @ SV91 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
| ~ ! [SY600: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY600 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SY600 ) )
| ~ ( apply @ SV25 @ SY600 @ SV94 ) ) )
| ~ ( ~ ~ ! [SY601: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY601 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SY601 ) )
| ~ ( apply @ SV25 @ SY601 @ SV94 ) )
| ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[377]) ).
thf(426,plain,
! [SV53: $i,SV26: $i,SV73: $i] :
( ( ( member @ SV73 @ ( inverse_image2 @ SV26 @ SV53 ) )
= $false )
| ( ( ~ ! [SY480: $i] :
~ ~ ( ~ ( member @ SY480 @ SV53 )
| ~ ( apply @ SV26 @ SV73 @ SY480 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(427,plain,
! [SV73: $i,SV26: $i,SV53: $i] :
( ( ( ~ ! [SY481: $i] :
~ ~ ( ~ ( member @ SY481 @ SV53 )
| ~ ( apply @ SV26 @ SV73 @ SY481 ) ) )
= $false )
| ( ( member @ SV73 @ ( inverse_image2 @ SV26 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(428,plain,
! [SV74: $i,SV54: $i,SV27: $i] :
( ( ( injective @ SV27 @ SV54 @ SV74 )
= $false )
| ( ( ! [SY482: $i,SY483: $i,SY484: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY482 @ SV54 )
| ~ ( member @ SY483 @ SV54 ) )
| ~ ( member @ SY484 @ SV74 ) )
| ~ ~ ( ~ ( apply @ SV27 @ SY482 @ SY484 )
| ~ ( apply @ SV27 @ SY483 @ SY484 ) )
| ( SY482 = SY483 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(429,plain,
! [SV27: $i,SV74: $i,SV54: $i] :
( ( ( ! [SY485: $i,SY486: $i,SY487: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY485 @ SV54 )
| ~ ( member @ SY486 @ SV54 ) )
| ~ ( member @ SY487 @ SV74 ) )
| ~ ~ ( ~ ( apply @ SV27 @ SY485 @ SY487 )
| ~ ( apply @ SV27 @ SY486 @ SY487 ) )
| ( SY485 = SY486 ) ) )
= $false )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(430,plain,
! [SV85: $i,SV75: $i,SV55: $i,SV28: $i] :
( ( ( ~ ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 ) )
= $true )
| ( ( ! [SY546: $i,SY547: $i,SY548: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY546 @ SV75 )
| ~ ( member @ SY547 @ SV85 ) )
| ~ ( member @ SY548 @ SV85 ) )
| ~ ~ ( ~ ( apply @ SV28 @ SY546 @ SY547 )
| ~ ( apply @ SV55 @ SY546 @ SY548 ) )
| ( SY547 = SY548 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[382]) ).
thf(431,plain,
! [SV55: $i,SV28: $i,SV85: $i,SV75: $i] :
( ( ( ~ ! [SY549: $i,SY550: $i,SY551: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY549 @ SV75 )
| ~ ( member @ SY550 @ SV85 ) )
| ~ ( member @ SY551 @ SV85 ) )
| ~ ~ ( ~ ( apply @ SV28 @ SY549 @ SY550 )
| ~ ( apply @ SV55 @ SY549 @ SY551 ) )
| ( SY550 = SY551 ) ) )
= $true )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[383]) ).
thf(432,plain,
! [SV2: $i,SV56: $i,SV86: $i,SV29: $i,SV76: $i] :
( ( ( ~ ( member @ SV76 @ SV29 ) )
= $true )
| ( ( ~ ( member @ SV86 @ SV56 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV2 @ SV76 @ SV86 )
| ( apply @ ( inverse_function @ SV2 @ SV29 @ SV56 ) @ SV86 @ SV76 ) )
| ~ ( ~ ( apply @ ( inverse_function @ SV2 @ SV29 @ SV56 ) @ SV86 @ SV76 )
| ( apply @ SV2 @ SV76 @ SV86 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[384]) ).
thf(433,plain,
! [SV57: $i,SV30: $i,SV3: $i,SV77: $i] :
( ( ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV77 @ SV57 )
| ~ ~ ! [SY496: $i] :
~ ~ ( ~ ( member @ SY496 @ SV30 )
| ~ ( apply @ SV3 @ SY496 @ SV77 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(434,plain,
! [SV3: $i,SV30: $i,SV57: $i,SV77: $i] :
( ( ( ~ ( ~ ( member @ SV77 @ SV57 )
| ~ ~ ! [SY497: $i] :
~ ~ ( ~ ( member @ SY497 @ SV30 )
| ~ ( apply @ SV3 @ SY497 @ SV77 ) ) ) )
= $false )
| ( ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(435,plain,
! [SV4: $i,SV31: $i,SV58: $i,SV98: $i] :
( ( ( ~ ( member @ SV98 @ SV58 )
| ~ ! [SY602: $i] :
~ ~ ( ~ ( member @ SY602 @ SV31 )
| ~ ( apply @ SV4 @ SY602 @ SV98 ) ) )
= $true )
| ( ( surjective @ SV4 @ SV31 @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(436,plain,
! [SV58: $i,SV31: $i,SV4: $i] :
( ( ( ~ ( member @ ( sK7_SY411 @ SV4 @ SV31 @ SV58 ) @ SV58 )
| ~ ! [SY603: $i] :
~ ~ ( ~ ( member @ SY603 @ SV31 )
| ~ ( apply @ SV4 @ SY603 @ ( sK7_SY411 @ SV4 @ SV31 @ SV58 ) ) ) )
= $false )
| ( ( surjective @ SV4 @ SV31 @ SV58 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[388]) ).
thf(437,plain,
! [SV32: $i,SV5: $i,SV95: $i] :
( ( ( ~ ( member @ SV95 @ SV5 ) )
= $true )
| ( ( member @ SV95 @ SV32 )
= $true )
| ( ( subset @ SV5 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[389]) ).
thf(438,plain,
! [SV5: $i,SV32: $i] :
( ( ( ~ ( member @ ( sK4_SY298 @ SV32 @ SV5 ) @ SV5 ) )
= $false )
| ( ( subset @ SV5 @ SV32 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[390]) ).
thf(439,plain,
! [SV5: $i,SV32: $i] :
( ( ( member @ ( sK4_SY298 @ SV32 @ SV5 ) @ SV32 )
= $false )
| ( ( subset @ SV5 @ SV32 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[390]) ).
thf(440,plain,
! [SV87: $i,SV78: $i,SV59: $i,SV33: $i,SV6: $i] :
( ( ( ~ ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 ) )
= $true )
| ( ( ! [SY552: $i,SY553: $i,SY554: $i,SY555: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY552 @ SV33 )
| ~ ( member @ SY553 @ SV78 ) )
| ~ ( member @ SY554 @ SV33 ) )
| ~ ( member @ SY555 @ SV78 ) )
| ~ ( apply @ SV59 @ SY552 @ SY554 ) )
| ~ ( apply @ SV6 @ SY552 @ SY553 ) )
| ~ ( apply @ SV6 @ SY554 @ SY555 ) )
| ( apply @ SV87 @ SY555 @ SY553 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[391]) ).
thf(441,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV78: $i,SV33: $i] :
( ( ( ~ ! [SY556: $i,SY557: $i,SY558: $i,SY559: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY556 @ SV33 )
| ~ ( member @ SY557 @ SV78 ) )
| ~ ( member @ SY558 @ SV33 ) )
| ~ ( member @ SY559 @ SV78 ) )
| ~ ( apply @ SV59 @ SY556 @ SY558 ) )
| ~ ( apply @ SV6 @ SY556 @ SY557 ) )
| ~ ( apply @ SV6 @ SY558 @ SY559 ) )
| ( apply @ SV87 @ SY559 @ SY557 ) ) )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[392]) ).
thf(442,plain,
! [SV88: $i,SV79: $i,SV60: $i,SV34: $i,SV7: $i] :
( ( ( ~ ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( maps @ SV7 @ SV34 @ SV79 )
| ~ ( one_to_one @ SV7 @ SV34 @ SV79 ) )
| ~ ! [SY560: $i,SY561: $i,SY562: $i,SY563: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY560 @ SV34 )
| ~ ( member @ SY561 @ SV79 ) )
| ~ ( member @ SY562 @ SV34 ) )
| ~ ( member @ SY563 @ SV79 ) )
| ~ ( apply @ SV7 @ SY560 @ SY561 ) )
| ~ ( apply @ SV7 @ SY562 @ SY563 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ SY560 @ SY562 )
| ( apply @ SV88 @ SY561 @ SY563 ) )
| ~ ( ~ ( apply @ SV88 @ SY561 @ SY563 )
| ( apply @ SV60 @ SY560 @ SY562 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[393]) ).
thf(443,plain,
! [SV88: $i,SV60: $i,SV79: $i,SV34: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( maps @ SV7 @ SV34 @ SV79 )
| ~ ( one_to_one @ SV7 @ SV34 @ SV79 ) )
| ~ ! [SY564: $i,SY565: $i,SY566: $i,SY567: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY564 @ SV34 )
| ~ ( member @ SY565 @ SV79 ) )
| ~ ( member @ SY566 @ SV34 ) )
| ~ ( member @ SY567 @ SV79 ) )
| ~ ( apply @ SV7 @ SY564 @ SY565 ) )
| ~ ( apply @ SV7 @ SY566 @ SY567 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ SY564 @ SY566 )
| ( apply @ SV88 @ SY565 @ SY567 ) )
| ~ ( ~ ( apply @ SV88 @ SY565 @ SY567 )
| ( apply @ SV60 @ SY564 @ SY566 ) ) ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(444,plain,
! [SV35: $i,SV61: $i,SV8: $i] :
( ( ( ~ ( member @ SV8 @ SV61 )
| ~ ~ ( member @ SV8 @ SV35 ) )
= $false )
| ( ( member @ SV8 @ ( difference @ SV61 @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(445,plain,
! [SV35: $i,SV61: $i,SV8: $i] :
( ( ( ~ ( member @ SV8 @ SV61 )
| ~ ~ ( member @ SV8 @ SV35 ) )
= $true )
| ( ( member @ SV8 @ ( difference @ SV61 @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[396]) ).
thf(446,plain,
! [SV89: $i,SV80: $i,SV62: $i,SV36: $i,SV9: $i] :
( ( ( ~ ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 ) )
= $true )
| ( ( ! [SY568: $i,SY569: $i,SY570: $i,SY571: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY568 @ SV36 )
| ~ ( member @ SY569 @ SV80 ) )
| ~ ( member @ SY570 @ SV36 ) )
| ~ ( member @ SY571 @ SV80 ) )
| ~ ( apply @ SV62 @ SY568 @ SY570 ) )
| ~ ( apply @ SV9 @ SY568 @ SY569 ) )
| ~ ( apply @ SV9 @ SY570 @ SY571 ) )
| ( apply @ SV89 @ SY569 @ SY571 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[397]) ).
thf(447,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV80: $i,SV36: $i] :
( ( ( ~ ! [SY572: $i,SY573: $i,SY574: $i,SY575: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY572 @ SV36 )
| ~ ( member @ SY573 @ SV80 ) )
| ~ ( member @ SY574 @ SV36 ) )
| ~ ( member @ SY575 @ SV80 ) )
| ~ ( apply @ SV62 @ SY572 @ SY574 ) )
| ~ ( apply @ SV9 @ SY572 @ SY573 ) )
| ~ ( apply @ SV9 @ SY574 @ SY575 ) )
| ( apply @ SV89 @ SY573 @ SY575 ) ) )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[398]) ).
thf(448,plain,
! [SV38: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK8_SY333 @ SV11 @ SV38 ) @ SV38 )
| ~ ( member @ SV11 @ ( sK8_SY333 @ SV11 @ SV38 ) ) ) )
= $false )
| ( ( member @ SV11 @ ( sum @ SV38 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[399]) ).
thf(449,plain,
! [SV11: $i,SV38: $i,SV99: $i] :
( ( ( ~ ~ ( ~ ( member @ SV99 @ SV38 )
| ~ ( member @ SV11 @ SV99 ) ) )
= $true )
| ( ( member @ SV11 @ ( sum @ SV38 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(450,plain,
! [SV63: $i,SV39: $i,SV12: $i] :
( ( ( SV12 = SV39 )
= $true )
| ( ( SV12 = SV63 )
= $true )
| ( ( member @ SV12 @ ( unordered_pair @ SV39 @ SV63 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(451,plain,
! [SV63: $i,SV39: $i,SV12: $i] :
( ( ( SV12 = SV39 )
= $false )
| ( ( member @ SV12 @ ( unordered_pair @ SV39 @ SV63 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[402]) ).
thf(452,plain,
! [SV39: $i,SV63: $i,SV12: $i] :
( ( ( SV12 = SV63 )
= $false )
| ( ( member @ SV12 @ ( unordered_pair @ SV39 @ SV63 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[402]) ).
thf(453,plain,
! [SV64: $i,SV40: $i,SV13: $i] :
( ( ( ~ ( injective @ SV13 @ SV40 @ SV64 )
| ~ ( surjective @ SV13 @ SV40 @ SV64 ) )
= $false )
| ( ( one_to_one @ SV13 @ SV40 @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(454,plain,
! [SV64: $i,SV40: $i,SV13: $i] :
( ( ( ~ ( injective @ SV13 @ SV40 @ SV64 )
| ~ ( surjective @ SV13 @ SV40 @ SV64 ) )
= $true )
| ( ( one_to_one @ SV13 @ SV40 @ SV64 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[404]) ).
thf(455,plain,
! [SV65: $i,SV14: $i,SV41: $i] :
( ( ( ! [SY443: $i] :
~ ~ ( ~ ( member @ SY443 @ SV41 )
| ~ ( apply @ SV14 @ SY443 @ SV65 ) ) )
= $false )
| ( ( member @ SV65 @ ( image2 @ SV14 @ SV41 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(456,plain,
! [SV65: $i,SV14: $i,SV41: $i] :
( ( ( ! [SY444: $i] :
~ ~ ( ~ ( member @ SY444 @ SV41 )
| ~ ( apply @ SV14 @ SY444 @ SV65 ) ) )
= $true )
| ( ( member @ SV65 @ ( image2 @ SV14 @ SV41 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[406]) ).
thf(457,plain,
! [SV42: $i,SV15: $i] :
( ( ( ~ ( subset @ SV15 @ SV42 ) )
= $false )
| ( ( equal_set @ SV15 @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[407]) ).
thf(458,plain,
! [SV15: $i,SV42: $i] :
( ( ( ~ ( subset @ SV42 @ SV15 ) )
= $false )
| ( ( equal_set @ SV15 @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[407]) ).
thf(459,plain,
! [SV42: $i,SV15: $i] :
( ( ( ~ ( subset @ SV15 @ SV42 ) )
= $true )
| ( ( ~ ( subset @ SV42 @ SV15 ) )
= $true )
| ( ( equal_set @ SV15 @ SV42 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(460,plain,
! [SV66: $i,SV43: $i,SV16: $i,SV81: $i] :
( ( ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV81 @ SV66 )
| ~ ~ ! [SY525: $i] :
~ ~ ( ~ ( member @ SY525 @ SV43 )
| ~ ( apply @ SV16 @ SV81 @ SY525 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(461,plain,
! [SV16: $i,SV43: $i,SV66: $i,SV81: $i] :
( ( ( ~ ( ~ ( member @ SV81 @ SV66 )
| ~ ~ ! [SY526: $i] :
~ ~ ( ~ ( member @ SY526 @ SV43 )
| ~ ( apply @ SV16 @ SV81 @ SY526 ) ) ) )
= $false )
| ( ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(462,plain,
! [SV82: $i,SV67: $i,SV44: $i,SV17: $i] :
( ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $false )
| ( ( ! [SY527: $i,SY528: $i] :
( ~ ~ ( ~ ( member @ SY527 @ SV67 )
| ~ ( member @ SY528 @ SV82 ) )
| ~ ( ~ ( ~ ( apply @ SV44 @ SY527 @ SY528 )
| ( apply @ SV17 @ SY528 @ SY527 ) )
| ~ ( ~ ( apply @ SV17 @ SY528 @ SY527 )
| ( apply @ SV44 @ SY527 @ SY528 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(463,plain,
! [SV17: $i,SV44: $i,SV82: $i,SV67: $i] :
( ( ( ! [SY529: $i,SY530: $i] :
( ~ ~ ( ~ ( member @ SY529 @ SV67 )
| ~ ( member @ SY530 @ SV82 ) )
| ~ ( ~ ( ~ ( apply @ SV44 @ SY529 @ SY530 )
| ( apply @ SV17 @ SY530 @ SY529 ) )
| ~ ( ~ ( apply @ SV17 @ SY530 @ SY529 )
| ( apply @ SV44 @ SY529 @ SY530 ) ) ) ) )
= $false )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(464,plain,
! [SV19: $i,SV46: $i,SV96: $i] :
( ( ( ~ ( member @ SV96 @ SV46 ) )
= $true )
| ( ( member @ SV19 @ SV96 )
= $true )
| ( ( member @ SV19 @ ( product @ SV46 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(465,plain,
! [SV46: $i,SV19: $i] :
( ( ( ~ ( member @ ( sK5_SY351 @ SV19 @ SV46 ) @ SV46 ) )
= $false )
| ( ( member @ SV19 @ ( product @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[414]) ).
thf(466,plain,
! [SV46: $i,SV19: $i] :
( ( ( member @ SV19 @ ( sK5_SY351 @ SV19 @ SV46 ) )
= $false )
| ( ( member @ SV19 @ ( product @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[414]) ).
thf(467,plain,
! [SV68: $i,SV47: $i,SV20: $i] :
( ( ( member @ SV20 @ SV47 )
= $true )
| ( ( member @ SV20 @ SV68 )
= $true )
| ( ( member @ SV20 @ ( union @ SV47 @ SV68 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(468,plain,
! [SV68: $i,SV47: $i,SV20: $i] :
( ( ( member @ SV20 @ SV47 )
= $false )
| ( ( member @ SV20 @ ( union @ SV47 @ SV68 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[416]) ).
thf(469,plain,
! [SV47: $i,SV68: $i,SV20: $i] :
( ( ( member @ SV20 @ SV68 )
= $false )
| ( ( member @ SV20 @ ( union @ SV47 @ SV68 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[416]) ).
thf(470,plain,
! [SV21: $i,SV69: $i,SV48: $i] :
( ( ( ~ ! [SY453: $i] :
( ~ ( member @ SY453 @ SV48 )
| ~ ! [SY454: $i] :
~ ~ ( ~ ( member @ SY454 @ SV69 )
| ~ ( apply @ SV21 @ SY453 @ SY454 ) ) )
| ~ ! [SY455: $i,SY456: $i,SY457: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY455 @ SV48 )
| ~ ( member @ SY456 @ SV69 ) )
| ~ ( member @ SY457 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY455 @ SY456 )
| ~ ( apply @ SV21 @ SY455 @ SY457 ) )
| ( SY456 = SY457 ) ) )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(471,plain,
! [SV21: $i,SV69: $i,SV48: $i] :
( ( ( ~ ! [SY458: $i] :
( ~ ( member @ SY458 @ SV48 )
| ~ ! [SY459: $i] :
~ ~ ( ~ ( member @ SY459 @ SV69 )
| ~ ( apply @ SV21 @ SY458 @ SY459 ) ) )
| ~ ! [SY460: $i,SY461: $i,SY462: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY460 @ SV48 )
| ~ ( member @ SY461 @ SV69 ) )
| ~ ( member @ SY462 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY460 @ SY461 )
| ~ ( apply @ SV21 @ SY460 @ SY462 ) )
| ( SY461 = SY462 ) ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[418]) ).
thf(472,plain,
! [SV22: $i,SV49: $i,SV97: $i] :
( ( ( ~ ( member @ SV97 @ SV49 ) )
= $true )
| ( ( apply @ SV22 @ SV97 @ SV97 )
= $true )
| ( ( identity @ SV22 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(473,plain,
! [SV49: $i,SV22: $i] :
( ( ( ~ ( member @ ( sK6_SY365 @ SV22 @ SV49 ) @ SV49 ) )
= $false )
| ( ( identity @ SV22 @ SV49 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[420]) ).
thf(474,plain,
! [SV49: $i,SV22: $i] :
( ( ( apply @ SV22 @ ( sK6_SY365 @ SV22 @ SV49 ) @ ( sK6_SY365 @ SV22 @ SV49 ) )
= $false )
| ( ( identity @ SV22 @ SV49 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[420]) ).
thf(475,plain,
! [SV92: $i,SV90: $i,SV83: $i,SV70: $i,SV50: $i,SV23: $i] :
( ( ~ ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
| ! [SY589: $i,SY590: $i] :
( ~ ~ ( ~ ( member @ SY589 @ SV83 )
| ~ ( member @ SY590 @ SV92 ) )
| ~ ( ~ ( ~ ( apply @ SV23 @ SY589 @ SY590 )
| ~ ! [SY579: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY579 @ SV90 )
| ~ ( apply @ SV70 @ SY589 @ SY579 ) )
| ~ ( apply @ SV50 @ SY579 @ SY590 ) ) )
| ~ ( ~ ~ ! [SY580: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY580 @ SV90 )
| ~ ( apply @ SV70 @ SY589 @ SY580 ) )
| ~ ( apply @ SV50 @ SY580 @ SY590 ) )
| ( apply @ SV23 @ SY589 @ SY590 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[421]) ).
thf(476,plain,
! [SV50: $i,SV70: $i,SV90: $i,SV23: $i,SV92: $i,SV83: $i] :
( ( ~ ! [SY593: $i,SY594: $i] :
( ~ ~ ( ~ ( member @ SY593 @ SV83 )
| ~ ( member @ SY594 @ SV92 ) )
| ~ ( ~ ( ~ ( apply @ SV23 @ SY593 @ SY594 )
| ~ ! [SY583: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY583 @ SV90 )
| ~ ( apply @ SV70 @ SY593 @ SY583 ) )
| ~ ( apply @ SV50 @ SY583 @ SY594 ) ) )
| ~ ( ~ ~ ! [SY584: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY584 @ SV90 )
| ~ ( apply @ SV70 @ SY593 @ SY584 ) )
| ~ ( apply @ SV50 @ SY584 @ SY594 ) )
| ( apply @ SV23 @ SY593 @ SY594 ) ) ) )
| ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[422]) ).
thf(477,plain,
! [SV71: $i,SV51: $i,SV24: $i] :
( ( ( ~ ( member @ SV24 @ SV51 )
| ~ ( member @ SV24 @ SV71 ) )
= $false )
| ( ( member @ SV24 @ ( intersection @ SV51 @ SV71 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(478,plain,
! [SV71: $i,SV51: $i,SV24: $i] :
( ( ( ~ ( member @ SV24 @ SV51 )
| ~ ( member @ SV24 @ SV71 ) )
= $true )
| ( ( member @ SV24 @ ( intersection @ SV51 @ SV71 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[424]) ).
thf(479,plain,
! [SV84: $i,SV52: $i,SV25: $i,SV91: $i,SV94: $i,SV72: $i,SV93: $i] :
( ( ( ~ ( ~ ( member @ SV93 @ SV72 )
| ~ ( member @ SV94 @ SV91 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
| ~ ! [SY600: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY600 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SY600 ) )
| ~ ( apply @ SV25 @ SY600 @ SV94 ) ) )
| ~ ( ~ ~ ! [SY601: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY601 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SY601 ) )
| ~ ( apply @ SV25 @ SY601 @ SV94 ) )
| ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(480,plain,
! [SV73: $i,SV26: $i,SV53: $i] :
( ( ( ! [SY480: $i] :
~ ~ ( ~ ( member @ SY480 @ SV53 )
| ~ ( apply @ SV26 @ SV73 @ SY480 ) ) )
= $false )
| ( ( member @ SV73 @ ( inverse_image2 @ SV26 @ SV53 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(481,plain,
! [SV73: $i,SV26: $i,SV53: $i] :
( ( ( ! [SY481: $i] :
~ ~ ( ~ ( member @ SY481 @ SV53 )
| ~ ( apply @ SV26 @ SV73 @ SY481 ) ) )
= $true )
| ( ( member @ SV73 @ ( inverse_image2 @ SV26 @ SV53 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[427]) ).
thf(482,plain,
! [SV27: $i,SV74: $i,SV54: $i,SV100: $i] :
( ( ( ! [SY604: $i,SY605: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SV100 @ SV54 )
| ~ ( member @ SY604 @ SV54 ) )
| ~ ( member @ SY605 @ SV74 ) )
| ~ ~ ( ~ ( apply @ SV27 @ SV100 @ SY605 )
| ~ ( apply @ SV27 @ SY604 @ SY605 ) )
| ( SV100 = SY604 ) ) )
= $true )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(483,plain,
! [SV54: $i,SV74: $i,SV27: $i] :
( ( ( ! [SY606: $i,SY607: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK9_SY485 @ SV27 @ SV74 @ SV54 ) @ SV54 )
| ~ ( member @ SY606 @ SV54 ) )
| ~ ( member @ SY607 @ SV74 ) )
| ~ ~ ( ~ ( apply @ SV27 @ ( sK9_SY485 @ SV27 @ SV74 @ SV54 ) @ SY607 )
| ~ ( apply @ SV27 @ SY606 @ SY607 ) )
| ( ( sK9_SY485 @ SV27 @ SV74 @ SV54 )
= SY606 ) ) )
= $false )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[429]) ).
thf(484,plain,
! [SV85: $i,SV75: $i,SV55: $i,SV28: $i] :
( ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $false )
| ( ( ! [SY546: $i,SY547: $i,SY548: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY546 @ SV75 )
| ~ ( member @ SY547 @ SV85 ) )
| ~ ( member @ SY548 @ SV85 ) )
| ~ ~ ( ~ ( apply @ SV28 @ SY546 @ SY547 )
| ~ ( apply @ SV55 @ SY546 @ SY548 ) )
| ( SY547 = SY548 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(485,plain,
! [SV55: $i,SV28: $i,SV85: $i,SV75: $i] :
( ( ( ! [SY549: $i,SY550: $i,SY551: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY549 @ SV75 )
| ~ ( member @ SY550 @ SV85 ) )
| ~ ( member @ SY551 @ SV85 ) )
| ~ ~ ( ~ ( apply @ SV28 @ SY549 @ SY550 )
| ~ ( apply @ SV55 @ SY549 @ SY551 ) )
| ( SY550 = SY551 ) ) )
= $false )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[431]) ).
thf(486,plain,
! [SV2: $i,SV56: $i,SV86: $i,SV29: $i,SV76: $i] :
( ( ( member @ SV76 @ SV29 )
= $false )
| ( ( ~ ( member @ SV86 @ SV56 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV2 @ SV76 @ SV86 )
| ( apply @ ( inverse_function @ SV2 @ SV29 @ SV56 ) @ SV86 @ SV76 ) )
| ~ ( ~ ( apply @ ( inverse_function @ SV2 @ SV29 @ SV56 ) @ SV86 @ SV76 )
| ( apply @ SV2 @ SV76 @ SV86 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(487,plain,
! [SV3: $i,SV30: $i,SV57: $i,SV77: $i] :
( ( ( ~ ( member @ SV77 @ SV57 )
| ~ ~ ! [SY496: $i] :
~ ~ ( ~ ( member @ SY496 @ SV30 )
| ~ ( apply @ SV3 @ SY496 @ SV77 ) ) )
= $false )
| ( ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(488,plain,
! [SV3: $i,SV30: $i,SV57: $i,SV77: $i] :
( ( ( ~ ( member @ SV77 @ SV57 )
| ~ ~ ! [SY497: $i] :
~ ~ ( ~ ( member @ SY497 @ SV30 )
| ~ ( apply @ SV3 @ SY497 @ SV77 ) ) )
= $true )
| ( ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[434]) ).
thf(489,plain,
! [SV4: $i,SV31: $i,SV58: $i,SV98: $i] :
( ( ( ~ ( member @ SV98 @ SV58 ) )
= $true )
| ( ( ~ ! [SY602: $i] :
~ ~ ( ~ ( member @ SY602 @ SV31 )
| ~ ( apply @ SV4 @ SY602 @ SV98 ) ) )
= $true )
| ( ( surjective @ SV4 @ SV31 @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[435]) ).
thf(490,plain,
! [SV58: $i,SV31: $i,SV4: $i] :
( ( ( ~ ( member @ ( sK7_SY411 @ SV4 @ SV31 @ SV58 ) @ SV58 ) )
= $false )
| ( ( surjective @ SV4 @ SV31 @ SV58 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[436]) ).
thf(491,plain,
! [SV58: $i,SV4: $i,SV31: $i] :
( ( ( ~ ! [SY603: $i] :
~ ~ ( ~ ( member @ SY603 @ SV31 )
| ~ ( apply @ SV4 @ SY603 @ ( sK7_SY411 @ SV4 @ SV31 @ SV58 ) ) ) )
= $false )
| ( ( surjective @ SV4 @ SV31 @ SV58 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[436]) ).
thf(492,plain,
! [SV32: $i,SV5: $i,SV95: $i] :
( ( ( member @ SV95 @ SV5 )
= $false )
| ( ( member @ SV95 @ SV32 )
= $true )
| ( ( subset @ SV5 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(493,plain,
! [SV5: $i,SV32: $i] :
( ( ( member @ ( sK4_SY298 @ SV32 @ SV5 ) @ SV5 )
= $true )
| ( ( subset @ SV5 @ SV32 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[438]) ).
thf(494,plain,
! [SV87: $i,SV78: $i,SV59: $i,SV33: $i,SV6: $i] :
( ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $false )
| ( ( ! [SY552: $i,SY553: $i,SY554: $i,SY555: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY552 @ SV33 )
| ~ ( member @ SY553 @ SV78 ) )
| ~ ( member @ SY554 @ SV33 ) )
| ~ ( member @ SY555 @ SV78 ) )
| ~ ( apply @ SV59 @ SY552 @ SY554 ) )
| ~ ( apply @ SV6 @ SY552 @ SY553 ) )
| ~ ( apply @ SV6 @ SY554 @ SY555 ) )
| ( apply @ SV87 @ SY555 @ SY553 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(495,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV78: $i,SV33: $i] :
( ( ( ! [SY556: $i,SY557: $i,SY558: $i,SY559: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY556 @ SV33 )
| ~ ( member @ SY557 @ SV78 ) )
| ~ ( member @ SY558 @ SV33 ) )
| ~ ( member @ SY559 @ SV78 ) )
| ~ ( apply @ SV59 @ SY556 @ SY558 ) )
| ~ ( apply @ SV6 @ SY556 @ SY557 ) )
| ~ ( apply @ SV6 @ SY558 @ SY559 ) )
| ( apply @ SV87 @ SY559 @ SY557 ) ) )
= $false )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(496,plain,
! [SV88: $i,SV79: $i,SV60: $i,SV34: $i,SV7: $i] :
( ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( maps @ SV7 @ SV34 @ SV79 )
| ~ ( one_to_one @ SV7 @ SV34 @ SV79 ) )
| ~ ! [SY560: $i,SY561: $i,SY562: $i,SY563: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY560 @ SV34 )
| ~ ( member @ SY561 @ SV79 ) )
| ~ ( member @ SY562 @ SV34 ) )
| ~ ( member @ SY563 @ SV79 ) )
| ~ ( apply @ SV7 @ SY560 @ SY561 ) )
| ~ ( apply @ SV7 @ SY562 @ SY563 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ SY560 @ SY562 )
| ( apply @ SV88 @ SY561 @ SY563 ) )
| ~ ( ~ ( apply @ SV88 @ SY561 @ SY563 )
| ( apply @ SV60 @ SY560 @ SY562 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[442]) ).
thf(497,plain,
! [SV88: $i,SV60: $i,SV79: $i,SV34: $i,SV7: $i] :
( ( ( ~ ( ~ ~ ( ~ ( maps @ SV7 @ SV34 @ SV79 )
| ~ ( one_to_one @ SV7 @ SV34 @ SV79 ) )
| ~ ! [SY564: $i,SY565: $i,SY566: $i,SY567: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY564 @ SV34 )
| ~ ( member @ SY565 @ SV79 ) )
| ~ ( member @ SY566 @ SV34 ) )
| ~ ( member @ SY567 @ SV79 ) )
| ~ ( apply @ SV7 @ SY564 @ SY565 ) )
| ~ ( apply @ SV7 @ SY566 @ SY567 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ SY564 @ SY566 )
| ( apply @ SV88 @ SY565 @ SY567 ) )
| ~ ( ~ ( apply @ SV88 @ SY565 @ SY567 )
| ( apply @ SV60 @ SY564 @ SY566 ) ) ) ) ) )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(498,plain,
! [SV35: $i,SV61: $i,SV8: $i] :
( ( ( ~ ( member @ SV8 @ SV61 ) )
= $false )
| ( ( member @ SV8 @ ( difference @ SV61 @ SV35 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[444]) ).
thf(499,plain,
! [SV61: $i,SV35: $i,SV8: $i] :
( ( ( ~ ~ ( member @ SV8 @ SV35 ) )
= $false )
| ( ( member @ SV8 @ ( difference @ SV61 @ SV35 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[444]) ).
thf(500,plain,
! [SV35: $i,SV61: $i,SV8: $i] :
( ( ( ~ ( member @ SV8 @ SV61 ) )
= $true )
| ( ( ~ ~ ( member @ SV8 @ SV35 ) )
= $true )
| ( ( member @ SV8 @ ( difference @ SV61 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[445]) ).
thf(501,plain,
! [SV89: $i,SV80: $i,SV62: $i,SV36: $i,SV9: $i] :
( ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $false )
| ( ( ! [SY568: $i,SY569: $i,SY570: $i,SY571: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY568 @ SV36 )
| ~ ( member @ SY569 @ SV80 ) )
| ~ ( member @ SY570 @ SV36 ) )
| ~ ( member @ SY571 @ SV80 ) )
| ~ ( apply @ SV62 @ SY568 @ SY570 ) )
| ~ ( apply @ SV9 @ SY568 @ SY569 ) )
| ~ ( apply @ SV9 @ SY570 @ SY571 ) )
| ( apply @ SV89 @ SY569 @ SY571 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(502,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV80: $i,SV36: $i] :
( ( ( ! [SY572: $i,SY573: $i,SY574: $i,SY575: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY572 @ SV36 )
| ~ ( member @ SY573 @ SV80 ) )
| ~ ( member @ SY574 @ SV36 ) )
| ~ ( member @ SY575 @ SV80 ) )
| ~ ( apply @ SV62 @ SY572 @ SY574 ) )
| ~ ( apply @ SV9 @ SY572 @ SY573 ) )
| ~ ( apply @ SV9 @ SY574 @ SY575 ) )
| ( apply @ SV89 @ SY573 @ SY575 ) ) )
= $false )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(503,plain,
! [SV38: $i,SV11: $i] :
( ( ( ~ ( ~ ( member @ ( sK8_SY333 @ SV11 @ SV38 ) @ SV38 )
| ~ ( member @ SV11 @ ( sK8_SY333 @ SV11 @ SV38 ) ) ) )
= $true )
| ( ( member @ SV11 @ ( sum @ SV38 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[448]) ).
thf(504,plain,
! [SV11: $i,SV38: $i,SV99: $i] :
( ( ( ~ ( ~ ( member @ SV99 @ SV38 )
| ~ ( member @ SV11 @ SV99 ) ) )
= $false )
| ( ( member @ SV11 @ ( sum @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(505,plain,
! [SV64: $i,SV40: $i,SV13: $i] :
( ( ( ~ ( injective @ SV13 @ SV40 @ SV64 ) )
= $false )
| ( ( one_to_one @ SV13 @ SV40 @ SV64 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(506,plain,
! [SV64: $i,SV40: $i,SV13: $i] :
( ( ( ~ ( surjective @ SV13 @ SV40 @ SV64 ) )
= $false )
| ( ( one_to_one @ SV13 @ SV40 @ SV64 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(507,plain,
! [SV64: $i,SV40: $i,SV13: $i] :
( ( ( ~ ( injective @ SV13 @ SV40 @ SV64 ) )
= $true )
| ( ( ~ ( surjective @ SV13 @ SV40 @ SV64 ) )
= $true )
| ( ( one_to_one @ SV13 @ SV40 @ SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[454]) ).
thf(508,plain,
! [SV41: $i,SV14: $i,SV65: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK10_SY443 @ SV65 @ SV14 @ SV41 ) @ SV41 )
| ~ ( apply @ SV14 @ ( sK10_SY443 @ SV65 @ SV14 @ SV41 ) @ SV65 ) ) )
= $false )
| ( ( member @ SV65 @ ( image2 @ SV14 @ SV41 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[455]) ).
thf(509,plain,
! [SV65: $i,SV14: $i,SV41: $i,SV101: $i] :
( ( ( ~ ~ ( ~ ( member @ SV101 @ SV41 )
| ~ ( apply @ SV14 @ SV101 @ SV65 ) ) )
= $true )
| ( ( member @ SV65 @ ( image2 @ SV14 @ SV41 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(510,plain,
! [SV42: $i,SV15: $i] :
( ( ( subset @ SV15 @ SV42 )
= $true )
| ( ( equal_set @ SV15 @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[457]) ).
thf(511,plain,
! [SV15: $i,SV42: $i] :
( ( ( subset @ SV42 @ SV15 )
= $true )
| ( ( equal_set @ SV15 @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[458]) ).
thf(512,plain,
! [SV42: $i,SV15: $i] :
( ( ( subset @ SV15 @ SV42 )
= $false )
| ( ( ~ ( subset @ SV42 @ SV15 ) )
= $true )
| ( ( equal_set @ SV15 @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(513,plain,
! [SV16: $i,SV43: $i,SV66: $i,SV81: $i] :
( ( ( ~ ( member @ SV81 @ SV66 )
| ~ ~ ! [SY525: $i] :
~ ~ ( ~ ( member @ SY525 @ SV43 )
| ~ ( apply @ SV16 @ SV81 @ SY525 ) ) )
= $false )
| ( ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[460]) ).
thf(514,plain,
! [SV16: $i,SV43: $i,SV66: $i,SV81: $i] :
( ( ( ~ ( member @ SV81 @ SV66 )
| ~ ~ ! [SY526: $i] :
~ ~ ( ~ ( member @ SY526 @ SV43 )
| ~ ( apply @ SV16 @ SV81 @ SY526 ) ) )
= $true )
| ( ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[461]) ).
thf(515,plain,
! [SV17: $i,SV44: $i,SV82: $i,SV67: $i,SV102: $i] :
( ( ( ! [SY608: $i] :
( ~ ~ ( ~ ( member @ SV102 @ SV67 )
| ~ ( member @ SY608 @ SV82 ) )
| ~ ( ~ ( ~ ( apply @ SV44 @ SV102 @ SY608 )
| ( apply @ SV17 @ SY608 @ SV102 ) )
| ~ ( ~ ( apply @ SV17 @ SY608 @ SV102 )
| ( apply @ SV44 @ SV102 @ SY608 ) ) ) ) )
= $true )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(516,plain,
! [SV67: $i,SV82: $i,SV44: $i,SV17: $i] :
( ( ( ! [SY609: $i] :
( ~ ~ ( ~ ( member @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ SV67 )
| ~ ( member @ SY609 @ SV82 ) )
| ~ ( ~ ( ~ ( apply @ SV44 @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ SY609 )
| ( apply @ SV17 @ SY609 @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) ) )
| ~ ( ~ ( apply @ SV17 @ SY609 @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) )
| ( apply @ SV44 @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ SY609 ) ) ) ) )
= $false )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[463]) ).
thf(517,plain,
! [SV19: $i,SV46: $i,SV96: $i] :
( ( ( member @ SV96 @ SV46 )
= $false )
| ( ( member @ SV19 @ SV96 )
= $true )
| ( ( member @ SV19 @ ( product @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(518,plain,
! [SV46: $i,SV19: $i] :
( ( ( member @ ( sK5_SY351 @ SV19 @ SV46 ) @ SV46 )
= $true )
| ( ( member @ SV19 @ ( product @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[465]) ).
thf(519,plain,
! [SV21: $i,SV69: $i,SV48: $i] :
( ( ( ~ ! [SY453: $i] :
( ~ ( member @ SY453 @ SV48 )
| ~ ! [SY454: $i] :
~ ~ ( ~ ( member @ SY454 @ SV69 )
| ~ ( apply @ SV21 @ SY453 @ SY454 ) ) ) )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[470]) ).
thf(520,plain,
! [SV21: $i,SV69: $i,SV48: $i] :
( ( ( ~ ! [SY455: $i,SY456: $i,SY457: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY455 @ SV48 )
| ~ ( member @ SY456 @ SV69 ) )
| ~ ( member @ SY457 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY455 @ SY456 )
| ~ ( apply @ SV21 @ SY455 @ SY457 ) )
| ( SY456 = SY457 ) ) )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[470]) ).
thf(521,plain,
! [SV21: $i,SV69: $i,SV48: $i] :
( ( ( ~ ! [SY458: $i] :
( ~ ( member @ SY458 @ SV48 )
| ~ ! [SY459: $i] :
~ ~ ( ~ ( member @ SY459 @ SV69 )
| ~ ( apply @ SV21 @ SY458 @ SY459 ) ) ) )
= $true )
| ( ( ~ ! [SY460: $i,SY461: $i,SY462: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY460 @ SV48 )
| ~ ( member @ SY461 @ SV69 ) )
| ~ ( member @ SY462 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY460 @ SY461 )
| ~ ( apply @ SV21 @ SY460 @ SY462 ) )
| ( SY461 = SY462 ) ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[471]) ).
thf(522,plain,
! [SV22: $i,SV49: $i,SV97: $i] :
( ( ( member @ SV97 @ SV49 )
= $false )
| ( ( apply @ SV22 @ SV97 @ SV97 )
= $true )
| ( ( identity @ SV22 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(523,plain,
! [SV49: $i,SV22: $i] :
( ( ( member @ ( sK6_SY365 @ SV22 @ SV49 ) @ SV49 )
= $true )
| ( ( identity @ SV22 @ SV49 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[473]) ).
thf(524,plain,
! [SV92: $i,SV90: $i,SV83: $i,SV70: $i,SV50: $i,SV23: $i] :
( ( ( ~ ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 ) )
= $true )
| ( ( ! [SY589: $i,SY590: $i] :
( ~ ~ ( ~ ( member @ SY589 @ SV83 )
| ~ ( member @ SY590 @ SV92 ) )
| ~ ( ~ ( ~ ( apply @ SV23 @ SY589 @ SY590 )
| ~ ! [SY579: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY579 @ SV90 )
| ~ ( apply @ SV70 @ SY589 @ SY579 ) )
| ~ ( apply @ SV50 @ SY579 @ SY590 ) ) )
| ~ ( ~ ~ ! [SY580: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY580 @ SV90 )
| ~ ( apply @ SV70 @ SY589 @ SY580 ) )
| ~ ( apply @ SV50 @ SY580 @ SY590 ) )
| ( apply @ SV23 @ SY589 @ SY590 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[475]) ).
thf(525,plain,
! [SV50: $i,SV70: $i,SV90: $i,SV23: $i,SV92: $i,SV83: $i] :
( ( ( ~ ! [SY593: $i,SY594: $i] :
( ~ ~ ( ~ ( member @ SY593 @ SV83 )
| ~ ( member @ SY594 @ SV92 ) )
| ~ ( ~ ( ~ ( apply @ SV23 @ SY593 @ SY594 )
| ~ ! [SY583: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY583 @ SV90 )
| ~ ( apply @ SV70 @ SY593 @ SY583 ) )
| ~ ( apply @ SV50 @ SY583 @ SY594 ) ) )
| ~ ( ~ ~ ! [SY584: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY584 @ SV90 )
| ~ ( apply @ SV70 @ SY593 @ SY584 ) )
| ~ ( apply @ SV50 @ SY584 @ SY594 ) )
| ( apply @ SV23 @ SY593 @ SY594 ) ) ) ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[476]) ).
thf(526,plain,
! [SV71: $i,SV51: $i,SV24: $i] :
( ( ( ~ ( member @ SV24 @ SV51 ) )
= $false )
| ( ( member @ SV24 @ ( intersection @ SV51 @ SV71 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[477]) ).
thf(527,plain,
! [SV51: $i,SV71: $i,SV24: $i] :
( ( ( ~ ( member @ SV24 @ SV71 ) )
= $false )
| ( ( member @ SV24 @ ( intersection @ SV51 @ SV71 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[477]) ).
thf(528,plain,
! [SV71: $i,SV51: $i,SV24: $i] :
( ( ( ~ ( member @ SV24 @ SV51 ) )
= $true )
| ( ( ~ ( member @ SV24 @ SV71 ) )
= $true )
| ( ( member @ SV24 @ ( intersection @ SV51 @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[478]) ).
thf(529,plain,
! [SV84: $i,SV52: $i,SV25: $i,SV91: $i,SV94: $i,SV72: $i,SV93: $i] :
( ( ( ~ ( member @ SV93 @ SV72 )
| ~ ( member @ SV94 @ SV91 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
| ~ ! [SY600: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY600 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SY600 ) )
| ~ ( apply @ SV25 @ SY600 @ SV94 ) ) )
| ~ ( ~ ~ ! [SY601: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY601 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SY601 ) )
| ~ ( apply @ SV25 @ SY601 @ SV94 ) )
| ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[479]) ).
thf(530,plain,
! [SV53: $i,SV26: $i,SV73: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK12_SY480 @ SV73 @ SV26 @ SV53 ) @ SV53 )
| ~ ( apply @ SV26 @ SV73 @ ( sK12_SY480 @ SV73 @ SV26 @ SV53 ) ) ) )
= $false )
| ( ( member @ SV73 @ ( inverse_image2 @ SV26 @ SV53 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[480]) ).
thf(531,plain,
! [SV73: $i,SV26: $i,SV53: $i,SV103: $i] :
( ( ( ~ ~ ( ~ ( member @ SV103 @ SV53 )
| ~ ( apply @ SV26 @ SV73 @ SV103 ) ) )
= $true )
| ( ( member @ SV73 @ ( inverse_image2 @ SV26 @ SV53 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(532,plain,
! [SV27: $i,SV74: $i,SV104: $i,SV54: $i,SV100: $i] :
( ( ( ! [SY610: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SV100 @ SV54 )
| ~ ( member @ SV104 @ SV54 ) )
| ~ ( member @ SY610 @ SV74 ) )
| ~ ~ ( ~ ( apply @ SV27 @ SV100 @ SY610 )
| ~ ( apply @ SV27 @ SV104 @ SY610 ) )
| ( SV100 = SV104 ) ) )
= $true )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(533,plain,
! [SV54: $i,SV74: $i,SV27: $i] :
( ( ( ! [SY611: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK9_SY485 @ SV27 @ SV74 @ SV54 ) @ SV54 )
| ~ ( member @ ( sK13_SY606 @ SV54 @ SV74 @ SV27 ) @ SV54 ) )
| ~ ( member @ SY611 @ SV74 ) )
| ~ ~ ( ~ ( apply @ SV27 @ ( sK9_SY485 @ SV27 @ SV74 @ SV54 ) @ SY611 )
| ~ ( apply @ SV27 @ ( sK13_SY606 @ SV54 @ SV74 @ SV27 ) @ SY611 ) )
| ( ( sK9_SY485 @ SV27 @ SV74 @ SV54 )
= ( sK13_SY606 @ SV54 @ SV74 @ SV27 ) ) ) )
= $false )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[483]) ).
thf(534,plain,
! [SV55: $i,SV28: $i,SV85: $i,SV75: $i,SV105: $i] :
( ( ( ! [SY612: $i,SY613: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SV105 @ SV75 )
| ~ ( member @ SY612 @ SV85 ) )
| ~ ( member @ SY613 @ SV85 ) )
| ~ ~ ( ~ ( apply @ SV28 @ SV105 @ SY612 )
| ~ ( apply @ SV55 @ SV105 @ SY613 ) )
| ( SY612 = SY613 ) ) )
= $true )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(535,plain,
! [SV75: $i,SV85: $i,SV28: $i,SV55: $i] :
( ( ( ! [SY614: $i,SY615: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK14_SY549 @ SV55 @ SV28 @ SV85 @ SV75 ) @ SV75 )
| ~ ( member @ SY614 @ SV85 ) )
| ~ ( member @ SY615 @ SV85 ) )
| ~ ~ ( ~ ( apply @ SV28 @ ( sK14_SY549 @ SV55 @ SV28 @ SV85 @ SV75 ) @ SY614 )
| ~ ( apply @ SV55 @ ( sK14_SY549 @ SV55 @ SV28 @ SV85 @ SV75 ) @ SY615 ) )
| ( SY614 = SY615 ) ) )
= $false )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[485]) ).
thf(536,plain,
! [SV2: $i,SV29: $i,SV76: $i,SV56: $i,SV86: $i] :
( ( ( member @ SV86 @ SV56 )
= $false )
| ( ( member @ SV76 @ SV29 )
= $false )
| ( ( ~ ( ~ ( ~ ( apply @ SV2 @ SV76 @ SV86 )
| ( apply @ ( inverse_function @ SV2 @ SV29 @ SV56 ) @ SV86 @ SV76 ) )
| ~ ( ~ ( apply @ ( inverse_function @ SV2 @ SV29 @ SV56 ) @ SV86 @ SV76 )
| ( apply @ SV2 @ SV76 @ SV86 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[486]) ).
thf(537,plain,
! [SV30: $i,SV3: $i,SV57: $i,SV77: $i] :
( ( ( ~ ( member @ SV77 @ SV57 ) )
= $false )
| ( ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[487]) ).
thf(538,plain,
! [SV57: $i,SV77: $i,SV3: $i,SV30: $i] :
( ( ( ~ ~ ! [SY496: $i] :
~ ~ ( ~ ( member @ SY496 @ SV30 )
| ~ ( apply @ SV3 @ SY496 @ SV77 ) ) )
= $false )
| ( ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[487]) ).
thf(539,plain,
! [SV3: $i,SV30: $i,SV57: $i,SV77: $i] :
( ( ( ~ ( member @ SV77 @ SV57 ) )
= $true )
| ( ( ~ ~ ! [SY497: $i] :
~ ~ ( ~ ( member @ SY497 @ SV30 )
| ~ ( apply @ SV3 @ SY497 @ SV77 ) ) )
= $true )
| ( ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[488]) ).
thf(540,plain,
! [SV4: $i,SV31: $i,SV58: $i,SV98: $i] :
( ( ( member @ SV98 @ SV58 )
= $false )
| ( ( ~ ! [SY602: $i] :
~ ~ ( ~ ( member @ SY602 @ SV31 )
| ~ ( apply @ SV4 @ SY602 @ SV98 ) ) )
= $true )
| ( ( surjective @ SV4 @ SV31 @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[489]) ).
thf(541,plain,
! [SV58: $i,SV31: $i,SV4: $i] :
( ( ( member @ ( sK7_SY411 @ SV4 @ SV31 @ SV58 ) @ SV58 )
= $true )
| ( ( surjective @ SV4 @ SV31 @ SV58 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[490]) ).
thf(542,plain,
! [SV58: $i,SV4: $i,SV31: $i] :
( ( ( ! [SY603: $i] :
~ ~ ( ~ ( member @ SY603 @ SV31 )
| ~ ( apply @ SV4 @ SY603 @ ( sK7_SY411 @ SV4 @ SV31 @ SV58 ) ) ) )
= $true )
| ( ( surjective @ SV4 @ SV31 @ SV58 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[491]) ).
thf(543,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV78: $i,SV33: $i,SV106: $i] :
( ( ( ! [SY616: $i,SY617: $i,SY618: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV106 @ SV33 )
| ~ ( member @ SY616 @ SV78 ) )
| ~ ( member @ SY617 @ SV33 ) )
| ~ ( member @ SY618 @ SV78 ) )
| ~ ( apply @ SV59 @ SV106 @ SY617 ) )
| ~ ( apply @ SV6 @ SV106 @ SY616 ) )
| ~ ( apply @ SV6 @ SY617 @ SY618 ) )
| ( apply @ SV87 @ SY618 @ SY616 ) ) )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(544,plain,
! [SV33: $i,SV78: $i,SV59: $i,SV6: $i,SV87: $i] :
( ( ( ! [SY619: $i,SY620: $i,SY621: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ SV33 )
| ~ ( member @ SY619 @ SV78 ) )
| ~ ( member @ SY620 @ SV33 ) )
| ~ ( member @ SY621 @ SV78 ) )
| ~ ( apply @ SV59 @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ SY620 ) )
| ~ ( apply @ SV6 @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ SY619 ) )
| ~ ( apply @ SV6 @ SY620 @ SY621 ) )
| ( apply @ SV87 @ SY621 @ SY619 ) ) )
= $false )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[495]) ).
thf(545,plain,
! [SV88: $i,SV60: $i,SV79: $i,SV34: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( maps @ SV7 @ SV34 @ SV79 )
| ~ ( one_to_one @ SV7 @ SV34 @ SV79 ) )
| ~ ! [SY560: $i,SY561: $i,SY562: $i,SY563: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY560 @ SV34 )
| ~ ( member @ SY561 @ SV79 ) )
| ~ ( member @ SY562 @ SV34 ) )
| ~ ( member @ SY563 @ SV79 ) )
| ~ ( apply @ SV7 @ SY560 @ SY561 ) )
| ~ ( apply @ SV7 @ SY562 @ SY563 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ SY560 @ SY562 )
| ( apply @ SV88 @ SY561 @ SY563 ) )
| ~ ( ~ ( apply @ SV88 @ SY561 @ SY563 )
| ( apply @ SV60 @ SY560 @ SY562 ) ) ) ) )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(546,plain,
! [SV88: $i,SV60: $i,SV79: $i,SV34: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( maps @ SV7 @ SV34 @ SV79 )
| ~ ( one_to_one @ SV7 @ SV34 @ SV79 ) )
| ~ ! [SY564: $i,SY565: $i,SY566: $i,SY567: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY564 @ SV34 )
| ~ ( member @ SY565 @ SV79 ) )
| ~ ( member @ SY566 @ SV34 ) )
| ~ ( member @ SY567 @ SV79 ) )
| ~ ( apply @ SV7 @ SY564 @ SY565 ) )
| ~ ( apply @ SV7 @ SY566 @ SY567 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ SY564 @ SY566 )
| ( apply @ SV88 @ SY565 @ SY567 ) )
| ~ ( ~ ( apply @ SV88 @ SY565 @ SY567 )
| ( apply @ SV60 @ SY564 @ SY566 ) ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[497]) ).
thf(547,plain,
! [SV35: $i,SV61: $i,SV8: $i] :
( ( ( member @ SV8 @ SV61 )
= $true )
| ( ( member @ SV8 @ ( difference @ SV61 @ SV35 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[498]) ).
thf(548,plain,
! [SV61: $i,SV35: $i,SV8: $i] :
( ( ( ~ ( member @ SV8 @ SV35 ) )
= $true )
| ( ( member @ SV8 @ ( difference @ SV61 @ SV35 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[499]) ).
thf(549,plain,
! [SV35: $i,SV61: $i,SV8: $i] :
( ( ( member @ SV8 @ SV61 )
= $false )
| ( ( ~ ~ ( member @ SV8 @ SV35 ) )
= $true )
| ( ( member @ SV8 @ ( difference @ SV61 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(550,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV80: $i,SV36: $i,SV107: $i] :
( ( ( ! [SY622: $i,SY623: $i,SY624: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV107 @ SV36 )
| ~ ( member @ SY622 @ SV80 ) )
| ~ ( member @ SY623 @ SV36 ) )
| ~ ( member @ SY624 @ SV80 ) )
| ~ ( apply @ SV62 @ SV107 @ SY623 ) )
| ~ ( apply @ SV9 @ SV107 @ SY622 ) )
| ~ ( apply @ SV9 @ SY623 @ SY624 ) )
| ( apply @ SV89 @ SY622 @ SY624 ) ) )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(551,plain,
! [SV36: $i,SV80: $i,SV62: $i,SV9: $i,SV89: $i] :
( ( ( ! [SY625: $i,SY626: $i,SY627: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ SV36 )
| ~ ( member @ SY625 @ SV80 ) )
| ~ ( member @ SY626 @ SV36 ) )
| ~ ( member @ SY627 @ SV80 ) )
| ~ ( apply @ SV62 @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ SY626 ) )
| ~ ( apply @ SV9 @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ SY625 ) )
| ~ ( apply @ SV9 @ SY626 @ SY627 ) )
| ( apply @ SV89 @ SY625 @ SY627 ) ) )
= $false )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[502]) ).
thf(552,plain,
! [SV38: $i,SV11: $i] :
( ( ( ~ ( member @ ( sK8_SY333 @ SV11 @ SV38 ) @ SV38 )
| ~ ( member @ SV11 @ ( sK8_SY333 @ SV11 @ SV38 ) ) )
= $false )
| ( ( member @ SV11 @ ( sum @ SV38 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(553,plain,
! [SV11: $i,SV38: $i,SV99: $i] :
( ( ( ~ ( member @ SV99 @ SV38 )
| ~ ( member @ SV11 @ SV99 ) )
= $true )
| ( ( member @ SV11 @ ( sum @ SV38 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[504]) ).
thf(554,plain,
! [SV64: $i,SV40: $i,SV13: $i] :
( ( ( injective @ SV13 @ SV40 @ SV64 )
= $true )
| ( ( one_to_one @ SV13 @ SV40 @ SV64 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[505]) ).
thf(555,plain,
! [SV64: $i,SV40: $i,SV13: $i] :
( ( ( surjective @ SV13 @ SV40 @ SV64 )
= $true )
| ( ( one_to_one @ SV13 @ SV40 @ SV64 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[506]) ).
thf(556,plain,
! [SV64: $i,SV40: $i,SV13: $i] :
( ( ( injective @ SV13 @ SV40 @ SV64 )
= $false )
| ( ( ~ ( surjective @ SV13 @ SV40 @ SV64 ) )
= $true )
| ( ( one_to_one @ SV13 @ SV40 @ SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(557,plain,
! [SV41: $i,SV14: $i,SV65: $i] :
( ( ( ~ ( ~ ( member @ ( sK10_SY443 @ SV65 @ SV14 @ SV41 ) @ SV41 )
| ~ ( apply @ SV14 @ ( sK10_SY443 @ SV65 @ SV14 @ SV41 ) @ SV65 ) ) )
= $true )
| ( ( member @ SV65 @ ( image2 @ SV14 @ SV41 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[508]) ).
thf(558,plain,
! [SV65: $i,SV14: $i,SV41: $i,SV101: $i] :
( ( ( ~ ( ~ ( member @ SV101 @ SV41 )
| ~ ( apply @ SV14 @ SV101 @ SV65 ) ) )
= $false )
| ( ( member @ SV65 @ ( image2 @ SV14 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[509]) ).
thf(559,plain,
! [SV15: $i,SV42: $i] :
( ( ( subset @ SV42 @ SV15 )
= $false )
| ( ( subset @ SV15 @ SV42 )
= $false )
| ( ( equal_set @ SV15 @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(560,plain,
! [SV43: $i,SV16: $i,SV66: $i,SV81: $i] :
( ( ( ~ ( member @ SV81 @ SV66 ) )
= $false )
| ( ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[513]) ).
thf(561,plain,
! [SV66: $i,SV81: $i,SV16: $i,SV43: $i] :
( ( ( ~ ~ ! [SY525: $i] :
~ ~ ( ~ ( member @ SY525 @ SV43 )
| ~ ( apply @ SV16 @ SV81 @ SY525 ) ) )
= $false )
| ( ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[513]) ).
thf(562,plain,
! [SV16: $i,SV43: $i,SV66: $i,SV81: $i] :
( ( ( ~ ( member @ SV81 @ SV66 ) )
= $true )
| ( ( ~ ~ ! [SY526: $i] :
~ ~ ( ~ ( member @ SY526 @ SV43 )
| ~ ( apply @ SV16 @ SV81 @ SY526 ) ) )
= $true )
| ( ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[514]) ).
thf(563,plain,
! [SV17: $i,SV44: $i,SV82: $i,SV108: $i,SV67: $i,SV102: $i] :
( ( ( ~ ~ ( ~ ( member @ SV102 @ SV67 )
| ~ ( member @ SV108 @ SV82 ) )
| ~ ( ~ ( ~ ( apply @ SV44 @ SV102 @ SV108 )
| ( apply @ SV17 @ SV108 @ SV102 ) )
| ~ ( ~ ( apply @ SV17 @ SV108 @ SV102 )
| ( apply @ SV44 @ SV102 @ SV108 ) ) ) )
= $true )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(564,plain,
! [SV67: $i,SV82: $i,SV44: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ SV67 )
| ~ ( member @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) @ SV82 ) )
| ~ ( ~ ( ~ ( apply @ SV44 @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) )
| ( apply @ SV17 @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) ) )
| ~ ( ~ ( apply @ SV17 @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) )
| ( apply @ SV44 @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) ) ) ) )
= $false )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[516]) ).
thf(565,plain,
! [SV21: $i,SV69: $i,SV48: $i] :
( ( ( ! [SY453: $i] :
( ~ ( member @ SY453 @ SV48 )
| ~ ! [SY454: $i] :
~ ~ ( ~ ( member @ SY454 @ SV69 )
| ~ ( apply @ SV21 @ SY453 @ SY454 ) ) ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[519]) ).
thf(566,plain,
! [SV21: $i,SV69: $i,SV48: $i] :
( ( ( ! [SY455: $i,SY456: $i,SY457: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY455 @ SV48 )
| ~ ( member @ SY456 @ SV69 ) )
| ~ ( member @ SY457 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY455 @ SY456 )
| ~ ( apply @ SV21 @ SY455 @ SY457 ) )
| ( SY456 = SY457 ) ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[520]) ).
thf(567,plain,
! [SV21: $i,SV69: $i,SV48: $i] :
( ( ( ! [SY458: $i] :
( ~ ( member @ SY458 @ SV48 )
| ~ ! [SY459: $i] :
~ ~ ( ~ ( member @ SY459 @ SV69 )
| ~ ( apply @ SV21 @ SY458 @ SY459 ) ) ) )
= $false )
| ( ( ~ ! [SY460: $i,SY461: $i,SY462: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY460 @ SV48 )
| ~ ( member @ SY461 @ SV69 ) )
| ~ ( member @ SY462 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY460 @ SY461 )
| ~ ( apply @ SV21 @ SY460 @ SY462 ) )
| ( SY461 = SY462 ) ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[521]) ).
thf(568,plain,
! [SV92: $i,SV90: $i,SV83: $i,SV70: $i,SV50: $i,SV23: $i] :
( ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false )
| ( ( ! [SY589: $i,SY590: $i] :
( ~ ~ ( ~ ( member @ SY589 @ SV83 )
| ~ ( member @ SY590 @ SV92 ) )
| ~ ( ~ ( ~ ( apply @ SV23 @ SY589 @ SY590 )
| ~ ! [SY579: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY579 @ SV90 )
| ~ ( apply @ SV70 @ SY589 @ SY579 ) )
| ~ ( apply @ SV50 @ SY579 @ SY590 ) ) )
| ~ ( ~ ~ ! [SY580: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY580 @ SV90 )
| ~ ( apply @ SV70 @ SY589 @ SY580 ) )
| ~ ( apply @ SV50 @ SY580 @ SY590 ) )
| ( apply @ SV23 @ SY589 @ SY590 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(569,plain,
! [SV50: $i,SV70: $i,SV90: $i,SV23: $i,SV92: $i,SV83: $i] :
( ( ( ! [SY593: $i,SY594: $i] :
( ~ ~ ( ~ ( member @ SY593 @ SV83 )
| ~ ( member @ SY594 @ SV92 ) )
| ~ ( ~ ( ~ ( apply @ SV23 @ SY593 @ SY594 )
| ~ ! [SY583: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY583 @ SV90 )
| ~ ( apply @ SV70 @ SY593 @ SY583 ) )
| ~ ( apply @ SV50 @ SY583 @ SY594 ) ) )
| ~ ( ~ ~ ! [SY584: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY584 @ SV90 )
| ~ ( apply @ SV70 @ SY593 @ SY584 ) )
| ~ ( apply @ SV50 @ SY584 @ SY594 ) )
| ( apply @ SV23 @ SY593 @ SY594 ) ) ) ) )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[525]) ).
thf(570,plain,
! [SV71: $i,SV51: $i,SV24: $i] :
( ( ( member @ SV24 @ SV51 )
= $true )
| ( ( member @ SV24 @ ( intersection @ SV51 @ SV71 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[526]) ).
thf(571,plain,
! [SV51: $i,SV71: $i,SV24: $i] :
( ( ( member @ SV24 @ SV71 )
= $true )
| ( ( member @ SV24 @ ( intersection @ SV51 @ SV71 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[527]) ).
thf(572,plain,
! [SV71: $i,SV51: $i,SV24: $i] :
( ( ( member @ SV24 @ SV51 )
= $false )
| ( ( ~ ( member @ SV24 @ SV71 ) )
= $true )
| ( ( member @ SV24 @ ( intersection @ SV51 @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(573,plain,
! [SV84: $i,SV52: $i,SV25: $i,SV91: $i,SV94: $i,SV72: $i,SV93: $i] :
( ( ( ~ ( member @ SV93 @ SV72 ) )
= $true )
| ( ( ~ ( member @ SV94 @ SV91 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
| ~ ! [SY600: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY600 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SY600 ) )
| ~ ( apply @ SV25 @ SY600 @ SV94 ) ) )
| ~ ( ~ ~ ! [SY601: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY601 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SY601 ) )
| ~ ( apply @ SV25 @ SY601 @ SV94 ) )
| ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[529]) ).
thf(574,plain,
! [SV53: $i,SV26: $i,SV73: $i] :
( ( ( ~ ( ~ ( member @ ( sK12_SY480 @ SV73 @ SV26 @ SV53 ) @ SV53 )
| ~ ( apply @ SV26 @ SV73 @ ( sK12_SY480 @ SV73 @ SV26 @ SV53 ) ) ) )
= $true )
| ( ( member @ SV73 @ ( inverse_image2 @ SV26 @ SV53 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[530]) ).
thf(575,plain,
! [SV73: $i,SV26: $i,SV53: $i,SV103: $i] :
( ( ( ~ ( ~ ( member @ SV103 @ SV53 )
| ~ ( apply @ SV26 @ SV73 @ SV103 ) ) )
= $false )
| ( ( member @ SV73 @ ( inverse_image2 @ SV26 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(576,plain,
! [SV27: $i,SV74: $i,SV109: $i,SV104: $i,SV54: $i,SV100: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV100 @ SV54 )
| ~ ( member @ SV104 @ SV54 ) )
| ~ ( member @ SV109 @ SV74 ) )
| ~ ~ ( ~ ( apply @ SV27 @ SV100 @ SV109 )
| ~ ( apply @ SV27 @ SV104 @ SV109 ) )
| ( SV100 = SV104 ) )
= $true )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(577,plain,
! [SV54: $i,SV74: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK9_SY485 @ SV27 @ SV74 @ SV54 ) @ SV54 )
| ~ ( member @ ( sK13_SY606 @ SV54 @ SV74 @ SV27 ) @ SV54 ) )
| ~ ( member @ ( sK18_SY611 @ SV54 @ SV74 @ SV27 ) @ SV74 ) )
| ~ ~ ( ~ ( apply @ SV27 @ ( sK9_SY485 @ SV27 @ SV74 @ SV54 ) @ ( sK18_SY611 @ SV54 @ SV74 @ SV27 ) )
| ~ ( apply @ SV27 @ ( sK13_SY606 @ SV54 @ SV74 @ SV27 ) @ ( sK18_SY611 @ SV54 @ SV74 @ SV27 ) ) )
| ( ( sK9_SY485 @ SV27 @ SV74 @ SV54 )
= ( sK13_SY606 @ SV54 @ SV74 @ SV27 ) ) )
= $false )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[533]) ).
thf(578,plain,
! [SV55: $i,SV28: $i,SV85: $i,SV110: $i,SV75: $i,SV105: $i] :
( ( ( ! [SY628: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SV105 @ SV75 )
| ~ ( member @ SV110 @ SV85 ) )
| ~ ( member @ SY628 @ SV85 ) )
| ~ ~ ( ~ ( apply @ SV28 @ SV105 @ SV110 )
| ~ ( apply @ SV55 @ SV105 @ SY628 ) )
| ( SV110 = SY628 ) ) )
= $true )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(579,plain,
! [SV75: $i,SV85: $i,SV28: $i,SV55: $i] :
( ( ( ! [SY629: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK14_SY549 @ SV55 @ SV28 @ SV85 @ SV75 ) @ SV75 )
| ~ ( member @ ( sK19_SY614 @ SV75 @ SV85 @ SV28 @ SV55 ) @ SV85 ) )
| ~ ( member @ SY629 @ SV85 ) )
| ~ ~ ( ~ ( apply @ SV28 @ ( sK14_SY549 @ SV55 @ SV28 @ SV85 @ SV75 ) @ ( sK19_SY614 @ SV75 @ SV85 @ SV28 @ SV55 ) )
| ~ ( apply @ SV55 @ ( sK14_SY549 @ SV55 @ SV28 @ SV85 @ SV75 ) @ SY629 ) )
| ( ( sK19_SY614 @ SV75 @ SV85 @ SV28 @ SV55 )
= SY629 ) ) )
= $false )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[535]) ).
thf(580,plain,
! [SV56: $i,SV29: $i,SV86: $i,SV76: $i,SV2: $i] :
( ( ( ~ ( ~ ( apply @ SV2 @ SV76 @ SV86 )
| ( apply @ ( inverse_function @ SV2 @ SV29 @ SV56 ) @ SV86 @ SV76 ) )
| ~ ( ~ ( apply @ ( inverse_function @ SV2 @ SV29 @ SV56 ) @ SV86 @ SV76 )
| ( apply @ SV2 @ SV76 @ SV86 ) ) )
= $false )
| ( ( member @ SV76 @ SV29 )
= $false )
| ( ( member @ SV86 @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[536]) ).
thf(581,plain,
! [SV30: $i,SV3: $i,SV57: $i,SV77: $i] :
( ( ( member @ SV77 @ SV57 )
= $true )
| ( ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[537]) ).
thf(582,plain,
! [SV57: $i,SV77: $i,SV3: $i,SV30: $i] :
( ( ( ~ ! [SY496: $i] :
~ ~ ( ~ ( member @ SY496 @ SV30 )
| ~ ( apply @ SV3 @ SY496 @ SV77 ) ) )
= $true )
| ( ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[538]) ).
thf(583,plain,
! [SV3: $i,SV30: $i,SV57: $i,SV77: $i] :
( ( ( member @ SV77 @ SV57 )
= $false )
| ( ( ~ ~ ! [SY497: $i] :
~ ~ ( ~ ( member @ SY497 @ SV30 )
| ~ ( apply @ SV3 @ SY497 @ SV77 ) ) )
= $true )
| ( ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(584,plain,
! [SV58: $i,SV98: $i,SV4: $i,SV31: $i] :
( ( ( ! [SY602: $i] :
~ ~ ( ~ ( member @ SY602 @ SV31 )
| ~ ( apply @ SV4 @ SY602 @ SV98 ) ) )
= $false )
| ( ( member @ SV98 @ SV58 )
= $false )
| ( ( surjective @ SV4 @ SV31 @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(585,plain,
! [SV58: $i,SV4: $i,SV31: $i,SV111: $i] :
( ( ( ~ ~ ( ~ ( member @ SV111 @ SV31 )
| ~ ( apply @ SV4 @ SV111 @ ( sK7_SY411 @ SV4 @ SV31 @ SV58 ) ) ) )
= $true )
| ( ( surjective @ SV4 @ SV31 @ SV58 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(586,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV78: $i,SV112: $i,SV33: $i,SV106: $i] :
( ( ( ! [SY630: $i,SY631: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV106 @ SV33 )
| ~ ( member @ SV112 @ SV78 ) )
| ~ ( member @ SY630 @ SV33 ) )
| ~ ( member @ SY631 @ SV78 ) )
| ~ ( apply @ SV59 @ SV106 @ SY630 ) )
| ~ ( apply @ SV6 @ SV106 @ SV112 ) )
| ~ ( apply @ SV6 @ SY630 @ SY631 ) )
| ( apply @ SV87 @ SY631 @ SV112 ) ) )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(587,plain,
! [SV33: $i,SV78: $i,SV59: $i,SV6: $i,SV87: $i] :
( ( ( ! [SY632: $i,SY633: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ SV33 )
| ~ ( member @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
| ~ ( member @ SY632 @ SV33 ) )
| ~ ( member @ SY633 @ SV78 ) )
| ~ ( apply @ SV59 @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ SY632 ) )
| ~ ( apply @ SV6 @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) ) )
| ~ ( apply @ SV6 @ SY632 @ SY633 ) )
| ( apply @ SV87 @ SY633 @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) ) ) )
= $false )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[544]) ).
thf(588,plain,
! [SV88: $i,SV60: $i,SV79: $i,SV34: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( maps @ SV7 @ SV34 @ SV79 )
| ~ ( one_to_one @ SV7 @ SV34 @ SV79 ) ) )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[545]) ).
thf(589,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV79: $i,SV34: $i] :
( ( ( ~ ! [SY560: $i,SY561: $i,SY562: $i,SY563: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY560 @ SV34 )
| ~ ( member @ SY561 @ SV79 ) )
| ~ ( member @ SY562 @ SV34 ) )
| ~ ( member @ SY563 @ SV79 ) )
| ~ ( apply @ SV7 @ SY560 @ SY561 ) )
| ~ ( apply @ SV7 @ SY562 @ SY563 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ SY560 @ SY562 )
| ( apply @ SV88 @ SY561 @ SY563 ) )
| ~ ( ~ ( apply @ SV88 @ SY561 @ SY563 )
| ( apply @ SV60 @ SY560 @ SY562 ) ) ) ) )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[545]) ).
thf(590,plain,
! [SV88: $i,SV60: $i,SV79: $i,SV34: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( maps @ SV7 @ SV34 @ SV79 )
| ~ ( one_to_one @ SV7 @ SV34 @ SV79 ) ) )
= $true )
| ( ( ~ ! [SY564: $i,SY565: $i,SY566: $i,SY567: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY564 @ SV34 )
| ~ ( member @ SY565 @ SV79 ) )
| ~ ( member @ SY566 @ SV34 ) )
| ~ ( member @ SY567 @ SV79 ) )
| ~ ( apply @ SV7 @ SY564 @ SY565 ) )
| ~ ( apply @ SV7 @ SY566 @ SY567 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ SY564 @ SY566 )
| ( apply @ SV88 @ SY565 @ SY567 ) )
| ~ ( ~ ( apply @ SV88 @ SY565 @ SY567 )
| ( apply @ SV60 @ SY564 @ SY566 ) ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[546]) ).
thf(591,plain,
! [SV61: $i,SV35: $i,SV8: $i] :
( ( ( member @ SV8 @ SV35 )
= $false )
| ( ( member @ SV8 @ ( difference @ SV61 @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(592,plain,
! [SV61: $i,SV35: $i,SV8: $i] :
( ( ( ~ ( member @ SV8 @ SV35 ) )
= $false )
| ( ( member @ SV8 @ SV61 )
= $false )
| ( ( member @ SV8 @ ( difference @ SV61 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(593,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV80: $i,SV113: $i,SV36: $i,SV107: $i] :
( ( ( ! [SY634: $i,SY635: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV107 @ SV36 )
| ~ ( member @ SV113 @ SV80 ) )
| ~ ( member @ SY634 @ SV36 ) )
| ~ ( member @ SY635 @ SV80 ) )
| ~ ( apply @ SV62 @ SV107 @ SY634 ) )
| ~ ( apply @ SV9 @ SV107 @ SV113 ) )
| ~ ( apply @ SV9 @ SY634 @ SY635 ) )
| ( apply @ SV89 @ SV113 @ SY635 ) ) )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(594,plain,
! [SV36: $i,SV80: $i,SV62: $i,SV9: $i,SV89: $i] :
( ( ( ! [SY636: $i,SY637: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ SV36 )
| ~ ( member @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
| ~ ( member @ SY636 @ SV36 ) )
| ~ ( member @ SY637 @ SV80 ) )
| ~ ( apply @ SV62 @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ SY636 ) )
| ~ ( apply @ SV9 @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) ) )
| ~ ( apply @ SV9 @ SY636 @ SY637 ) )
| ( apply @ SV89 @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SY637 ) ) )
= $false )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[551]) ).
thf(595,plain,
! [SV38: $i,SV11: $i] :
( ( ( ~ ( member @ ( sK8_SY333 @ SV11 @ SV38 ) @ SV38 ) )
= $false )
| ( ( member @ SV11 @ ( sum @ SV38 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[552]) ).
thf(596,plain,
! [SV38: $i,SV11: $i] :
( ( ( ~ ( member @ SV11 @ ( sK8_SY333 @ SV11 @ SV38 ) ) )
= $false )
| ( ( member @ SV11 @ ( sum @ SV38 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[552]) ).
thf(597,plain,
! [SV11: $i,SV38: $i,SV99: $i] :
( ( ( ~ ( member @ SV99 @ SV38 ) )
= $true )
| ( ( ~ ( member @ SV11 @ SV99 ) )
= $true )
| ( ( member @ SV11 @ ( sum @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[553]) ).
thf(598,plain,
! [SV64: $i,SV40: $i,SV13: $i] :
( ( ( surjective @ SV13 @ SV40 @ SV64 )
= $false )
| ( ( injective @ SV13 @ SV40 @ SV64 )
= $false )
| ( ( one_to_one @ SV13 @ SV40 @ SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[556]) ).
thf(599,plain,
! [SV41: $i,SV14: $i,SV65: $i] :
( ( ( ~ ( member @ ( sK10_SY443 @ SV65 @ SV14 @ SV41 ) @ SV41 )
| ~ ( apply @ SV14 @ ( sK10_SY443 @ SV65 @ SV14 @ SV41 ) @ SV65 ) )
= $false )
| ( ( member @ SV65 @ ( image2 @ SV14 @ SV41 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[557]) ).
thf(600,plain,
! [SV65: $i,SV14: $i,SV41: $i,SV101: $i] :
( ( ( ~ ( member @ SV101 @ SV41 )
| ~ ( apply @ SV14 @ SV101 @ SV65 ) )
= $true )
| ( ( member @ SV65 @ ( image2 @ SV14 @ SV41 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[558]) ).
thf(601,plain,
! [SV43: $i,SV16: $i,SV66: $i,SV81: $i] :
( ( ( member @ SV81 @ SV66 )
= $true )
| ( ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[560]) ).
thf(602,plain,
! [SV66: $i,SV81: $i,SV16: $i,SV43: $i] :
( ( ( ~ ! [SY525: $i] :
~ ~ ( ~ ( member @ SY525 @ SV43 )
| ~ ( apply @ SV16 @ SV81 @ SY525 ) ) )
= $true )
| ( ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[561]) ).
thf(603,plain,
! [SV16: $i,SV43: $i,SV66: $i,SV81: $i] :
( ( ( member @ SV81 @ SV66 )
= $false )
| ( ( ~ ~ ! [SY526: $i] :
~ ~ ( ~ ( member @ SY526 @ SV43 )
| ~ ( apply @ SV16 @ SV81 @ SY526 ) ) )
= $true )
| ( ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(604,plain,
! [SV17: $i,SV44: $i,SV82: $i,SV108: $i,SV67: $i,SV102: $i] :
( ( ( ~ ~ ( ~ ( member @ SV102 @ SV67 )
| ~ ( member @ SV108 @ SV82 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV44 @ SV102 @ SV108 )
| ( apply @ SV17 @ SV108 @ SV102 ) )
| ~ ( ~ ( apply @ SV17 @ SV108 @ SV102 )
| ( apply @ SV44 @ SV102 @ SV108 ) ) ) )
= $true )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[563]) ).
thf(605,plain,
! [SV67: $i,SV82: $i,SV44: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ SV67 )
| ~ ( member @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) @ SV82 ) ) )
= $false )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[564]) ).
thf(606,plain,
! [SV67: $i,SV82: $i,SV17: $i,SV44: $i] :
( ( ( ~ ( ~ ( ~ ( apply @ SV44 @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) )
| ( apply @ SV17 @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) ) )
| ~ ( ~ ( apply @ SV17 @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) )
| ( apply @ SV44 @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) ) ) ) )
= $false )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[564]) ).
thf(607,plain,
! [SV21: $i,SV69: $i,SV48: $i,SV114: $i] :
( ( ( ~ ( member @ SV114 @ SV48 )
| ~ ! [SY638: $i] :
~ ~ ( ~ ( member @ SY638 @ SV69 )
| ~ ( apply @ SV21 @ SV114 @ SY638 ) ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(608,plain,
! [SV21: $i,SV69: $i,SV48: $i,SV115: $i] :
( ( ( ! [SY639: $i,SY640: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SV115 @ SV48 )
| ~ ( member @ SY639 @ SV69 ) )
| ~ ( member @ SY640 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SV115 @ SY639 )
| ~ ( apply @ SV21 @ SV115 @ SY640 ) )
| ( SY639 = SY640 ) ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(609,plain,
! [SV48: $i,SV69: $i,SV21: $i] :
( ( ( ~ ( member @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV48 )
| ~ ! [SY641: $i] :
~ ~ ( ~ ( member @ SY641 @ SV69 )
| ~ ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SY641 ) ) )
= $false )
| ( ( ~ ! [SY460: $i,SY461: $i,SY462: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY460 @ SV48 )
| ~ ( member @ SY461 @ SV69 ) )
| ~ ( member @ SY462 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY460 @ SY461 )
| ~ ( apply @ SV21 @ SY460 @ SY462 ) )
| ( SY461 = SY462 ) ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[567]) ).
thf(610,plain,
! [SV50: $i,SV70: $i,SV90: $i,SV23: $i,SV92: $i,SV83: $i,SV116: $i] :
( ( ( ! [SY642: $i] :
( ~ ~ ( ~ ( member @ SV116 @ SV83 )
| ~ ( member @ SY642 @ SV92 ) )
| ~ ( ~ ( ~ ( apply @ SV23 @ SV116 @ SY642 )
| ~ ! [SY643: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY643 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SY643 ) )
| ~ ( apply @ SV50 @ SY643 @ SY642 ) ) )
| ~ ( ~ ~ ! [SY644: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY644 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SY644 ) )
| ~ ( apply @ SV50 @ SY644 @ SY642 ) )
| ( apply @ SV23 @ SV116 @ SY642 ) ) ) ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(611,plain,
! [SV83: $i,SV92: $i,SV23: $i,SV90: $i,SV70: $i,SV50: $i] :
( ( ( ! [SY645: $i] :
( ~ ~ ( ~ ( member @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV83 )
| ~ ( member @ SY645 @ SV92 ) )
| ~ ( ~ ( ~ ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY645 )
| ~ ! [SY646: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY646 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY646 ) )
| ~ ( apply @ SV50 @ SY646 @ SY645 ) ) )
| ~ ( ~ ~ ! [SY647: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY647 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY647 ) )
| ~ ( apply @ SV50 @ SY647 @ SY645 ) )
| ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY645 ) ) ) ) )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[569]) ).
thf(612,plain,
! [SV51: $i,SV71: $i,SV24: $i] :
( ( ( member @ SV24 @ SV71 )
= $false )
| ( ( member @ SV24 @ SV51 )
= $false )
| ( ( member @ SV24 @ ( intersection @ SV51 @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[572]) ).
thf(613,plain,
! [SV84: $i,SV52: $i,SV25: $i,SV91: $i,SV94: $i,SV72: $i,SV93: $i] :
( ( ( member @ SV93 @ SV72 )
= $false )
| ( ( ~ ( member @ SV94 @ SV91 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
| ~ ! [SY600: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY600 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SY600 ) )
| ~ ( apply @ SV25 @ SY600 @ SV94 ) ) )
| ~ ( ~ ~ ! [SY601: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY601 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SY601 ) )
| ~ ( apply @ SV25 @ SY601 @ SV94 ) )
| ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[573]) ).
thf(614,plain,
! [SV53: $i,SV26: $i,SV73: $i] :
( ( ( ~ ( member @ ( sK12_SY480 @ SV73 @ SV26 @ SV53 ) @ SV53 )
| ~ ( apply @ SV26 @ SV73 @ ( sK12_SY480 @ SV73 @ SV26 @ SV53 ) ) )
= $false )
| ( ( member @ SV73 @ ( inverse_image2 @ SV26 @ SV53 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[574]) ).
thf(615,plain,
! [SV73: $i,SV26: $i,SV53: $i,SV103: $i] :
( ( ( ~ ( member @ SV103 @ SV53 )
| ~ ( apply @ SV26 @ SV73 @ SV103 ) )
= $true )
| ( ( member @ SV73 @ ( inverse_image2 @ SV26 @ SV53 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[575]) ).
thf(616,plain,
! [SV27: $i,SV74: $i,SV109: $i,SV104: $i,SV54: $i,SV100: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV100 @ SV54 )
| ~ ( member @ SV104 @ SV54 ) )
| ~ ( member @ SV109 @ SV74 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV27 @ SV100 @ SV109 )
| ~ ( apply @ SV27 @ SV104 @ SV109 ) )
| ( SV100 = SV104 ) )
= $true )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[576]) ).
thf(617,plain,
! [SV54: $i,SV74: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK9_SY485 @ SV27 @ SV74 @ SV54 ) @ SV54 )
| ~ ( member @ ( sK13_SY606 @ SV54 @ SV74 @ SV27 ) @ SV54 ) )
| ~ ( member @ ( sK18_SY611 @ SV54 @ SV74 @ SV27 ) @ SV74 ) ) )
= $false )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[577]) ).
thf(618,plain,
! [SV54: $i,SV74: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV27 @ ( sK9_SY485 @ SV27 @ SV74 @ SV54 ) @ ( sK18_SY611 @ SV54 @ SV74 @ SV27 ) )
| ~ ( apply @ SV27 @ ( sK13_SY606 @ SV54 @ SV74 @ SV27 ) @ ( sK18_SY611 @ SV54 @ SV74 @ SV27 ) ) )
| ( ( sK9_SY485 @ SV27 @ SV74 @ SV54 )
= ( sK13_SY606 @ SV54 @ SV74 @ SV27 ) ) )
= $false )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[577]) ).
thf(619,plain,
! [SV55: $i,SV28: $i,SV117: $i,SV85: $i,SV110: $i,SV75: $i,SV105: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV105 @ SV75 )
| ~ ( member @ SV110 @ SV85 ) )
| ~ ( member @ SV117 @ SV85 ) )
| ~ ~ ( ~ ( apply @ SV28 @ SV105 @ SV110 )
| ~ ( apply @ SV55 @ SV105 @ SV117 ) )
| ( SV110 = SV117 ) )
= $true )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(620,plain,
! [SV75: $i,SV85: $i,SV28: $i,SV55: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK14_SY549 @ SV55 @ SV28 @ SV85 @ SV75 ) @ SV75 )
| ~ ( member @ ( sK19_SY614 @ SV75 @ SV85 @ SV28 @ SV55 ) @ SV85 ) )
| ~ ( member @ ( sK24_SY629 @ SV75 @ SV85 @ SV28 @ SV55 ) @ SV85 ) )
| ~ ~ ( ~ ( apply @ SV28 @ ( sK14_SY549 @ SV55 @ SV28 @ SV85 @ SV75 ) @ ( sK19_SY614 @ SV75 @ SV85 @ SV28 @ SV55 ) )
| ~ ( apply @ SV55 @ ( sK14_SY549 @ SV55 @ SV28 @ SV85 @ SV75 ) @ ( sK24_SY629 @ SV75 @ SV85 @ SV28 @ SV55 ) ) )
| ( ( sK19_SY614 @ SV75 @ SV85 @ SV28 @ SV55 )
= ( sK24_SY629 @ SV75 @ SV85 @ SV28 @ SV55 ) ) )
= $false )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[579]) ).
thf(621,plain,
! [SV56: $i,SV29: $i,SV86: $i,SV76: $i,SV2: $i] :
( ( ( ~ ( ~ ( apply @ SV2 @ SV76 @ SV86 )
| ( apply @ ( inverse_function @ SV2 @ SV29 @ SV56 ) @ SV86 @ SV76 ) ) )
= $false )
| ( ( member @ SV76 @ SV29 )
= $false )
| ( ( member @ SV86 @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[580]) ).
thf(622,plain,
! [SV76: $i,SV86: $i,SV56: $i,SV29: $i,SV2: $i] :
( ( ( ~ ( ~ ( apply @ ( inverse_function @ SV2 @ SV29 @ SV56 ) @ SV86 @ SV76 )
| ( apply @ SV2 @ SV76 @ SV86 ) ) )
= $false )
| ( ( member @ SV76 @ SV29 )
= $false )
| ( ( member @ SV86 @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[580]) ).
thf(623,plain,
! [SV57: $i,SV77: $i,SV3: $i,SV30: $i] :
( ( ( ! [SY496: $i] :
~ ~ ( ~ ( member @ SY496 @ SV30 )
| ~ ( apply @ SV3 @ SY496 @ SV77 ) ) )
= $false )
| ( ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[582]) ).
thf(624,plain,
! [SV57: $i,SV77: $i,SV3: $i,SV30: $i] :
( ( ( ~ ! [SY497: $i] :
~ ~ ( ~ ( member @ SY497 @ SV30 )
| ~ ( apply @ SV3 @ SY497 @ SV77 ) ) )
= $false )
| ( ( member @ SV77 @ SV57 )
= $false )
| ( ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[583]) ).
thf(625,plain,
! [SV31: $i,SV4: $i,SV98: $i,SV58: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK25_SY602 @ SV58 @ SV98 @ SV4 @ SV31 ) @ SV31 )
| ~ ( apply @ SV4 @ ( sK25_SY602 @ SV58 @ SV98 @ SV4 @ SV31 ) @ SV98 ) ) )
= $false )
| ( ( member @ SV98 @ SV58 )
= $false )
| ( ( surjective @ SV4 @ SV31 @ SV58 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[584]) ).
thf(626,plain,
! [SV58: $i,SV4: $i,SV31: $i,SV111: $i] :
( ( ( ~ ( ~ ( member @ SV111 @ SV31 )
| ~ ( apply @ SV4 @ SV111 @ ( sK7_SY411 @ SV4 @ SV31 @ SV58 ) ) ) )
= $false )
| ( ( surjective @ SV4 @ SV31 @ SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(627,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV118: $i,SV78: $i,SV112: $i,SV33: $i,SV106: $i] :
( ( ( ! [SY648: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV106 @ SV33 )
| ~ ( member @ SV112 @ SV78 ) )
| ~ ( member @ SV118 @ SV33 ) )
| ~ ( member @ SY648 @ SV78 ) )
| ~ ( apply @ SV59 @ SV106 @ SV118 ) )
| ~ ( apply @ SV6 @ SV106 @ SV112 ) )
| ~ ( apply @ SV6 @ SV118 @ SY648 ) )
| ( apply @ SV87 @ SY648 @ SV112 ) ) )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(628,plain,
! [SV33: $i,SV78: $i,SV59: $i,SV6: $i,SV87: $i] :
( ( ( ! [SY649: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ SV33 )
| ~ ( member @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
| ~ ( member @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV33 ) )
| ~ ( member @ SY649 @ SV78 ) )
| ~ ( apply @ SV59 @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) ) )
| ~ ( apply @ SV6 @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) ) )
| ~ ( apply @ SV6 @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SY649 ) )
| ( apply @ SV87 @ SY649 @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) ) ) )
= $false )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[587]) ).
thf(629,plain,
! [SV88: $i,SV60: $i,SV79: $i,SV34: $i,SV7: $i] :
( ( ( ~ ( ~ ( maps @ SV7 @ SV34 @ SV79 )
| ~ ( one_to_one @ SV7 @ SV34 @ SV79 ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[588]) ).
thf(630,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV79: $i,SV34: $i] :
( ( ( ! [SY560: $i,SY561: $i,SY562: $i,SY563: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY560 @ SV34 )
| ~ ( member @ SY561 @ SV79 ) )
| ~ ( member @ SY562 @ SV34 ) )
| ~ ( member @ SY563 @ SV79 ) )
| ~ ( apply @ SV7 @ SY560 @ SY561 ) )
| ~ ( apply @ SV7 @ SY562 @ SY563 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ SY560 @ SY562 )
| ( apply @ SV88 @ SY561 @ SY563 ) )
| ~ ( ~ ( apply @ SV88 @ SY561 @ SY563 )
| ( apply @ SV60 @ SY560 @ SY562 ) ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[589]) ).
thf(631,plain,
! [SV88: $i,SV60: $i,SV79: $i,SV34: $i,SV7: $i] :
( ( ( ~ ( ~ ( maps @ SV7 @ SV34 @ SV79 )
| ~ ( one_to_one @ SV7 @ SV34 @ SV79 ) ) )
= $false )
| ( ( ~ ! [SY564: $i,SY565: $i,SY566: $i,SY567: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY564 @ SV34 )
| ~ ( member @ SY565 @ SV79 ) )
| ~ ( member @ SY566 @ SV34 ) )
| ~ ( member @ SY567 @ SV79 ) )
| ~ ( apply @ SV7 @ SY564 @ SY565 ) )
| ~ ( apply @ SV7 @ SY566 @ SY567 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ SY564 @ SY566 )
| ( apply @ SV88 @ SY565 @ SY567 ) )
| ~ ( ~ ( apply @ SV88 @ SY565 @ SY567 )
| ( apply @ SV60 @ SY564 @ SY566 ) ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[590]) ).
thf(632,plain,
! [SV61: $i,SV35: $i,SV8: $i] :
( ( ( member @ SV8 @ SV35 )
= $true )
| ( ( member @ SV8 @ SV61 )
= $false )
| ( ( member @ SV8 @ ( difference @ SV61 @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[592]) ).
thf(633,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV119: $i,SV80: $i,SV113: $i,SV36: $i,SV107: $i] :
( ( ( ! [SY650: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV107 @ SV36 )
| ~ ( member @ SV113 @ SV80 ) )
| ~ ( member @ SV119 @ SV36 ) )
| ~ ( member @ SY650 @ SV80 ) )
| ~ ( apply @ SV62 @ SV107 @ SV119 ) )
| ~ ( apply @ SV9 @ SV107 @ SV113 ) )
| ~ ( apply @ SV9 @ SV119 @ SY650 ) )
| ( apply @ SV89 @ SV113 @ SY650 ) ) )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(634,plain,
! [SV36: $i,SV80: $i,SV62: $i,SV9: $i,SV89: $i] :
( ( ( ! [SY651: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ SV36 )
| ~ ( member @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
| ~ ( member @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV36 ) )
| ~ ( member @ SY651 @ SV80 ) )
| ~ ( apply @ SV62 @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) ) )
| ~ ( apply @ SV9 @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) ) )
| ~ ( apply @ SV9 @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SY651 ) )
| ( apply @ SV89 @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SY651 ) ) )
= $false )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[594]) ).
thf(635,plain,
! [SV38: $i,SV11: $i] :
( ( ( member @ ( sK8_SY333 @ SV11 @ SV38 ) @ SV38 )
= $true )
| ( ( member @ SV11 @ ( sum @ SV38 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[595]) ).
thf(636,plain,
! [SV38: $i,SV11: $i] :
( ( ( member @ SV11 @ ( sK8_SY333 @ SV11 @ SV38 ) )
= $true )
| ( ( member @ SV11 @ ( sum @ SV38 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[596]) ).
thf(637,plain,
! [SV11: $i,SV38: $i,SV99: $i] :
( ( ( member @ SV99 @ SV38 )
= $false )
| ( ( ~ ( member @ SV11 @ SV99 ) )
= $true )
| ( ( member @ SV11 @ ( sum @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[597]) ).
thf(638,plain,
! [SV41: $i,SV14: $i,SV65: $i] :
( ( ( ~ ( member @ ( sK10_SY443 @ SV65 @ SV14 @ SV41 ) @ SV41 ) )
= $false )
| ( ( member @ SV65 @ ( image2 @ SV14 @ SV41 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[599]) ).
thf(639,plain,
! [SV41: $i,SV65: $i,SV14: $i] :
( ( ( ~ ( apply @ SV14 @ ( sK10_SY443 @ SV65 @ SV14 @ SV41 ) @ SV65 ) )
= $false )
| ( ( member @ SV65 @ ( image2 @ SV14 @ SV41 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[599]) ).
thf(640,plain,
! [SV65: $i,SV14: $i,SV41: $i,SV101: $i] :
( ( ( ~ ( member @ SV101 @ SV41 ) )
= $true )
| ( ( ~ ( apply @ SV14 @ SV101 @ SV65 ) )
= $true )
| ( ( member @ SV65 @ ( image2 @ SV14 @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[600]) ).
thf(641,plain,
! [SV66: $i,SV81: $i,SV16: $i,SV43: $i] :
( ( ( ! [SY525: $i] :
~ ~ ( ~ ( member @ SY525 @ SV43 )
| ~ ( apply @ SV16 @ SV81 @ SY525 ) ) )
= $false )
| ( ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[602]) ).
thf(642,plain,
! [SV66: $i,SV81: $i,SV16: $i,SV43: $i] :
( ( ( ~ ! [SY526: $i] :
~ ~ ( ~ ( member @ SY526 @ SV43 )
| ~ ( apply @ SV16 @ SV81 @ SY526 ) ) )
= $false )
| ( ( member @ SV81 @ SV66 )
= $false )
| ( ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[603]) ).
thf(643,plain,
! [SV17: $i,SV44: $i,SV82: $i,SV108: $i,SV67: $i,SV102: $i] :
( ( ( ~ ( ~ ( member @ SV102 @ SV67 )
| ~ ( member @ SV108 @ SV82 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( apply @ SV44 @ SV102 @ SV108 )
| ( apply @ SV17 @ SV108 @ SV102 ) )
| ~ ( ~ ( apply @ SV17 @ SV108 @ SV102 )
| ( apply @ SV44 @ SV102 @ SV108 ) ) ) )
= $true )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(644,plain,
! [SV67: $i,SV82: $i,SV44: $i,SV17: $i] :
( ( ( ~ ( ~ ( member @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ SV67 )
| ~ ( member @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) @ SV82 ) ) )
= $true )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[605]) ).
thf(645,plain,
! [SV67: $i,SV82: $i,SV17: $i,SV44: $i] :
( ( ( ~ ( ~ ( apply @ SV44 @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) )
| ( apply @ SV17 @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) ) )
| ~ ( ~ ( apply @ SV17 @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) )
| ( apply @ SV44 @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) ) ) )
= $true )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[606]) ).
thf(646,plain,
! [SV21: $i,SV69: $i,SV48: $i,SV114: $i] :
( ( ( ~ ( member @ SV114 @ SV48 ) )
= $true )
| ( ( ~ ! [SY638: $i] :
~ ~ ( ~ ( member @ SY638 @ SV69 )
| ~ ( apply @ SV21 @ SV114 @ SY638 ) ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[607]) ).
thf(647,plain,
! [SV21: $i,SV69: $i,SV120: $i,SV48: $i,SV115: $i] :
( ( ( ! [SY652: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SV115 @ SV48 )
| ~ ( member @ SV120 @ SV69 ) )
| ~ ( member @ SY652 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SV115 @ SV120 )
| ~ ( apply @ SV21 @ SV115 @ SY652 ) )
| ( SV120 = SY652 ) ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(648,plain,
! [SV48: $i,SV69: $i,SV21: $i] :
( ( ( ~ ( member @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV48 ) )
= $false )
| ( ( ~ ! [SY460: $i,SY461: $i,SY462: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY460 @ SV48 )
| ~ ( member @ SY461 @ SV69 ) )
| ~ ( member @ SY462 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY460 @ SY461 )
| ~ ( apply @ SV21 @ SY460 @ SY462 ) )
| ( SY461 = SY462 ) ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[609]) ).
thf(649,plain,
! [SV48: $i,SV21: $i,SV69: $i] :
( ( ( ~ ! [SY641: $i] :
~ ~ ( ~ ( member @ SY641 @ SV69 )
| ~ ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SY641 ) ) )
= $false )
| ( ( ~ ! [SY460: $i,SY461: $i,SY462: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY460 @ SV48 )
| ~ ( member @ SY461 @ SV69 ) )
| ~ ( member @ SY462 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY460 @ SY461 )
| ~ ( apply @ SV21 @ SY460 @ SY462 ) )
| ( SY461 = SY462 ) ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[609]) ).
thf(650,plain,
! [SV50: $i,SV70: $i,SV90: $i,SV23: $i,SV92: $i,SV121: $i,SV83: $i,SV116: $i] :
( ( ( ~ ~ ( ~ ( member @ SV116 @ SV83 )
| ~ ( member @ SV121 @ SV92 ) )
| ~ ( ~ ( ~ ( apply @ SV23 @ SV116 @ SV121 )
| ~ ! [SY653: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY653 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SY653 ) )
| ~ ( apply @ SV50 @ SY653 @ SV121 ) ) )
| ~ ( ~ ~ ! [SY654: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY654 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SY654 ) )
| ~ ( apply @ SV50 @ SY654 @ SV121 ) )
| ( apply @ SV23 @ SV116 @ SV121 ) ) ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(651,plain,
! [SV83: $i,SV92: $i,SV23: $i,SV90: $i,SV70: $i,SV50: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV83 )
| ~ ( member @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) @ SV92 ) )
| ~ ( ~ ( ~ ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
| ~ ! [SY655: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY655 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY655 ) )
| ~ ( apply @ SV50 @ SY655 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
| ~ ( ~ ~ ! [SY656: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY656 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY656 ) )
| ~ ( apply @ SV50 @ SY656 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
| ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) ) )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[611]) ).
thf(652,plain,
! [SV84: $i,SV52: $i,SV25: $i,SV72: $i,SV93: $i,SV91: $i,SV94: $i] :
( ( ( member @ SV94 @ SV91 )
= $false )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( ~ ( ~ ( ~ ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
| ~ ! [SY600: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY600 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SY600 ) )
| ~ ( apply @ SV25 @ SY600 @ SV94 ) ) )
| ~ ( ~ ~ ! [SY601: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY601 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SY601 ) )
| ~ ( apply @ SV25 @ SY601 @ SV94 ) )
| ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[613]) ).
thf(653,plain,
! [SV53: $i,SV26: $i,SV73: $i] :
( ( ( ~ ( member @ ( sK12_SY480 @ SV73 @ SV26 @ SV53 ) @ SV53 ) )
= $false )
| ( ( member @ SV73 @ ( inverse_image2 @ SV26 @ SV53 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[614]) ).
thf(654,plain,
! [SV53: $i,SV73: $i,SV26: $i] :
( ( ( ~ ( apply @ SV26 @ SV73 @ ( sK12_SY480 @ SV73 @ SV26 @ SV53 ) ) )
= $false )
| ( ( member @ SV73 @ ( inverse_image2 @ SV26 @ SV53 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[614]) ).
thf(655,plain,
! [SV73: $i,SV26: $i,SV53: $i,SV103: $i] :
( ( ( ~ ( member @ SV103 @ SV53 ) )
= $true )
| ( ( ~ ( apply @ SV26 @ SV73 @ SV103 ) )
= $true )
| ( ( member @ SV73 @ ( inverse_image2 @ SV26 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[615]) ).
thf(656,plain,
! [SV27: $i,SV74: $i,SV109: $i,SV104: $i,SV54: $i,SV100: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ SV100 @ SV54 )
| ~ ( member @ SV104 @ SV54 ) )
| ~ ( member @ SV109 @ SV74 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( apply @ SV27 @ SV100 @ SV109 )
| ~ ( apply @ SV27 @ SV104 @ SV109 ) )
| ( SV100 = SV104 ) )
= $true )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[616]) ).
thf(657,plain,
! [SV54: $i,SV74: $i,SV27: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK9_SY485 @ SV27 @ SV74 @ SV54 ) @ SV54 )
| ~ ( member @ ( sK13_SY606 @ SV54 @ SV74 @ SV27 ) @ SV54 ) )
| ~ ( member @ ( sK18_SY611 @ SV54 @ SV74 @ SV27 ) @ SV74 ) ) )
= $true )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[617]) ).
thf(658,plain,
! [SV54: $i,SV74: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV27 @ ( sK9_SY485 @ SV27 @ SV74 @ SV54 ) @ ( sK18_SY611 @ SV54 @ SV74 @ SV27 ) )
| ~ ( apply @ SV27 @ ( sK13_SY606 @ SV54 @ SV74 @ SV27 ) @ ( sK18_SY611 @ SV54 @ SV74 @ SV27 ) ) ) )
= $false )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[618]) ).
thf(659,plain,
! [SV54: $i,SV74: $i,SV27: $i] :
( ( ( ( sK9_SY485 @ SV27 @ SV74 @ SV54 )
= ( sK13_SY606 @ SV54 @ SV74 @ SV27 ) )
= $false )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[618]) ).
thf(660,plain,
! [SV55: $i,SV28: $i,SV117: $i,SV85: $i,SV110: $i,SV75: $i,SV105: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV105 @ SV75 )
| ~ ( member @ SV110 @ SV85 ) )
| ~ ( member @ SV117 @ SV85 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV28 @ SV105 @ SV110 )
| ~ ( apply @ SV55 @ SV105 @ SV117 ) )
| ( SV110 = SV117 ) )
= $true )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[619]) ).
thf(661,plain,
! [SV75: $i,SV85: $i,SV28: $i,SV55: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK14_SY549 @ SV55 @ SV28 @ SV85 @ SV75 ) @ SV75 )
| ~ ( member @ ( sK19_SY614 @ SV75 @ SV85 @ SV28 @ SV55 ) @ SV85 ) )
| ~ ( member @ ( sK24_SY629 @ SV75 @ SV85 @ SV28 @ SV55 ) @ SV85 ) ) )
= $false )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[620]) ).
thf(662,plain,
! [SV75: $i,SV85: $i,SV55: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV28 @ ( sK14_SY549 @ SV55 @ SV28 @ SV85 @ SV75 ) @ ( sK19_SY614 @ SV75 @ SV85 @ SV28 @ SV55 ) )
| ~ ( apply @ SV55 @ ( sK14_SY549 @ SV55 @ SV28 @ SV85 @ SV75 ) @ ( sK24_SY629 @ SV75 @ SV85 @ SV28 @ SV55 ) ) )
| ( ( sK19_SY614 @ SV75 @ SV85 @ SV28 @ SV55 )
= ( sK24_SY629 @ SV75 @ SV85 @ SV28 @ SV55 ) ) )
= $false )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[620]) ).
thf(663,plain,
! [SV56: $i,SV29: $i,SV86: $i,SV76: $i,SV2: $i] :
( ( ( ~ ( apply @ SV2 @ SV76 @ SV86 )
| ( apply @ ( inverse_function @ SV2 @ SV29 @ SV56 ) @ SV86 @ SV76 ) )
= $true )
| ( ( member @ SV76 @ SV29 )
= $false )
| ( ( member @ SV86 @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[621]) ).
thf(664,plain,
! [SV76: $i,SV86: $i,SV56: $i,SV29: $i,SV2: $i] :
( ( ( ~ ( apply @ ( inverse_function @ SV2 @ SV29 @ SV56 ) @ SV86 @ SV76 )
| ( apply @ SV2 @ SV76 @ SV86 ) )
= $true )
| ( ( member @ SV76 @ SV29 )
= $false )
| ( ( member @ SV86 @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[622]) ).
thf(665,plain,
! [SV30: $i,SV3: $i,SV77: $i,SV57: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK29_SY496 @ SV57 @ SV77 @ SV3 @ SV30 ) @ SV30 )
| ~ ( apply @ SV3 @ ( sK29_SY496 @ SV57 @ SV77 @ SV3 @ SV30 ) @ SV77 ) ) )
= $false )
| ( ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[623]) ).
thf(666,plain,
! [SV57: $i,SV77: $i,SV3: $i,SV30: $i] :
( ( ( ! [SY497: $i] :
~ ~ ( ~ ( member @ SY497 @ SV30 )
| ~ ( apply @ SV3 @ SY497 @ SV77 ) ) )
= $true )
| ( ( member @ SV77 @ SV57 )
= $false )
| ( ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[624]) ).
thf(667,plain,
! [SV31: $i,SV4: $i,SV98: $i,SV58: $i] :
( ( ( ~ ( ~ ( member @ ( sK25_SY602 @ SV58 @ SV98 @ SV4 @ SV31 ) @ SV31 )
| ~ ( apply @ SV4 @ ( sK25_SY602 @ SV58 @ SV98 @ SV4 @ SV31 ) @ SV98 ) ) )
= $true )
| ( ( member @ SV98 @ SV58 )
= $false )
| ( ( surjective @ SV4 @ SV31 @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[625]) ).
thf(668,plain,
! [SV58: $i,SV4: $i,SV31: $i,SV111: $i] :
( ( ( ~ ( member @ SV111 @ SV31 )
| ~ ( apply @ SV4 @ SV111 @ ( sK7_SY411 @ SV4 @ SV31 @ SV58 ) ) )
= $true )
| ( ( surjective @ SV4 @ SV31 @ SV58 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[626]) ).
thf(669,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV122: $i,SV118: $i,SV78: $i,SV112: $i,SV33: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV106 @ SV33 )
| ~ ( member @ SV112 @ SV78 ) )
| ~ ( member @ SV118 @ SV33 ) )
| ~ ( member @ SV122 @ SV78 ) )
| ~ ( apply @ SV59 @ SV106 @ SV118 ) )
| ~ ( apply @ SV6 @ SV106 @ SV112 ) )
| ~ ( apply @ SV6 @ SV118 @ SV122 ) )
| ( apply @ SV87 @ SV122 @ SV112 ) )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(670,plain,
! [SV33: $i,SV78: $i,SV59: $i,SV6: $i,SV87: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ SV33 )
| ~ ( member @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
| ~ ( member @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV33 ) )
| ~ ( member @ ( sK30_SY649 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
| ~ ( apply @ SV59 @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) ) )
| ~ ( apply @ SV6 @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) ) )
| ~ ( apply @ SV6 @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ ( sK30_SY649 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) ) )
| ( apply @ SV87 @ ( sK30_SY649 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) ) )
= $false )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[628]) ).
thf(671,plain,
! [SV88: $i,SV60: $i,SV79: $i,SV34: $i,SV7: $i] :
( ( ( ~ ( maps @ SV7 @ SV34 @ SV79 )
| ~ ( one_to_one @ SV7 @ SV34 @ SV79 ) )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[629]) ).
thf(672,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV79: $i,SV34: $i,SV123: $i] :
( ( ( ! [SY657: $i,SY658: $i,SY659: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV123 @ SV34 )
| ~ ( member @ SY657 @ SV79 ) )
| ~ ( member @ SY658 @ SV34 ) )
| ~ ( member @ SY659 @ SV79 ) )
| ~ ( apply @ SV7 @ SV123 @ SY657 ) )
| ~ ( apply @ SV7 @ SY658 @ SY659 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ SV123 @ SY658 )
| ( apply @ SV88 @ SY657 @ SY659 ) )
| ~ ( ~ ( apply @ SV88 @ SY657 @ SY659 )
| ( apply @ SV60 @ SV123 @ SY658 ) ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(673,plain,
! [SV88: $i,SV60: $i,SV79: $i,SV34: $i,SV7: $i] :
( ( ( ~ ( maps @ SV7 @ SV34 @ SV79 )
| ~ ( one_to_one @ SV7 @ SV34 @ SV79 ) )
= $true )
| ( ( ~ ! [SY564: $i,SY565: $i,SY566: $i,SY567: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY564 @ SV34 )
| ~ ( member @ SY565 @ SV79 ) )
| ~ ( member @ SY566 @ SV34 ) )
| ~ ( member @ SY567 @ SV79 ) )
| ~ ( apply @ SV7 @ SY564 @ SY565 ) )
| ~ ( apply @ SV7 @ SY566 @ SY567 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ SY564 @ SY566 )
| ( apply @ SV88 @ SY565 @ SY567 ) )
| ~ ( ~ ( apply @ SV88 @ SY565 @ SY567 )
| ( apply @ SV60 @ SY564 @ SY566 ) ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[631]) ).
thf(674,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV124: $i,SV119: $i,SV80: $i,SV113: $i,SV36: $i,SV107: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV107 @ SV36 )
| ~ ( member @ SV113 @ SV80 ) )
| ~ ( member @ SV119 @ SV36 ) )
| ~ ( member @ SV124 @ SV80 ) )
| ~ ( apply @ SV62 @ SV107 @ SV119 ) )
| ~ ( apply @ SV9 @ SV107 @ SV113 ) )
| ~ ( apply @ SV9 @ SV119 @ SV124 ) )
| ( apply @ SV89 @ SV113 @ SV124 ) )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(675,plain,
! [SV36: $i,SV80: $i,SV62: $i,SV9: $i,SV89: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ SV36 )
| ~ ( member @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
| ~ ( member @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV36 ) )
| ~ ( member @ ( sK31_SY651 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
| ~ ( apply @ SV62 @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) ) )
| ~ ( apply @ SV9 @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) ) )
| ~ ( apply @ SV9 @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ ( sK31_SY651 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) ) )
| ( apply @ SV89 @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ ( sK31_SY651 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) ) )
= $false )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[634]) ).
thf(676,plain,
! [SV38: $i,SV99: $i,SV11: $i] :
( ( ( member @ SV11 @ SV99 )
= $false )
| ( ( member @ SV99 @ SV38 )
= $false )
| ( ( member @ SV11 @ ( sum @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[637]) ).
thf(677,plain,
! [SV41: $i,SV14: $i,SV65: $i] :
( ( ( member @ ( sK10_SY443 @ SV65 @ SV14 @ SV41 ) @ SV41 )
= $true )
| ( ( member @ SV65 @ ( image2 @ SV14 @ SV41 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[638]) ).
thf(678,plain,
! [SV41: $i,SV65: $i,SV14: $i] :
( ( ( apply @ SV14 @ ( sK10_SY443 @ SV65 @ SV14 @ SV41 ) @ SV65 )
= $true )
| ( ( member @ SV65 @ ( image2 @ SV14 @ SV41 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[639]) ).
thf(679,plain,
! [SV65: $i,SV14: $i,SV41: $i,SV101: $i] :
( ( ( member @ SV101 @ SV41 )
= $false )
| ( ( ~ ( apply @ SV14 @ SV101 @ SV65 ) )
= $true )
| ( ( member @ SV65 @ ( image2 @ SV14 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[640]) ).
thf(680,plain,
! [SV43: $i,SV16: $i,SV81: $i,SV66: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK32_SY525 @ SV66 @ SV81 @ SV16 @ SV43 ) @ SV43 )
| ~ ( apply @ SV16 @ SV81 @ ( sK32_SY525 @ SV66 @ SV81 @ SV16 @ SV43 ) ) ) )
= $false )
| ( ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[641]) ).
thf(681,plain,
! [SV66: $i,SV81: $i,SV16: $i,SV43: $i] :
( ( ( ! [SY526: $i] :
~ ~ ( ~ ( member @ SY526 @ SV43 )
| ~ ( apply @ SV16 @ SV81 @ SY526 ) ) )
= $true )
| ( ( member @ SV81 @ SV66 )
= $false )
| ( ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[642]) ).
thf(682,plain,
! [SV17: $i,SV44: $i,SV82: $i,SV108: $i,SV67: $i,SV102: $i] :
( ( ( ~ ( member @ SV102 @ SV67 )
| ~ ( member @ SV108 @ SV82 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV44 @ SV102 @ SV108 )
| ( apply @ SV17 @ SV108 @ SV102 ) )
| ~ ( ~ ( apply @ SV17 @ SV108 @ SV102 )
| ( apply @ SV44 @ SV102 @ SV108 ) ) ) )
= $true )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[643]) ).
thf(683,plain,
! [SV67: $i,SV82: $i,SV44: $i,SV17: $i] :
( ( ( ~ ( member @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ SV67 )
| ~ ( member @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) @ SV82 ) )
= $false )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[644]) ).
thf(684,plain,
! [SV67: $i,SV82: $i,SV17: $i,SV44: $i] :
( ( ( ~ ( ~ ( apply @ SV44 @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) )
| ( apply @ SV17 @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) ) ) )
= $true )
| ( ( ~ ( ~ ( apply @ SV17 @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) )
| ( apply @ SV44 @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) ) ) )
= $true )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[645]) ).
thf(685,plain,
! [SV21: $i,SV69: $i,SV48: $i,SV114: $i] :
( ( ( member @ SV114 @ SV48 )
= $false )
| ( ( ~ ! [SY638: $i] :
~ ~ ( ~ ( member @ SY638 @ SV69 )
| ~ ( apply @ SV21 @ SV114 @ SY638 ) ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[646]) ).
thf(686,plain,
! [SV21: $i,SV125: $i,SV69: $i,SV120: $i,SV48: $i,SV115: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV115 @ SV48 )
| ~ ( member @ SV120 @ SV69 ) )
| ~ ( member @ SV125 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SV115 @ SV120 )
| ~ ( apply @ SV21 @ SV115 @ SV125 ) )
| ( SV120 = SV125 ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(687,plain,
! [SV48: $i,SV69: $i,SV21: $i] :
( ( ( member @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV48 )
= $true )
| ( ( ~ ! [SY460: $i,SY461: $i,SY462: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY460 @ SV48 )
| ~ ( member @ SY461 @ SV69 ) )
| ~ ( member @ SY462 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY460 @ SY461 )
| ~ ( apply @ SV21 @ SY460 @ SY462 ) )
| ( SY461 = SY462 ) ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[648]) ).
thf(688,plain,
! [SV48: $i,SV21: $i,SV69: $i] :
( ( ( ! [SY641: $i] :
~ ~ ( ~ ( member @ SY641 @ SV69 )
| ~ ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SY641 ) ) )
= $true )
| ( ( ~ ! [SY460: $i,SY461: $i,SY462: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY460 @ SV48 )
| ~ ( member @ SY461 @ SV69 ) )
| ~ ( member @ SY462 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY460 @ SY461 )
| ~ ( apply @ SV21 @ SY460 @ SY462 ) )
| ( SY461 = SY462 ) ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[649]) ).
thf(689,plain,
! [SV50: $i,SV70: $i,SV90: $i,SV23: $i,SV92: $i,SV121: $i,SV83: $i,SV116: $i] :
( ( ( ~ ~ ( ~ ( member @ SV116 @ SV83 )
| ~ ( member @ SV121 @ SV92 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV23 @ SV116 @ SV121 )
| ~ ! [SY653: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY653 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SY653 ) )
| ~ ( apply @ SV50 @ SY653 @ SV121 ) ) )
| ~ ( ~ ~ ! [SY654: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY654 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SY654 ) )
| ~ ( apply @ SV50 @ SY654 @ SV121 ) )
| ( apply @ SV23 @ SV116 @ SV121 ) ) ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[650]) ).
thf(690,plain,
! [SV83: $i,SV92: $i,SV23: $i,SV90: $i,SV70: $i,SV50: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV83 )
| ~ ( member @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) @ SV92 ) ) )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[651]) ).
thf(691,plain,
! [SV83: $i,SV92: $i,SV90: $i,SV70: $i,SV50: $i,SV23: $i] :
( ( ( ~ ( ~ ( ~ ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
| ~ ! [SY655: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY655 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY655 ) )
| ~ ( apply @ SV50 @ SY655 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
| ~ ( ~ ~ ! [SY656: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY656 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY656 ) )
| ~ ( apply @ SV50 @ SY656 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
| ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) ) )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[651]) ).
thf(692,plain,
! [SV94: $i,SV93: $i,SV91: $i,SV84: $i,SV72: $i,SV52: $i,SV25: $i] :
( ( ( ~ ( ~ ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
| ~ ! [SY600: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY600 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SY600 ) )
| ~ ( apply @ SV25 @ SY600 @ SV94 ) ) )
| ~ ( ~ ~ ! [SY601: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY601 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SY601 ) )
| ~ ( apply @ SV25 @ SY601 @ SV94 ) )
| ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 ) ) )
= $false )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(693,plain,
! [SV53: $i,SV26: $i,SV73: $i] :
( ( ( member @ ( sK12_SY480 @ SV73 @ SV26 @ SV53 ) @ SV53 )
= $true )
| ( ( member @ SV73 @ ( inverse_image2 @ SV26 @ SV53 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[653]) ).
thf(694,plain,
! [SV53: $i,SV73: $i,SV26: $i] :
( ( ( apply @ SV26 @ SV73 @ ( sK12_SY480 @ SV73 @ SV26 @ SV53 ) )
= $true )
| ( ( member @ SV73 @ ( inverse_image2 @ SV26 @ SV53 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[654]) ).
thf(695,plain,
! [SV73: $i,SV26: $i,SV53: $i,SV103: $i] :
( ( ( member @ SV103 @ SV53 )
= $false )
| ( ( ~ ( apply @ SV26 @ SV73 @ SV103 ) )
= $true )
| ( ( member @ SV73 @ ( inverse_image2 @ SV26 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[655]) ).
thf(696,plain,
! [SV27: $i,SV74: $i,SV109: $i,SV104: $i,SV54: $i,SV100: $i] :
( ( ( ~ ~ ( ~ ( member @ SV100 @ SV54 )
| ~ ( member @ SV104 @ SV54 ) )
| ~ ( member @ SV109 @ SV74 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV27 @ SV100 @ SV109 )
| ~ ( apply @ SV27 @ SV104 @ SV109 ) )
| ( SV100 = SV104 ) )
= $true )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[656]) ).
thf(697,plain,
! [SV54: $i,SV74: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK9_SY485 @ SV27 @ SV74 @ SV54 ) @ SV54 )
| ~ ( member @ ( sK13_SY606 @ SV54 @ SV74 @ SV27 ) @ SV54 ) )
| ~ ( member @ ( sK18_SY611 @ SV54 @ SV74 @ SV27 ) @ SV74 ) )
= $false )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[657]) ).
thf(698,plain,
! [SV54: $i,SV74: $i,SV27: $i] :
( ( ( ~ ( ~ ( apply @ SV27 @ ( sK9_SY485 @ SV27 @ SV74 @ SV54 ) @ ( sK18_SY611 @ SV54 @ SV74 @ SV27 ) )
| ~ ( apply @ SV27 @ ( sK13_SY606 @ SV54 @ SV74 @ SV27 ) @ ( sK18_SY611 @ SV54 @ SV74 @ SV27 ) ) ) )
= $true )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[658]) ).
thf(699,plain,
! [SV55: $i,SV28: $i,SV117: $i,SV85: $i,SV110: $i,SV75: $i,SV105: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ SV105 @ SV75 )
| ~ ( member @ SV110 @ SV85 ) )
| ~ ( member @ SV117 @ SV85 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( apply @ SV28 @ SV105 @ SV110 )
| ~ ( apply @ SV55 @ SV105 @ SV117 ) )
| ( SV110 = SV117 ) )
= $true )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[660]) ).
thf(700,plain,
! [SV75: $i,SV85: $i,SV28: $i,SV55: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK14_SY549 @ SV55 @ SV28 @ SV85 @ SV75 ) @ SV75 )
| ~ ( member @ ( sK19_SY614 @ SV75 @ SV85 @ SV28 @ SV55 ) @ SV85 ) )
| ~ ( member @ ( sK24_SY629 @ SV75 @ SV85 @ SV28 @ SV55 ) @ SV85 ) ) )
= $true )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[661]) ).
thf(701,plain,
! [SV75: $i,SV85: $i,SV55: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV28 @ ( sK14_SY549 @ SV55 @ SV28 @ SV85 @ SV75 ) @ ( sK19_SY614 @ SV75 @ SV85 @ SV28 @ SV55 ) )
| ~ ( apply @ SV55 @ ( sK14_SY549 @ SV55 @ SV28 @ SV85 @ SV75 ) @ ( sK24_SY629 @ SV75 @ SV85 @ SV28 @ SV55 ) ) ) )
= $false )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[662]) ).
thf(702,plain,
! [SV55: $i,SV28: $i,SV85: $i,SV75: $i] :
( ( ( ( sK19_SY614 @ SV75 @ SV85 @ SV28 @ SV55 )
= ( sK24_SY629 @ SV75 @ SV85 @ SV28 @ SV55 ) )
= $false )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[662]) ).
thf(703,plain,
! [SV56: $i,SV29: $i,SV86: $i,SV76: $i,SV2: $i] :
( ( ( ~ ( apply @ SV2 @ SV76 @ SV86 ) )
= $true )
| ( ( apply @ ( inverse_function @ SV2 @ SV29 @ SV56 ) @ SV86 @ SV76 )
= $true )
| ( ( member @ SV76 @ SV29 )
= $false )
| ( ( member @ SV86 @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[663]) ).
thf(704,plain,
! [SV76: $i,SV86: $i,SV56: $i,SV29: $i,SV2: $i] :
( ( ( ~ ( apply @ ( inverse_function @ SV2 @ SV29 @ SV56 ) @ SV86 @ SV76 ) )
= $true )
| ( ( apply @ SV2 @ SV76 @ SV86 )
= $true )
| ( ( member @ SV76 @ SV29 )
= $false )
| ( ( member @ SV86 @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[664]) ).
thf(705,plain,
! [SV30: $i,SV3: $i,SV77: $i,SV57: $i] :
( ( ( ~ ( ~ ( member @ ( sK29_SY496 @ SV57 @ SV77 @ SV3 @ SV30 ) @ SV30 )
| ~ ( apply @ SV3 @ ( sK29_SY496 @ SV57 @ SV77 @ SV3 @ SV30 ) @ SV77 ) ) )
= $true )
| ( ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[665]) ).
thf(706,plain,
! [SV57: $i,SV77: $i,SV3: $i,SV30: $i,SV126: $i] :
( ( ( ~ ~ ( ~ ( member @ SV126 @ SV30 )
| ~ ( apply @ SV3 @ SV126 @ SV77 ) ) )
= $true )
| ( ( member @ SV77 @ SV57 )
= $false )
| ( ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(707,plain,
! [SV31: $i,SV4: $i,SV98: $i,SV58: $i] :
( ( ( ~ ( member @ ( sK25_SY602 @ SV58 @ SV98 @ SV4 @ SV31 ) @ SV31 )
| ~ ( apply @ SV4 @ ( sK25_SY602 @ SV58 @ SV98 @ SV4 @ SV31 ) @ SV98 ) )
= $false )
| ( ( member @ SV98 @ SV58 )
= $false )
| ( ( surjective @ SV4 @ SV31 @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[667]) ).
thf(708,plain,
! [SV58: $i,SV4: $i,SV31: $i,SV111: $i] :
( ( ( ~ ( member @ SV111 @ SV31 ) )
= $true )
| ( ( ~ ( apply @ SV4 @ SV111 @ ( sK7_SY411 @ SV4 @ SV31 @ SV58 ) ) )
= $true )
| ( ( surjective @ SV4 @ SV31 @ SV58 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[668]) ).
thf(709,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV122: $i,SV118: $i,SV78: $i,SV112: $i,SV33: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV106 @ SV33 )
| ~ ( member @ SV112 @ SV78 ) )
| ~ ( member @ SV118 @ SV33 ) )
| ~ ( member @ SV122 @ SV78 ) )
| ~ ( apply @ SV59 @ SV106 @ SV118 ) )
| ~ ( apply @ SV6 @ SV106 @ SV112 ) )
| ~ ( apply @ SV6 @ SV118 @ SV122 ) ) )
= $true )
| ( ( apply @ SV87 @ SV122 @ SV112 )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[669]) ).
thf(710,plain,
! [SV33: $i,SV78: $i,SV59: $i,SV6: $i,SV87: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ SV33 )
| ~ ( member @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
| ~ ( member @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV33 ) )
| ~ ( member @ ( sK30_SY649 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
| ~ ( apply @ SV59 @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) ) )
| ~ ( apply @ SV6 @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) ) )
| ~ ( apply @ SV6 @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ ( sK30_SY649 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) ) ) )
= $false )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[670]) ).
thf(711,plain,
! [SV6: $i,SV59: $i,SV78: $i,SV33: $i,SV87: $i] :
( ( ( apply @ SV87 @ ( sK30_SY649 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) )
= $false )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[670]) ).
thf(712,plain,
! [SV88: $i,SV60: $i,SV79: $i,SV34: $i,SV7: $i] :
( ( ( ~ ( maps @ SV7 @ SV34 @ SV79 ) )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[671]) ).
thf(713,plain,
! [SV88: $i,SV60: $i,SV79: $i,SV34: $i,SV7: $i] :
( ( ( ~ ( one_to_one @ SV7 @ SV34 @ SV79 ) )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[671]) ).
thf(714,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV79: $i,SV127: $i,SV34: $i,SV123: $i] :
( ( ( ! [SY660: $i,SY661: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV123 @ SV34 )
| ~ ( member @ SV127 @ SV79 ) )
| ~ ( member @ SY660 @ SV34 ) )
| ~ ( member @ SY661 @ SV79 ) )
| ~ ( apply @ SV7 @ SV123 @ SV127 ) )
| ~ ( apply @ SV7 @ SY660 @ SY661 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ SV123 @ SY660 )
| ( apply @ SV88 @ SV127 @ SY661 ) )
| ~ ( ~ ( apply @ SV88 @ SV127 @ SY661 )
| ( apply @ SV60 @ SV123 @ SY660 ) ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(715,plain,
! [SV88: $i,SV60: $i,SV79: $i,SV34: $i,SV7: $i] :
( ( ( ~ ( maps @ SV7 @ SV34 @ SV79 ) )
= $true )
| ( ( ~ ( one_to_one @ SV7 @ SV34 @ SV79 ) )
= $true )
| ( ( ~ ! [SY564: $i,SY565: $i,SY566: $i,SY567: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY564 @ SV34 )
| ~ ( member @ SY565 @ SV79 ) )
| ~ ( member @ SY566 @ SV34 ) )
| ~ ( member @ SY567 @ SV79 ) )
| ~ ( apply @ SV7 @ SY564 @ SY565 ) )
| ~ ( apply @ SV7 @ SY566 @ SY567 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ SY564 @ SY566 )
| ( apply @ SV88 @ SY565 @ SY567 ) )
| ~ ( ~ ( apply @ SV88 @ SY565 @ SY567 )
| ( apply @ SV60 @ SY564 @ SY566 ) ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[673]) ).
thf(716,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV124: $i,SV119: $i,SV80: $i,SV113: $i,SV36: $i,SV107: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV107 @ SV36 )
| ~ ( member @ SV113 @ SV80 ) )
| ~ ( member @ SV119 @ SV36 ) )
| ~ ( member @ SV124 @ SV80 ) )
| ~ ( apply @ SV62 @ SV107 @ SV119 ) )
| ~ ( apply @ SV9 @ SV107 @ SV113 ) )
| ~ ( apply @ SV9 @ SV119 @ SV124 ) ) )
= $true )
| ( ( apply @ SV89 @ SV113 @ SV124 )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[674]) ).
thf(717,plain,
! [SV36: $i,SV80: $i,SV62: $i,SV9: $i,SV89: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ SV36 )
| ~ ( member @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
| ~ ( member @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV36 ) )
| ~ ( member @ ( sK31_SY651 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
| ~ ( apply @ SV62 @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) ) )
| ~ ( apply @ SV9 @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) ) )
| ~ ( apply @ SV9 @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ ( sK31_SY651 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) ) ) )
= $false )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[675]) ).
thf(718,plain,
! [SV9: $i,SV62: $i,SV80: $i,SV36: $i,SV89: $i] :
( ( ( apply @ SV89 @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ ( sK31_SY651 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) )
= $false )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[675]) ).
thf(719,plain,
! [SV41: $i,SV65: $i,SV101: $i,SV14: $i] :
( ( ( apply @ SV14 @ SV101 @ SV65 )
= $false )
| ( ( member @ SV101 @ SV41 )
= $false )
| ( ( member @ SV65 @ ( image2 @ SV14 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[679]) ).
thf(720,plain,
! [SV43: $i,SV16: $i,SV81: $i,SV66: $i] :
( ( ( ~ ( ~ ( member @ ( sK32_SY525 @ SV66 @ SV81 @ SV16 @ SV43 ) @ SV43 )
| ~ ( apply @ SV16 @ SV81 @ ( sK32_SY525 @ SV66 @ SV81 @ SV16 @ SV43 ) ) ) )
= $true )
| ( ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[680]) ).
thf(721,plain,
! [SV66: $i,SV81: $i,SV16: $i,SV43: $i,SV128: $i] :
( ( ( ~ ~ ( ~ ( member @ SV128 @ SV43 )
| ~ ( apply @ SV16 @ SV81 @ SV128 ) ) )
= $true )
| ( ( member @ SV81 @ SV66 )
= $false )
| ( ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(722,plain,
! [SV17: $i,SV44: $i,SV82: $i,SV108: $i,SV67: $i,SV102: $i] :
( ( ( ~ ( member @ SV102 @ SV67 ) )
= $true )
| ( ( ~ ( member @ SV108 @ SV82 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV44 @ SV102 @ SV108 )
| ( apply @ SV17 @ SV108 @ SV102 ) )
| ~ ( ~ ( apply @ SV17 @ SV108 @ SV102 )
| ( apply @ SV44 @ SV102 @ SV108 ) ) ) )
= $true )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[682]) ).
thf(723,plain,
! [SV67: $i,SV82: $i,SV44: $i,SV17: $i] :
( ( ( ~ ( member @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ SV67 ) )
= $false )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[683]) ).
thf(724,plain,
! [SV17: $i,SV44: $i,SV82: $i,SV67: $i] :
( ( ( ~ ( member @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) @ SV82 ) )
= $false )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[683]) ).
thf(725,plain,
! [SV67: $i,SV82: $i,SV17: $i,SV44: $i] :
( ( ( ~ ( apply @ SV44 @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) )
| ( apply @ SV17 @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) ) )
= $false )
| ( ( ~ ( ~ ( apply @ SV17 @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) )
| ( apply @ SV44 @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) ) ) )
= $true )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[684]) ).
thf(726,plain,
! [SV48: $i,SV114: $i,SV21: $i,SV69: $i] :
( ( ( ! [SY638: $i] :
~ ~ ( ~ ( member @ SY638 @ SV69 )
| ~ ( apply @ SV21 @ SV114 @ SY638 ) ) )
= $false )
| ( ( member @ SV114 @ SV48 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[685]) ).
thf(727,plain,
! [SV21: $i,SV125: $i,SV69: $i,SV120: $i,SV48: $i,SV115: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV115 @ SV48 )
| ~ ( member @ SV120 @ SV69 ) )
| ~ ( member @ SV125 @ SV69 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV21 @ SV115 @ SV120 )
| ~ ( apply @ SV21 @ SV115 @ SV125 ) )
| ( SV120 = SV125 ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[686]) ).
thf(728,plain,
! [SV21: $i,SV69: $i,SV48: $i] :
( ( ( ! [SY460: $i,SY461: $i,SY462: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY460 @ SV48 )
| ~ ( member @ SY461 @ SV69 ) )
| ~ ( member @ SY462 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY460 @ SY461 )
| ~ ( apply @ SV21 @ SY460 @ SY462 ) )
| ( SY461 = SY462 ) ) )
= $false )
| ( ( member @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV48 )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[687]) ).
thf(729,plain,
! [SV48: $i,SV21: $i,SV69: $i,SV129: $i] :
( ( ( ~ ~ ( ~ ( member @ SV129 @ SV69 )
| ~ ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV129 ) ) )
= $true )
| ( ( ~ ! [SY460: $i,SY461: $i,SY462: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY460 @ SV48 )
| ~ ( member @ SY461 @ SV69 ) )
| ~ ( member @ SY462 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY460 @ SY461 )
| ~ ( apply @ SV21 @ SY460 @ SY462 ) )
| ( SY461 = SY462 ) ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(730,plain,
! [SV50: $i,SV70: $i,SV90: $i,SV23: $i,SV92: $i,SV121: $i,SV83: $i,SV116: $i] :
( ( ( ~ ( ~ ( member @ SV116 @ SV83 )
| ~ ( member @ SV121 @ SV92 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( apply @ SV23 @ SV116 @ SV121 )
| ~ ! [SY653: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY653 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SY653 ) )
| ~ ( apply @ SV50 @ SY653 @ SV121 ) ) )
| ~ ( ~ ~ ! [SY654: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY654 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SY654 ) )
| ~ ( apply @ SV50 @ SY654 @ SV121 ) )
| ( apply @ SV23 @ SV116 @ SV121 ) ) ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[689]) ).
thf(731,plain,
! [SV83: $i,SV92: $i,SV23: $i,SV90: $i,SV70: $i,SV50: $i] :
( ( ( ~ ( ~ ( member @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV83 )
| ~ ( member @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) @ SV92 ) ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[690]) ).
thf(732,plain,
! [SV83: $i,SV92: $i,SV90: $i,SV70: $i,SV50: $i,SV23: $i] :
( ( ( ~ ( ~ ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
| ~ ! [SY655: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY655 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY655 ) )
| ~ ( apply @ SV50 @ SY655 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
| ~ ( ~ ~ ! [SY656: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY656 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY656 ) )
| ~ ( apply @ SV50 @ SY656 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
| ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[691]) ).
thf(733,plain,
! [SV94: $i,SV93: $i,SV91: $i,SV84: $i,SV72: $i,SV52: $i,SV25: $i] :
( ( ( ~ ( ~ ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
| ~ ! [SY600: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY600 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SY600 ) )
| ~ ( apply @ SV25 @ SY600 @ SV94 ) ) ) )
= $false )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[692]) ).
thf(734,plain,
! [SV91: $i,SV72: $i,SV94: $i,SV25: $i,SV93: $i,SV52: $i,SV84: $i] :
( ( ( ~ ( ~ ~ ! [SY601: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY601 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SY601 ) )
| ~ ( apply @ SV25 @ SY601 @ SV94 ) )
| ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 ) ) )
= $false )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[692]) ).
thf(735,plain,
! [SV53: $i,SV103: $i,SV73: $i,SV26: $i] :
( ( ( apply @ SV26 @ SV73 @ SV103 )
= $false )
| ( ( member @ SV103 @ SV53 )
= $false )
| ( ( member @ SV73 @ ( inverse_image2 @ SV26 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[695]) ).
thf(736,plain,
! [SV27: $i,SV74: $i,SV109: $i,SV104: $i,SV54: $i,SV100: $i] :
( ( ( ~ ~ ( ~ ( member @ SV100 @ SV54 )
| ~ ( member @ SV104 @ SV54 ) ) )
= $true )
| ( ( ~ ( member @ SV109 @ SV74 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV27 @ SV100 @ SV109 )
| ~ ( apply @ SV27 @ SV104 @ SV109 ) )
| ( SV100 = SV104 ) )
= $true )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[696]) ).
thf(737,plain,
! [SV54: $i,SV74: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK9_SY485 @ SV27 @ SV74 @ SV54 ) @ SV54 )
| ~ ( member @ ( sK13_SY606 @ SV54 @ SV74 @ SV27 ) @ SV54 ) ) )
= $false )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[697]) ).
thf(738,plain,
! [SV27: $i,SV74: $i,SV54: $i] :
( ( ( ~ ( member @ ( sK18_SY611 @ SV54 @ SV74 @ SV27 ) @ SV74 ) )
= $false )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[697]) ).
thf(739,plain,
! [SV54: $i,SV74: $i,SV27: $i] :
( ( ( ~ ( apply @ SV27 @ ( sK9_SY485 @ SV27 @ SV74 @ SV54 ) @ ( sK18_SY611 @ SV54 @ SV74 @ SV27 ) )
| ~ ( apply @ SV27 @ ( sK13_SY606 @ SV54 @ SV74 @ SV27 ) @ ( sK18_SY611 @ SV54 @ SV74 @ SV27 ) ) )
= $false )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[698]) ).
thf(740,plain,
! [SV55: $i,SV28: $i,SV117: $i,SV85: $i,SV110: $i,SV75: $i,SV105: $i] :
( ( ( ~ ~ ( ~ ( member @ SV105 @ SV75 )
| ~ ( member @ SV110 @ SV85 ) )
| ~ ( member @ SV117 @ SV85 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV28 @ SV105 @ SV110 )
| ~ ( apply @ SV55 @ SV105 @ SV117 ) )
| ( SV110 = SV117 ) )
= $true )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[699]) ).
thf(741,plain,
! [SV75: $i,SV85: $i,SV28: $i,SV55: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK14_SY549 @ SV55 @ SV28 @ SV85 @ SV75 ) @ SV75 )
| ~ ( member @ ( sK19_SY614 @ SV75 @ SV85 @ SV28 @ SV55 ) @ SV85 ) )
| ~ ( member @ ( sK24_SY629 @ SV75 @ SV85 @ SV28 @ SV55 ) @ SV85 ) )
= $false )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[700]) ).
thf(742,plain,
! [SV75: $i,SV85: $i,SV55: $i,SV28: $i] :
( ( ( ~ ( ~ ( apply @ SV28 @ ( sK14_SY549 @ SV55 @ SV28 @ SV85 @ SV75 ) @ ( sK19_SY614 @ SV75 @ SV85 @ SV28 @ SV55 ) )
| ~ ( apply @ SV55 @ ( sK14_SY549 @ SV55 @ SV28 @ SV85 @ SV75 ) @ ( sK24_SY629 @ SV75 @ SV85 @ SV28 @ SV55 ) ) ) )
= $true )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[701]) ).
thf(743,plain,
! [SV56: $i,SV29: $i,SV86: $i,SV76: $i,SV2: $i] :
( ( ( apply @ SV2 @ SV76 @ SV86 )
= $false )
| ( ( apply @ ( inverse_function @ SV2 @ SV29 @ SV56 ) @ SV86 @ SV76 )
= $true )
| ( ( member @ SV76 @ SV29 )
= $false )
| ( ( member @ SV86 @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[703]) ).
thf(744,plain,
! [SV76: $i,SV86: $i,SV56: $i,SV29: $i,SV2: $i] :
( ( ( apply @ ( inverse_function @ SV2 @ SV29 @ SV56 ) @ SV86 @ SV76 )
= $false )
| ( ( apply @ SV2 @ SV76 @ SV86 )
= $true )
| ( ( member @ SV76 @ SV29 )
= $false )
| ( ( member @ SV86 @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[704]) ).
thf(745,plain,
! [SV30: $i,SV3: $i,SV77: $i,SV57: $i] :
( ( ( ~ ( member @ ( sK29_SY496 @ SV57 @ SV77 @ SV3 @ SV30 ) @ SV30 )
| ~ ( apply @ SV3 @ ( sK29_SY496 @ SV57 @ SV77 @ SV3 @ SV30 ) @ SV77 ) )
= $false )
| ( ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[705]) ).
thf(746,plain,
! [SV57: $i,SV77: $i,SV3: $i,SV30: $i,SV126: $i] :
( ( ( ~ ( ~ ( member @ SV126 @ SV30 )
| ~ ( apply @ SV3 @ SV126 @ SV77 ) ) )
= $false )
| ( ( member @ SV77 @ SV57 )
= $false )
| ( ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[706]) ).
thf(747,plain,
! [SV31: $i,SV4: $i,SV98: $i,SV58: $i] :
( ( ( ~ ( member @ ( sK25_SY602 @ SV58 @ SV98 @ SV4 @ SV31 ) @ SV31 ) )
= $false )
| ( ( member @ SV98 @ SV58 )
= $false )
| ( ( surjective @ SV4 @ SV31 @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[707]) ).
thf(748,plain,
! [SV31: $i,SV98: $i,SV58: $i,SV4: $i] :
( ( ( ~ ( apply @ SV4 @ ( sK25_SY602 @ SV58 @ SV98 @ SV4 @ SV31 ) @ SV98 ) )
= $false )
| ( ( member @ SV98 @ SV58 )
= $false )
| ( ( surjective @ SV4 @ SV31 @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[707]) ).
thf(749,plain,
! [SV58: $i,SV4: $i,SV31: $i,SV111: $i] :
( ( ( member @ SV111 @ SV31 )
= $false )
| ( ( ~ ( apply @ SV4 @ SV111 @ ( sK7_SY411 @ SV4 @ SV31 @ SV58 ) ) )
= $true )
| ( ( surjective @ SV4 @ SV31 @ SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[708]) ).
thf(750,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV122: $i,SV118: $i,SV78: $i,SV112: $i,SV33: $i,SV106: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV106 @ SV33 )
| ~ ( member @ SV112 @ SV78 ) )
| ~ ( member @ SV118 @ SV33 ) )
| ~ ( member @ SV122 @ SV78 ) )
| ~ ( apply @ SV59 @ SV106 @ SV118 ) )
| ~ ( apply @ SV6 @ SV106 @ SV112 ) )
| ~ ( apply @ SV6 @ SV118 @ SV122 ) ) )
= $false )
| ( ( apply @ SV87 @ SV122 @ SV112 )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[709]) ).
thf(751,plain,
! [SV33: $i,SV78: $i,SV59: $i,SV6: $i,SV87: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ SV33 )
| ~ ( member @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
| ~ ( member @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV33 ) )
| ~ ( member @ ( sK30_SY649 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
| ~ ( apply @ SV59 @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) ) )
| ~ ( apply @ SV6 @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) ) )
| ~ ( apply @ SV6 @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ ( sK30_SY649 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) ) ) )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[710]) ).
thf(752,plain,
! [SV88: $i,SV60: $i,SV79: $i,SV34: $i,SV7: $i] :
( ( ( maps @ SV7 @ SV34 @ SV79 )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[712]) ).
thf(753,plain,
! [SV88: $i,SV60: $i,SV79: $i,SV34: $i,SV7: $i] :
( ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[713]) ).
thf(754,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV130: $i,SV79: $i,SV127: $i,SV34: $i,SV123: $i] :
( ( ( ! [SY662: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV123 @ SV34 )
| ~ ( member @ SV127 @ SV79 ) )
| ~ ( member @ SV130 @ SV34 ) )
| ~ ( member @ SY662 @ SV79 ) )
| ~ ( apply @ SV7 @ SV123 @ SV127 ) )
| ~ ( apply @ SV7 @ SV130 @ SY662 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ SV123 @ SV130 )
| ( apply @ SV88 @ SV127 @ SY662 ) )
| ~ ( ~ ( apply @ SV88 @ SV127 @ SY662 )
| ( apply @ SV60 @ SV123 @ SV130 ) ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(755,plain,
! [SV88: $i,SV60: $i,SV79: $i,SV34: $i,SV7: $i] :
( ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( ~ ( one_to_one @ SV7 @ SV34 @ SV79 ) )
= $true )
| ( ( ~ ! [SY564: $i,SY565: $i,SY566: $i,SY567: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY564 @ SV34 )
| ~ ( member @ SY565 @ SV79 ) )
| ~ ( member @ SY566 @ SV34 ) )
| ~ ( member @ SY567 @ SV79 ) )
| ~ ( apply @ SV7 @ SY564 @ SY565 ) )
| ~ ( apply @ SV7 @ SY566 @ SY567 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ SY564 @ SY566 )
| ( apply @ SV88 @ SY565 @ SY567 ) )
| ~ ( ~ ( apply @ SV88 @ SY565 @ SY567 )
| ( apply @ SV60 @ SY564 @ SY566 ) ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[715]) ).
thf(756,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV124: $i,SV119: $i,SV80: $i,SV113: $i,SV36: $i,SV107: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV107 @ SV36 )
| ~ ( member @ SV113 @ SV80 ) )
| ~ ( member @ SV119 @ SV36 ) )
| ~ ( member @ SV124 @ SV80 ) )
| ~ ( apply @ SV62 @ SV107 @ SV119 ) )
| ~ ( apply @ SV9 @ SV107 @ SV113 ) )
| ~ ( apply @ SV9 @ SV119 @ SV124 ) ) )
= $false )
| ( ( apply @ SV89 @ SV113 @ SV124 )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[716]) ).
thf(757,plain,
! [SV36: $i,SV80: $i,SV62: $i,SV9: $i,SV89: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ SV36 )
| ~ ( member @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
| ~ ( member @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV36 ) )
| ~ ( member @ ( sK31_SY651 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
| ~ ( apply @ SV62 @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) ) )
| ~ ( apply @ SV9 @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) ) )
| ~ ( apply @ SV9 @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ ( sK31_SY651 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) ) ) )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[717]) ).
thf(758,plain,
! [SV43: $i,SV16: $i,SV81: $i,SV66: $i] :
( ( ( ~ ( member @ ( sK32_SY525 @ SV66 @ SV81 @ SV16 @ SV43 ) @ SV43 )
| ~ ( apply @ SV16 @ SV81 @ ( sK32_SY525 @ SV66 @ SV81 @ SV16 @ SV43 ) ) )
= $false )
| ( ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[720]) ).
thf(759,plain,
! [SV66: $i,SV81: $i,SV16: $i,SV43: $i,SV128: $i] :
( ( ( ~ ( ~ ( member @ SV128 @ SV43 )
| ~ ( apply @ SV16 @ SV81 @ SV128 ) ) )
= $false )
| ( ( member @ SV81 @ SV66 )
= $false )
| ( ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[721]) ).
thf(760,plain,
! [SV17: $i,SV44: $i,SV82: $i,SV108: $i,SV67: $i,SV102: $i] :
( ( ( member @ SV102 @ SV67 )
= $false )
| ( ( ~ ( member @ SV108 @ SV82 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV44 @ SV102 @ SV108 )
| ( apply @ SV17 @ SV108 @ SV102 ) )
| ~ ( ~ ( apply @ SV17 @ SV108 @ SV102 )
| ( apply @ SV44 @ SV102 @ SV108 ) ) ) )
= $true )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[722]) ).
thf(761,plain,
! [SV67: $i,SV82: $i,SV44: $i,SV17: $i] :
( ( ( member @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ SV67 )
= $true )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[723]) ).
thf(762,plain,
! [SV17: $i,SV44: $i,SV82: $i,SV67: $i] :
( ( ( member @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) @ SV82 )
= $true )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[724]) ).
thf(763,plain,
! [SV67: $i,SV82: $i,SV17: $i,SV44: $i] :
( ( ( ~ ( apply @ SV44 @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) ) )
= $false )
| ( ( ~ ( ~ ( apply @ SV17 @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) )
| ( apply @ SV44 @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) ) ) )
= $true )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[725]) ).
thf(764,plain,
! [SV44: $i,SV82: $i,SV67: $i,SV17: $i] :
( ( ( apply @ SV17 @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) )
= $false )
| ( ( ~ ( ~ ( apply @ SV17 @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) )
| ( apply @ SV44 @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) ) ) )
= $true )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[725]) ).
thf(765,plain,
! [SV69: $i,SV21: $i,SV114: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK33_SY638 @ SV48 @ SV114 @ SV21 @ SV69 ) @ SV69 )
| ~ ( apply @ SV21 @ SV114 @ ( sK33_SY638 @ SV48 @ SV114 @ SV21 @ SV69 ) ) ) )
= $false )
| ( ( member @ SV114 @ SV48 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[726]) ).
thf(766,plain,
! [SV21: $i,SV125: $i,SV69: $i,SV120: $i,SV48: $i,SV115: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ SV115 @ SV48 )
| ~ ( member @ SV120 @ SV69 ) )
| ~ ( member @ SV125 @ SV69 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( apply @ SV21 @ SV115 @ SV120 )
| ~ ( apply @ SV21 @ SV115 @ SV125 ) )
| ( SV120 = SV125 ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[727]) ).
thf(767,plain,
! [SV48: $i,SV69: $i,SV21: $i] :
( ( ( ! [SY663: $i,SY664: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK34_SY460 @ SV21 @ SV69 @ SV48 ) @ SV48 )
| ~ ( member @ SY663 @ SV69 ) )
| ~ ( member @ SY664 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ ( sK34_SY460 @ SV21 @ SV69 @ SV48 ) @ SY663 )
| ~ ( apply @ SV21 @ ( sK34_SY460 @ SV21 @ SV69 @ SV48 ) @ SY664 ) )
| ( SY663 = SY664 ) ) )
= $false )
| ( ( member @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV48 )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[728]) ).
thf(768,plain,
! [SV48: $i,SV21: $i,SV69: $i,SV129: $i] :
( ( ( ~ ( ~ ( member @ SV129 @ SV69 )
| ~ ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV129 ) ) )
= $false )
| ( ( ~ ! [SY460: $i,SY461: $i,SY462: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY460 @ SV48 )
| ~ ( member @ SY461 @ SV69 ) )
| ~ ( member @ SY462 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY460 @ SY461 )
| ~ ( apply @ SV21 @ SY460 @ SY462 ) )
| ( SY461 = SY462 ) ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[729]) ).
thf(769,plain,
! [SV50: $i,SV70: $i,SV90: $i,SV23: $i,SV92: $i,SV121: $i,SV83: $i,SV116: $i] :
( ( ( ~ ( member @ SV116 @ SV83 )
| ~ ( member @ SV121 @ SV92 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV23 @ SV116 @ SV121 )
| ~ ! [SY653: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY653 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SY653 ) )
| ~ ( apply @ SV50 @ SY653 @ SV121 ) ) )
| ~ ( ~ ~ ! [SY654: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY654 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SY654 ) )
| ~ ( apply @ SV50 @ SY654 @ SV121 ) )
| ( apply @ SV23 @ SV116 @ SV121 ) ) ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[730]) ).
thf(770,plain,
! [SV83: $i,SV92: $i,SV23: $i,SV90: $i,SV70: $i,SV50: $i] :
( ( ( ~ ( member @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV83 )
| ~ ( member @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) @ SV92 ) )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[731]) ).
thf(771,plain,
! [SV83: $i,SV92: $i,SV90: $i,SV70: $i,SV50: $i,SV23: $i] :
( ( ( ~ ( ~ ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
| ~ ! [SY655: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY655 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY655 ) )
| ~ ( apply @ SV50 @ SY655 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY656: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY656 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY656 ) )
| ~ ( apply @ SV50 @ SY656 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
| ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[732]) ).
thf(772,plain,
! [SV94: $i,SV93: $i,SV91: $i,SV84: $i,SV72: $i,SV52: $i,SV25: $i] :
( ( ( ~ ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
| ~ ! [SY600: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY600 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SY600 ) )
| ~ ( apply @ SV25 @ SY600 @ SV94 ) ) )
= $true )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[733]) ).
thf(773,plain,
! [SV91: $i,SV72: $i,SV94: $i,SV25: $i,SV93: $i,SV52: $i,SV84: $i] :
( ( ( ~ ~ ! [SY601: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY601 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SY601 ) )
| ~ ( apply @ SV25 @ SY601 @ SV94 ) )
| ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 ) )
= $true )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[734]) ).
thf(774,plain,
! [SV27: $i,SV74: $i,SV109: $i,SV104: $i,SV54: $i,SV100: $i] :
( ( ( ~ ( ~ ( member @ SV100 @ SV54 )
| ~ ( member @ SV104 @ SV54 ) ) )
= $false )
| ( ( ~ ( member @ SV109 @ SV74 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV27 @ SV100 @ SV109 )
| ~ ( apply @ SV27 @ SV104 @ SV109 ) )
| ( SV100 = SV104 ) )
= $true )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[736]) ).
thf(775,plain,
! [SV54: $i,SV74: $i,SV27: $i] :
( ( ( ~ ( ~ ( member @ ( sK9_SY485 @ SV27 @ SV74 @ SV54 ) @ SV54 )
| ~ ( member @ ( sK13_SY606 @ SV54 @ SV74 @ SV27 ) @ SV54 ) ) )
= $true )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[737]) ).
thf(776,plain,
! [SV27: $i,SV74: $i,SV54: $i] :
( ( ( member @ ( sK18_SY611 @ SV54 @ SV74 @ SV27 ) @ SV74 )
= $true )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[738]) ).
thf(777,plain,
! [SV54: $i,SV74: $i,SV27: $i] :
( ( ( ~ ( apply @ SV27 @ ( sK9_SY485 @ SV27 @ SV74 @ SV54 ) @ ( sK18_SY611 @ SV54 @ SV74 @ SV27 ) ) )
= $false )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[739]) ).
thf(778,plain,
! [SV74: $i,SV54: $i,SV27: $i] :
( ( ( ~ ( apply @ SV27 @ ( sK13_SY606 @ SV54 @ SV74 @ SV27 ) @ ( sK18_SY611 @ SV54 @ SV74 @ SV27 ) ) )
= $false )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[739]) ).
thf(779,plain,
! [SV55: $i,SV28: $i,SV117: $i,SV85: $i,SV110: $i,SV75: $i,SV105: $i] :
( ( ( ~ ~ ( ~ ( member @ SV105 @ SV75 )
| ~ ( member @ SV110 @ SV85 ) ) )
= $true )
| ( ( ~ ( member @ SV117 @ SV85 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV28 @ SV105 @ SV110 )
| ~ ( apply @ SV55 @ SV105 @ SV117 ) )
| ( SV110 = SV117 ) )
= $true )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[740]) ).
thf(780,plain,
! [SV75: $i,SV85: $i,SV28: $i,SV55: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK14_SY549 @ SV55 @ SV28 @ SV85 @ SV75 ) @ SV75 )
| ~ ( member @ ( sK19_SY614 @ SV75 @ SV85 @ SV28 @ SV55 ) @ SV85 ) ) )
= $false )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[741]) ).
thf(781,plain,
! [SV55: $i,SV28: $i,SV85: $i,SV75: $i] :
( ( ( ~ ( member @ ( sK24_SY629 @ SV75 @ SV85 @ SV28 @ SV55 ) @ SV85 ) )
= $false )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[741]) ).
thf(782,plain,
! [SV75: $i,SV85: $i,SV55: $i,SV28: $i] :
( ( ( ~ ( apply @ SV28 @ ( sK14_SY549 @ SV55 @ SV28 @ SV85 @ SV75 ) @ ( sK19_SY614 @ SV75 @ SV85 @ SV28 @ SV55 ) )
| ~ ( apply @ SV55 @ ( sK14_SY549 @ SV55 @ SV28 @ SV85 @ SV75 ) @ ( sK24_SY629 @ SV75 @ SV85 @ SV28 @ SV55 ) ) )
= $false )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[742]) ).
thf(783,plain,
! [SV30: $i,SV3: $i,SV77: $i,SV57: $i] :
( ( ( ~ ( member @ ( sK29_SY496 @ SV57 @ SV77 @ SV3 @ SV30 ) @ SV30 ) )
= $false )
| ( ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[745]) ).
thf(784,plain,
! [SV30: $i,SV77: $i,SV57: $i,SV3: $i] :
( ( ( ~ ( apply @ SV3 @ ( sK29_SY496 @ SV57 @ SV77 @ SV3 @ SV30 ) @ SV77 ) )
= $false )
| ( ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[745]) ).
thf(785,plain,
! [SV57: $i,SV77: $i,SV3: $i,SV30: $i,SV126: $i] :
( ( ( ~ ( member @ SV126 @ SV30 )
| ~ ( apply @ SV3 @ SV126 @ SV77 ) )
= $true )
| ( ( member @ SV77 @ SV57 )
= $false )
| ( ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[746]) ).
thf(786,plain,
! [SV31: $i,SV4: $i,SV98: $i,SV58: $i] :
( ( ( member @ ( sK25_SY602 @ SV58 @ SV98 @ SV4 @ SV31 ) @ SV31 )
= $true )
| ( ( member @ SV98 @ SV58 )
= $false )
| ( ( surjective @ SV4 @ SV31 @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[747]) ).
thf(787,plain,
! [SV31: $i,SV98: $i,SV58: $i,SV4: $i] :
( ( ( apply @ SV4 @ ( sK25_SY602 @ SV58 @ SV98 @ SV4 @ SV31 ) @ SV98 )
= $true )
| ( ( member @ SV98 @ SV58 )
= $false )
| ( ( surjective @ SV4 @ SV31 @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[748]) ).
thf(788,plain,
! [SV58: $i,SV31: $i,SV111: $i,SV4: $i] :
( ( ( apply @ SV4 @ SV111 @ ( sK7_SY411 @ SV4 @ SV31 @ SV58 ) )
= $false )
| ( ( member @ SV111 @ SV31 )
= $false )
| ( ( surjective @ SV4 @ SV31 @ SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[749]) ).
thf(789,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV122: $i,SV118: $i,SV78: $i,SV112: $i,SV33: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV106 @ SV33 )
| ~ ( member @ SV112 @ SV78 ) )
| ~ ( member @ SV118 @ SV33 ) )
| ~ ( member @ SV122 @ SV78 ) )
| ~ ( apply @ SV59 @ SV106 @ SV118 ) )
| ~ ( apply @ SV6 @ SV106 @ SV112 ) )
| ~ ( apply @ SV6 @ SV118 @ SV122 ) )
= $true )
| ( ( apply @ SV87 @ SV122 @ SV112 )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[750]) ).
thf(790,plain,
! [SV33: $i,SV78: $i,SV59: $i,SV6: $i,SV87: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ SV33 )
| ~ ( member @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
| ~ ( member @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV33 ) )
| ~ ( member @ ( sK30_SY649 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
| ~ ( apply @ SV59 @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) ) )
| ~ ( apply @ SV6 @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) ) )
| ~ ( apply @ SV6 @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ ( sK30_SY649 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) ) )
= $false )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[751]) ).
thf(791,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV131: $i,SV130: $i,SV79: $i,SV127: $i,SV34: $i,SV123: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV123 @ SV34 )
| ~ ( member @ SV127 @ SV79 ) )
| ~ ( member @ SV130 @ SV34 ) )
| ~ ( member @ SV131 @ SV79 ) )
| ~ ( apply @ SV7 @ SV123 @ SV127 ) )
| ~ ( apply @ SV7 @ SV130 @ SV131 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ SV123 @ SV130 )
| ( apply @ SV88 @ SV127 @ SV131 ) )
| ~ ( ~ ( apply @ SV88 @ SV127 @ SV131 )
| ( apply @ SV60 @ SV123 @ SV130 ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(792,plain,
! [SV88: $i,SV60: $i,SV79: $i,SV34: $i,SV7: $i] :
( ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( ~ ! [SY564: $i,SY565: $i,SY566: $i,SY567: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY564 @ SV34 )
| ~ ( member @ SY565 @ SV79 ) )
| ~ ( member @ SY566 @ SV34 ) )
| ~ ( member @ SY567 @ SV79 ) )
| ~ ( apply @ SV7 @ SY564 @ SY565 ) )
| ~ ( apply @ SV7 @ SY566 @ SY567 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ SY564 @ SY566 )
| ( apply @ SV88 @ SY565 @ SY567 ) )
| ~ ( ~ ( apply @ SV88 @ SY565 @ SY567 )
| ( apply @ SV60 @ SY564 @ SY566 ) ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[755]) ).
thf(793,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV124: $i,SV119: $i,SV80: $i,SV113: $i,SV36: $i,SV107: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV107 @ SV36 )
| ~ ( member @ SV113 @ SV80 ) )
| ~ ( member @ SV119 @ SV36 ) )
| ~ ( member @ SV124 @ SV80 ) )
| ~ ( apply @ SV62 @ SV107 @ SV119 ) )
| ~ ( apply @ SV9 @ SV107 @ SV113 ) )
| ~ ( apply @ SV9 @ SV119 @ SV124 ) )
= $true )
| ( ( apply @ SV89 @ SV113 @ SV124 )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[756]) ).
thf(794,plain,
! [SV36: $i,SV80: $i,SV62: $i,SV9: $i,SV89: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ SV36 )
| ~ ( member @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
| ~ ( member @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV36 ) )
| ~ ( member @ ( sK31_SY651 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
| ~ ( apply @ SV62 @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) ) )
| ~ ( apply @ SV9 @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) ) )
| ~ ( apply @ SV9 @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ ( sK31_SY651 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) ) )
= $false )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[757]) ).
thf(795,plain,
! [SV43: $i,SV16: $i,SV81: $i,SV66: $i] :
( ( ( ~ ( member @ ( sK32_SY525 @ SV66 @ SV81 @ SV16 @ SV43 ) @ SV43 ) )
= $false )
| ( ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[758]) ).
thf(796,plain,
! [SV43: $i,SV66: $i,SV81: $i,SV16: $i] :
( ( ( ~ ( apply @ SV16 @ SV81 @ ( sK32_SY525 @ SV66 @ SV81 @ SV16 @ SV43 ) ) )
= $false )
| ( ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[758]) ).
thf(797,plain,
! [SV66: $i,SV81: $i,SV16: $i,SV43: $i,SV128: $i] :
( ( ( ~ ( member @ SV128 @ SV43 )
| ~ ( apply @ SV16 @ SV81 @ SV128 ) )
= $true )
| ( ( member @ SV81 @ SV66 )
= $false )
| ( ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[759]) ).
thf(798,plain,
! [SV17: $i,SV44: $i,SV67: $i,SV102: $i,SV82: $i,SV108: $i] :
( ( ( member @ SV108 @ SV82 )
= $false )
| ( ( member @ SV102 @ SV67 )
= $false )
| ( ( ~ ( ~ ( ~ ( apply @ SV44 @ SV102 @ SV108 )
| ( apply @ SV17 @ SV108 @ SV102 ) )
| ~ ( ~ ( apply @ SV17 @ SV108 @ SV102 )
| ( apply @ SV44 @ SV102 @ SV108 ) ) ) )
= $true )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[760]) ).
thf(799,plain,
! [SV67: $i,SV82: $i,SV17: $i,SV44: $i] :
( ( ( apply @ SV44 @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) )
= $true )
| ( ( ~ ( ~ ( apply @ SV17 @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) )
| ( apply @ SV44 @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) ) ) )
= $true )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[763]) ).
thf(800,plain,
! [SV44: $i,SV82: $i,SV67: $i,SV17: $i] :
( ( ( ~ ( apply @ SV17 @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) )
| ( apply @ SV44 @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) ) )
= $false )
| ( ( apply @ SV17 @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) )
= $false )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[764]) ).
thf(801,plain,
! [SV69: $i,SV21: $i,SV114: $i,SV48: $i] :
( ( ( ~ ( ~ ( member @ ( sK33_SY638 @ SV48 @ SV114 @ SV21 @ SV69 ) @ SV69 )
| ~ ( apply @ SV21 @ SV114 @ ( sK33_SY638 @ SV48 @ SV114 @ SV21 @ SV69 ) ) ) )
= $true )
| ( ( member @ SV114 @ SV48 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[765]) ).
thf(802,plain,
! [SV21: $i,SV125: $i,SV69: $i,SV120: $i,SV48: $i,SV115: $i] :
( ( ( ~ ~ ( ~ ( member @ SV115 @ SV48 )
| ~ ( member @ SV120 @ SV69 ) )
| ~ ( member @ SV125 @ SV69 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV21 @ SV115 @ SV120 )
| ~ ( apply @ SV21 @ SV115 @ SV125 ) )
| ( SV120 = SV125 ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[766]) ).
thf(803,plain,
! [SV48: $i,SV69: $i,SV21: $i] :
( ( ( ! [SY665: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK34_SY460 @ SV21 @ SV69 @ SV48 ) @ SV48 )
| ~ ( member @ ( sK35_SY663 @ SV48 @ SV69 @ SV21 ) @ SV69 ) )
| ~ ( member @ SY665 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ ( sK34_SY460 @ SV21 @ SV69 @ SV48 ) @ ( sK35_SY663 @ SV48 @ SV69 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK34_SY460 @ SV21 @ SV69 @ SV48 ) @ SY665 ) )
| ( ( sK35_SY663 @ SV48 @ SV69 @ SV21 )
= SY665 ) ) )
= $false )
| ( ( member @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV48 )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[767]) ).
thf(804,plain,
! [SV48: $i,SV21: $i,SV69: $i,SV129: $i] :
( ( ( ~ ( member @ SV129 @ SV69 )
| ~ ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV129 ) )
= $true )
| ( ( ~ ! [SY460: $i,SY461: $i,SY462: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY460 @ SV48 )
| ~ ( member @ SY461 @ SV69 ) )
| ~ ( member @ SY462 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY460 @ SY461 )
| ~ ( apply @ SV21 @ SY460 @ SY462 ) )
| ( SY461 = SY462 ) ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[768]) ).
thf(805,plain,
! [SV50: $i,SV70: $i,SV90: $i,SV23: $i,SV92: $i,SV121: $i,SV83: $i,SV116: $i] :
( ( ( ~ ( member @ SV116 @ SV83 ) )
= $true )
| ( ( ~ ( member @ SV121 @ SV92 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV23 @ SV116 @ SV121 )
| ~ ! [SY653: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY653 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SY653 ) )
| ~ ( apply @ SV50 @ SY653 @ SV121 ) ) )
| ~ ( ~ ~ ! [SY654: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY654 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SY654 ) )
| ~ ( apply @ SV50 @ SY654 @ SV121 ) )
| ( apply @ SV23 @ SV116 @ SV121 ) ) ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[769]) ).
thf(806,plain,
! [SV83: $i,SV92: $i,SV23: $i,SV90: $i,SV70: $i,SV50: $i] :
( ( ( ~ ( member @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV83 ) )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[770]) ).
thf(807,plain,
! [SV50: $i,SV70: $i,SV90: $i,SV23: $i,SV92: $i,SV83: $i] :
( ( ( ~ ( member @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) @ SV92 ) )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[770]) ).
thf(808,plain,
! [SV83: $i,SV92: $i,SV90: $i,SV70: $i,SV50: $i,SV23: $i] :
( ( ( ~ ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
| ~ ! [SY655: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY655 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY655 ) )
| ~ ( apply @ SV50 @ SY655 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY656: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY656 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY656 ) )
| ~ ( apply @ SV50 @ SY656 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
| ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[771]) ).
thf(809,plain,
! [SV94: $i,SV93: $i,SV91: $i,SV84: $i,SV72: $i,SV52: $i,SV25: $i] :
( ( ( ~ ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 ) )
= $true )
| ( ( ~ ! [SY600: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY600 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SY600 ) )
| ~ ( apply @ SV25 @ SY600 @ SV94 ) ) )
= $true )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[772]) ).
thf(810,plain,
! [SV91: $i,SV72: $i,SV94: $i,SV25: $i,SV93: $i,SV52: $i,SV84: $i] :
( ( ( ~ ~ ! [SY601: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY601 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SY601 ) )
| ~ ( apply @ SV25 @ SY601 @ SV94 ) ) )
= $true )
| ( ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
= $true )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[773]) ).
thf(811,plain,
! [SV27: $i,SV74: $i,SV109: $i,SV104: $i,SV54: $i,SV100: $i] :
( ( ( ~ ( member @ SV100 @ SV54 )
| ~ ( member @ SV104 @ SV54 ) )
= $true )
| ( ( ~ ( member @ SV109 @ SV74 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV27 @ SV100 @ SV109 )
| ~ ( apply @ SV27 @ SV104 @ SV109 ) )
| ( SV100 = SV104 ) )
= $true )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[774]) ).
thf(812,plain,
! [SV54: $i,SV74: $i,SV27: $i] :
( ( ( ~ ( member @ ( sK9_SY485 @ SV27 @ SV74 @ SV54 ) @ SV54 )
| ~ ( member @ ( sK13_SY606 @ SV54 @ SV74 @ SV27 ) @ SV54 ) )
= $false )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[775]) ).
thf(813,plain,
! [SV54: $i,SV74: $i,SV27: $i] :
( ( ( apply @ SV27 @ ( sK9_SY485 @ SV27 @ SV74 @ SV54 ) @ ( sK18_SY611 @ SV54 @ SV74 @ SV27 ) )
= $true )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[777]) ).
thf(814,plain,
! [SV74: $i,SV54: $i,SV27: $i] :
( ( ( apply @ SV27 @ ( sK13_SY606 @ SV54 @ SV74 @ SV27 ) @ ( sK18_SY611 @ SV54 @ SV74 @ SV27 ) )
= $true )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[778]) ).
thf(815,plain,
! [SV55: $i,SV28: $i,SV117: $i,SV85: $i,SV110: $i,SV75: $i,SV105: $i] :
( ( ( ~ ( ~ ( member @ SV105 @ SV75 )
| ~ ( member @ SV110 @ SV85 ) ) )
= $false )
| ( ( ~ ( member @ SV117 @ SV85 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV28 @ SV105 @ SV110 )
| ~ ( apply @ SV55 @ SV105 @ SV117 ) )
| ( SV110 = SV117 ) )
= $true )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[779]) ).
thf(816,plain,
! [SV75: $i,SV85: $i,SV28: $i,SV55: $i] :
( ( ( ~ ( ~ ( member @ ( sK14_SY549 @ SV55 @ SV28 @ SV85 @ SV75 ) @ SV75 )
| ~ ( member @ ( sK19_SY614 @ SV75 @ SV85 @ SV28 @ SV55 ) @ SV85 ) ) )
= $true )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[780]) ).
thf(817,plain,
! [SV55: $i,SV28: $i,SV85: $i,SV75: $i] :
( ( ( member @ ( sK24_SY629 @ SV75 @ SV85 @ SV28 @ SV55 ) @ SV85 )
= $true )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[781]) ).
thf(818,plain,
! [SV75: $i,SV85: $i,SV55: $i,SV28: $i] :
( ( ( ~ ( apply @ SV28 @ ( sK14_SY549 @ SV55 @ SV28 @ SV85 @ SV75 ) @ ( sK19_SY614 @ SV75 @ SV85 @ SV28 @ SV55 ) ) )
= $false )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[782]) ).
thf(819,plain,
! [SV75: $i,SV85: $i,SV28: $i,SV55: $i] :
( ( ( ~ ( apply @ SV55 @ ( sK14_SY549 @ SV55 @ SV28 @ SV85 @ SV75 ) @ ( sK24_SY629 @ SV75 @ SV85 @ SV28 @ SV55 ) ) )
= $false )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[782]) ).
thf(820,plain,
! [SV30: $i,SV3: $i,SV77: $i,SV57: $i] :
( ( ( member @ ( sK29_SY496 @ SV57 @ SV77 @ SV3 @ SV30 ) @ SV30 )
= $true )
| ( ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[783]) ).
thf(821,plain,
! [SV30: $i,SV77: $i,SV57: $i,SV3: $i] :
( ( ( apply @ SV3 @ ( sK29_SY496 @ SV57 @ SV77 @ SV3 @ SV30 ) @ SV77 )
= $true )
| ( ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[784]) ).
thf(822,plain,
! [SV57: $i,SV77: $i,SV3: $i,SV30: $i,SV126: $i] :
( ( ( ~ ( member @ SV126 @ SV30 ) )
= $true )
| ( ( ~ ( apply @ SV3 @ SV126 @ SV77 ) )
= $true )
| ( ( member @ SV77 @ SV57 )
= $false )
| ( ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[785]) ).
thf(823,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV122: $i,SV118: $i,SV78: $i,SV112: $i,SV33: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV106 @ SV33 )
| ~ ( member @ SV112 @ SV78 ) )
| ~ ( member @ SV118 @ SV33 ) )
| ~ ( member @ SV122 @ SV78 ) )
| ~ ( apply @ SV59 @ SV106 @ SV118 ) )
| ~ ( apply @ SV6 @ SV106 @ SV112 ) ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV118 @ SV122 ) )
= $true )
| ( ( apply @ SV87 @ SV122 @ SV112 )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[789]) ).
thf(824,plain,
! [SV33: $i,SV78: $i,SV59: $i,SV6: $i,SV87: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ SV33 )
| ~ ( member @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
| ~ ( member @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV33 ) )
| ~ ( member @ ( sK30_SY649 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
| ~ ( apply @ SV59 @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) ) )
| ~ ( apply @ SV6 @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) ) ) )
= $false )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[790]) ).
thf(825,plain,
! [SV87: $i,SV59: $i,SV78: $i,SV33: $i,SV6: $i] :
( ( ( ~ ( apply @ SV6 @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ ( sK30_SY649 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) ) )
= $false )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[790]) ).
thf(826,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV131: $i,SV130: $i,SV79: $i,SV127: $i,SV34: $i,SV123: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV123 @ SV34 )
| ~ ( member @ SV127 @ SV79 ) )
| ~ ( member @ SV130 @ SV34 ) )
| ~ ( member @ SV131 @ SV79 ) )
| ~ ( apply @ SV7 @ SV123 @ SV127 ) )
| ~ ( apply @ SV7 @ SV130 @ SV131 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV60 @ SV123 @ SV130 )
| ( apply @ SV88 @ SV127 @ SV131 ) )
| ~ ( ~ ( apply @ SV88 @ SV127 @ SV131 )
| ( apply @ SV60 @ SV123 @ SV130 ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[791]) ).
thf(827,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV79: $i,SV34: $i] :
( ( ( ! [SY564: $i,SY565: $i,SY566: $i,SY567: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY564 @ SV34 )
| ~ ( member @ SY565 @ SV79 ) )
| ~ ( member @ SY566 @ SV34 ) )
| ~ ( member @ SY567 @ SV79 ) )
| ~ ( apply @ SV7 @ SY564 @ SY565 ) )
| ~ ( apply @ SV7 @ SY566 @ SY567 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ SY564 @ SY566 )
| ( apply @ SV88 @ SY565 @ SY567 ) )
| ~ ( ~ ( apply @ SV88 @ SY565 @ SY567 )
| ( apply @ SV60 @ SY564 @ SY566 ) ) ) ) )
= $false )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[792]) ).
thf(828,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV124: $i,SV119: $i,SV80: $i,SV113: $i,SV36: $i,SV107: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV107 @ SV36 )
| ~ ( member @ SV113 @ SV80 ) )
| ~ ( member @ SV119 @ SV36 ) )
| ~ ( member @ SV124 @ SV80 ) )
| ~ ( apply @ SV62 @ SV107 @ SV119 ) )
| ~ ( apply @ SV9 @ SV107 @ SV113 ) ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV119 @ SV124 ) )
= $true )
| ( ( apply @ SV89 @ SV113 @ SV124 )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[793]) ).
thf(829,plain,
! [SV36: $i,SV80: $i,SV62: $i,SV9: $i,SV89: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ SV36 )
| ~ ( member @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
| ~ ( member @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV36 ) )
| ~ ( member @ ( sK31_SY651 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
| ~ ( apply @ SV62 @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) ) )
| ~ ( apply @ SV9 @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) ) ) )
= $false )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[794]) ).
thf(830,plain,
! [SV89: $i,SV62: $i,SV80: $i,SV36: $i,SV9: $i] :
( ( ( ~ ( apply @ SV9 @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ ( sK31_SY651 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) ) )
= $false )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[794]) ).
thf(831,plain,
! [SV43: $i,SV16: $i,SV81: $i,SV66: $i] :
( ( ( member @ ( sK32_SY525 @ SV66 @ SV81 @ SV16 @ SV43 ) @ SV43 )
= $true )
| ( ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[795]) ).
thf(832,plain,
! [SV43: $i,SV66: $i,SV81: $i,SV16: $i] :
( ( ( apply @ SV16 @ SV81 @ ( sK32_SY525 @ SV66 @ SV81 @ SV16 @ SV43 ) )
= $true )
| ( ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[796]) ).
thf(833,plain,
! [SV66: $i,SV81: $i,SV16: $i,SV43: $i,SV128: $i] :
( ( ( ~ ( member @ SV128 @ SV43 ) )
= $true )
| ( ( ~ ( apply @ SV16 @ SV81 @ SV128 ) )
= $true )
| ( ( member @ SV81 @ SV66 )
= $false )
| ( ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[797]) ).
thf(834,plain,
! [SV82: $i,SV67: $i,SV17: $i,SV108: $i,SV102: $i,SV44: $i] :
( ( ( ~ ( ~ ( apply @ SV44 @ SV102 @ SV108 )
| ( apply @ SV17 @ SV108 @ SV102 ) )
| ~ ( ~ ( apply @ SV17 @ SV108 @ SV102 )
| ( apply @ SV44 @ SV102 @ SV108 ) ) )
= $false )
| ( ( member @ SV102 @ SV67 )
= $false )
| ( ( member @ SV108 @ SV82 )
= $false )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[798]) ).
thf(835,plain,
! [SV44: $i,SV82: $i,SV67: $i,SV17: $i] :
( ( ( ~ ( apply @ SV17 @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) )
| ( apply @ SV44 @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) ) )
= $false )
| ( ( apply @ SV44 @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) )
= $true )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[799]) ).
thf(836,plain,
! [SV44: $i,SV82: $i,SV67: $i,SV17: $i] :
( ( ( ~ ( apply @ SV17 @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) ) )
= $false )
| ( ( apply @ SV17 @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) )
= $false )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[800]) ).
thf(837,plain,
! [SV67: $i,SV82: $i,SV17: $i,SV44: $i] :
( ( ( apply @ SV44 @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) )
= $false )
| ( ( apply @ SV17 @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) )
= $false )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[800]) ).
thf(838,plain,
! [SV69: $i,SV21: $i,SV114: $i,SV48: $i] :
( ( ( ~ ( member @ ( sK33_SY638 @ SV48 @ SV114 @ SV21 @ SV69 ) @ SV69 )
| ~ ( apply @ SV21 @ SV114 @ ( sK33_SY638 @ SV48 @ SV114 @ SV21 @ SV69 ) ) )
= $false )
| ( ( member @ SV114 @ SV48 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[801]) ).
thf(839,plain,
! [SV21: $i,SV125: $i,SV69: $i,SV120: $i,SV48: $i,SV115: $i] :
( ( ( ~ ~ ( ~ ( member @ SV115 @ SV48 )
| ~ ( member @ SV120 @ SV69 ) ) )
= $true )
| ( ( ~ ( member @ SV125 @ SV69 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV21 @ SV115 @ SV120 )
| ~ ( apply @ SV21 @ SV115 @ SV125 ) )
| ( SV120 = SV125 ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[802]) ).
thf(840,plain,
! [SV48: $i,SV69: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK34_SY460 @ SV21 @ SV69 @ SV48 ) @ SV48 )
| ~ ( member @ ( sK35_SY663 @ SV48 @ SV69 @ SV21 ) @ SV69 ) )
| ~ ( member @ ( sK36_SY665 @ SV48 @ SV69 @ SV21 ) @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ ( sK34_SY460 @ SV21 @ SV69 @ SV48 ) @ ( sK35_SY663 @ SV48 @ SV69 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK34_SY460 @ SV21 @ SV69 @ SV48 ) @ ( sK36_SY665 @ SV48 @ SV69 @ SV21 ) ) )
| ( ( sK35_SY663 @ SV48 @ SV69 @ SV21 )
= ( sK36_SY665 @ SV48 @ SV69 @ SV21 ) ) )
= $false )
| ( ( member @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV48 )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[803]) ).
thf(841,plain,
! [SV48: $i,SV21: $i,SV69: $i,SV129: $i] :
( ( ( ~ ( member @ SV129 @ SV69 ) )
= $true )
| ( ( ~ ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV129 ) )
= $true )
| ( ( ~ ! [SY460: $i,SY461: $i,SY462: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY460 @ SV48 )
| ~ ( member @ SY461 @ SV69 ) )
| ~ ( member @ SY462 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY460 @ SY461 )
| ~ ( apply @ SV21 @ SY460 @ SY462 ) )
| ( SY461 = SY462 ) ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[804]) ).
thf(842,plain,
! [SV50: $i,SV70: $i,SV90: $i,SV23: $i,SV92: $i,SV121: $i,SV83: $i,SV116: $i] :
( ( ( member @ SV116 @ SV83 )
= $false )
| ( ( ~ ( member @ SV121 @ SV92 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV23 @ SV116 @ SV121 )
| ~ ! [SY653: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY653 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SY653 ) )
| ~ ( apply @ SV50 @ SY653 @ SV121 ) ) )
| ~ ( ~ ~ ! [SY654: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY654 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SY654 ) )
| ~ ( apply @ SV50 @ SY654 @ SV121 ) )
| ( apply @ SV23 @ SV116 @ SV121 ) ) ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[805]) ).
thf(843,plain,
! [SV83: $i,SV92: $i,SV23: $i,SV90: $i,SV70: $i,SV50: $i] :
( ( ( member @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV83 )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[806]) ).
thf(844,plain,
! [SV50: $i,SV70: $i,SV90: $i,SV23: $i,SV92: $i,SV83: $i] :
( ( ( member @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) @ SV92 )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[807]) ).
thf(845,plain,
! [SV83: $i,SV92: $i,SV90: $i,SV70: $i,SV50: $i,SV23: $i] :
( ( ( ~ ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY656: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY656 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY656 ) )
| ~ ( apply @ SV50 @ SY656 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
| ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[808]) ).
thf(846,plain,
! [SV83: $i,SV92: $i,SV23: $i,SV50: $i,SV70: $i,SV90: $i] :
( ( ( ~ ! [SY655: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY655 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY655 ) )
| ~ ( apply @ SV50 @ SY655 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY656: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY656 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY656 ) )
| ~ ( apply @ SV50 @ SY656 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
| ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[808]) ).
thf(847,plain,
! [SV94: $i,SV93: $i,SV91: $i,SV84: $i,SV72: $i,SV52: $i,SV25: $i] :
( ( ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
= $false )
| ( ( ~ ! [SY600: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY600 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SY600 ) )
| ~ ( apply @ SV25 @ SY600 @ SV94 ) ) )
= $true )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[809]) ).
thf(848,plain,
! [SV91: $i,SV72: $i,SV94: $i,SV25: $i,SV93: $i,SV52: $i,SV84: $i] :
( ( ( ~ ! [SY601: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY601 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SY601 ) )
| ~ ( apply @ SV25 @ SY601 @ SV94 ) ) )
= $false )
| ( ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
= $true )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[810]) ).
thf(849,plain,
! [SV27: $i,SV74: $i,SV109: $i,SV104: $i,SV54: $i,SV100: $i] :
( ( ( ~ ( member @ SV100 @ SV54 ) )
= $true )
| ( ( ~ ( member @ SV104 @ SV54 ) )
= $true )
| ( ( ~ ( member @ SV109 @ SV74 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV27 @ SV100 @ SV109 )
| ~ ( apply @ SV27 @ SV104 @ SV109 ) )
| ( SV100 = SV104 ) )
= $true )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[811]) ).
thf(850,plain,
! [SV54: $i,SV74: $i,SV27: $i] :
( ( ( ~ ( member @ ( sK9_SY485 @ SV27 @ SV74 @ SV54 ) @ SV54 ) )
= $false )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[812]) ).
thf(851,plain,
! [SV27: $i,SV74: $i,SV54: $i] :
( ( ( ~ ( member @ ( sK13_SY606 @ SV54 @ SV74 @ SV27 ) @ SV54 ) )
= $false )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[812]) ).
thf(852,plain,
! [SV55: $i,SV28: $i,SV117: $i,SV85: $i,SV110: $i,SV75: $i,SV105: $i] :
( ( ( ~ ( member @ SV105 @ SV75 )
| ~ ( member @ SV110 @ SV85 ) )
= $true )
| ( ( ~ ( member @ SV117 @ SV85 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV28 @ SV105 @ SV110 )
| ~ ( apply @ SV55 @ SV105 @ SV117 ) )
| ( SV110 = SV117 ) )
= $true )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[815]) ).
thf(853,plain,
! [SV75: $i,SV85: $i,SV28: $i,SV55: $i] :
( ( ( ~ ( member @ ( sK14_SY549 @ SV55 @ SV28 @ SV85 @ SV75 ) @ SV75 )
| ~ ( member @ ( sK19_SY614 @ SV75 @ SV85 @ SV28 @ SV55 ) @ SV85 ) )
= $false )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[816]) ).
thf(854,plain,
! [SV75: $i,SV85: $i,SV55: $i,SV28: $i] :
( ( ( apply @ SV28 @ ( sK14_SY549 @ SV55 @ SV28 @ SV85 @ SV75 ) @ ( sK19_SY614 @ SV75 @ SV85 @ SV28 @ SV55 ) )
= $true )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[818]) ).
thf(855,plain,
! [SV75: $i,SV85: $i,SV28: $i,SV55: $i] :
( ( ( apply @ SV55 @ ( sK14_SY549 @ SV55 @ SV28 @ SV85 @ SV75 ) @ ( sK24_SY629 @ SV75 @ SV85 @ SV28 @ SV55 ) )
= $true )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[819]) ).
thf(856,plain,
! [SV57: $i,SV77: $i,SV3: $i,SV30: $i,SV126: $i] :
( ( ( member @ SV126 @ SV30 )
= $false )
| ( ( ~ ( apply @ SV3 @ SV126 @ SV77 ) )
= $true )
| ( ( member @ SV77 @ SV57 )
= $false )
| ( ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[822]) ).
thf(857,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV122: $i,SV118: $i,SV78: $i,SV112: $i,SV33: $i,SV106: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV106 @ SV33 )
| ~ ( member @ SV112 @ SV78 ) )
| ~ ( member @ SV118 @ SV33 ) )
| ~ ( member @ SV122 @ SV78 ) )
| ~ ( apply @ SV59 @ SV106 @ SV118 ) )
| ~ ( apply @ SV6 @ SV106 @ SV112 ) ) )
= $false )
| ( ( ~ ( apply @ SV6 @ SV118 @ SV122 ) )
= $true )
| ( ( apply @ SV87 @ SV122 @ SV112 )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[823]) ).
thf(858,plain,
! [SV33: $i,SV78: $i,SV59: $i,SV6: $i,SV87: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ SV33 )
| ~ ( member @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
| ~ ( member @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV33 ) )
| ~ ( member @ ( sK30_SY649 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
| ~ ( apply @ SV59 @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) ) )
| ~ ( apply @ SV6 @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) ) ) )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[824]) ).
thf(859,plain,
! [SV87: $i,SV59: $i,SV78: $i,SV33: $i,SV6: $i] :
( ( ( apply @ SV6 @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ ( sK30_SY649 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[825]) ).
thf(860,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV131: $i,SV130: $i,SV79: $i,SV127: $i,SV34: $i,SV123: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV123 @ SV34 )
| ~ ( member @ SV127 @ SV79 ) )
| ~ ( member @ SV130 @ SV34 ) )
| ~ ( member @ SV131 @ SV79 ) )
| ~ ( apply @ SV7 @ SV123 @ SV127 ) )
| ~ ( apply @ SV7 @ SV130 @ SV131 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( apply @ SV60 @ SV123 @ SV130 )
| ( apply @ SV88 @ SV127 @ SV131 ) )
| ~ ( ~ ( apply @ SV88 @ SV127 @ SV131 )
| ( apply @ SV60 @ SV123 @ SV130 ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[826]) ).
thf(861,plain,
! [SV34: $i,SV79: $i,SV7: $i,SV60: $i,SV88: $i] :
( ( ( ! [SY666: $i,SY667: $i,SY668: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ SV34 )
| ~ ( member @ SY666 @ SV79 ) )
| ~ ( member @ SY667 @ SV34 ) )
| ~ ( member @ SY668 @ SV79 ) )
| ~ ( apply @ SV7 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ SY666 ) )
| ~ ( apply @ SV7 @ SY667 @ SY668 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ SY667 )
| ( apply @ SV88 @ SY666 @ SY668 ) )
| ~ ( ~ ( apply @ SV88 @ SY666 @ SY668 )
| ( apply @ SV60 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ SY667 ) ) ) ) )
= $false )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[827]) ).
thf(862,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV124: $i,SV119: $i,SV80: $i,SV113: $i,SV36: $i,SV107: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV107 @ SV36 )
| ~ ( member @ SV113 @ SV80 ) )
| ~ ( member @ SV119 @ SV36 ) )
| ~ ( member @ SV124 @ SV80 ) )
| ~ ( apply @ SV62 @ SV107 @ SV119 ) )
| ~ ( apply @ SV9 @ SV107 @ SV113 ) ) )
= $false )
| ( ( ~ ( apply @ SV9 @ SV119 @ SV124 ) )
= $true )
| ( ( apply @ SV89 @ SV113 @ SV124 )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[828]) ).
thf(863,plain,
! [SV36: $i,SV80: $i,SV62: $i,SV9: $i,SV89: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ SV36 )
| ~ ( member @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
| ~ ( member @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV36 ) )
| ~ ( member @ ( sK31_SY651 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
| ~ ( apply @ SV62 @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) ) )
| ~ ( apply @ SV9 @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) ) ) )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[829]) ).
thf(864,plain,
! [SV89: $i,SV62: $i,SV80: $i,SV36: $i,SV9: $i] :
( ( ( apply @ SV9 @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ ( sK31_SY651 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[830]) ).
thf(865,plain,
! [SV66: $i,SV81: $i,SV16: $i,SV43: $i,SV128: $i] :
( ( ( member @ SV128 @ SV43 )
= $false )
| ( ( ~ ( apply @ SV16 @ SV81 @ SV128 ) )
= $true )
| ( ( member @ SV81 @ SV66 )
= $false )
| ( ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[833]) ).
thf(866,plain,
! [SV82: $i,SV67: $i,SV17: $i,SV108: $i,SV102: $i,SV44: $i] :
( ( ( ~ ( ~ ( apply @ SV44 @ SV102 @ SV108 )
| ( apply @ SV17 @ SV108 @ SV102 ) ) )
= $false )
| ( ( member @ SV102 @ SV67 )
= $false )
| ( ( member @ SV108 @ SV82 )
= $false )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[834]) ).
thf(867,plain,
! [SV82: $i,SV67: $i,SV44: $i,SV102: $i,SV108: $i,SV17: $i] :
( ( ( ~ ( ~ ( apply @ SV17 @ SV108 @ SV102 )
| ( apply @ SV44 @ SV102 @ SV108 ) ) )
= $false )
| ( ( member @ SV102 @ SV67 )
= $false )
| ( ( member @ SV108 @ SV82 )
= $false )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[834]) ).
thf(868,plain,
! [SV44: $i,SV82: $i,SV67: $i,SV17: $i] :
( ( ( ~ ( apply @ SV17 @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) ) )
= $false )
| ( ( apply @ SV44 @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) )
= $true )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[835]) ).
thf(869,plain,
! [SV67: $i,SV82: $i,SV17: $i,SV44: $i] :
( ( ( apply @ SV44 @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) )
= $false )
| ( ( apply @ SV44 @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) )
= $true )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[835]) ).
thf(870,plain,
! [SV44: $i,SV82: $i,SV67: $i,SV17: $i] :
( ( ( apply @ SV17 @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) )
= $true )
| ( ( apply @ SV17 @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) )
= $false )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[836]) ).
thf(871,plain,
! [SV69: $i,SV21: $i,SV114: $i,SV48: $i] :
( ( ( ~ ( member @ ( sK33_SY638 @ SV48 @ SV114 @ SV21 @ SV69 ) @ SV69 ) )
= $false )
| ( ( member @ SV114 @ SV48 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[838]) ).
thf(872,plain,
! [SV69: $i,SV48: $i,SV114: $i,SV21: $i] :
( ( ( ~ ( apply @ SV21 @ SV114 @ ( sK33_SY638 @ SV48 @ SV114 @ SV21 @ SV69 ) ) )
= $false )
| ( ( member @ SV114 @ SV48 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[838]) ).
thf(873,plain,
! [SV21: $i,SV125: $i,SV69: $i,SV120: $i,SV48: $i,SV115: $i] :
( ( ( ~ ( ~ ( member @ SV115 @ SV48 )
| ~ ( member @ SV120 @ SV69 ) ) )
= $false )
| ( ( ~ ( member @ SV125 @ SV69 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV21 @ SV115 @ SV120 )
| ~ ( apply @ SV21 @ SV115 @ SV125 ) )
| ( SV120 = SV125 ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[839]) ).
thf(874,plain,
! [SV48: $i,SV69: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK34_SY460 @ SV21 @ SV69 @ SV48 ) @ SV48 )
| ~ ( member @ ( sK35_SY663 @ SV48 @ SV69 @ SV21 ) @ SV69 ) )
| ~ ( member @ ( sK36_SY665 @ SV48 @ SV69 @ SV21 ) @ SV69 ) ) )
= $false )
| ( ( member @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV48 )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[840]) ).
thf(875,plain,
! [SV48: $i,SV69: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV21 @ ( sK34_SY460 @ SV21 @ SV69 @ SV48 ) @ ( sK35_SY663 @ SV48 @ SV69 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK34_SY460 @ SV21 @ SV69 @ SV48 ) @ ( sK36_SY665 @ SV48 @ SV69 @ SV21 ) ) )
| ( ( sK35_SY663 @ SV48 @ SV69 @ SV21 )
= ( sK36_SY665 @ SV48 @ SV69 @ SV21 ) ) )
= $false )
| ( ( member @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV48 )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[840]) ).
thf(876,plain,
! [SV48: $i,SV21: $i,SV69: $i,SV129: $i] :
( ( ( member @ SV129 @ SV69 )
= $false )
| ( ( ~ ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV129 ) )
= $true )
| ( ( ~ ! [SY460: $i,SY461: $i,SY462: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY460 @ SV48 )
| ~ ( member @ SY461 @ SV69 ) )
| ~ ( member @ SY462 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY460 @ SY461 )
| ~ ( apply @ SV21 @ SY460 @ SY462 ) )
| ( SY461 = SY462 ) ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[841]) ).
thf(877,plain,
! [SV50: $i,SV70: $i,SV90: $i,SV23: $i,SV83: $i,SV116: $i,SV92: $i,SV121: $i] :
( ( ( member @ SV121 @ SV92 )
= $false )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( ~ ( ~ ( ~ ( apply @ SV23 @ SV116 @ SV121 )
| ~ ! [SY653: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY653 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SY653 ) )
| ~ ( apply @ SV50 @ SY653 @ SV121 ) ) )
| ~ ( ~ ~ ! [SY654: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY654 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SY654 ) )
| ~ ( apply @ SV50 @ SY654 @ SV121 ) )
| ( apply @ SV23 @ SV116 @ SV121 ) ) ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[842]) ).
thf(878,plain,
! [SV83: $i,SV92: $i,SV90: $i,SV70: $i,SV50: $i,SV23: $i] :
( ( ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY656: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY656 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY656 ) )
| ~ ( apply @ SV50 @ SY656 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
| ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[845]) ).
thf(879,plain,
! [SV83: $i,SV92: $i,SV23: $i,SV50: $i,SV70: $i,SV90: $i] :
( ( ( ! [SY655: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY655 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY655 ) )
| ~ ( apply @ SV50 @ SY655 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY656: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY656 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY656 ) )
| ~ ( apply @ SV50 @ SY656 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
| ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[846]) ).
thf(880,plain,
! [SV91: $i,SV72: $i,SV94: $i,SV25: $i,SV93: $i,SV52: $i,SV84: $i] :
( ( ( ! [SY600: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY600 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SY600 ) )
| ~ ( apply @ SV25 @ SY600 @ SV94 ) ) )
= $false )
| ( ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
= $false )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[847]) ).
thf(881,plain,
! [SV91: $i,SV72: $i,SV94: $i,SV25: $i,SV93: $i,SV52: $i,SV84: $i] :
( ( ( ! [SY601: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY601 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SY601 ) )
| ~ ( apply @ SV25 @ SY601 @ SV94 ) ) )
= $true )
| ( ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
= $true )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[848]) ).
thf(882,plain,
! [SV27: $i,SV74: $i,SV109: $i,SV104: $i,SV54: $i,SV100: $i] :
( ( ( member @ SV100 @ SV54 )
= $false )
| ( ( ~ ( member @ SV104 @ SV54 ) )
= $true )
| ( ( ~ ( member @ SV109 @ SV74 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV27 @ SV100 @ SV109 )
| ~ ( apply @ SV27 @ SV104 @ SV109 ) )
| ( SV100 = SV104 ) )
= $true )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[849]) ).
thf(883,plain,
! [SV54: $i,SV74: $i,SV27: $i] :
( ( ( member @ ( sK9_SY485 @ SV27 @ SV74 @ SV54 ) @ SV54 )
= $true )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[850]) ).
thf(884,plain,
! [SV27: $i,SV74: $i,SV54: $i] :
( ( ( member @ ( sK13_SY606 @ SV54 @ SV74 @ SV27 ) @ SV54 )
= $true )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[851]) ).
thf(885,plain,
! [SV55: $i,SV28: $i,SV117: $i,SV85: $i,SV110: $i,SV75: $i,SV105: $i] :
( ( ( ~ ( member @ SV105 @ SV75 ) )
= $true )
| ( ( ~ ( member @ SV110 @ SV85 ) )
= $true )
| ( ( ~ ( member @ SV117 @ SV85 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV28 @ SV105 @ SV110 )
| ~ ( apply @ SV55 @ SV105 @ SV117 ) )
| ( SV110 = SV117 ) )
= $true )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[852]) ).
thf(886,plain,
! [SV75: $i,SV85: $i,SV28: $i,SV55: $i] :
( ( ( ~ ( member @ ( sK14_SY549 @ SV55 @ SV28 @ SV85 @ SV75 ) @ SV75 ) )
= $false )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[853]) ).
thf(887,plain,
! [SV55: $i,SV28: $i,SV85: $i,SV75: $i] :
( ( ( ~ ( member @ ( sK19_SY614 @ SV75 @ SV85 @ SV28 @ SV55 ) @ SV85 ) )
= $false )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[853]) ).
thf(888,plain,
! [SV57: $i,SV30: $i,SV77: $i,SV126: $i,SV3: $i] :
( ( ( apply @ SV3 @ SV126 @ SV77 )
= $false )
| ( ( member @ SV126 @ SV30 )
= $false )
| ( ( member @ SV77 @ SV57 )
= $false )
| ( ( member @ SV77 @ ( image3 @ SV3 @ SV30 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[856]) ).
thf(889,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV122: $i,SV118: $i,SV78: $i,SV112: $i,SV33: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV106 @ SV33 )
| ~ ( member @ SV112 @ SV78 ) )
| ~ ( member @ SV118 @ SV33 ) )
| ~ ( member @ SV122 @ SV78 ) )
| ~ ( apply @ SV59 @ SV106 @ SV118 ) )
| ~ ( apply @ SV6 @ SV106 @ SV112 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV118 @ SV122 ) )
= $true )
| ( ( apply @ SV87 @ SV122 @ SV112 )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[857]) ).
thf(890,plain,
! [SV33: $i,SV78: $i,SV59: $i,SV6: $i,SV87: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ SV33 )
| ~ ( member @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
| ~ ( member @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV33 ) )
| ~ ( member @ ( sK30_SY649 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
| ~ ( apply @ SV59 @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) ) )
| ~ ( apply @ SV6 @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) ) )
= $false )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[858]) ).
thf(891,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV131: $i,SV130: $i,SV79: $i,SV127: $i,SV34: $i,SV123: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV123 @ SV34 )
| ~ ( member @ SV127 @ SV79 ) )
| ~ ( member @ SV130 @ SV34 ) )
| ~ ( member @ SV131 @ SV79 ) )
| ~ ( apply @ SV7 @ SV123 @ SV127 ) )
| ~ ( apply @ SV7 @ SV130 @ SV131 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV60 @ SV123 @ SV130 )
| ( apply @ SV88 @ SV127 @ SV131 ) )
| ~ ( ~ ( apply @ SV88 @ SV127 @ SV131 )
| ( apply @ SV60 @ SV123 @ SV130 ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[860]) ).
thf(892,plain,
! [SV34: $i,SV79: $i,SV7: $i,SV60: $i,SV88: $i] :
( ( ( ! [SY669: $i,SY670: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ SV34 )
| ~ ( member @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 ) )
| ~ ( member @ SY669 @ SV34 ) )
| ~ ( member @ SY670 @ SV79 ) )
| ~ ( apply @ SV7 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) )
| ~ ( apply @ SV7 @ SY669 @ SY670 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ SY669 )
| ( apply @ SV88 @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SY670 ) )
| ~ ( ~ ( apply @ SV88 @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SY670 )
| ( apply @ SV60 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ SY669 ) ) ) ) )
= $false )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[861]) ).
thf(893,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV124: $i,SV119: $i,SV80: $i,SV113: $i,SV36: $i,SV107: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV107 @ SV36 )
| ~ ( member @ SV113 @ SV80 ) )
| ~ ( member @ SV119 @ SV36 ) )
| ~ ( member @ SV124 @ SV80 ) )
| ~ ( apply @ SV62 @ SV107 @ SV119 ) )
| ~ ( apply @ SV9 @ SV107 @ SV113 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV119 @ SV124 ) )
= $true )
| ( ( apply @ SV89 @ SV113 @ SV124 )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[862]) ).
thf(894,plain,
! [SV36: $i,SV80: $i,SV62: $i,SV9: $i,SV89: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ SV36 )
| ~ ( member @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
| ~ ( member @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV36 ) )
| ~ ( member @ ( sK31_SY651 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
| ~ ( apply @ SV62 @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) ) )
| ~ ( apply @ SV9 @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) ) )
= $false )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[863]) ).
thf(895,plain,
! [SV66: $i,SV43: $i,SV128: $i,SV81: $i,SV16: $i] :
( ( ( apply @ SV16 @ SV81 @ SV128 )
= $false )
| ( ( member @ SV128 @ SV43 )
= $false )
| ( ( member @ SV81 @ SV66 )
= $false )
| ( ( member @ SV81 @ ( inverse_image3 @ SV16 @ SV43 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(896,plain,
! [SV82: $i,SV67: $i,SV17: $i,SV108: $i,SV102: $i,SV44: $i] :
( ( ( ~ ( apply @ SV44 @ SV102 @ SV108 )
| ( apply @ SV17 @ SV108 @ SV102 ) )
= $true )
| ( ( member @ SV102 @ SV67 )
= $false )
| ( ( member @ SV108 @ SV82 )
= $false )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[866]) ).
thf(897,plain,
! [SV82: $i,SV67: $i,SV44: $i,SV102: $i,SV108: $i,SV17: $i] :
( ( ( ~ ( apply @ SV17 @ SV108 @ SV102 )
| ( apply @ SV44 @ SV102 @ SV108 ) )
= $true )
| ( ( member @ SV102 @ SV67 )
= $false )
| ( ( member @ SV108 @ SV82 )
= $false )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[867]) ).
thf(898,plain,
! [SV44: $i,SV82: $i,SV67: $i,SV17: $i] :
( ( ( apply @ SV17 @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) )
= $true )
| ( ( apply @ SV44 @ ( sK11_SY529 @ SV17 @ SV44 @ SV82 @ SV67 ) @ ( sK17_SY609 @ SV67 @ SV82 @ SV44 @ SV17 ) )
= $true )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[868]) ).
thf(899,plain,
! [SV69: $i,SV21: $i,SV114: $i,SV48: $i] :
( ( ( member @ ( sK33_SY638 @ SV48 @ SV114 @ SV21 @ SV69 ) @ SV69 )
= $true )
| ( ( member @ SV114 @ SV48 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[871]) ).
thf(900,plain,
! [SV69: $i,SV48: $i,SV114: $i,SV21: $i] :
( ( ( apply @ SV21 @ SV114 @ ( sK33_SY638 @ SV48 @ SV114 @ SV21 @ SV69 ) )
= $true )
| ( ( member @ SV114 @ SV48 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[872]) ).
thf(901,plain,
! [SV21: $i,SV125: $i,SV69: $i,SV120: $i,SV48: $i,SV115: $i] :
( ( ( ~ ( member @ SV115 @ SV48 )
| ~ ( member @ SV120 @ SV69 ) )
= $true )
| ( ( ~ ( member @ SV125 @ SV69 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV21 @ SV115 @ SV120 )
| ~ ( apply @ SV21 @ SV115 @ SV125 ) )
| ( SV120 = SV125 ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[873]) ).
thf(902,plain,
! [SV48: $i,SV69: $i,SV21: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK34_SY460 @ SV21 @ SV69 @ SV48 ) @ SV48 )
| ~ ( member @ ( sK35_SY663 @ SV48 @ SV69 @ SV21 ) @ SV69 ) )
| ~ ( member @ ( sK36_SY665 @ SV48 @ SV69 @ SV21 ) @ SV69 ) ) )
= $true )
| ( ( member @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV48 )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[874]) ).
thf(903,plain,
! [SV48: $i,SV69: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV21 @ ( sK34_SY460 @ SV21 @ SV69 @ SV48 ) @ ( sK35_SY663 @ SV48 @ SV69 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK34_SY460 @ SV21 @ SV69 @ SV48 ) @ ( sK36_SY665 @ SV48 @ SV69 @ SV21 ) ) ) )
= $false )
| ( ( member @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV48 )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[875]) ).
thf(904,plain,
! [SV21: $i,SV69: $i,SV48: $i] :
( ( ( ( sK35_SY663 @ SV48 @ SV69 @ SV21 )
= ( sK36_SY665 @ SV48 @ SV69 @ SV21 ) )
= $false )
| ( ( member @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV48 )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[875]) ).
thf(905,plain,
! [SV129: $i,SV48: $i,SV69: $i,SV21: $i] :
( ( ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV129 )
= $false )
| ( ( member @ SV129 @ SV69 )
= $false )
| ( ( ~ ! [SY460: $i,SY461: $i,SY462: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY460 @ SV48 )
| ~ ( member @ SY461 @ SV69 ) )
| ~ ( member @ SY462 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY460 @ SY461 )
| ~ ( apply @ SV21 @ SY460 @ SY462 ) )
| ( SY461 = SY462 ) ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[876]) ).
thf(906,plain,
! [SV92: $i,SV83: $i,SV50: $i,SV70: $i,SV90: $i,SV121: $i,SV116: $i,SV23: $i] :
( ( ( ~ ( ~ ( apply @ SV23 @ SV116 @ SV121 )
| ~ ! [SY653: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY653 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SY653 ) )
| ~ ( apply @ SV50 @ SY653 @ SV121 ) ) )
| ~ ( ~ ~ ! [SY654: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY654 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SY654 ) )
| ~ ( apply @ SV50 @ SY654 @ SV121 ) )
| ( apply @ SV23 @ SV116 @ SV121 ) ) )
= $false )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(907,plain,
! [SV83: $i,SV92: $i,SV23: $i,SV50: $i,SV70: $i,SV90: $i] :
( ( ( ~ ~ ! [SY656: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY656 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY656 ) )
| ~ ( apply @ SV50 @ SY656 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
| ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
= $false )
| ( ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[878]) ).
thf(908,plain,
! [SV83: $i,SV92: $i,SV23: $i,SV50: $i,SV70: $i,SV90: $i,SV132: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV132 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV132 ) )
| ~ ( apply @ SV50 @ SV132 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY656: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY656 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY656 ) )
| ~ ( apply @ SV50 @ SY656 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
| ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(909,plain,
! [SV84: $i,SV52: $i,SV93: $i,SV25: $i,SV94: $i,SV72: $i,SV91: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK39_SY600 @ SV91 @ SV72 @ SV94 @ SV25 @ SV93 @ SV52 @ SV84 ) @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ ( sK39_SY600 @ SV91 @ SV72 @ SV94 @ SV25 @ SV93 @ SV52 @ SV84 ) ) )
| ~ ( apply @ SV25 @ ( sK39_SY600 @ SV91 @ SV72 @ SV94 @ SV25 @ SV93 @ SV52 @ SV84 ) @ SV94 ) ) )
= $false )
| ( ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
= $false )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[880]) ).
thf(910,plain,
! [SV91: $i,SV72: $i,SV94: $i,SV25: $i,SV93: $i,SV52: $i,SV84: $i,SV133: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV133 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SV133 ) )
| ~ ( apply @ SV25 @ SV133 @ SV94 ) ) )
= $true )
| ( ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
= $true )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(911,plain,
! [SV27: $i,SV74: $i,SV109: $i,SV100: $i,SV54: $i,SV104: $i] :
( ( ( member @ SV104 @ SV54 )
= $false )
| ( ( member @ SV100 @ SV54 )
= $false )
| ( ( ~ ( member @ SV109 @ SV74 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV27 @ SV100 @ SV109 )
| ~ ( apply @ SV27 @ SV104 @ SV109 ) )
| ( SV100 = SV104 ) )
= $true )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(912,plain,
! [SV55: $i,SV28: $i,SV117: $i,SV85: $i,SV110: $i,SV75: $i,SV105: $i] :
( ( ( member @ SV105 @ SV75 )
= $false )
| ( ( ~ ( member @ SV110 @ SV85 ) )
= $true )
| ( ( ~ ( member @ SV117 @ SV85 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV28 @ SV105 @ SV110 )
| ~ ( apply @ SV55 @ SV105 @ SV117 ) )
| ( SV110 = SV117 ) )
= $true )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[885]) ).
thf(913,plain,
! [SV75: $i,SV85: $i,SV28: $i,SV55: $i] :
( ( ( member @ ( sK14_SY549 @ SV55 @ SV28 @ SV85 @ SV75 ) @ SV75 )
= $true )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[886]) ).
thf(914,plain,
! [SV55: $i,SV28: $i,SV85: $i,SV75: $i] :
( ( ( member @ ( sK19_SY614 @ SV75 @ SV85 @ SV28 @ SV55 ) @ SV85 )
= $true )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[887]) ).
thf(915,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV122: $i,SV118: $i,SV78: $i,SV112: $i,SV33: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV106 @ SV33 )
| ~ ( member @ SV112 @ SV78 ) )
| ~ ( member @ SV118 @ SV33 ) )
| ~ ( member @ SV122 @ SV78 ) )
| ~ ( apply @ SV59 @ SV106 @ SV118 ) ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV106 @ SV112 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV118 @ SV122 ) )
= $true )
| ( ( apply @ SV87 @ SV122 @ SV112 )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[889]) ).
thf(916,plain,
! [SV33: $i,SV78: $i,SV59: $i,SV6: $i,SV87: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ SV33 )
| ~ ( member @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
| ~ ( member @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV33 ) )
| ~ ( member @ ( sK30_SY649 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
| ~ ( apply @ SV59 @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) ) ) )
= $false )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[890]) ).
thf(917,plain,
! [SV33: $i,SV78: $i,SV59: $i,SV87: $i,SV6: $i] :
( ( ( ~ ( apply @ SV6 @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) ) )
= $false )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[890]) ).
thf(918,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV131: $i,SV130: $i,SV79: $i,SV127: $i,SV34: $i,SV123: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV123 @ SV34 )
| ~ ( member @ SV127 @ SV79 ) )
| ~ ( member @ SV130 @ SV34 ) )
| ~ ( member @ SV131 @ SV79 ) )
| ~ ( apply @ SV7 @ SV123 @ SV127 ) ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV130 @ SV131 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV60 @ SV123 @ SV130 )
| ( apply @ SV88 @ SV127 @ SV131 ) )
| ~ ( ~ ( apply @ SV88 @ SV127 @ SV131 )
| ( apply @ SV60 @ SV123 @ SV130 ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[891]) ).
thf(919,plain,
! [SV34: $i,SV79: $i,SV7: $i,SV60: $i,SV88: $i] :
( ( ( ! [SY671: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ SV34 )
| ~ ( member @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 ) )
| ~ ( member @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV34 ) )
| ~ ( member @ SY671 @ SV79 ) )
| ~ ( apply @ SV7 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) )
| ~ ( apply @ SV7 @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SY671 ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
| ( apply @ SV88 @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SY671 ) )
| ~ ( ~ ( apply @ SV88 @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SY671 )
| ( apply @ SV60 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) ) ) ) )
= $false )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[892]) ).
thf(920,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV124: $i,SV119: $i,SV80: $i,SV113: $i,SV36: $i,SV107: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV107 @ SV36 )
| ~ ( member @ SV113 @ SV80 ) )
| ~ ( member @ SV119 @ SV36 ) )
| ~ ( member @ SV124 @ SV80 ) )
| ~ ( apply @ SV62 @ SV107 @ SV119 ) ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV107 @ SV113 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV119 @ SV124 ) )
= $true )
| ( ( apply @ SV89 @ SV113 @ SV124 )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[893]) ).
thf(921,plain,
! [SV36: $i,SV80: $i,SV62: $i,SV9: $i,SV89: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ SV36 )
| ~ ( member @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
| ~ ( member @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV36 ) )
| ~ ( member @ ( sK31_SY651 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
| ~ ( apply @ SV62 @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) ) ) )
= $false )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[894]) ).
thf(922,plain,
! [SV36: $i,SV80: $i,SV62: $i,SV89: $i,SV9: $i] :
( ( ( ~ ( apply @ SV9 @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) ) )
= $false )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[894]) ).
thf(923,plain,
! [SV82: $i,SV67: $i,SV17: $i,SV108: $i,SV102: $i,SV44: $i] :
( ( ( ~ ( apply @ SV44 @ SV102 @ SV108 ) )
= $true )
| ( ( apply @ SV17 @ SV108 @ SV102 )
= $true )
| ( ( member @ SV102 @ SV67 )
= $false )
| ( ( member @ SV108 @ SV82 )
= $false )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[896]) ).
thf(924,plain,
! [SV82: $i,SV67: $i,SV44: $i,SV102: $i,SV108: $i,SV17: $i] :
( ( ( ~ ( apply @ SV17 @ SV108 @ SV102 ) )
= $true )
| ( ( apply @ SV44 @ SV102 @ SV108 )
= $true )
| ( ( member @ SV102 @ SV67 )
= $false )
| ( ( member @ SV108 @ SV82 )
= $false )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[897]) ).
thf(925,plain,
! [SV21: $i,SV125: $i,SV69: $i,SV120: $i,SV48: $i,SV115: $i] :
( ( ( ~ ( member @ SV115 @ SV48 ) )
= $true )
| ( ( ~ ( member @ SV120 @ SV69 ) )
= $true )
| ( ( ~ ( member @ SV125 @ SV69 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV21 @ SV115 @ SV120 )
| ~ ( apply @ SV21 @ SV115 @ SV125 ) )
| ( SV120 = SV125 ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[901]) ).
thf(926,plain,
! [SV48: $i,SV69: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK34_SY460 @ SV21 @ SV69 @ SV48 ) @ SV48 )
| ~ ( member @ ( sK35_SY663 @ SV48 @ SV69 @ SV21 ) @ SV69 ) )
| ~ ( member @ ( sK36_SY665 @ SV48 @ SV69 @ SV21 ) @ SV69 ) )
= $false )
| ( ( member @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV48 )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(927,plain,
! [SV48: $i,SV69: $i,SV21: $i] :
( ( ( ~ ( ~ ( apply @ SV21 @ ( sK34_SY460 @ SV21 @ SV69 @ SV48 ) @ ( sK35_SY663 @ SV48 @ SV69 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK34_SY460 @ SV21 @ SV69 @ SV48 ) @ ( sK36_SY665 @ SV48 @ SV69 @ SV21 ) ) ) )
= $true )
| ( ( member @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV48 )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[903]) ).
thf(928,plain,
! [SV129: $i,SV21: $i,SV69: $i,SV48: $i] :
( ( ( ! [SY460: $i,SY461: $i,SY462: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY460 @ SV48 )
| ~ ( member @ SY461 @ SV69 ) )
| ~ ( member @ SY462 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ SY460 @ SY461 )
| ~ ( apply @ SV21 @ SY460 @ SY462 ) )
| ( SY461 = SY462 ) ) )
= $false )
| ( ( member @ SV129 @ SV69 )
= $false )
| ( ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV129 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[905]) ).
thf(929,plain,
! [SV92: $i,SV83: $i,SV50: $i,SV70: $i,SV90: $i,SV121: $i,SV116: $i,SV23: $i] :
( ( ( ~ ( ~ ( apply @ SV23 @ SV116 @ SV121 )
| ~ ! [SY653: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY653 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SY653 ) )
| ~ ( apply @ SV50 @ SY653 @ SV121 ) ) ) )
= $false )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[906]) ).
thf(930,plain,
! [SV92: $i,SV83: $i,SV23: $i,SV121: $i,SV50: $i,SV116: $i,SV70: $i,SV90: $i] :
( ( ( ~ ( ~ ~ ! [SY654: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY654 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SY654 ) )
| ~ ( apply @ SV50 @ SY654 @ SV121 ) )
| ( apply @ SV23 @ SV116 @ SV121 ) ) )
= $false )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[906]) ).
thf(931,plain,
! [SV83: $i,SV92: $i,SV23: $i,SV50: $i,SV70: $i,SV90: $i] :
( ( ( ~ ~ ! [SY656: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY656 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY656 ) )
| ~ ( apply @ SV50 @ SY656 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $false )
| ( ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[907]) ).
thf(932,plain,
! [SV83: $i,SV92: $i,SV90: $i,SV70: $i,SV50: $i,SV23: $i] :
( ( ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $false )
| ( ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[907]) ).
thf(933,plain,
! [SV83: $i,SV92: $i,SV23: $i,SV50: $i,SV70: $i,SV90: $i,SV132: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ SV132 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV132 ) )
| ~ ( apply @ SV50 @ SV132 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY656: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY656 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY656 ) )
| ~ ( apply @ SV50 @ SY656 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
| ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[908]) ).
thf(934,plain,
! [SV84: $i,SV52: $i,SV93: $i,SV25: $i,SV94: $i,SV72: $i,SV91: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK39_SY600 @ SV91 @ SV72 @ SV94 @ SV25 @ SV93 @ SV52 @ SV84 ) @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ ( sK39_SY600 @ SV91 @ SV72 @ SV94 @ SV25 @ SV93 @ SV52 @ SV84 ) ) )
| ~ ( apply @ SV25 @ ( sK39_SY600 @ SV91 @ SV72 @ SV94 @ SV25 @ SV93 @ SV52 @ SV84 ) @ SV94 ) ) )
= $true )
| ( ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
= $false )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[909]) ).
thf(935,plain,
! [SV91: $i,SV72: $i,SV94: $i,SV25: $i,SV93: $i,SV52: $i,SV84: $i,SV133: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ SV133 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SV133 ) )
| ~ ( apply @ SV25 @ SV133 @ SV94 ) ) )
= $false )
| ( ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
= $true )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[910]) ).
thf(936,plain,
! [SV27: $i,SV104: $i,SV54: $i,SV100: $i,SV74: $i,SV109: $i] :
( ( ( member @ SV109 @ SV74 )
= $false )
| ( ( member @ SV100 @ SV54 )
= $false )
| ( ( member @ SV104 @ SV54 )
= $false )
| ( ( ~ ~ ( ~ ( apply @ SV27 @ SV100 @ SV109 )
| ~ ( apply @ SV27 @ SV104 @ SV109 ) )
| ( SV100 = SV104 ) )
= $true )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[911]) ).
thf(937,plain,
! [SV55: $i,SV28: $i,SV117: $i,SV75: $i,SV105: $i,SV85: $i,SV110: $i] :
( ( ( member @ SV110 @ SV85 )
= $false )
| ( ( member @ SV105 @ SV75 )
= $false )
| ( ( ~ ( member @ SV117 @ SV85 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV28 @ SV105 @ SV110 )
| ~ ( apply @ SV55 @ SV105 @ SV117 ) )
| ( SV110 = SV117 ) )
= $true )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[912]) ).
thf(938,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV122: $i,SV118: $i,SV78: $i,SV112: $i,SV33: $i,SV106: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV106 @ SV33 )
| ~ ( member @ SV112 @ SV78 ) )
| ~ ( member @ SV118 @ SV33 ) )
| ~ ( member @ SV122 @ SV78 ) )
| ~ ( apply @ SV59 @ SV106 @ SV118 ) ) )
= $false )
| ( ( ~ ( apply @ SV6 @ SV106 @ SV112 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV118 @ SV122 ) )
= $true )
| ( ( apply @ SV87 @ SV122 @ SV112 )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[915]) ).
thf(939,plain,
! [SV33: $i,SV78: $i,SV59: $i,SV6: $i,SV87: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ SV33 )
| ~ ( member @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
| ~ ( member @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV33 ) )
| ~ ( member @ ( sK30_SY649 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
| ~ ( apply @ SV59 @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) ) ) )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[916]) ).
thf(940,plain,
! [SV33: $i,SV78: $i,SV59: $i,SV87: $i,SV6: $i] :
( ( ( apply @ SV6 @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[917]) ).
thf(941,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV131: $i,SV130: $i,SV79: $i,SV127: $i,SV34: $i,SV123: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV123 @ SV34 )
| ~ ( member @ SV127 @ SV79 ) )
| ~ ( member @ SV130 @ SV34 ) )
| ~ ( member @ SV131 @ SV79 ) )
| ~ ( apply @ SV7 @ SV123 @ SV127 ) ) )
= $false )
| ( ( ~ ( apply @ SV7 @ SV130 @ SV131 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV60 @ SV123 @ SV130 )
| ( apply @ SV88 @ SV127 @ SV131 ) )
| ~ ( ~ ( apply @ SV88 @ SV127 @ SV131 )
| ( apply @ SV60 @ SV123 @ SV130 ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[918]) ).
thf(942,plain,
! [SV34: $i,SV79: $i,SV7: $i,SV60: $i,SV88: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ SV34 )
| ~ ( member @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 ) )
| ~ ( member @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV34 ) )
| ~ ( member @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 ) )
| ~ ( apply @ SV7 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) )
| ~ ( apply @ SV7 @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) )
| ~ ( ~ ( ~ ( apply @ SV60 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
| ( apply @ SV88 @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) )
| ~ ( ~ ( apply @ SV88 @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
| ( apply @ SV60 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) ) ) )
= $false )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[919]) ).
thf(943,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV124: $i,SV119: $i,SV80: $i,SV113: $i,SV36: $i,SV107: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV107 @ SV36 )
| ~ ( member @ SV113 @ SV80 ) )
| ~ ( member @ SV119 @ SV36 ) )
| ~ ( member @ SV124 @ SV80 ) )
| ~ ( apply @ SV62 @ SV107 @ SV119 ) ) )
= $false )
| ( ( ~ ( apply @ SV9 @ SV107 @ SV113 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV119 @ SV124 ) )
= $true )
| ( ( apply @ SV89 @ SV113 @ SV124 )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[920]) ).
thf(944,plain,
! [SV36: $i,SV80: $i,SV62: $i,SV9: $i,SV89: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ SV36 )
| ~ ( member @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
| ~ ( member @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV36 ) )
| ~ ( member @ ( sK31_SY651 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
| ~ ( apply @ SV62 @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) ) ) )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[921]) ).
thf(945,plain,
! [SV36: $i,SV80: $i,SV62: $i,SV89: $i,SV9: $i] :
( ( ( apply @ SV9 @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[922]) ).
thf(946,plain,
! [SV82: $i,SV67: $i,SV17: $i,SV108: $i,SV102: $i,SV44: $i] :
( ( ( apply @ SV44 @ SV102 @ SV108 )
= $false )
| ( ( apply @ SV17 @ SV108 @ SV102 )
= $true )
| ( ( member @ SV102 @ SV67 )
= $false )
| ( ( member @ SV108 @ SV82 )
= $false )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[923]) ).
thf(947,plain,
! [SV82: $i,SV67: $i,SV44: $i,SV102: $i,SV108: $i,SV17: $i] :
( ( ( apply @ SV17 @ SV108 @ SV102 )
= $false )
| ( ( apply @ SV44 @ SV102 @ SV108 )
= $true )
| ( ( member @ SV102 @ SV67 )
= $false )
| ( ( member @ SV108 @ SV82 )
= $false )
| ( ( inverse_predicate @ SV17 @ SV44 @ SV67 @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[924]) ).
thf(948,plain,
! [SV21: $i,SV125: $i,SV69: $i,SV120: $i,SV48: $i,SV115: $i] :
( ( ( member @ SV115 @ SV48 )
= $false )
| ( ( ~ ( member @ SV120 @ SV69 ) )
= $true )
| ( ( ~ ( member @ SV125 @ SV69 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV21 @ SV115 @ SV120 )
| ~ ( apply @ SV21 @ SV115 @ SV125 ) )
| ( SV120 = SV125 ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[925]) ).
thf(949,plain,
! [SV48: $i,SV69: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK34_SY460 @ SV21 @ SV69 @ SV48 ) @ SV48 )
| ~ ( member @ ( sK35_SY663 @ SV48 @ SV69 @ SV21 ) @ SV69 ) ) )
= $false )
| ( ( member @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV48 )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[926]) ).
thf(950,plain,
! [SV21: $i,SV69: $i,SV48: $i] :
( ( ( ~ ( member @ ( sK36_SY665 @ SV48 @ SV69 @ SV21 ) @ SV69 ) )
= $false )
| ( ( member @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV48 )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[926]) ).
thf(951,plain,
! [SV48: $i,SV69: $i,SV21: $i] :
( ( ( ~ ( apply @ SV21 @ ( sK34_SY460 @ SV21 @ SV69 @ SV48 ) @ ( sK35_SY663 @ SV48 @ SV69 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK34_SY460 @ SV21 @ SV69 @ SV48 ) @ ( sK36_SY665 @ SV48 @ SV69 @ SV21 ) ) )
= $false )
| ( ( member @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV48 )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[927]) ).
thf(952,plain,
! [SV48: $i,SV69: $i,SV21: $i,SV129: $i] :
( ( ( ! [SY672: $i,SY673: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK42_SY460 @ SV129 @ SV21 @ SV69 @ SV48 ) @ SV48 )
| ~ ( member @ SY672 @ SV69 ) )
| ~ ( member @ SY673 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ ( sK42_SY460 @ SV129 @ SV21 @ SV69 @ SV48 ) @ SY672 )
| ~ ( apply @ SV21 @ ( sK42_SY460 @ SV129 @ SV21 @ SV69 @ SV48 ) @ SY673 ) )
| ( SY672 = SY673 ) ) )
= $false )
| ( ( member @ SV129 @ SV69 )
= $false )
| ( ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV129 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[928]) ).
thf(953,plain,
! [SV92: $i,SV83: $i,SV50: $i,SV70: $i,SV90: $i,SV121: $i,SV116: $i,SV23: $i] :
( ( ( ~ ( apply @ SV23 @ SV116 @ SV121 )
| ~ ! [SY653: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY653 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SY653 ) )
| ~ ( apply @ SV50 @ SY653 @ SV121 ) ) )
= $true )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[929]) ).
thf(954,plain,
! [SV92: $i,SV83: $i,SV23: $i,SV121: $i,SV50: $i,SV116: $i,SV70: $i,SV90: $i] :
( ( ( ~ ~ ! [SY654: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY654 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SY654 ) )
| ~ ( apply @ SV50 @ SY654 @ SV121 ) )
| ( apply @ SV23 @ SV116 @ SV121 ) )
= $true )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[930]) ).
thf(955,plain,
! [SV83: $i,SV92: $i,SV23: $i,SV50: $i,SV70: $i,SV90: $i] :
( ( ( ~ ! [SY656: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY656 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY656 ) )
| ~ ( apply @ SV50 @ SY656 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $true )
| ( ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[931]) ).
thf(956,plain,
! [SV83: $i,SV92: $i,SV23: $i,SV50: $i,SV70: $i,SV90: $i,SV132: $i] :
( ( ( ~ ~ ( ~ ( member @ SV132 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV132 ) )
| ~ ( apply @ SV50 @ SV132 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY656: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY656 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY656 ) )
| ~ ( apply @ SV50 @ SY656 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
| ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[933]) ).
thf(957,plain,
! [SV84: $i,SV52: $i,SV93: $i,SV25: $i,SV94: $i,SV72: $i,SV91: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK39_SY600 @ SV91 @ SV72 @ SV94 @ SV25 @ SV93 @ SV52 @ SV84 ) @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ ( sK39_SY600 @ SV91 @ SV72 @ SV94 @ SV25 @ SV93 @ SV52 @ SV84 ) ) )
| ~ ( apply @ SV25 @ ( sK39_SY600 @ SV91 @ SV72 @ SV94 @ SV25 @ SV93 @ SV52 @ SV84 ) @ SV94 ) )
= $false )
| ( ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
= $false )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[934]) ).
thf(958,plain,
! [SV91: $i,SV72: $i,SV94: $i,SV25: $i,SV93: $i,SV52: $i,SV84: $i,SV133: $i] :
( ( ( ~ ~ ( ~ ( member @ SV133 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SV133 ) )
| ~ ( apply @ SV25 @ SV133 @ SV94 ) )
= $true )
| ( ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
= $true )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[935]) ).
thf(959,plain,
! [SV74: $i,SV54: $i,SV104: $i,SV109: $i,SV100: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV27 @ SV100 @ SV109 )
| ~ ( apply @ SV27 @ SV104 @ SV109 ) ) )
= $true )
| ( ( SV100 = SV104 )
= $true )
| ( ( member @ SV104 @ SV54 )
= $false )
| ( ( member @ SV100 @ SV54 )
= $false )
| ( ( member @ SV109 @ SV74 )
= $false )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[936]) ).
thf(960,plain,
! [SV55: $i,SV28: $i,SV110: $i,SV75: $i,SV105: $i,SV85: $i,SV117: $i] :
( ( ( member @ SV117 @ SV85 )
= $false )
| ( ( member @ SV105 @ SV75 )
= $false )
| ( ( member @ SV110 @ SV85 )
= $false )
| ( ( ~ ~ ( ~ ( apply @ SV28 @ SV105 @ SV110 )
| ~ ( apply @ SV55 @ SV105 @ SV117 ) )
| ( SV110 = SV117 ) )
= $true )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[937]) ).
thf(961,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV122: $i,SV118: $i,SV78: $i,SV112: $i,SV33: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV106 @ SV33 )
| ~ ( member @ SV112 @ SV78 ) )
| ~ ( member @ SV118 @ SV33 ) )
| ~ ( member @ SV122 @ SV78 ) )
| ~ ( apply @ SV59 @ SV106 @ SV118 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV106 @ SV112 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV118 @ SV122 ) )
= $true )
| ( ( apply @ SV87 @ SV122 @ SV112 )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[938]) ).
thf(962,plain,
! [SV33: $i,SV78: $i,SV59: $i,SV6: $i,SV87: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ SV33 )
| ~ ( member @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
| ~ ( member @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV33 ) )
| ~ ( member @ ( sK30_SY649 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
| ~ ( apply @ SV59 @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) ) )
= $false )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[939]) ).
thf(963,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV131: $i,SV130: $i,SV79: $i,SV127: $i,SV34: $i,SV123: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV123 @ SV34 )
| ~ ( member @ SV127 @ SV79 ) )
| ~ ( member @ SV130 @ SV34 ) )
| ~ ( member @ SV131 @ SV79 ) )
| ~ ( apply @ SV7 @ SV123 @ SV127 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV130 @ SV131 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV60 @ SV123 @ SV130 )
| ( apply @ SV88 @ SV127 @ SV131 ) )
| ~ ( ~ ( apply @ SV88 @ SV127 @ SV131 )
| ( apply @ SV60 @ SV123 @ SV130 ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[941]) ).
thf(964,plain,
! [SV34: $i,SV79: $i,SV7: $i,SV60: $i,SV88: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ SV34 )
| ~ ( member @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 ) )
| ~ ( member @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV34 ) )
| ~ ( member @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 ) )
| ~ ( apply @ SV7 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) )
| ~ ( apply @ SV7 @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) ) )
= $false )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[942]) ).
thf(965,plain,
! [SV34: $i,SV79: $i,SV7: $i,SV88: $i,SV60: $i] :
( ( ( ~ ( ~ ( ~ ( apply @ SV60 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
| ( apply @ SV88 @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) )
| ~ ( ~ ( apply @ SV88 @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
| ( apply @ SV60 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) ) ) )
= $false )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[942]) ).
thf(966,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV124: $i,SV119: $i,SV80: $i,SV113: $i,SV36: $i,SV107: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV107 @ SV36 )
| ~ ( member @ SV113 @ SV80 ) )
| ~ ( member @ SV119 @ SV36 ) )
| ~ ( member @ SV124 @ SV80 ) )
| ~ ( apply @ SV62 @ SV107 @ SV119 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV107 @ SV113 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV119 @ SV124 ) )
= $true )
| ( ( apply @ SV89 @ SV113 @ SV124 )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[943]) ).
thf(967,plain,
! [SV36: $i,SV80: $i,SV62: $i,SV9: $i,SV89: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ SV36 )
| ~ ( member @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
| ~ ( member @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV36 ) )
| ~ ( member @ ( sK31_SY651 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
| ~ ( apply @ SV62 @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) ) )
= $false )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[944]) ).
thf(968,plain,
! [SV21: $i,SV125: $i,SV48: $i,SV115: $i,SV69: $i,SV120: $i] :
( ( ( member @ SV120 @ SV69 )
= $false )
| ( ( member @ SV115 @ SV48 )
= $false )
| ( ( ~ ( member @ SV125 @ SV69 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV21 @ SV115 @ SV120 )
| ~ ( apply @ SV21 @ SV115 @ SV125 ) )
| ( SV120 = SV125 ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[948]) ).
thf(969,plain,
! [SV48: $i,SV69: $i,SV21: $i] :
( ( ( ~ ( ~ ( member @ ( sK34_SY460 @ SV21 @ SV69 @ SV48 ) @ SV48 )
| ~ ( member @ ( sK35_SY663 @ SV48 @ SV69 @ SV21 ) @ SV69 ) ) )
= $true )
| ( ( member @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV48 )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[949]) ).
thf(970,plain,
! [SV21: $i,SV69: $i,SV48: $i] :
( ( ( member @ ( sK36_SY665 @ SV48 @ SV69 @ SV21 ) @ SV69 )
= $true )
| ( ( member @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV48 )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[950]) ).
thf(971,plain,
! [SV48: $i,SV69: $i,SV21: $i] :
( ( ( ~ ( apply @ SV21 @ ( sK34_SY460 @ SV21 @ SV69 @ SV48 ) @ ( sK35_SY663 @ SV48 @ SV69 @ SV21 ) ) )
= $false )
| ( ( member @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV48 )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[951]) ).
thf(972,plain,
! [SV48: $i,SV69: $i,SV21: $i] :
( ( ( ~ ( apply @ SV21 @ ( sK34_SY460 @ SV21 @ SV69 @ SV48 ) @ ( sK36_SY665 @ SV48 @ SV69 @ SV21 ) ) )
= $false )
| ( ( member @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV48 )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[951]) ).
thf(973,plain,
! [SV48: $i,SV69: $i,SV21: $i,SV129: $i] :
( ( ( ! [SY674: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK42_SY460 @ SV129 @ SV21 @ SV69 @ SV48 ) @ SV48 )
| ~ ( member @ ( sK43_SY672 @ SV48 @ SV69 @ SV21 @ SV129 ) @ SV69 ) )
| ~ ( member @ SY674 @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ ( sK42_SY460 @ SV129 @ SV21 @ SV69 @ SV48 ) @ ( sK43_SY672 @ SV48 @ SV69 @ SV21 @ SV129 ) )
| ~ ( apply @ SV21 @ ( sK42_SY460 @ SV129 @ SV21 @ SV69 @ SV48 ) @ SY674 ) )
| ( ( sK43_SY672 @ SV48 @ SV69 @ SV21 @ SV129 )
= SY674 ) ) )
= $false )
| ( ( member @ SV129 @ SV69 )
= $false )
| ( ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV129 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[952]) ).
thf(974,plain,
! [SV92: $i,SV83: $i,SV50: $i,SV70: $i,SV90: $i,SV121: $i,SV116: $i,SV23: $i] :
( ( ( ~ ( apply @ SV23 @ SV116 @ SV121 ) )
= $true )
| ( ( ~ ! [SY653: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY653 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SY653 ) )
| ~ ( apply @ SV50 @ SY653 @ SV121 ) ) )
= $true )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[953]) ).
thf(975,plain,
! [SV92: $i,SV83: $i,SV23: $i,SV121: $i,SV50: $i,SV116: $i,SV70: $i,SV90: $i] :
( ( ( ~ ~ ! [SY654: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY654 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SY654 ) )
| ~ ( apply @ SV50 @ SY654 @ SV121 ) ) )
= $true )
| ( ( apply @ SV23 @ SV116 @ SV121 )
= $true )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[954]) ).
thf(976,plain,
! [SV83: $i,SV92: $i,SV23: $i,SV50: $i,SV70: $i,SV90: $i] :
( ( ( ! [SY656: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY656 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY656 ) )
| ~ ( apply @ SV50 @ SY656 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $false )
| ( ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[955]) ).
thf(977,plain,
! [SV83: $i,SV92: $i,SV23: $i,SV50: $i,SV70: $i,SV90: $i,SV132: $i] :
( ( ( ~ ~ ( ~ ( member @ SV132 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV132 ) ) )
= $true )
| ( ( ~ ( apply @ SV50 @ SV132 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY656: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY656 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY656 ) )
| ~ ( apply @ SV50 @ SY656 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
| ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[956]) ).
thf(978,plain,
! [SV84: $i,SV52: $i,SV93: $i,SV25: $i,SV94: $i,SV72: $i,SV91: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK39_SY600 @ SV91 @ SV72 @ SV94 @ SV25 @ SV93 @ SV52 @ SV84 ) @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ ( sK39_SY600 @ SV91 @ SV72 @ SV94 @ SV25 @ SV93 @ SV52 @ SV84 ) ) ) )
= $false )
| ( ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
= $false )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[957]) ).
thf(979,plain,
! [SV84: $i,SV52: $i,SV93: $i,SV94: $i,SV72: $i,SV91: $i,SV25: $i] :
( ( ( ~ ( apply @ SV25 @ ( sK39_SY600 @ SV91 @ SV72 @ SV94 @ SV25 @ SV93 @ SV52 @ SV84 ) @ SV94 ) )
= $false )
| ( ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
= $false )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[957]) ).
thf(980,plain,
! [SV91: $i,SV72: $i,SV94: $i,SV25: $i,SV93: $i,SV52: $i,SV84: $i,SV133: $i] :
( ( ( ~ ~ ( ~ ( member @ SV133 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SV133 ) ) )
= $true )
| ( ( ~ ( apply @ SV25 @ SV133 @ SV94 ) )
= $true )
| ( ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
= $true )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[958]) ).
thf(981,plain,
! [SV74: $i,SV54: $i,SV104: $i,SV109: $i,SV100: $i,SV27: $i] :
( ( ( ~ ( ~ ( apply @ SV27 @ SV100 @ SV109 )
| ~ ( apply @ SV27 @ SV104 @ SV109 ) ) )
= $false )
| ( ( SV100 = SV104 )
= $true )
| ( ( member @ SV104 @ SV54 )
= $false )
| ( ( member @ SV100 @ SV54 )
= $false )
| ( ( member @ SV109 @ SV74 )
= $false )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[959]) ).
thf(982,plain,
! [SV75: $i,SV85: $i,SV117: $i,SV55: $i,SV110: $i,SV105: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV28 @ SV105 @ SV110 )
| ~ ( apply @ SV55 @ SV105 @ SV117 ) ) )
= $true )
| ( ( SV110 = SV117 )
= $true )
| ( ( member @ SV110 @ SV85 )
= $false )
| ( ( member @ SV105 @ SV75 )
= $false )
| ( ( member @ SV117 @ SV85 )
= $false )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[960]) ).
thf(983,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV122: $i,SV118: $i,SV78: $i,SV112: $i,SV33: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV106 @ SV33 )
| ~ ( member @ SV112 @ SV78 ) )
| ~ ( member @ SV118 @ SV33 ) )
| ~ ( member @ SV122 @ SV78 ) ) )
= $true )
| ( ( ~ ( apply @ SV59 @ SV106 @ SV118 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV106 @ SV112 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV118 @ SV122 ) )
= $true )
| ( ( apply @ SV87 @ SV122 @ SV112 )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[961]) ).
thf(984,plain,
! [SV33: $i,SV78: $i,SV59: $i,SV6: $i,SV87: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ SV33 )
| ~ ( member @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
| ~ ( member @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV33 ) )
| ~ ( member @ ( sK30_SY649 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) ) )
= $false )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[962]) ).
thf(985,plain,
! [SV33: $i,SV78: $i,SV6: $i,SV87: $i,SV59: $i] :
( ( ( ~ ( apply @ SV59 @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) ) )
= $false )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[962]) ).
thf(986,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV131: $i,SV130: $i,SV79: $i,SV127: $i,SV34: $i,SV123: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV123 @ SV34 )
| ~ ( member @ SV127 @ SV79 ) )
| ~ ( member @ SV130 @ SV34 ) )
| ~ ( member @ SV131 @ SV79 ) ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV123 @ SV127 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV130 @ SV131 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV60 @ SV123 @ SV130 )
| ( apply @ SV88 @ SV127 @ SV131 ) )
| ~ ( ~ ( apply @ SV88 @ SV127 @ SV131 )
| ( apply @ SV60 @ SV123 @ SV130 ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[963]) ).
thf(987,plain,
! [SV34: $i,SV79: $i,SV7: $i,SV60: $i,SV88: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ SV34 )
| ~ ( member @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 ) )
| ~ ( member @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV34 ) )
| ~ ( member @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 ) )
| ~ ( apply @ SV7 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) )
| ~ ( apply @ SV7 @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) ) )
= $true )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[964]) ).
thf(988,plain,
! [SV34: $i,SV79: $i,SV7: $i,SV88: $i,SV60: $i] :
( ( ( ~ ( ~ ( apply @ SV60 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
| ( apply @ SV88 @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) )
| ~ ( ~ ( apply @ SV88 @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
| ( apply @ SV60 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) ) )
= $true )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[965]) ).
thf(989,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV124: $i,SV119: $i,SV80: $i,SV113: $i,SV36: $i,SV107: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV107 @ SV36 )
| ~ ( member @ SV113 @ SV80 ) )
| ~ ( member @ SV119 @ SV36 ) )
| ~ ( member @ SV124 @ SV80 ) ) )
= $true )
| ( ( ~ ( apply @ SV62 @ SV107 @ SV119 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV107 @ SV113 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV119 @ SV124 ) )
= $true )
| ( ( apply @ SV89 @ SV113 @ SV124 )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[966]) ).
thf(990,plain,
! [SV36: $i,SV80: $i,SV62: $i,SV9: $i,SV89: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ SV36 )
| ~ ( member @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
| ~ ( member @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV36 ) )
| ~ ( member @ ( sK31_SY651 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) ) )
= $false )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[967]) ).
thf(991,plain,
! [SV36: $i,SV80: $i,SV9: $i,SV89: $i,SV62: $i] :
( ( ( ~ ( apply @ SV62 @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) ) )
= $false )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[967]) ).
thf(992,plain,
! [SV21: $i,SV120: $i,SV48: $i,SV115: $i,SV69: $i,SV125: $i] :
( ( ( member @ SV125 @ SV69 )
= $false )
| ( ( member @ SV115 @ SV48 )
= $false )
| ( ( member @ SV120 @ SV69 )
= $false )
| ( ( ~ ~ ( ~ ( apply @ SV21 @ SV115 @ SV120 )
| ~ ( apply @ SV21 @ SV115 @ SV125 ) )
| ( SV120 = SV125 ) )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[968]) ).
thf(993,plain,
! [SV48: $i,SV69: $i,SV21: $i] :
( ( ( ~ ( member @ ( sK34_SY460 @ SV21 @ SV69 @ SV48 ) @ SV48 )
| ~ ( member @ ( sK35_SY663 @ SV48 @ SV69 @ SV21 ) @ SV69 ) )
= $false )
| ( ( member @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV48 )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[969]) ).
thf(994,plain,
! [SV48: $i,SV69: $i,SV21: $i] :
( ( ( apply @ SV21 @ ( sK34_SY460 @ SV21 @ SV69 @ SV48 ) @ ( sK35_SY663 @ SV48 @ SV69 @ SV21 ) )
= $true )
| ( ( member @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV48 )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[971]) ).
thf(995,plain,
! [SV48: $i,SV69: $i,SV21: $i] :
( ( ( apply @ SV21 @ ( sK34_SY460 @ SV21 @ SV69 @ SV48 ) @ ( sK36_SY665 @ SV48 @ SV69 @ SV21 ) )
= $true )
| ( ( member @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV48 )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[972]) ).
thf(996,plain,
! [SV48: $i,SV69: $i,SV21: $i,SV129: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK42_SY460 @ SV129 @ SV21 @ SV69 @ SV48 ) @ SV48 )
| ~ ( member @ ( sK43_SY672 @ SV48 @ SV69 @ SV21 @ SV129 ) @ SV69 ) )
| ~ ( member @ ( sK44_SY674 @ SV48 @ SV69 @ SV21 @ SV129 ) @ SV69 ) )
| ~ ~ ( ~ ( apply @ SV21 @ ( sK42_SY460 @ SV129 @ SV21 @ SV69 @ SV48 ) @ ( sK43_SY672 @ SV48 @ SV69 @ SV21 @ SV129 ) )
| ~ ( apply @ SV21 @ ( sK42_SY460 @ SV129 @ SV21 @ SV69 @ SV48 ) @ ( sK44_SY674 @ SV48 @ SV69 @ SV21 @ SV129 ) ) )
| ( ( sK43_SY672 @ SV48 @ SV69 @ SV21 @ SV129 )
= ( sK44_SY674 @ SV48 @ SV69 @ SV21 @ SV129 ) ) )
= $false )
| ( ( member @ SV129 @ SV69 )
= $false )
| ( ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV129 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[973]) ).
thf(997,plain,
! [SV92: $i,SV83: $i,SV50: $i,SV70: $i,SV90: $i,SV121: $i,SV116: $i,SV23: $i] :
( ( ( apply @ SV23 @ SV116 @ SV121 )
= $false )
| ( ( ~ ! [SY653: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY653 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SY653 ) )
| ~ ( apply @ SV50 @ SY653 @ SV121 ) ) )
= $true )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[974]) ).
thf(998,plain,
! [SV92: $i,SV83: $i,SV23: $i,SV121: $i,SV50: $i,SV116: $i,SV70: $i,SV90: $i] :
( ( ( ~ ! [SY654: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY654 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SY654 ) )
| ~ ( apply @ SV50 @ SY654 @ SV121 ) ) )
= $false )
| ( ( apply @ SV23 @ SV116 @ SV121 )
= $true )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[975]) ).
thf(999,plain,
! [SV90: $i,SV70: $i,SV50: $i,SV23: $i,SV92: $i,SV83: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK45_SY656 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK45_SY656 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) ) )
| ~ ( apply @ SV50 @ ( sK45_SY656 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $false )
| ( ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[976]) ).
thf(1000,plain,
! [SV83: $i,SV92: $i,SV23: $i,SV50: $i,SV70: $i,SV90: $i,SV132: $i] :
( ( ( ~ ( ~ ( member @ SV132 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV132 ) ) )
= $false )
| ( ( ~ ( apply @ SV50 @ SV132 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY656: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY656 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY656 ) )
| ~ ( apply @ SV50 @ SY656 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
| ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[977]) ).
thf(1001,plain,
! [SV84: $i,SV52: $i,SV93: $i,SV25: $i,SV94: $i,SV72: $i,SV91: $i] :
( ( ( ~ ( ~ ( member @ ( sK39_SY600 @ SV91 @ SV72 @ SV94 @ SV25 @ SV93 @ SV52 @ SV84 ) @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ ( sK39_SY600 @ SV91 @ SV72 @ SV94 @ SV25 @ SV93 @ SV52 @ SV84 ) ) ) )
= $true )
| ( ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
= $false )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[978]) ).
thf(1002,plain,
! [SV84: $i,SV52: $i,SV93: $i,SV94: $i,SV72: $i,SV91: $i,SV25: $i] :
( ( ( apply @ SV25 @ ( sK39_SY600 @ SV91 @ SV72 @ SV94 @ SV25 @ SV93 @ SV52 @ SV84 ) @ SV94 )
= $true )
| ( ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
= $false )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[979]) ).
thf(1003,plain,
! [SV91: $i,SV72: $i,SV94: $i,SV25: $i,SV93: $i,SV52: $i,SV84: $i,SV133: $i] :
( ( ( ~ ( ~ ( member @ SV133 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SV133 ) ) )
= $false )
| ( ( ~ ( apply @ SV25 @ SV133 @ SV94 ) )
= $true )
| ( ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
= $true )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[980]) ).
thf(1004,plain,
! [SV74: $i,SV54: $i,SV104: $i,SV109: $i,SV100: $i,SV27: $i] :
( ( ( ~ ( apply @ SV27 @ SV100 @ SV109 )
| ~ ( apply @ SV27 @ SV104 @ SV109 ) )
= $true )
| ( ( SV100 = SV104 )
= $true )
| ( ( member @ SV104 @ SV54 )
= $false )
| ( ( member @ SV100 @ SV54 )
= $false )
| ( ( member @ SV109 @ SV74 )
= $false )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[981]) ).
thf(1005,plain,
! [SV75: $i,SV85: $i,SV117: $i,SV55: $i,SV110: $i,SV105: $i,SV28: $i] :
( ( ( ~ ( ~ ( apply @ SV28 @ SV105 @ SV110 )
| ~ ( apply @ SV55 @ SV105 @ SV117 ) ) )
= $false )
| ( ( SV110 = SV117 )
= $true )
| ( ( member @ SV110 @ SV85 )
= $false )
| ( ( member @ SV105 @ SV75 )
= $false )
| ( ( member @ SV117 @ SV85 )
= $false )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1006,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV122: $i,SV118: $i,SV78: $i,SV112: $i,SV33: $i,SV106: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV106 @ SV33 )
| ~ ( member @ SV112 @ SV78 ) )
| ~ ( member @ SV118 @ SV33 ) )
| ~ ( member @ SV122 @ SV78 ) ) )
= $false )
| ( ( ~ ( apply @ SV59 @ SV106 @ SV118 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV106 @ SV112 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV118 @ SV122 ) )
= $true )
| ( ( apply @ SV87 @ SV122 @ SV112 )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[983]) ).
thf(1007,plain,
! [SV33: $i,SV78: $i,SV59: $i,SV6: $i,SV87: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ SV33 )
| ~ ( member @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
| ~ ( member @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV33 ) )
| ~ ( member @ ( sK30_SY649 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) ) )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[984]) ).
thf(1008,plain,
! [SV33: $i,SV78: $i,SV6: $i,SV87: $i,SV59: $i] :
( ( ( apply @ SV59 @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[985]) ).
thf(1009,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV131: $i,SV130: $i,SV79: $i,SV127: $i,SV34: $i,SV123: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV123 @ SV34 )
| ~ ( member @ SV127 @ SV79 ) )
| ~ ( member @ SV130 @ SV34 ) )
| ~ ( member @ SV131 @ SV79 ) ) )
= $false )
| ( ( ~ ( apply @ SV7 @ SV123 @ SV127 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV130 @ SV131 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV60 @ SV123 @ SV130 )
| ( apply @ SV88 @ SV127 @ SV131 ) )
| ~ ( ~ ( apply @ SV88 @ SV127 @ SV131 )
| ( apply @ SV60 @ SV123 @ SV130 ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[986]) ).
thf(1010,plain,
! [SV34: $i,SV79: $i,SV7: $i,SV60: $i,SV88: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ SV34 )
| ~ ( member @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 ) )
| ~ ( member @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV34 ) )
| ~ ( member @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 ) )
| ~ ( apply @ SV7 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) )
| ~ ( apply @ SV7 @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) )
= $false )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[987]) ).
thf(1011,plain,
! [SV34: $i,SV79: $i,SV7: $i,SV88: $i,SV60: $i] :
( ( ( ~ ( ~ ( apply @ SV60 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
| ( apply @ SV88 @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) ) )
= $true )
| ( ( ~ ( ~ ( apply @ SV88 @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
| ( apply @ SV60 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) ) )
= $true )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[988]) ).
thf(1012,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV124: $i,SV119: $i,SV80: $i,SV113: $i,SV36: $i,SV107: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV107 @ SV36 )
| ~ ( member @ SV113 @ SV80 ) )
| ~ ( member @ SV119 @ SV36 ) )
| ~ ( member @ SV124 @ SV80 ) ) )
= $false )
| ( ( ~ ( apply @ SV62 @ SV107 @ SV119 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV107 @ SV113 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV119 @ SV124 ) )
= $true )
| ( ( apply @ SV89 @ SV113 @ SV124 )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(1013,plain,
! [SV36: $i,SV80: $i,SV62: $i,SV9: $i,SV89: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ SV36 )
| ~ ( member @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
| ~ ( member @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV36 ) )
| ~ ( member @ ( sK31_SY651 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) ) )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[990]) ).
thf(1014,plain,
! [SV36: $i,SV80: $i,SV9: $i,SV89: $i,SV62: $i] :
( ( ( apply @ SV62 @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[991]) ).
thf(1015,plain,
! [SV48: $i,SV69: $i,SV125: $i,SV120: $i,SV115: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV21 @ SV115 @ SV120 )
| ~ ( apply @ SV21 @ SV115 @ SV125 ) ) )
= $true )
| ( ( SV120 = SV125 )
= $true )
| ( ( member @ SV120 @ SV69 )
= $false )
| ( ( member @ SV115 @ SV48 )
= $false )
| ( ( member @ SV125 @ SV69 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[992]) ).
thf(1016,plain,
! [SV48: $i,SV69: $i,SV21: $i] :
( ( ( ~ ( member @ ( sK34_SY460 @ SV21 @ SV69 @ SV48 ) @ SV48 ) )
= $false )
| ( ( member @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV48 )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[993]) ).
thf(1017,plain,
! [SV21: $i,SV69: $i,SV48: $i] :
( ( ( ~ ( member @ ( sK35_SY663 @ SV48 @ SV69 @ SV21 ) @ SV69 ) )
= $false )
| ( ( member @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV48 )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[993]) ).
thf(1018,plain,
! [SV48: $i,SV69: $i,SV21: $i,SV129: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK42_SY460 @ SV129 @ SV21 @ SV69 @ SV48 ) @ SV48 )
| ~ ( member @ ( sK43_SY672 @ SV48 @ SV69 @ SV21 @ SV129 ) @ SV69 ) )
| ~ ( member @ ( sK44_SY674 @ SV48 @ SV69 @ SV21 @ SV129 ) @ SV69 ) ) )
= $false )
| ( ( member @ SV129 @ SV69 )
= $false )
| ( ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV129 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[996]) ).
thf(1019,plain,
! [SV48: $i,SV69: $i,SV129: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV21 @ ( sK42_SY460 @ SV129 @ SV21 @ SV69 @ SV48 ) @ ( sK43_SY672 @ SV48 @ SV69 @ SV21 @ SV129 ) )
| ~ ( apply @ SV21 @ ( sK42_SY460 @ SV129 @ SV21 @ SV69 @ SV48 ) @ ( sK44_SY674 @ SV48 @ SV69 @ SV21 @ SV129 ) ) )
| ( ( sK43_SY672 @ SV48 @ SV69 @ SV21 @ SV129 )
= ( sK44_SY674 @ SV48 @ SV69 @ SV21 @ SV129 ) ) )
= $false )
| ( ( member @ SV129 @ SV69 )
= $false )
| ( ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV129 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[996]) ).
thf(1020,plain,
! [SV92: $i,SV83: $i,SV23: $i,SV121: $i,SV50: $i,SV116: $i,SV70: $i,SV90: $i] :
( ( ( ! [SY653: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY653 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SY653 ) )
| ~ ( apply @ SV50 @ SY653 @ SV121 ) ) )
= $false )
| ( ( apply @ SV23 @ SV116 @ SV121 )
= $false )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[997]) ).
thf(1021,plain,
! [SV92: $i,SV83: $i,SV23: $i,SV121: $i,SV50: $i,SV116: $i,SV70: $i,SV90: $i] :
( ( ( ! [SY654: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY654 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SY654 ) )
| ~ ( apply @ SV50 @ SY654 @ SV121 ) ) )
= $true )
| ( ( apply @ SV23 @ SV116 @ SV121 )
= $true )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[998]) ).
thf(1022,plain,
! [SV90: $i,SV70: $i,SV50: $i,SV23: $i,SV92: $i,SV83: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK45_SY656 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK45_SY656 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) ) )
| ~ ( apply @ SV50 @ ( sK45_SY656 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $true )
| ( ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[999]) ).
thf(1023,plain,
! [SV83: $i,SV92: $i,SV23: $i,SV50: $i,SV70: $i,SV90: $i,SV132: $i] :
( ( ( ~ ( member @ SV132 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV132 ) )
= $true )
| ( ( ~ ( apply @ SV50 @ SV132 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY656: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY656 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY656 ) )
| ~ ( apply @ SV50 @ SY656 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
| ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1000]) ).
thf(1024,plain,
! [SV84: $i,SV52: $i,SV93: $i,SV25: $i,SV94: $i,SV72: $i,SV91: $i] :
( ( ( ~ ( member @ ( sK39_SY600 @ SV91 @ SV72 @ SV94 @ SV25 @ SV93 @ SV52 @ SV84 ) @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ ( sK39_SY600 @ SV91 @ SV72 @ SV94 @ SV25 @ SV93 @ SV52 @ SV84 ) ) )
= $false )
| ( ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
= $false )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1001]) ).
thf(1025,plain,
! [SV91: $i,SV72: $i,SV94: $i,SV25: $i,SV93: $i,SV52: $i,SV84: $i,SV133: $i] :
( ( ( ~ ( member @ SV133 @ SV84 )
| ~ ( apply @ SV52 @ SV93 @ SV133 ) )
= $true )
| ( ( ~ ( apply @ SV25 @ SV133 @ SV94 ) )
= $true )
| ( ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
= $true )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1003]) ).
thf(1026,plain,
! [SV74: $i,SV54: $i,SV104: $i,SV109: $i,SV100: $i,SV27: $i] :
( ( ( ~ ( apply @ SV27 @ SV100 @ SV109 ) )
= $true )
| ( ( ~ ( apply @ SV27 @ SV104 @ SV109 ) )
= $true )
| ( ( SV100 = SV104 )
= $true )
| ( ( member @ SV104 @ SV54 )
= $false )
| ( ( member @ SV100 @ SV54 )
= $false )
| ( ( member @ SV109 @ SV74 )
= $false )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1004]) ).
thf(1027,plain,
! [SV75: $i,SV85: $i,SV117: $i,SV55: $i,SV110: $i,SV105: $i,SV28: $i] :
( ( ( ~ ( apply @ SV28 @ SV105 @ SV110 )
| ~ ( apply @ SV55 @ SV105 @ SV117 ) )
= $true )
| ( ( SV110 = SV117 )
= $true )
| ( ( member @ SV110 @ SV85 )
= $false )
| ( ( member @ SV105 @ SV75 )
= $false )
| ( ( member @ SV117 @ SV85 )
= $false )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1005]) ).
thf(1028,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV122: $i,SV118: $i,SV78: $i,SV112: $i,SV33: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV106 @ SV33 )
| ~ ( member @ SV112 @ SV78 ) )
| ~ ( member @ SV118 @ SV33 ) )
| ~ ( member @ SV122 @ SV78 ) )
= $true )
| ( ( ~ ( apply @ SV59 @ SV106 @ SV118 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV106 @ SV112 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV118 @ SV122 ) )
= $true )
| ( ( apply @ SV87 @ SV122 @ SV112 )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1006]) ).
thf(1029,plain,
! [SV33: $i,SV78: $i,SV59: $i,SV6: $i,SV87: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ SV33 )
| ~ ( member @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
| ~ ( member @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV33 ) )
| ~ ( member @ ( sK30_SY649 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
= $false )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1007]) ).
thf(1030,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV131: $i,SV130: $i,SV79: $i,SV127: $i,SV34: $i,SV123: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV123 @ SV34 )
| ~ ( member @ SV127 @ SV79 ) )
| ~ ( member @ SV130 @ SV34 ) )
| ~ ( member @ SV131 @ SV79 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV123 @ SV127 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV130 @ SV131 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV60 @ SV123 @ SV130 )
| ( apply @ SV88 @ SV127 @ SV131 ) )
| ~ ( ~ ( apply @ SV88 @ SV127 @ SV131 )
| ( apply @ SV60 @ SV123 @ SV130 ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1009]) ).
thf(1031,plain,
! [SV34: $i,SV79: $i,SV7: $i,SV60: $i,SV88: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ SV34 )
| ~ ( member @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 ) )
| ~ ( member @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV34 ) )
| ~ ( member @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 ) )
| ~ ( apply @ SV7 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) ) )
= $false )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1010]) ).
thf(1032,plain,
! [SV88: $i,SV60: $i,SV79: $i,SV34: $i,SV7: $i] :
( ( ( ~ ( apply @ SV7 @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) )
= $false )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1010]) ).
thf(1033,plain,
! [SV34: $i,SV79: $i,SV7: $i,SV88: $i,SV60: $i] :
( ( ( ~ ( apply @ SV60 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
| ( apply @ SV88 @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) )
= $false )
| ( ( ~ ( ~ ( apply @ SV88 @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
| ( apply @ SV60 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) ) )
= $true )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1011]) ).
thf(1034,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV124: $i,SV119: $i,SV80: $i,SV113: $i,SV36: $i,SV107: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV107 @ SV36 )
| ~ ( member @ SV113 @ SV80 ) )
| ~ ( member @ SV119 @ SV36 ) )
| ~ ( member @ SV124 @ SV80 ) )
= $true )
| ( ( ~ ( apply @ SV62 @ SV107 @ SV119 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV107 @ SV113 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV119 @ SV124 ) )
= $true )
| ( ( apply @ SV89 @ SV113 @ SV124 )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1012]) ).
thf(1035,plain,
! [SV36: $i,SV80: $i,SV62: $i,SV9: $i,SV89: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ SV36 )
| ~ ( member @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
| ~ ( member @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV36 ) )
| ~ ( member @ ( sK31_SY651 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
= $false )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1013]) ).
thf(1036,plain,
! [SV48: $i,SV69: $i,SV125: $i,SV120: $i,SV115: $i,SV21: $i] :
( ( ( ~ ( ~ ( apply @ SV21 @ SV115 @ SV120 )
| ~ ( apply @ SV21 @ SV115 @ SV125 ) ) )
= $false )
| ( ( SV120 = SV125 )
= $true )
| ( ( member @ SV120 @ SV69 )
= $false )
| ( ( member @ SV115 @ SV48 )
= $false )
| ( ( member @ SV125 @ SV69 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1037,plain,
! [SV48: $i,SV69: $i,SV21: $i] :
( ( ( member @ ( sK34_SY460 @ SV21 @ SV69 @ SV48 ) @ SV48 )
= $true )
| ( ( member @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV48 )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1016]) ).
thf(1038,plain,
! [SV21: $i,SV69: $i,SV48: $i] :
( ( ( member @ ( sK35_SY663 @ SV48 @ SV69 @ SV21 ) @ SV69 )
= $true )
| ( ( member @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV48 )
= $true )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1017]) ).
thf(1039,plain,
! [SV48: $i,SV69: $i,SV21: $i,SV129: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK42_SY460 @ SV129 @ SV21 @ SV69 @ SV48 ) @ SV48 )
| ~ ( member @ ( sK43_SY672 @ SV48 @ SV69 @ SV21 @ SV129 ) @ SV69 ) )
| ~ ( member @ ( sK44_SY674 @ SV48 @ SV69 @ SV21 @ SV129 ) @ SV69 ) ) )
= $true )
| ( ( member @ SV129 @ SV69 )
= $false )
| ( ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV129 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1018]) ).
thf(1040,plain,
! [SV48: $i,SV69: $i,SV129: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV21 @ ( sK42_SY460 @ SV129 @ SV21 @ SV69 @ SV48 ) @ ( sK43_SY672 @ SV48 @ SV69 @ SV21 @ SV129 ) )
| ~ ( apply @ SV21 @ ( sK42_SY460 @ SV129 @ SV21 @ SV69 @ SV48 ) @ ( sK44_SY674 @ SV48 @ SV69 @ SV21 @ SV129 ) ) ) )
= $false )
| ( ( member @ SV129 @ SV69 )
= $false )
| ( ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV129 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1019]) ).
thf(1041,plain,
! [SV129: $i,SV21: $i,SV69: $i,SV48: $i] :
( ( ( ( sK43_SY672 @ SV48 @ SV69 @ SV21 @ SV129 )
= ( sK44_SY674 @ SV48 @ SV69 @ SV21 @ SV129 ) )
= $false )
| ( ( member @ SV129 @ SV69 )
= $false )
| ( ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV129 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1019]) ).
thf(1042,plain,
! [SV90: $i,SV70: $i,SV116: $i,SV50: $i,SV121: $i,SV23: $i,SV83: $i,SV92: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK46_SY653 @ SV92 @ SV83 @ SV23 @ SV121 @ SV50 @ SV116 @ SV70 @ SV90 ) @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ ( sK46_SY653 @ SV92 @ SV83 @ SV23 @ SV121 @ SV50 @ SV116 @ SV70 @ SV90 ) ) )
| ~ ( apply @ SV50 @ ( sK46_SY653 @ SV92 @ SV83 @ SV23 @ SV121 @ SV50 @ SV116 @ SV70 @ SV90 ) @ SV121 ) ) )
= $false )
| ( ( apply @ SV23 @ SV116 @ SV121 )
= $false )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1020]) ).
thf(1043,plain,
! [SV92: $i,SV83: $i,SV23: $i,SV121: $i,SV50: $i,SV116: $i,SV70: $i,SV90: $i,SV134: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV134 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SV134 ) )
| ~ ( apply @ SV50 @ SV134 @ SV121 ) ) )
= $true )
| ( ( apply @ SV23 @ SV116 @ SV121 )
= $true )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1044,plain,
! [SV90: $i,SV70: $i,SV50: $i,SV23: $i,SV92: $i,SV83: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK45_SY656 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK45_SY656 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) ) )
| ~ ( apply @ SV50 @ ( sK45_SY656 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
= $false )
| ( ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1045,plain,
! [SV83: $i,SV92: $i,SV23: $i,SV50: $i,SV70: $i,SV90: $i,SV132: $i] :
( ( ( ~ ( member @ SV132 @ SV90 ) )
= $true )
| ( ( ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV132 ) )
= $true )
| ( ( ~ ( apply @ SV50 @ SV132 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY656: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY656 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY656 ) )
| ~ ( apply @ SV50 @ SY656 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
| ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1023]) ).
thf(1046,plain,
! [SV84: $i,SV52: $i,SV93: $i,SV25: $i,SV94: $i,SV72: $i,SV91: $i] :
( ( ( ~ ( member @ ( sK39_SY600 @ SV91 @ SV72 @ SV94 @ SV25 @ SV93 @ SV52 @ SV84 ) @ SV84 ) )
= $false )
| ( ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
= $false )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1024]) ).
thf(1047,plain,
! [SV84: $i,SV25: $i,SV94: $i,SV72: $i,SV91: $i,SV93: $i,SV52: $i] :
( ( ( ~ ( apply @ SV52 @ SV93 @ ( sK39_SY600 @ SV91 @ SV72 @ SV94 @ SV25 @ SV93 @ SV52 @ SV84 ) ) )
= $false )
| ( ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
= $false )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1024]) ).
thf(1048,plain,
! [SV91: $i,SV72: $i,SV94: $i,SV25: $i,SV93: $i,SV52: $i,SV84: $i,SV133: $i] :
( ( ( ~ ( member @ SV133 @ SV84 ) )
= $true )
| ( ( ~ ( apply @ SV52 @ SV93 @ SV133 ) )
= $true )
| ( ( ~ ( apply @ SV25 @ SV133 @ SV94 ) )
= $true )
| ( ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
= $true )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1025]) ).
thf(1049,plain,
! [SV74: $i,SV54: $i,SV104: $i,SV109: $i,SV100: $i,SV27: $i] :
( ( ( apply @ SV27 @ SV100 @ SV109 )
= $false )
| ( ( ~ ( apply @ SV27 @ SV104 @ SV109 ) )
= $true )
| ( ( SV100 = SV104 )
= $true )
| ( ( member @ SV104 @ SV54 )
= $false )
| ( ( member @ SV100 @ SV54 )
= $false )
| ( ( member @ SV109 @ SV74 )
= $false )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1026]) ).
thf(1050,plain,
! [SV75: $i,SV85: $i,SV117: $i,SV55: $i,SV110: $i,SV105: $i,SV28: $i] :
( ( ( ~ ( apply @ SV28 @ SV105 @ SV110 ) )
= $true )
| ( ( ~ ( apply @ SV55 @ SV105 @ SV117 ) )
= $true )
| ( ( SV110 = SV117 )
= $true )
| ( ( member @ SV110 @ SV85 )
= $false )
| ( ( member @ SV105 @ SV75 )
= $false )
| ( ( member @ SV117 @ SV85 )
= $false )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1027]) ).
thf(1051,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV122: $i,SV118: $i,SV78: $i,SV112: $i,SV33: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV106 @ SV33 )
| ~ ( member @ SV112 @ SV78 ) )
| ~ ( member @ SV118 @ SV33 ) ) )
= $true )
| ( ( ~ ( member @ SV122 @ SV78 ) )
= $true )
| ( ( ~ ( apply @ SV59 @ SV106 @ SV118 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV106 @ SV112 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV118 @ SV122 ) )
= $true )
| ( ( apply @ SV87 @ SV122 @ SV112 )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1028]) ).
thf(1052,plain,
! [SV33: $i,SV78: $i,SV59: $i,SV6: $i,SV87: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ SV33 )
| ~ ( member @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
| ~ ( member @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV33 ) ) )
= $false )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1029]) ).
thf(1053,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV78: $i,SV33: $i] :
( ( ( ~ ( member @ ( sK30_SY649 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
= $false )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1029]) ).
thf(1054,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV131: $i,SV130: $i,SV79: $i,SV127: $i,SV34: $i,SV123: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV123 @ SV34 )
| ~ ( member @ SV127 @ SV79 ) )
| ~ ( member @ SV130 @ SV34 ) ) )
= $true )
| ( ( ~ ( member @ SV131 @ SV79 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV123 @ SV127 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV130 @ SV131 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV60 @ SV123 @ SV130 )
| ( apply @ SV88 @ SV127 @ SV131 ) )
| ~ ( ~ ( apply @ SV88 @ SV127 @ SV131 )
| ( apply @ SV60 @ SV123 @ SV130 ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1030]) ).
thf(1055,plain,
! [SV34: $i,SV79: $i,SV7: $i,SV60: $i,SV88: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ SV34 )
| ~ ( member @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 ) )
| ~ ( member @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV34 ) )
| ~ ( member @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 ) )
| ~ ( apply @ SV7 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) ) )
= $true )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1031]) ).
thf(1056,plain,
! [SV88: $i,SV60: $i,SV79: $i,SV34: $i,SV7: $i] :
( ( ( apply @ SV7 @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
= $true )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1032]) ).
thf(1057,plain,
! [SV34: $i,SV79: $i,SV7: $i,SV88: $i,SV60: $i] :
( ( ( ~ ( apply @ SV60 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) )
= $false )
| ( ( ~ ( ~ ( apply @ SV88 @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
| ( apply @ SV60 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) ) )
= $true )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1033]) ).
thf(1058,plain,
! [SV60: $i,SV7: $i,SV79: $i,SV34: $i,SV88: $i] :
( ( ( apply @ SV88 @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
= $false )
| ( ( ~ ( ~ ( apply @ SV88 @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
| ( apply @ SV60 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) ) )
= $true )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1033]) ).
thf(1059,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV124: $i,SV119: $i,SV80: $i,SV113: $i,SV36: $i,SV107: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV107 @ SV36 )
| ~ ( member @ SV113 @ SV80 ) )
| ~ ( member @ SV119 @ SV36 ) ) )
= $true )
| ( ( ~ ( member @ SV124 @ SV80 ) )
= $true )
| ( ( ~ ( apply @ SV62 @ SV107 @ SV119 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV107 @ SV113 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV119 @ SV124 ) )
= $true )
| ( ( apply @ SV89 @ SV113 @ SV124 )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1034]) ).
thf(1060,plain,
! [SV36: $i,SV80: $i,SV62: $i,SV9: $i,SV89: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ SV36 )
| ~ ( member @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
| ~ ( member @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV36 ) ) )
= $false )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1035]) ).
thf(1061,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV80: $i,SV36: $i] :
( ( ( ~ ( member @ ( sK31_SY651 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
= $false )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1035]) ).
thf(1062,plain,
! [SV48: $i,SV69: $i,SV125: $i,SV120: $i,SV115: $i,SV21: $i] :
( ( ( ~ ( apply @ SV21 @ SV115 @ SV120 )
| ~ ( apply @ SV21 @ SV115 @ SV125 ) )
= $true )
| ( ( SV120 = SV125 )
= $true )
| ( ( member @ SV120 @ SV69 )
= $false )
| ( ( member @ SV115 @ SV48 )
= $false )
| ( ( member @ SV125 @ SV69 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1036]) ).
thf(1063,plain,
! [SV48: $i,SV69: $i,SV21: $i,SV129: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK42_SY460 @ SV129 @ SV21 @ SV69 @ SV48 ) @ SV48 )
| ~ ( member @ ( sK43_SY672 @ SV48 @ SV69 @ SV21 @ SV129 ) @ SV69 ) )
| ~ ( member @ ( sK44_SY674 @ SV48 @ SV69 @ SV21 @ SV129 ) @ SV69 ) )
= $false )
| ( ( member @ SV129 @ SV69 )
= $false )
| ( ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV129 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1039]) ).
thf(1064,plain,
! [SV48: $i,SV69: $i,SV129: $i,SV21: $i] :
( ( ( ~ ( ~ ( apply @ SV21 @ ( sK42_SY460 @ SV129 @ SV21 @ SV69 @ SV48 ) @ ( sK43_SY672 @ SV48 @ SV69 @ SV21 @ SV129 ) )
| ~ ( apply @ SV21 @ ( sK42_SY460 @ SV129 @ SV21 @ SV69 @ SV48 ) @ ( sK44_SY674 @ SV48 @ SV69 @ SV21 @ SV129 ) ) ) )
= $true )
| ( ( member @ SV129 @ SV69 )
= $false )
| ( ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV129 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1040]) ).
thf(1065,plain,
! [SV90: $i,SV70: $i,SV116: $i,SV50: $i,SV121: $i,SV23: $i,SV83: $i,SV92: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK46_SY653 @ SV92 @ SV83 @ SV23 @ SV121 @ SV50 @ SV116 @ SV70 @ SV90 ) @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ ( sK46_SY653 @ SV92 @ SV83 @ SV23 @ SV121 @ SV50 @ SV116 @ SV70 @ SV90 ) ) )
| ~ ( apply @ SV50 @ ( sK46_SY653 @ SV92 @ SV83 @ SV23 @ SV121 @ SV50 @ SV116 @ SV70 @ SV90 ) @ SV121 ) ) )
= $true )
| ( ( apply @ SV23 @ SV116 @ SV121 )
= $false )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1042]) ).
thf(1066,plain,
! [SV92: $i,SV83: $i,SV23: $i,SV121: $i,SV50: $i,SV116: $i,SV70: $i,SV90: $i,SV134: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ SV134 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SV134 ) )
| ~ ( apply @ SV50 @ SV134 @ SV121 ) ) )
= $false )
| ( ( apply @ SV23 @ SV116 @ SV121 )
= $true )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1043]) ).
thf(1067,plain,
! [SV90: $i,SV70: $i,SV50: $i,SV23: $i,SV92: $i,SV83: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK45_SY656 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK45_SY656 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) ) ) )
= $false )
| ( ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1044]) ).
thf(1068,plain,
! [SV90: $i,SV70: $i,SV23: $i,SV92: $i,SV83: $i,SV50: $i] :
( ( ( ~ ( apply @ SV50 @ ( sK45_SY656 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
= $false )
| ( ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1044]) ).
thf(1069,plain,
! [SV83: $i,SV92: $i,SV23: $i,SV50: $i,SV70: $i,SV90: $i,SV132: $i] :
( ( ( member @ SV132 @ SV90 )
= $false )
| ( ( ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV132 ) )
= $true )
| ( ( ~ ( apply @ SV50 @ SV132 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY656: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY656 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY656 ) )
| ~ ( apply @ SV50 @ SY656 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
| ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1045]) ).
thf(1070,plain,
! [SV84: $i,SV52: $i,SV93: $i,SV25: $i,SV94: $i,SV72: $i,SV91: $i] :
( ( ( member @ ( sK39_SY600 @ SV91 @ SV72 @ SV94 @ SV25 @ SV93 @ SV52 @ SV84 ) @ SV84 )
= $true )
| ( ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
= $false )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1046]) ).
thf(1071,plain,
! [SV84: $i,SV25: $i,SV94: $i,SV72: $i,SV91: $i,SV93: $i,SV52: $i] :
( ( ( apply @ SV52 @ SV93 @ ( sK39_SY600 @ SV91 @ SV72 @ SV94 @ SV25 @ SV93 @ SV52 @ SV84 ) )
= $true )
| ( ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
= $false )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1047]) ).
thf(1072,plain,
! [SV91: $i,SV72: $i,SV94: $i,SV25: $i,SV93: $i,SV52: $i,SV84: $i,SV133: $i] :
( ( ( member @ SV133 @ SV84 )
= $false )
| ( ( ~ ( apply @ SV52 @ SV93 @ SV133 ) )
= $true )
| ( ( ~ ( apply @ SV25 @ SV133 @ SV94 ) )
= $true )
| ( ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
= $true )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1048]) ).
thf(1073,plain,
! [SV74: $i,SV54: $i,SV100: $i,SV109: $i,SV104: $i,SV27: $i] :
( ( ( apply @ SV27 @ SV104 @ SV109 )
= $false )
| ( ( apply @ SV27 @ SV100 @ SV109 )
= $false )
| ( ( SV100 = SV104 )
= $true )
| ( ( member @ SV104 @ SV54 )
= $false )
| ( ( member @ SV100 @ SV54 )
= $false )
| ( ( member @ SV109 @ SV74 )
= $false )
| ( ( injective @ SV27 @ SV54 @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1049]) ).
thf(1074,plain,
! [SV75: $i,SV85: $i,SV117: $i,SV55: $i,SV110: $i,SV105: $i,SV28: $i] :
( ( ( apply @ SV28 @ SV105 @ SV110 )
= $false )
| ( ( ~ ( apply @ SV55 @ SV105 @ SV117 ) )
= $true )
| ( ( SV110 = SV117 )
= $true )
| ( ( member @ SV110 @ SV85 )
= $false )
| ( ( member @ SV105 @ SV75 )
= $false )
| ( ( member @ SV117 @ SV85 )
= $false )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1050]) ).
thf(1075,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV122: $i,SV118: $i,SV78: $i,SV112: $i,SV33: $i,SV106: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ SV106 @ SV33 )
| ~ ( member @ SV112 @ SV78 ) )
| ~ ( member @ SV118 @ SV33 ) ) )
= $false )
| ( ( ~ ( member @ SV122 @ SV78 ) )
= $true )
| ( ( ~ ( apply @ SV59 @ SV106 @ SV118 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV106 @ SV112 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV118 @ SV122 ) )
= $true )
| ( ( apply @ SV87 @ SV122 @ SV112 )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1051]) ).
thf(1076,plain,
! [SV33: $i,SV78: $i,SV59: $i,SV6: $i,SV87: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ SV33 )
| ~ ( member @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
| ~ ( member @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV33 ) ) )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1052]) ).
thf(1077,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV78: $i,SV33: $i] :
( ( ( member @ ( sK30_SY649 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1053]) ).
thf(1078,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV131: $i,SV130: $i,SV79: $i,SV127: $i,SV34: $i,SV123: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ SV123 @ SV34 )
| ~ ( member @ SV127 @ SV79 ) )
| ~ ( member @ SV130 @ SV34 ) ) )
= $false )
| ( ( ~ ( member @ SV131 @ SV79 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV123 @ SV127 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV130 @ SV131 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV60 @ SV123 @ SV130 )
| ( apply @ SV88 @ SV127 @ SV131 ) )
| ~ ( ~ ( apply @ SV88 @ SV127 @ SV131 )
| ( apply @ SV60 @ SV123 @ SV130 ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1054]) ).
thf(1079,plain,
! [SV34: $i,SV79: $i,SV7: $i,SV60: $i,SV88: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ SV34 )
| ~ ( member @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 ) )
| ~ ( member @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV34 ) )
| ~ ( member @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 ) )
| ~ ( apply @ SV7 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) )
= $false )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1055]) ).
thf(1080,plain,
! [SV34: $i,SV79: $i,SV7: $i,SV88: $i,SV60: $i] :
( ( ( apply @ SV60 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
= $true )
| ( ( ~ ( ~ ( apply @ SV88 @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
| ( apply @ SV60 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) ) )
= $true )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1057]) ).
thf(1081,plain,
! [SV60: $i,SV7: $i,SV79: $i,SV34: $i,SV88: $i] :
( ( ( ~ ( apply @ SV88 @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
| ( apply @ SV60 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) )
= $false )
| ( ( apply @ SV88 @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
= $false )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1058]) ).
thf(1082,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV124: $i,SV119: $i,SV80: $i,SV113: $i,SV36: $i,SV107: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ SV107 @ SV36 )
| ~ ( member @ SV113 @ SV80 ) )
| ~ ( member @ SV119 @ SV36 ) ) )
= $false )
| ( ( ~ ( member @ SV124 @ SV80 ) )
= $true )
| ( ( ~ ( apply @ SV62 @ SV107 @ SV119 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV107 @ SV113 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV119 @ SV124 ) )
= $true )
| ( ( apply @ SV89 @ SV113 @ SV124 )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1059]) ).
thf(1083,plain,
! [SV36: $i,SV80: $i,SV62: $i,SV9: $i,SV89: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ SV36 )
| ~ ( member @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
| ~ ( member @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV36 ) ) )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1060]) ).
thf(1084,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV80: $i,SV36: $i] :
( ( ( member @ ( sK31_SY651 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1061]) ).
thf(1085,plain,
! [SV48: $i,SV69: $i,SV125: $i,SV120: $i,SV115: $i,SV21: $i] :
( ( ( ~ ( apply @ SV21 @ SV115 @ SV120 ) )
= $true )
| ( ( ~ ( apply @ SV21 @ SV115 @ SV125 ) )
= $true )
| ( ( SV120 = SV125 )
= $true )
| ( ( member @ SV120 @ SV69 )
= $false )
| ( ( member @ SV115 @ SV48 )
= $false )
| ( ( member @ SV125 @ SV69 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1062]) ).
thf(1086,plain,
! [SV48: $i,SV69: $i,SV21: $i,SV129: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK42_SY460 @ SV129 @ SV21 @ SV69 @ SV48 ) @ SV48 )
| ~ ( member @ ( sK43_SY672 @ SV48 @ SV69 @ SV21 @ SV129 ) @ SV69 ) ) )
= $false )
| ( ( member @ SV129 @ SV69 )
= $false )
| ( ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV129 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1063]) ).
thf(1087,plain,
! [SV129: $i,SV21: $i,SV69: $i,SV48: $i] :
( ( ( ~ ( member @ ( sK44_SY674 @ SV48 @ SV69 @ SV21 @ SV129 ) @ SV69 ) )
= $false )
| ( ( member @ SV129 @ SV69 )
= $false )
| ( ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV129 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1063]) ).
thf(1088,plain,
! [SV48: $i,SV69: $i,SV129: $i,SV21: $i] :
( ( ( ~ ( apply @ SV21 @ ( sK42_SY460 @ SV129 @ SV21 @ SV69 @ SV48 ) @ ( sK43_SY672 @ SV48 @ SV69 @ SV21 @ SV129 ) )
| ~ ( apply @ SV21 @ ( sK42_SY460 @ SV129 @ SV21 @ SV69 @ SV48 ) @ ( sK44_SY674 @ SV48 @ SV69 @ SV21 @ SV129 ) ) )
= $false )
| ( ( member @ SV129 @ SV69 )
= $false )
| ( ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV129 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1064]) ).
thf(1089,plain,
! [SV90: $i,SV70: $i,SV116: $i,SV50: $i,SV121: $i,SV23: $i,SV83: $i,SV92: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK46_SY653 @ SV92 @ SV83 @ SV23 @ SV121 @ SV50 @ SV116 @ SV70 @ SV90 ) @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ ( sK46_SY653 @ SV92 @ SV83 @ SV23 @ SV121 @ SV50 @ SV116 @ SV70 @ SV90 ) ) )
| ~ ( apply @ SV50 @ ( sK46_SY653 @ SV92 @ SV83 @ SV23 @ SV121 @ SV50 @ SV116 @ SV70 @ SV90 ) @ SV121 ) )
= $false )
| ( ( apply @ SV23 @ SV116 @ SV121 )
= $false )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1065]) ).
thf(1090,plain,
! [SV92: $i,SV83: $i,SV23: $i,SV121: $i,SV50: $i,SV116: $i,SV70: $i,SV90: $i,SV134: $i] :
( ( ( ~ ~ ( ~ ( member @ SV134 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SV134 ) )
| ~ ( apply @ SV50 @ SV134 @ SV121 ) )
= $true )
| ( ( apply @ SV23 @ SV116 @ SV121 )
= $true )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1066]) ).
thf(1091,plain,
! [SV90: $i,SV70: $i,SV50: $i,SV23: $i,SV92: $i,SV83: $i] :
( ( ( ~ ( ~ ( member @ ( sK45_SY656 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK45_SY656 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) ) ) )
= $true )
| ( ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1067]) ).
thf(1092,plain,
! [SV90: $i,SV70: $i,SV23: $i,SV92: $i,SV83: $i,SV50: $i] :
( ( ( apply @ SV50 @ ( sK45_SY656 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $true )
| ( ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1068]) ).
thf(1093,plain,
! [SV132: $i,SV83: $i,SV92: $i,SV23: $i,SV90: $i,SV50: $i,SV70: $i] :
( ( ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV132 )
= $false )
| ( ( member @ SV132 @ SV90 )
= $false )
| ( ( ~ ( apply @ SV50 @ SV132 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY656: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY656 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY656 ) )
| ~ ( apply @ SV50 @ SY656 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
| ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1069]) ).
thf(1094,plain,
! [SV91: $i,SV72: $i,SV94: $i,SV25: $i,SV84: $i,SV133: $i,SV93: $i,SV52: $i] :
( ( ( apply @ SV52 @ SV93 @ SV133 )
= $false )
| ( ( member @ SV133 @ SV84 )
= $false )
| ( ( ~ ( apply @ SV25 @ SV133 @ SV94 ) )
= $true )
| ( ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
= $true )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1072]) ).
thf(1095,plain,
! [SV75: $i,SV85: $i,SV110: $i,SV28: $i,SV117: $i,SV105: $i,SV55: $i] :
( ( ( apply @ SV55 @ SV105 @ SV117 )
= $false )
| ( ( apply @ SV28 @ SV105 @ SV110 )
= $false )
| ( ( SV110 = SV117 )
= $true )
| ( ( member @ SV110 @ SV85 )
= $false )
| ( ( member @ SV105 @ SV75 )
= $false )
| ( ( member @ SV117 @ SV85 )
= $false )
| ( ( equal_maps @ SV28 @ SV55 @ SV75 @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1074]) ).
thf(1096,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV122: $i,SV118: $i,SV78: $i,SV112: $i,SV33: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ( member @ SV106 @ SV33 )
| ~ ( member @ SV112 @ SV78 ) )
| ~ ( member @ SV118 @ SV33 ) )
= $true )
| ( ( ~ ( member @ SV122 @ SV78 ) )
= $true )
| ( ( ~ ( apply @ SV59 @ SV106 @ SV118 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV106 @ SV112 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV118 @ SV122 ) )
= $true )
| ( ( apply @ SV87 @ SV122 @ SV112 )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1075]) ).
thf(1097,plain,
! [SV33: $i,SV78: $i,SV59: $i,SV6: $i,SV87: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ SV33 )
| ~ ( member @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
| ~ ( member @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV33 ) )
= $false )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1076]) ).
thf(1098,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV131: $i,SV130: $i,SV79: $i,SV127: $i,SV34: $i,SV123: $i] :
( ( ( ~ ~ ( ~ ( member @ SV123 @ SV34 )
| ~ ( member @ SV127 @ SV79 ) )
| ~ ( member @ SV130 @ SV34 ) )
= $true )
| ( ( ~ ( member @ SV131 @ SV79 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV123 @ SV127 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV130 @ SV131 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV60 @ SV123 @ SV130 )
| ( apply @ SV88 @ SV127 @ SV131 ) )
| ~ ( ~ ( apply @ SV88 @ SV127 @ SV131 )
| ( apply @ SV60 @ SV123 @ SV130 ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1078]) ).
thf(1099,plain,
! [SV34: $i,SV79: $i,SV7: $i,SV60: $i,SV88: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ SV34 )
| ~ ( member @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 ) )
| ~ ( member @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV34 ) )
| ~ ( member @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 ) ) )
= $false )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1079]) ).
thf(1100,plain,
! [SV34: $i,SV79: $i,SV60: $i,SV88: $i,SV7: $i] :
( ( ( ~ ( apply @ SV7 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) )
= $false )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1079]) ).
thf(1101,plain,
! [SV60: $i,SV7: $i,SV79: $i,SV34: $i,SV88: $i] :
( ( ( ~ ( apply @ SV88 @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
| ( apply @ SV60 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) )
= $false )
| ( ( apply @ SV60 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
= $true )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1080]) ).
thf(1102,plain,
! [SV60: $i,SV7: $i,SV79: $i,SV34: $i,SV88: $i] :
( ( ( ~ ( apply @ SV88 @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) )
= $false )
| ( ( apply @ SV88 @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
= $false )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1081]) ).
thf(1103,plain,
! [SV34: $i,SV79: $i,SV7: $i,SV88: $i,SV60: $i] :
( ( ( apply @ SV60 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
= $false )
| ( ( apply @ SV88 @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
= $false )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1081]) ).
thf(1104,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV124: $i,SV119: $i,SV80: $i,SV113: $i,SV36: $i,SV107: $i] :
( ( ( ~ ~ ( ~ ( member @ SV107 @ SV36 )
| ~ ( member @ SV113 @ SV80 ) )
| ~ ( member @ SV119 @ SV36 ) )
= $true )
| ( ( ~ ( member @ SV124 @ SV80 ) )
= $true )
| ( ( ~ ( apply @ SV62 @ SV107 @ SV119 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV107 @ SV113 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV119 @ SV124 ) )
= $true )
| ( ( apply @ SV89 @ SV113 @ SV124 )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1082]) ).
thf(1105,plain,
! [SV36: $i,SV80: $i,SV62: $i,SV9: $i,SV89: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ SV36 )
| ~ ( member @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
| ~ ( member @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV36 ) )
= $false )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1083]) ).
thf(1106,plain,
! [SV48: $i,SV69: $i,SV125: $i,SV120: $i,SV115: $i,SV21: $i] :
( ( ( apply @ SV21 @ SV115 @ SV120 )
= $false )
| ( ( ~ ( apply @ SV21 @ SV115 @ SV125 ) )
= $true )
| ( ( SV120 = SV125 )
= $true )
| ( ( member @ SV120 @ SV69 )
= $false )
| ( ( member @ SV115 @ SV48 )
= $false )
| ( ( member @ SV125 @ SV69 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1085]) ).
thf(1107,plain,
! [SV48: $i,SV69: $i,SV21: $i,SV129: $i] :
( ( ( ~ ( ~ ( member @ ( sK42_SY460 @ SV129 @ SV21 @ SV69 @ SV48 ) @ SV48 )
| ~ ( member @ ( sK43_SY672 @ SV48 @ SV69 @ SV21 @ SV129 ) @ SV69 ) ) )
= $true )
| ( ( member @ SV129 @ SV69 )
= $false )
| ( ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV129 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1086]) ).
thf(1108,plain,
! [SV129: $i,SV21: $i,SV69: $i,SV48: $i] :
( ( ( member @ ( sK44_SY674 @ SV48 @ SV69 @ SV21 @ SV129 ) @ SV69 )
= $true )
| ( ( member @ SV129 @ SV69 )
= $false )
| ( ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV129 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1087]) ).
thf(1109,plain,
! [SV48: $i,SV69: $i,SV129: $i,SV21: $i] :
( ( ( ~ ( apply @ SV21 @ ( sK42_SY460 @ SV129 @ SV21 @ SV69 @ SV48 ) @ ( sK43_SY672 @ SV48 @ SV69 @ SV21 @ SV129 ) ) )
= $false )
| ( ( member @ SV129 @ SV69 )
= $false )
| ( ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV129 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1088]) ).
thf(1110,plain,
! [SV48: $i,SV69: $i,SV129: $i,SV21: $i] :
( ( ( ~ ( apply @ SV21 @ ( sK42_SY460 @ SV129 @ SV21 @ SV69 @ SV48 ) @ ( sK44_SY674 @ SV48 @ SV69 @ SV21 @ SV129 ) ) )
= $false )
| ( ( member @ SV129 @ SV69 )
= $false )
| ( ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV129 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1088]) ).
thf(1111,plain,
! [SV90: $i,SV70: $i,SV116: $i,SV50: $i,SV121: $i,SV23: $i,SV83: $i,SV92: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK46_SY653 @ SV92 @ SV83 @ SV23 @ SV121 @ SV50 @ SV116 @ SV70 @ SV90 ) @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ ( sK46_SY653 @ SV92 @ SV83 @ SV23 @ SV121 @ SV50 @ SV116 @ SV70 @ SV90 ) ) ) )
= $false )
| ( ( apply @ SV23 @ SV116 @ SV121 )
= $false )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1089]) ).
thf(1112,plain,
! [SV90: $i,SV70: $i,SV116: $i,SV121: $i,SV23: $i,SV83: $i,SV92: $i,SV50: $i] :
( ( ( ~ ( apply @ SV50 @ ( sK46_SY653 @ SV92 @ SV83 @ SV23 @ SV121 @ SV50 @ SV116 @ SV70 @ SV90 ) @ SV121 ) )
= $false )
| ( ( apply @ SV23 @ SV116 @ SV121 )
= $false )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1089]) ).
thf(1113,plain,
! [SV92: $i,SV83: $i,SV23: $i,SV121: $i,SV50: $i,SV116: $i,SV70: $i,SV90: $i,SV134: $i] :
( ( ( ~ ~ ( ~ ( member @ SV134 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SV134 ) ) )
= $true )
| ( ( ~ ( apply @ SV50 @ SV134 @ SV121 ) )
= $true )
| ( ( apply @ SV23 @ SV116 @ SV121 )
= $true )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1090]) ).
thf(1114,plain,
! [SV90: $i,SV70: $i,SV50: $i,SV23: $i,SV92: $i,SV83: $i] :
( ( ( ~ ( member @ ( sK45_SY656 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK45_SY656 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) ) )
= $false )
| ( ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1091]) ).
thf(1115,plain,
! [SV70: $i,SV90: $i,SV23: $i,SV92: $i,SV83: $i,SV132: $i,SV50: $i] :
( ( ( apply @ SV50 @ SV132 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $false )
| ( ( member @ SV132 @ SV90 )
= $false )
| ( ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV132 )
= $false )
| ( ( ~ ( ~ ~ ! [SY656: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY656 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY656 ) )
| ~ ( apply @ SV50 @ SY656 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
| ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1093]) ).
thf(1116,plain,
! [SV91: $i,SV72: $i,SV93: $i,SV52: $i,SV84: $i,SV94: $i,SV133: $i,SV25: $i] :
( ( ( apply @ SV25 @ SV133 @ SV94 )
= $false )
| ( ( member @ SV133 @ SV84 )
= $false )
| ( ( apply @ SV52 @ SV93 @ SV133 )
= $false )
| ( ( apply @ ( compose_function @ SV25 @ SV52 @ SV72 @ SV84 @ SV91 ) @ SV93 @ SV94 )
= $true )
| ( ( member @ SV93 @ SV72 )
= $false )
| ( ( member @ SV94 @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1094]) ).
thf(1117,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV122: $i,SV118: $i,SV78: $i,SV112: $i,SV33: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ( member @ SV106 @ SV33 )
| ~ ( member @ SV112 @ SV78 ) ) )
= $true )
| ( ( ~ ( member @ SV118 @ SV33 ) )
= $true )
| ( ( ~ ( member @ SV122 @ SV78 ) )
= $true )
| ( ( ~ ( apply @ SV59 @ SV106 @ SV118 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV106 @ SV112 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV118 @ SV122 ) )
= $true )
| ( ( apply @ SV87 @ SV122 @ SV112 )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1096]) ).
thf(1118,plain,
! [SV33: $i,SV78: $i,SV59: $i,SV6: $i,SV87: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ SV33 )
| ~ ( member @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) ) )
= $false )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1097]) ).
thf(1119,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV78: $i,SV33: $i] :
( ( ( ~ ( member @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV33 ) )
= $false )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1097]) ).
thf(1120,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV131: $i,SV130: $i,SV79: $i,SV127: $i,SV34: $i,SV123: $i] :
( ( ( ~ ~ ( ~ ( member @ SV123 @ SV34 )
| ~ ( member @ SV127 @ SV79 ) ) )
= $true )
| ( ( ~ ( member @ SV130 @ SV34 ) )
= $true )
| ( ( ~ ( member @ SV131 @ SV79 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV123 @ SV127 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV130 @ SV131 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV60 @ SV123 @ SV130 )
| ( apply @ SV88 @ SV127 @ SV131 ) )
| ~ ( ~ ( apply @ SV88 @ SV127 @ SV131 )
| ( apply @ SV60 @ SV123 @ SV130 ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1098]) ).
thf(1121,plain,
! [SV34: $i,SV79: $i,SV7: $i,SV60: $i,SV88: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ SV34 )
| ~ ( member @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 ) )
| ~ ( member @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV34 ) )
| ~ ( member @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 ) ) )
= $true )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1099]) ).
thf(1122,plain,
! [SV34: $i,SV79: $i,SV60: $i,SV88: $i,SV7: $i] :
( ( ( apply @ SV7 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
= $true )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1100]) ).
thf(1123,plain,
! [SV60: $i,SV7: $i,SV79: $i,SV34: $i,SV88: $i] :
( ( ( ~ ( apply @ SV88 @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) ) )
= $false )
| ( ( apply @ SV60 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
= $true )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1101]) ).
thf(1124,plain,
! [SV34: $i,SV79: $i,SV7: $i,SV88: $i,SV60: $i] :
( ( ( apply @ SV60 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
= $false )
| ( ( apply @ SV60 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
= $true )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1101]) ).
thf(1125,plain,
! [SV60: $i,SV7: $i,SV79: $i,SV34: $i,SV88: $i] :
( ( ( apply @ SV88 @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
= $true )
| ( ( apply @ SV88 @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
= $false )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1102]) ).
thf(1126,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV124: $i,SV119: $i,SV80: $i,SV113: $i,SV36: $i,SV107: $i] :
( ( ( ~ ~ ( ~ ( member @ SV107 @ SV36 )
| ~ ( member @ SV113 @ SV80 ) ) )
= $true )
| ( ( ~ ( member @ SV119 @ SV36 ) )
= $true )
| ( ( ~ ( member @ SV124 @ SV80 ) )
= $true )
| ( ( ~ ( apply @ SV62 @ SV107 @ SV119 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV107 @ SV113 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV119 @ SV124 ) )
= $true )
| ( ( apply @ SV89 @ SV113 @ SV124 )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1104]) ).
thf(1127,plain,
! [SV36: $i,SV80: $i,SV62: $i,SV9: $i,SV89: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ SV36 )
| ~ ( member @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) ) )
= $false )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1105]) ).
thf(1128,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV80: $i,SV36: $i] :
( ( ( ~ ( member @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV36 ) )
= $false )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1105]) ).
thf(1129,plain,
! [SV48: $i,SV69: $i,SV120: $i,SV125: $i,SV115: $i,SV21: $i] :
( ( ( apply @ SV21 @ SV115 @ SV125 )
= $false )
| ( ( apply @ SV21 @ SV115 @ SV120 )
= $false )
| ( ( SV120 = SV125 )
= $true )
| ( ( member @ SV120 @ SV69 )
= $false )
| ( ( member @ SV115 @ SV48 )
= $false )
| ( ( member @ SV125 @ SV69 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1106]) ).
thf(1130,plain,
! [SV48: $i,SV69: $i,SV21: $i,SV129: $i] :
( ( ( ~ ( member @ ( sK42_SY460 @ SV129 @ SV21 @ SV69 @ SV48 ) @ SV48 )
| ~ ( member @ ( sK43_SY672 @ SV48 @ SV69 @ SV21 @ SV129 ) @ SV69 ) )
= $false )
| ( ( member @ SV129 @ SV69 )
= $false )
| ( ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV129 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1107]) ).
thf(1131,plain,
! [SV48: $i,SV69: $i,SV129: $i,SV21: $i] :
( ( ( apply @ SV21 @ ( sK42_SY460 @ SV129 @ SV21 @ SV69 @ SV48 ) @ ( sK43_SY672 @ SV48 @ SV69 @ SV21 @ SV129 ) )
= $true )
| ( ( member @ SV129 @ SV69 )
= $false )
| ( ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV129 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1109]) ).
thf(1132,plain,
! [SV48: $i,SV69: $i,SV129: $i,SV21: $i] :
( ( ( apply @ SV21 @ ( sK42_SY460 @ SV129 @ SV21 @ SV69 @ SV48 ) @ ( sK44_SY674 @ SV48 @ SV69 @ SV21 @ SV129 ) )
= $true )
| ( ( member @ SV129 @ SV69 )
= $false )
| ( ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV129 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1110]) ).
thf(1133,plain,
! [SV90: $i,SV70: $i,SV116: $i,SV50: $i,SV121: $i,SV23: $i,SV83: $i,SV92: $i] :
( ( ( ~ ( ~ ( member @ ( sK46_SY653 @ SV92 @ SV83 @ SV23 @ SV121 @ SV50 @ SV116 @ SV70 @ SV90 ) @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ ( sK46_SY653 @ SV92 @ SV83 @ SV23 @ SV121 @ SV50 @ SV116 @ SV70 @ SV90 ) ) ) )
= $true )
| ( ( apply @ SV23 @ SV116 @ SV121 )
= $false )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1111]) ).
thf(1134,plain,
! [SV90: $i,SV70: $i,SV116: $i,SV121: $i,SV23: $i,SV83: $i,SV92: $i,SV50: $i] :
( ( ( apply @ SV50 @ ( sK46_SY653 @ SV92 @ SV83 @ SV23 @ SV121 @ SV50 @ SV116 @ SV70 @ SV90 ) @ SV121 )
= $true )
| ( ( apply @ SV23 @ SV116 @ SV121 )
= $false )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1112]) ).
thf(1135,plain,
! [SV92: $i,SV83: $i,SV23: $i,SV121: $i,SV50: $i,SV116: $i,SV70: $i,SV90: $i,SV134: $i] :
( ( ( ~ ( ~ ( member @ SV134 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SV134 ) ) )
= $false )
| ( ( ~ ( apply @ SV50 @ SV134 @ SV121 ) )
= $true )
| ( ( apply @ SV23 @ SV116 @ SV121 )
= $true )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1113]) ).
thf(1136,plain,
! [SV90: $i,SV70: $i,SV50: $i,SV23: $i,SV92: $i,SV83: $i] :
( ( ( ~ ( member @ ( sK45_SY656 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) @ SV90 ) )
= $false )
| ( ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1114]) ).
thf(1137,plain,
! [SV83: $i,SV92: $i,SV23: $i,SV90: $i,SV50: $i,SV70: $i] :
( ( ( ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK45_SY656 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) ) )
= $false )
| ( ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1114]) ).
thf(1138,plain,
! [SV132: $i,SV83: $i,SV92: $i,SV23: $i,SV50: $i,SV70: $i,SV90: $i] :
( ( ( ~ ~ ! [SY656: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY656 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY656 ) )
| ~ ( apply @ SV50 @ SY656 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
| ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
= $false )
| ( ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV132 )
= $false )
| ( ( member @ SV132 @ SV90 )
= $false )
| ( ( apply @ SV50 @ SV132 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1115]) ).
thf(1139,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV122: $i,SV118: $i,SV78: $i,SV112: $i,SV33: $i,SV106: $i] :
( ( ( ~ ( ~ ( member @ SV106 @ SV33 )
| ~ ( member @ SV112 @ SV78 ) ) )
= $false )
| ( ( ~ ( member @ SV118 @ SV33 ) )
= $true )
| ( ( ~ ( member @ SV122 @ SV78 ) )
= $true )
| ( ( ~ ( apply @ SV59 @ SV106 @ SV118 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV106 @ SV112 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV118 @ SV122 ) )
= $true )
| ( ( apply @ SV87 @ SV122 @ SV112 )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1117]) ).
thf(1140,plain,
! [SV33: $i,SV78: $i,SV59: $i,SV6: $i,SV87: $i] :
( ( ( ~ ( ~ ( member @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ SV33 )
| ~ ( member @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) ) )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1118]) ).
thf(1141,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV78: $i,SV33: $i] :
( ( ( member @ ( sK26_SY632 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV33 )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1119]) ).
thf(1142,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV131: $i,SV130: $i,SV79: $i,SV127: $i,SV34: $i,SV123: $i] :
( ( ( ~ ( ~ ( member @ SV123 @ SV34 )
| ~ ( member @ SV127 @ SV79 ) ) )
= $false )
| ( ( ~ ( member @ SV130 @ SV34 ) )
= $true )
| ( ( ~ ( member @ SV131 @ SV79 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV123 @ SV127 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV130 @ SV131 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV60 @ SV123 @ SV130 )
| ( apply @ SV88 @ SV127 @ SV131 ) )
| ~ ( ~ ( apply @ SV88 @ SV127 @ SV131 )
| ( apply @ SV60 @ SV123 @ SV130 ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1120]) ).
thf(1143,plain,
! [SV34: $i,SV79: $i,SV7: $i,SV60: $i,SV88: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ SV34 )
| ~ ( member @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 ) )
| ~ ( member @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV34 ) )
| ~ ( member @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 ) )
= $false )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1121]) ).
thf(1144,plain,
! [SV60: $i,SV7: $i,SV79: $i,SV34: $i,SV88: $i] :
( ( ( apply @ SV88 @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
= $true )
| ( ( apply @ SV60 @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) )
= $true )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1123]) ).
thf(1145,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV124: $i,SV119: $i,SV80: $i,SV113: $i,SV36: $i,SV107: $i] :
( ( ( ~ ( ~ ( member @ SV107 @ SV36 )
| ~ ( member @ SV113 @ SV80 ) ) )
= $false )
| ( ( ~ ( member @ SV119 @ SV36 ) )
= $true )
| ( ( ~ ( member @ SV124 @ SV80 ) )
= $true )
| ( ( ~ ( apply @ SV62 @ SV107 @ SV119 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV107 @ SV113 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV119 @ SV124 ) )
= $true )
| ( ( apply @ SV89 @ SV113 @ SV124 )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1126]) ).
thf(1146,plain,
! [SV36: $i,SV80: $i,SV62: $i,SV9: $i,SV89: $i] :
( ( ( ~ ( ~ ( member @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ SV36 )
| ~ ( member @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) ) )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1127]) ).
thf(1147,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV80: $i,SV36: $i] :
( ( ( member @ ( sK27_SY636 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV36 )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1128]) ).
thf(1148,plain,
! [SV48: $i,SV69: $i,SV21: $i,SV129: $i] :
( ( ( ~ ( member @ ( sK42_SY460 @ SV129 @ SV21 @ SV69 @ SV48 ) @ SV48 ) )
= $false )
| ( ( member @ SV129 @ SV69 )
= $false )
| ( ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV129 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1130]) ).
thf(1149,plain,
! [SV129: $i,SV21: $i,SV69: $i,SV48: $i] :
( ( ( ~ ( member @ ( sK43_SY672 @ SV48 @ SV69 @ SV21 @ SV129 ) @ SV69 ) )
= $false )
| ( ( member @ SV129 @ SV69 )
= $false )
| ( ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV129 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1130]) ).
thf(1150,plain,
! [SV90: $i,SV70: $i,SV116: $i,SV50: $i,SV121: $i,SV23: $i,SV83: $i,SV92: $i] :
( ( ( ~ ( member @ ( sK46_SY653 @ SV92 @ SV83 @ SV23 @ SV121 @ SV50 @ SV116 @ SV70 @ SV90 ) @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ ( sK46_SY653 @ SV92 @ SV83 @ SV23 @ SV121 @ SV50 @ SV116 @ SV70 @ SV90 ) ) )
= $false )
| ( ( apply @ SV23 @ SV116 @ SV121 )
= $false )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1133]) ).
thf(1151,plain,
! [SV92: $i,SV83: $i,SV23: $i,SV121: $i,SV50: $i,SV116: $i,SV70: $i,SV90: $i,SV134: $i] :
( ( ( ~ ( member @ SV134 @ SV90 )
| ~ ( apply @ SV70 @ SV116 @ SV134 ) )
= $true )
| ( ( ~ ( apply @ SV50 @ SV134 @ SV121 ) )
= $true )
| ( ( apply @ SV23 @ SV116 @ SV121 )
= $true )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1135]) ).
thf(1152,plain,
! [SV90: $i,SV70: $i,SV50: $i,SV23: $i,SV92: $i,SV83: $i] :
( ( ( member @ ( sK45_SY656 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) @ SV90 )
= $true )
| ( ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1136]) ).
thf(1153,plain,
! [SV83: $i,SV92: $i,SV23: $i,SV90: $i,SV50: $i,SV70: $i] :
( ( ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK45_SY656 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) )
= $true )
| ( ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $true )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1137]) ).
thf(1154,plain,
! [SV132: $i,SV83: $i,SV92: $i,SV23: $i,SV50: $i,SV70: $i,SV90: $i] :
( ( ( ~ ~ ! [SY656: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY656 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY656 ) )
| ~ ( apply @ SV50 @ SY656 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $false )
| ( ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV132 )
= $false )
| ( ( member @ SV132 @ SV90 )
= $false )
| ( ( apply @ SV50 @ SV132 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1138]) ).
thf(1155,plain,
! [SV132: $i,SV83: $i,SV92: $i,SV90: $i,SV70: $i,SV50: $i,SV23: $i] :
( ( ( apply @ SV23 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $false )
| ( ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV132 )
= $false )
| ( ( member @ SV132 @ SV90 )
= $false )
| ( ( apply @ SV50 @ SV132 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1138]) ).
thf(1156,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV122: $i,SV118: $i,SV78: $i,SV112: $i,SV33: $i,SV106: $i] :
( ( ( ~ ( member @ SV106 @ SV33 )
| ~ ( member @ SV112 @ SV78 ) )
= $true )
| ( ( ~ ( member @ SV118 @ SV33 ) )
= $true )
| ( ( ~ ( member @ SV122 @ SV78 ) )
= $true )
| ( ( ~ ( apply @ SV59 @ SV106 @ SV118 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV106 @ SV112 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV118 @ SV122 ) )
= $true )
| ( ( apply @ SV87 @ SV122 @ SV112 )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1139]) ).
thf(1157,plain,
! [SV33: $i,SV78: $i,SV59: $i,SV6: $i,SV87: $i] :
( ( ( ~ ( member @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ SV33 )
| ~ ( member @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
= $false )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1140]) ).
thf(1158,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV131: $i,SV130: $i,SV79: $i,SV127: $i,SV34: $i,SV123: $i] :
( ( ( ~ ( member @ SV123 @ SV34 )
| ~ ( member @ SV127 @ SV79 ) )
= $true )
| ( ( ~ ( member @ SV130 @ SV34 ) )
= $true )
| ( ( ~ ( member @ SV131 @ SV79 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV123 @ SV127 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV130 @ SV131 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV60 @ SV123 @ SV130 )
| ( apply @ SV88 @ SV127 @ SV131 ) )
| ~ ( ~ ( apply @ SV88 @ SV127 @ SV131 )
| ( apply @ SV60 @ SV123 @ SV130 ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1142]) ).
thf(1159,plain,
! [SV34: $i,SV79: $i,SV7: $i,SV60: $i,SV88: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ SV34 )
| ~ ( member @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 ) )
| ~ ( member @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV34 ) ) )
= $false )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1143]) ).
thf(1160,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV79: $i,SV34: $i] :
( ( ( ~ ( member @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 ) )
= $false )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1143]) ).
thf(1161,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV124: $i,SV119: $i,SV80: $i,SV113: $i,SV36: $i,SV107: $i] :
( ( ( ~ ( member @ SV107 @ SV36 )
| ~ ( member @ SV113 @ SV80 ) )
= $true )
| ( ( ~ ( member @ SV119 @ SV36 ) )
= $true )
| ( ( ~ ( member @ SV124 @ SV80 ) )
= $true )
| ( ( ~ ( apply @ SV62 @ SV107 @ SV119 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV107 @ SV113 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV119 @ SV124 ) )
= $true )
| ( ( apply @ SV89 @ SV113 @ SV124 )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1145]) ).
thf(1162,plain,
! [SV36: $i,SV80: $i,SV62: $i,SV9: $i,SV89: $i] :
( ( ( ~ ( member @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ SV36 )
| ~ ( member @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
= $false )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1146]) ).
thf(1163,plain,
! [SV48: $i,SV69: $i,SV21: $i,SV129: $i] :
( ( ( member @ ( sK42_SY460 @ SV129 @ SV21 @ SV69 @ SV48 ) @ SV48 )
= $true )
| ( ( member @ SV129 @ SV69 )
= $false )
| ( ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV129 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1148]) ).
thf(1164,plain,
! [SV129: $i,SV21: $i,SV69: $i,SV48: $i] :
( ( ( member @ ( sK43_SY672 @ SV48 @ SV69 @ SV21 @ SV129 ) @ SV69 )
= $true )
| ( ( member @ SV129 @ SV69 )
= $false )
| ( ( apply @ SV21 @ ( sK22_SY458 @ SV21 @ SV69 @ SV48 ) @ SV129 )
= $false )
| ( ( maps @ SV21 @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1149]) ).
thf(1165,plain,
! [SV90: $i,SV70: $i,SV116: $i,SV50: $i,SV121: $i,SV23: $i,SV83: $i,SV92: $i] :
( ( ( ~ ( member @ ( sK46_SY653 @ SV92 @ SV83 @ SV23 @ SV121 @ SV50 @ SV116 @ SV70 @ SV90 ) @ SV90 ) )
= $false )
| ( ( apply @ SV23 @ SV116 @ SV121 )
= $false )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1150]) ).
thf(1166,plain,
! [SV90: $i,SV50: $i,SV121: $i,SV23: $i,SV83: $i,SV92: $i,SV116: $i,SV70: $i] :
( ( ( ~ ( apply @ SV70 @ SV116 @ ( sK46_SY653 @ SV92 @ SV83 @ SV23 @ SV121 @ SV50 @ SV116 @ SV70 @ SV90 ) ) )
= $false )
| ( ( apply @ SV23 @ SV116 @ SV121 )
= $false )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1150]) ).
thf(1167,plain,
! [SV92: $i,SV83: $i,SV23: $i,SV121: $i,SV50: $i,SV116: $i,SV70: $i,SV90: $i,SV134: $i] :
( ( ( ~ ( member @ SV134 @ SV90 ) )
= $true )
| ( ( ~ ( apply @ SV70 @ SV116 @ SV134 ) )
= $true )
| ( ( ~ ( apply @ SV50 @ SV134 @ SV121 ) )
= $true )
| ( ( apply @ SV23 @ SV116 @ SV121 )
= $true )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1151]) ).
thf(1168,plain,
! [SV132: $i,SV83: $i,SV92: $i,SV23: $i,SV50: $i,SV70: $i,SV90: $i] :
( ( ( ~ ! [SY656: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY656 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY656 ) )
| ~ ( apply @ SV50 @ SY656 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $true )
| ( ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV132 )
= $false )
| ( ( member @ SV132 @ SV90 )
= $false )
| ( ( apply @ SV50 @ SV132 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1154]) ).
thf(1169,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV122: $i,SV118: $i,SV78: $i,SV112: $i,SV33: $i,SV106: $i] :
( ( ( ~ ( member @ SV106 @ SV33 ) )
= $true )
| ( ( ~ ( member @ SV112 @ SV78 ) )
= $true )
| ( ( ~ ( member @ SV118 @ SV33 ) )
= $true )
| ( ( ~ ( member @ SV122 @ SV78 ) )
= $true )
| ( ( ~ ( apply @ SV59 @ SV106 @ SV118 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV106 @ SV112 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV118 @ SV122 ) )
= $true )
| ( ( apply @ SV87 @ SV122 @ SV112 )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1156]) ).
thf(1170,plain,
! [SV33: $i,SV78: $i,SV59: $i,SV6: $i,SV87: $i] :
( ( ( ~ ( member @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ SV33 ) )
= $false )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1157]) ).
thf(1171,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV78: $i,SV33: $i] :
( ( ( ~ ( member @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 ) )
= $false )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1157]) ).
thf(1172,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV131: $i,SV130: $i,SV79: $i,SV127: $i,SV34: $i,SV123: $i] :
( ( ( ~ ( member @ SV123 @ SV34 ) )
= $true )
| ( ( ~ ( member @ SV127 @ SV79 ) )
= $true )
| ( ( ~ ( member @ SV130 @ SV34 ) )
= $true )
| ( ( ~ ( member @ SV131 @ SV79 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV123 @ SV127 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV130 @ SV131 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV60 @ SV123 @ SV130 )
| ( apply @ SV88 @ SV127 @ SV131 ) )
| ~ ( ~ ( apply @ SV88 @ SV127 @ SV131 )
| ( apply @ SV60 @ SV123 @ SV130 ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1158]) ).
thf(1173,plain,
! [SV34: $i,SV79: $i,SV7: $i,SV60: $i,SV88: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ SV34 )
| ~ ( member @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 ) )
| ~ ( member @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV34 ) ) )
= $true )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1159]) ).
thf(1174,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV79: $i,SV34: $i] :
( ( ( member @ ( sK41_SY671 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 )
= $true )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1160]) ).
thf(1175,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV124: $i,SV119: $i,SV80: $i,SV113: $i,SV36: $i,SV107: $i] :
( ( ( ~ ( member @ SV107 @ SV36 ) )
= $true )
| ( ( ~ ( member @ SV113 @ SV80 ) )
= $true )
| ( ( ~ ( member @ SV119 @ SV36 ) )
= $true )
| ( ( ~ ( member @ SV124 @ SV80 ) )
= $true )
| ( ( ~ ( apply @ SV62 @ SV107 @ SV119 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV107 @ SV113 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV119 @ SV124 ) )
= $true )
| ( ( apply @ SV89 @ SV113 @ SV124 )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1161]) ).
thf(1176,plain,
! [SV36: $i,SV80: $i,SV62: $i,SV9: $i,SV89: $i] :
( ( ( ~ ( member @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ SV36 ) )
= $false )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1162]) ).
thf(1177,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV80: $i,SV36: $i] :
( ( ( ~ ( member @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 ) )
= $false )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1162]) ).
thf(1178,plain,
! [SV90: $i,SV70: $i,SV116: $i,SV50: $i,SV121: $i,SV23: $i,SV83: $i,SV92: $i] :
( ( ( member @ ( sK46_SY653 @ SV92 @ SV83 @ SV23 @ SV121 @ SV50 @ SV116 @ SV70 @ SV90 ) @ SV90 )
= $true )
| ( ( apply @ SV23 @ SV116 @ SV121 )
= $false )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1165]) ).
thf(1179,plain,
! [SV90: $i,SV50: $i,SV121: $i,SV23: $i,SV83: $i,SV92: $i,SV116: $i,SV70: $i] :
( ( ( apply @ SV70 @ SV116 @ ( sK46_SY653 @ SV92 @ SV83 @ SV23 @ SV121 @ SV50 @ SV116 @ SV70 @ SV90 ) )
= $true )
| ( ( apply @ SV23 @ SV116 @ SV121 )
= $false )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1166]) ).
thf(1180,plain,
! [SV92: $i,SV83: $i,SV23: $i,SV121: $i,SV50: $i,SV116: $i,SV70: $i,SV90: $i,SV134: $i] :
( ( ( member @ SV134 @ SV90 )
= $false )
| ( ( ~ ( apply @ SV70 @ SV116 @ SV134 ) )
= $true )
| ( ( ~ ( apply @ SV50 @ SV134 @ SV121 ) )
= $true )
| ( ( apply @ SV23 @ SV116 @ SV121 )
= $true )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1167]) ).
thf(1181,plain,
! [SV132: $i,SV83: $i,SV92: $i,SV23: $i,SV50: $i,SV70: $i,SV90: $i] :
( ( ( ! [SY656: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY656 @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SY656 ) )
| ~ ( apply @ SV50 @ SY656 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $false )
| ( ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV132 )
= $false )
| ( ( member @ SV132 @ SV90 )
= $false )
| ( ( apply @ SV50 @ SV132 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1168]) ).
thf(1182,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV122: $i,SV118: $i,SV78: $i,SV112: $i,SV33: $i,SV106: $i] :
( ( ( member @ SV106 @ SV33 )
= $false )
| ( ( ~ ( member @ SV112 @ SV78 ) )
= $true )
| ( ( ~ ( member @ SV118 @ SV33 ) )
= $true )
| ( ( ~ ( member @ SV122 @ SV78 ) )
= $true )
| ( ( ~ ( apply @ SV59 @ SV106 @ SV118 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV106 @ SV112 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV118 @ SV122 ) )
= $true )
| ( ( apply @ SV87 @ SV122 @ SV112 )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1169]) ).
thf(1183,plain,
! [SV33: $i,SV78: $i,SV59: $i,SV6: $i,SV87: $i] :
( ( ( member @ ( sK15_SY556 @ SV87 @ SV6 @ SV59 @ SV78 @ SV33 ) @ SV33 )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1170]) ).
thf(1184,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV78: $i,SV33: $i] :
( ( ( member @ ( sK20_SY619 @ SV33 @ SV78 @ SV59 @ SV6 @ SV87 ) @ SV78 )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1171]) ).
thf(1185,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV131: $i,SV130: $i,SV79: $i,SV127: $i,SV34: $i,SV123: $i] :
( ( ( member @ SV123 @ SV34 )
= $false )
| ( ( ~ ( member @ SV127 @ SV79 ) )
= $true )
| ( ( ~ ( member @ SV130 @ SV34 ) )
= $true )
| ( ( ~ ( member @ SV131 @ SV79 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV123 @ SV127 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV130 @ SV131 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV60 @ SV123 @ SV130 )
| ( apply @ SV88 @ SV127 @ SV131 ) )
| ~ ( ~ ( apply @ SV88 @ SV127 @ SV131 )
| ( apply @ SV60 @ SV123 @ SV130 ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1172]) ).
thf(1186,plain,
! [SV34: $i,SV79: $i,SV7: $i,SV60: $i,SV88: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ SV34 )
| ~ ( member @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 ) )
| ~ ( member @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV34 ) )
= $false )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1173]) ).
thf(1187,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV124: $i,SV119: $i,SV80: $i,SV113: $i,SV36: $i,SV107: $i] :
( ( ( member @ SV107 @ SV36 )
= $false )
| ( ( ~ ( member @ SV113 @ SV80 ) )
= $true )
| ( ( ~ ( member @ SV119 @ SV36 ) )
= $true )
| ( ( ~ ( member @ SV124 @ SV80 ) )
= $true )
| ( ( ~ ( apply @ SV62 @ SV107 @ SV119 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV107 @ SV113 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV119 @ SV124 ) )
= $true )
| ( ( apply @ SV89 @ SV113 @ SV124 )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1188,plain,
! [SV36: $i,SV80: $i,SV62: $i,SV9: $i,SV89: $i] :
( ( ( member @ ( sK16_SY572 @ SV89 @ SV9 @ SV62 @ SV80 @ SV36 ) @ SV36 )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1176]) ).
thf(1189,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV80: $i,SV36: $i] :
( ( ( member @ ( sK21_SY625 @ SV36 @ SV80 @ SV62 @ SV9 @ SV89 ) @ SV80 )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1177]) ).
thf(1190,plain,
! [SV92: $i,SV83: $i,SV23: $i,SV121: $i,SV50: $i,SV90: $i,SV134: $i,SV116: $i,SV70: $i] :
( ( ( apply @ SV70 @ SV116 @ SV134 )
= $false )
| ( ( member @ SV134 @ SV90 )
= $false )
| ( ( ~ ( apply @ SV50 @ SV134 @ SV121 ) )
= $true )
| ( ( apply @ SV23 @ SV116 @ SV121 )
= $true )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1180]) ).
thf(1191,plain,
! [SV90: $i,SV70: $i,SV50: $i,SV23: $i,SV92: $i,SV83: $i,SV132: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK47_SY656 @ SV132 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK47_SY656 @ SV132 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) ) )
| ~ ( apply @ SV50 @ ( sK47_SY656 @ SV132 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $false )
| ( ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV132 )
= $false )
| ( ( member @ SV132 @ SV90 )
= $false )
| ( ( apply @ SV50 @ SV132 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1181]) ).
thf(1192,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV122: $i,SV118: $i,SV33: $i,SV106: $i,SV78: $i,SV112: $i] :
( ( ( member @ SV112 @ SV78 )
= $false )
| ( ( member @ SV106 @ SV33 )
= $false )
| ( ( ~ ( member @ SV118 @ SV33 ) )
= $true )
| ( ( ~ ( member @ SV122 @ SV78 ) )
= $true )
| ( ( ~ ( apply @ SV59 @ SV106 @ SV118 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV106 @ SV112 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV118 @ SV122 ) )
= $true )
| ( ( apply @ SV87 @ SV122 @ SV112 )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1182]) ).
thf(1193,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV131: $i,SV130: $i,SV34: $i,SV123: $i,SV79: $i,SV127: $i] :
( ( ( member @ SV127 @ SV79 )
= $false )
| ( ( member @ SV123 @ SV34 )
= $false )
| ( ( ~ ( member @ SV130 @ SV34 ) )
= $true )
| ( ( ~ ( member @ SV131 @ SV79 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV123 @ SV127 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV130 @ SV131 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV60 @ SV123 @ SV130 )
| ( apply @ SV88 @ SV127 @ SV131 ) )
| ~ ( ~ ( apply @ SV88 @ SV127 @ SV131 )
| ( apply @ SV60 @ SV123 @ SV130 ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1185]) ).
thf(1194,plain,
! [SV34: $i,SV79: $i,SV7: $i,SV60: $i,SV88: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ SV34 )
| ~ ( member @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 ) ) )
= $false )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1186]) ).
thf(1195,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV79: $i,SV34: $i] :
( ( ( ~ ( member @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV34 ) )
= $false )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1186]) ).
thf(1196,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV124: $i,SV119: $i,SV36: $i,SV107: $i,SV80: $i,SV113: $i] :
( ( ( member @ SV113 @ SV80 )
= $false )
| ( ( member @ SV107 @ SV36 )
= $false )
| ( ( ~ ( member @ SV119 @ SV36 ) )
= $true )
| ( ( ~ ( member @ SV124 @ SV80 ) )
= $true )
| ( ( ~ ( apply @ SV62 @ SV107 @ SV119 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV107 @ SV113 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV119 @ SV124 ) )
= $true )
| ( ( apply @ SV89 @ SV113 @ SV124 )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1187]) ).
thf(1197,plain,
! [SV92: $i,SV83: $i,SV23: $i,SV116: $i,SV70: $i,SV90: $i,SV121: $i,SV134: $i,SV50: $i] :
( ( ( apply @ SV50 @ SV134 @ SV121 )
= $false )
| ( ( member @ SV134 @ SV90 )
= $false )
| ( ( apply @ SV70 @ SV116 @ SV134 )
= $false )
| ( ( apply @ SV23 @ SV116 @ SV121 )
= $true )
| ( ( member @ SV116 @ SV83 )
= $false )
| ( ( member @ SV121 @ SV92 )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1190]) ).
thf(1198,plain,
! [SV90: $i,SV70: $i,SV50: $i,SV23: $i,SV92: $i,SV83: $i,SV132: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK47_SY656 @ SV132 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK47_SY656 @ SV132 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) ) )
| ~ ( apply @ SV50 @ ( sK47_SY656 @ SV132 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) ) )
= $true )
| ( ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV132 )
= $false )
| ( ( member @ SV132 @ SV90 )
= $false )
| ( ( apply @ SV50 @ SV132 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1191]) ).
thf(1199,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV122: $i,SV78: $i,SV112: $i,SV106: $i,SV33: $i,SV118: $i] :
( ( ( member @ SV118 @ SV33 )
= $false )
| ( ( member @ SV106 @ SV33 )
= $false )
| ( ( member @ SV112 @ SV78 )
= $false )
| ( ( ~ ( member @ SV122 @ SV78 ) )
= $true )
| ( ( ~ ( apply @ SV59 @ SV106 @ SV118 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV106 @ SV112 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV118 @ SV122 ) )
= $true )
| ( ( apply @ SV87 @ SV122 @ SV112 )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1192]) ).
thf(1200,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV131: $i,SV79: $i,SV127: $i,SV123: $i,SV34: $i,SV130: $i] :
( ( ( member @ SV130 @ SV34 )
= $false )
| ( ( member @ SV123 @ SV34 )
= $false )
| ( ( member @ SV127 @ SV79 )
= $false )
| ( ( ~ ( member @ SV131 @ SV79 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV123 @ SV127 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV130 @ SV131 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV60 @ SV123 @ SV130 )
| ( apply @ SV88 @ SV127 @ SV131 ) )
| ~ ( ~ ( apply @ SV88 @ SV127 @ SV131 )
| ( apply @ SV60 @ SV123 @ SV130 ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1193]) ).
thf(1201,plain,
! [SV34: $i,SV79: $i,SV7: $i,SV60: $i,SV88: $i] :
( ( ( ~ ( ~ ( member @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ SV34 )
| ~ ( member @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 ) ) )
= $true )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1194]) ).
thf(1202,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV79: $i,SV34: $i] :
( ( ( member @ ( sK40_SY669 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV34 )
= $true )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1195]) ).
thf(1203,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV124: $i,SV80: $i,SV113: $i,SV107: $i,SV36: $i,SV119: $i] :
( ( ( member @ SV119 @ SV36 )
= $false )
| ( ( member @ SV107 @ SV36 )
= $false )
| ( ( member @ SV113 @ SV80 )
= $false )
| ( ( ~ ( member @ SV124 @ SV80 ) )
= $true )
| ( ( ~ ( apply @ SV62 @ SV107 @ SV119 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV107 @ SV113 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV119 @ SV124 ) )
= $true )
| ( ( apply @ SV89 @ SV113 @ SV124 )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1196]) ).
thf(1204,plain,
! [SV90: $i,SV70: $i,SV50: $i,SV23: $i,SV92: $i,SV83: $i,SV132: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK47_SY656 @ SV132 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK47_SY656 @ SV132 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) ) )
| ~ ( apply @ SV50 @ ( sK47_SY656 @ SV132 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
= $false )
| ( ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV132 )
= $false )
| ( ( member @ SV132 @ SV90 )
= $false )
| ( ( apply @ SV50 @ SV132 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1198]) ).
thf(1205,plain,
! [SV87: $i,SV6: $i,SV59: $i,SV118: $i,SV33: $i,SV106: $i,SV112: $i,SV78: $i,SV122: $i] :
( ( ( member @ SV122 @ SV78 )
= $false )
| ( ( member @ SV112 @ SV78 )
= $false )
| ( ( member @ SV106 @ SV33 )
= $false )
| ( ( member @ SV118 @ SV33 )
= $false )
| ( ( ~ ( apply @ SV59 @ SV106 @ SV118 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV106 @ SV112 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV118 @ SV122 ) )
= $true )
| ( ( apply @ SV87 @ SV122 @ SV112 )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1199]) ).
thf(1206,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV130: $i,SV34: $i,SV123: $i,SV127: $i,SV79: $i,SV131: $i] :
( ( ( member @ SV131 @ SV79 )
= $false )
| ( ( member @ SV127 @ SV79 )
= $false )
| ( ( member @ SV123 @ SV34 )
= $false )
| ( ( member @ SV130 @ SV34 )
= $false )
| ( ( ~ ( apply @ SV7 @ SV123 @ SV127 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV130 @ SV131 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV60 @ SV123 @ SV130 )
| ( apply @ SV88 @ SV127 @ SV131 ) )
| ~ ( ~ ( apply @ SV88 @ SV127 @ SV131 )
| ( apply @ SV60 @ SV123 @ SV130 ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1200]) ).
thf(1207,plain,
! [SV34: $i,SV79: $i,SV7: $i,SV60: $i,SV88: $i] :
( ( ( ~ ( member @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ SV34 )
| ~ ( member @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 ) )
= $false )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1201]) ).
thf(1208,plain,
! [SV89: $i,SV9: $i,SV62: $i,SV119: $i,SV36: $i,SV107: $i,SV113: $i,SV80: $i,SV124: $i] :
( ( ( member @ SV124 @ SV80 )
= $false )
| ( ( member @ SV113 @ SV80 )
= $false )
| ( ( member @ SV107 @ SV36 )
= $false )
| ( ( member @ SV119 @ SV36 )
= $false )
| ( ( ~ ( apply @ SV62 @ SV107 @ SV119 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV107 @ SV113 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV119 @ SV124 ) )
= $true )
| ( ( apply @ SV89 @ SV113 @ SV124 )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1203]) ).
thf(1209,plain,
! [SV90: $i,SV70: $i,SV50: $i,SV23: $i,SV92: $i,SV83: $i,SV132: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK47_SY656 @ SV132 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK47_SY656 @ SV132 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) ) ) )
= $false )
| ( ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV132 )
= $false )
| ( ( member @ SV132 @ SV90 )
= $false )
| ( ( apply @ SV50 @ SV132 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1204]) ).
thf(1210,plain,
! [SV90: $i,SV70: $i,SV23: $i,SV92: $i,SV83: $i,SV132: $i,SV50: $i] :
( ( ( ~ ( apply @ SV50 @ ( sK47_SY656 @ SV132 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) ) )
= $false )
| ( ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV132 )
= $false )
| ( ( member @ SV132 @ SV90 )
= $false )
| ( ( apply @ SV50 @ SV132 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1204]) ).
thf(1211,plain,
! [SV87: $i,SV6: $i,SV122: $i,SV78: $i,SV112: $i,SV33: $i,SV118: $i,SV106: $i,SV59: $i] :
( ( ( apply @ SV59 @ SV106 @ SV118 )
= $false )
| ( ( member @ SV118 @ SV33 )
= $false )
| ( ( member @ SV106 @ SV33 )
= $false )
| ( ( member @ SV112 @ SV78 )
= $false )
| ( ( member @ SV122 @ SV78 )
= $false )
| ( ( ~ ( apply @ SV6 @ SV106 @ SV112 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV118 @ SV122 ) )
= $true )
| ( ( apply @ SV87 @ SV122 @ SV112 )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1205]) ).
thf(1212,plain,
! [SV88: $i,SV60: $i,SV131: $i,SV79: $i,SV34: $i,SV130: $i,SV127: $i,SV123: $i,SV7: $i] :
( ( ( apply @ SV7 @ SV123 @ SV127 )
= $false )
| ( ( member @ SV130 @ SV34 )
= $false )
| ( ( member @ SV123 @ SV34 )
= $false )
| ( ( member @ SV127 @ SV79 )
= $false )
| ( ( member @ SV131 @ SV79 )
= $false )
| ( ( ~ ( apply @ SV7 @ SV130 @ SV131 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV60 @ SV123 @ SV130 )
| ( apply @ SV88 @ SV127 @ SV131 ) )
| ~ ( ~ ( apply @ SV88 @ SV127 @ SV131 )
| ( apply @ SV60 @ SV123 @ SV130 ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1206]) ).
thf(1213,plain,
! [SV34: $i,SV79: $i,SV7: $i,SV60: $i,SV88: $i] :
( ( ( ~ ( member @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ SV34 ) )
= $false )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1207]) ).
thf(1214,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV79: $i,SV34: $i] :
( ( ( ~ ( member @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 ) )
= $false )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1207]) ).
thf(1215,plain,
! [SV89: $i,SV9: $i,SV124: $i,SV80: $i,SV113: $i,SV36: $i,SV119: $i,SV107: $i,SV62: $i] :
( ( ( apply @ SV62 @ SV107 @ SV119 )
= $false )
| ( ( member @ SV119 @ SV36 )
= $false )
| ( ( member @ SV107 @ SV36 )
= $false )
| ( ( member @ SV113 @ SV80 )
= $false )
| ( ( member @ SV124 @ SV80 )
= $false )
| ( ( ~ ( apply @ SV9 @ SV107 @ SV113 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV119 @ SV124 ) )
= $true )
| ( ( apply @ SV89 @ SV113 @ SV124 )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1208]) ).
thf(1216,plain,
! [SV90: $i,SV70: $i,SV50: $i,SV23: $i,SV92: $i,SV83: $i,SV132: $i] :
( ( ( ~ ( ~ ( member @ ( sK47_SY656 @ SV132 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK47_SY656 @ SV132 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) ) ) )
= $true )
| ( ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV132 )
= $false )
| ( ( member @ SV132 @ SV90 )
= $false )
| ( ( apply @ SV50 @ SV132 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1209]) ).
thf(1217,plain,
! [SV90: $i,SV70: $i,SV23: $i,SV92: $i,SV83: $i,SV132: $i,SV50: $i] :
( ( ( apply @ SV50 @ ( sK47_SY656 @ SV132 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $true )
| ( ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV132 )
= $false )
| ( ( member @ SV132 @ SV90 )
= $false )
| ( ( apply @ SV50 @ SV132 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1210]) ).
thf(1218,plain,
! [SV87: $i,SV59: $i,SV118: $i,SV33: $i,SV78: $i,SV122: $i,SV112: $i,SV106: $i,SV6: $i] :
( ( ( apply @ SV6 @ SV106 @ SV112 )
= $false )
| ( ( member @ SV122 @ SV78 )
= $false )
| ( ( member @ SV112 @ SV78 )
= $false )
| ( ( member @ SV106 @ SV33 )
= $false )
| ( ( member @ SV118 @ SV33 )
= $false )
| ( ( apply @ SV59 @ SV106 @ SV118 )
= $false )
| ( ( ~ ( apply @ SV6 @ SV118 @ SV122 ) )
= $true )
| ( ( apply @ SV87 @ SV122 @ SV112 )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1211]) ).
thf(1219,plain,
! [SV88: $i,SV60: $i,SV34: $i,SV123: $i,SV127: $i,SV79: $i,SV131: $i,SV130: $i,SV7: $i] :
( ( ( apply @ SV7 @ SV130 @ SV131 )
= $false )
| ( ( member @ SV131 @ SV79 )
= $false )
| ( ( member @ SV127 @ SV79 )
= $false )
| ( ( member @ SV123 @ SV34 )
= $false )
| ( ( member @ SV130 @ SV34 )
= $false )
| ( ( apply @ SV7 @ SV123 @ SV127 )
= $false )
| ( ( ~ ( ~ ( ~ ( apply @ SV60 @ SV123 @ SV130 )
| ( apply @ SV88 @ SV127 @ SV131 ) )
| ~ ( ~ ( apply @ SV88 @ SV127 @ SV131 )
| ( apply @ SV60 @ SV123 @ SV130 ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1212]) ).
thf(1220,plain,
! [SV34: $i,SV79: $i,SV7: $i,SV60: $i,SV88: $i] :
( ( ( member @ ( sK37_SY564 @ SV88 @ SV60 @ SV7 @ SV79 @ SV34 ) @ SV34 )
= $true )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1213]) ).
thf(1221,plain,
! [SV88: $i,SV60: $i,SV7: $i,SV79: $i,SV34: $i] :
( ( ( member @ ( sK38_SY666 @ SV34 @ SV79 @ SV7 @ SV60 @ SV88 ) @ SV79 )
= $true )
| ( ( maps @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( one_to_one @ SV7 @ SV34 @ SV79 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1214]) ).
thf(1222,plain,
! [SV89: $i,SV62: $i,SV119: $i,SV36: $i,SV80: $i,SV124: $i,SV113: $i,SV107: $i,SV9: $i] :
( ( ( apply @ SV9 @ SV107 @ SV113 )
= $false )
| ( ( member @ SV124 @ SV80 )
= $false )
| ( ( member @ SV113 @ SV80 )
= $false )
| ( ( member @ SV107 @ SV36 )
= $false )
| ( ( member @ SV119 @ SV36 )
= $false )
| ( ( apply @ SV62 @ SV107 @ SV119 )
= $false )
| ( ( ~ ( apply @ SV9 @ SV119 @ SV124 ) )
= $true )
| ( ( apply @ SV89 @ SV113 @ SV124 )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1215]) ).
thf(1223,plain,
! [SV90: $i,SV70: $i,SV50: $i,SV23: $i,SV92: $i,SV83: $i,SV132: $i] :
( ( ( ~ ( member @ ( sK47_SY656 @ SV132 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) @ SV90 )
| ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK47_SY656 @ SV132 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) ) )
= $false )
| ( ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV132 )
= $false )
| ( ( member @ SV132 @ SV90 )
= $false )
| ( ( apply @ SV50 @ SV132 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1224,plain,
! [SV87: $i,SV78: $i,SV112: $i,SV33: $i,SV106: $i,SV59: $i,SV122: $i,SV118: $i,SV6: $i] :
( ( ( apply @ SV6 @ SV118 @ SV122 )
= $false )
| ( ( apply @ SV59 @ SV106 @ SV118 )
= $false )
| ( ( member @ SV118 @ SV33 )
= $false )
| ( ( member @ SV106 @ SV33 )
= $false )
| ( ( member @ SV112 @ SV78 )
= $false )
| ( ( member @ SV122 @ SV78 )
= $false )
| ( ( apply @ SV6 @ SV106 @ SV112 )
= $false )
| ( ( apply @ SV87 @ SV122 @ SV112 )
= $true )
| ( ( decreasing @ SV6 @ SV33 @ SV59 @ SV78 @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1218]) ).
thf(1225,plain,
! [SV79: $i,SV34: $i,SV7: $i,SV131: $i,SV127: $i,SV88: $i,SV130: $i,SV123: $i,SV60: $i] :
( ( ( ~ ( ~ ( apply @ SV60 @ SV123 @ SV130 )
| ( apply @ SV88 @ SV127 @ SV131 ) )
| ~ ( ~ ( apply @ SV88 @ SV127 @ SV131 )
| ( apply @ SV60 @ SV123 @ SV130 ) ) )
= $false )
| ( ( apply @ SV7 @ SV123 @ SV127 )
= $false )
| ( ( member @ SV130 @ SV34 )
= $false )
| ( ( member @ SV123 @ SV34 )
= $false )
| ( ( member @ SV127 @ SV79 )
= $false )
| ( ( member @ SV131 @ SV79 )
= $false )
| ( ( apply @ SV7 @ SV130 @ SV131 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1219]) ).
thf(1226,plain,
! [SV89: $i,SV80: $i,SV113: $i,SV36: $i,SV107: $i,SV62: $i,SV124: $i,SV119: $i,SV9: $i] :
( ( ( apply @ SV9 @ SV119 @ SV124 )
= $false )
| ( ( apply @ SV62 @ SV107 @ SV119 )
= $false )
| ( ( member @ SV119 @ SV36 )
= $false )
| ( ( member @ SV107 @ SV36 )
= $false )
| ( ( member @ SV113 @ SV80 )
= $false )
| ( ( member @ SV124 @ SV80 )
= $false )
| ( ( apply @ SV9 @ SV107 @ SV113 )
= $false )
| ( ( apply @ SV89 @ SV113 @ SV124 )
= $true )
| ( ( increasing @ SV9 @ SV36 @ SV62 @ SV80 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1222]) ).
thf(1227,plain,
! [SV90: $i,SV70: $i,SV50: $i,SV23: $i,SV92: $i,SV83: $i,SV132: $i] :
( ( ( ~ ( member @ ( sK47_SY656 @ SV132 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) @ SV90 ) )
= $false )
| ( ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV132 )
= $false )
| ( ( member @ SV132 @ SV90 )
= $false )
| ( ( apply @ SV50 @ SV132 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1223]) ).
thf(1228,plain,
! [SV132: $i,SV83: $i,SV92: $i,SV23: $i,SV90: $i,SV50: $i,SV70: $i] :
( ( ( ~ ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK47_SY656 @ SV132 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) ) )
= $false )
| ( ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV132 )
= $false )
| ( ( member @ SV132 @ SV90 )
= $false )
| ( ( apply @ SV50 @ SV132 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1223]) ).
thf(1229,plain,
! [SV79: $i,SV34: $i,SV7: $i,SV131: $i,SV127: $i,SV88: $i,SV130: $i,SV123: $i,SV60: $i] :
( ( ( ~ ( ~ ( apply @ SV60 @ SV123 @ SV130 )
| ( apply @ SV88 @ SV127 @ SV131 ) ) )
= $false )
| ( ( apply @ SV7 @ SV123 @ SV127 )
= $false )
| ( ( member @ SV130 @ SV34 )
= $false )
| ( ( member @ SV123 @ SV34 )
= $false )
| ( ( member @ SV127 @ SV79 )
= $false )
| ( ( member @ SV131 @ SV79 )
= $false )
| ( ( apply @ SV7 @ SV130 @ SV131 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1225]) ).
thf(1230,plain,
! [SV79: $i,SV34: $i,SV7: $i,SV130: $i,SV123: $i,SV60: $i,SV131: $i,SV127: $i,SV88: $i] :
( ( ( ~ ( ~ ( apply @ SV88 @ SV127 @ SV131 )
| ( apply @ SV60 @ SV123 @ SV130 ) ) )
= $false )
| ( ( apply @ SV7 @ SV123 @ SV127 )
= $false )
| ( ( member @ SV130 @ SV34 )
= $false )
| ( ( member @ SV123 @ SV34 )
= $false )
| ( ( member @ SV127 @ SV79 )
= $false )
| ( ( member @ SV131 @ SV79 )
= $false )
| ( ( apply @ SV7 @ SV130 @ SV131 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1225]) ).
thf(1231,plain,
! [SV90: $i,SV70: $i,SV50: $i,SV23: $i,SV92: $i,SV83: $i,SV132: $i] :
( ( ( member @ ( sK47_SY656 @ SV132 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) @ SV90 )
= $true )
| ( ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV132 )
= $false )
| ( ( member @ SV132 @ SV90 )
= $false )
| ( ( apply @ SV50 @ SV132 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1227]) ).
thf(1232,plain,
! [SV132: $i,SV83: $i,SV92: $i,SV23: $i,SV90: $i,SV50: $i,SV70: $i] :
( ( ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ ( sK47_SY656 @ SV132 @ SV83 @ SV92 @ SV23 @ SV50 @ SV70 @ SV90 ) )
= $true )
| ( ( apply @ SV70 @ ( sK23_SY593 @ SV50 @ SV70 @ SV90 @ SV23 @ SV92 @ SV83 ) @ SV132 )
= $false )
| ( ( member @ SV132 @ SV90 )
= $false )
| ( ( apply @ SV50 @ SV132 @ ( sK28_SY645 @ SV83 @ SV92 @ SV23 @ SV90 @ SV70 @ SV50 ) )
= $false )
| ( ( compose_predicate @ SV23 @ SV50 @ SV70 @ SV83 @ SV90 @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1228]) ).
thf(1233,plain,
! [SV79: $i,SV34: $i,SV7: $i,SV131: $i,SV127: $i,SV88: $i,SV130: $i,SV123: $i,SV60: $i] :
( ( ( ~ ( apply @ SV60 @ SV123 @ SV130 )
| ( apply @ SV88 @ SV127 @ SV131 ) )
= $true )
| ( ( apply @ SV7 @ SV123 @ SV127 )
= $false )
| ( ( member @ SV130 @ SV34 )
= $false )
| ( ( member @ SV123 @ SV34 )
= $false )
| ( ( member @ SV127 @ SV79 )
= $false )
| ( ( member @ SV131 @ SV79 )
= $false )
| ( ( apply @ SV7 @ SV130 @ SV131 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1229]) ).
thf(1234,plain,
! [SV79: $i,SV34: $i,SV7: $i,SV130: $i,SV123: $i,SV60: $i,SV131: $i,SV127: $i,SV88: $i] :
( ( ( ~ ( apply @ SV88 @ SV127 @ SV131 )
| ( apply @ SV60 @ SV123 @ SV130 ) )
= $true )
| ( ( apply @ SV7 @ SV123 @ SV127 )
= $false )
| ( ( member @ SV130 @ SV34 )
= $false )
| ( ( member @ SV123 @ SV34 )
= $false )
| ( ( member @ SV127 @ SV79 )
= $false )
| ( ( member @ SV131 @ SV79 )
= $false )
| ( ( apply @ SV7 @ SV130 @ SV131 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1230]) ).
thf(1235,plain,
! [SV79: $i,SV34: $i,SV7: $i,SV131: $i,SV127: $i,SV88: $i,SV130: $i,SV123: $i,SV60: $i] :
( ( ( ~ ( apply @ SV60 @ SV123 @ SV130 ) )
= $true )
| ( ( apply @ SV88 @ SV127 @ SV131 )
= $true )
| ( ( apply @ SV7 @ SV123 @ SV127 )
= $false )
| ( ( member @ SV130 @ SV34 )
= $false )
| ( ( member @ SV123 @ SV34 )
= $false )
| ( ( member @ SV127 @ SV79 )
= $false )
| ( ( member @ SV131 @ SV79 )
= $false )
| ( ( apply @ SV7 @ SV130 @ SV131 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1233]) ).
thf(1236,plain,
! [SV79: $i,SV34: $i,SV7: $i,SV130: $i,SV123: $i,SV60: $i,SV131: $i,SV127: $i,SV88: $i] :
( ( ( ~ ( apply @ SV88 @ SV127 @ SV131 ) )
= $true )
| ( ( apply @ SV60 @ SV123 @ SV130 )
= $true )
| ( ( apply @ SV7 @ SV123 @ SV127 )
= $false )
| ( ( member @ SV130 @ SV34 )
= $false )
| ( ( member @ SV123 @ SV34 )
= $false )
| ( ( member @ SV127 @ SV79 )
= $false )
| ( ( member @ SV131 @ SV79 )
= $false )
| ( ( apply @ SV7 @ SV130 @ SV131 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1234]) ).
thf(1237,plain,
! [SV79: $i,SV34: $i,SV7: $i,SV131: $i,SV127: $i,SV88: $i,SV130: $i,SV123: $i,SV60: $i] :
( ( ( apply @ SV60 @ SV123 @ SV130 )
= $false )
| ( ( apply @ SV88 @ SV127 @ SV131 )
= $true )
| ( ( apply @ SV7 @ SV123 @ SV127 )
= $false )
| ( ( member @ SV130 @ SV34 )
= $false )
| ( ( member @ SV123 @ SV34 )
= $false )
| ( ( member @ SV127 @ SV79 )
= $false )
| ( ( member @ SV131 @ SV79 )
= $false )
| ( ( apply @ SV7 @ SV130 @ SV131 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1235]) ).
thf(1238,plain,
! [SV79: $i,SV34: $i,SV7: $i,SV130: $i,SV123: $i,SV60: $i,SV131: $i,SV127: $i,SV88: $i] :
( ( ( apply @ SV88 @ SV127 @ SV131 )
= $false )
| ( ( apply @ SV60 @ SV123 @ SV130 )
= $true )
| ( ( apply @ SV7 @ SV123 @ SV127 )
= $false )
| ( ( member @ SV130 @ SV34 )
= $false )
| ( ( member @ SV123 @ SV34 )
= $false )
| ( ( member @ SV127 @ SV79 )
= $false )
| ( ( member @ SV131 @ SV79 )
= $false )
| ( ( apply @ SV7 @ SV130 @ SV131 )
= $false )
| ( ( isomorphism @ SV7 @ SV34 @ SV60 @ SV79 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1236]) ).
thf(1239,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[94,1238,1237,1232,1231,1226,1224,1221,1220,1217,1202,1197,1189,1188,1184,1183,1179,1178,1174,1164,1163,1155,1153,1152,1147,1144,1141,1134,1132,1131,1129,1125,1124,1122,1116,1108,1103,1095,1092,1084,1077,1073,1071,1070,1056,1041,1038,1037,1014,1008,1002,995,994,970,947,946,945,940,932,914,913,904,900,899,898,895,888,884,883,870,869,864,859,855,854,844,843,837,832,831,821,820,817,814,813,788,787,786,776,762,761,753,752,744,743,735,719,718,711,702,694,693,678,677,676,659,636,635,632,612,601,598,591,581,571,570,559,555,554,547,541,523,522,518,517,511,510,493,492,474,469,468,467,466,452,451,450,439,365,364,349,348,152,124]) ).
thf(1240,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1239]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET764+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n018.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 14:53:52 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.17/1.48
% 7.17/1.48 No.of.Axioms: 28
% 7.17/1.48
% 7.17/1.48 Length.of.Defs: 0
% 7.17/1.48
% 7.17/1.48 Contains.Choice.Funs: false
% 7.17/1.48 ..............................................................
% 7.17/1.48
% 7.17/1.48 ********************************
% 7.17/1.48 * All subproblems solved! *
% 7.17/1.48 ********************************
% 7.17/1.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:29,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1239,loop_count:0,foatp_calls:1,translation:fof_full)
% 7.17/1.48
% 7.17/1.48 %**** Beginning of derivation protocol ****
% 7.17/1.48 % SZS output start CNFRefutation
% See solution above
% 7.17/1.50
% 7.17/1.50 %**** End of derivation protocol ****
% 7.17/1.50 %**** no. of clauses in derivation: 1240 ****
% 7.17/1.50 %**** clause counter: 1239 ****
% 7.17/1.50
% 7.17/1.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:29,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1239,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------