TSTP Solution File: SET764+4 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET764+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 03:04:46 EDT 2022
% Result : Theorem 1.23s 1.56s
% Output : CNFRefutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 102
% Syntax : Number of formulae : 1315 ( 479 unt; 73 typ; 0 def)
% Number of atoms : 12591 (3035 equ; 0 cnn)
% Maximal formula atoms : 11 ( 10 avg)
% Number of connectives : 44002 (6777 ~;5333 |; 302 &;31488 @)
% ( 60 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 249 ( 249 >; 0 *; 0 +; 0 <<)
% Number of symbols : 76 ( 73 usr; 6 con; 0-8 aty)
% Number of variables : 6622 ( 0 ^6604 !; 18 ?;6622 :)
% 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_SY148,type,
sK10_SY148: $i > $i > $i > $i > $i > $i ).
thf(tp_sK11_SY150,type,
sK11_SY150: $i > $i > $i > $i > $i > $i ).
thf(tp_sK12_X1,type,
sK12_X1: $i > $i > $i > $i > $i > $i ).
thf(tp_sK13_SY151,type,
sK13_SY151: $i > $i > $i > $i > $i > $i ).
thf(tp_sK14_SY154,type,
sK14_SY154: $i > $i > $i > $i > $i > $i ).
thf(tp_sK15_SY156,type,
sK15_SY156: $i > $i > $i > $i > $i > $i ).
thf(tp_sK16_Y,type,
sK16_Y: $i > $i > $i > $i > $i ).
thf(tp_sK17_Y,type,
sK17_Y: $i > $i > $i > $i ).
thf(tp_sK18_X,type,
sK18_X: $i > $i > $i > $i > $i ).
thf(tp_sK19_X,type,
sK19_X: $i > $i > $i > $i ).
thf(tp_sK1_F,type,
sK1_F: $i ).
thf(tp_sK20_X,type,
sK20_X: $i > $i > $i > $i > $i ).
thf(tp_sK21_SY157,type,
sK21_SY157: $i > $i > $i > $i > $i ).
thf(tp_sK22_E,type,
sK22_E: $i > $i > $i > $i > $i ).
thf(tp_sK23_Y,type,
sK23_Y: $i > $i > $i > $i ).
thf(tp_sK24_X1,type,
sK24_X1: $i > $i > $i > $i ).
thf(tp_sK25_SY159,type,
sK25_SY159: $i > $i > $i > $i ).
thf(tp_sK26_SY161,type,
sK26_SY161: $i > $i > $i > $i ).
thf(tp_sK27_X,type,
sK27_X: $i > $i > $i ).
thf(tp_sK28_X,type,
sK28_X: $i > $i > $i > $i > $i ).
thf(tp_sK29_SY162,type,
sK29_SY162: $i > $i > $i > $i > $i ).
thf(tp_sK2_SY136,type,
sK2_SY136: $i ).
thf(tp_sK30_SY164,type,
sK30_SY164: $i > $i > $i > $i > $i ).
thf(tp_sK31_Y,type,
sK31_Y: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK32_Y,type,
sK32_Y: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK33_X,type,
sK33_X: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK34_SY165,type,
sK34_SY165: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK35_SY169,type,
sK35_SY169: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK36_Y,type,
sK36_Y: $i > $i > $i > $i > $i ).
thf(tp_sK37_X,type,
sK37_X: $i > $i > $i > $i ).
thf(tp_sK38_SY170,type,
sK38_SY170: $i > $i > $i > $i ).
thf(tp_sK39_SY172,type,
sK39_SY172: $i > $i > $i > $i ).
thf(tp_sK3_SY138,type,
sK3_SY138: $i ).
thf(tp_sK40_X,type,
sK40_X: $i > $i > $i > $i ).
thf(tp_sK41_Y,type,
sK41_Y: $i > $i > $i ).
thf(tp_sK42_Y,type,
sK42_Y: $i > $i > $i ).
thf(tp_sK43_X,type,
sK43_X: $i > $i > $i ).
thf(tp_sK4_X1,type,
sK4_X1: $i > $i > $i > $i > $i > $i ).
thf(tp_sK5_SY139,type,
sK5_SY139: $i > $i > $i > $i > $i > $i ).
thf(tp_sK6_SY142,type,
sK6_SY142: $i > $i > $i > $i > $i > $i ).
thf(tp_sK7_SY144,type,
sK7_SY144: $i > $i > $i > $i > $i > $i ).
thf(tp_sK8_X1,type,
sK8_X1: $i > $i > $i > $i > $i > $i ).
thf(tp_sK9_SY145,type,
sK9_SY145: $i > $i > $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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',unordered_pair) ).
thf(21,axiom,
! [X: $i,A: $i] :
( ( member @ X @ ( singleton @ A ) )
<=> ( X = A ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',difference) ).
thf(23,axiom,
! [X: $i] :
~ ( member @ X @ empty_set ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',intersection) ).
thf(26,axiom,
! [X: $i,A: $i] :
( ( member @ X @ ( power_set @ A ) )
<=> ( subset @ X @ A ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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,
( ( ! [F: $i,A: $i,R: $i] :
( ! [B: $i,S: $i] :
( ( ( member @ ( sK4_X1 @ S @ B @ R @ A @ F ) @ A )
& ( member @ ( sK5_SY139 @ S @ B @ R @ A @ F ) @ B )
& ( member @ ( sK6_SY142 @ S @ B @ R @ A @ F ) @ A )
& ( member @ ( sK7_SY144 @ S @ B @ R @ A @ F ) @ B )
& ( apply @ F @ ( sK4_X1 @ S @ B @ R @ A @ F ) @ ( sK5_SY139 @ S @ B @ R @ A @ F ) )
& ( apply @ F @ ( sK6_SY142 @ S @ B @ R @ A @ F ) @ ( sK7_SY144 @ S @ B @ R @ A @ F ) )
& ( ~ ( apply @ R @ ( sK4_X1 @ S @ B @ R @ A @ F ) @ ( sK6_SY142 @ S @ B @ R @ A @ F ) )
| ~ ( apply @ S @ ( sK5_SY139 @ S @ B @ R @ A @ F ) @ ( sK7_SY144 @ S @ B @ R @ A @ F ) ) )
& ( ( apply @ R @ ( sK4_X1 @ S @ B @ R @ A @ F ) @ ( sK6_SY142 @ S @ B @ R @ A @ F ) )
| ( apply @ S @ ( sK5_SY139 @ S @ B @ R @ A @ F ) @ ( sK7_SY144 @ S @ B @ R @ A @ F ) ) ) )
| ~ ( maps @ F @ A @ B )
| ~ ( one_to_one @ F @ A @ B )
| ( isomorphism @ F @ A @ R @ B @ S ) )
& ! [B: $i,S: $i] :
( ~ ( isomorphism @ 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 @ F @ X1 @ Y1 )
| ~ ( apply @ F @ X2 @ Y2 )
| ~ ( apply @ R @ X1 @ X2 )
| ( apply @ S @ Y1 @ Y2 ) )
& ! [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 @ S @ Y1 @ Y2 )
| ( apply @ R @ X1 @ X2 ) ) ) )
& ! [B: $i] :
( ! [S: $i] :
~ ( isomorphism @ F @ A @ R @ B @ S )
| ( maps @ F @ A @ B ) )
& ! [B: $i] :
( ! [S: $i] :
~ ( isomorphism @ F @ A @ R @ B @ S )
| ( one_to_one @ F @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[32]) ).
thf(67,plain,
( ( ! [F: $i,A: $i,R: $i] :
( ! [B: $i,S: $i] :
( ( ( member @ ( sK8_X1 @ S @ B @ R @ A @ F ) @ A )
& ( member @ ( sK9_SY145 @ S @ B @ R @ A @ F ) @ B )
& ( member @ ( sK10_SY148 @ S @ B @ R @ A @ F ) @ A )
& ( member @ ( sK11_SY150 @ S @ B @ R @ A @ F ) @ B )
& ( apply @ R @ ( sK8_X1 @ S @ B @ R @ A @ F ) @ ( sK10_SY148 @ S @ B @ R @ A @ F ) )
& ( apply @ F @ ( sK8_X1 @ S @ B @ R @ A @ F ) @ ( sK9_SY145 @ S @ B @ R @ A @ F ) )
& ( apply @ F @ ( sK10_SY148 @ S @ B @ R @ A @ F ) @ ( sK11_SY150 @ S @ B @ R @ A @ F ) )
& ~ ( apply @ S @ ( sK11_SY150 @ S @ B @ R @ A @ F ) @ ( sK9_SY145 @ S @ B @ R @ A @ F ) ) )
| ( decreasing @ F @ A @ R @ B @ S ) )
& ! [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(extcnf_combined,[status(esa)],[33]) ).
thf(68,plain,
( ( ! [F: $i,A: $i,R: $i] :
( ! [B: $i,S: $i] :
( ( ( member @ ( sK12_X1 @ S @ B @ R @ A @ F ) @ A )
& ( member @ ( sK13_SY151 @ S @ B @ R @ A @ F ) @ B )
& ( member @ ( sK14_SY154 @ S @ B @ R @ A @ F ) @ A )
& ( member @ ( sK15_SY156 @ S @ B @ R @ A @ F ) @ B )
& ( apply @ R @ ( sK12_X1 @ S @ B @ R @ A @ F ) @ ( sK14_SY154 @ S @ B @ R @ A @ F ) )
& ( apply @ F @ ( sK12_X1 @ S @ B @ R @ A @ F ) @ ( sK13_SY151 @ S @ B @ R @ A @ F ) )
& ( apply @ F @ ( sK14_SY154 @ S @ B @ R @ A @ F ) @ ( sK15_SY156 @ S @ B @ R @ A @ F ) )
& ~ ( apply @ S @ ( sK13_SY151 @ S @ B @ R @ A @ F ) @ ( sK15_SY156 @ S @ B @ R @ A @ F ) ) )
| ( increasing @ F @ A @ R @ B @ S ) )
& ! [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(extcnf_combined,[status(esa)],[34]) ).
thf(69,plain,
( ( ! [F: $i,B: $i] :
( ! [A: $i,X: $i] :
( ! [Y: $i] :
( ~ ( apply @ F @ X @ Y )
| ~ ( member @ Y @ B ) )
| ~ ( member @ X @ A )
| ( member @ X @ ( inverse_image3 @ F @ B @ A ) ) )
& ! [A: $i,X: $i] :
( ~ ( member @ X @ ( inverse_image3 @ F @ B @ A ) )
| ( ( apply @ F @ X @ ( sK16_Y @ X @ A @ B @ F ) )
& ( member @ ( sK16_Y @ X @ A @ B @ F ) @ B ) ) )
& ! [A: $i,X: $i] :
( ~ ( member @ X @ ( inverse_image3 @ F @ B @ A ) )
| ( member @ X @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(70,plain,
( ( ! [F: $i] :
( ! [B: $i,X: $i] :
( ! [Y: $i] :
( ~ ( apply @ F @ X @ Y )
| ~ ( member @ Y @ B ) )
| ( member @ X @ ( inverse_image2 @ F @ B ) ) )
& ! [B: $i,X: $i] :
( ~ ( member @ X @ ( inverse_image2 @ F @ B ) )
| ( ( apply @ F @ X @ ( sK17_Y @ X @ B @ F ) )
& ( member @ ( sK17_Y @ X @ B @ F ) @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(71,plain,
( ( ! [F: $i,A: $i] :
( ! [B: $i,Y: $i] :
( ! [X: $i] :
( ~ ( apply @ F @ X @ Y )
| ~ ( member @ X @ A ) )
| ~ ( member @ Y @ B )
| ( member @ Y @ ( image3 @ F @ A @ B ) ) )
& ! [B: $i,Y: $i] :
( ~ ( member @ Y @ ( image3 @ F @ A @ B ) )
| ( ( apply @ F @ ( sK18_X @ Y @ B @ A @ F ) @ Y )
& ( member @ ( sK18_X @ Y @ B @ A @ F ) @ A ) ) )
& ! [B: $i,Y: $i] :
( ~ ( member @ Y @ ( image3 @ F @ A @ B ) )
| ( member @ Y @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(72,plain,
( ( ! [F: $i] :
( ! [A: $i,Y: $i] :
( ! [X: $i] :
( ~ ( apply @ F @ X @ Y )
| ~ ( member @ X @ A ) )
| ( member @ Y @ ( image2 @ F @ A ) ) )
& ! [A: $i,Y: $i] :
( ~ ( member @ Y @ ( image2 @ F @ A ) )
| ( ( apply @ F @ ( sK19_X @ Y @ A @ F ) @ Y )
& ( member @ ( sK19_X @ Y @ A @ F ) @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(73,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 ) )
& ! [X: $i,Y: $i] :
( ~ ( member @ X @ A )
| ~ ( member @ Y @ B )
| ~ ( apply @ ( inverse_function @ F @ A @ B ) @ Y @ X )
| ( apply @ F @ X @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(74,plain,
( ( ! [G: $i,F: $i] :
( ! [A: $i,B: $i] :
( ( ( member @ ( sK20_X @ B @ A @ F @ G ) @ A )
& ( member @ ( sK21_SY157 @ B @ A @ F @ G ) @ B )
& ( ~ ( apply @ F @ ( sK20_X @ B @ A @ F @ G ) @ ( sK21_SY157 @ B @ A @ F @ G ) )
| ~ ( apply @ G @ ( sK21_SY157 @ B @ A @ F @ G ) @ ( sK20_X @ B @ A @ F @ G ) ) )
& ( ( apply @ F @ ( sK20_X @ B @ A @ F @ G ) @ ( sK21_SY157 @ B @ A @ F @ G ) )
| ( apply @ G @ ( sK21_SY157 @ B @ A @ F @ G ) @ ( sK20_X @ B @ A @ F @ G ) ) ) )
| ( inverse_predicate @ G @ F @ A @ B ) )
& ! [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 ) )
& ! [X: $i,Y: $i] :
( ~ ( member @ X @ A )
| ~ ( member @ Y @ B )
| ~ ( apply @ G @ Y @ X )
| ( apply @ F @ X @ Y ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(75,plain,
( ( ! [F: $i] :
( ! [A: $i,B: $i] :
( ~ ( injective @ F @ A @ B )
| ~ ( surjective @ F @ A @ B )
| ( one_to_one @ F @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( one_to_one @ F @ A @ B )
| ( injective @ F @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( one_to_one @ F @ A @ B )
| ( surjective @ F @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(76,plain,
( ( ! [F: $i] :
( ! [A: $i,B: $i] :
( ( ( member @ ( sK23_Y @ B @ A @ F ) @ B )
& ! [SY158: $i] :
( ~ ( apply @ F @ SY158 @ ( sK23_Y @ B @ A @ F ) )
| ~ ( member @ SY158 @ A ) ) )
| ( surjective @ F @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( surjective @ F @ A @ B )
| ! [Y: $i] :
( ~ ( member @ Y @ B )
| ( ( apply @ F @ ( sK22_E @ Y @ B @ A @ F ) @ Y )
& ( member @ ( sK22_E @ Y @ B @ A @ F ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(77,plain,
( ( ! [F: $i] :
( ! [A: $i,B: $i] :
( ( ( member @ ( sK24_X1 @ B @ A @ F ) @ A )
& ( member @ ( sK25_SY159 @ B @ A @ F ) @ A )
& ( member @ ( sK26_SY161 @ B @ A @ F ) @ B )
& ( apply @ F @ ( sK24_X1 @ B @ A @ F ) @ ( sK26_SY161 @ B @ A @ F ) )
& ( apply @ F @ ( sK25_SY159 @ B @ A @ F ) @ ( sK26_SY161 @ B @ A @ F ) )
& ( ( sK24_X1 @ B @ A @ F )
!= ( sK25_SY159 @ B @ A @ F ) ) )
| ( injective @ F @ A @ B ) )
& ! [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(extcnf_combined,[status(esa)],[43]) ).
thf(78,plain,
( ( ! [F: $i,A: $i] :
( ( ( member @ ( sK27_X @ A @ F ) @ A )
& ~ ( apply @ F @ ( sK27_X @ A @ F ) @ ( sK27_X @ A @ F ) ) )
| ( identity @ F @ A ) )
& ! [F: $i,A: $i] :
( ~ ( identity @ F @ A )
| ! [X: $i] :
( ~ ( member @ X @ A )
| ( apply @ F @ X @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(79,plain,
( ( ! [F: $i,G: $i] :
( ! [A: $i,B: $i] :
( ( ( member @ ( sK28_X @ B @ A @ G @ F ) @ A )
& ( member @ ( sK29_SY162 @ B @ A @ G @ F ) @ B )
& ( member @ ( sK30_SY164 @ B @ A @ G @ F ) @ B )
& ( apply @ F @ ( sK28_X @ B @ A @ G @ F ) @ ( sK29_SY162 @ B @ A @ G @ F ) )
& ( apply @ G @ ( sK28_X @ B @ A @ G @ F ) @ ( sK30_SY164 @ B @ A @ G @ F ) )
& ( ( sK29_SY162 @ B @ A @ G @ F )
!= ( sK30_SY164 @ B @ A @ G @ F ) ) )
| ( equal_maps @ F @ G @ A @ B ) )
& ! [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(extcnf_combined,[status(esa)],[45]) ).
thf(80,plain,
( ( ! [G: $i,F: $i,A: $i,B: $i,C: $i] :
( ! [X: $i,Z: $i] :
( ~ ( member @ X @ A )
| ~ ( member @ Z @ C )
| ! [Y: $i] :
( ~ ( apply @ F @ X @ Y )
| ~ ( member @ Y @ B )
| ~ ( apply @ G @ Y @ Z ) )
| ( apply @ ( compose_function @ G @ F @ A @ B @ C ) @ X @ Z ) )
& ! [X: $i,Z: $i] :
( ~ ( member @ X @ A )
| ~ ( member @ Z @ C )
| ~ ( apply @ ( compose_function @ G @ F @ A @ B @ C ) @ X @ Z )
| ( ( apply @ F @ X @ ( sK31_Y @ Z @ X @ C @ B @ A @ F @ G ) )
& ( member @ ( sK31_Y @ Z @ X @ C @ B @ A @ F @ G ) @ B )
& ( apply @ G @ ( sK31_Y @ Z @ X @ C @ B @ A @ F @ G ) @ Z ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(81,plain,
( ( ! [H: $i,G: $i,F: $i,A: $i] :
( ! [B: $i,C: $i] :
( ( ( member @ ( sK33_X @ C @ B @ A @ F @ G @ H ) @ A )
& ( member @ ( sK34_SY165 @ C @ B @ A @ F @ G @ H ) @ C )
& ( ! [SY168: $i] :
( ~ ( apply @ F @ ( sK33_X @ C @ B @ A @ F @ G @ H ) @ SY168 )
| ~ ( member @ SY168 @ B )
| ~ ( apply @ G @ SY168 @ ( sK34_SY165 @ C @ B @ A @ F @ G @ H ) ) )
| ~ ( apply @ H @ ( sK33_X @ C @ B @ A @ F @ G @ H ) @ ( sK34_SY165 @ C @ B @ A @ F @ G @ H ) ) )
& ( ( ( apply @ F @ ( sK33_X @ C @ B @ A @ F @ G @ H ) @ ( sK35_SY169 @ C @ B @ A @ F @ G @ H ) )
& ( member @ ( sK35_SY169 @ C @ B @ A @ F @ G @ H ) @ B )
& ( apply @ G @ ( sK35_SY169 @ C @ B @ A @ F @ G @ H ) @ ( sK34_SY165 @ C @ B @ A @ F @ G @ H ) ) )
| ( apply @ H @ ( sK33_X @ C @ B @ A @ F @ G @ H ) @ ( sK34_SY165 @ C @ B @ A @ F @ G @ H ) ) ) )
| ( compose_predicate @ H @ G @ F @ A @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( compose_predicate @ H @ G @ F @ A @ B @ C )
| ( ! [X: $i,Z: $i] :
( ~ ( member @ X @ A )
| ~ ( member @ Z @ C )
| ! [Y: $i] :
( ~ ( apply @ F @ X @ Y )
| ~ ( member @ Y @ B )
| ~ ( apply @ G @ Y @ Z ) )
| ( apply @ H @ X @ Z ) )
& ! [X: $i,Z: $i] :
( ~ ( member @ X @ A )
| ~ ( member @ Z @ C )
| ~ ( apply @ H @ X @ Z )
| ( ( apply @ F @ X @ ( sK32_Y @ Z @ X @ C @ B @ A @ F @ G @ H ) )
& ( member @ ( sK32_Y @ Z @ X @ C @ B @ A @ F @ G @ H ) @ B )
& ( apply @ G @ ( sK32_Y @ Z @ X @ C @ B @ A @ F @ G @ H ) @ Z ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(82,plain,
( ( ! [F: $i] :
( ! [A: $i,B: $i] :
( ( ( member @ ( sK40_X @ B @ A @ F ) @ A )
& ! [SY173: $i] :
( ~ ( apply @ F @ ( sK40_X @ B @ A @ F ) @ SY173 )
| ~ ( member @ SY173 @ B ) ) )
| ( ( member @ ( sK37_X @ B @ A @ F ) @ A )
& ( member @ ( sK38_SY170 @ B @ A @ F ) @ B )
& ( member @ ( sK39_SY172 @ B @ A @ F ) @ B )
& ( apply @ F @ ( sK37_X @ B @ A @ F ) @ ( sK38_SY170 @ B @ A @ F ) )
& ( apply @ F @ ( sK37_X @ B @ A @ F ) @ ( sK39_SY172 @ B @ A @ F ) )
& ( ( sK38_SY170 @ B @ A @ F )
!= ( sK39_SY172 @ B @ A @ F ) ) )
| ( maps @ F @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( maps @ F @ A @ B )
| ! [X: $i] :
( ~ ( member @ X @ A )
| ( ( apply @ F @ X @ ( sK36_Y @ X @ B @ A @ F ) )
& ( member @ ( sK36_Y @ X @ B @ A @ F ) @ B ) ) ) )
& ! [A: $i,B: $i] :
( ~ ( maps @ F @ A @ B )
| ! [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(extcnf_combined,[status(esa)],[48]) ).
thf(83,plain,
( ( ! [X: $i,A: $i] :
( ( ( member @ ( sK41_Y @ A @ X ) @ A )
& ~ ( member @ X @ ( sK41_Y @ A @ X ) ) )
| ( member @ X @ ( product @ A ) ) )
& ! [X: $i,A: $i] :
( ~ ( member @ X @ ( product @ A ) )
| ! [Y: $i] :
( ~ ( member @ Y @ A )
| ( member @ X @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(84,plain,
( ( ! [X: $i,A: $i] :
( ! [Y: $i] :
( ~ ( member @ Y @ A )
| ~ ( member @ X @ Y ) )
| ( member @ X @ ( sum @ A ) ) )
& ! [X: $i,A: $i] :
( ~ ( member @ X @ ( sum @ A ) )
| ( ( member @ ( sK42_Y @ A @ X ) @ A )
& ( member @ X @ ( sK42_Y @ A @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(85,plain,
( ( ! [X: $i] :
( ! [A: $i,B: $i] :
( ~ ( member @ X @ ( unordered_pair @ A @ B ) )
| ( X = A )
| ( X = B ) )
& ! [A: $i] :
( ( X != A )
| ! [B: $i] : ( member @ X @ ( unordered_pair @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ( X != B )
| ( member @ X @ ( unordered_pair @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(86,plain,
( ( ! [X: $i,A: $i] :
( ( X != A )
| ( member @ X @ ( singleton @ A ) ) )
& ! [X: $i,A: $i] :
( ~ ( member @ X @ ( singleton @ A ) )
| ( X = A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[52]) ).
thf(87,plain,
( ( ! [B: $i] :
( ! [A: $i,E: $i] :
( ~ ( member @ B @ E )
| ( member @ B @ A )
| ( member @ B @ ( difference @ E @ A ) ) )
& ! [A: $i,E: $i] :
( ~ ( member @ B @ ( difference @ E @ A ) )
| ( member @ B @ E ) )
& ! [A: $i] :
( ! [E: $i] :
~ ( member @ B @ ( difference @ E @ A ) )
| ~ ( member @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(88,plain,
( ( ! [X: $i] :
( ! [A: $i,B: $i] :
( ~ ( member @ X @ ( union @ A @ B ) )
| ( member @ X @ A )
| ( member @ X @ B ) )
& ! [A: $i] :
( ~ ( member @ X @ A )
| ! [B: $i] : ( member @ X @ ( union @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( member @ X @ B )
| ( member @ X @ ( union @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[55]) ).
thf(89,plain,
( ( ! [X: $i] :
( ! [A: $i,B: $i] :
( ~ ( member @ X @ A )
| ~ ( member @ X @ B )
| ( member @ X @ ( intersection @ A @ B ) ) )
& ! [A: $i] :
( ! [B: $i] :
~ ( member @ X @ ( intersection @ A @ B ) )
| ( member @ X @ A ) )
& ! [A: $i,B: $i] :
( ~ ( member @ X @ ( intersection @ A @ B ) )
| ( member @ X @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[56]) ).
thf(90,plain,
( ( ! [X: $i,A: $i] :
( ~ ( member @ X @ ( power_set @ A ) )
| ( subset @ X @ A ) )
& ! [X: $i,A: $i] :
( ~ ( subset @ X @ A )
| ( member @ X @ ( power_set @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[57]) ).
thf(91,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( equal_set @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( equal_set @ A @ B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( equal_set @ A @ B )
| ( subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[58]) ).
thf(92,plain,
( ( ! [A: $i,B: $i] :
( ( ( member @ ( sK43_X @ B @ A ) @ A )
& ~ ( member @ ( sK43_X @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [X: $i] :
( ~ ( member @ X @ A )
| ( member @ X @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[59]) ).
thf(93,plain,
( ( ! [A: $i,B: $i] :
( ( ( member @ ( sK43_X @ B @ A ) @ A )
& ~ ( member @ ( sK43_X @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [X: $i] :
( ~ ( member @ X @ A )
| ( member @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(94,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( equal_set @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( equal_set @ A @ B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( equal_set @ A @ B )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(95,plain,
( ( ! [X: $i,A: $i] :
( ~ ( member @ X @ ( power_set @ A ) )
| ( subset @ X @ A ) )
& ! [X: $i,A: $i] :
( ~ ( subset @ X @ A )
| ( member @ X @ ( power_set @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(96,plain,
( ( ! [X: $i] :
( ! [A: $i,B: $i] :
( ~ ( member @ X @ A )
| ~ ( member @ X @ B )
| ( member @ X @ ( intersection @ A @ B ) ) )
& ! [A: $i] :
( ! [B: $i] :
~ ( member @ X @ ( intersection @ A @ B ) )
| ( member @ X @ A ) )
& ! [A: $i,B: $i] :
( ~ ( member @ X @ ( intersection @ A @ B ) )
| ( member @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(97,plain,
( ( ! [X: $i] :
( ! [A: $i,B: $i] :
( ~ ( member @ X @ ( union @ A @ B ) )
| ( member @ X @ A )
| ( member @ X @ B ) )
& ! [A: $i] :
( ~ ( member @ X @ A )
| ! [B: $i] : ( member @ X @ ( union @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( member @ X @ B )
| ( member @ X @ ( union @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(98,plain,
( ( ! [X: $i] :
~ ( member @ X @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(99,plain,
( ( ! [B: $i] :
( ! [A: $i,E: $i] :
( ~ ( member @ B @ E )
| ( member @ B @ A )
| ( member @ B @ ( difference @ E @ A ) ) )
& ! [A: $i,E: $i] :
( ~ ( member @ B @ ( difference @ E @ A ) )
| ( member @ B @ E ) )
& ! [A: $i] :
( ! [E: $i] :
~ ( member @ B @ ( difference @ E @ A ) )
| ~ ( member @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(100,plain,
( ( ! [X: $i,A: $i] :
( ( X != A )
| ( member @ X @ ( singleton @ A ) ) )
& ! [X: $i,A: $i] :
( ~ ( member @ X @ ( singleton @ A ) )
| ( X = A ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(101,plain,
( ( ! [X: $i] :
( ! [A: $i,B: $i] :
( ~ ( member @ X @ ( unordered_pair @ A @ B ) )
| ( X = A )
| ( X = B ) )
& ! [A: $i] :
( ( X != A )
| ! [B: $i] : ( member @ X @ ( unordered_pair @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ( X != B )
| ( member @ X @ ( unordered_pair @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(102,plain,
( ( ! [X: $i,A: $i] :
( ! [Y: $i] :
( ~ ( member @ Y @ A )
| ~ ( member @ X @ Y ) )
| ( member @ X @ ( sum @ A ) ) )
& ! [X: $i,A: $i] :
( ~ ( member @ X @ ( sum @ A ) )
| ( ( member @ ( sK42_Y @ A @ X ) @ A )
& ( member @ X @ ( sK42_Y @ A @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(103,plain,
( ( ! [X: $i,A: $i] :
( ( ( member @ ( sK41_Y @ A @ X ) @ A )
& ~ ( member @ X @ ( sK41_Y @ A @ X ) ) )
| ( member @ X @ ( product @ A ) ) )
& ! [X: $i,A: $i] :
( ~ ( member @ X @ ( product @ A ) )
| ! [Y: $i] :
( ~ ( member @ Y @ A )
| ( member @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(104,plain,
( ( ! [F: $i] :
( ! [A: $i,B: $i] :
( ( ( member @ ( sK40_X @ B @ A @ F ) @ A )
& ! [SY173: $i] :
( ~ ( apply @ F @ ( sK40_X @ B @ A @ F ) @ SY173 )
| ~ ( member @ SY173 @ B ) ) )
| ( ( member @ ( sK37_X @ B @ A @ F ) @ A )
& ( member @ ( sK38_SY170 @ B @ A @ F ) @ B )
& ( member @ ( sK39_SY172 @ B @ A @ F ) @ B )
& ( apply @ F @ ( sK37_X @ B @ A @ F ) @ ( sK38_SY170 @ B @ A @ F ) )
& ( apply @ F @ ( sK37_X @ B @ A @ F ) @ ( sK39_SY172 @ B @ A @ F ) )
& ( ( sK38_SY170 @ B @ A @ F )
!= ( sK39_SY172 @ B @ A @ F ) ) )
| ( maps @ F @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( maps @ F @ A @ B )
| ! [X: $i] :
( ~ ( member @ X @ A )
| ( ( apply @ F @ X @ ( sK36_Y @ X @ B @ A @ F ) )
& ( member @ ( sK36_Y @ X @ B @ A @ F ) @ B ) ) ) )
& ! [A: $i,B: $i] :
( ~ ( maps @ F @ A @ B )
| ! [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)],[82]) ).
thf(105,plain,
( ( ! [H: $i,G: $i,F: $i,A: $i] :
( ! [B: $i,C: $i] :
( ( ( member @ ( sK33_X @ C @ B @ A @ F @ G @ H ) @ A )
& ( member @ ( sK34_SY165 @ C @ B @ A @ F @ G @ H ) @ C )
& ( ! [SY168: $i] :
( ~ ( apply @ F @ ( sK33_X @ C @ B @ A @ F @ G @ H ) @ SY168 )
| ~ ( member @ SY168 @ B )
| ~ ( apply @ G @ SY168 @ ( sK34_SY165 @ C @ B @ A @ F @ G @ H ) ) )
| ~ ( apply @ H @ ( sK33_X @ C @ B @ A @ F @ G @ H ) @ ( sK34_SY165 @ C @ B @ A @ F @ G @ H ) ) )
& ( ( ( apply @ F @ ( sK33_X @ C @ B @ A @ F @ G @ H ) @ ( sK35_SY169 @ C @ B @ A @ F @ G @ H ) )
& ( member @ ( sK35_SY169 @ C @ B @ A @ F @ G @ H ) @ B )
& ( apply @ G @ ( sK35_SY169 @ C @ B @ A @ F @ G @ H ) @ ( sK34_SY165 @ C @ B @ A @ F @ G @ H ) ) )
| ( apply @ H @ ( sK33_X @ C @ B @ A @ F @ G @ H ) @ ( sK34_SY165 @ C @ B @ A @ F @ G @ H ) ) ) )
| ( compose_predicate @ H @ G @ F @ A @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( compose_predicate @ H @ G @ F @ A @ B @ C )
| ( ! [X: $i,Z: $i] :
( ~ ( member @ X @ A )
| ~ ( member @ Z @ C )
| ! [Y: $i] :
( ~ ( apply @ F @ X @ Y )
| ~ ( member @ Y @ B )
| ~ ( apply @ G @ Y @ Z ) )
| ( apply @ H @ X @ Z ) )
& ! [X: $i,Z: $i] :
( ~ ( member @ X @ A )
| ~ ( member @ Z @ C )
| ~ ( apply @ H @ X @ Z )
| ( ( apply @ F @ X @ ( sK32_Y @ Z @ X @ C @ B @ A @ F @ G @ H ) )
& ( member @ ( sK32_Y @ Z @ X @ C @ B @ A @ F @ G @ H ) @ B )
& ( apply @ G @ ( sK32_Y @ Z @ X @ C @ B @ A @ F @ G @ H ) @ Z ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(106,plain,
( ( ! [G: $i,F: $i,A: $i,B: $i,C: $i] :
( ! [X: $i,Z: $i] :
( ~ ( member @ X @ A )
| ~ ( member @ Z @ C )
| ! [Y: $i] :
( ~ ( apply @ F @ X @ Y )
| ~ ( member @ Y @ B )
| ~ ( apply @ G @ Y @ Z ) )
| ( apply @ ( compose_function @ G @ F @ A @ B @ C ) @ X @ Z ) )
& ! [X: $i,Z: $i] :
( ~ ( member @ X @ A )
| ~ ( member @ Z @ C )
| ~ ( apply @ ( compose_function @ G @ F @ A @ B @ C ) @ X @ Z )
| ( ( apply @ F @ X @ ( sK31_Y @ Z @ X @ C @ B @ A @ F @ G ) )
& ( member @ ( sK31_Y @ Z @ X @ C @ B @ A @ F @ G ) @ B )
& ( apply @ G @ ( sK31_Y @ Z @ X @ C @ B @ A @ F @ G ) @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(107,plain,
( ( ! [F: $i,G: $i] :
( ! [A: $i,B: $i] :
( ( ( member @ ( sK28_X @ B @ A @ G @ F ) @ A )
& ( member @ ( sK29_SY162 @ B @ A @ G @ F ) @ B )
& ( member @ ( sK30_SY164 @ B @ A @ G @ F ) @ B )
& ( apply @ F @ ( sK28_X @ B @ A @ G @ F ) @ ( sK29_SY162 @ B @ A @ G @ F ) )
& ( apply @ G @ ( sK28_X @ B @ A @ G @ F ) @ ( sK30_SY164 @ B @ A @ G @ F ) )
& ( ( sK29_SY162 @ B @ A @ G @ F )
!= ( sK30_SY164 @ B @ A @ G @ F ) ) )
| ( equal_maps @ F @ G @ A @ B ) )
& ! [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)],[79]) ).
thf(108,plain,
( ( ! [F: $i,A: $i] :
( ( ( member @ ( sK27_X @ A @ F ) @ A )
& ~ ( apply @ F @ ( sK27_X @ A @ F ) @ ( sK27_X @ A @ F ) ) )
| ( identity @ F @ A ) )
& ! [F: $i,A: $i] :
( ~ ( identity @ F @ A )
| ! [X: $i] :
( ~ ( member @ X @ A )
| ( apply @ F @ X @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(109,plain,
( ( ! [F: $i] :
( ! [A: $i,B: $i] :
( ( ( member @ ( sK24_X1 @ B @ A @ F ) @ A )
& ( member @ ( sK25_SY159 @ B @ A @ F ) @ A )
& ( member @ ( sK26_SY161 @ B @ A @ F ) @ B )
& ( apply @ F @ ( sK24_X1 @ B @ A @ F ) @ ( sK26_SY161 @ B @ A @ F ) )
& ( apply @ F @ ( sK25_SY159 @ B @ A @ F ) @ ( sK26_SY161 @ B @ A @ F ) )
& ( ( sK24_X1 @ B @ A @ F )
!= ( sK25_SY159 @ B @ A @ F ) ) )
| ( injective @ F @ A @ B ) )
& ! [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)],[77]) ).
thf(110,plain,
( ( ! [F: $i] :
( ! [A: $i,B: $i] :
( ( ( member @ ( sK23_Y @ B @ A @ F ) @ B )
& ! [SY158: $i] :
( ~ ( apply @ F @ SY158 @ ( sK23_Y @ B @ A @ F ) )
| ~ ( member @ SY158 @ A ) ) )
| ( surjective @ F @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( surjective @ F @ A @ B )
| ! [Y: $i] :
( ~ ( member @ Y @ B )
| ( ( apply @ F @ ( sK22_E @ Y @ B @ A @ F ) @ Y )
& ( member @ ( sK22_E @ Y @ B @ A @ F ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(111,plain,
( ( ! [F: $i] :
( ! [A: $i,B: $i] :
( ~ ( injective @ F @ A @ B )
| ~ ( surjective @ F @ A @ B )
| ( one_to_one @ F @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( one_to_one @ F @ A @ B )
| ( injective @ F @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( one_to_one @ F @ A @ B )
| ( surjective @ F @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(112,plain,
( ( ! [G: $i,F: $i] :
( ! [A: $i,B: $i] :
( ( ( member @ ( sK20_X @ B @ A @ F @ G ) @ A )
& ( member @ ( sK21_SY157 @ B @ A @ F @ G ) @ B )
& ( ~ ( apply @ F @ ( sK20_X @ B @ A @ F @ G ) @ ( sK21_SY157 @ B @ A @ F @ G ) )
| ~ ( apply @ G @ ( sK21_SY157 @ B @ A @ F @ G ) @ ( sK20_X @ B @ A @ F @ G ) ) )
& ( ( apply @ F @ ( sK20_X @ B @ A @ F @ G ) @ ( sK21_SY157 @ B @ A @ F @ G ) )
| ( apply @ G @ ( sK21_SY157 @ B @ A @ F @ G ) @ ( sK20_X @ B @ A @ F @ G ) ) ) )
| ( inverse_predicate @ G @ F @ A @ B ) )
& ! [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 ) )
& ! [X: $i,Y: $i] :
( ~ ( member @ X @ A )
| ~ ( member @ Y @ B )
| ~ ( apply @ G @ Y @ X )
| ( apply @ F @ X @ Y ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(113,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 ) )
& ! [X: $i,Y: $i] :
( ~ ( member @ X @ A )
| ~ ( member @ Y @ B )
| ~ ( apply @ ( inverse_function @ F @ A @ B ) @ Y @ X )
| ( apply @ F @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(114,plain,
( ( ! [F: $i] :
( ! [A: $i,Y: $i] :
( ! [X: $i] :
( ~ ( apply @ F @ X @ Y )
| ~ ( member @ X @ A ) )
| ( member @ Y @ ( image2 @ F @ A ) ) )
& ! [A: $i,Y: $i] :
( ~ ( member @ Y @ ( image2 @ F @ A ) )
| ( ( apply @ F @ ( sK19_X @ Y @ A @ F ) @ Y )
& ( member @ ( sK19_X @ Y @ A @ F ) @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(115,plain,
( ( ! [F: $i,A: $i] :
( ! [B: $i,Y: $i] :
( ! [X: $i] :
( ~ ( apply @ F @ X @ Y )
| ~ ( member @ X @ A ) )
| ~ ( member @ Y @ B )
| ( member @ Y @ ( image3 @ F @ A @ B ) ) )
& ! [B: $i,Y: $i] :
( ~ ( member @ Y @ ( image3 @ F @ A @ B ) )
| ( ( apply @ F @ ( sK18_X @ Y @ B @ A @ F ) @ Y )
& ( member @ ( sK18_X @ Y @ B @ A @ F ) @ A ) ) )
& ! [B: $i,Y: $i] :
( ~ ( member @ Y @ ( image3 @ F @ A @ B ) )
| ( member @ Y @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(116,plain,
( ( ! [F: $i] :
( ! [B: $i,X: $i] :
( ! [Y: $i] :
( ~ ( apply @ F @ X @ Y )
| ~ ( member @ Y @ B ) )
| ( member @ X @ ( inverse_image2 @ F @ B ) ) )
& ! [B: $i,X: $i] :
( ~ ( member @ X @ ( inverse_image2 @ F @ B ) )
| ( ( apply @ F @ X @ ( sK17_Y @ X @ B @ F ) )
& ( member @ ( sK17_Y @ X @ B @ F ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(117,plain,
( ( ! [F: $i,B: $i] :
( ! [A: $i,X: $i] :
( ! [Y: $i] :
( ~ ( apply @ F @ X @ Y )
| ~ ( member @ Y @ B ) )
| ~ ( member @ X @ A )
| ( member @ X @ ( inverse_image3 @ F @ B @ A ) ) )
& ! [A: $i,X: $i] :
( ~ ( member @ X @ ( inverse_image3 @ F @ B @ A ) )
| ( ( apply @ F @ X @ ( sK16_Y @ X @ A @ B @ F ) )
& ( member @ ( sK16_Y @ X @ A @ B @ F ) @ B ) ) )
& ! [A: $i,X: $i] :
( ~ ( member @ X @ ( inverse_image3 @ F @ B @ A ) )
| ( member @ X @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(118,plain,
( ( ! [F: $i,A: $i,R: $i] :
( ! [B: $i,S: $i] :
( ( ( member @ ( sK12_X1 @ S @ B @ R @ A @ F ) @ A )
& ( member @ ( sK13_SY151 @ S @ B @ R @ A @ F ) @ B )
& ( member @ ( sK14_SY154 @ S @ B @ R @ A @ F ) @ A )
& ( member @ ( sK15_SY156 @ S @ B @ R @ A @ F ) @ B )
& ( apply @ R @ ( sK12_X1 @ S @ B @ R @ A @ F ) @ ( sK14_SY154 @ S @ B @ R @ A @ F ) )
& ( apply @ F @ ( sK12_X1 @ S @ B @ R @ A @ F ) @ ( sK13_SY151 @ S @ B @ R @ A @ F ) )
& ( apply @ F @ ( sK14_SY154 @ S @ B @ R @ A @ F ) @ ( sK15_SY156 @ S @ B @ R @ A @ F ) )
& ~ ( apply @ S @ ( sK13_SY151 @ S @ B @ R @ A @ F ) @ ( sK15_SY156 @ S @ B @ R @ A @ F ) ) )
| ( increasing @ F @ A @ R @ B @ S ) )
& ! [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)],[68]) ).
thf(119,plain,
( ( ! [F: $i,A: $i,R: $i] :
( ! [B: $i,S: $i] :
( ( ( member @ ( sK8_X1 @ S @ B @ R @ A @ F ) @ A )
& ( member @ ( sK9_SY145 @ S @ B @ R @ A @ F ) @ B )
& ( member @ ( sK10_SY148 @ S @ B @ R @ A @ F ) @ A )
& ( member @ ( sK11_SY150 @ S @ B @ R @ A @ F ) @ B )
& ( apply @ R @ ( sK8_X1 @ S @ B @ R @ A @ F ) @ ( sK10_SY148 @ S @ B @ R @ A @ F ) )
& ( apply @ F @ ( sK8_X1 @ S @ B @ R @ A @ F ) @ ( sK9_SY145 @ S @ B @ R @ A @ F ) )
& ( apply @ F @ ( sK10_SY148 @ S @ B @ R @ A @ F ) @ ( sK11_SY150 @ S @ B @ R @ A @ F ) )
& ~ ( apply @ S @ ( sK11_SY150 @ S @ B @ R @ A @ F ) @ ( sK9_SY145 @ S @ B @ R @ A @ F ) ) )
| ( decreasing @ F @ A @ R @ B @ S ) )
& ! [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)],[67]) ).
thf(120,plain,
( ( ! [F: $i,A: $i,R: $i] :
( ! [B: $i,S: $i] :
( ( ( member @ ( sK4_X1 @ S @ B @ R @ A @ F ) @ A )
& ( member @ ( sK5_SY139 @ S @ B @ R @ A @ F ) @ B )
& ( member @ ( sK6_SY142 @ S @ B @ R @ A @ F ) @ A )
& ( member @ ( sK7_SY144 @ S @ B @ R @ A @ F ) @ B )
& ( apply @ F @ ( sK4_X1 @ S @ B @ R @ A @ F ) @ ( sK5_SY139 @ S @ B @ R @ A @ F ) )
& ( apply @ F @ ( sK6_SY142 @ S @ B @ R @ A @ F ) @ ( sK7_SY144 @ S @ B @ R @ A @ F ) )
& ( ~ ( apply @ R @ ( sK4_X1 @ S @ B @ R @ A @ F ) @ ( sK6_SY142 @ S @ B @ R @ A @ F ) )
| ~ ( apply @ S @ ( sK5_SY139 @ S @ B @ R @ A @ F ) @ ( sK7_SY144 @ S @ B @ R @ A @ F ) ) )
& ( ( apply @ R @ ( sK4_X1 @ S @ B @ R @ A @ F ) @ ( sK6_SY142 @ S @ B @ R @ A @ F ) )
| ( apply @ S @ ( sK5_SY139 @ S @ B @ R @ A @ F ) @ ( sK7_SY144 @ S @ B @ R @ A @ F ) ) ) )
| ~ ( maps @ F @ A @ B )
| ~ ( one_to_one @ F @ A @ B )
| ( isomorphism @ F @ A @ R @ B @ S ) )
& ! [B: $i,S: $i] :
( ~ ( isomorphism @ 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 @ F @ X1 @ Y1 )
| ~ ( apply @ F @ X2 @ Y2 )
| ~ ( apply @ R @ X1 @ X2 )
| ( apply @ S @ Y1 @ Y2 ) )
& ! [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 @ S @ Y1 @ Y2 )
| ( apply @ R @ X1 @ X2 ) ) ) )
& ! [B: $i] :
( ! [S: $i] :
~ ( isomorphism @ F @ A @ R @ B @ S )
| ( maps @ F @ A @ B ) )
& ! [B: $i] :
( ! [S: $i] :
~ ( isomorphism @ F @ A @ R @ B @ S )
| ( one_to_one @ F @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(121,plain,
( ( maps @ sK1_F @ sK2_SY136 @ sK3_SY138 )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(122,plain,
( ( ~ ( equal_set @ ( inverse_image2 @ sK1_F @ empty_set ) @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(123,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ! [SX4: $i] :
( ~ ( apply @ SX0 @ SX4 @ SX3 )
| ~ ( member @ SX4 @ SX1 ) )
| ~ ( member @ SX3 @ SX2 )
| ( member @ SX3 @ ( image3 @ SX0 @ SX1 @ SX2 ) ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( member @ SX3 @ ( image3 @ SX0 @ SX1 @ SX2 ) )
| ~ ( ~ ( apply @ SX0 @ ( sK18_X @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 )
| ~ ( member @ ( sK18_X @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( member @ SX3 @ ( image3 @ SX0 @ SX1 @ SX2 ) )
| ( member @ SX3 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(124,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_set @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( member @ SX0 @ ( power_set @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(125,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_X1 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ ( sK9_SY145 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 ) )
| ~ ( member @ ( sK10_SY148 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( member @ ( sK11_SY150 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 ) )
| ~ ( apply @ SX2 @ ( sK8_X1 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK10_SY148 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( apply @ SX0 @ ( sK8_X1 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK9_SY145 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( apply @ SX0 @ ( sK10_SY148 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK11_SY150 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ~ ( apply @ SX4 @ ( sK11_SY150 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK9_SY145 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ( decreasing @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) )
| ~ ! [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 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(126,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK43_X @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK43_X @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(127,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ! [SX3: $i] :
( ~ ( apply @ SX0 @ SX3 @ SX2 )
| ~ ( member @ SX3 @ SX1 ) )
| ( member @ SX2 @ ( image2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ ( image2 @ SX0 @ SX1 ) )
| ~ ( ~ ( apply @ SX0 @ ( sK19_X @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( member @ ( sK19_X @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(128,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ SX2 )
| ( member @ SX0 @ SX1 )
| ( member @ SX0 @ ( difference @ SX2 @ SX1 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ ( difference @ SX2 @ SX1 ) )
| ( member @ SX0 @ SX2 ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( member @ SX0 @ ( difference @ SX2 @ SX1 ) )
| ~ ( member @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(129,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ ( union @ SX1 @ SX2 ) )
| ( member @ SX0 @ SX1 )
| ( member @ SX0 @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( member @ SX0 @ SX1 )
| ! [SX2: $i] : ( member @ SX0 @ ( union @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ SX2 )
| ( member @ SX0 @ ( union @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(130,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK4_X1 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ ( sK5_SY139 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 ) )
| ~ ( member @ ( sK6_SY142 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( member @ ( sK7_SY144 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 ) )
| ~ ( apply @ SX0 @ ( sK4_X1 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK5_SY139 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( apply @ SX0 @ ( sK6_SY142 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK7_SY144 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ~ ( apply @ SX2 @ ( sK4_X1 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK6_SY142 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( apply @ SX4 @ ( sK5_SY139 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK7_SY144 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ( apply @ SX2 @ ( sK4_X1 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK6_SY142 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ( apply @ SX4 @ ( sK5_SY139 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK7_SY144 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ~ ( maps @ SX0 @ SX1 @ SX3 )
| ~ ( one_to_one @ SX0 @ SX1 @ SX3 )
| ( isomorphism @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) )
| ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( isomorphism @ 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 @ SX0 @ SX5 @ SX6 )
| ~ ( apply @ SX0 @ SX7 @ SX8 )
| ~ ( apply @ SX2 @ SX5 @ SX7 )
| ( apply @ SX4 @ SX6 @ SX8 ) )
| ~ ! [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 @ SX4 @ SX6 @ SX8 )
| ( apply @ SX2 @ SX5 @ SX7 ) ) ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( isomorphism @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 )
| ( maps @ SX0 @ SX1 @ SX3 ) )
| ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( isomorphism @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 )
| ( one_to_one @ SX0 @ SX1 @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(131,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( ~ ~ ( ~ ( member @ ( sK20_X @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( member @ ( sK21_SY157 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 ) )
| ~ ~ ( ~ ( ~ ( apply @ SX1 @ ( sK20_X @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK21_SY157 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( apply @ SX0 @ ( sK21_SY157 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK20_X @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ( apply @ SX1 @ ( sK20_X @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK21_SY157 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ( apply @ SX0 @ ( sK21_SY157 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK20_X @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ( inverse_predicate @ SX0 @ SX1 @ SX2 @ SX3 ) )
| ~ ! [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 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( member @ SX4 @ SX2 )
| ~ ( member @ SX5 @ SX3 )
| ~ ( apply @ SX0 @ SX5 @ SX4 )
| ( apply @ SX1 @ SX4 @ SX5 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(132,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 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( member @ SX3 @ SX1 )
| ~ ( member @ SX4 @ SX2 )
| ~ ( apply @ ( inverse_function @ SX0 @ SX1 @ SX2 ) @ SX4 @ SX3 )
| ( apply @ SX0 @ SX3 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(133,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ! [SX3: $i] :
( ~ ( apply @ SX0 @ SX2 @ SX3 )
| ~ ( member @ SX3 @ SX1 ) )
| ( member @ SX2 @ ( inverse_image2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ ( inverse_image2 @ SX0 @ SX1 ) )
| ~ ( ~ ( apply @ SX0 @ SX2 @ ( sK17_Y @ SX2 @ SX1 @ SX0 ) )
| ~ ( member @ ( sK17_Y @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(134,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( member @ ( sK23_Y @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( apply @ SX0 @ SX3 @ ( sK23_Y @ SX2 @ SX1 @ SX0 ) )
| ~ ( member @ SX3 @ SX1 ) ) )
| ( surjective @ SX0 @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( surjective @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( member @ SX3 @ SX2 )
| ~ ( ~ ( apply @ SX0 @ ( sK22_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 )
| ~ ( member @ ( sK22_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(135,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ! [SX4: $i] :
( ~ ( apply @ SX0 @ SX3 @ SX4 )
| ~ ( member @ SX4 @ SX1 ) )
| ~ ( member @ SX3 @ SX2 )
| ( member @ SX3 @ ( inverse_image3 @ SX0 @ SX1 @ SX2 ) ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( member @ SX3 @ ( inverse_image3 @ SX0 @ SX1 @ SX2 ) )
| ~ ( ~ ( apply @ SX0 @ SX3 @ ( sK16_Y @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( member @ ( sK16_Y @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( member @ SX3 @ ( inverse_image3 @ SX0 @ SX1 @ SX2 ) )
| ( member @ SX3 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(136,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK28_X @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( member @ ( sK29_SY162 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 ) )
| ~ ( member @ ( sK30_SY164 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SX0 @ ( sK28_X @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK29_SY162 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( apply @ SX1 @ ( sK28_X @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK30_SY164 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ( ( sK29_SY162 @ SX3 @ SX2 @ SX1 @ SX0 )
!= ( sK30_SY164 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ( equal_maps @ SX0 @ SX1 @ SX2 @ SX3 ) )
| ~ ! [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 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(137,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ! [SX4: $i,SX5: $i] :
( ~ ( ~ ~ ( ~ ( member @ ( sK33_X @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 )
| ~ ( member @ ( sK34_SY165 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX5 ) )
| ~ ~ ( ~ ( ! [SX6: $i] :
( ~ ( apply @ SX2 @ ( sK33_X @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX6 )
| ~ ( member @ SX6 @ SX4 )
| ~ ( apply @ SX1 @ SX6 @ ( sK34_SY165 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( apply @ SX0 @ ( sK33_X @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK34_SY165 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( apply @ SX2 @ ( sK33_X @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK35_SY169 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( member @ ( sK35_SY169 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX4 ) )
| ~ ( apply @ SX1 @ ( sK35_SY169 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK34_SY165 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ( apply @ SX0 @ ( sK33_X @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK34_SY165 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ( compose_predicate @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 @ SX5 ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( compose_predicate @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 @ SX5 )
| ~ ( ~ ! [SX6: $i,SX7: $i] :
( ~ ( member @ SX6 @ SX3 )
| ~ ( member @ SX7 @ SX5 )
| ! [SX8: $i] :
( ~ ( apply @ SX2 @ SX6 @ SX8 )
| ~ ( member @ SX8 @ SX4 )
| ~ ( apply @ SX1 @ SX8 @ SX7 ) )
| ( apply @ SX0 @ SX6 @ SX7 ) )
| ~ ! [SX6: $i,SX7: $i] :
( ~ ( member @ SX6 @ SX3 )
| ~ ( member @ SX7 @ SX5 )
| ~ ( apply @ SX0 @ SX6 @ SX7 )
| ~ ( ~ ~ ( ~ ( apply @ SX2 @ SX6 @ ( sK32_Y @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( member @ ( sK32_Y @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX4 ) )
| ~ ( apply @ SX1 @ ( sK32_Y @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX7 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(138,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( member @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(139,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK24_X1 @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ ( sK25_SY159 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( member @ ( sK26_SY161 @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SX0 @ ( sK24_X1 @ SX2 @ SX1 @ SX0 ) @ ( sK26_SY161 @ SX2 @ SX1 @ SX0 ) )
| ~ ( apply @ SX0 @ ( sK25_SY159 @ SX2 @ SX1 @ SX0 ) @ ( sK26_SY161 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ( ( sK24_X1 @ SX2 @ SX1 @ SX0 )
!= ( sK25_SY159 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ( injective @ SX0 @ SX1 @ SX2 ) )
| ~ ! [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 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(140,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( equal_set @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(141,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK12_X1 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ ( sK13_SY151 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 ) )
| ~ ( member @ ( sK14_SY154 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( member @ ( sK15_SY156 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 ) )
| ~ ( apply @ SX2 @ ( sK12_X1 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK14_SY154 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( apply @ SX0 @ ( sK12_X1 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK13_SY151 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( apply @ SX0 @ ( sK14_SY154 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK15_SY156 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ~ ( apply @ SX4 @ ( sK13_SY151 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK15_SY156 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ( increasing @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) )
| ~ ! [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 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(142,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ SX1 )
| ~ ( member @ SX0 @ SX2 )
| ( member @ SX0 @ ( intersection @ SX1 @ SX2 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( member @ SX0 @ ( intersection @ SX1 @ SX2 ) )
| ( member @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ ( intersection @ SX1 @ SX2 ) )
| ( member @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(143,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) )
| ( SX0 = SX1 )
| ( SX0 = SX2 ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i] : ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX0 != SX2 )
| ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(144,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( injective @ SX0 @ SX1 @ SX2 )
| ~ ( surjective @ SX0 @ SX1 @ SX2 )
| ( one_to_one @ SX0 @ SX1 @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( one_to_one @ SX0 @ SX1 @ SX2 )
| ( injective @ SX0 @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( one_to_one @ SX0 @ SX1 @ SX2 )
| ( surjective @ SX0 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(145,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ! [SX5: $i,SX6: $i] :
( ~ ( member @ SX5 @ SX2 )
| ~ ( member @ SX6 @ SX4 )
| ! [SX7: $i] :
( ~ ( apply @ SX1 @ SX5 @ SX7 )
| ~ ( member @ SX7 @ SX3 )
| ~ ( apply @ SX0 @ SX7 @ SX6 ) )
| ( apply @ ( compose_function @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) @ SX5 @ SX6 ) )
| ~ ! [SX5: $i,SX6: $i] :
( ~ ( member @ SX5 @ SX2 )
| ~ ( member @ SX6 @ SX4 )
| ~ ( apply @ ( compose_function @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) @ SX5 @ SX6 )
| ~ ( ~ ~ ( ~ ( apply @ SX1 @ SX5 @ ( sK31_Y @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( member @ ( sK31_Y @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 ) )
| ~ ( apply @ SX0 @ ( sK31_Y @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX6 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(146,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( sum @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( sum @ SX1 ) )
| ~ ( ~ ( member @ ( sK42_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ SX0 @ ( sK42_Y @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(147,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK41_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( member @ SX0 @ ( sK41_Y @ SX1 @ SX0 ) ) )
| ( member @ SX0 @ ( product @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( product @ SX1 ) )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(148,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( member @ ( sK40_X @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ! [SX3: $i] :
( ~ ( apply @ SX0 @ ( sK40_X @ SX2 @ SX1 @ SX0 ) @ SX3 )
| ~ ( member @ SX3 @ SX2 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_X @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ ( sK38_SY170 @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( member @ ( sK39_SY172 @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SX0 @ ( sK37_X @ SX2 @ SX1 @ SX0 ) @ ( sK38_SY170 @ SX2 @ SX1 @ SX0 ) )
| ~ ( apply @ SX0 @ ( sK37_X @ SX2 @ SX1 @ SX0 ) @ ( sK39_SY172 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ( ( sK38_SY170 @ SX2 @ SX1 @ SX0 )
!= ( sK39_SY172 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ( maps @ SX0 @ SX1 @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( maps @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( member @ SX3 @ SX1 )
| ~ ( ~ ( apply @ SX0 @ SX3 @ ( sK36_Y @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( member @ ( sK36_Y @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( maps @ SX0 @ SX1 @ SX2 )
| ! [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 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(149,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK27_X @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( apply @ SX0 @ ( sK27_X @ SX1 @ SX0 ) @ ( sK27_X @ SX1 @ SX0 ) ) )
| ( identity @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( identity @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( apply @ SX0 @ SX2 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(150,plain,
! [SV1: $i] :
( ( ~ ( member @ SV1 @ empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(151,plain,
( ( equal_set @ ( inverse_image2 @ sK1_F @ empty_set ) @ empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(152,plain,
! [SV2: $i] :
( ( ! [SY174: $i] :
~ ( ~ ! [SY175: $i,SY176: $i] :
( ! [SY177: $i] :
( ~ ( apply @ SV2 @ SY177 @ SY176 )
| ~ ( member @ SY177 @ SY174 ) )
| ~ ( member @ SY176 @ SY175 )
| ( member @ SY176 @ ( image3 @ SV2 @ SY174 @ SY175 ) ) )
| ~ ~ ( ~ ! [SY178: $i,SY179: $i] :
( ~ ( member @ SY179 @ ( image3 @ SV2 @ SY174 @ SY178 ) )
| ~ ( ~ ( apply @ SV2 @ ( sK18_X @ SY179 @ SY178 @ SY174 @ SV2 ) @ SY179 )
| ~ ( member @ ( sK18_X @ SY179 @ SY178 @ SY174 @ SV2 ) @ SY174 ) ) )
| ~ ! [SY180: $i,SY181: $i] :
( ~ ( member @ SY181 @ ( image3 @ SV2 @ SY174 @ SY180 ) )
| ( member @ SY181 @ SY180 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(153,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_set @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( member @ SX0 @ ( power_set @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(154,plain,
! [SV3: $i] :
( ( ! [SY182: $i,SY183: $i] :
~ ( ~ ! [SY184: $i,SY185: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_X1 @ SY185 @ SY184 @ SY183 @ SY182 @ SV3 ) @ SY182 )
| ~ ( member @ ( sK9_SY145 @ SY185 @ SY184 @ SY183 @ SY182 @ SV3 ) @ SY184 ) )
| ~ ( member @ ( sK10_SY148 @ SY185 @ SY184 @ SY183 @ SY182 @ SV3 ) @ SY182 ) )
| ~ ( member @ ( sK11_SY150 @ SY185 @ SY184 @ SY183 @ SY182 @ SV3 ) @ SY184 ) )
| ~ ( apply @ SY183 @ ( sK8_X1 @ SY185 @ SY184 @ SY183 @ SY182 @ SV3 ) @ ( sK10_SY148 @ SY185 @ SY184 @ SY183 @ SY182 @ SV3 ) ) )
| ~ ( apply @ SV3 @ ( sK8_X1 @ SY185 @ SY184 @ SY183 @ SY182 @ SV3 ) @ ( sK9_SY145 @ SY185 @ SY184 @ SY183 @ SY182 @ SV3 ) ) )
| ~ ( apply @ SV3 @ ( sK10_SY148 @ SY185 @ SY184 @ SY183 @ SY182 @ SV3 ) @ ( sK11_SY150 @ SY185 @ SY184 @ SY183 @ SY182 @ SV3 ) ) )
| ~ ~ ( apply @ SY185 @ ( sK11_SY150 @ SY185 @ SY184 @ SY183 @ SY182 @ SV3 ) @ ( sK9_SY145 @ SY185 @ SY184 @ SY183 @ SY182 @ SV3 ) ) )
| ( decreasing @ SV3 @ SY182 @ SY183 @ SY184 @ SY185 ) )
| ~ ! [SY186: $i,SY187: $i] :
( ~ ( decreasing @ SV3 @ SY182 @ SY183 @ SY186 @ SY187 )
| ! [SY188: $i,SY189: $i,SY190: $i,SY191: $i] :
( ~ ( member @ SY188 @ SY182 )
| ~ ( member @ SY189 @ SY186 )
| ~ ( member @ SY190 @ SY182 )
| ~ ( member @ SY191 @ SY186 )
| ~ ( apply @ SY183 @ SY188 @ SY190 )
| ~ ( apply @ SV3 @ SY188 @ SY189 )
| ~ ( apply @ SV3 @ SY190 @ SY191 )
| ( apply @ SY187 @ SY191 @ SY189 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(155,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK43_X @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK43_X @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(156,plain,
! [SV4: $i] :
( ( ~ ( ~ ! [SY192: $i,SY193: $i] :
( ! [SY194: $i] :
( ~ ( apply @ SV4 @ SY194 @ SY193 )
| ~ ( member @ SY194 @ SY192 ) )
| ( member @ SY193 @ ( image2 @ SV4 @ SY192 ) ) )
| ~ ! [SY195: $i,SY196: $i] :
( ~ ( member @ SY196 @ ( image2 @ SV4 @ SY195 ) )
| ~ ( ~ ( apply @ SV4 @ ( sK19_X @ SY196 @ SY195 @ SV4 ) @ SY196 )
| ~ ( member @ ( sK19_X @ SY196 @ SY195 @ SV4 ) @ SY195 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(157,plain,
! [SV5: $i] :
( ( ~ ( ~ ! [SY197: $i,SY198: $i] :
( ~ ( member @ SV5 @ SY198 )
| ( member @ SV5 @ SY197 )
| ( member @ SV5 @ ( difference @ SY198 @ SY197 ) ) )
| ~ ~ ( ~ ! [SY199: $i,SY200: $i] :
( ~ ( member @ SV5 @ ( difference @ SY200 @ SY199 ) )
| ( member @ SV5 @ SY200 ) )
| ~ ! [SY201: $i] :
( ! [SY202: $i] :
~ ( member @ SV5 @ ( difference @ SY202 @ SY201 ) )
| ~ ( member @ SV5 @ SY201 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(158,plain,
! [SV6: $i] :
( ( ~ ( ~ ! [SY203: $i,SY204: $i] :
( ~ ( member @ SV6 @ ( union @ SY203 @ SY204 ) )
| ( member @ SV6 @ SY203 )
| ( member @ SV6 @ SY204 ) )
| ~ ~ ( ~ ! [SY205: $i] :
( ~ ( member @ SV6 @ SY205 )
| ! [SY206: $i] : ( member @ SV6 @ ( union @ SY205 @ SY206 ) ) )
| ~ ! [SY207: $i,SY208: $i] :
( ~ ( member @ SV6 @ SY208 )
| ( member @ SV6 @ ( union @ SY207 @ SY208 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(159,plain,
! [SV7: $i] :
( ( ! [SY209: $i,SY210: $i] :
~ ( ~ ! [SY211: $i,SY212: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK4_X1 @ SY212 @ SY211 @ SY210 @ SY209 @ SV7 ) @ SY209 )
| ~ ( member @ ( sK5_SY139 @ SY212 @ SY211 @ SY210 @ SY209 @ SV7 ) @ SY211 ) )
| ~ ( member @ ( sK6_SY142 @ SY212 @ SY211 @ SY210 @ SY209 @ SV7 ) @ SY209 ) )
| ~ ( member @ ( sK7_SY144 @ SY212 @ SY211 @ SY210 @ SY209 @ SV7 ) @ SY211 ) )
| ~ ( apply @ SV7 @ ( sK4_X1 @ SY212 @ SY211 @ SY210 @ SY209 @ SV7 ) @ ( sK5_SY139 @ SY212 @ SY211 @ SY210 @ SY209 @ SV7 ) ) )
| ~ ( apply @ SV7 @ ( sK6_SY142 @ SY212 @ SY211 @ SY210 @ SY209 @ SV7 ) @ ( sK7_SY144 @ SY212 @ SY211 @ SY210 @ SY209 @ SV7 ) ) )
| ~ ~ ( ~ ( ~ ( apply @ SY210 @ ( sK4_X1 @ SY212 @ SY211 @ SY210 @ SY209 @ SV7 ) @ ( sK6_SY142 @ SY212 @ SY211 @ SY210 @ SY209 @ SV7 ) )
| ~ ( apply @ SY212 @ ( sK5_SY139 @ SY212 @ SY211 @ SY210 @ SY209 @ SV7 ) @ ( sK7_SY144 @ SY212 @ SY211 @ SY210 @ SY209 @ SV7 ) ) )
| ~ ( ( apply @ SY210 @ ( sK4_X1 @ SY212 @ SY211 @ SY210 @ SY209 @ SV7 ) @ ( sK6_SY142 @ SY212 @ SY211 @ SY210 @ SY209 @ SV7 ) )
| ( apply @ SY212 @ ( sK5_SY139 @ SY212 @ SY211 @ SY210 @ SY209 @ SV7 ) @ ( sK7_SY144 @ SY212 @ SY211 @ SY210 @ SY209 @ SV7 ) ) ) ) )
| ~ ( maps @ SV7 @ SY209 @ SY211 )
| ~ ( one_to_one @ SV7 @ SY209 @ SY211 )
| ( isomorphism @ SV7 @ SY209 @ SY210 @ SY211 @ SY212 ) )
| ~ ~ ( ~ ! [SY213: $i,SY214: $i] :
( ~ ( isomorphism @ SV7 @ SY209 @ SY210 @ SY213 @ SY214 )
| ! [SY215: $i,SY216: $i] :
~ ( ~ ! [SY217: $i,SY218: $i] :
( ~ ( member @ SY215 @ SY209 )
| ~ ( member @ SY216 @ SY213 )
| ~ ( member @ SY217 @ SY209 )
| ~ ( member @ SY218 @ SY213 )
| ~ ( apply @ SV7 @ SY215 @ SY216 )
| ~ ( apply @ SV7 @ SY217 @ SY218 )
| ~ ( apply @ SY210 @ SY215 @ SY217 )
| ( apply @ SY214 @ SY216 @ SY218 ) )
| ~ ! [SY219: $i,SY220: $i] :
( ~ ( member @ SY215 @ SY209 )
| ~ ( member @ SY216 @ SY213 )
| ~ ( member @ SY219 @ SY209 )
| ~ ( member @ SY220 @ SY213 )
| ~ ( apply @ SV7 @ SY215 @ SY216 )
| ~ ( apply @ SV7 @ SY219 @ SY220 )
| ~ ( apply @ SY214 @ SY216 @ SY220 )
| ( apply @ SY210 @ SY215 @ SY219 ) ) ) )
| ~ ~ ( ~ ! [SY221: $i] :
( ! [SY222: $i] :
~ ( isomorphism @ SV7 @ SY209 @ SY210 @ SY221 @ SY222 )
| ( maps @ SV7 @ SY209 @ SY221 ) )
| ~ ! [SY223: $i] :
( ! [SY224: $i] :
~ ( isomorphism @ SV7 @ SY209 @ SY210 @ SY223 @ SY224 )
| ( one_to_one @ SV7 @ SY209 @ SY223 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(160,plain,
! [SV8: $i] :
( ( ! [SY225: $i] :
~ ( ~ ! [SY226: $i,SY227: $i] :
( ~ ( ~ ~ ( ~ ( member @ ( sK20_X @ SY227 @ SY226 @ SY225 @ SV8 ) @ SY226 )
| ~ ( member @ ( sK21_SY157 @ SY227 @ SY226 @ SY225 @ SV8 ) @ SY227 ) )
| ~ ~ ( ~ ( ~ ( apply @ SY225 @ ( sK20_X @ SY227 @ SY226 @ SY225 @ SV8 ) @ ( sK21_SY157 @ SY227 @ SY226 @ SY225 @ SV8 ) )
| ~ ( apply @ SV8 @ ( sK21_SY157 @ SY227 @ SY226 @ SY225 @ SV8 ) @ ( sK20_X @ SY227 @ SY226 @ SY225 @ SV8 ) ) )
| ~ ( ( apply @ SY225 @ ( sK20_X @ SY227 @ SY226 @ SY225 @ SV8 ) @ ( sK21_SY157 @ SY227 @ SY226 @ SY225 @ SV8 ) )
| ( apply @ SV8 @ ( sK21_SY157 @ SY227 @ SY226 @ SY225 @ SV8 ) @ ( sK20_X @ SY227 @ SY226 @ SY225 @ SV8 ) ) ) ) )
| ( inverse_predicate @ SV8 @ SY225 @ SY226 @ SY227 ) )
| ~ ! [SY228: $i,SY229: $i] :
( ~ ( inverse_predicate @ SV8 @ SY225 @ SY228 @ SY229 )
| ~ ( ~ ! [SY230: $i,SY231: $i] :
( ~ ( member @ SY230 @ SY228 )
| ~ ( member @ SY231 @ SY229 )
| ~ ( apply @ SY225 @ SY230 @ SY231 )
| ( apply @ SV8 @ SY231 @ SY230 ) )
| ~ ! [SY232: $i,SY233: $i] :
( ~ ( member @ SY232 @ SY228 )
| ~ ( member @ SY233 @ SY229 )
| ~ ( apply @ SV8 @ SY233 @ SY232 )
| ( apply @ SY225 @ SY232 @ SY233 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(161,plain,
! [SV9: $i] :
( ( ! [SY234: $i,SY235: $i] :
~ ( ~ ! [SY236: $i,SY237: $i] :
( ~ ( member @ SY236 @ SY234 )
| ~ ( member @ SY237 @ SY235 )
| ~ ( apply @ SV9 @ SY236 @ SY237 )
| ( apply @ ( inverse_function @ SV9 @ SY234 @ SY235 ) @ SY237 @ SY236 ) )
| ~ ! [SY238: $i,SY239: $i] :
( ~ ( member @ SY238 @ SY234 )
| ~ ( member @ SY239 @ SY235 )
| ~ ( apply @ ( inverse_function @ SV9 @ SY234 @ SY235 ) @ SY239 @ SY238 )
| ( apply @ SV9 @ SY238 @ SY239 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(162,plain,
! [SV10: $i] :
( ( ~ ( ~ ! [SY240: $i,SY241: $i] :
( ! [SY242: $i] :
( ~ ( apply @ SV10 @ SY241 @ SY242 )
| ~ ( member @ SY242 @ SY240 ) )
| ( member @ SY241 @ ( inverse_image2 @ SV10 @ SY240 ) ) )
| ~ ! [SY243: $i,SY244: $i] :
( ~ ( member @ SY244 @ ( inverse_image2 @ SV10 @ SY243 ) )
| ~ ( ~ ( apply @ SV10 @ SY244 @ ( sK17_Y @ SY244 @ SY243 @ SV10 ) )
| ~ ( member @ ( sK17_Y @ SY244 @ SY243 @ SV10 ) @ SY243 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(163,plain,
! [SV11: $i] :
( ( ~ ( ~ ! [SY245: $i,SY246: $i] :
( ~ ( ~ ( member @ ( sK23_Y @ SY246 @ SY245 @ SV11 ) @ SY246 )
| ~ ! [SY247: $i] :
( ~ ( apply @ SV11 @ SY247 @ ( sK23_Y @ SY246 @ SY245 @ SV11 ) )
| ~ ( member @ SY247 @ SY245 ) ) )
| ( surjective @ SV11 @ SY245 @ SY246 ) )
| ~ ! [SY248: $i,SY249: $i] :
( ~ ( surjective @ SV11 @ SY248 @ SY249 )
| ! [SY250: $i] :
( ~ ( member @ SY250 @ SY249 )
| ~ ( ~ ( apply @ SV11 @ ( sK22_E @ SY250 @ SY249 @ SY248 @ SV11 ) @ SY250 )
| ~ ( member @ ( sK22_E @ SY250 @ SY249 @ SY248 @ SV11 ) @ SY248 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(164,plain,
! [SV12: $i] :
( ( ! [SY251: $i] :
~ ( ~ ! [SY252: $i,SY253: $i] :
( ! [SY254: $i] :
( ~ ( apply @ SV12 @ SY253 @ SY254 )
| ~ ( member @ SY254 @ SY251 ) )
| ~ ( member @ SY253 @ SY252 )
| ( member @ SY253 @ ( inverse_image3 @ SV12 @ SY251 @ SY252 ) ) )
| ~ ~ ( ~ ! [SY255: $i,SY256: $i] :
( ~ ( member @ SY256 @ ( inverse_image3 @ SV12 @ SY251 @ SY255 ) )
| ~ ( ~ ( apply @ SV12 @ SY256 @ ( sK16_Y @ SY256 @ SY255 @ SY251 @ SV12 ) )
| ~ ( member @ ( sK16_Y @ SY256 @ SY255 @ SY251 @ SV12 ) @ SY251 ) ) )
| ~ ! [SY257: $i,SY258: $i] :
( ~ ( member @ SY258 @ ( inverse_image3 @ SV12 @ SY251 @ SY257 ) )
| ( member @ SY258 @ SY257 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(165,plain,
! [SV13: $i] :
( ( ! [SY259: $i] :
~ ( ~ ! [SY260: $i,SY261: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK28_X @ SY261 @ SY260 @ SY259 @ SV13 ) @ SY260 )
| ~ ( member @ ( sK29_SY162 @ SY261 @ SY260 @ SY259 @ SV13 ) @ SY261 ) )
| ~ ( member @ ( sK30_SY164 @ SY261 @ SY260 @ SY259 @ SV13 ) @ SY261 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV13 @ ( sK28_X @ SY261 @ SY260 @ SY259 @ SV13 ) @ ( sK29_SY162 @ SY261 @ SY260 @ SY259 @ SV13 ) )
| ~ ( apply @ SY259 @ ( sK28_X @ SY261 @ SY260 @ SY259 @ SV13 ) @ ( sK30_SY164 @ SY261 @ SY260 @ SY259 @ SV13 ) ) )
| ~ ( ( ( sK29_SY162 @ SY261 @ SY260 @ SY259 @ SV13 )
!= ( sK30_SY164 @ SY261 @ SY260 @ SY259 @ SV13 ) ) ) ) )
| ( equal_maps @ SV13 @ SY259 @ SY260 @ SY261 ) )
| ~ ! [SY262: $i,SY263: $i] :
( ~ ( equal_maps @ SV13 @ SY259 @ SY262 @ SY263 )
| ! [SY264: $i,SY265: $i,SY266: $i] :
( ~ ( member @ SY264 @ SY262 )
| ~ ( member @ SY265 @ SY263 )
| ~ ( member @ SY266 @ SY263 )
| ~ ( apply @ SV13 @ SY264 @ SY265 )
| ~ ( apply @ SY259 @ SY264 @ SY266 )
| ( SY265 = SY266 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(166,plain,
! [SV14: $i] :
( ( ! [SY267: $i,SY268: $i,SY269: $i] :
~ ( ~ ! [SY270: $i,SY271: $i] :
( ~ ( ~ ~ ( ~ ( member @ ( sK33_X @ SY271 @ SY270 @ SY269 @ SY268 @ SY267 @ SV14 ) @ SY269 )
| ~ ( member @ ( sK34_SY165 @ SY271 @ SY270 @ SY269 @ SY268 @ SY267 @ SV14 ) @ SY271 ) )
| ~ ~ ( ~ ( ! [SY272: $i] :
( ~ ( apply @ SY268 @ ( sK33_X @ SY271 @ SY270 @ SY269 @ SY268 @ SY267 @ SV14 ) @ SY272 )
| ~ ( member @ SY272 @ SY270 )
| ~ ( apply @ SY267 @ SY272 @ ( sK34_SY165 @ SY271 @ SY270 @ SY269 @ SY268 @ SY267 @ SV14 ) ) )
| ~ ( apply @ SV14 @ ( sK33_X @ SY271 @ SY270 @ SY269 @ SY268 @ SY267 @ SV14 ) @ ( sK34_SY165 @ SY271 @ SY270 @ SY269 @ SY268 @ SY267 @ SV14 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( apply @ SY268 @ ( sK33_X @ SY271 @ SY270 @ SY269 @ SY268 @ SY267 @ SV14 ) @ ( sK35_SY169 @ SY271 @ SY270 @ SY269 @ SY268 @ SY267 @ SV14 ) )
| ~ ( member @ ( sK35_SY169 @ SY271 @ SY270 @ SY269 @ SY268 @ SY267 @ SV14 ) @ SY270 ) )
| ~ ( apply @ SY267 @ ( sK35_SY169 @ SY271 @ SY270 @ SY269 @ SY268 @ SY267 @ SV14 ) @ ( sK34_SY165 @ SY271 @ SY270 @ SY269 @ SY268 @ SY267 @ SV14 ) ) )
| ( apply @ SV14 @ ( sK33_X @ SY271 @ SY270 @ SY269 @ SY268 @ SY267 @ SV14 ) @ ( sK34_SY165 @ SY271 @ SY270 @ SY269 @ SY268 @ SY267 @ SV14 ) ) ) ) )
| ( compose_predicate @ SV14 @ SY267 @ SY268 @ SY269 @ SY270 @ SY271 ) )
| ~ ! [SY273: $i,SY274: $i] :
( ~ ( compose_predicate @ SV14 @ SY267 @ SY268 @ SY269 @ SY273 @ SY274 )
| ~ ( ~ ! [SY275: $i,SY276: $i] :
( ~ ( member @ SY275 @ SY269 )
| ~ ( member @ SY276 @ SY274 )
| ! [SX8: $i] :
( ~ ( apply @ SY268 @ SY275 @ SX8 )
| ~ ( member @ SX8 @ SY273 )
| ~ ( apply @ SY267 @ SX8 @ SY276 ) )
| ( apply @ SV14 @ SY275 @ SY276 ) )
| ~ ! [SY278: $i,SY279: $i] :
( ~ ( member @ SY278 @ SY269 )
| ~ ( member @ SY279 @ SY274 )
| ~ ( apply @ SV14 @ SY278 @ SY279 )
| ~ ( ~ ~ ( ~ ( apply @ SY268 @ SY278 @ ( sK32_Y @ SY279 @ SY278 @ SY274 @ SY273 @ SY269 @ SY268 @ SY267 @ SV14 ) )
| ~ ( member @ ( sK32_Y @ SY279 @ SY278 @ SY274 @ SY273 @ SY269 @ SY268 @ SY267 @ SV14 ) @ SY273 ) )
| ~ ( apply @ SY267 @ ( sK32_Y @ SY279 @ SY278 @ SY274 @ SY273 @ SY269 @ SY268 @ SY267 @ SV14 ) @ SY279 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(167,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( member @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(168,plain,
! [SV15: $i] :
( ( ~ ( ~ ! [SY280: $i,SY281: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK24_X1 @ SY281 @ SY280 @ SV15 ) @ SY280 )
| ~ ( member @ ( sK25_SY159 @ SY281 @ SY280 @ SV15 ) @ SY280 ) )
| ~ ( member @ ( sK26_SY161 @ SY281 @ SY280 @ SV15 ) @ SY281 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV15 @ ( sK24_X1 @ SY281 @ SY280 @ SV15 ) @ ( sK26_SY161 @ SY281 @ SY280 @ SV15 ) )
| ~ ( apply @ SV15 @ ( sK25_SY159 @ SY281 @ SY280 @ SV15 ) @ ( sK26_SY161 @ SY281 @ SY280 @ SV15 ) ) )
| ~ ( ( ( sK24_X1 @ SY281 @ SY280 @ SV15 )
!= ( sK25_SY159 @ SY281 @ SY280 @ SV15 ) ) ) ) )
| ( injective @ SV15 @ SY280 @ SY281 ) )
| ~ ! [SY282: $i,SY283: $i] :
( ~ ( injective @ SV15 @ SY282 @ SY283 )
| ! [SY284: $i,SY285: $i,SY286: $i] :
( ~ ( member @ SY284 @ SY282 )
| ~ ( member @ SY285 @ SY282 )
| ~ ( member @ SY286 @ SY283 )
| ~ ( apply @ SV15 @ SY284 @ SY286 )
| ~ ( apply @ SV15 @ SY285 @ SY286 )
| ( SY284 = SY285 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(169,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( equal_set @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(170,plain,
! [SV16: $i] :
( ( ! [SY287: $i,SY288: $i] :
~ ( ~ ! [SY289: $i,SY290: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK12_X1 @ SY290 @ SY289 @ SY288 @ SY287 @ SV16 ) @ SY287 )
| ~ ( member @ ( sK13_SY151 @ SY290 @ SY289 @ SY288 @ SY287 @ SV16 ) @ SY289 ) )
| ~ ( member @ ( sK14_SY154 @ SY290 @ SY289 @ SY288 @ SY287 @ SV16 ) @ SY287 ) )
| ~ ( member @ ( sK15_SY156 @ SY290 @ SY289 @ SY288 @ SY287 @ SV16 ) @ SY289 ) )
| ~ ( apply @ SY288 @ ( sK12_X1 @ SY290 @ SY289 @ SY288 @ SY287 @ SV16 ) @ ( sK14_SY154 @ SY290 @ SY289 @ SY288 @ SY287 @ SV16 ) ) )
| ~ ( apply @ SV16 @ ( sK12_X1 @ SY290 @ SY289 @ SY288 @ SY287 @ SV16 ) @ ( sK13_SY151 @ SY290 @ SY289 @ SY288 @ SY287 @ SV16 ) ) )
| ~ ( apply @ SV16 @ ( sK14_SY154 @ SY290 @ SY289 @ SY288 @ SY287 @ SV16 ) @ ( sK15_SY156 @ SY290 @ SY289 @ SY288 @ SY287 @ SV16 ) ) )
| ~ ~ ( apply @ SY290 @ ( sK13_SY151 @ SY290 @ SY289 @ SY288 @ SY287 @ SV16 ) @ ( sK15_SY156 @ SY290 @ SY289 @ SY288 @ SY287 @ SV16 ) ) )
| ( increasing @ SV16 @ SY287 @ SY288 @ SY289 @ SY290 ) )
| ~ ! [SY291: $i,SY292: $i] :
( ~ ( increasing @ SV16 @ SY287 @ SY288 @ SY291 @ SY292 )
| ! [SY293: $i,SY294: $i,SY295: $i,SY296: $i] :
( ~ ( member @ SY293 @ SY287 )
| ~ ( member @ SY294 @ SY291 )
| ~ ( member @ SY295 @ SY287 )
| ~ ( member @ SY296 @ SY291 )
| ~ ( apply @ SY288 @ SY293 @ SY295 )
| ~ ( apply @ SV16 @ SY293 @ SY294 )
| ~ ( apply @ SV16 @ SY295 @ SY296 )
| ( apply @ SY292 @ SY294 @ SY296 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(171,plain,
! [SV17: $i] :
( ( ~ ( ~ ! [SY297: $i,SY298: $i] :
( ~ ( member @ SV17 @ SY297 )
| ~ ( member @ SV17 @ SY298 )
| ( member @ SV17 @ ( intersection @ SY297 @ SY298 ) ) )
| ~ ~ ( ~ ! [SY299: $i] :
( ! [SY300: $i] :
~ ( member @ SV17 @ ( intersection @ SY299 @ SY300 ) )
| ( member @ SV17 @ SY299 ) )
| ~ ! [SY301: $i,SY302: $i] :
( ~ ( member @ SV17 @ ( intersection @ SY301 @ SY302 ) )
| ( member @ SV17 @ SY302 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(172,plain,
! [SV18: $i] :
( ( ~ ( ~ ! [SY303: $i,SY304: $i] :
( ~ ( member @ SV18 @ ( unordered_pair @ SY303 @ SY304 ) )
| ( SV18 = SY303 )
| ( SV18 = SY304 ) )
| ~ ~ ( ~ ! [SY305: $i] :
( ( SV18 != SY305 )
| ! [SY306: $i] : ( member @ SV18 @ ( unordered_pair @ SY305 @ SY306 ) ) )
| ~ ! [SY307: $i,SY308: $i] :
( ( SV18 != SY308 )
| ( member @ SV18 @ ( unordered_pair @ SY307 @ SY308 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(173,plain,
! [SV19: $i] :
( ( ~ ( ~ ! [SY309: $i,SY310: $i] :
( ~ ( injective @ SV19 @ SY309 @ SY310 )
| ~ ( surjective @ SV19 @ SY309 @ SY310 )
| ( one_to_one @ SV19 @ SY309 @ SY310 ) )
| ~ ~ ( ~ ! [SY311: $i,SY312: $i] :
( ~ ( one_to_one @ SV19 @ SY311 @ SY312 )
| ( injective @ SV19 @ SY311 @ SY312 ) )
| ~ ! [SY313: $i,SY314: $i] :
( ~ ( one_to_one @ SV19 @ SY313 @ SY314 )
| ( surjective @ SV19 @ SY313 @ SY314 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(174,plain,
! [SV20: $i] :
( ( ! [SY315: $i,SY316: $i,SY317: $i,SY318: $i] :
~ ( ~ ! [SY319: $i,SY320: $i] :
( ~ ( member @ SY319 @ SY316 )
| ~ ( member @ SY320 @ SY318 )
| ! [SY321: $i] :
( ~ ( apply @ SY315 @ SY319 @ SY321 )
| ~ ( member @ SY321 @ SY317 )
| ~ ( apply @ SV20 @ SY321 @ SY320 ) )
| ( apply @ ( compose_function @ SV20 @ SY315 @ SY316 @ SY317 @ SY318 ) @ SY319 @ SY320 ) )
| ~ ! [SY322: $i,SY323: $i] :
( ~ ( member @ SY322 @ SY316 )
| ~ ( member @ SY323 @ SY318 )
| ~ ( apply @ ( compose_function @ SV20 @ SY315 @ SY316 @ SY317 @ SY318 ) @ SY322 @ SY323 )
| ~ ( ~ ~ ( ~ ( apply @ SY315 @ SY322 @ ( sK31_Y @ SY323 @ SY322 @ SY318 @ SY317 @ SY316 @ SY315 @ SV20 ) )
| ~ ( member @ ( sK31_Y @ SY323 @ SY322 @ SY318 @ SY317 @ SY316 @ SY315 @ SV20 ) @ SY317 ) )
| ~ ( apply @ SV20 @ ( sK31_Y @ SY323 @ SY322 @ SY318 @ SY317 @ SY316 @ SY315 @ SV20 ) @ SY323 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(175,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( sum @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( sum @ SX1 ) )
| ~ ( ~ ( member @ ( sK42_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ SX0 @ ( sK42_Y @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(176,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK41_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( member @ SX0 @ ( sK41_Y @ SX1 @ SX0 ) ) )
| ( member @ SX0 @ ( product @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( product @ SX1 ) )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX0 @ SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(177,plain,
! [SV21: $i] :
( ( ~ ( ~ ! [SY324: $i,SY325: $i] :
( ~ ( ~ ( member @ ( sK40_X @ SY325 @ SY324 @ SV21 ) @ SY324 )
| ~ ! [SY326: $i] :
( ~ ( apply @ SV21 @ ( sK40_X @ SY325 @ SY324 @ SV21 ) @ SY326 )
| ~ ( member @ SY326 @ SY325 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_X @ SY325 @ SY324 @ SV21 ) @ SY324 )
| ~ ( member @ ( sK38_SY170 @ SY325 @ SY324 @ SV21 ) @ SY325 ) )
| ~ ( member @ ( sK39_SY172 @ SY325 @ SY324 @ SV21 ) @ SY325 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV21 @ ( sK37_X @ SY325 @ SY324 @ SV21 ) @ ( sK38_SY170 @ SY325 @ SY324 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK37_X @ SY325 @ SY324 @ SV21 ) @ ( sK39_SY172 @ SY325 @ SY324 @ SV21 ) ) )
| ~ ( ( ( sK38_SY170 @ SY325 @ SY324 @ SV21 )
!= ( sK39_SY172 @ SY325 @ SY324 @ SV21 ) ) ) ) )
| ( maps @ SV21 @ SY324 @ SY325 ) )
| ~ ~ ( ~ ! [SY327: $i,SY328: $i] :
( ~ ( maps @ SV21 @ SY327 @ SY328 )
| ! [SY329: $i] :
( ~ ( member @ SY329 @ SY327 )
| ~ ( ~ ( apply @ SV21 @ SY329 @ ( sK36_Y @ SY329 @ SY328 @ SY327 @ SV21 ) )
| ~ ( member @ ( sK36_Y @ SY329 @ SY328 @ SY327 @ SV21 ) @ SY328 ) ) ) )
| ~ ! [SY330: $i,SY331: $i] :
( ~ ( maps @ SV21 @ SY330 @ SY331 )
| ! [SY332: $i,SY333: $i,SY334: $i] :
( ~ ( member @ SY332 @ SY330 )
| ~ ( member @ SY333 @ SY331 )
| ~ ( member @ SY334 @ SY331 )
| ~ ( apply @ SV21 @ SY332 @ SY333 )
| ~ ( apply @ SV21 @ SY332 @ SY334 )
| ( SY333 = SY334 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(178,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK27_X @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( apply @ SX0 @ ( sK27_X @ SX1 @ SX0 ) @ ( sK27_X @ SX1 @ SX0 ) ) )
| ( identity @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( identity @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( apply @ SX0 @ SX2 @ SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(179,plain,
! [SV1: $i] :
( ( member @ SV1 @ empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(180,plain,
! [SV22: $i,SV2: $i] :
( ( ~ ( ~ ! [SY335: $i,SY336: $i] :
( ! [SY337: $i] :
( ~ ( apply @ SV2 @ SY337 @ SY336 )
| ~ ( member @ SY337 @ SV22 ) )
| ~ ( member @ SY336 @ SY335 )
| ( member @ SY336 @ ( image3 @ SV2 @ SV22 @ SY335 ) ) )
| ~ ~ ( ~ ! [SY338: $i,SY339: $i] :
( ~ ( member @ SY339 @ ( image3 @ SV2 @ SV22 @ SY338 ) )
| ~ ( ~ ( apply @ SV2 @ ( sK18_X @ SY339 @ SY338 @ SV22 @ SV2 ) @ SY339 )
| ~ ( member @ ( sK18_X @ SY339 @ SY338 @ SV22 @ SV2 ) @ SV22 ) ) )
| ~ ! [SY340: $i,SY341: $i] :
( ~ ( member @ SY341 @ ( image3 @ SV2 @ SV22 @ SY340 ) )
| ( member @ SY341 @ SY340 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(181,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_set @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(182,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( member @ SX0 @ ( power_set @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(183,plain,
! [SV3: $i,SV23: $i] :
( ( ! [SY342: $i] :
~ ( ~ ! [SY343: $i,SY344: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_X1 @ SY344 @ SY343 @ SY342 @ SV23 @ SV3 ) @ SV23 )
| ~ ( member @ ( sK9_SY145 @ SY344 @ SY343 @ SY342 @ SV23 @ SV3 ) @ SY343 ) )
| ~ ( member @ ( sK10_SY148 @ SY344 @ SY343 @ SY342 @ SV23 @ SV3 ) @ SV23 ) )
| ~ ( member @ ( sK11_SY150 @ SY344 @ SY343 @ SY342 @ SV23 @ SV3 ) @ SY343 ) )
| ~ ( apply @ SY342 @ ( sK8_X1 @ SY344 @ SY343 @ SY342 @ SV23 @ SV3 ) @ ( sK10_SY148 @ SY344 @ SY343 @ SY342 @ SV23 @ SV3 ) ) )
| ~ ( apply @ SV3 @ ( sK8_X1 @ SY344 @ SY343 @ SY342 @ SV23 @ SV3 ) @ ( sK9_SY145 @ SY344 @ SY343 @ SY342 @ SV23 @ SV3 ) ) )
| ~ ( apply @ SV3 @ ( sK10_SY148 @ SY344 @ SY343 @ SY342 @ SV23 @ SV3 ) @ ( sK11_SY150 @ SY344 @ SY343 @ SY342 @ SV23 @ SV3 ) ) )
| ~ ~ ( apply @ SY344 @ ( sK11_SY150 @ SY344 @ SY343 @ SY342 @ SV23 @ SV3 ) @ ( sK9_SY145 @ SY344 @ SY343 @ SY342 @ SV23 @ SV3 ) ) )
| ( decreasing @ SV3 @ SV23 @ SY342 @ SY343 @ SY344 ) )
| ~ ! [SY345: $i,SY346: $i] :
( ~ ( decreasing @ SV3 @ SV23 @ SY342 @ SY345 @ SY346 )
| ! [SY347: $i,SY348: $i,SY349: $i,SY350: $i] :
( ~ ( member @ SY347 @ SV23 )
| ~ ( member @ SY348 @ SY345 )
| ~ ( member @ SY349 @ SV23 )
| ~ ( member @ SY350 @ SY345 )
| ~ ( apply @ SY342 @ SY347 @ SY349 )
| ~ ( apply @ SV3 @ SY347 @ SY348 )
| ~ ( apply @ SV3 @ SY349 @ SY350 )
| ( apply @ SY346 @ SY350 @ SY348 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(184,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK43_X @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK43_X @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(185,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(186,plain,
! [SV4: $i] :
( ( ~ ! [SY192: $i,SY193: $i] :
( ! [SY194: $i] :
( ~ ( apply @ SV4 @ SY194 @ SY193 )
| ~ ( member @ SY194 @ SY192 ) )
| ( member @ SY193 @ ( image2 @ SV4 @ SY192 ) ) )
| ~ ! [SY195: $i,SY196: $i] :
( ~ ( member @ SY196 @ ( image2 @ SV4 @ SY195 ) )
| ~ ( ~ ( apply @ SV4 @ ( sK19_X @ SY196 @ SY195 @ SV4 ) @ SY196 )
| ~ ( member @ ( sK19_X @ SY196 @ SY195 @ SV4 ) @ SY195 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(187,plain,
! [SV5: $i] :
( ( ~ ! [SY197: $i,SY198: $i] :
( ~ ( member @ SV5 @ SY198 )
| ( member @ SV5 @ SY197 )
| ( member @ SV5 @ ( difference @ SY198 @ SY197 ) ) )
| ~ ~ ( ~ ! [SY199: $i,SY200: $i] :
( ~ ( member @ SV5 @ ( difference @ SY200 @ SY199 ) )
| ( member @ SV5 @ SY200 ) )
| ~ ! [SY201: $i] :
( ! [SY202: $i] :
~ ( member @ SV5 @ ( difference @ SY202 @ SY201 ) )
| ~ ( member @ SV5 @ SY201 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(188,plain,
! [SV6: $i] :
( ( ~ ! [SY203: $i,SY204: $i] :
( ~ ( member @ SV6 @ ( union @ SY203 @ SY204 ) )
| ( member @ SV6 @ SY203 )
| ( member @ SV6 @ SY204 ) )
| ~ ~ ( ~ ! [SY205: $i] :
( ~ ( member @ SV6 @ SY205 )
| ! [SY206: $i] : ( member @ SV6 @ ( union @ SY205 @ SY206 ) ) )
| ~ ! [SY207: $i,SY208: $i] :
( ~ ( member @ SV6 @ SY208 )
| ( member @ SV6 @ ( union @ SY207 @ SY208 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(189,plain,
! [SV7: $i,SV24: $i] :
( ( ! [SY351: $i] :
~ ( ~ ! [SY352: $i,SY353: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK4_X1 @ SY353 @ SY352 @ SY351 @ SV24 @ SV7 ) @ SV24 )
| ~ ( member @ ( sK5_SY139 @ SY353 @ SY352 @ SY351 @ SV24 @ SV7 ) @ SY352 ) )
| ~ ( member @ ( sK6_SY142 @ SY353 @ SY352 @ SY351 @ SV24 @ SV7 ) @ SV24 ) )
| ~ ( member @ ( sK7_SY144 @ SY353 @ SY352 @ SY351 @ SV24 @ SV7 ) @ SY352 ) )
| ~ ( apply @ SV7 @ ( sK4_X1 @ SY353 @ SY352 @ SY351 @ SV24 @ SV7 ) @ ( sK5_SY139 @ SY353 @ SY352 @ SY351 @ SV24 @ SV7 ) ) )
| ~ ( apply @ SV7 @ ( sK6_SY142 @ SY353 @ SY352 @ SY351 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SY353 @ SY352 @ SY351 @ SV24 @ SV7 ) ) )
| ~ ~ ( ~ ( ~ ( apply @ SY351 @ ( sK4_X1 @ SY353 @ SY352 @ SY351 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SY353 @ SY352 @ SY351 @ SV24 @ SV7 ) )
| ~ ( apply @ SY353 @ ( sK5_SY139 @ SY353 @ SY352 @ SY351 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SY353 @ SY352 @ SY351 @ SV24 @ SV7 ) ) )
| ~ ( ( apply @ SY351 @ ( sK4_X1 @ SY353 @ SY352 @ SY351 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SY353 @ SY352 @ SY351 @ SV24 @ SV7 ) )
| ( apply @ SY353 @ ( sK5_SY139 @ SY353 @ SY352 @ SY351 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SY353 @ SY352 @ SY351 @ SV24 @ SV7 ) ) ) ) )
| ~ ( maps @ SV7 @ SV24 @ SY352 )
| ~ ( one_to_one @ SV7 @ SV24 @ SY352 )
| ( isomorphism @ SV7 @ SV24 @ SY351 @ SY352 @ SY353 ) )
| ~ ~ ( ~ ! [SY354: $i,SY355: $i] :
( ~ ( isomorphism @ SV7 @ SV24 @ SY351 @ SY354 @ SY355 )
| ! [SY356: $i,SY357: $i] :
~ ( ~ ! [SY358: $i,SY359: $i] :
( ~ ( member @ SY356 @ SV24 )
| ~ ( member @ SY357 @ SY354 )
| ~ ( member @ SY358 @ SV24 )
| ~ ( member @ SY359 @ SY354 )
| ~ ( apply @ SV7 @ SY356 @ SY357 )
| ~ ( apply @ SV7 @ SY358 @ SY359 )
| ~ ( apply @ SY351 @ SY356 @ SY358 )
| ( apply @ SY355 @ SY357 @ SY359 ) )
| ~ ! [SY360: $i,SY361: $i] :
( ~ ( member @ SY356 @ SV24 )
| ~ ( member @ SY357 @ SY354 )
| ~ ( member @ SY360 @ SV24 )
| ~ ( member @ SY361 @ SY354 )
| ~ ( apply @ SV7 @ SY356 @ SY357 )
| ~ ( apply @ SV7 @ SY360 @ SY361 )
| ~ ( apply @ SY355 @ SY357 @ SY361 )
| ( apply @ SY351 @ SY356 @ SY360 ) ) ) )
| ~ ~ ( ~ ! [SY362: $i] :
( ! [SY363: $i] :
~ ( isomorphism @ SV7 @ SV24 @ SY351 @ SY362 @ SY363 )
| ( maps @ SV7 @ SV24 @ SY362 ) )
| ~ ! [SY364: $i] :
( ! [SY365: $i] :
~ ( isomorphism @ SV7 @ SV24 @ SY351 @ SY364 @ SY365 )
| ( one_to_one @ SV7 @ SV24 @ SY364 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(190,plain,
! [SV8: $i,SV25: $i] :
( ( ~ ( ~ ! [SY366: $i,SY367: $i] :
( ~ ( ~ ~ ( ~ ( member @ ( sK20_X @ SY367 @ SY366 @ SV25 @ SV8 ) @ SY366 )
| ~ ( member @ ( sK21_SY157 @ SY367 @ SY366 @ SV25 @ SV8 ) @ SY367 ) )
| ~ ~ ( ~ ( ~ ( apply @ SV25 @ ( sK20_X @ SY367 @ SY366 @ SV25 @ SV8 ) @ ( sK21_SY157 @ SY367 @ SY366 @ SV25 @ SV8 ) )
| ~ ( apply @ SV8 @ ( sK21_SY157 @ SY367 @ SY366 @ SV25 @ SV8 ) @ ( sK20_X @ SY367 @ SY366 @ SV25 @ SV8 ) ) )
| ~ ( ( apply @ SV25 @ ( sK20_X @ SY367 @ SY366 @ SV25 @ SV8 ) @ ( sK21_SY157 @ SY367 @ SY366 @ SV25 @ SV8 ) )
| ( apply @ SV8 @ ( sK21_SY157 @ SY367 @ SY366 @ SV25 @ SV8 ) @ ( sK20_X @ SY367 @ SY366 @ SV25 @ SV8 ) ) ) ) )
| ( inverse_predicate @ SV8 @ SV25 @ SY366 @ SY367 ) )
| ~ ! [SY368: $i,SY369: $i] :
( ~ ( inverse_predicate @ SV8 @ SV25 @ SY368 @ SY369 )
| ~ ( ~ ! [SY370: $i,SY371: $i] :
( ~ ( member @ SY370 @ SY368 )
| ~ ( member @ SY371 @ SY369 )
| ~ ( apply @ SV25 @ SY370 @ SY371 )
| ( apply @ SV8 @ SY371 @ SY370 ) )
| ~ ! [SY372: $i,SY373: $i] :
( ~ ( member @ SY372 @ SY368 )
| ~ ( member @ SY373 @ SY369 )
| ~ ( apply @ SV8 @ SY373 @ SY372 )
| ( apply @ SV25 @ SY372 @ SY373 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(191,plain,
! [SV9: $i,SV26: $i] :
( ( ! [SY374: $i] :
~ ( ~ ! [SY375: $i,SY376: $i] :
( ~ ( member @ SY375 @ SV26 )
| ~ ( member @ SY376 @ SY374 )
| ~ ( apply @ SV9 @ SY375 @ SY376 )
| ( apply @ ( inverse_function @ SV9 @ SV26 @ SY374 ) @ SY376 @ SY375 ) )
| ~ ! [SY377: $i,SY378: $i] :
( ~ ( member @ SY377 @ SV26 )
| ~ ( member @ SY378 @ SY374 )
| ~ ( apply @ ( inverse_function @ SV9 @ SV26 @ SY374 ) @ SY378 @ SY377 )
| ( apply @ SV9 @ SY377 @ SY378 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(192,plain,
! [SV10: $i] :
( ( ~ ! [SY240: $i,SY241: $i] :
( ! [SY242: $i] :
( ~ ( apply @ SV10 @ SY241 @ SY242 )
| ~ ( member @ SY242 @ SY240 ) )
| ( member @ SY241 @ ( inverse_image2 @ SV10 @ SY240 ) ) )
| ~ ! [SY243: $i,SY244: $i] :
( ~ ( member @ SY244 @ ( inverse_image2 @ SV10 @ SY243 ) )
| ~ ( ~ ( apply @ SV10 @ SY244 @ ( sK17_Y @ SY244 @ SY243 @ SV10 ) )
| ~ ( member @ ( sK17_Y @ SY244 @ SY243 @ SV10 ) @ SY243 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(193,plain,
! [SV11: $i] :
( ( ~ ! [SY245: $i,SY246: $i] :
( ~ ( ~ ( member @ ( sK23_Y @ SY246 @ SY245 @ SV11 ) @ SY246 )
| ~ ! [SY247: $i] :
( ~ ( apply @ SV11 @ SY247 @ ( sK23_Y @ SY246 @ SY245 @ SV11 ) )
| ~ ( member @ SY247 @ SY245 ) ) )
| ( surjective @ SV11 @ SY245 @ SY246 ) )
| ~ ! [SY248: $i,SY249: $i] :
( ~ ( surjective @ SV11 @ SY248 @ SY249 )
| ! [SY250: $i] :
( ~ ( member @ SY250 @ SY249 )
| ~ ( ~ ( apply @ SV11 @ ( sK22_E @ SY250 @ SY249 @ SY248 @ SV11 ) @ SY250 )
| ~ ( member @ ( sK22_E @ SY250 @ SY249 @ SY248 @ SV11 ) @ SY248 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(194,plain,
! [SV27: $i,SV12: $i] :
( ( ~ ( ~ ! [SY379: $i,SY380: $i] :
( ! [SY381: $i] :
( ~ ( apply @ SV12 @ SY380 @ SY381 )
| ~ ( member @ SY381 @ SV27 ) )
| ~ ( member @ SY380 @ SY379 )
| ( member @ SY380 @ ( inverse_image3 @ SV12 @ SV27 @ SY379 ) ) )
| ~ ~ ( ~ ! [SY382: $i,SY383: $i] :
( ~ ( member @ SY383 @ ( inverse_image3 @ SV12 @ SV27 @ SY382 ) )
| ~ ( ~ ( apply @ SV12 @ SY383 @ ( sK16_Y @ SY383 @ SY382 @ SV27 @ SV12 ) )
| ~ ( member @ ( sK16_Y @ SY383 @ SY382 @ SV27 @ SV12 ) @ SV27 ) ) )
| ~ ! [SY384: $i,SY385: $i] :
( ~ ( member @ SY385 @ ( inverse_image3 @ SV12 @ SV27 @ SY384 ) )
| ( member @ SY385 @ SY384 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(195,plain,
! [SV13: $i,SV28: $i] :
( ( ~ ( ~ ! [SY386: $i,SY387: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK28_X @ SY387 @ SY386 @ SV28 @ SV13 ) @ SY386 )
| ~ ( member @ ( sK29_SY162 @ SY387 @ SY386 @ SV28 @ SV13 ) @ SY387 ) )
| ~ ( member @ ( sK30_SY164 @ SY387 @ SY386 @ SV28 @ SV13 ) @ SY387 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV13 @ ( sK28_X @ SY387 @ SY386 @ SV28 @ SV13 ) @ ( sK29_SY162 @ SY387 @ SY386 @ SV28 @ SV13 ) )
| ~ ( apply @ SV28 @ ( sK28_X @ SY387 @ SY386 @ SV28 @ SV13 ) @ ( sK30_SY164 @ SY387 @ SY386 @ SV28 @ SV13 ) ) )
| ~ ( ( ( sK29_SY162 @ SY387 @ SY386 @ SV28 @ SV13 )
!= ( sK30_SY164 @ SY387 @ SY386 @ SV28 @ SV13 ) ) ) ) )
| ( equal_maps @ SV13 @ SV28 @ SY386 @ SY387 ) )
| ~ ! [SY388: $i,SY389: $i] :
( ~ ( equal_maps @ SV13 @ SV28 @ SY388 @ SY389 )
| ! [SY390: $i,SY391: $i,SY392: $i] :
( ~ ( member @ SY390 @ SY388 )
| ~ ( member @ SY391 @ SY389 )
| ~ ( member @ SY392 @ SY389 )
| ~ ( apply @ SV13 @ SY390 @ SY391 )
| ~ ( apply @ SV28 @ SY390 @ SY392 )
| ( SY391 = SY392 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(196,plain,
! [SV14: $i,SV29: $i] :
( ( ! [SY393: $i,SY394: $i] :
~ ( ~ ! [SY395: $i,SY396: $i] :
( ~ ( ~ ~ ( ~ ( member @ ( sK33_X @ SY396 @ SY395 @ SY394 @ SY393 @ SV29 @ SV14 ) @ SY394 )
| ~ ( member @ ( sK34_SY165 @ SY396 @ SY395 @ SY394 @ SY393 @ SV29 @ SV14 ) @ SY396 ) )
| ~ ~ ( ~ ( ! [SY397: $i] :
( ~ ( apply @ SY393 @ ( sK33_X @ SY396 @ SY395 @ SY394 @ SY393 @ SV29 @ SV14 ) @ SY397 )
| ~ ( member @ SY397 @ SY395 )
| ~ ( apply @ SV29 @ SY397 @ ( sK34_SY165 @ SY396 @ SY395 @ SY394 @ SY393 @ SV29 @ SV14 ) ) )
| ~ ( apply @ SV14 @ ( sK33_X @ SY396 @ SY395 @ SY394 @ SY393 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SY396 @ SY395 @ SY394 @ SY393 @ SV29 @ SV14 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( apply @ SY393 @ ( sK33_X @ SY396 @ SY395 @ SY394 @ SY393 @ SV29 @ SV14 ) @ ( sK35_SY169 @ SY396 @ SY395 @ SY394 @ SY393 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK35_SY169 @ SY396 @ SY395 @ SY394 @ SY393 @ SV29 @ SV14 ) @ SY395 ) )
| ~ ( apply @ SV29 @ ( sK35_SY169 @ SY396 @ SY395 @ SY394 @ SY393 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SY396 @ SY395 @ SY394 @ SY393 @ SV29 @ SV14 ) ) )
| ( apply @ SV14 @ ( sK33_X @ SY396 @ SY395 @ SY394 @ SY393 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SY396 @ SY395 @ SY394 @ SY393 @ SV29 @ SV14 ) ) ) ) )
| ( compose_predicate @ SV14 @ SV29 @ SY393 @ SY394 @ SY395 @ SY396 ) )
| ~ ! [SY398: $i,SY399: $i] :
( ~ ( compose_predicate @ SV14 @ SV29 @ SY393 @ SY394 @ SY398 @ SY399 )
| ~ ( ~ ! [SY400: $i,SY401: $i] :
( ~ ( member @ SY400 @ SY394 )
| ~ ( member @ SY401 @ SY399 )
| ! [SY402: $i] :
( ~ ( apply @ SY393 @ SY400 @ SY402 )
| ~ ( member @ SY402 @ SY398 )
| ~ ( apply @ SV29 @ SY402 @ SY401 ) )
| ( apply @ SV14 @ SY400 @ SY401 ) )
| ~ ! [SY403: $i,SY404: $i] :
( ~ ( member @ SY403 @ SY394 )
| ~ ( member @ SY404 @ SY399 )
| ~ ( apply @ SV14 @ SY403 @ SY404 )
| ~ ( ~ ~ ( ~ ( apply @ SY393 @ SY403 @ ( sK32_Y @ SY404 @ SY403 @ SY399 @ SY398 @ SY394 @ SY393 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK32_Y @ SY404 @ SY403 @ SY399 @ SY398 @ SY394 @ SY393 @ SV29 @ SV14 ) @ SY398 ) )
| ~ ( apply @ SV29 @ ( sK32_Y @ SY404 @ SY403 @ SY399 @ SY398 @ SY394 @ SY393 @ SV29 @ SV14 ) @ SY404 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(197,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( member @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(198,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(199,plain,
! [SV15: $i] :
( ( ~ ! [SY280: $i,SY281: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK24_X1 @ SY281 @ SY280 @ SV15 ) @ SY280 )
| ~ ( member @ ( sK25_SY159 @ SY281 @ SY280 @ SV15 ) @ SY280 ) )
| ~ ( member @ ( sK26_SY161 @ SY281 @ SY280 @ SV15 ) @ SY281 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV15 @ ( sK24_X1 @ SY281 @ SY280 @ SV15 ) @ ( sK26_SY161 @ SY281 @ SY280 @ SV15 ) )
| ~ ( apply @ SV15 @ ( sK25_SY159 @ SY281 @ SY280 @ SV15 ) @ ( sK26_SY161 @ SY281 @ SY280 @ SV15 ) ) )
| ~ ( ( ( sK24_X1 @ SY281 @ SY280 @ SV15 )
!= ( sK25_SY159 @ SY281 @ SY280 @ SV15 ) ) ) ) )
| ( injective @ SV15 @ SY280 @ SY281 ) )
| ~ ! [SY282: $i,SY283: $i] :
( ~ ( injective @ SV15 @ SY282 @ SY283 )
| ! [SY284: $i,SY285: $i,SY286: $i] :
( ~ ( member @ SY284 @ SY282 )
| ~ ( member @ SY285 @ SY282 )
| ~ ( member @ SY286 @ SY283 )
| ~ ( apply @ SV15 @ SY284 @ SY286 )
| ~ ( apply @ SV15 @ SY285 @ SY286 )
| ( SY284 = SY285 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(200,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( equal_set @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[169]) ).
thf(201,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[169]) ).
thf(202,plain,
! [SV16: $i,SV30: $i] :
( ( ! [SY405: $i] :
~ ( ~ ! [SY406: $i,SY407: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK12_X1 @ SY407 @ SY406 @ SY405 @ SV30 @ SV16 ) @ SV30 )
| ~ ( member @ ( sK13_SY151 @ SY407 @ SY406 @ SY405 @ SV30 @ SV16 ) @ SY406 ) )
| ~ ( member @ ( sK14_SY154 @ SY407 @ SY406 @ SY405 @ SV30 @ SV16 ) @ SV30 ) )
| ~ ( member @ ( sK15_SY156 @ SY407 @ SY406 @ SY405 @ SV30 @ SV16 ) @ SY406 ) )
| ~ ( apply @ SY405 @ ( sK12_X1 @ SY407 @ SY406 @ SY405 @ SV30 @ SV16 ) @ ( sK14_SY154 @ SY407 @ SY406 @ SY405 @ SV30 @ SV16 ) ) )
| ~ ( apply @ SV16 @ ( sK12_X1 @ SY407 @ SY406 @ SY405 @ SV30 @ SV16 ) @ ( sK13_SY151 @ SY407 @ SY406 @ SY405 @ SV30 @ SV16 ) ) )
| ~ ( apply @ SV16 @ ( sK14_SY154 @ SY407 @ SY406 @ SY405 @ SV30 @ SV16 ) @ ( sK15_SY156 @ SY407 @ SY406 @ SY405 @ SV30 @ SV16 ) ) )
| ~ ~ ( apply @ SY407 @ ( sK13_SY151 @ SY407 @ SY406 @ SY405 @ SV30 @ SV16 ) @ ( sK15_SY156 @ SY407 @ SY406 @ SY405 @ SV30 @ SV16 ) ) )
| ( increasing @ SV16 @ SV30 @ SY405 @ SY406 @ SY407 ) )
| ~ ! [SY408: $i,SY409: $i] :
( ~ ( increasing @ SV16 @ SV30 @ SY405 @ SY408 @ SY409 )
| ! [SY410: $i,SY411: $i,SY412: $i,SY413: $i] :
( ~ ( member @ SY410 @ SV30 )
| ~ ( member @ SY411 @ SY408 )
| ~ ( member @ SY412 @ SV30 )
| ~ ( member @ SY413 @ SY408 )
| ~ ( apply @ SY405 @ SY410 @ SY412 )
| ~ ( apply @ SV16 @ SY410 @ SY411 )
| ~ ( apply @ SV16 @ SY412 @ SY413 )
| ( apply @ SY409 @ SY411 @ SY413 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(203,plain,
! [SV17: $i] :
( ( ~ ! [SY297: $i,SY298: $i] :
( ~ ( member @ SV17 @ SY297 )
| ~ ( member @ SV17 @ SY298 )
| ( member @ SV17 @ ( intersection @ SY297 @ SY298 ) ) )
| ~ ~ ( ~ ! [SY299: $i] :
( ! [SY300: $i] :
~ ( member @ SV17 @ ( intersection @ SY299 @ SY300 ) )
| ( member @ SV17 @ SY299 ) )
| ~ ! [SY301: $i,SY302: $i] :
( ~ ( member @ SV17 @ ( intersection @ SY301 @ SY302 ) )
| ( member @ SV17 @ SY302 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(204,plain,
! [SV18: $i] :
( ( ~ ! [SY303: $i,SY304: $i] :
( ~ ( member @ SV18 @ ( unordered_pair @ SY303 @ SY304 ) )
| ( SV18 = SY303 )
| ( SV18 = SY304 ) )
| ~ ~ ( ~ ! [SY305: $i] :
( ( SV18 != SY305 )
| ! [SY306: $i] : ( member @ SV18 @ ( unordered_pair @ SY305 @ SY306 ) ) )
| ~ ! [SY307: $i,SY308: $i] :
( ( SV18 != SY308 )
| ( member @ SV18 @ ( unordered_pair @ SY307 @ SY308 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(205,plain,
! [SV19: $i] :
( ( ~ ! [SY309: $i,SY310: $i] :
( ~ ( injective @ SV19 @ SY309 @ SY310 )
| ~ ( surjective @ SV19 @ SY309 @ SY310 )
| ( one_to_one @ SV19 @ SY309 @ SY310 ) )
| ~ ~ ( ~ ! [SY311: $i,SY312: $i] :
( ~ ( one_to_one @ SV19 @ SY311 @ SY312 )
| ( injective @ SV19 @ SY311 @ SY312 ) )
| ~ ! [SY313: $i,SY314: $i] :
( ~ ( one_to_one @ SV19 @ SY313 @ SY314 )
| ( surjective @ SV19 @ SY313 @ SY314 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(206,plain,
! [SV20: $i,SV31: $i] :
( ( ! [SY414: $i,SY415: $i,SY416: $i] :
~ ( ~ ! [SY417: $i,SY418: $i] :
( ~ ( member @ SY417 @ SY414 )
| ~ ( member @ SY418 @ SY416 )
| ! [SY419: $i] :
( ~ ( apply @ SV31 @ SY417 @ SY419 )
| ~ ( member @ SY419 @ SY415 )
| ~ ( apply @ SV20 @ SY419 @ SY418 ) )
| ( apply @ ( compose_function @ SV20 @ SV31 @ SY414 @ SY415 @ SY416 ) @ SY417 @ SY418 ) )
| ~ ! [SY420: $i,SY421: $i] :
( ~ ( member @ SY420 @ SY414 )
| ~ ( member @ SY421 @ SY416 )
| ~ ( apply @ ( compose_function @ SV20 @ SV31 @ SY414 @ SY415 @ SY416 ) @ SY420 @ SY421 )
| ~ ( ~ ~ ( ~ ( apply @ SV31 @ SY420 @ ( sK31_Y @ SY421 @ SY420 @ SY416 @ SY415 @ SY414 @ SV31 @ SV20 ) )
| ~ ( member @ ( sK31_Y @ SY421 @ SY420 @ SY416 @ SY415 @ SY414 @ SV31 @ SV20 ) @ SY415 ) )
| ~ ( apply @ SV20 @ ( sK31_Y @ SY421 @ SY420 @ SY416 @ SY415 @ SY414 @ SV31 @ SV20 ) @ SY421 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(207,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( sum @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(208,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( sum @ SX1 ) )
| ~ ( ~ ( member @ ( sK42_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ SX0 @ ( sK42_Y @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(209,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK41_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( member @ SX0 @ ( sK41_Y @ SX1 @ SX0 ) ) )
| ( member @ SX0 @ ( product @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[176]) ).
thf(210,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( product @ SX1 ) )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX0 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[176]) ).
thf(211,plain,
! [SV21: $i] :
( ( ~ ! [SY324: $i,SY325: $i] :
( ~ ( ~ ( member @ ( sK40_X @ SY325 @ SY324 @ SV21 ) @ SY324 )
| ~ ! [SY326: $i] :
( ~ ( apply @ SV21 @ ( sK40_X @ SY325 @ SY324 @ SV21 ) @ SY326 )
| ~ ( member @ SY326 @ SY325 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_X @ SY325 @ SY324 @ SV21 ) @ SY324 )
| ~ ( member @ ( sK38_SY170 @ SY325 @ SY324 @ SV21 ) @ SY325 ) )
| ~ ( member @ ( sK39_SY172 @ SY325 @ SY324 @ SV21 ) @ SY325 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV21 @ ( sK37_X @ SY325 @ SY324 @ SV21 ) @ ( sK38_SY170 @ SY325 @ SY324 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK37_X @ SY325 @ SY324 @ SV21 ) @ ( sK39_SY172 @ SY325 @ SY324 @ SV21 ) ) )
| ~ ( ( ( sK38_SY170 @ SY325 @ SY324 @ SV21 )
!= ( sK39_SY172 @ SY325 @ SY324 @ SV21 ) ) ) ) )
| ( maps @ SV21 @ SY324 @ SY325 ) )
| ~ ~ ( ~ ! [SY327: $i,SY328: $i] :
( ~ ( maps @ SV21 @ SY327 @ SY328 )
| ! [SY329: $i] :
( ~ ( member @ SY329 @ SY327 )
| ~ ( ~ ( apply @ SV21 @ SY329 @ ( sK36_Y @ SY329 @ SY328 @ SY327 @ SV21 ) )
| ~ ( member @ ( sK36_Y @ SY329 @ SY328 @ SY327 @ SV21 ) @ SY328 ) ) ) )
| ~ ! [SY330: $i,SY331: $i] :
( ~ ( maps @ SV21 @ SY330 @ SY331 )
| ! [SY332: $i,SY333: $i,SY334: $i] :
( ~ ( member @ SY332 @ SY330 )
| ~ ( member @ SY333 @ SY331 )
| ~ ( member @ SY334 @ SY331 )
| ~ ( apply @ SV21 @ SY332 @ SY333 )
| ~ ( apply @ SV21 @ SY332 @ SY334 )
| ( SY333 = SY334 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(212,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK27_X @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( apply @ SX0 @ ( sK27_X @ SX1 @ SX0 ) @ ( sK27_X @ SX1 @ SX0 ) ) )
| ( identity @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(213,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( identity @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( apply @ SX0 @ SX2 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(214,plain,
! [SV22: $i,SV2: $i] :
( ( ~ ! [SY335: $i,SY336: $i] :
( ! [SY337: $i] :
( ~ ( apply @ SV2 @ SY337 @ SY336 )
| ~ ( member @ SY337 @ SV22 ) )
| ~ ( member @ SY336 @ SY335 )
| ( member @ SY336 @ ( image3 @ SV2 @ SV22 @ SY335 ) ) )
| ~ ~ ( ~ ! [SY338: $i,SY339: $i] :
( ~ ( member @ SY339 @ ( image3 @ SV2 @ SV22 @ SY338 ) )
| ~ ( ~ ( apply @ SV2 @ ( sK18_X @ SY339 @ SY338 @ SV22 @ SV2 ) @ SY339 )
| ~ ( member @ ( sK18_X @ SY339 @ SY338 @ SV22 @ SV2 ) @ SV22 ) ) )
| ~ ! [SY340: $i,SY341: $i] :
( ~ ( member @ SY341 @ ( image3 @ SV2 @ SV22 @ SY340 ) )
| ( member @ SY341 @ SY340 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(215,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_set @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(216,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( member @ SX0 @ ( power_set @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(217,plain,
! [SV3: $i,SV23: $i,SV32: $i] :
( ( ~ ( ~ ! [SY422: $i,SY423: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_X1 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ SV23 )
| ~ ( member @ ( sK9_SY145 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ SY422 ) )
| ~ ( member @ ( sK10_SY148 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ SV23 ) )
| ~ ( member @ ( sK11_SY150 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ SY422 ) )
| ~ ( apply @ SV32 @ ( sK8_X1 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ ( sK10_SY148 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ( apply @ SV3 @ ( sK8_X1 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ ( sK9_SY145 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ( apply @ SV3 @ ( sK10_SY148 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ ( sK11_SY150 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ~ ( apply @ SY423 @ ( sK11_SY150 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ ( sK9_SY145 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) ) )
| ( decreasing @ SV3 @ SV23 @ SV32 @ SY422 @ SY423 ) )
| ~ ! [SY424: $i,SY425: $i] :
( ~ ( decreasing @ SV3 @ SV23 @ SV32 @ SY424 @ SY425 )
| ! [SY426: $i,SY427: $i,SY428: $i,SY429: $i] :
( ~ ( member @ SY426 @ SV23 )
| ~ ( member @ SY427 @ SY424 )
| ~ ( member @ SY428 @ SV23 )
| ~ ( member @ SY429 @ SY424 )
| ~ ( apply @ SV32 @ SY426 @ SY428 )
| ~ ( apply @ SV3 @ SY426 @ SY427 )
| ~ ( apply @ SV3 @ SY428 @ SY429 )
| ( apply @ SY425 @ SY429 @ SY427 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(218,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK43_X @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK43_X @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(219,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(220,plain,
! [SV4: $i] :
( ( ~ ! [SY192: $i,SY193: $i] :
( ! [SY194: $i] :
( ~ ( apply @ SV4 @ SY194 @ SY193 )
| ~ ( member @ SY194 @ SY192 ) )
| ( member @ SY193 @ ( image2 @ SV4 @ SY192 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[186]) ).
thf(221,plain,
! [SV4: $i] :
( ( ~ ! [SY195: $i,SY196: $i] :
( ~ ( member @ SY196 @ ( image2 @ SV4 @ SY195 ) )
| ~ ( ~ ( apply @ SV4 @ ( sK19_X @ SY196 @ SY195 @ SV4 ) @ SY196 )
| ~ ( member @ ( sK19_X @ SY196 @ SY195 @ SV4 ) @ SY195 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[186]) ).
thf(222,plain,
! [SV5: $i] :
( ( ~ ! [SY197: $i,SY198: $i] :
( ~ ( member @ SV5 @ SY198 )
| ( member @ SV5 @ SY197 )
| ( member @ SV5 @ ( difference @ SY198 @ SY197 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[187]) ).
thf(223,plain,
! [SV5: $i] :
( ( ~ ~ ( ~ ! [SY199: $i,SY200: $i] :
( ~ ( member @ SV5 @ ( difference @ SY200 @ SY199 ) )
| ( member @ SV5 @ SY200 ) )
| ~ ! [SY201: $i] :
( ! [SY202: $i] :
~ ( member @ SV5 @ ( difference @ SY202 @ SY201 ) )
| ~ ( member @ SV5 @ SY201 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[187]) ).
thf(224,plain,
! [SV6: $i] :
( ( ~ ! [SY203: $i,SY204: $i] :
( ~ ( member @ SV6 @ ( union @ SY203 @ SY204 ) )
| ( member @ SV6 @ SY203 )
| ( member @ SV6 @ SY204 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(225,plain,
! [SV6: $i] :
( ( ~ ~ ( ~ ! [SY205: $i] :
( ~ ( member @ SV6 @ SY205 )
| ! [SY206: $i] : ( member @ SV6 @ ( union @ SY205 @ SY206 ) ) )
| ~ ! [SY207: $i,SY208: $i] :
( ~ ( member @ SV6 @ SY208 )
| ( member @ SV6 @ ( union @ SY207 @ SY208 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(226,plain,
! [SV7: $i,SV24: $i,SV33: $i] :
( ( ~ ( ~ ! [SY430: $i,SY431: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK4_X1 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ SV24 )
| ~ ( member @ ( sK5_SY139 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ SY430 ) )
| ~ ( member @ ( sK6_SY142 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ SV24 ) )
| ~ ( member @ ( sK7_SY144 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ SY430 ) )
| ~ ( apply @ SV7 @ ( sK4_X1 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ ( sK5_SY139 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ( apply @ SV7 @ ( sK6_SY142 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ~ ( ~ ( ~ ( apply @ SV33 @ ( sK4_X1 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) )
| ~ ( apply @ SY431 @ ( sK5_SY139 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ( ( apply @ SV33 @ ( sK4_X1 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) )
| ( apply @ SY431 @ ( sK5_SY139 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) ) ) ) )
| ~ ( maps @ SV7 @ SV24 @ SY430 )
| ~ ( one_to_one @ SV7 @ SV24 @ SY430 )
| ( isomorphism @ SV7 @ SV24 @ SV33 @ SY430 @ SY431 ) )
| ~ ~ ( ~ ! [SY432: $i,SY433: $i] :
( ~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SY432 @ SY433 )
| ! [SY434: $i,SY435: $i] :
~ ( ~ ! [SY436: $i,SY437: $i] :
( ~ ( member @ SY434 @ SV24 )
| ~ ( member @ SY435 @ SY432 )
| ~ ( member @ SY436 @ SV24 )
| ~ ( member @ SY437 @ SY432 )
| ~ ( apply @ SV7 @ SY434 @ SY435 )
| ~ ( apply @ SV7 @ SY436 @ SY437 )
| ~ ( apply @ SV33 @ SY434 @ SY436 )
| ( apply @ SY433 @ SY435 @ SY437 ) )
| ~ ! [SY438: $i,SY439: $i] :
( ~ ( member @ SY434 @ SV24 )
| ~ ( member @ SY435 @ SY432 )
| ~ ( member @ SY438 @ SV24 )
| ~ ( member @ SY439 @ SY432 )
| ~ ( apply @ SV7 @ SY434 @ SY435 )
| ~ ( apply @ SV7 @ SY438 @ SY439 )
| ~ ( apply @ SY433 @ SY435 @ SY439 )
| ( apply @ SV33 @ SY434 @ SY438 ) ) ) )
| ~ ~ ( ~ ! [SY440: $i] :
( ! [SY441: $i] :
~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SY440 @ SY441 )
| ( maps @ SV7 @ SV24 @ SY440 ) )
| ~ ! [SY442: $i] :
( ! [SY443: $i] :
~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SY442 @ SY443 )
| ( one_to_one @ SV7 @ SV24 @ SY442 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(227,plain,
! [SV8: $i,SV25: $i] :
( ( ~ ! [SY366: $i,SY367: $i] :
( ~ ( ~ ~ ( ~ ( member @ ( sK20_X @ SY367 @ SY366 @ SV25 @ SV8 ) @ SY366 )
| ~ ( member @ ( sK21_SY157 @ SY367 @ SY366 @ SV25 @ SV8 ) @ SY367 ) )
| ~ ~ ( ~ ( ~ ( apply @ SV25 @ ( sK20_X @ SY367 @ SY366 @ SV25 @ SV8 ) @ ( sK21_SY157 @ SY367 @ SY366 @ SV25 @ SV8 ) )
| ~ ( apply @ SV8 @ ( sK21_SY157 @ SY367 @ SY366 @ SV25 @ SV8 ) @ ( sK20_X @ SY367 @ SY366 @ SV25 @ SV8 ) ) )
| ~ ( ( apply @ SV25 @ ( sK20_X @ SY367 @ SY366 @ SV25 @ SV8 ) @ ( sK21_SY157 @ SY367 @ SY366 @ SV25 @ SV8 ) )
| ( apply @ SV8 @ ( sK21_SY157 @ SY367 @ SY366 @ SV25 @ SV8 ) @ ( sK20_X @ SY367 @ SY366 @ SV25 @ SV8 ) ) ) ) )
| ( inverse_predicate @ SV8 @ SV25 @ SY366 @ SY367 ) )
| ~ ! [SY368: $i,SY369: $i] :
( ~ ( inverse_predicate @ SV8 @ SV25 @ SY368 @ SY369 )
| ~ ( ~ ! [SY370: $i,SY371: $i] :
( ~ ( member @ SY370 @ SY368 )
| ~ ( member @ SY371 @ SY369 )
| ~ ( apply @ SV25 @ SY370 @ SY371 )
| ( apply @ SV8 @ SY371 @ SY370 ) )
| ~ ! [SY372: $i,SY373: $i] :
( ~ ( member @ SY372 @ SY368 )
| ~ ( member @ SY373 @ SY369 )
| ~ ( apply @ SV8 @ SY373 @ SY372 )
| ( apply @ SV25 @ SY372 @ SY373 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(228,plain,
! [SV9: $i,SV34: $i,SV26: $i] :
( ( ~ ( ~ ! [SY444: $i,SY445: $i] :
( ~ ( member @ SY444 @ SV26 )
| ~ ( member @ SY445 @ SV34 )
| ~ ( apply @ SV9 @ SY444 @ SY445 )
| ( apply @ ( inverse_function @ SV9 @ SV26 @ SV34 ) @ SY445 @ SY444 ) )
| ~ ! [SY446: $i,SY447: $i] :
( ~ ( member @ SY446 @ SV26 )
| ~ ( member @ SY447 @ SV34 )
| ~ ( apply @ ( inverse_function @ SV9 @ SV26 @ SV34 ) @ SY447 @ SY446 )
| ( apply @ SV9 @ SY446 @ SY447 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(229,plain,
! [SV10: $i] :
( ( ~ ! [SY240: $i,SY241: $i] :
( ! [SY242: $i] :
( ~ ( apply @ SV10 @ SY241 @ SY242 )
| ~ ( member @ SY242 @ SY240 ) )
| ( member @ SY241 @ ( inverse_image2 @ SV10 @ SY240 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[192]) ).
thf(230,plain,
! [SV10: $i] :
( ( ~ ! [SY243: $i,SY244: $i] :
( ~ ( member @ SY244 @ ( inverse_image2 @ SV10 @ SY243 ) )
| ~ ( ~ ( apply @ SV10 @ SY244 @ ( sK17_Y @ SY244 @ SY243 @ SV10 ) )
| ~ ( member @ ( sK17_Y @ SY244 @ SY243 @ SV10 ) @ SY243 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[192]) ).
thf(231,plain,
! [SV11: $i] :
( ( ~ ! [SY245: $i,SY246: $i] :
( ~ ( ~ ( member @ ( sK23_Y @ SY246 @ SY245 @ SV11 ) @ SY246 )
| ~ ! [SY247: $i] :
( ~ ( apply @ SV11 @ SY247 @ ( sK23_Y @ SY246 @ SY245 @ SV11 ) )
| ~ ( member @ SY247 @ SY245 ) ) )
| ( surjective @ SV11 @ SY245 @ SY246 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(232,plain,
! [SV11: $i] :
( ( ~ ! [SY248: $i,SY249: $i] :
( ~ ( surjective @ SV11 @ SY248 @ SY249 )
| ! [SY250: $i] :
( ~ ( member @ SY250 @ SY249 )
| ~ ( ~ ( apply @ SV11 @ ( sK22_E @ SY250 @ SY249 @ SY248 @ SV11 ) @ SY250 )
| ~ ( member @ ( sK22_E @ SY250 @ SY249 @ SY248 @ SV11 ) @ SY248 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(233,plain,
! [SV27: $i,SV12: $i] :
( ( ~ ! [SY379: $i,SY380: $i] :
( ! [SY381: $i] :
( ~ ( apply @ SV12 @ SY380 @ SY381 )
| ~ ( member @ SY381 @ SV27 ) )
| ~ ( member @ SY380 @ SY379 )
| ( member @ SY380 @ ( inverse_image3 @ SV12 @ SV27 @ SY379 ) ) )
| ~ ~ ( ~ ! [SY382: $i,SY383: $i] :
( ~ ( member @ SY383 @ ( inverse_image3 @ SV12 @ SV27 @ SY382 ) )
| ~ ( ~ ( apply @ SV12 @ SY383 @ ( sK16_Y @ SY383 @ SY382 @ SV27 @ SV12 ) )
| ~ ( member @ ( sK16_Y @ SY383 @ SY382 @ SV27 @ SV12 ) @ SV27 ) ) )
| ~ ! [SY384: $i,SY385: $i] :
( ~ ( member @ SY385 @ ( inverse_image3 @ SV12 @ SV27 @ SY384 ) )
| ( member @ SY385 @ SY384 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(234,plain,
! [SV13: $i,SV28: $i] :
( ( ~ ! [SY386: $i,SY387: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK28_X @ SY387 @ SY386 @ SV28 @ SV13 ) @ SY386 )
| ~ ( member @ ( sK29_SY162 @ SY387 @ SY386 @ SV28 @ SV13 ) @ SY387 ) )
| ~ ( member @ ( sK30_SY164 @ SY387 @ SY386 @ SV28 @ SV13 ) @ SY387 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV13 @ ( sK28_X @ SY387 @ SY386 @ SV28 @ SV13 ) @ ( sK29_SY162 @ SY387 @ SY386 @ SV28 @ SV13 ) )
| ~ ( apply @ SV28 @ ( sK28_X @ SY387 @ SY386 @ SV28 @ SV13 ) @ ( sK30_SY164 @ SY387 @ SY386 @ SV28 @ SV13 ) ) )
| ~ ( ( ( sK29_SY162 @ SY387 @ SY386 @ SV28 @ SV13 )
!= ( sK30_SY164 @ SY387 @ SY386 @ SV28 @ SV13 ) ) ) ) )
| ( equal_maps @ SV13 @ SV28 @ SY386 @ SY387 ) )
| ~ ! [SY388: $i,SY389: $i] :
( ~ ( equal_maps @ SV13 @ SV28 @ SY388 @ SY389 )
| ! [SY390: $i,SY391: $i,SY392: $i] :
( ~ ( member @ SY390 @ SY388 )
| ~ ( member @ SY391 @ SY389 )
| ~ ( member @ SY392 @ SY389 )
| ~ ( apply @ SV13 @ SY390 @ SY391 )
| ~ ( apply @ SV28 @ SY390 @ SY392 )
| ( SY391 = SY392 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(235,plain,
! [SV14: $i,SV29: $i,SV35: $i] :
( ( ! [SY448: $i] :
~ ( ~ ! [SY449: $i,SY450: $i] :
( ~ ( ~ ~ ( ~ ( member @ ( sK33_X @ SY450 @ SY449 @ SY448 @ SV35 @ SV29 @ SV14 ) @ SY448 )
| ~ ( member @ ( sK34_SY165 @ SY450 @ SY449 @ SY448 @ SV35 @ SV29 @ SV14 ) @ SY450 ) )
| ~ ~ ( ~ ( ! [SY451: $i] :
( ~ ( apply @ SV35 @ ( sK33_X @ SY450 @ SY449 @ SY448 @ SV35 @ SV29 @ SV14 ) @ SY451 )
| ~ ( member @ SY451 @ SY449 )
| ~ ( apply @ SV29 @ SY451 @ ( sK34_SY165 @ SY450 @ SY449 @ SY448 @ SV35 @ SV29 @ SV14 ) ) )
| ~ ( apply @ SV14 @ ( sK33_X @ SY450 @ SY449 @ SY448 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SY450 @ SY449 @ SY448 @ SV35 @ SV29 @ SV14 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( apply @ SV35 @ ( sK33_X @ SY450 @ SY449 @ SY448 @ SV35 @ SV29 @ SV14 ) @ ( sK35_SY169 @ SY450 @ SY449 @ SY448 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK35_SY169 @ SY450 @ SY449 @ SY448 @ SV35 @ SV29 @ SV14 ) @ SY449 ) )
| ~ ( apply @ SV29 @ ( sK35_SY169 @ SY450 @ SY449 @ SY448 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SY450 @ SY449 @ SY448 @ SV35 @ SV29 @ SV14 ) ) )
| ( apply @ SV14 @ ( sK33_X @ SY450 @ SY449 @ SY448 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SY450 @ SY449 @ SY448 @ SV35 @ SV29 @ SV14 ) ) ) ) )
| ( compose_predicate @ SV14 @ SV29 @ SV35 @ SY448 @ SY449 @ SY450 ) )
| ~ ! [SY452: $i,SY453: $i] :
( ~ ( compose_predicate @ SV14 @ SV29 @ SV35 @ SY448 @ SY452 @ SY453 )
| ~ ( ~ ! [SY454: $i,SY455: $i] :
( ~ ( member @ SY454 @ SY448 )
| ~ ( member @ SY455 @ SY453 )
| ! [SY456: $i] :
( ~ ( apply @ SV35 @ SY454 @ SY456 )
| ~ ( member @ SY456 @ SY452 )
| ~ ( apply @ SV29 @ SY456 @ SY455 ) )
| ( apply @ SV14 @ SY454 @ SY455 ) )
| ~ ! [SY457: $i,SY458: $i] :
( ~ ( member @ SY457 @ SY448 )
| ~ ( member @ SY458 @ SY453 )
| ~ ( apply @ SV14 @ SY457 @ SY458 )
| ~ ( ~ ~ ( ~ ( apply @ SV35 @ SY457 @ ( sK32_Y @ SY458 @ SY457 @ SY453 @ SY452 @ SY448 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK32_Y @ SY458 @ SY457 @ SY453 @ SY452 @ SY448 @ SV35 @ SV29 @ SV14 ) @ SY452 ) )
| ~ ( apply @ SV29 @ ( sK32_Y @ SY458 @ SY457 @ SY453 @ SY452 @ SY448 @ SV35 @ SV29 @ SV14 ) @ SY458 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(236,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( member @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[197]) ).
thf(237,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[198]) ).
thf(238,plain,
! [SV15: $i] :
( ( ~ ! [SY280: $i,SY281: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK24_X1 @ SY281 @ SY280 @ SV15 ) @ SY280 )
| ~ ( member @ ( sK25_SY159 @ SY281 @ SY280 @ SV15 ) @ SY280 ) )
| ~ ( member @ ( sK26_SY161 @ SY281 @ SY280 @ SV15 ) @ SY281 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV15 @ ( sK24_X1 @ SY281 @ SY280 @ SV15 ) @ ( sK26_SY161 @ SY281 @ SY280 @ SV15 ) )
| ~ ( apply @ SV15 @ ( sK25_SY159 @ SY281 @ SY280 @ SV15 ) @ ( sK26_SY161 @ SY281 @ SY280 @ SV15 ) ) )
| ~ ( ( ( sK24_X1 @ SY281 @ SY280 @ SV15 )
!= ( sK25_SY159 @ SY281 @ SY280 @ SV15 ) ) ) ) )
| ( injective @ SV15 @ SY280 @ SY281 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(239,plain,
! [SV15: $i] :
( ( ~ ! [SY282: $i,SY283: $i] :
( ~ ( injective @ SV15 @ SY282 @ SY283 )
| ! [SY284: $i,SY285: $i,SY286: $i] :
( ~ ( member @ SY284 @ SY282 )
| ~ ( member @ SY285 @ SY282 )
| ~ ( member @ SY286 @ SY283 )
| ~ ( apply @ SV15 @ SY284 @ SY286 )
| ~ ( apply @ SV15 @ SY285 @ SY286 )
| ( SY284 = SY285 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(240,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( equal_set @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[200]) ).
thf(241,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(242,plain,
! [SV16: $i,SV30: $i,SV36: $i] :
( ( ~ ( ~ ! [SY459: $i,SY460: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK12_X1 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ SV30 )
| ~ ( member @ ( sK13_SY151 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ SY459 ) )
| ~ ( member @ ( sK14_SY154 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ SV30 ) )
| ~ ( member @ ( sK15_SY156 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ SY459 ) )
| ~ ( apply @ SV36 @ ( sK12_X1 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ ( sK14_SY154 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ( apply @ SV16 @ ( sK12_X1 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ ( sK13_SY151 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ( apply @ SV16 @ ( sK14_SY154 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ ( sK15_SY156 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ~ ( apply @ SY460 @ ( sK13_SY151 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ ( sK15_SY156 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) ) )
| ( increasing @ SV16 @ SV30 @ SV36 @ SY459 @ SY460 ) )
| ~ ! [SY461: $i,SY462: $i] :
( ~ ( increasing @ SV16 @ SV30 @ SV36 @ SY461 @ SY462 )
| ! [SY463: $i,SY464: $i,SY465: $i,SY466: $i] :
( ~ ( member @ SY463 @ SV30 )
| ~ ( member @ SY464 @ SY461 )
| ~ ( member @ SY465 @ SV30 )
| ~ ( member @ SY466 @ SY461 )
| ~ ( apply @ SV36 @ SY463 @ SY465 )
| ~ ( apply @ SV16 @ SY463 @ SY464 )
| ~ ( apply @ SV16 @ SY465 @ SY466 )
| ( apply @ SY462 @ SY464 @ SY466 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(243,plain,
! [SV17: $i] :
( ( ~ ! [SY297: $i,SY298: $i] :
( ~ ( member @ SV17 @ SY297 )
| ~ ( member @ SV17 @ SY298 )
| ( member @ SV17 @ ( intersection @ SY297 @ SY298 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[203]) ).
thf(244,plain,
! [SV17: $i] :
( ( ~ ~ ( ~ ! [SY299: $i] :
( ! [SY300: $i] :
~ ( member @ SV17 @ ( intersection @ SY299 @ SY300 ) )
| ( member @ SV17 @ SY299 ) )
| ~ ! [SY301: $i,SY302: $i] :
( ~ ( member @ SV17 @ ( intersection @ SY301 @ SY302 ) )
| ( member @ SV17 @ SY302 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[203]) ).
thf(245,plain,
! [SV18: $i] :
( ( ~ ! [SY303: $i,SY304: $i] :
( ~ ( member @ SV18 @ ( unordered_pair @ SY303 @ SY304 ) )
| ( SV18 = SY303 )
| ( SV18 = SY304 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[204]) ).
thf(246,plain,
! [SV18: $i] :
( ( ~ ~ ( ~ ! [SY305: $i] :
( ( SV18 != SY305 )
| ! [SY306: $i] : ( member @ SV18 @ ( unordered_pair @ SY305 @ SY306 ) ) )
| ~ ! [SY307: $i,SY308: $i] :
( ( SV18 != SY308 )
| ( member @ SV18 @ ( unordered_pair @ SY307 @ SY308 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[204]) ).
thf(247,plain,
! [SV19: $i] :
( ( ~ ! [SY309: $i,SY310: $i] :
( ~ ( injective @ SV19 @ SY309 @ SY310 )
| ~ ( surjective @ SV19 @ SY309 @ SY310 )
| ( one_to_one @ SV19 @ SY309 @ SY310 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[205]) ).
thf(248,plain,
! [SV19: $i] :
( ( ~ ~ ( ~ ! [SY311: $i,SY312: $i] :
( ~ ( one_to_one @ SV19 @ SY311 @ SY312 )
| ( injective @ SV19 @ SY311 @ SY312 ) )
| ~ ! [SY313: $i,SY314: $i] :
( ~ ( one_to_one @ SV19 @ SY313 @ SY314 )
| ( surjective @ SV19 @ SY313 @ SY314 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[205]) ).
thf(249,plain,
! [SV20: $i,SV31: $i,SV37: $i] :
( ( ! [SY467: $i,SY468: $i] :
~ ( ~ ! [SY469: $i,SY470: $i] :
( ~ ( member @ SY469 @ SV37 )
| ~ ( member @ SY470 @ SY468 )
| ! [SY419: $i] :
( ~ ( apply @ SV31 @ SY469 @ SY419 )
| ~ ( member @ SY419 @ SY467 )
| ~ ( apply @ SV20 @ SY419 @ SY470 ) )
| ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SY467 @ SY468 ) @ SY469 @ SY470 ) )
| ~ ! [SY472: $i,SY473: $i] :
( ~ ( member @ SY472 @ SV37 )
| ~ ( member @ SY473 @ SY468 )
| ~ ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SY467 @ SY468 ) @ SY472 @ SY473 )
| ~ ( ~ ~ ( ~ ( apply @ SV31 @ SY472 @ ( sK31_Y @ SY473 @ SY472 @ SY468 @ SY467 @ SV37 @ SV31 @ SV20 ) )
| ~ ( member @ ( sK31_Y @ SY473 @ SY472 @ SY468 @ SY467 @ SV37 @ SV31 @ SV20 ) @ SY467 ) )
| ~ ( apply @ SV20 @ ( sK31_Y @ SY473 @ SY472 @ SY468 @ SY467 @ SV37 @ SV31 @ SV20 ) @ SY473 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(250,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( sum @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(251,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( sum @ SX1 ) )
| ~ ( ~ ( member @ ( sK42_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ SX0 @ ( sK42_Y @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(252,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK41_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( member @ SX0 @ ( sK41_Y @ SX1 @ SX0 ) ) )
| ( member @ SX0 @ ( product @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(253,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( product @ SX1 ) )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX0 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(254,plain,
! [SV21: $i] :
( ( ~ ! [SY324: $i,SY325: $i] :
( ~ ( ~ ( member @ ( sK40_X @ SY325 @ SY324 @ SV21 ) @ SY324 )
| ~ ! [SY326: $i] :
( ~ ( apply @ SV21 @ ( sK40_X @ SY325 @ SY324 @ SV21 ) @ SY326 )
| ~ ( member @ SY326 @ SY325 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_X @ SY325 @ SY324 @ SV21 ) @ SY324 )
| ~ ( member @ ( sK38_SY170 @ SY325 @ SY324 @ SV21 ) @ SY325 ) )
| ~ ( member @ ( sK39_SY172 @ SY325 @ SY324 @ SV21 ) @ SY325 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV21 @ ( sK37_X @ SY325 @ SY324 @ SV21 ) @ ( sK38_SY170 @ SY325 @ SY324 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK37_X @ SY325 @ SY324 @ SV21 ) @ ( sK39_SY172 @ SY325 @ SY324 @ SV21 ) ) )
| ~ ( ( ( sK38_SY170 @ SY325 @ SY324 @ SV21 )
!= ( sK39_SY172 @ SY325 @ SY324 @ SV21 ) ) ) ) )
| ( maps @ SV21 @ SY324 @ SY325 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[211]) ).
thf(255,plain,
! [SV21: $i] :
( ( ~ ~ ( ~ ! [SY327: $i,SY328: $i] :
( ~ ( maps @ SV21 @ SY327 @ SY328 )
| ! [SY329: $i] :
( ~ ( member @ SY329 @ SY327 )
| ~ ( ~ ( apply @ SV21 @ SY329 @ ( sK36_Y @ SY329 @ SY328 @ SY327 @ SV21 ) )
| ~ ( member @ ( sK36_Y @ SY329 @ SY328 @ SY327 @ SV21 ) @ SY328 ) ) ) )
| ~ ! [SY330: $i,SY331: $i] :
( ~ ( maps @ SV21 @ SY330 @ SY331 )
| ! [SY332: $i,SY333: $i,SY334: $i] :
( ~ ( member @ SY332 @ SY330 )
| ~ ( member @ SY333 @ SY331 )
| ~ ( member @ SY334 @ SY331 )
| ~ ( apply @ SV21 @ SY332 @ SY333 )
| ~ ( apply @ SV21 @ SY332 @ SY334 )
| ( SY333 = SY334 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[211]) ).
thf(256,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK27_X @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( apply @ SX0 @ ( sK27_X @ SX1 @ SX0 ) @ ( sK27_X @ SX1 @ SX0 ) ) )
| ( identity @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(257,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( identity @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( apply @ SX0 @ SX2 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[213]) ).
thf(258,plain,
! [SV22: $i,SV2: $i] :
( ( ~ ! [SY335: $i,SY336: $i] :
( ! [SY337: $i] :
( ~ ( apply @ SV2 @ SY337 @ SY336 )
| ~ ( member @ SY337 @ SV22 ) )
| ~ ( member @ SY336 @ SY335 )
| ( member @ SY336 @ ( image3 @ SV2 @ SV22 @ SY335 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(259,plain,
! [SV22: $i,SV2: $i] :
( ( ~ ~ ( ~ ! [SY338: $i,SY339: $i] :
( ~ ( member @ SY339 @ ( image3 @ SV2 @ SV22 @ SY338 ) )
| ~ ( ~ ( apply @ SV2 @ ( sK18_X @ SY339 @ SY338 @ SV22 @ SV2 ) @ SY339 )
| ~ ( member @ ( sK18_X @ SY339 @ SY338 @ SV22 @ SV2 ) @ SV22 ) ) )
| ~ ! [SY340: $i,SY341: $i] :
( ~ ( member @ SY341 @ ( image3 @ SV2 @ SV22 @ SY340 ) )
| ( member @ SY341 @ SY340 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(260,plain,
! [SV38: $i] :
( ( ! [SY474: $i] :
( ~ ( member @ SV38 @ ( power_set @ SY474 ) )
| ( subset @ SV38 @ SY474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(261,plain,
! [SV39: $i] :
( ( ! [SY475: $i] :
( ~ ( subset @ SV39 @ SY475 )
| ( member @ SV39 @ ( power_set @ SY475 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(262,plain,
! [SV3: $i,SV23: $i,SV32: $i] :
( ( ~ ! [SY422: $i,SY423: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_X1 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ SV23 )
| ~ ( member @ ( sK9_SY145 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ SY422 ) )
| ~ ( member @ ( sK10_SY148 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ SV23 ) )
| ~ ( member @ ( sK11_SY150 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ SY422 ) )
| ~ ( apply @ SV32 @ ( sK8_X1 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ ( sK10_SY148 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ( apply @ SV3 @ ( sK8_X1 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ ( sK9_SY145 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ( apply @ SV3 @ ( sK10_SY148 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ ( sK11_SY150 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ~ ( apply @ SY423 @ ( sK11_SY150 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ ( sK9_SY145 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) ) )
| ( decreasing @ SV3 @ SV23 @ SV32 @ SY422 @ SY423 ) )
| ~ ! [SY424: $i,SY425: $i] :
( ~ ( decreasing @ SV3 @ SV23 @ SV32 @ SY424 @ SY425 )
| ! [SY426: $i,SY427: $i,SY428: $i,SY429: $i] :
( ~ ( member @ SY426 @ SV23 )
| ~ ( member @ SY427 @ SY424 )
| ~ ( member @ SY428 @ SV23 )
| ~ ( member @ SY429 @ SY424 )
| ~ ( apply @ SV32 @ SY426 @ SY428 )
| ~ ( apply @ SV3 @ SY426 @ SY427 )
| ~ ( apply @ SV3 @ SY428 @ SY429 )
| ( apply @ SY425 @ SY429 @ SY427 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(263,plain,
! [SV40: $i] :
( ( ! [SY476: $i] :
( ~ ( ~ ( member @ ( sK43_X @ SY476 @ SV40 ) @ SV40 )
| ~ ~ ( member @ ( sK43_X @ SY476 @ SV40 ) @ SY476 ) )
| ( subset @ SV40 @ SY476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(264,plain,
! [SV41: $i] :
( ( ! [SY477: $i] :
( ~ ( subset @ SV41 @ SY477 )
| ! [SY478: $i] :
( ~ ( member @ SY478 @ SV41 )
| ( member @ SY478 @ SY477 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(265,plain,
! [SV4: $i] :
( ( ! [SY192: $i,SY193: $i] :
( ! [SY194: $i] :
( ~ ( apply @ SV4 @ SY194 @ SY193 )
| ~ ( member @ SY194 @ SY192 ) )
| ( member @ SY193 @ ( image2 @ SV4 @ SY192 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(266,plain,
! [SV4: $i] :
( ( ! [SY195: $i,SY196: $i] :
( ~ ( member @ SY196 @ ( image2 @ SV4 @ SY195 ) )
| ~ ( ~ ( apply @ SV4 @ ( sK19_X @ SY196 @ SY195 @ SV4 ) @ SY196 )
| ~ ( member @ ( sK19_X @ SY196 @ SY195 @ SV4 ) @ SY195 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[221]) ).
thf(267,plain,
! [SV5: $i] :
( ( ! [SY197: $i,SY198: $i] :
( ~ ( member @ SV5 @ SY198 )
| ( member @ SV5 @ SY197 )
| ( member @ SV5 @ ( difference @ SY198 @ SY197 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(268,plain,
! [SV5: $i] :
( ( ~ ( ~ ! [SY199: $i,SY200: $i] :
( ~ ( member @ SV5 @ ( difference @ SY200 @ SY199 ) )
| ( member @ SV5 @ SY200 ) )
| ~ ! [SY201: $i] :
( ! [SY202: $i] :
~ ( member @ SV5 @ ( difference @ SY202 @ SY201 ) )
| ~ ( member @ SV5 @ SY201 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(269,plain,
! [SV6: $i] :
( ( ! [SY203: $i,SY204: $i] :
( ~ ( member @ SV6 @ ( union @ SY203 @ SY204 ) )
| ( member @ SV6 @ SY203 )
| ( member @ SV6 @ SY204 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[224]) ).
thf(270,plain,
! [SV6: $i] :
( ( ~ ( ~ ! [SY205: $i] :
( ~ ( member @ SV6 @ SY205 )
| ! [SY206: $i] : ( member @ SV6 @ ( union @ SY205 @ SY206 ) ) )
| ~ ! [SY207: $i,SY208: $i] :
( ~ ( member @ SV6 @ SY208 )
| ( member @ SV6 @ ( union @ SY207 @ SY208 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(271,plain,
! [SV7: $i,SV24: $i,SV33: $i] :
( ( ~ ! [SY430: $i,SY431: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK4_X1 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ SV24 )
| ~ ( member @ ( sK5_SY139 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ SY430 ) )
| ~ ( member @ ( sK6_SY142 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ SV24 ) )
| ~ ( member @ ( sK7_SY144 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ SY430 ) )
| ~ ( apply @ SV7 @ ( sK4_X1 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ ( sK5_SY139 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ( apply @ SV7 @ ( sK6_SY142 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ~ ( ~ ( ~ ( apply @ SV33 @ ( sK4_X1 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) )
| ~ ( apply @ SY431 @ ( sK5_SY139 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ( ( apply @ SV33 @ ( sK4_X1 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) )
| ( apply @ SY431 @ ( sK5_SY139 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) ) ) ) )
| ~ ( maps @ SV7 @ SV24 @ SY430 )
| ~ ( one_to_one @ SV7 @ SV24 @ SY430 )
| ( isomorphism @ SV7 @ SV24 @ SV33 @ SY430 @ SY431 ) )
| ~ ~ ( ~ ! [SY432: $i,SY433: $i] :
( ~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SY432 @ SY433 )
| ! [SY434: $i,SY435: $i] :
~ ( ~ ! [SY436: $i,SY437: $i] :
( ~ ( member @ SY434 @ SV24 )
| ~ ( member @ SY435 @ SY432 )
| ~ ( member @ SY436 @ SV24 )
| ~ ( member @ SY437 @ SY432 )
| ~ ( apply @ SV7 @ SY434 @ SY435 )
| ~ ( apply @ SV7 @ SY436 @ SY437 )
| ~ ( apply @ SV33 @ SY434 @ SY436 )
| ( apply @ SY433 @ SY435 @ SY437 ) )
| ~ ! [SY438: $i,SY439: $i] :
( ~ ( member @ SY434 @ SV24 )
| ~ ( member @ SY435 @ SY432 )
| ~ ( member @ SY438 @ SV24 )
| ~ ( member @ SY439 @ SY432 )
| ~ ( apply @ SV7 @ SY434 @ SY435 )
| ~ ( apply @ SV7 @ SY438 @ SY439 )
| ~ ( apply @ SY433 @ SY435 @ SY439 )
| ( apply @ SV33 @ SY434 @ SY438 ) ) ) )
| ~ ~ ( ~ ! [SY440: $i] :
( ! [SY441: $i] :
~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SY440 @ SY441 )
| ( maps @ SV7 @ SV24 @ SY440 ) )
| ~ ! [SY442: $i] :
( ! [SY443: $i] :
~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SY442 @ SY443 )
| ( one_to_one @ SV7 @ SV24 @ SY442 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(272,plain,
! [SV8: $i,SV25: $i] :
( ( ~ ! [SY366: $i,SY367: $i] :
( ~ ( ~ ~ ( ~ ( member @ ( sK20_X @ SY367 @ SY366 @ SV25 @ SV8 ) @ SY366 )
| ~ ( member @ ( sK21_SY157 @ SY367 @ SY366 @ SV25 @ SV8 ) @ SY367 ) )
| ~ ~ ( ~ ( ~ ( apply @ SV25 @ ( sK20_X @ SY367 @ SY366 @ SV25 @ SV8 ) @ ( sK21_SY157 @ SY367 @ SY366 @ SV25 @ SV8 ) )
| ~ ( apply @ SV8 @ ( sK21_SY157 @ SY367 @ SY366 @ SV25 @ SV8 ) @ ( sK20_X @ SY367 @ SY366 @ SV25 @ SV8 ) ) )
| ~ ( ( apply @ SV25 @ ( sK20_X @ SY367 @ SY366 @ SV25 @ SV8 ) @ ( sK21_SY157 @ SY367 @ SY366 @ SV25 @ SV8 ) )
| ( apply @ SV8 @ ( sK21_SY157 @ SY367 @ SY366 @ SV25 @ SV8 ) @ ( sK20_X @ SY367 @ SY366 @ SV25 @ SV8 ) ) ) ) )
| ( inverse_predicate @ SV8 @ SV25 @ SY366 @ SY367 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(273,plain,
! [SV25: $i,SV8: $i] :
( ( ~ ! [SY368: $i,SY369: $i] :
( ~ ( inverse_predicate @ SV8 @ SV25 @ SY368 @ SY369 )
| ~ ( ~ ! [SY370: $i,SY371: $i] :
( ~ ( member @ SY370 @ SY368 )
| ~ ( member @ SY371 @ SY369 )
| ~ ( apply @ SV25 @ SY370 @ SY371 )
| ( apply @ SV8 @ SY371 @ SY370 ) )
| ~ ! [SY372: $i,SY373: $i] :
( ~ ( member @ SY372 @ SY368 )
| ~ ( member @ SY373 @ SY369 )
| ~ ( apply @ SV8 @ SY373 @ SY372 )
| ( apply @ SV25 @ SY372 @ SY373 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(274,plain,
! [SV9: $i,SV34: $i,SV26: $i] :
( ( ~ ! [SY444: $i,SY445: $i] :
( ~ ( member @ SY444 @ SV26 )
| ~ ( member @ SY445 @ SV34 )
| ~ ( apply @ SV9 @ SY444 @ SY445 )
| ( apply @ ( inverse_function @ SV9 @ SV26 @ SV34 ) @ SY445 @ SY444 ) )
| ~ ! [SY446: $i,SY447: $i] :
( ~ ( member @ SY446 @ SV26 )
| ~ ( member @ SY447 @ SV34 )
| ~ ( apply @ ( inverse_function @ SV9 @ SV26 @ SV34 ) @ SY447 @ SY446 )
| ( apply @ SV9 @ SY446 @ SY447 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(275,plain,
! [SV10: $i] :
( ( ! [SY240: $i,SY241: $i] :
( ! [SY242: $i] :
( ~ ( apply @ SV10 @ SY241 @ SY242 )
| ~ ( member @ SY242 @ SY240 ) )
| ( member @ SY241 @ ( inverse_image2 @ SV10 @ SY240 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(276,plain,
! [SV10: $i] :
( ( ! [SY243: $i,SY244: $i] :
( ~ ( member @ SY244 @ ( inverse_image2 @ SV10 @ SY243 ) )
| ~ ( ~ ( apply @ SV10 @ SY244 @ ( sK17_Y @ SY244 @ SY243 @ SV10 ) )
| ~ ( member @ ( sK17_Y @ SY244 @ SY243 @ SV10 ) @ SY243 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(277,plain,
! [SV11: $i] :
( ( ! [SY245: $i,SY246: $i] :
( ~ ( ~ ( member @ ( sK23_Y @ SY246 @ SY245 @ SV11 ) @ SY246 )
| ~ ! [SY247: $i] :
( ~ ( apply @ SV11 @ SY247 @ ( sK23_Y @ SY246 @ SY245 @ SV11 ) )
| ~ ( member @ SY247 @ SY245 ) ) )
| ( surjective @ SV11 @ SY245 @ SY246 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(278,plain,
! [SV11: $i] :
( ( ! [SY248: $i,SY249: $i] :
( ~ ( surjective @ SV11 @ SY248 @ SY249 )
| ! [SY250: $i] :
( ~ ( member @ SY250 @ SY249 )
| ~ ( ~ ( apply @ SV11 @ ( sK22_E @ SY250 @ SY249 @ SY248 @ SV11 ) @ SY250 )
| ~ ( member @ ( sK22_E @ SY250 @ SY249 @ SY248 @ SV11 ) @ SY248 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[232]) ).
thf(279,plain,
! [SV27: $i,SV12: $i] :
( ( ~ ! [SY379: $i,SY380: $i] :
( ! [SY381: $i] :
( ~ ( apply @ SV12 @ SY380 @ SY381 )
| ~ ( member @ SY381 @ SV27 ) )
| ~ ( member @ SY380 @ SY379 )
| ( member @ SY380 @ ( inverse_image3 @ SV12 @ SV27 @ SY379 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[233]) ).
thf(280,plain,
! [SV27: $i,SV12: $i] :
( ( ~ ~ ( ~ ! [SY382: $i,SY383: $i] :
( ~ ( member @ SY383 @ ( inverse_image3 @ SV12 @ SV27 @ SY382 ) )
| ~ ( ~ ( apply @ SV12 @ SY383 @ ( sK16_Y @ SY383 @ SY382 @ SV27 @ SV12 ) )
| ~ ( member @ ( sK16_Y @ SY383 @ SY382 @ SV27 @ SV12 ) @ SV27 ) ) )
| ~ ! [SY384: $i,SY385: $i] :
( ~ ( member @ SY385 @ ( inverse_image3 @ SV12 @ SV27 @ SY384 ) )
| ( member @ SY385 @ SY384 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[233]) ).
thf(281,plain,
! [SV13: $i,SV28: $i] :
( ( ~ ! [SY386: $i,SY387: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK28_X @ SY387 @ SY386 @ SV28 @ SV13 ) @ SY386 )
| ~ ( member @ ( sK29_SY162 @ SY387 @ SY386 @ SV28 @ SV13 ) @ SY387 ) )
| ~ ( member @ ( sK30_SY164 @ SY387 @ SY386 @ SV28 @ SV13 ) @ SY387 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV13 @ ( sK28_X @ SY387 @ SY386 @ SV28 @ SV13 ) @ ( sK29_SY162 @ SY387 @ SY386 @ SV28 @ SV13 ) )
| ~ ( apply @ SV28 @ ( sK28_X @ SY387 @ SY386 @ SV28 @ SV13 ) @ ( sK30_SY164 @ SY387 @ SY386 @ SV28 @ SV13 ) ) )
| ~ ( ( ( sK29_SY162 @ SY387 @ SY386 @ SV28 @ SV13 )
!= ( sK30_SY164 @ SY387 @ SY386 @ SV28 @ SV13 ) ) ) ) )
| ( equal_maps @ SV13 @ SV28 @ SY386 @ SY387 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[234]) ).
thf(282,plain,
! [SV28: $i,SV13: $i] :
( ( ~ ! [SY388: $i,SY389: $i] :
( ~ ( equal_maps @ SV13 @ SV28 @ SY388 @ SY389 )
| ! [SY390: $i,SY391: $i,SY392: $i] :
( ~ ( member @ SY390 @ SY388 )
| ~ ( member @ SY391 @ SY389 )
| ~ ( member @ SY392 @ SY389 )
| ~ ( apply @ SV13 @ SY390 @ SY391 )
| ~ ( apply @ SV28 @ SY390 @ SY392 )
| ( SY391 = SY392 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[234]) ).
thf(283,plain,
! [SV14: $i,SV29: $i,SV35: $i,SV42: $i] :
( ( ~ ( ~ ! [SY479: $i,SY480: $i] :
( ~ ( ~ ~ ( ~ ( member @ ( sK33_X @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV42 )
| ~ ( member @ ( sK34_SY165 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY480 ) )
| ~ ~ ( ~ ( ! [SY481: $i] :
( ~ ( apply @ SV35 @ ( sK33_X @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY481 )
| ~ ( member @ SY481 @ SY479 )
| ~ ( apply @ SV29 @ SY481 @ ( sK34_SY165 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ~ ( apply @ SV14 @ ( sK33_X @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( apply @ SV35 @ ( sK33_X @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK35_SY169 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK35_SY169 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY479 ) )
| ~ ( apply @ SV29 @ ( sK35_SY169 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ( apply @ SV14 @ ( sK33_X @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) ) ) ) )
| ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SY479 @ SY480 ) )
| ~ ! [SY482: $i,SY483: $i] :
( ~ ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SY482 @ SY483 )
| ~ ( ~ ! [SY484: $i,SY485: $i] :
( ~ ( member @ SY484 @ SV42 )
| ~ ( member @ SY485 @ SY483 )
| ! [SY456: $i] :
( ~ ( apply @ SV35 @ SY484 @ SY456 )
| ~ ( member @ SY456 @ SY482 )
| ~ ( apply @ SV29 @ SY456 @ SY485 ) )
| ( apply @ SV14 @ SY484 @ SY485 ) )
| ~ ! [SY487: $i,SY488: $i] :
( ~ ( member @ SY487 @ SV42 )
| ~ ( member @ SY488 @ SY483 )
| ~ ( apply @ SV14 @ SY487 @ SY488 )
| ~ ( ~ ~ ( ~ ( apply @ SV35 @ SY487 @ ( sK32_Y @ SY488 @ SY487 @ SY483 @ SY482 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK32_Y @ SY488 @ SY487 @ SY483 @ SY482 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY482 ) )
| ~ ( apply @ SV29 @ ( sK32_Y @ SY488 @ SY487 @ SY483 @ SY482 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY488 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(284,plain,
! [SV43: $i] :
( ( ! [SY489: $i] :
( ( SV43 != SY489 )
| ( member @ SV43 @ ( singleton @ SY489 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(285,plain,
! [SV44: $i] :
( ( ! [SY490: $i] :
( ~ ( member @ SV44 @ ( singleton @ SY490 ) )
| ( SV44 = SY490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(286,plain,
! [SV15: $i] :
( ( ! [SY280: $i,SY281: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK24_X1 @ SY281 @ SY280 @ SV15 ) @ SY280 )
| ~ ( member @ ( sK25_SY159 @ SY281 @ SY280 @ SV15 ) @ SY280 ) )
| ~ ( member @ ( sK26_SY161 @ SY281 @ SY280 @ SV15 ) @ SY281 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV15 @ ( sK24_X1 @ SY281 @ SY280 @ SV15 ) @ ( sK26_SY161 @ SY281 @ SY280 @ SV15 ) )
| ~ ( apply @ SV15 @ ( sK25_SY159 @ SY281 @ SY280 @ SV15 ) @ ( sK26_SY161 @ SY281 @ SY280 @ SV15 ) ) )
| ~ ( ( ( sK24_X1 @ SY281 @ SY280 @ SV15 )
!= ( sK25_SY159 @ SY281 @ SY280 @ SV15 ) ) ) ) )
| ( injective @ SV15 @ SY280 @ SY281 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[238]) ).
thf(287,plain,
! [SV15: $i] :
( ( ! [SY282: $i,SY283: $i] :
( ~ ( injective @ SV15 @ SY282 @ SY283 )
| ! [SY284: $i,SY285: $i,SY286: $i] :
( ~ ( member @ SY284 @ SY282 )
| ~ ( member @ SY285 @ SY282 )
| ~ ( member @ SY286 @ SY283 )
| ~ ( apply @ SV15 @ SY284 @ SY286 )
| ~ ( apply @ SV15 @ SY285 @ SY286 )
| ( SY284 = SY285 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[239]) ).
thf(288,plain,
! [SV45: $i] :
( ( ! [SY491: $i] :
( ~ ( subset @ SV45 @ SY491 )
| ~ ( subset @ SY491 @ SV45 )
| ( equal_set @ SV45 @ SY491 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(289,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(290,plain,
! [SV16: $i,SV30: $i,SV36: $i] :
( ( ~ ! [SY459: $i,SY460: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK12_X1 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ SV30 )
| ~ ( member @ ( sK13_SY151 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ SY459 ) )
| ~ ( member @ ( sK14_SY154 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ SV30 ) )
| ~ ( member @ ( sK15_SY156 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ SY459 ) )
| ~ ( apply @ SV36 @ ( sK12_X1 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ ( sK14_SY154 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ( apply @ SV16 @ ( sK12_X1 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ ( sK13_SY151 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ( apply @ SV16 @ ( sK14_SY154 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ ( sK15_SY156 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ~ ( apply @ SY460 @ ( sK13_SY151 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ ( sK15_SY156 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) ) )
| ( increasing @ SV16 @ SV30 @ SV36 @ SY459 @ SY460 ) )
| ~ ! [SY461: $i,SY462: $i] :
( ~ ( increasing @ SV16 @ SV30 @ SV36 @ SY461 @ SY462 )
| ! [SY463: $i,SY464: $i,SY465: $i,SY466: $i] :
( ~ ( member @ SY463 @ SV30 )
| ~ ( member @ SY464 @ SY461 )
| ~ ( member @ SY465 @ SV30 )
| ~ ( member @ SY466 @ SY461 )
| ~ ( apply @ SV36 @ SY463 @ SY465 )
| ~ ( apply @ SV16 @ SY463 @ SY464 )
| ~ ( apply @ SV16 @ SY465 @ SY466 )
| ( apply @ SY462 @ SY464 @ SY466 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(291,plain,
! [SV17: $i] :
( ( ! [SY297: $i,SY298: $i] :
( ~ ( member @ SV17 @ SY297 )
| ~ ( member @ SV17 @ SY298 )
| ( member @ SV17 @ ( intersection @ SY297 @ SY298 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(292,plain,
! [SV17: $i] :
( ( ~ ( ~ ! [SY299: $i] :
( ! [SY300: $i] :
~ ( member @ SV17 @ ( intersection @ SY299 @ SY300 ) )
| ( member @ SV17 @ SY299 ) )
| ~ ! [SY301: $i,SY302: $i] :
( ~ ( member @ SV17 @ ( intersection @ SY301 @ SY302 ) )
| ( member @ SV17 @ SY302 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(293,plain,
! [SV18: $i] :
( ( ! [SY303: $i,SY304: $i] :
( ~ ( member @ SV18 @ ( unordered_pair @ SY303 @ SY304 ) )
| ( SV18 = SY303 )
| ( SV18 = SY304 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(294,plain,
! [SV18: $i] :
( ( ~ ( ~ ! [SY305: $i] :
( ( SV18 != SY305 )
| ! [SY306: $i] : ( member @ SV18 @ ( unordered_pair @ SY305 @ SY306 ) ) )
| ~ ! [SY307: $i,SY308: $i] :
( ( SV18 != SY308 )
| ( member @ SV18 @ ( unordered_pair @ SY307 @ SY308 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(295,plain,
! [SV19: $i] :
( ( ! [SY309: $i,SY310: $i] :
( ~ ( injective @ SV19 @ SY309 @ SY310 )
| ~ ( surjective @ SV19 @ SY309 @ SY310 )
| ( one_to_one @ SV19 @ SY309 @ SY310 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(296,plain,
! [SV19: $i] :
( ( ~ ( ~ ! [SY311: $i,SY312: $i] :
( ~ ( one_to_one @ SV19 @ SY311 @ SY312 )
| ( injective @ SV19 @ SY311 @ SY312 ) )
| ~ ! [SY313: $i,SY314: $i] :
( ~ ( one_to_one @ SV19 @ SY313 @ SY314 )
| ( surjective @ SV19 @ SY313 @ SY314 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(297,plain,
! [SV20: $i,SV46: $i,SV31: $i,SV37: $i] :
( ( ! [SY492: $i] :
~ ( ~ ! [SY493: $i,SY494: $i] :
( ~ ( member @ SY493 @ SV37 )
| ~ ( member @ SY494 @ SY492 )
| ! [SY495: $i] :
( ~ ( apply @ SV31 @ SY493 @ SY495 )
| ~ ( member @ SY495 @ SV46 )
| ~ ( apply @ SV20 @ SY495 @ SY494 ) )
| ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SY492 ) @ SY493 @ SY494 ) )
| ~ ! [SY496: $i,SY497: $i] :
( ~ ( member @ SY496 @ SV37 )
| ~ ( member @ SY497 @ SY492 )
| ~ ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SY492 ) @ SY496 @ SY497 )
| ~ ( ~ ~ ( ~ ( apply @ SV31 @ SY496 @ ( sK31_Y @ SY497 @ SY496 @ SY492 @ SV46 @ SV37 @ SV31 @ SV20 ) )
| ~ ( member @ ( sK31_Y @ SY497 @ SY496 @ SY492 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SV46 ) )
| ~ ( apply @ SV20 @ ( sK31_Y @ SY497 @ SY496 @ SY492 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SY497 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(298,plain,
! [SV47: $i] :
( ( ! [SY498: $i] :
( ! [SY499: $i] :
( ~ ( member @ SY499 @ SY498 )
| ~ ( member @ SV47 @ SY499 ) )
| ( member @ SV47 @ ( sum @ SY498 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(299,plain,
! [SV48: $i] :
( ( ! [SY500: $i] :
( ~ ( member @ SV48 @ ( sum @ SY500 ) )
| ~ ( ~ ( member @ ( sK42_Y @ SY500 @ SV48 ) @ SY500 )
| ~ ( member @ SV48 @ ( sK42_Y @ SY500 @ SV48 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(300,plain,
! [SV49: $i] :
( ( ! [SY501: $i] :
( ~ ( ~ ( member @ ( sK41_Y @ SY501 @ SV49 ) @ SY501 )
| ~ ~ ( member @ SV49 @ ( sK41_Y @ SY501 @ SV49 ) ) )
| ( member @ SV49 @ ( product @ SY501 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(301,plain,
! [SV50: $i] :
( ( ! [SY502: $i] :
( ~ ( member @ SV50 @ ( product @ SY502 ) )
| ! [SY503: $i] :
( ~ ( member @ SY503 @ SY502 )
| ( member @ SV50 @ SY503 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(302,plain,
! [SV21: $i] :
( ( ! [SY324: $i,SY325: $i] :
( ~ ( ~ ( member @ ( sK40_X @ SY325 @ SY324 @ SV21 ) @ SY324 )
| ~ ! [SY326: $i] :
( ~ ( apply @ SV21 @ ( sK40_X @ SY325 @ SY324 @ SV21 ) @ SY326 )
| ~ ( member @ SY326 @ SY325 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_X @ SY325 @ SY324 @ SV21 ) @ SY324 )
| ~ ( member @ ( sK38_SY170 @ SY325 @ SY324 @ SV21 ) @ SY325 ) )
| ~ ( member @ ( sK39_SY172 @ SY325 @ SY324 @ SV21 ) @ SY325 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV21 @ ( sK37_X @ SY325 @ SY324 @ SV21 ) @ ( sK38_SY170 @ SY325 @ SY324 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK37_X @ SY325 @ SY324 @ SV21 ) @ ( sK39_SY172 @ SY325 @ SY324 @ SV21 ) ) )
| ~ ( ( ( sK38_SY170 @ SY325 @ SY324 @ SV21 )
!= ( sK39_SY172 @ SY325 @ SY324 @ SV21 ) ) ) ) )
| ( maps @ SV21 @ SY324 @ SY325 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(303,plain,
! [SV21: $i] :
( ( ~ ( ~ ! [SY327: $i,SY328: $i] :
( ~ ( maps @ SV21 @ SY327 @ SY328 )
| ! [SY329: $i] :
( ~ ( member @ SY329 @ SY327 )
| ~ ( ~ ( apply @ SV21 @ SY329 @ ( sK36_Y @ SY329 @ SY328 @ SY327 @ SV21 ) )
| ~ ( member @ ( sK36_Y @ SY329 @ SY328 @ SY327 @ SV21 ) @ SY328 ) ) ) )
| ~ ! [SY330: $i,SY331: $i] :
( ~ ( maps @ SV21 @ SY330 @ SY331 )
| ! [SY332: $i,SY333: $i,SY334: $i] :
( ~ ( member @ SY332 @ SY330 )
| ~ ( member @ SY333 @ SY331 )
| ~ ( member @ SY334 @ SY331 )
| ~ ( apply @ SV21 @ SY332 @ SY333 )
| ~ ( apply @ SV21 @ SY332 @ SY334 )
| ( SY333 = SY334 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(304,plain,
! [SV51: $i] :
( ( ! [SY504: $i] :
( ~ ( ~ ( member @ ( sK27_X @ SY504 @ SV51 ) @ SY504 )
| ~ ~ ( apply @ SV51 @ ( sK27_X @ SY504 @ SV51 ) @ ( sK27_X @ SY504 @ SV51 ) ) )
| ( identity @ SV51 @ SY504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(305,plain,
! [SV52: $i] :
( ( ! [SY505: $i] :
( ~ ( identity @ SV52 @ SY505 )
| ! [SY506: $i] :
( ~ ( member @ SY506 @ SY505 )
| ( apply @ SV52 @ SY506 @ SY506 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(306,plain,
! [SV22: $i,SV2: $i] :
( ( ! [SY335: $i,SY336: $i] :
( ! [SY337: $i] :
( ~ ( apply @ SV2 @ SY337 @ SY336 )
| ~ ( member @ SY337 @ SV22 ) )
| ~ ( member @ SY336 @ SY335 )
| ( member @ SY336 @ ( image3 @ SV2 @ SV22 @ SY335 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[258]) ).
thf(307,plain,
! [SV22: $i,SV2: $i] :
( ( ~ ( ~ ! [SY338: $i,SY339: $i] :
( ~ ( member @ SY339 @ ( image3 @ SV2 @ SV22 @ SY338 ) )
| ~ ( ~ ( apply @ SV2 @ ( sK18_X @ SY339 @ SY338 @ SV22 @ SV2 ) @ SY339 )
| ~ ( member @ ( sK18_X @ SY339 @ SY338 @ SV22 @ SV2 ) @ SV22 ) ) )
| ~ ! [SY340: $i,SY341: $i] :
( ~ ( member @ SY341 @ ( image3 @ SV2 @ SV22 @ SY340 ) )
| ( member @ SY341 @ SY340 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[259]) ).
thf(308,plain,
! [SV53: $i,SV38: $i] :
( ( ~ ( member @ SV38 @ ( power_set @ SV53 ) )
| ( subset @ SV38 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(309,plain,
! [SV54: $i,SV39: $i] :
( ( ~ ( subset @ SV39 @ SV54 )
| ( member @ SV39 @ ( power_set @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(310,plain,
! [SV3: $i,SV23: $i,SV32: $i] :
( ( ~ ! [SY422: $i,SY423: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_X1 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ SV23 )
| ~ ( member @ ( sK9_SY145 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ SY422 ) )
| ~ ( member @ ( sK10_SY148 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ SV23 ) )
| ~ ( member @ ( sK11_SY150 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ SY422 ) )
| ~ ( apply @ SV32 @ ( sK8_X1 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ ( sK10_SY148 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ( apply @ SV3 @ ( sK8_X1 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ ( sK9_SY145 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ( apply @ SV3 @ ( sK10_SY148 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ ( sK11_SY150 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ~ ( apply @ SY423 @ ( sK11_SY150 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ ( sK9_SY145 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) ) )
| ( decreasing @ SV3 @ SV23 @ SV32 @ SY422 @ SY423 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(311,plain,
! [SV32: $i,SV23: $i,SV3: $i] :
( ( ~ ! [SY424: $i,SY425: $i] :
( ~ ( decreasing @ SV3 @ SV23 @ SV32 @ SY424 @ SY425 )
| ! [SY426: $i,SY427: $i,SY428: $i,SY429: $i] :
( ~ ( member @ SY426 @ SV23 )
| ~ ( member @ SY427 @ SY424 )
| ~ ( member @ SY428 @ SV23 )
| ~ ( member @ SY429 @ SY424 )
| ~ ( apply @ SV32 @ SY426 @ SY428 )
| ~ ( apply @ SV3 @ SY426 @ SY427 )
| ~ ( apply @ SV3 @ SY428 @ SY429 )
| ( apply @ SY425 @ SY429 @ SY427 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(312,plain,
! [SV40: $i,SV55: $i] :
( ( ~ ( ~ ( member @ ( sK43_X @ SV55 @ SV40 ) @ SV40 )
| ~ ~ ( member @ ( sK43_X @ SV55 @ SV40 ) @ SV55 ) )
| ( subset @ SV40 @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(313,plain,
! [SV56: $i,SV41: $i] :
( ( ~ ( subset @ SV41 @ SV56 )
| ! [SY507: $i] :
( ~ ( member @ SY507 @ SV41 )
| ( member @ SY507 @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(314,plain,
! [SV57: $i,SV4: $i] :
( ( ! [SY508: $i] :
( ! [SY509: $i] :
( ~ ( apply @ SV4 @ SY509 @ SY508 )
| ~ ( member @ SY509 @ SV57 ) )
| ( member @ SY508 @ ( image2 @ SV4 @ SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(315,plain,
! [SV58: $i,SV4: $i] :
( ( ! [SY510: $i] :
( ~ ( member @ SY510 @ ( image2 @ SV4 @ SV58 ) )
| ~ ( ~ ( apply @ SV4 @ ( sK19_X @ SY510 @ SV58 @ SV4 ) @ SY510 )
| ~ ( member @ ( sK19_X @ SY510 @ SV58 @ SV4 ) @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(316,plain,
! [SV59: $i,SV5: $i] :
( ( ! [SY511: $i] :
( ~ ( member @ SV5 @ SY511 )
| ( member @ SV5 @ SV59 )
| ( member @ SV5 @ ( difference @ SY511 @ SV59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(317,plain,
! [SV5: $i] :
( ( ~ ! [SY199: $i,SY200: $i] :
( ~ ( member @ SV5 @ ( difference @ SY200 @ SY199 ) )
| ( member @ SV5 @ SY200 ) )
| ~ ! [SY201: $i] :
( ! [SY202: $i] :
~ ( member @ SV5 @ ( difference @ SY202 @ SY201 ) )
| ~ ( member @ SV5 @ SY201 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(318,plain,
! [SV60: $i,SV6: $i] :
( ( ! [SY512: $i] :
( ~ ( member @ SV6 @ ( union @ SV60 @ SY512 ) )
| ( member @ SV6 @ SV60 )
| ( member @ SV6 @ SY512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(319,plain,
! [SV6: $i] :
( ( ~ ! [SY205: $i] :
( ~ ( member @ SV6 @ SY205 )
| ! [SY206: $i] : ( member @ SV6 @ ( union @ SY205 @ SY206 ) ) )
| ~ ! [SY207: $i,SY208: $i] :
( ~ ( member @ SV6 @ SY208 )
| ( member @ SV6 @ ( union @ SY207 @ SY208 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(320,plain,
! [SV7: $i,SV24: $i,SV33: $i] :
( ( ~ ! [SY430: $i,SY431: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK4_X1 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ SV24 )
| ~ ( member @ ( sK5_SY139 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ SY430 ) )
| ~ ( member @ ( sK6_SY142 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ SV24 ) )
| ~ ( member @ ( sK7_SY144 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ SY430 ) )
| ~ ( apply @ SV7 @ ( sK4_X1 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ ( sK5_SY139 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ( apply @ SV7 @ ( sK6_SY142 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ~ ( ~ ( ~ ( apply @ SV33 @ ( sK4_X1 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) )
| ~ ( apply @ SY431 @ ( sK5_SY139 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ( ( apply @ SV33 @ ( sK4_X1 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) )
| ( apply @ SY431 @ ( sK5_SY139 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) ) ) ) )
| ~ ( maps @ SV7 @ SV24 @ SY430 )
| ~ ( one_to_one @ SV7 @ SV24 @ SY430 )
| ( isomorphism @ SV7 @ SV24 @ SV33 @ SY430 @ SY431 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[271]) ).
thf(321,plain,
! [SV33: $i,SV24: $i,SV7: $i] :
( ( ~ ~ ( ~ ! [SY432: $i,SY433: $i] :
( ~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SY432 @ SY433 )
| ! [SY434: $i,SY435: $i] :
~ ( ~ ! [SY436: $i,SY437: $i] :
( ~ ( member @ SY434 @ SV24 )
| ~ ( member @ SY435 @ SY432 )
| ~ ( member @ SY436 @ SV24 )
| ~ ( member @ SY437 @ SY432 )
| ~ ( apply @ SV7 @ SY434 @ SY435 )
| ~ ( apply @ SV7 @ SY436 @ SY437 )
| ~ ( apply @ SV33 @ SY434 @ SY436 )
| ( apply @ SY433 @ SY435 @ SY437 ) )
| ~ ! [SY438: $i,SY439: $i] :
( ~ ( member @ SY434 @ SV24 )
| ~ ( member @ SY435 @ SY432 )
| ~ ( member @ SY438 @ SV24 )
| ~ ( member @ SY439 @ SY432 )
| ~ ( apply @ SV7 @ SY434 @ SY435 )
| ~ ( apply @ SV7 @ SY438 @ SY439 )
| ~ ( apply @ SY433 @ SY435 @ SY439 )
| ( apply @ SV33 @ SY434 @ SY438 ) ) ) )
| ~ ~ ( ~ ! [SY440: $i] :
( ! [SY441: $i] :
~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SY440 @ SY441 )
| ( maps @ SV7 @ SV24 @ SY440 ) )
| ~ ! [SY442: $i] :
( ! [SY443: $i] :
~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SY442 @ SY443 )
| ( one_to_one @ SV7 @ SV24 @ SY442 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[271]) ).
thf(322,plain,
! [SV8: $i,SV25: $i] :
( ( ! [SY366: $i,SY367: $i] :
( ~ ( ~ ~ ( ~ ( member @ ( sK20_X @ SY367 @ SY366 @ SV25 @ SV8 ) @ SY366 )
| ~ ( member @ ( sK21_SY157 @ SY367 @ SY366 @ SV25 @ SV8 ) @ SY367 ) )
| ~ ~ ( ~ ( ~ ( apply @ SV25 @ ( sK20_X @ SY367 @ SY366 @ SV25 @ SV8 ) @ ( sK21_SY157 @ SY367 @ SY366 @ SV25 @ SV8 ) )
| ~ ( apply @ SV8 @ ( sK21_SY157 @ SY367 @ SY366 @ SV25 @ SV8 ) @ ( sK20_X @ SY367 @ SY366 @ SV25 @ SV8 ) ) )
| ~ ( ( apply @ SV25 @ ( sK20_X @ SY367 @ SY366 @ SV25 @ SV8 ) @ ( sK21_SY157 @ SY367 @ SY366 @ SV25 @ SV8 ) )
| ( apply @ SV8 @ ( sK21_SY157 @ SY367 @ SY366 @ SV25 @ SV8 ) @ ( sK20_X @ SY367 @ SY366 @ SV25 @ SV8 ) ) ) ) )
| ( inverse_predicate @ SV8 @ SV25 @ SY366 @ SY367 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[272]) ).
thf(323,plain,
! [SV25: $i,SV8: $i] :
( ( ! [SY368: $i,SY369: $i] :
( ~ ( inverse_predicate @ SV8 @ SV25 @ SY368 @ SY369 )
| ~ ( ~ ! [SY370: $i,SY371: $i] :
( ~ ( member @ SY370 @ SY368 )
| ~ ( member @ SY371 @ SY369 )
| ~ ( apply @ SV25 @ SY370 @ SY371 )
| ( apply @ SV8 @ SY371 @ SY370 ) )
| ~ ! [SY372: $i,SY373: $i] :
( ~ ( member @ SY372 @ SY368 )
| ~ ( member @ SY373 @ SY369 )
| ~ ( apply @ SV8 @ SY373 @ SY372 )
| ( apply @ SV25 @ SY372 @ SY373 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[273]) ).
thf(324,plain,
! [SV9: $i,SV34: $i,SV26: $i] :
( ( ~ ! [SY444: $i,SY445: $i] :
( ~ ( member @ SY444 @ SV26 )
| ~ ( member @ SY445 @ SV34 )
| ~ ( apply @ SV9 @ SY444 @ SY445 )
| ( apply @ ( inverse_function @ SV9 @ SV26 @ SV34 ) @ SY445 @ SY444 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[274]) ).
thf(325,plain,
! [SV9: $i,SV34: $i,SV26: $i] :
( ( ~ ! [SY446: $i,SY447: $i] :
( ~ ( member @ SY446 @ SV26 )
| ~ ( member @ SY447 @ SV34 )
| ~ ( apply @ ( inverse_function @ SV9 @ SV26 @ SV34 ) @ SY447 @ SY446 )
| ( apply @ SV9 @ SY446 @ SY447 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[274]) ).
thf(326,plain,
! [SV61: $i,SV10: $i] :
( ( ! [SY513: $i] :
( ! [SY514: $i] :
( ~ ( apply @ SV10 @ SY513 @ SY514 )
| ~ ( member @ SY514 @ SV61 ) )
| ( member @ SY513 @ ( inverse_image2 @ SV10 @ SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(327,plain,
! [SV62: $i,SV10: $i] :
( ( ! [SY515: $i] :
( ~ ( member @ SY515 @ ( inverse_image2 @ SV10 @ SV62 ) )
| ~ ( ~ ( apply @ SV10 @ SY515 @ ( sK17_Y @ SY515 @ SV62 @ SV10 ) )
| ~ ( member @ ( sK17_Y @ SY515 @ SV62 @ SV10 ) @ SV62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(328,plain,
! [SV11: $i,SV63: $i] :
( ( ! [SY516: $i] :
( ~ ( ~ ( member @ ( sK23_Y @ SY516 @ SV63 @ SV11 ) @ SY516 )
| ~ ! [SY517: $i] :
( ~ ( apply @ SV11 @ SY517 @ ( sK23_Y @ SY516 @ SV63 @ SV11 ) )
| ~ ( member @ SY517 @ SV63 ) ) )
| ( surjective @ SV11 @ SV63 @ SY516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(329,plain,
! [SV64: $i,SV11: $i] :
( ( ! [SY518: $i] :
( ~ ( surjective @ SV11 @ SV64 @ SY518 )
| ! [SY519: $i] :
( ~ ( member @ SY519 @ SY518 )
| ~ ( ~ ( apply @ SV11 @ ( sK22_E @ SY519 @ SY518 @ SV64 @ SV11 ) @ SY519 )
| ~ ( member @ ( sK22_E @ SY519 @ SY518 @ SV64 @ SV11 ) @ SV64 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(330,plain,
! [SV27: $i,SV12: $i] :
( ( ! [SY379: $i,SY380: $i] :
( ! [SY381: $i] :
( ~ ( apply @ SV12 @ SY380 @ SY381 )
| ~ ( member @ SY381 @ SV27 ) )
| ~ ( member @ SY380 @ SY379 )
| ( member @ SY380 @ ( inverse_image3 @ SV12 @ SV27 @ SY379 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[279]) ).
thf(331,plain,
! [SV27: $i,SV12: $i] :
( ( ~ ( ~ ! [SY382: $i,SY383: $i] :
( ~ ( member @ SY383 @ ( inverse_image3 @ SV12 @ SV27 @ SY382 ) )
| ~ ( ~ ( apply @ SV12 @ SY383 @ ( sK16_Y @ SY383 @ SY382 @ SV27 @ SV12 ) )
| ~ ( member @ ( sK16_Y @ SY383 @ SY382 @ SV27 @ SV12 ) @ SV27 ) ) )
| ~ ! [SY384: $i,SY385: $i] :
( ~ ( member @ SY385 @ ( inverse_image3 @ SV12 @ SV27 @ SY384 ) )
| ( member @ SY385 @ SY384 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[280]) ).
thf(332,plain,
! [SV13: $i,SV28: $i] :
( ( ! [SY386: $i,SY387: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK28_X @ SY387 @ SY386 @ SV28 @ SV13 ) @ SY386 )
| ~ ( member @ ( sK29_SY162 @ SY387 @ SY386 @ SV28 @ SV13 ) @ SY387 ) )
| ~ ( member @ ( sK30_SY164 @ SY387 @ SY386 @ SV28 @ SV13 ) @ SY387 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV13 @ ( sK28_X @ SY387 @ SY386 @ SV28 @ SV13 ) @ ( sK29_SY162 @ SY387 @ SY386 @ SV28 @ SV13 ) )
| ~ ( apply @ SV28 @ ( sK28_X @ SY387 @ SY386 @ SV28 @ SV13 ) @ ( sK30_SY164 @ SY387 @ SY386 @ SV28 @ SV13 ) ) )
| ~ ( ( ( sK29_SY162 @ SY387 @ SY386 @ SV28 @ SV13 )
!= ( sK30_SY164 @ SY387 @ SY386 @ SV28 @ SV13 ) ) ) ) )
| ( equal_maps @ SV13 @ SV28 @ SY386 @ SY387 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(333,plain,
! [SV28: $i,SV13: $i] :
( ( ! [SY388: $i,SY389: $i] :
( ~ ( equal_maps @ SV13 @ SV28 @ SY388 @ SY389 )
| ! [SY390: $i,SY391: $i,SY392: $i] :
( ~ ( member @ SY390 @ SY388 )
| ~ ( member @ SY391 @ SY389 )
| ~ ( member @ SY392 @ SY389 )
| ~ ( apply @ SV13 @ SY390 @ SY391 )
| ~ ( apply @ SV28 @ SY390 @ SY392 )
| ( SY391 = SY392 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[282]) ).
thf(334,plain,
! [SV14: $i,SV29: $i,SV35: $i,SV42: $i] :
( ( ~ ! [SY479: $i,SY480: $i] :
( ~ ( ~ ~ ( ~ ( member @ ( sK33_X @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV42 )
| ~ ( member @ ( sK34_SY165 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY480 ) )
| ~ ~ ( ~ ( ! [SY481: $i] :
( ~ ( apply @ SV35 @ ( sK33_X @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY481 )
| ~ ( member @ SY481 @ SY479 )
| ~ ( apply @ SV29 @ SY481 @ ( sK34_SY165 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ~ ( apply @ SV14 @ ( sK33_X @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( apply @ SV35 @ ( sK33_X @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK35_SY169 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK35_SY169 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY479 ) )
| ~ ( apply @ SV29 @ ( sK35_SY169 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ( apply @ SV14 @ ( sK33_X @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) ) ) ) )
| ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SY479 @ SY480 ) )
| ~ ! [SY482: $i,SY483: $i] :
( ~ ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SY482 @ SY483 )
| ~ ( ~ ! [SY484: $i,SY485: $i] :
( ~ ( member @ SY484 @ SV42 )
| ~ ( member @ SY485 @ SY483 )
| ! [SY456: $i] :
( ~ ( apply @ SV35 @ SY484 @ SY456 )
| ~ ( member @ SY456 @ SY482 )
| ~ ( apply @ SV29 @ SY456 @ SY485 ) )
| ( apply @ SV14 @ SY484 @ SY485 ) )
| ~ ! [SY487: $i,SY488: $i] :
( ~ ( member @ SY487 @ SV42 )
| ~ ( member @ SY488 @ SY483 )
| ~ ( apply @ SV14 @ SY487 @ SY488 )
| ~ ( ~ ~ ( ~ ( apply @ SV35 @ SY487 @ ( sK32_Y @ SY488 @ SY487 @ SY483 @ SY482 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK32_Y @ SY488 @ SY487 @ SY483 @ SY482 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY482 ) )
| ~ ( apply @ SV29 @ ( sK32_Y @ SY488 @ SY487 @ SY483 @ SY482 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY488 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(335,plain,
! [SV65: $i,SV43: $i] :
( ( ( SV43 != SV65 )
| ( member @ SV43 @ ( singleton @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(336,plain,
! [SV66: $i,SV44: $i] :
( ( ~ ( member @ SV44 @ ( singleton @ SV66 ) )
| ( SV44 = SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(337,plain,
! [SV15: $i,SV67: $i] :
( ( ! [SY520: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK24_X1 @ SY520 @ SV67 @ SV15 ) @ SV67 )
| ~ ( member @ ( sK25_SY159 @ SY520 @ SV67 @ SV15 ) @ SV67 ) )
| ~ ( member @ ( sK26_SY161 @ SY520 @ SV67 @ SV15 ) @ SY520 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV15 @ ( sK24_X1 @ SY520 @ SV67 @ SV15 ) @ ( sK26_SY161 @ SY520 @ SV67 @ SV15 ) )
| ~ ( apply @ SV15 @ ( sK25_SY159 @ SY520 @ SV67 @ SV15 ) @ ( sK26_SY161 @ SY520 @ SV67 @ SV15 ) ) )
| ~ ( ( ( sK24_X1 @ SY520 @ SV67 @ SV15 )
!= ( sK25_SY159 @ SY520 @ SV67 @ SV15 ) ) ) ) )
| ( injective @ SV15 @ SV67 @ SY520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(338,plain,
! [SV68: $i,SV15: $i] :
( ( ! [SY521: $i] :
( ~ ( injective @ SV15 @ SV68 @ SY521 )
| ! [SY522: $i,SY523: $i,SY524: $i] :
( ~ ( member @ SY522 @ SV68 )
| ~ ( member @ SY523 @ SV68 )
| ~ ( member @ SY524 @ SY521 )
| ~ ( apply @ SV15 @ SY522 @ SY524 )
| ~ ( apply @ SV15 @ SY523 @ SY524 )
| ( SY522 = SY523 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(339,plain,
! [SV69: $i,SV45: $i] :
( ( ~ ( subset @ SV45 @ SV69 )
| ~ ( subset @ SV69 @ SV45 )
| ( equal_set @ SV45 @ SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(340,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[289]) ).
thf(341,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[289]) ).
thf(342,plain,
! [SV16: $i,SV30: $i,SV36: $i] :
( ( ~ ! [SY459: $i,SY460: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK12_X1 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ SV30 )
| ~ ( member @ ( sK13_SY151 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ SY459 ) )
| ~ ( member @ ( sK14_SY154 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ SV30 ) )
| ~ ( member @ ( sK15_SY156 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ SY459 ) )
| ~ ( apply @ SV36 @ ( sK12_X1 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ ( sK14_SY154 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ( apply @ SV16 @ ( sK12_X1 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ ( sK13_SY151 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ( apply @ SV16 @ ( sK14_SY154 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ ( sK15_SY156 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ~ ( apply @ SY460 @ ( sK13_SY151 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ ( sK15_SY156 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) ) )
| ( increasing @ SV16 @ SV30 @ SV36 @ SY459 @ SY460 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[290]) ).
thf(343,plain,
! [SV36: $i,SV30: $i,SV16: $i] :
( ( ~ ! [SY461: $i,SY462: $i] :
( ~ ( increasing @ SV16 @ SV30 @ SV36 @ SY461 @ SY462 )
| ! [SY463: $i,SY464: $i,SY465: $i,SY466: $i] :
( ~ ( member @ SY463 @ SV30 )
| ~ ( member @ SY464 @ SY461 )
| ~ ( member @ SY465 @ SV30 )
| ~ ( member @ SY466 @ SY461 )
| ~ ( apply @ SV36 @ SY463 @ SY465 )
| ~ ( apply @ SV16 @ SY463 @ SY464 )
| ~ ( apply @ SV16 @ SY465 @ SY466 )
| ( apply @ SY462 @ SY464 @ SY466 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[290]) ).
thf(344,plain,
! [SV70: $i,SV17: $i] :
( ( ! [SY525: $i] :
( ~ ( member @ SV17 @ SV70 )
| ~ ( member @ SV17 @ SY525 )
| ( member @ SV17 @ ( intersection @ SV70 @ SY525 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(345,plain,
! [SV17: $i] :
( ( ~ ! [SY299: $i] :
( ! [SY300: $i] :
~ ( member @ SV17 @ ( intersection @ SY299 @ SY300 ) )
| ( member @ SV17 @ SY299 ) )
| ~ ! [SY301: $i,SY302: $i] :
( ~ ( member @ SV17 @ ( intersection @ SY301 @ SY302 ) )
| ( member @ SV17 @ SY302 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(346,plain,
! [SV71: $i,SV18: $i] :
( ( ! [SY526: $i] :
( ~ ( member @ SV18 @ ( unordered_pair @ SV71 @ SY526 ) )
| ( SV18 = SV71 )
| ( SV18 = SY526 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(347,plain,
! [SV18: $i] :
( ( ~ ! [SY305: $i] :
( ( SV18 != SY305 )
| ! [SY306: $i] : ( member @ SV18 @ ( unordered_pair @ SY305 @ SY306 ) ) )
| ~ ! [SY307: $i,SY308: $i] :
( ( SV18 != SY308 )
| ( member @ SV18 @ ( unordered_pair @ SY307 @ SY308 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(348,plain,
! [SV72: $i,SV19: $i] :
( ( ! [SY527: $i] :
( ~ ( injective @ SV19 @ SV72 @ SY527 )
| ~ ( surjective @ SV19 @ SV72 @ SY527 )
| ( one_to_one @ SV19 @ SV72 @ SY527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(349,plain,
! [SV19: $i] :
( ( ~ ! [SY311: $i,SY312: $i] :
( ~ ( one_to_one @ SV19 @ SY311 @ SY312 )
| ( injective @ SV19 @ SY311 @ SY312 ) )
| ~ ! [SY313: $i,SY314: $i] :
( ~ ( one_to_one @ SV19 @ SY313 @ SY314 )
| ( surjective @ SV19 @ SY313 @ SY314 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(350,plain,
! [SV20: $i,SV46: $i,SV31: $i,SV73: $i,SV37: $i] :
( ( ~ ( ~ ! [SY528: $i,SY529: $i] :
( ~ ( member @ SY528 @ SV37 )
| ~ ( member @ SY529 @ SV73 )
| ! [SY495: $i] :
( ~ ( apply @ SV31 @ SY528 @ SY495 )
| ~ ( member @ SY495 @ SV46 )
| ~ ( apply @ SV20 @ SY495 @ SY529 ) )
| ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SY528 @ SY529 ) )
| ~ ! [SY531: $i,SY532: $i] :
( ~ ( member @ SY531 @ SV37 )
| ~ ( member @ SY532 @ SV73 )
| ~ ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SY531 @ SY532 )
| ~ ( ~ ~ ( ~ ( apply @ SV31 @ SY531 @ ( sK31_Y @ SY532 @ SY531 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) )
| ~ ( member @ ( sK31_Y @ SY532 @ SY531 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SV46 ) )
| ~ ( apply @ SV20 @ ( sK31_Y @ SY532 @ SY531 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SY532 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(351,plain,
! [SV47: $i,SV74: $i] :
( ( ! [SY533: $i] :
( ~ ( member @ SY533 @ SV74 )
| ~ ( member @ SV47 @ SY533 ) )
| ( member @ SV47 @ ( sum @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(352,plain,
! [SV75: $i,SV48: $i] :
( ( ~ ( member @ SV48 @ ( sum @ SV75 ) )
| ~ ( ~ ( member @ ( sK42_Y @ SV75 @ SV48 ) @ SV75 )
| ~ ( member @ SV48 @ ( sK42_Y @ SV75 @ SV48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(353,plain,
! [SV49: $i,SV76: $i] :
( ( ~ ( ~ ( member @ ( sK41_Y @ SV76 @ SV49 ) @ SV76 )
| ~ ~ ( member @ SV49 @ ( sK41_Y @ SV76 @ SV49 ) ) )
| ( member @ SV49 @ ( product @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(354,plain,
! [SV77: $i,SV50: $i] :
( ( ~ ( member @ SV50 @ ( product @ SV77 ) )
| ! [SY534: $i] :
( ~ ( member @ SY534 @ SV77 )
| ( member @ SV50 @ SY534 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(355,plain,
! [SV21: $i,SV78: $i] :
( ( ! [SY535: $i] :
( ~ ( ~ ( member @ ( sK40_X @ SY535 @ SV78 @ SV21 ) @ SV78 )
| ~ ! [SY536: $i] :
( ~ ( apply @ SV21 @ ( sK40_X @ SY535 @ SV78 @ SV21 ) @ SY536 )
| ~ ( member @ SY536 @ SY535 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_X @ SY535 @ SV78 @ SV21 ) @ SV78 )
| ~ ( member @ ( sK38_SY170 @ SY535 @ SV78 @ SV21 ) @ SY535 ) )
| ~ ( member @ ( sK39_SY172 @ SY535 @ SV78 @ SV21 ) @ SY535 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV21 @ ( sK37_X @ SY535 @ SV78 @ SV21 ) @ ( sK38_SY170 @ SY535 @ SV78 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK37_X @ SY535 @ SV78 @ SV21 ) @ ( sK39_SY172 @ SY535 @ SV78 @ SV21 ) ) )
| ~ ( ( ( sK38_SY170 @ SY535 @ SV78 @ SV21 )
!= ( sK39_SY172 @ SY535 @ SV78 @ SV21 ) ) ) ) )
| ( maps @ SV21 @ SV78 @ SY535 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(356,plain,
! [SV21: $i] :
( ( ~ ! [SY327: $i,SY328: $i] :
( ~ ( maps @ SV21 @ SY327 @ SY328 )
| ! [SY329: $i] :
( ~ ( member @ SY329 @ SY327 )
| ~ ( ~ ( apply @ SV21 @ SY329 @ ( sK36_Y @ SY329 @ SY328 @ SY327 @ SV21 ) )
| ~ ( member @ ( sK36_Y @ SY329 @ SY328 @ SY327 @ SV21 ) @ SY328 ) ) ) )
| ~ ! [SY330: $i,SY331: $i] :
( ~ ( maps @ SV21 @ SY330 @ SY331 )
| ! [SY332: $i,SY333: $i,SY334: $i] :
( ~ ( member @ SY332 @ SY330 )
| ~ ( member @ SY333 @ SY331 )
| ~ ( member @ SY334 @ SY331 )
| ~ ( apply @ SV21 @ SY332 @ SY333 )
| ~ ( apply @ SV21 @ SY332 @ SY334 )
| ( SY333 = SY334 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(357,plain,
! [SV51: $i,SV79: $i] :
( ( ~ ( ~ ( member @ ( sK27_X @ SV79 @ SV51 ) @ SV79 )
| ~ ~ ( apply @ SV51 @ ( sK27_X @ SV79 @ SV51 ) @ ( sK27_X @ SV79 @ SV51 ) ) )
| ( identity @ SV51 @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(358,plain,
! [SV80: $i,SV52: $i] :
( ( ~ ( identity @ SV52 @ SV80 )
| ! [SY537: $i] :
( ~ ( member @ SY537 @ SV80 )
| ( apply @ SV52 @ SY537 @ SY537 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(359,plain,
! [SV81: $i,SV22: $i,SV2: $i] :
( ( ! [SY538: $i] :
( ! [SY337: $i] :
( ~ ( apply @ SV2 @ SY337 @ SY538 )
| ~ ( member @ SY337 @ SV22 ) )
| ~ ( member @ SY538 @ SV81 )
| ( member @ SY538 @ ( image3 @ SV2 @ SV22 @ SV81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(360,plain,
! [SV22: $i,SV2: $i] :
( ( ~ ! [SY338: $i,SY339: $i] :
( ~ ( member @ SY339 @ ( image3 @ SV2 @ SV22 @ SY338 ) )
| ~ ( ~ ( apply @ SV2 @ ( sK18_X @ SY339 @ SY338 @ SV22 @ SV2 ) @ SY339 )
| ~ ( member @ ( sK18_X @ SY339 @ SY338 @ SV22 @ SV2 ) @ SV22 ) ) )
| ~ ! [SY340: $i,SY341: $i] :
( ~ ( member @ SY341 @ ( image3 @ SV2 @ SV22 @ SY340 ) )
| ( member @ SY341 @ SY340 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(361,plain,
! [SV53: $i,SV38: $i] :
( ( ( ~ ( member @ SV38 @ ( power_set @ SV53 ) ) )
= $true )
| ( ( subset @ SV38 @ SV53 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[308]) ).
thf(362,plain,
! [SV54: $i,SV39: $i] :
( ( ( ~ ( subset @ SV39 @ SV54 ) )
= $true )
| ( ( member @ SV39 @ ( power_set @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[309]) ).
thf(363,plain,
! [SV3: $i,SV23: $i,SV32: $i] :
( ( ! [SY422: $i,SY423: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_X1 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ SV23 )
| ~ ( member @ ( sK9_SY145 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ SY422 ) )
| ~ ( member @ ( sK10_SY148 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ SV23 ) )
| ~ ( member @ ( sK11_SY150 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ SY422 ) )
| ~ ( apply @ SV32 @ ( sK8_X1 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ ( sK10_SY148 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ( apply @ SV3 @ ( sK8_X1 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ ( sK9_SY145 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ( apply @ SV3 @ ( sK10_SY148 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ ( sK11_SY150 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ~ ( apply @ SY423 @ ( sK11_SY150 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) @ ( sK9_SY145 @ SY423 @ SY422 @ SV32 @ SV23 @ SV3 ) ) )
| ( decreasing @ SV3 @ SV23 @ SV32 @ SY422 @ SY423 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[310]) ).
thf(364,plain,
! [SV32: $i,SV23: $i,SV3: $i] :
( ( ! [SY424: $i,SY425: $i] :
( ~ ( decreasing @ SV3 @ SV23 @ SV32 @ SY424 @ SY425 )
| ! [SY426: $i,SY427: $i,SY428: $i,SY429: $i] :
( ~ ( member @ SY426 @ SV23 )
| ~ ( member @ SY427 @ SY424 )
| ~ ( member @ SY428 @ SV23 )
| ~ ( member @ SY429 @ SY424 )
| ~ ( apply @ SV32 @ SY426 @ SY428 )
| ~ ( apply @ SV3 @ SY426 @ SY427 )
| ~ ( apply @ SV3 @ SY428 @ SY429 )
| ( apply @ SY425 @ SY429 @ SY427 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[311]) ).
thf(365,plain,
! [SV40: $i,SV55: $i] :
( ( ( ~ ( ~ ( member @ ( sK43_X @ SV55 @ SV40 ) @ SV40 )
| ~ ~ ( member @ ( sK43_X @ SV55 @ SV40 ) @ SV55 ) ) )
= $true )
| ( ( subset @ SV40 @ SV55 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(366,plain,
! [SV56: $i,SV41: $i] :
( ( ( ~ ( subset @ SV41 @ SV56 ) )
= $true )
| ( ( ! [SY507: $i] :
( ~ ( member @ SY507 @ SV41 )
| ( member @ SY507 @ SV56 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(367,plain,
! [SV57: $i,SV82: $i,SV4: $i] :
( ( ! [SY540: $i] :
( ~ ( apply @ SV4 @ SY540 @ SV82 )
| ~ ( member @ SY540 @ SV57 ) )
| ( member @ SV82 @ ( image2 @ SV4 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(368,plain,
! [SV58: $i,SV4: $i,SV83: $i] :
( ( ~ ( member @ SV83 @ ( image2 @ SV4 @ SV58 ) )
| ~ ( ~ ( apply @ SV4 @ ( sK19_X @ SV83 @ SV58 @ SV4 ) @ SV83 )
| ~ ( member @ ( sK19_X @ SV83 @ SV58 @ SV4 ) @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(369,plain,
! [SV59: $i,SV84: $i,SV5: $i] :
( ( ~ ( member @ SV5 @ SV84 )
| ( member @ SV5 @ SV59 )
| ( member @ SV5 @ ( difference @ SV84 @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(370,plain,
! [SV5: $i] :
( ( ~ ! [SY199: $i,SY200: $i] :
( ~ ( member @ SV5 @ ( difference @ SY200 @ SY199 ) )
| ( member @ SV5 @ SY200 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[317]) ).
thf(371,plain,
! [SV5: $i] :
( ( ~ ! [SY201: $i] :
( ! [SY202: $i] :
~ ( member @ SV5 @ ( difference @ SY202 @ SY201 ) )
| ~ ( member @ SV5 @ SY201 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[317]) ).
thf(372,plain,
! [SV85: $i,SV60: $i,SV6: $i] :
( ( ~ ( member @ SV6 @ ( union @ SV60 @ SV85 ) )
| ( member @ SV6 @ SV60 )
| ( member @ SV6 @ SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(373,plain,
! [SV6: $i] :
( ( ~ ! [SY205: $i] :
( ~ ( member @ SV6 @ SY205 )
| ! [SY206: $i] : ( member @ SV6 @ ( union @ SY205 @ SY206 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[319]) ).
thf(374,plain,
! [SV6: $i] :
( ( ~ ! [SY207: $i,SY208: $i] :
( ~ ( member @ SV6 @ SY208 )
| ( member @ SV6 @ ( union @ SY207 @ SY208 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[319]) ).
thf(375,plain,
! [SV7: $i,SV24: $i,SV33: $i] :
( ( ! [SY430: $i,SY431: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK4_X1 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ SV24 )
| ~ ( member @ ( sK5_SY139 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ SY430 ) )
| ~ ( member @ ( sK6_SY142 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ SV24 ) )
| ~ ( member @ ( sK7_SY144 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ SY430 ) )
| ~ ( apply @ SV7 @ ( sK4_X1 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ ( sK5_SY139 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ( apply @ SV7 @ ( sK6_SY142 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ~ ( ~ ( ~ ( apply @ SV33 @ ( sK4_X1 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) )
| ~ ( apply @ SY431 @ ( sK5_SY139 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ( ( apply @ SV33 @ ( sK4_X1 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) )
| ( apply @ SY431 @ ( sK5_SY139 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SY431 @ SY430 @ SV33 @ SV24 @ SV7 ) ) ) ) )
| ~ ( maps @ SV7 @ SV24 @ SY430 )
| ~ ( one_to_one @ SV7 @ SV24 @ SY430 )
| ( isomorphism @ SV7 @ SV24 @ SV33 @ SY430 @ SY431 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[320]) ).
thf(376,plain,
! [SV33: $i,SV24: $i,SV7: $i] :
( ( ~ ( ~ ! [SY432: $i,SY433: $i] :
( ~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SY432 @ SY433 )
| ! [SY434: $i,SY435: $i] :
~ ( ~ ! [SY436: $i,SY437: $i] :
( ~ ( member @ SY434 @ SV24 )
| ~ ( member @ SY435 @ SY432 )
| ~ ( member @ SY436 @ SV24 )
| ~ ( member @ SY437 @ SY432 )
| ~ ( apply @ SV7 @ SY434 @ SY435 )
| ~ ( apply @ SV7 @ SY436 @ SY437 )
| ~ ( apply @ SV33 @ SY434 @ SY436 )
| ( apply @ SY433 @ SY435 @ SY437 ) )
| ~ ! [SY438: $i,SY439: $i] :
( ~ ( member @ SY434 @ SV24 )
| ~ ( member @ SY435 @ SY432 )
| ~ ( member @ SY438 @ SV24 )
| ~ ( member @ SY439 @ SY432 )
| ~ ( apply @ SV7 @ SY434 @ SY435 )
| ~ ( apply @ SV7 @ SY438 @ SY439 )
| ~ ( apply @ SY433 @ SY435 @ SY439 )
| ( apply @ SV33 @ SY434 @ SY438 ) ) ) )
| ~ ~ ( ~ ! [SY440: $i] :
( ! [SY441: $i] :
~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SY440 @ SY441 )
| ( maps @ SV7 @ SV24 @ SY440 ) )
| ~ ! [SY442: $i] :
( ! [SY443: $i] :
~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SY442 @ SY443 )
| ( one_to_one @ SV7 @ SV24 @ SY442 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[321]) ).
thf(377,plain,
! [SV8: $i,SV25: $i,SV86: $i] :
( ( ! [SY541: $i] :
( ~ ( ~ ~ ( ~ ( member @ ( sK20_X @ SY541 @ SV86 @ SV25 @ SV8 ) @ SV86 )
| ~ ( member @ ( sK21_SY157 @ SY541 @ SV86 @ SV25 @ SV8 ) @ SY541 ) )
| ~ ~ ( ~ ( ~ ( apply @ SV25 @ ( sK20_X @ SY541 @ SV86 @ SV25 @ SV8 ) @ ( sK21_SY157 @ SY541 @ SV86 @ SV25 @ SV8 ) )
| ~ ( apply @ SV8 @ ( sK21_SY157 @ SY541 @ SV86 @ SV25 @ SV8 ) @ ( sK20_X @ SY541 @ SV86 @ SV25 @ SV8 ) ) )
| ~ ( ( apply @ SV25 @ ( sK20_X @ SY541 @ SV86 @ SV25 @ SV8 ) @ ( sK21_SY157 @ SY541 @ SV86 @ SV25 @ SV8 ) )
| ( apply @ SV8 @ ( sK21_SY157 @ SY541 @ SV86 @ SV25 @ SV8 ) @ ( sK20_X @ SY541 @ SV86 @ SV25 @ SV8 ) ) ) ) )
| ( inverse_predicate @ SV8 @ SV25 @ SV86 @ SY541 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(378,plain,
! [SV87: $i,SV25: $i,SV8: $i] :
( ( ! [SY542: $i] :
( ~ ( inverse_predicate @ SV8 @ SV25 @ SV87 @ SY542 )
| ~ ( ~ ! [SY543: $i,SY544: $i] :
( ~ ( member @ SY543 @ SV87 )
| ~ ( member @ SY544 @ SY542 )
| ~ ( apply @ SV25 @ SY543 @ SY544 )
| ( apply @ SV8 @ SY544 @ SY543 ) )
| ~ ! [SY545: $i,SY546: $i] :
( ~ ( member @ SY545 @ SV87 )
| ~ ( member @ SY546 @ SY542 )
| ~ ( apply @ SV8 @ SY546 @ SY545 )
| ( apply @ SV25 @ SY545 @ SY546 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(379,plain,
! [SV9: $i,SV34: $i,SV26: $i] :
( ( ! [SY444: $i,SY445: $i] :
( ~ ( member @ SY444 @ SV26 )
| ~ ( member @ SY445 @ SV34 )
| ~ ( apply @ SV9 @ SY444 @ SY445 )
| ( apply @ ( inverse_function @ SV9 @ SV26 @ SV34 ) @ SY445 @ SY444 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[324]) ).
thf(380,plain,
! [SV9: $i,SV34: $i,SV26: $i] :
( ( ! [SY446: $i,SY447: $i] :
( ~ ( member @ SY446 @ SV26 )
| ~ ( member @ SY447 @ SV34 )
| ~ ( apply @ ( inverse_function @ SV9 @ SV26 @ SV34 ) @ SY447 @ SY446 )
| ( apply @ SV9 @ SY446 @ SY447 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[325]) ).
thf(381,plain,
! [SV61: $i,SV88: $i,SV10: $i] :
( ( ! [SY547: $i] :
( ~ ( apply @ SV10 @ SV88 @ SY547 )
| ~ ( member @ SY547 @ SV61 ) )
| ( member @ SV88 @ ( inverse_image2 @ SV10 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(382,plain,
! [SV62: $i,SV10: $i,SV89: $i] :
( ( ~ ( member @ SV89 @ ( inverse_image2 @ SV10 @ SV62 ) )
| ~ ( ~ ( apply @ SV10 @ SV89 @ ( sK17_Y @ SV89 @ SV62 @ SV10 ) )
| ~ ( member @ ( sK17_Y @ SV89 @ SV62 @ SV10 ) @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(383,plain,
! [SV11: $i,SV63: $i,SV90: $i] :
( ( ~ ( ~ ( member @ ( sK23_Y @ SV90 @ SV63 @ SV11 ) @ SV90 )
| ~ ! [SY548: $i] :
( ~ ( apply @ SV11 @ SY548 @ ( sK23_Y @ SV90 @ SV63 @ SV11 ) )
| ~ ( member @ SY548 @ SV63 ) ) )
| ( surjective @ SV11 @ SV63 @ SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(384,plain,
! [SV91: $i,SV64: $i,SV11: $i] :
( ( ~ ( surjective @ SV11 @ SV64 @ SV91 )
| ! [SY549: $i] :
( ~ ( member @ SY549 @ SV91 )
| ~ ( ~ ( apply @ SV11 @ ( sK22_E @ SY549 @ SV91 @ SV64 @ SV11 ) @ SY549 )
| ~ ( member @ ( sK22_E @ SY549 @ SV91 @ SV64 @ SV11 ) @ SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(385,plain,
! [SV92: $i,SV27: $i,SV12: $i] :
( ( ! [SY550: $i] :
( ! [SY381: $i] :
( ~ ( apply @ SV12 @ SY550 @ SY381 )
| ~ ( member @ SY381 @ SV27 ) )
| ~ ( member @ SY550 @ SV92 )
| ( member @ SY550 @ ( inverse_image3 @ SV12 @ SV27 @ SV92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(386,plain,
! [SV27: $i,SV12: $i] :
( ( ~ ! [SY382: $i,SY383: $i] :
( ~ ( member @ SY383 @ ( inverse_image3 @ SV12 @ SV27 @ SY382 ) )
| ~ ( ~ ( apply @ SV12 @ SY383 @ ( sK16_Y @ SY383 @ SY382 @ SV27 @ SV12 ) )
| ~ ( member @ ( sK16_Y @ SY383 @ SY382 @ SV27 @ SV12 ) @ SV27 ) ) )
| ~ ! [SY384: $i,SY385: $i] :
( ~ ( member @ SY385 @ ( inverse_image3 @ SV12 @ SV27 @ SY384 ) )
| ( member @ SY385 @ SY384 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(387,plain,
! [SV13: $i,SV28: $i,SV93: $i] :
( ( ! [SY552: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK28_X @ SY552 @ SV93 @ SV28 @ SV13 ) @ SV93 )
| ~ ( member @ ( sK29_SY162 @ SY552 @ SV93 @ SV28 @ SV13 ) @ SY552 ) )
| ~ ( member @ ( sK30_SY164 @ SY552 @ SV93 @ SV28 @ SV13 ) @ SY552 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV13 @ ( sK28_X @ SY552 @ SV93 @ SV28 @ SV13 ) @ ( sK29_SY162 @ SY552 @ SV93 @ SV28 @ SV13 ) )
| ~ ( apply @ SV28 @ ( sK28_X @ SY552 @ SV93 @ SV28 @ SV13 ) @ ( sK30_SY164 @ SY552 @ SV93 @ SV28 @ SV13 ) ) )
| ~ ( ( ( sK29_SY162 @ SY552 @ SV93 @ SV28 @ SV13 )
!= ( sK30_SY164 @ SY552 @ SV93 @ SV28 @ SV13 ) ) ) ) )
| ( equal_maps @ SV13 @ SV28 @ SV93 @ SY552 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(388,plain,
! [SV94: $i,SV28: $i,SV13: $i] :
( ( ! [SY553: $i] :
( ~ ( equal_maps @ SV13 @ SV28 @ SV94 @ SY553 )
| ! [SY554: $i,SY555: $i,SY556: $i] :
( ~ ( member @ SY554 @ SV94 )
| ~ ( member @ SY555 @ SY553 )
| ~ ( member @ SY556 @ SY553 )
| ~ ( apply @ SV13 @ SY554 @ SY555 )
| ~ ( apply @ SV28 @ SY554 @ SY556 )
| ( SY555 = SY556 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(389,plain,
! [SV14: $i,SV29: $i,SV35: $i,SV42: $i] :
( ( ~ ! [SY479: $i,SY480: $i] :
( ~ ( ~ ~ ( ~ ( member @ ( sK33_X @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV42 )
| ~ ( member @ ( sK34_SY165 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY480 ) )
| ~ ~ ( ~ ( ! [SY481: $i] :
( ~ ( apply @ SV35 @ ( sK33_X @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY481 )
| ~ ( member @ SY481 @ SY479 )
| ~ ( apply @ SV29 @ SY481 @ ( sK34_SY165 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ~ ( apply @ SV14 @ ( sK33_X @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( apply @ SV35 @ ( sK33_X @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK35_SY169 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK35_SY169 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY479 ) )
| ~ ( apply @ SV29 @ ( sK35_SY169 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ( apply @ SV14 @ ( sK33_X @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) ) ) ) )
| ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SY479 @ SY480 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[334]) ).
thf(390,plain,
! [SV42: $i,SV35: $i,SV29: $i,SV14: $i] :
( ( ~ ! [SY482: $i,SY483: $i] :
( ~ ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SY482 @ SY483 )
| ~ ( ~ ! [SY484: $i,SY485: $i] :
( ~ ( member @ SY484 @ SV42 )
| ~ ( member @ SY485 @ SY483 )
| ! [SY456: $i] :
( ~ ( apply @ SV35 @ SY484 @ SY456 )
| ~ ( member @ SY456 @ SY482 )
| ~ ( apply @ SV29 @ SY456 @ SY485 ) )
| ( apply @ SV14 @ SY484 @ SY485 ) )
| ~ ! [SY487: $i,SY488: $i] :
( ~ ( member @ SY487 @ SV42 )
| ~ ( member @ SY488 @ SY483 )
| ~ ( apply @ SV14 @ SY487 @ SY488 )
| ~ ( ~ ~ ( ~ ( apply @ SV35 @ SY487 @ ( sK32_Y @ SY488 @ SY487 @ SY483 @ SY482 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK32_Y @ SY488 @ SY487 @ SY483 @ SY482 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY482 ) )
| ~ ( apply @ SV29 @ ( sK32_Y @ SY488 @ SY487 @ SY483 @ SY482 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY488 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[334]) ).
thf(391,plain,
! [SV65: $i,SV43: $i] :
( ( ( ( SV43 != SV65 ) )
= $true )
| ( ( member @ SV43 @ ( singleton @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(392,plain,
! [SV66: $i,SV44: $i] :
( ( ( ~ ( member @ SV44 @ ( singleton @ SV66 ) ) )
= $true )
| ( ( SV44 = SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(393,plain,
! [SV15: $i,SV67: $i,SV95: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK24_X1 @ SV95 @ SV67 @ SV15 ) @ SV67 )
| ~ ( member @ ( sK25_SY159 @ SV95 @ SV67 @ SV15 ) @ SV67 ) )
| ~ ( member @ ( sK26_SY161 @ SV95 @ SV67 @ SV15 ) @ SV95 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV15 @ ( sK24_X1 @ SV95 @ SV67 @ SV15 ) @ ( sK26_SY161 @ SV95 @ SV67 @ SV15 ) )
| ~ ( apply @ SV15 @ ( sK25_SY159 @ SV95 @ SV67 @ SV15 ) @ ( sK26_SY161 @ SV95 @ SV67 @ SV15 ) ) )
| ~ ( ( ( sK24_X1 @ SV95 @ SV67 @ SV15 )
!= ( sK25_SY159 @ SV95 @ SV67 @ SV15 ) ) ) ) )
| ( injective @ SV15 @ SV67 @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(394,plain,
! [SV96: $i,SV68: $i,SV15: $i] :
( ( ~ ( injective @ SV15 @ SV68 @ SV96 )
| ! [SY557: $i,SY558: $i,SY559: $i] :
( ~ ( member @ SY557 @ SV68 )
| ~ ( member @ SY558 @ SV68 )
| ~ ( member @ SY559 @ SV96 )
| ~ ( apply @ SV15 @ SY557 @ SY559 )
| ~ ( apply @ SV15 @ SY558 @ SY559 )
| ( SY557 = SY558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(395,plain,
! [SV69: $i,SV45: $i] :
( ( ( ~ ( subset @ SV45 @ SV69 )
| ~ ( subset @ SV69 @ SV45 ) )
= $true )
| ( ( equal_set @ SV45 @ SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[339]) ).
thf(396,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[340]) ).
thf(397,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[341]) ).
thf(398,plain,
! [SV16: $i,SV30: $i,SV36: $i] :
( ( ! [SY459: $i,SY460: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK12_X1 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ SV30 )
| ~ ( member @ ( sK13_SY151 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ SY459 ) )
| ~ ( member @ ( sK14_SY154 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ SV30 ) )
| ~ ( member @ ( sK15_SY156 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ SY459 ) )
| ~ ( apply @ SV36 @ ( sK12_X1 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ ( sK14_SY154 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ( apply @ SV16 @ ( sK12_X1 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ ( sK13_SY151 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ( apply @ SV16 @ ( sK14_SY154 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ ( sK15_SY156 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ~ ( apply @ SY460 @ ( sK13_SY151 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) @ ( sK15_SY156 @ SY460 @ SY459 @ SV36 @ SV30 @ SV16 ) ) )
| ( increasing @ SV16 @ SV30 @ SV36 @ SY459 @ SY460 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[342]) ).
thf(399,plain,
! [SV36: $i,SV30: $i,SV16: $i] :
( ( ! [SY461: $i,SY462: $i] :
( ~ ( increasing @ SV16 @ SV30 @ SV36 @ SY461 @ SY462 )
| ! [SY463: $i,SY464: $i,SY465: $i,SY466: $i] :
( ~ ( member @ SY463 @ SV30 )
| ~ ( member @ SY464 @ SY461 )
| ~ ( member @ SY465 @ SV30 )
| ~ ( member @ SY466 @ SY461 )
| ~ ( apply @ SV36 @ SY463 @ SY465 )
| ~ ( apply @ SV16 @ SY463 @ SY464 )
| ~ ( apply @ SV16 @ SY465 @ SY466 )
| ( apply @ SY462 @ SY464 @ SY466 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[343]) ).
thf(400,plain,
! [SV97: $i,SV70: $i,SV17: $i] :
( ( ~ ( member @ SV17 @ SV70 )
| ~ ( member @ SV17 @ SV97 )
| ( member @ SV17 @ ( intersection @ SV70 @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(401,plain,
! [SV17: $i] :
( ( ~ ! [SY299: $i] :
( ! [SY300: $i] :
~ ( member @ SV17 @ ( intersection @ SY299 @ SY300 ) )
| ( member @ SV17 @ SY299 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[345]) ).
thf(402,plain,
! [SV17: $i] :
( ( ~ ! [SY301: $i,SY302: $i] :
( ~ ( member @ SV17 @ ( intersection @ SY301 @ SY302 ) )
| ( member @ SV17 @ SY302 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[345]) ).
thf(403,plain,
! [SV98: $i,SV71: $i,SV18: $i] :
( ( ~ ( member @ SV18 @ ( unordered_pair @ SV71 @ SV98 ) )
| ( SV18 = SV71 )
| ( SV18 = SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(404,plain,
! [SV18: $i] :
( ( ~ ! [SY305: $i] :
( ( SV18 != SY305 )
| ! [SY306: $i] : ( member @ SV18 @ ( unordered_pair @ SY305 @ SY306 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[347]) ).
thf(405,plain,
! [SV18: $i] :
( ( ~ ! [SY307: $i,SY308: $i] :
( ( SV18 != SY308 )
| ( member @ SV18 @ ( unordered_pair @ SY307 @ SY308 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[347]) ).
thf(406,plain,
! [SV99: $i,SV72: $i,SV19: $i] :
( ( ~ ( injective @ SV19 @ SV72 @ SV99 )
| ~ ( surjective @ SV19 @ SV72 @ SV99 )
| ( one_to_one @ SV19 @ SV72 @ SV99 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(407,plain,
! [SV19: $i] :
( ( ~ ! [SY311: $i,SY312: $i] :
( ~ ( one_to_one @ SV19 @ SY311 @ SY312 )
| ( injective @ SV19 @ SY311 @ SY312 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[349]) ).
thf(408,plain,
! [SV19: $i] :
( ( ~ ! [SY313: $i,SY314: $i] :
( ~ ( one_to_one @ SV19 @ SY313 @ SY314 )
| ( surjective @ SV19 @ SY313 @ SY314 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[349]) ).
thf(409,plain,
! [SV20: $i,SV46: $i,SV31: $i,SV73: $i,SV37: $i] :
( ( ~ ! [SY528: $i,SY529: $i] :
( ~ ( member @ SY528 @ SV37 )
| ~ ( member @ SY529 @ SV73 )
| ! [SY495: $i] :
( ~ ( apply @ SV31 @ SY528 @ SY495 )
| ~ ( member @ SY495 @ SV46 )
| ~ ( apply @ SV20 @ SY495 @ SY529 ) )
| ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SY528 @ SY529 ) )
| ~ ! [SY531: $i,SY532: $i] :
( ~ ( member @ SY531 @ SV37 )
| ~ ( member @ SY532 @ SV73 )
| ~ ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SY531 @ SY532 )
| ~ ( ~ ~ ( ~ ( apply @ SV31 @ SY531 @ ( sK31_Y @ SY532 @ SY531 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) )
| ~ ( member @ ( sK31_Y @ SY532 @ SY531 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SV46 ) )
| ~ ( apply @ SV20 @ ( sK31_Y @ SY532 @ SY531 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SY532 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(410,plain,
! [SV47: $i,SV74: $i] :
( ( ( ! [SY533: $i] :
( ~ ( member @ SY533 @ SV74 )
| ~ ( member @ SV47 @ SY533 ) ) )
= $true )
| ( ( member @ SV47 @ ( sum @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(411,plain,
! [SV75: $i,SV48: $i] :
( ( ( ~ ( member @ SV48 @ ( sum @ SV75 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ ( sK42_Y @ SV75 @ SV48 ) @ SV75 )
| ~ ( member @ SV48 @ ( sK42_Y @ SV75 @ SV48 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[352]) ).
thf(412,plain,
! [SV49: $i,SV76: $i] :
( ( ( ~ ( ~ ( member @ ( sK41_Y @ SV76 @ SV49 ) @ SV76 )
| ~ ~ ( member @ SV49 @ ( sK41_Y @ SV76 @ SV49 ) ) ) )
= $true )
| ( ( member @ SV49 @ ( product @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[353]) ).
thf(413,plain,
! [SV77: $i,SV50: $i] :
( ( ( ~ ( member @ SV50 @ ( product @ SV77 ) ) )
= $true )
| ( ( ! [SY534: $i] :
( ~ ( member @ SY534 @ SV77 )
| ( member @ SV50 @ SY534 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[354]) ).
thf(414,plain,
! [SV21: $i,SV78: $i,SV100: $i] :
( ( ~ ( ~ ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
| ~ ! [SY560: $i] :
( ~ ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SY560 )
| ~ ( member @ SY560 @ SV100 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
| ~ ( member @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ( member @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) )
| ~ ( ( ( sK38_SY170 @ SV100 @ SV78 @ SV21 )
!= ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) ) ) )
| ( maps @ SV21 @ SV78 @ SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(415,plain,
! [SV21: $i] :
( ( ~ ! [SY327: $i,SY328: $i] :
( ~ ( maps @ SV21 @ SY327 @ SY328 )
| ! [SY329: $i] :
( ~ ( member @ SY329 @ SY327 )
| ~ ( ~ ( apply @ SV21 @ SY329 @ ( sK36_Y @ SY329 @ SY328 @ SY327 @ SV21 ) )
| ~ ( member @ ( sK36_Y @ SY329 @ SY328 @ SY327 @ SV21 ) @ SY328 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[356]) ).
thf(416,plain,
! [SV21: $i] :
( ( ~ ! [SY330: $i,SY331: $i] :
( ~ ( maps @ SV21 @ SY330 @ SY331 )
| ! [SY332: $i,SY333: $i,SY334: $i] :
( ~ ( member @ SY332 @ SY330 )
| ~ ( member @ SY333 @ SY331 )
| ~ ( member @ SY334 @ SY331 )
| ~ ( apply @ SV21 @ SY332 @ SY333 )
| ~ ( apply @ SV21 @ SY332 @ SY334 )
| ( SY333 = SY334 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[356]) ).
thf(417,plain,
! [SV51: $i,SV79: $i] :
( ( ( ~ ( ~ ( member @ ( sK27_X @ SV79 @ SV51 ) @ SV79 )
| ~ ~ ( apply @ SV51 @ ( sK27_X @ SV79 @ SV51 ) @ ( sK27_X @ SV79 @ SV51 ) ) ) )
= $true )
| ( ( identity @ SV51 @ SV79 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(418,plain,
! [SV80: $i,SV52: $i] :
( ( ( ~ ( identity @ SV52 @ SV80 ) )
= $true )
| ( ( ! [SY537: $i] :
( ~ ( member @ SY537 @ SV80 )
| ( apply @ SV52 @ SY537 @ SY537 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[358]) ).
thf(419,plain,
! [SV81: $i,SV22: $i,SV101: $i,SV2: $i] :
( ( ! [SY561: $i] :
( ~ ( apply @ SV2 @ SY561 @ SV101 )
| ~ ( member @ SY561 @ SV22 ) )
| ~ ( member @ SV101 @ SV81 )
| ( member @ SV101 @ ( image3 @ SV2 @ SV22 @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(420,plain,
! [SV22: $i,SV2: $i] :
( ( ~ ! [SY338: $i,SY339: $i] :
( ~ ( member @ SY339 @ ( image3 @ SV2 @ SV22 @ SY338 ) )
| ~ ( ~ ( apply @ SV2 @ ( sK18_X @ SY339 @ SY338 @ SV22 @ SV2 ) @ SY339 )
| ~ ( member @ ( sK18_X @ SY339 @ SY338 @ SV22 @ SV2 ) @ SV22 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[360]) ).
thf(421,plain,
! [SV22: $i,SV2: $i] :
( ( ~ ! [SY340: $i,SY341: $i] :
( ~ ( member @ SY341 @ ( image3 @ SV2 @ SV22 @ SY340 ) )
| ( member @ SY341 @ SY340 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[360]) ).
thf(422,plain,
! [SV53: $i,SV38: $i] :
( ( ( member @ SV38 @ ( power_set @ SV53 ) )
= $false )
| ( ( subset @ SV38 @ SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(423,plain,
! [SV54: $i,SV39: $i] :
( ( ( subset @ SV39 @ SV54 )
= $false )
| ( ( member @ SV39 @ ( power_set @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(424,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i] :
( ( ! [SY562: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_X1 @ SY562 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 )
| ~ ( member @ ( sK9_SY145 @ SY562 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( member @ ( sK10_SY148 @ SY562 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 ) )
| ~ ( member @ ( sK11_SY150 @ SY562 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( apply @ SV32 @ ( sK8_X1 @ SY562 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK10_SY148 @ SY562 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ( apply @ SV3 @ ( sK8_X1 @ SY562 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK9_SY145 @ SY562 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ( apply @ SV3 @ ( sK10_SY148 @ SY562 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK11_SY150 @ SY562 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ~ ( apply @ SY562 @ ( sK11_SY150 @ SY562 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK9_SY145 @ SY562 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
| ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SY562 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(425,plain,
! [SV103: $i,SV32: $i,SV23: $i,SV3: $i] :
( ( ! [SY563: $i] :
( ~ ( decreasing @ SV3 @ SV23 @ SV32 @ SV103 @ SY563 )
| ! [SY564: $i,SY565: $i,SY566: $i,SY567: $i] :
( ~ ( member @ SY564 @ SV23 )
| ~ ( member @ SY565 @ SV103 )
| ~ ( member @ SY566 @ SV23 )
| ~ ( member @ SY567 @ SV103 )
| ~ ( apply @ SV32 @ SY564 @ SY566 )
| ~ ( apply @ SV3 @ SY564 @ SY565 )
| ~ ( apply @ SV3 @ SY566 @ SY567 )
| ( apply @ SY563 @ SY567 @ SY565 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(426,plain,
! [SV40: $i,SV55: $i] :
( ( ( ~ ( member @ ( sK43_X @ SV55 @ SV40 ) @ SV40 )
| ~ ~ ( member @ ( sK43_X @ SV55 @ SV40 ) @ SV55 ) )
= $false )
| ( ( subset @ SV40 @ SV55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(427,plain,
! [SV56: $i,SV41: $i] :
( ( ( subset @ SV41 @ SV56 )
= $false )
| ( ( ! [SY507: $i] :
( ~ ( member @ SY507 @ SV41 )
| ( member @ SY507 @ SV56 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(428,plain,
! [SV57: $i,SV82: $i,SV4: $i] :
( ( ( ! [SY540: $i] :
( ~ ( apply @ SV4 @ SY540 @ SV82 )
| ~ ( member @ SY540 @ SV57 ) ) )
= $true )
| ( ( member @ SV82 @ ( image2 @ SV4 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[367]) ).
thf(429,plain,
! [SV58: $i,SV4: $i,SV83: $i] :
( ( ( ~ ( member @ SV83 @ ( image2 @ SV4 @ SV58 ) ) )
= $true )
| ( ( ~ ( ~ ( apply @ SV4 @ ( sK19_X @ SV83 @ SV58 @ SV4 ) @ SV83 )
| ~ ( member @ ( sK19_X @ SV83 @ SV58 @ SV4 ) @ SV58 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[368]) ).
thf(430,plain,
! [SV59: $i,SV84: $i,SV5: $i] :
( ( ( ~ ( member @ SV5 @ SV84 )
| ( member @ SV5 @ SV59 ) )
= $true )
| ( ( member @ SV5 @ ( difference @ SV84 @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[369]) ).
thf(431,plain,
! [SV5: $i] :
( ( ! [SY199: $i,SY200: $i] :
( ~ ( member @ SV5 @ ( difference @ SY200 @ SY199 ) )
| ( member @ SV5 @ SY200 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[370]) ).
thf(432,plain,
! [SV5: $i] :
( ( ! [SY201: $i] :
( ! [SY202: $i] :
~ ( member @ SV5 @ ( difference @ SY202 @ SY201 ) )
| ~ ( member @ SV5 @ SY201 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[371]) ).
thf(433,plain,
! [SV85: $i,SV60: $i,SV6: $i] :
( ( ( ~ ( member @ SV6 @ ( union @ SV60 @ SV85 ) ) )
= $true )
| ( ( ( member @ SV6 @ SV60 )
| ( member @ SV6 @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[372]) ).
thf(434,plain,
! [SV6: $i] :
( ( ! [SY205: $i] :
( ~ ( member @ SV6 @ SY205 )
| ! [SY206: $i] : ( member @ SV6 @ ( union @ SY205 @ SY206 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[373]) ).
thf(435,plain,
! [SV6: $i] :
( ( ! [SY207: $i,SY208: $i] :
( ~ ( member @ SV6 @ SY208 )
| ( member @ SV6 @ ( union @ SY207 @ SY208 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[374]) ).
thf(436,plain,
! [SV7: $i,SV24: $i,SV33: $i,SV104: $i] :
( ( ! [SY568: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK4_X1 @ SY568 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 )
| ~ ( member @ ( sK5_SY139 @ SY568 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
| ~ ( member @ ( sK6_SY142 @ SY568 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 ) )
| ~ ( member @ ( sK7_SY144 @ SY568 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
| ~ ( apply @ SV7 @ ( sK4_X1 @ SY568 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK5_SY139 @ SY568 @ SV104 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ( apply @ SV7 @ ( sK6_SY142 @ SY568 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SY568 @ SV104 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ~ ( ~ ( ~ ( apply @ SV33 @ ( sK4_X1 @ SY568 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SY568 @ SV104 @ SV33 @ SV24 @ SV7 ) )
| ~ ( apply @ SY568 @ ( sK5_SY139 @ SY568 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SY568 @ SV104 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ( ( apply @ SV33 @ ( sK4_X1 @ SY568 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SY568 @ SV104 @ SV33 @ SV24 @ SV7 ) )
| ( apply @ SY568 @ ( sK5_SY139 @ SY568 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SY568 @ SV104 @ SV33 @ SV24 @ SV7 ) ) ) ) )
| ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 )
| ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SY568 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(437,plain,
! [SV33: $i,SV24: $i,SV7: $i] :
( ( ~ ! [SY432: $i,SY433: $i] :
( ~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SY432 @ SY433 )
| ! [SY434: $i,SY435: $i] :
~ ( ~ ! [SY436: $i,SY437: $i] :
( ~ ( member @ SY434 @ SV24 )
| ~ ( member @ SY435 @ SY432 )
| ~ ( member @ SY436 @ SV24 )
| ~ ( member @ SY437 @ SY432 )
| ~ ( apply @ SV7 @ SY434 @ SY435 )
| ~ ( apply @ SV7 @ SY436 @ SY437 )
| ~ ( apply @ SV33 @ SY434 @ SY436 )
| ( apply @ SY433 @ SY435 @ SY437 ) )
| ~ ! [SY438: $i,SY439: $i] :
( ~ ( member @ SY434 @ SV24 )
| ~ ( member @ SY435 @ SY432 )
| ~ ( member @ SY438 @ SV24 )
| ~ ( member @ SY439 @ SY432 )
| ~ ( apply @ SV7 @ SY434 @ SY435 )
| ~ ( apply @ SV7 @ SY438 @ SY439 )
| ~ ( apply @ SY433 @ SY435 @ SY439 )
| ( apply @ SV33 @ SY434 @ SY438 ) ) ) )
| ~ ~ ( ~ ! [SY440: $i] :
( ! [SY441: $i] :
~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SY440 @ SY441 )
| ( maps @ SV7 @ SV24 @ SY440 ) )
| ~ ! [SY442: $i] :
( ! [SY443: $i] :
~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SY442 @ SY443 )
| ( one_to_one @ SV7 @ SV24 @ SY442 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(438,plain,
! [SV8: $i,SV25: $i,SV86: $i,SV105: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) @ SV86 )
| ~ ( member @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) @ SV105 ) )
| ~ ~ ( ~ ( ~ ( apply @ SV25 @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) )
| ~ ( apply @ SV8 @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) ) )
| ~ ( ( apply @ SV25 @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) )
| ( apply @ SV8 @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) ) ) ) )
| ( inverse_predicate @ SV8 @ SV25 @ SV86 @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(439,plain,
! [SV106: $i,SV87: $i,SV25: $i,SV8: $i] :
( ( ~ ( inverse_predicate @ SV8 @ SV25 @ SV87 @ SV106 )
| ~ ( ~ ! [SY569: $i,SY570: $i] :
( ~ ( member @ SY569 @ SV87 )
| ~ ( member @ SY570 @ SV106 )
| ~ ( apply @ SV25 @ SY569 @ SY570 )
| ( apply @ SV8 @ SY570 @ SY569 ) )
| ~ ! [SY571: $i,SY572: $i] :
( ~ ( member @ SY571 @ SV87 )
| ~ ( member @ SY572 @ SV106 )
| ~ ( apply @ SV8 @ SY572 @ SY571 )
| ( apply @ SV25 @ SY571 @ SY572 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(440,plain,
! [SV9: $i,SV34: $i,SV26: $i,SV107: $i] :
( ( ! [SY573: $i] :
( ~ ( member @ SV107 @ SV26 )
| ~ ( member @ SY573 @ SV34 )
| ~ ( apply @ SV9 @ SV107 @ SY573 )
| ( apply @ ( inverse_function @ SV9 @ SV26 @ SV34 ) @ SY573 @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(441,plain,
! [SV9: $i,SV34: $i,SV26: $i,SV108: $i] :
( ( ! [SY574: $i] :
( ~ ( member @ SV108 @ SV26 )
| ~ ( member @ SY574 @ SV34 )
| ~ ( apply @ ( inverse_function @ SV9 @ SV26 @ SV34 ) @ SY574 @ SV108 )
| ( apply @ SV9 @ SV108 @ SY574 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(442,plain,
! [SV61: $i,SV88: $i,SV10: $i] :
( ( ( ! [SY547: $i] :
( ~ ( apply @ SV10 @ SV88 @ SY547 )
| ~ ( member @ SY547 @ SV61 ) ) )
= $true )
| ( ( member @ SV88 @ ( inverse_image2 @ SV10 @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[381]) ).
thf(443,plain,
! [SV62: $i,SV10: $i,SV89: $i] :
( ( ( ~ ( member @ SV89 @ ( inverse_image2 @ SV10 @ SV62 ) ) )
= $true )
| ( ( ~ ( ~ ( apply @ SV10 @ SV89 @ ( sK17_Y @ SV89 @ SV62 @ SV10 ) )
| ~ ( member @ ( sK17_Y @ SV89 @ SV62 @ SV10 ) @ SV62 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[382]) ).
thf(444,plain,
! [SV11: $i,SV63: $i,SV90: $i] :
( ( ( ~ ( ~ ( member @ ( sK23_Y @ SV90 @ SV63 @ SV11 ) @ SV90 )
| ~ ! [SY548: $i] :
( ~ ( apply @ SV11 @ SY548 @ ( sK23_Y @ SV90 @ SV63 @ SV11 ) )
| ~ ( member @ SY548 @ SV63 ) ) ) )
= $true )
| ( ( surjective @ SV11 @ SV63 @ SV90 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[383]) ).
thf(445,plain,
! [SV91: $i,SV64: $i,SV11: $i] :
( ( ( ~ ( surjective @ SV11 @ SV64 @ SV91 ) )
= $true )
| ( ( ! [SY549: $i] :
( ~ ( member @ SY549 @ SV91 )
| ~ ( ~ ( apply @ SV11 @ ( sK22_E @ SY549 @ SV91 @ SV64 @ SV11 ) @ SY549 )
| ~ ( member @ ( sK22_E @ SY549 @ SV91 @ SV64 @ SV11 ) @ SV64 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[384]) ).
thf(446,plain,
! [SV92: $i,SV27: $i,SV109: $i,SV12: $i] :
( ( ! [SY575: $i] :
( ~ ( apply @ SV12 @ SV109 @ SY575 )
| ~ ( member @ SY575 @ SV27 ) )
| ~ ( member @ SV109 @ SV92 )
| ( member @ SV109 @ ( inverse_image3 @ SV12 @ SV27 @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(447,plain,
! [SV27: $i,SV12: $i] :
( ( ~ ! [SY382: $i,SY383: $i] :
( ~ ( member @ SY383 @ ( inverse_image3 @ SV12 @ SV27 @ SY382 ) )
| ~ ( ~ ( apply @ SV12 @ SY383 @ ( sK16_Y @ SY383 @ SY382 @ SV27 @ SV12 ) )
| ~ ( member @ ( sK16_Y @ SY383 @ SY382 @ SV27 @ SV12 ) @ SV27 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[386]) ).
thf(448,plain,
! [SV27: $i,SV12: $i] :
( ( ~ ! [SY384: $i,SY385: $i] :
( ~ ( member @ SY385 @ ( inverse_image3 @ SV12 @ SV27 @ SY384 ) )
| ( member @ SY385 @ SY384 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[386]) ).
thf(449,plain,
! [SV13: $i,SV28: $i,SV93: $i,SV110: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ SV93 )
| ~ ( member @ ( sK29_SY162 @ SV110 @ SV93 @ SV28 @ SV13 ) @ SV110 ) )
| ~ ( member @ ( sK30_SY164 @ SV110 @ SV93 @ SV28 @ SV13 ) @ SV110 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV13 @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ ( sK29_SY162 @ SV110 @ SV93 @ SV28 @ SV13 ) )
| ~ ( apply @ SV28 @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ ( sK30_SY164 @ SV110 @ SV93 @ SV28 @ SV13 ) ) )
| ~ ( ( ( sK29_SY162 @ SV110 @ SV93 @ SV28 @ SV13 )
!= ( sK30_SY164 @ SV110 @ SV93 @ SV28 @ SV13 ) ) ) ) )
| ( equal_maps @ SV13 @ SV28 @ SV93 @ SV110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(450,plain,
! [SV111: $i,SV94: $i,SV28: $i,SV13: $i] :
( ( ~ ( equal_maps @ SV13 @ SV28 @ SV94 @ SV111 )
| ! [SY576: $i,SY577: $i,SY578: $i] :
( ~ ( member @ SY576 @ SV94 )
| ~ ( member @ SY577 @ SV111 )
| ~ ( member @ SY578 @ SV111 )
| ~ ( apply @ SV13 @ SY576 @ SY577 )
| ~ ( apply @ SV28 @ SY576 @ SY578 )
| ( SY577 = SY578 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(451,plain,
! [SV14: $i,SV29: $i,SV35: $i,SV42: $i] :
( ( ! [SY479: $i,SY480: $i] :
( ~ ( ~ ~ ( ~ ( member @ ( sK33_X @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV42 )
| ~ ( member @ ( sK34_SY165 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY480 ) )
| ~ ~ ( ~ ( ! [SY481: $i] :
( ~ ( apply @ SV35 @ ( sK33_X @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY481 )
| ~ ( member @ SY481 @ SY479 )
| ~ ( apply @ SV29 @ SY481 @ ( sK34_SY165 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ~ ( apply @ SV14 @ ( sK33_X @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( apply @ SV35 @ ( sK33_X @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK35_SY169 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK35_SY169 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY479 ) )
| ~ ( apply @ SV29 @ ( sK35_SY169 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ( apply @ SV14 @ ( sK33_X @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SY480 @ SY479 @ SV42 @ SV35 @ SV29 @ SV14 ) ) ) ) )
| ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SY479 @ SY480 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[389]) ).
thf(452,plain,
! [SV42: $i,SV35: $i,SV29: $i,SV14: $i] :
( ( ! [SY482: $i,SY483: $i] :
( ~ ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SY482 @ SY483 )
| ~ ( ~ ! [SY484: $i,SY485: $i] :
( ~ ( member @ SY484 @ SV42 )
| ~ ( member @ SY485 @ SY483 )
| ! [SY456: $i] :
( ~ ( apply @ SV35 @ SY484 @ SY456 )
| ~ ( member @ SY456 @ SY482 )
| ~ ( apply @ SV29 @ SY456 @ SY485 ) )
| ( apply @ SV14 @ SY484 @ SY485 ) )
| ~ ! [SY487: $i,SY488: $i] :
( ~ ( member @ SY487 @ SV42 )
| ~ ( member @ SY488 @ SY483 )
| ~ ( apply @ SV14 @ SY487 @ SY488 )
| ~ ( ~ ~ ( ~ ( apply @ SV35 @ SY487 @ ( sK32_Y @ SY488 @ SY487 @ SY483 @ SY482 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK32_Y @ SY488 @ SY487 @ SY483 @ SY482 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY482 ) )
| ~ ( apply @ SV29 @ ( sK32_Y @ SY488 @ SY487 @ SY483 @ SY482 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY488 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[390]) ).
thf(453,plain,
! [SV65: $i,SV43: $i] :
( ( ( SV43 = SV65 )
= $false )
| ( ( member @ SV43 @ ( singleton @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[391]) ).
thf(454,plain,
! [SV66: $i,SV44: $i] :
( ( ( member @ SV44 @ ( singleton @ SV66 ) )
= $false )
| ( ( SV44 = SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(455,plain,
! [SV15: $i,SV67: $i,SV95: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK24_X1 @ SV95 @ SV67 @ SV15 ) @ SV67 )
| ~ ( member @ ( sK25_SY159 @ SV95 @ SV67 @ SV15 ) @ SV67 ) )
| ~ ( member @ ( sK26_SY161 @ SV95 @ SV67 @ SV15 ) @ SV95 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV15 @ ( sK24_X1 @ SV95 @ SV67 @ SV15 ) @ ( sK26_SY161 @ SV95 @ SV67 @ SV15 ) )
| ~ ( apply @ SV15 @ ( sK25_SY159 @ SV95 @ SV67 @ SV15 ) @ ( sK26_SY161 @ SV95 @ SV67 @ SV15 ) ) )
| ~ ( ( ( sK24_X1 @ SV95 @ SV67 @ SV15 )
!= ( sK25_SY159 @ SV95 @ SV67 @ SV15 ) ) ) ) ) )
= $true )
| ( ( injective @ SV15 @ SV67 @ SV95 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[393]) ).
thf(456,plain,
! [SV96: $i,SV68: $i,SV15: $i] :
( ( ( ~ ( injective @ SV15 @ SV68 @ SV96 ) )
= $true )
| ( ( ! [SY557: $i,SY558: $i,SY559: $i] :
( ~ ( member @ SY557 @ SV68 )
| ~ ( member @ SY558 @ SV68 )
| ~ ( member @ SY559 @ SV96 )
| ~ ( apply @ SV15 @ SY557 @ SY559 )
| ~ ( apply @ SV15 @ SY558 @ SY559 )
| ( SY557 = SY558 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(457,plain,
! [SV69: $i,SV45: $i] :
( ( ( ~ ( subset @ SV45 @ SV69 ) )
= $true )
| ( ( ~ ( subset @ SV69 @ SV45 ) )
= $true )
| ( ( equal_set @ SV45 @ SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[395]) ).
thf(458,plain,
! [SV112: $i] :
( ( ! [SY579: $i] :
( ~ ( equal_set @ SV112 @ SY579 )
| ( subset @ SV112 @ SY579 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(459,plain,
! [SV113: $i] :
( ( ! [SY580: $i] :
( ~ ( equal_set @ SV113 @ SY580 )
| ( subset @ SY580 @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(460,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i] :
( ( ! [SY581: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK12_X1 @ SY581 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 )
| ~ ( member @ ( sK13_SY151 @ SY581 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( member @ ( sK14_SY154 @ SY581 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 ) )
| ~ ( member @ ( sK15_SY156 @ SY581 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( apply @ SV36 @ ( sK12_X1 @ SY581 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK14_SY154 @ SY581 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ( apply @ SV16 @ ( sK12_X1 @ SY581 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK13_SY151 @ SY581 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ( apply @ SV16 @ ( sK14_SY154 @ SY581 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK15_SY156 @ SY581 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ~ ( apply @ SY581 @ ( sK13_SY151 @ SY581 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK15_SY156 @ SY581 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
| ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SY581 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(461,plain,
! [SV115: $i,SV36: $i,SV30: $i,SV16: $i] :
( ( ! [SY582: $i] :
( ~ ( increasing @ SV16 @ SV30 @ SV36 @ SV115 @ SY582 )
| ! [SY583: $i,SY584: $i,SY585: $i,SY586: $i] :
( ~ ( member @ SY583 @ SV30 )
| ~ ( member @ SY584 @ SV115 )
| ~ ( member @ SY585 @ SV30 )
| ~ ( member @ SY586 @ SV115 )
| ~ ( apply @ SV36 @ SY583 @ SY585 )
| ~ ( apply @ SV16 @ SY583 @ SY584 )
| ~ ( apply @ SV16 @ SY585 @ SY586 )
| ( apply @ SY582 @ SY584 @ SY586 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(462,plain,
! [SV97: $i,SV70: $i,SV17: $i] :
( ( ( ~ ( member @ SV17 @ SV70 )
| ~ ( member @ SV17 @ SV97 ) )
= $true )
| ( ( member @ SV17 @ ( intersection @ SV70 @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[400]) ).
thf(463,plain,
! [SV17: $i] :
( ( ! [SY299: $i] :
( ! [SY300: $i] :
~ ( member @ SV17 @ ( intersection @ SY299 @ SY300 ) )
| ( member @ SV17 @ SY299 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[401]) ).
thf(464,plain,
! [SV17: $i] :
( ( ! [SY301: $i,SY302: $i] :
( ~ ( member @ SV17 @ ( intersection @ SY301 @ SY302 ) )
| ( member @ SV17 @ SY302 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[402]) ).
thf(465,plain,
! [SV98: $i,SV71: $i,SV18: $i] :
( ( ( ~ ( member @ SV18 @ ( unordered_pair @ SV71 @ SV98 ) ) )
= $true )
| ( ( ( SV18 = SV71 )
| ( SV18 = SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(466,plain,
! [SV18: $i] :
( ( ! [SY305: $i] :
( ( SV18 != SY305 )
| ! [SY306: $i] : ( member @ SV18 @ ( unordered_pair @ SY305 @ SY306 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[404]) ).
thf(467,plain,
! [SV18: $i] :
( ( ! [SY307: $i,SY308: $i] :
( ( SV18 != SY308 )
| ( member @ SV18 @ ( unordered_pair @ SY307 @ SY308 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[405]) ).
thf(468,plain,
! [SV99: $i,SV72: $i,SV19: $i] :
( ( ( ~ ( injective @ SV19 @ SV72 @ SV99 )
| ~ ( surjective @ SV19 @ SV72 @ SV99 ) )
= $true )
| ( ( one_to_one @ SV19 @ SV72 @ SV99 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[406]) ).
thf(469,plain,
! [SV19: $i] :
( ( ! [SY311: $i,SY312: $i] :
( ~ ( one_to_one @ SV19 @ SY311 @ SY312 )
| ( injective @ SV19 @ SY311 @ SY312 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[407]) ).
thf(470,plain,
! [SV19: $i] :
( ( ! [SY313: $i,SY314: $i] :
( ~ ( one_to_one @ SV19 @ SY313 @ SY314 )
| ( surjective @ SV19 @ SY313 @ SY314 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[408]) ).
thf(471,plain,
! [SV20: $i,SV46: $i,SV31: $i,SV73: $i,SV37: $i] :
( ( ~ ! [SY528: $i,SY529: $i] :
( ~ ( member @ SY528 @ SV37 )
| ~ ( member @ SY529 @ SV73 )
| ! [SY495: $i] :
( ~ ( apply @ SV31 @ SY528 @ SY495 )
| ~ ( member @ SY495 @ SV46 )
| ~ ( apply @ SV20 @ SY495 @ SY529 ) )
| ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SY528 @ SY529 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[409]) ).
thf(472,plain,
! [SV46: $i,SV31: $i,SV20: $i,SV73: $i,SV37: $i] :
( ( ~ ! [SY531: $i,SY532: $i] :
( ~ ( member @ SY531 @ SV37 )
| ~ ( member @ SY532 @ SV73 )
| ~ ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SY531 @ SY532 )
| ~ ( ~ ~ ( ~ ( apply @ SV31 @ SY531 @ ( sK31_Y @ SY532 @ SY531 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) )
| ~ ( member @ ( sK31_Y @ SY532 @ SY531 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SV46 ) )
| ~ ( apply @ SV20 @ ( sK31_Y @ SY532 @ SY531 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SY532 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[409]) ).
thf(473,plain,
! [SV47: $i,SV74: $i,SV116: $i] :
( ( ( ~ ( member @ SV116 @ SV74 )
| ~ ( member @ SV47 @ SV116 ) )
= $true )
| ( ( member @ SV47 @ ( sum @ SV74 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(474,plain,
! [SV75: $i,SV48: $i] :
( ( ( member @ SV48 @ ( sum @ SV75 ) )
= $false )
| ( ( ~ ( ~ ( member @ ( sK42_Y @ SV75 @ SV48 ) @ SV75 )
| ~ ( member @ SV48 @ ( sK42_Y @ SV75 @ SV48 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(475,plain,
! [SV49: $i,SV76: $i] :
( ( ( ~ ( member @ ( sK41_Y @ SV76 @ SV49 ) @ SV76 )
| ~ ~ ( member @ SV49 @ ( sK41_Y @ SV76 @ SV49 ) ) )
= $false )
| ( ( member @ SV49 @ ( product @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(476,plain,
! [SV77: $i,SV50: $i] :
( ( ( member @ SV50 @ ( product @ SV77 ) )
= $false )
| ( ( ! [SY534: $i] :
( ~ ( member @ SY534 @ SV77 )
| ( member @ SV50 @ SY534 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(477,plain,
! [SV21: $i,SV78: $i,SV100: $i] :
( ( ( ~ ( ~ ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
| ~ ! [SY560: $i] :
( ~ ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SY560 )
| ~ ( member @ SY560 @ SV100 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
| ~ ( member @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ( member @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) )
| ~ ( ( ( sK38_SY170 @ SV100 @ SV78 @ SV21 )
!= ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) ) ) ) )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(478,plain,
! [SV21: $i] :
( ( ! [SY327: $i,SY328: $i] :
( ~ ( maps @ SV21 @ SY327 @ SY328 )
| ! [SY329: $i] :
( ~ ( member @ SY329 @ SY327 )
| ~ ( ~ ( apply @ SV21 @ SY329 @ ( sK36_Y @ SY329 @ SY328 @ SY327 @ SV21 ) )
| ~ ( member @ ( sK36_Y @ SY329 @ SY328 @ SY327 @ SV21 ) @ SY328 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[415]) ).
thf(479,plain,
! [SV21: $i] :
( ( ! [SY330: $i,SY331: $i] :
( ~ ( maps @ SV21 @ SY330 @ SY331 )
| ! [SY332: $i,SY333: $i,SY334: $i] :
( ~ ( member @ SY332 @ SY330 )
| ~ ( member @ SY333 @ SY331 )
| ~ ( member @ SY334 @ SY331 )
| ~ ( apply @ SV21 @ SY332 @ SY333 )
| ~ ( apply @ SV21 @ SY332 @ SY334 )
| ( SY333 = SY334 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[416]) ).
thf(480,plain,
! [SV51: $i,SV79: $i] :
( ( ( ~ ( member @ ( sK27_X @ SV79 @ SV51 ) @ SV79 )
| ~ ~ ( apply @ SV51 @ ( sK27_X @ SV79 @ SV51 ) @ ( sK27_X @ SV79 @ SV51 ) ) )
= $false )
| ( ( identity @ SV51 @ SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(481,plain,
! [SV80: $i,SV52: $i] :
( ( ( identity @ SV52 @ SV80 )
= $false )
| ( ( ! [SY537: $i] :
( ~ ( member @ SY537 @ SV80 )
| ( apply @ SV52 @ SY537 @ SY537 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(482,plain,
! [SV81: $i,SV22: $i,SV101: $i,SV2: $i] :
( ( ( ! [SY561: $i] :
( ~ ( apply @ SV2 @ SY561 @ SV101 )
| ~ ( member @ SY561 @ SV22 ) )
| ~ ( member @ SV101 @ SV81 ) )
= $true )
| ( ( member @ SV101 @ ( image3 @ SV2 @ SV22 @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(483,plain,
! [SV22: $i,SV2: $i] :
( ( ! [SY338: $i,SY339: $i] :
( ~ ( member @ SY339 @ ( image3 @ SV2 @ SV22 @ SY338 ) )
| ~ ( ~ ( apply @ SV2 @ ( sK18_X @ SY339 @ SY338 @ SV22 @ SV2 ) @ SY339 )
| ~ ( member @ ( sK18_X @ SY339 @ SY338 @ SV22 @ SV2 ) @ SV22 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[420]) ).
thf(484,plain,
! [SV22: $i,SV2: $i] :
( ( ! [SY340: $i,SY341: $i] :
( ~ ( member @ SY341 @ ( image3 @ SV2 @ SV22 @ SY340 ) )
| ( member @ SY341 @ SY340 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[421]) ).
thf(485,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 )
| ~ ( member @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( member @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 ) )
| ~ ( member @ ( sK11_SY150 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( apply @ SV32 @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ( apply @ SV3 @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ( apply @ SV3 @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK11_SY150 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ~ ( apply @ SV117 @ ( sK11_SY150 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
| ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(486,plain,
! [SV118: $i,SV103: $i,SV32: $i,SV23: $i,SV3: $i] :
( ( ~ ( decreasing @ SV3 @ SV23 @ SV32 @ SV103 @ SV118 )
| ! [SY587: $i,SY588: $i,SY589: $i,SY590: $i] :
( ~ ( member @ SY587 @ SV23 )
| ~ ( member @ SY588 @ SV103 )
| ~ ( member @ SY589 @ SV23 )
| ~ ( member @ SY590 @ SV103 )
| ~ ( apply @ SV32 @ SY587 @ SY589 )
| ~ ( apply @ SV3 @ SY587 @ SY588 )
| ~ ( apply @ SV3 @ SY589 @ SY590 )
| ( apply @ SV118 @ SY590 @ SY588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(487,plain,
! [SV40: $i,SV55: $i] :
( ( ( ~ ( member @ ( sK43_X @ SV55 @ SV40 ) @ SV40 ) )
= $false )
| ( ( subset @ SV40 @ SV55 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[426]) ).
thf(488,plain,
! [SV40: $i,SV55: $i] :
( ( ( ~ ~ ( member @ ( sK43_X @ SV55 @ SV40 ) @ SV55 ) )
= $false )
| ( ( subset @ SV40 @ SV55 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[426]) ).
thf(489,plain,
! [SV56: $i,SV41: $i,SV119: $i] :
( ( ( ~ ( member @ SV119 @ SV41 )
| ( member @ SV119 @ SV56 ) )
= $true )
| ( ( subset @ SV41 @ SV56 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(490,plain,
! [SV57: $i,SV82: $i,SV120: $i,SV4: $i] :
( ( ( ~ ( apply @ SV4 @ SV120 @ SV82 )
| ~ ( member @ SV120 @ SV57 ) )
= $true )
| ( ( member @ SV82 @ ( image2 @ SV4 @ SV57 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(491,plain,
! [SV58: $i,SV4: $i,SV83: $i] :
( ( ( member @ SV83 @ ( image2 @ SV4 @ SV58 ) )
= $false )
| ( ( ~ ( ~ ( apply @ SV4 @ ( sK19_X @ SV83 @ SV58 @ SV4 ) @ SV83 )
| ~ ( member @ ( sK19_X @ SV83 @ SV58 @ SV4 ) @ SV58 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(492,plain,
! [SV59: $i,SV84: $i,SV5: $i] :
( ( ( ~ ( member @ SV5 @ SV84 ) )
= $true )
| ( ( member @ SV5 @ SV59 )
= $true )
| ( ( member @ SV5 @ ( difference @ SV84 @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[430]) ).
thf(493,plain,
! [SV121: $i,SV5: $i] :
( ( ! [SY591: $i] :
( ~ ( member @ SV5 @ ( difference @ SY591 @ SV121 ) )
| ( member @ SV5 @ SY591 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(494,plain,
! [SV122: $i,SV5: $i] :
( ( ! [SY592: $i] :
~ ( member @ SV5 @ ( difference @ SY592 @ SV122 ) )
| ~ ( member @ SV5 @ SV122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(495,plain,
! [SV85: $i,SV60: $i,SV6: $i] :
( ( ( member @ SV6 @ ( union @ SV60 @ SV85 ) )
= $false )
| ( ( ( member @ SV6 @ SV60 )
| ( member @ SV6 @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(496,plain,
! [SV123: $i,SV6: $i] :
( ( ~ ( member @ SV6 @ SV123 )
| ! [SY593: $i] : ( member @ SV6 @ ( union @ SV123 @ SY593 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(497,plain,
! [SV124: $i,SV6: $i] :
( ( ! [SY594: $i] :
( ~ ( member @ SV6 @ SY594 )
| ( member @ SV6 @ ( union @ SV124 @ SY594 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(498,plain,
! [SV7: $i,SV24: $i,SV33: $i,SV104: $i,SV125: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 )
| ~ ( member @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
| ~ ( member @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 ) )
| ~ ( member @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
| ~ ( apply @ SV7 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ( apply @ SV7 @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ~ ( ~ ( ~ ( apply @ SV33 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
| ~ ( apply @ SV125 @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ( ( apply @ SV33 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
| ( apply @ SV125 @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) ) ) )
| ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 )
| ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(499,plain,
! [SV33: $i,SV24: $i,SV7: $i] :
( ( ~ ! [SY432: $i,SY433: $i] :
( ~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SY432 @ SY433 )
| ! [SY434: $i,SY435: $i] :
~ ( ~ ! [SY436: $i,SY437: $i] :
( ~ ( member @ SY434 @ SV24 )
| ~ ( member @ SY435 @ SY432 )
| ~ ( member @ SY436 @ SV24 )
| ~ ( member @ SY437 @ SY432 )
| ~ ( apply @ SV7 @ SY434 @ SY435 )
| ~ ( apply @ SV7 @ SY436 @ SY437 )
| ~ ( apply @ SV33 @ SY434 @ SY436 )
| ( apply @ SY433 @ SY435 @ SY437 ) )
| ~ ! [SY438: $i,SY439: $i] :
( ~ ( member @ SY434 @ SV24 )
| ~ ( member @ SY435 @ SY432 )
| ~ ( member @ SY438 @ SV24 )
| ~ ( member @ SY439 @ SY432 )
| ~ ( apply @ SV7 @ SY434 @ SY435 )
| ~ ( apply @ SV7 @ SY438 @ SY439 )
| ~ ( apply @ SY433 @ SY435 @ SY439 )
| ( apply @ SV33 @ SY434 @ SY438 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[437]) ).
thf(500,plain,
! [SV33: $i,SV24: $i,SV7: $i] :
( ( ~ ~ ( ~ ! [SY440: $i] :
( ! [SY441: $i] :
~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SY440 @ SY441 )
| ( maps @ SV7 @ SV24 @ SY440 ) )
| ~ ! [SY442: $i] :
( ! [SY443: $i] :
~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SY442 @ SY443 )
| ( one_to_one @ SV7 @ SV24 @ SY442 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[437]) ).
thf(501,plain,
! [SV8: $i,SV25: $i,SV86: $i,SV105: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) @ SV86 )
| ~ ( member @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) @ SV105 ) )
| ~ ~ ( ~ ( ~ ( apply @ SV25 @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) )
| ~ ( apply @ SV8 @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) ) )
| ~ ( ( apply @ SV25 @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) )
| ( apply @ SV8 @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) ) ) ) ) )
= $true )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV86 @ SV105 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[438]) ).
thf(502,plain,
! [SV106: $i,SV87: $i,SV25: $i,SV8: $i] :
( ( ( ~ ( inverse_predicate @ SV8 @ SV25 @ SV87 @ SV106 ) )
= $true )
| ( ( ~ ( ~ ! [SY569: $i,SY570: $i] :
( ~ ( member @ SY569 @ SV87 )
| ~ ( member @ SY570 @ SV106 )
| ~ ( apply @ SV25 @ SY569 @ SY570 )
| ( apply @ SV8 @ SY570 @ SY569 ) )
| ~ ! [SY571: $i,SY572: $i] :
( ~ ( member @ SY571 @ SV87 )
| ~ ( member @ SY572 @ SV106 )
| ~ ( apply @ SV8 @ SY572 @ SY571 )
| ( apply @ SV25 @ SY571 @ SY572 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[439]) ).
thf(503,plain,
! [SV9: $i,SV34: $i,SV126: $i,SV26: $i,SV107: $i] :
( ( ~ ( member @ SV107 @ SV26 )
| ~ ( member @ SV126 @ SV34 )
| ~ ( apply @ SV9 @ SV107 @ SV126 )
| ( apply @ ( inverse_function @ SV9 @ SV26 @ SV34 ) @ SV126 @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(504,plain,
! [SV9: $i,SV34: $i,SV127: $i,SV26: $i,SV108: $i] :
( ( ~ ( member @ SV108 @ SV26 )
| ~ ( member @ SV127 @ SV34 )
| ~ ( apply @ ( inverse_function @ SV9 @ SV26 @ SV34 ) @ SV127 @ SV108 )
| ( apply @ SV9 @ SV108 @ SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(505,plain,
! [SV61: $i,SV128: $i,SV88: $i,SV10: $i] :
( ( ( ~ ( apply @ SV10 @ SV88 @ SV128 )
| ~ ( member @ SV128 @ SV61 ) )
= $true )
| ( ( member @ SV88 @ ( inverse_image2 @ SV10 @ SV61 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(506,plain,
! [SV62: $i,SV10: $i,SV89: $i] :
( ( ( member @ SV89 @ ( inverse_image2 @ SV10 @ SV62 ) )
= $false )
| ( ( ~ ( ~ ( apply @ SV10 @ SV89 @ ( sK17_Y @ SV89 @ SV62 @ SV10 ) )
| ~ ( member @ ( sK17_Y @ SV89 @ SV62 @ SV10 ) @ SV62 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(507,plain,
! [SV11: $i,SV63: $i,SV90: $i] :
( ( ( ~ ( member @ ( sK23_Y @ SV90 @ SV63 @ SV11 ) @ SV90 )
| ~ ! [SY548: $i] :
( ~ ( apply @ SV11 @ SY548 @ ( sK23_Y @ SV90 @ SV63 @ SV11 ) )
| ~ ( member @ SY548 @ SV63 ) ) )
= $false )
| ( ( surjective @ SV11 @ SV63 @ SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(508,plain,
! [SV91: $i,SV64: $i,SV11: $i] :
( ( ( surjective @ SV11 @ SV64 @ SV91 )
= $false )
| ( ( ! [SY549: $i] :
( ~ ( member @ SY549 @ SV91 )
| ~ ( ~ ( apply @ SV11 @ ( sK22_E @ SY549 @ SV91 @ SV64 @ SV11 ) @ SY549 )
| ~ ( member @ ( sK22_E @ SY549 @ SV91 @ SV64 @ SV11 ) @ SV64 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(509,plain,
! [SV92: $i,SV27: $i,SV109: $i,SV12: $i] :
( ( ( ! [SY575: $i] :
( ~ ( apply @ SV12 @ SV109 @ SY575 )
| ~ ( member @ SY575 @ SV27 ) )
| ~ ( member @ SV109 @ SV92 ) )
= $true )
| ( ( member @ SV109 @ ( inverse_image3 @ SV12 @ SV27 @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[446]) ).
thf(510,plain,
! [SV27: $i,SV12: $i] :
( ( ! [SY382: $i,SY383: $i] :
( ~ ( member @ SY383 @ ( inverse_image3 @ SV12 @ SV27 @ SY382 ) )
| ~ ( ~ ( apply @ SV12 @ SY383 @ ( sK16_Y @ SY383 @ SY382 @ SV27 @ SV12 ) )
| ~ ( member @ ( sK16_Y @ SY383 @ SY382 @ SV27 @ SV12 ) @ SV27 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[447]) ).
thf(511,plain,
! [SV27: $i,SV12: $i] :
( ( ! [SY384: $i,SY385: $i] :
( ~ ( member @ SY385 @ ( inverse_image3 @ SV12 @ SV27 @ SY384 ) )
| ( member @ SY385 @ SY384 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[448]) ).
thf(512,plain,
! [SV13: $i,SV28: $i,SV93: $i,SV110: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ SV93 )
| ~ ( member @ ( sK29_SY162 @ SV110 @ SV93 @ SV28 @ SV13 ) @ SV110 ) )
| ~ ( member @ ( sK30_SY164 @ SV110 @ SV93 @ SV28 @ SV13 ) @ SV110 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV13 @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ ( sK29_SY162 @ SV110 @ SV93 @ SV28 @ SV13 ) )
| ~ ( apply @ SV28 @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ ( sK30_SY164 @ SV110 @ SV93 @ SV28 @ SV13 ) ) )
| ~ ( ( ( sK29_SY162 @ SV110 @ SV93 @ SV28 @ SV13 )
!= ( sK30_SY164 @ SV110 @ SV93 @ SV28 @ SV13 ) ) ) ) ) )
= $true )
| ( ( equal_maps @ SV13 @ SV28 @ SV93 @ SV110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[449]) ).
thf(513,plain,
! [SV111: $i,SV94: $i,SV28: $i,SV13: $i] :
( ( ( ~ ( equal_maps @ SV13 @ SV28 @ SV94 @ SV111 ) )
= $true )
| ( ( ! [SY576: $i,SY577: $i,SY578: $i] :
( ~ ( member @ SY576 @ SV94 )
| ~ ( member @ SY577 @ SV111 )
| ~ ( member @ SY578 @ SV111 )
| ~ ( apply @ SV13 @ SY576 @ SY577 )
| ~ ( apply @ SV28 @ SY576 @ SY578 )
| ( SY577 = SY578 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[450]) ).
thf(514,plain,
! [SV14: $i,SV29: $i,SV35: $i,SV42: $i,SV129: $i] :
( ( ! [SY595: $i] :
( ~ ( ~ ~ ( ~ ( member @ ( sK33_X @ SY595 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV42 )
| ~ ( member @ ( sK34_SY165 @ SY595 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY595 ) )
| ~ ~ ( ~ ( ! [SY596: $i] :
( ~ ( apply @ SV35 @ ( sK33_X @ SY595 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY596 )
| ~ ( member @ SY596 @ SV129 )
| ~ ( apply @ SV29 @ SY596 @ ( sK34_SY165 @ SY595 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ~ ( apply @ SV14 @ ( sK33_X @ SY595 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SY595 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( apply @ SV35 @ ( sK33_X @ SY595 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK35_SY169 @ SY595 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK35_SY169 @ SY595 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV129 ) )
| ~ ( apply @ SV29 @ ( sK35_SY169 @ SY595 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SY595 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ( apply @ SV14 @ ( sK33_X @ SY595 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SY595 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) ) ) )
| ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SY595 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(515,plain,
! [SV130: $i,SV42: $i,SV35: $i,SV29: $i,SV14: $i] :
( ( ! [SY597: $i] :
( ~ ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SY597 )
| ~ ( ~ ! [SY598: $i,SY599: $i] :
( ~ ( member @ SY598 @ SV42 )
| ~ ( member @ SY599 @ SY597 )
| ! [SY600: $i] :
( ~ ( apply @ SV35 @ SY598 @ SY600 )
| ~ ( member @ SY600 @ SV130 )
| ~ ( apply @ SV29 @ SY600 @ SY599 ) )
| ( apply @ SV14 @ SY598 @ SY599 ) )
| ~ ! [SY601: $i,SY602: $i] :
( ~ ( member @ SY601 @ SV42 )
| ~ ( member @ SY602 @ SY597 )
| ~ ( apply @ SV14 @ SY601 @ SY602 )
| ~ ( ~ ~ ( ~ ( apply @ SV35 @ SY601 @ ( sK32_Y @ SY602 @ SY601 @ SY597 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK32_Y @ SY602 @ SY601 @ SY597 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV130 ) )
| ~ ( apply @ SV29 @ ( sK32_Y @ SY602 @ SY601 @ SY597 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY602 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(516,plain,
! [SV15: $i,SV67: $i,SV95: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK24_X1 @ SV95 @ SV67 @ SV15 ) @ SV67 )
| ~ ( member @ ( sK25_SY159 @ SV95 @ SV67 @ SV15 ) @ SV67 ) )
| ~ ( member @ ( sK26_SY161 @ SV95 @ SV67 @ SV15 ) @ SV95 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV15 @ ( sK24_X1 @ SV95 @ SV67 @ SV15 ) @ ( sK26_SY161 @ SV95 @ SV67 @ SV15 ) )
| ~ ( apply @ SV15 @ ( sK25_SY159 @ SV95 @ SV67 @ SV15 ) @ ( sK26_SY161 @ SV95 @ SV67 @ SV15 ) ) )
| ~ ( ( ( sK24_X1 @ SV95 @ SV67 @ SV15 )
!= ( sK25_SY159 @ SV95 @ SV67 @ SV15 ) ) ) ) )
= $false )
| ( ( injective @ SV15 @ SV67 @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(517,plain,
! [SV96: $i,SV68: $i,SV15: $i] :
( ( ( injective @ SV15 @ SV68 @ SV96 )
= $false )
| ( ( ! [SY557: $i,SY558: $i,SY559: $i] :
( ~ ( member @ SY557 @ SV68 )
| ~ ( member @ SY558 @ SV68 )
| ~ ( member @ SY559 @ SV96 )
| ~ ( apply @ SV15 @ SY557 @ SY559 )
| ~ ( apply @ SV15 @ SY558 @ SY559 )
| ( SY557 = SY558 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(518,plain,
! [SV69: $i,SV45: $i] :
( ( ( subset @ SV45 @ SV69 )
= $false )
| ( ( ~ ( subset @ SV69 @ SV45 ) )
= $true )
| ( ( equal_set @ SV45 @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(519,plain,
! [SV131: $i,SV112: $i] :
( ( ~ ( equal_set @ SV112 @ SV131 )
| ( subset @ SV112 @ SV131 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(520,plain,
! [SV132: $i,SV113: $i] :
( ( ~ ( equal_set @ SV113 @ SV132 )
| ( subset @ SV132 @ SV113 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(521,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 )
| ~ ( member @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( member @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 ) )
| ~ ( member @ ( sK15_SY156 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( apply @ SV36 @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ( apply @ SV16 @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ( apply @ SV16 @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK15_SY156 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ~ ( apply @ SV133 @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK15_SY156 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
| ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(522,plain,
! [SV134: $i,SV115: $i,SV36: $i,SV30: $i,SV16: $i] :
( ( ~ ( increasing @ SV16 @ SV30 @ SV36 @ SV115 @ SV134 )
| ! [SY603: $i,SY604: $i,SY605: $i,SY606: $i] :
( ~ ( member @ SY603 @ SV30 )
| ~ ( member @ SY604 @ SV115 )
| ~ ( member @ SY605 @ SV30 )
| ~ ( member @ SY606 @ SV115 )
| ~ ( apply @ SV36 @ SY603 @ SY605 )
| ~ ( apply @ SV16 @ SY603 @ SY604 )
| ~ ( apply @ SV16 @ SY605 @ SY606 )
| ( apply @ SV134 @ SY604 @ SY606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(523,plain,
! [SV97: $i,SV70: $i,SV17: $i] :
( ( ( ~ ( member @ SV17 @ SV70 ) )
= $true )
| ( ( ~ ( member @ SV17 @ SV97 ) )
= $true )
| ( ( member @ SV17 @ ( intersection @ SV70 @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(524,plain,
! [SV135: $i,SV17: $i] :
( ( ! [SY607: $i] :
~ ( member @ SV17 @ ( intersection @ SV135 @ SY607 ) )
| ( member @ SV17 @ SV135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(525,plain,
! [SV136: $i,SV17: $i] :
( ( ! [SY608: $i] :
( ~ ( member @ SV17 @ ( intersection @ SV136 @ SY608 ) )
| ( member @ SV17 @ SY608 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(526,plain,
! [SV98: $i,SV71: $i,SV18: $i] :
( ( ( member @ SV18 @ ( unordered_pair @ SV71 @ SV98 ) )
= $false )
| ( ( ( SV18 = SV71 )
| ( SV18 = SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(527,plain,
! [SV137: $i,SV18: $i] :
( ( ( SV18 != SV137 )
| ! [SY609: $i] : ( member @ SV18 @ ( unordered_pair @ SV137 @ SY609 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(528,plain,
! [SV138: $i,SV18: $i] :
( ( ! [SY610: $i] :
( ( SV18 != SY610 )
| ( member @ SV18 @ ( unordered_pair @ SV138 @ SY610 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(529,plain,
! [SV99: $i,SV72: $i,SV19: $i] :
( ( ( ~ ( injective @ SV19 @ SV72 @ SV99 ) )
= $true )
| ( ( ~ ( surjective @ SV19 @ SV72 @ SV99 ) )
= $true )
| ( ( one_to_one @ SV19 @ SV72 @ SV99 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[468]) ).
thf(530,plain,
! [SV139: $i,SV19: $i] :
( ( ! [SY611: $i] :
( ~ ( one_to_one @ SV19 @ SV139 @ SY611 )
| ( injective @ SV19 @ SV139 @ SY611 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(531,plain,
! [SV140: $i,SV19: $i] :
( ( ! [SY612: $i] :
( ~ ( one_to_one @ SV19 @ SV140 @ SY612 )
| ( surjective @ SV19 @ SV140 @ SY612 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(532,plain,
! [SV20: $i,SV46: $i,SV31: $i,SV73: $i,SV37: $i] :
( ( ! [SY528: $i,SY529: $i] :
( ~ ( member @ SY528 @ SV37 )
| ~ ( member @ SY529 @ SV73 )
| ! [SY495: $i] :
( ~ ( apply @ SV31 @ SY528 @ SY495 )
| ~ ( member @ SY495 @ SV46 )
| ~ ( apply @ SV20 @ SY495 @ SY529 ) )
| ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SY528 @ SY529 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[471]) ).
thf(533,plain,
! [SV46: $i,SV31: $i,SV20: $i,SV73: $i,SV37: $i] :
( ( ! [SY531: $i,SY532: $i] :
( ~ ( member @ SY531 @ SV37 )
| ~ ( member @ SY532 @ SV73 )
| ~ ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SY531 @ SY532 )
| ~ ( ~ ~ ( ~ ( apply @ SV31 @ SY531 @ ( sK31_Y @ SY532 @ SY531 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) )
| ~ ( member @ ( sK31_Y @ SY532 @ SY531 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SV46 ) )
| ~ ( apply @ SV20 @ ( sK31_Y @ SY532 @ SY531 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SY532 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[472]) ).
thf(534,plain,
! [SV47: $i,SV74: $i,SV116: $i] :
( ( ( ~ ( member @ SV116 @ SV74 ) )
= $true )
| ( ( ~ ( member @ SV47 @ SV116 ) )
= $true )
| ( ( member @ SV47 @ ( sum @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(535,plain,
! [SV48: $i,SV75: $i] :
( ( ( ~ ( member @ ( sK42_Y @ SV75 @ SV48 ) @ SV75 )
| ~ ( member @ SV48 @ ( sK42_Y @ SV75 @ SV48 ) ) )
= $false )
| ( ( member @ SV48 @ ( sum @ SV75 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(536,plain,
! [SV49: $i,SV76: $i] :
( ( ( ~ ( member @ ( sK41_Y @ SV76 @ SV49 ) @ SV76 ) )
= $false )
| ( ( member @ SV49 @ ( product @ SV76 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[475]) ).
thf(537,plain,
! [SV76: $i,SV49: $i] :
( ( ( ~ ~ ( member @ SV49 @ ( sK41_Y @ SV76 @ SV49 ) ) )
= $false )
| ( ( member @ SV49 @ ( product @ SV76 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[475]) ).
thf(538,plain,
! [SV50: $i,SV77: $i,SV141: $i] :
( ( ( ~ ( member @ SV141 @ SV77 )
| ( member @ SV50 @ SV141 ) )
= $true )
| ( ( member @ SV50 @ ( product @ SV77 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(539,plain,
! [SV21: $i,SV78: $i,SV100: $i] :
( ( ( ~ ( ~ ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
| ~ ! [SY560: $i] :
( ~ ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SY560 )
| ~ ( member @ SY560 @ SV100 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
| ~ ( member @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ( member @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) )
| ~ ( ( ( sK38_SY170 @ SV100 @ SV78 @ SV21 )
!= ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) ) ) ) )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[477]) ).
thf(540,plain,
! [SV142: $i,SV21: $i] :
( ( ! [SY613: $i] :
( ~ ( maps @ SV21 @ SV142 @ SY613 )
| ! [SY614: $i] :
( ~ ( member @ SY614 @ SV142 )
| ~ ( ~ ( apply @ SV21 @ SY614 @ ( sK36_Y @ SY614 @ SY613 @ SV142 @ SV21 ) )
| ~ ( member @ ( sK36_Y @ SY614 @ SY613 @ SV142 @ SV21 ) @ SY613 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(541,plain,
! [SV143: $i,SV21: $i] :
( ( ! [SY615: $i] :
( ~ ( maps @ SV21 @ SV143 @ SY615 )
| ! [SY616: $i,SY617: $i,SY618: $i] :
( ~ ( member @ SY616 @ SV143 )
| ~ ( member @ SY617 @ SY615 )
| ~ ( member @ SY618 @ SY615 )
| ~ ( apply @ SV21 @ SY616 @ SY617 )
| ~ ( apply @ SV21 @ SY616 @ SY618 )
| ( SY617 = SY618 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(542,plain,
! [SV51: $i,SV79: $i] :
( ( ( ~ ( member @ ( sK27_X @ SV79 @ SV51 ) @ SV79 ) )
= $false )
| ( ( identity @ SV51 @ SV79 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[480]) ).
thf(543,plain,
! [SV79: $i,SV51: $i] :
( ( ( ~ ~ ( apply @ SV51 @ ( sK27_X @ SV79 @ SV51 ) @ ( sK27_X @ SV79 @ SV51 ) ) )
= $false )
| ( ( identity @ SV51 @ SV79 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[480]) ).
thf(544,plain,
! [SV52: $i,SV80: $i,SV144: $i] :
( ( ( ~ ( member @ SV144 @ SV80 )
| ( apply @ SV52 @ SV144 @ SV144 ) )
= $true )
| ( ( identity @ SV52 @ SV80 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(545,plain,
! [SV81: $i,SV22: $i,SV101: $i,SV2: $i] :
( ( ( ! [SY561: $i] :
( ~ ( apply @ SV2 @ SY561 @ SV101 )
| ~ ( member @ SY561 @ SV22 ) ) )
= $true )
| ( ( ~ ( member @ SV101 @ SV81 ) )
= $true )
| ( ( member @ SV101 @ ( image3 @ SV2 @ SV22 @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[482]) ).
thf(546,plain,
! [SV145: $i,SV22: $i,SV2: $i] :
( ( ! [SY619: $i] :
( ~ ( member @ SY619 @ ( image3 @ SV2 @ SV22 @ SV145 ) )
| ~ ( ~ ( apply @ SV2 @ ( sK18_X @ SY619 @ SV145 @ SV22 @ SV2 ) @ SY619 )
| ~ ( member @ ( sK18_X @ SY619 @ SV145 @ SV22 @ SV2 ) @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(547,plain,
! [SV146: $i,SV22: $i,SV2: $i] :
( ( ! [SY620: $i] :
( ~ ( member @ SY620 @ ( image3 @ SV2 @ SV22 @ SV146 ) )
| ( member @ SY620 @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(548,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 )
| ~ ( member @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( member @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 ) )
| ~ ( member @ ( sK11_SY150 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( apply @ SV32 @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ( apply @ SV3 @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ( apply @ SV3 @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK11_SY150 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ~ ( apply @ SV117 @ ( sK11_SY150 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) ) )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[485]) ).
thf(549,plain,
! [SV118: $i,SV103: $i,SV32: $i,SV23: $i,SV3: $i] :
( ( ( ~ ( decreasing @ SV3 @ SV23 @ SV32 @ SV103 @ SV118 ) )
= $true )
| ( ( ! [SY587: $i,SY588: $i,SY589: $i,SY590: $i] :
( ~ ( member @ SY587 @ SV23 )
| ~ ( member @ SY588 @ SV103 )
| ~ ( member @ SY589 @ SV23 )
| ~ ( member @ SY590 @ SV103 )
| ~ ( apply @ SV32 @ SY587 @ SY589 )
| ~ ( apply @ SV3 @ SY587 @ SY588 )
| ~ ( apply @ SV3 @ SY589 @ SY590 )
| ( apply @ SV118 @ SY590 @ SY588 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[486]) ).
thf(550,plain,
! [SV40: $i,SV55: $i] :
( ( ( member @ ( sK43_X @ SV55 @ SV40 ) @ SV40 )
= $true )
| ( ( subset @ SV40 @ SV55 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[487]) ).
thf(551,plain,
! [SV40: $i,SV55: $i] :
( ( ( ~ ( member @ ( sK43_X @ SV55 @ SV40 ) @ SV55 ) )
= $true )
| ( ( subset @ SV40 @ SV55 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[488]) ).
thf(552,plain,
! [SV56: $i,SV41: $i,SV119: $i] :
( ( ( ~ ( member @ SV119 @ SV41 ) )
= $true )
| ( ( member @ SV119 @ SV56 )
= $true )
| ( ( subset @ SV41 @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[489]) ).
thf(553,plain,
! [SV57: $i,SV82: $i,SV120: $i,SV4: $i] :
( ( ( ~ ( apply @ SV4 @ SV120 @ SV82 ) )
= $true )
| ( ( ~ ( member @ SV120 @ SV57 ) )
= $true )
| ( ( member @ SV82 @ ( image2 @ SV4 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[490]) ).
thf(554,plain,
! [SV58: $i,SV83: $i,SV4: $i] :
( ( ( ~ ( apply @ SV4 @ ( sK19_X @ SV83 @ SV58 @ SV4 ) @ SV83 )
| ~ ( member @ ( sK19_X @ SV83 @ SV58 @ SV4 ) @ SV58 ) )
= $false )
| ( ( member @ SV83 @ ( image2 @ SV4 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(555,plain,
! [SV59: $i,SV84: $i,SV5: $i] :
( ( ( member @ SV5 @ SV84 )
= $false )
| ( ( member @ SV5 @ SV59 )
= $true )
| ( ( member @ SV5 @ ( difference @ SV84 @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[492]) ).
thf(556,plain,
! [SV121: $i,SV147: $i,SV5: $i] :
( ( ~ ( member @ SV5 @ ( difference @ SV147 @ SV121 ) )
| ( member @ SV5 @ SV147 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(557,plain,
! [SV122: $i,SV5: $i] :
( ( ( ! [SY592: $i] :
~ ( member @ SV5 @ ( difference @ SY592 @ SV122 ) ) )
= $true )
| ( ( ~ ( member @ SV5 @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[494]) ).
thf(558,plain,
! [SV85: $i,SV60: $i,SV6: $i] :
( ( ( member @ SV6 @ SV60 )
= $true )
| ( ( member @ SV6 @ SV85 )
= $true )
| ( ( member @ SV6 @ ( union @ SV60 @ SV85 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[495]) ).
thf(559,plain,
! [SV123: $i,SV6: $i] :
( ( ( ~ ( member @ SV6 @ SV123 ) )
= $true )
| ( ( ! [SY593: $i] : ( member @ SV6 @ ( union @ SV123 @ SY593 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[496]) ).
thf(560,plain,
! [SV124: $i,SV148: $i,SV6: $i] :
( ( ~ ( member @ SV6 @ SV148 )
| ( member @ SV6 @ ( union @ SV124 @ SV148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(561,plain,
! [SV7: $i,SV24: $i,SV33: $i,SV104: $i,SV125: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 )
| ~ ( member @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
| ~ ( member @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 ) )
| ~ ( member @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
| ~ ( apply @ SV7 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ( apply @ SV7 @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ~ ( ~ ( ~ ( apply @ SV33 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
| ~ ( apply @ SV125 @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ( ( apply @ SV33 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
| ( apply @ SV125 @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) ) ) )
| ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[498]) ).
thf(562,plain,
! [SV33: $i,SV24: $i,SV7: $i] :
( ( ! [SY432: $i,SY433: $i] :
( ~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SY432 @ SY433 )
| ! [SY434: $i,SY435: $i] :
~ ( ~ ! [SY436: $i,SY437: $i] :
( ~ ( member @ SY434 @ SV24 )
| ~ ( member @ SY435 @ SY432 )
| ~ ( member @ SY436 @ SV24 )
| ~ ( member @ SY437 @ SY432 )
| ~ ( apply @ SV7 @ SY434 @ SY435 )
| ~ ( apply @ SV7 @ SY436 @ SY437 )
| ~ ( apply @ SV33 @ SY434 @ SY436 )
| ( apply @ SY433 @ SY435 @ SY437 ) )
| ~ ! [SY438: $i,SY439: $i] :
( ~ ( member @ SY434 @ SV24 )
| ~ ( member @ SY435 @ SY432 )
| ~ ( member @ SY438 @ SV24 )
| ~ ( member @ SY439 @ SY432 )
| ~ ( apply @ SV7 @ SY434 @ SY435 )
| ~ ( apply @ SV7 @ SY438 @ SY439 )
| ~ ( apply @ SY433 @ SY435 @ SY439 )
| ( apply @ SV33 @ SY434 @ SY438 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[499]) ).
thf(563,plain,
! [SV33: $i,SV24: $i,SV7: $i] :
( ( ~ ( ~ ! [SY440: $i] :
( ! [SY441: $i] :
~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SY440 @ SY441 )
| ( maps @ SV7 @ SV24 @ SY440 ) )
| ~ ! [SY442: $i] :
( ! [SY443: $i] :
~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SY442 @ SY443 )
| ( one_to_one @ SV7 @ SV24 @ SY442 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[500]) ).
thf(564,plain,
! [SV8: $i,SV25: $i,SV86: $i,SV105: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) @ SV86 )
| ~ ( member @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) @ SV105 ) )
| ~ ~ ( ~ ( ~ ( apply @ SV25 @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) )
| ~ ( apply @ SV8 @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) ) )
| ~ ( ( apply @ SV25 @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) )
| ( apply @ SV8 @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) ) ) ) )
= $false )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV86 @ SV105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(565,plain,
! [SV106: $i,SV87: $i,SV25: $i,SV8: $i] :
( ( ( inverse_predicate @ SV8 @ SV25 @ SV87 @ SV106 )
= $false )
| ( ( ~ ( ~ ! [SY569: $i,SY570: $i] :
( ~ ( member @ SY569 @ SV87 )
| ~ ( member @ SY570 @ SV106 )
| ~ ( apply @ SV25 @ SY569 @ SY570 )
| ( apply @ SV8 @ SY570 @ SY569 ) )
| ~ ! [SY571: $i,SY572: $i] :
( ~ ( member @ SY571 @ SV87 )
| ~ ( member @ SY572 @ SV106 )
| ~ ( apply @ SV8 @ SY572 @ SY571 )
| ( apply @ SV25 @ SY571 @ SY572 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(566,plain,
! [SV9: $i,SV34: $i,SV126: $i,SV26: $i,SV107: $i] :
( ( ( ~ ( member @ SV107 @ SV26 )
| ~ ( member @ SV126 @ SV34 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV107 @ SV126 )
| ( apply @ ( inverse_function @ SV9 @ SV26 @ SV34 ) @ SV126 @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[503]) ).
thf(567,plain,
! [SV9: $i,SV34: $i,SV127: $i,SV26: $i,SV108: $i] :
( ( ( ~ ( member @ SV108 @ SV26 )
| ~ ( member @ SV127 @ SV34 ) )
= $true )
| ( ( ~ ( apply @ ( inverse_function @ SV9 @ SV26 @ SV34 ) @ SV127 @ SV108 )
| ( apply @ SV9 @ SV108 @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[504]) ).
thf(568,plain,
! [SV61: $i,SV128: $i,SV88: $i,SV10: $i] :
( ( ( ~ ( apply @ SV10 @ SV88 @ SV128 ) )
= $true )
| ( ( ~ ( member @ SV128 @ SV61 ) )
= $true )
| ( ( member @ SV88 @ ( inverse_image2 @ SV10 @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[505]) ).
thf(569,plain,
! [SV62: $i,SV89: $i,SV10: $i] :
( ( ( ~ ( apply @ SV10 @ SV89 @ ( sK17_Y @ SV89 @ SV62 @ SV10 ) )
| ~ ( member @ ( sK17_Y @ SV89 @ SV62 @ SV10 ) @ SV62 ) )
= $false )
| ( ( member @ SV89 @ ( inverse_image2 @ SV10 @ SV62 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[506]) ).
thf(570,plain,
! [SV11: $i,SV63: $i,SV90: $i] :
( ( ( ~ ( member @ ( sK23_Y @ SV90 @ SV63 @ SV11 ) @ SV90 ) )
= $false )
| ( ( surjective @ SV11 @ SV63 @ SV90 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[507]) ).
thf(571,plain,
! [SV63: $i,SV90: $i,SV11: $i] :
( ( ( ~ ! [SY548: $i] :
( ~ ( apply @ SV11 @ SY548 @ ( sK23_Y @ SV90 @ SV63 @ SV11 ) )
| ~ ( member @ SY548 @ SV63 ) ) )
= $false )
| ( ( surjective @ SV11 @ SV63 @ SV90 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[507]) ).
thf(572,plain,
! [SV64: $i,SV11: $i,SV91: $i,SV149: $i] :
( ( ( ~ ( member @ SV149 @ SV91 )
| ~ ( ~ ( apply @ SV11 @ ( sK22_E @ SV149 @ SV91 @ SV64 @ SV11 ) @ SV149 )
| ~ ( member @ ( sK22_E @ SV149 @ SV91 @ SV64 @ SV11 ) @ SV64 ) ) )
= $true )
| ( ( surjective @ SV11 @ SV64 @ SV91 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(573,plain,
! [SV92: $i,SV27: $i,SV109: $i,SV12: $i] :
( ( ( ! [SY575: $i] :
( ~ ( apply @ SV12 @ SV109 @ SY575 )
| ~ ( member @ SY575 @ SV27 ) ) )
= $true )
| ( ( ~ ( member @ SV109 @ SV92 ) )
= $true )
| ( ( member @ SV109 @ ( inverse_image3 @ SV12 @ SV27 @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[509]) ).
thf(574,plain,
! [SV150: $i,SV27: $i,SV12: $i] :
( ( ! [SY621: $i] :
( ~ ( member @ SY621 @ ( inverse_image3 @ SV12 @ SV27 @ SV150 ) )
| ~ ( ~ ( apply @ SV12 @ SY621 @ ( sK16_Y @ SY621 @ SV150 @ SV27 @ SV12 ) )
| ~ ( member @ ( sK16_Y @ SY621 @ SV150 @ SV27 @ SV12 ) @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(575,plain,
! [SV151: $i,SV27: $i,SV12: $i] :
( ( ! [SY622: $i] :
( ~ ( member @ SY622 @ ( inverse_image3 @ SV12 @ SV27 @ SV151 ) )
| ( member @ SY622 @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(576,plain,
! [SV13: $i,SV28: $i,SV93: $i,SV110: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ SV93 )
| ~ ( member @ ( sK29_SY162 @ SV110 @ SV93 @ SV28 @ SV13 ) @ SV110 ) )
| ~ ( member @ ( sK30_SY164 @ SV110 @ SV93 @ SV28 @ SV13 ) @ SV110 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV13 @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ ( sK29_SY162 @ SV110 @ SV93 @ SV28 @ SV13 ) )
| ~ ( apply @ SV28 @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ ( sK30_SY164 @ SV110 @ SV93 @ SV28 @ SV13 ) ) )
| ~ ( ( ( sK29_SY162 @ SV110 @ SV93 @ SV28 @ SV13 )
!= ( sK30_SY164 @ SV110 @ SV93 @ SV28 @ SV13 ) ) ) ) )
= $false )
| ( ( equal_maps @ SV13 @ SV28 @ SV93 @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(577,plain,
! [SV111: $i,SV94: $i,SV28: $i,SV13: $i] :
( ( ( equal_maps @ SV13 @ SV28 @ SV94 @ SV111 )
= $false )
| ( ( ! [SY576: $i,SY577: $i,SY578: $i] :
( ~ ( member @ SY576 @ SV94 )
| ~ ( member @ SY577 @ SV111 )
| ~ ( member @ SY578 @ SV111 )
| ~ ( apply @ SV13 @ SY576 @ SY577 )
| ~ ( apply @ SV28 @ SY576 @ SY578 )
| ( SY577 = SY578 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[513]) ).
thf(578,plain,
! [SV14: $i,SV29: $i,SV35: $i,SV42: $i,SV129: $i,SV152: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV42 )
| ~ ( member @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV152 ) )
| ~ ~ ( ~ ( ! [SY623: $i] :
( ~ ( apply @ SV35 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY623 )
| ~ ( member @ SY623 @ SV129 )
| ~ ( apply @ SV29 @ SY623 @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ~ ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( apply @ SV35 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV129 ) )
| ~ ( apply @ SV29 @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) ) ) )
| ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(579,plain,
! [SV153: $i,SV130: $i,SV42: $i,SV35: $i,SV29: $i,SV14: $i] :
( ( ~ ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
| ~ ( ~ ! [SY624: $i,SY625: $i] :
( ~ ( member @ SY624 @ SV42 )
| ~ ( member @ SY625 @ SV153 )
| ! [SY600: $i] :
( ~ ( apply @ SV35 @ SY624 @ SY600 )
| ~ ( member @ SY600 @ SV130 )
| ~ ( apply @ SV29 @ SY600 @ SY625 ) )
| ( apply @ SV14 @ SY624 @ SY625 ) )
| ~ ! [SY627: $i,SY628: $i] :
( ~ ( member @ SY627 @ SV42 )
| ~ ( member @ SY628 @ SV153 )
| ~ ( apply @ SV14 @ SY627 @ SY628 )
| ~ ( ~ ~ ( ~ ( apply @ SV35 @ SY627 @ ( sK32_Y @ SY628 @ SY627 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK32_Y @ SY628 @ SY627 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV130 ) )
| ~ ( apply @ SV29 @ ( sK32_Y @ SY628 @ SY627 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY628 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(580,plain,
! [SV15: $i,SV67: $i,SV95: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK24_X1 @ SV95 @ SV67 @ SV15 ) @ SV67 )
| ~ ( member @ ( sK25_SY159 @ SV95 @ SV67 @ SV15 ) @ SV67 ) )
| ~ ( member @ ( sK26_SY161 @ SV95 @ SV67 @ SV15 ) @ SV95 ) ) )
= $false )
| ( ( injective @ SV15 @ SV67 @ SV95 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[516]) ).
thf(581,plain,
! [SV67: $i,SV95: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( apply @ SV15 @ ( sK24_X1 @ SV95 @ SV67 @ SV15 ) @ ( sK26_SY161 @ SV95 @ SV67 @ SV15 ) )
| ~ ( apply @ SV15 @ ( sK25_SY159 @ SV95 @ SV67 @ SV15 ) @ ( sK26_SY161 @ SV95 @ SV67 @ SV15 ) ) )
| ~ ( ( ( sK24_X1 @ SV95 @ SV67 @ SV15 )
!= ( sK25_SY159 @ SV95 @ SV67 @ SV15 ) ) ) ) )
= $false )
| ( ( injective @ SV15 @ SV67 @ SV95 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[516]) ).
thf(582,plain,
! [SV15: $i,SV96: $i,SV68: $i,SV154: $i] :
( ( ( ! [SY629: $i,SY630: $i] :
( ~ ( member @ SV154 @ SV68 )
| ~ ( member @ SY629 @ SV68 )
| ~ ( member @ SY630 @ SV96 )
| ~ ( apply @ SV15 @ SV154 @ SY630 )
| ~ ( apply @ SV15 @ SY629 @ SY630 )
| ( SV154 = SY629 ) ) )
= $true )
| ( ( injective @ SV15 @ SV68 @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(583,plain,
! [SV45: $i,SV69: $i] :
( ( ( subset @ SV69 @ SV45 )
= $false )
| ( ( subset @ SV45 @ SV69 )
= $false )
| ( ( equal_set @ SV45 @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(584,plain,
! [SV131: $i,SV112: $i] :
( ( ( ~ ( equal_set @ SV112 @ SV131 ) )
= $true )
| ( ( subset @ SV112 @ SV131 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[519]) ).
thf(585,plain,
! [SV132: $i,SV113: $i] :
( ( ( ~ ( equal_set @ SV113 @ SV132 ) )
= $true )
| ( ( subset @ SV132 @ SV113 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[520]) ).
thf(586,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 )
| ~ ( member @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( member @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 ) )
| ~ ( member @ ( sK15_SY156 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( apply @ SV36 @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ( apply @ SV16 @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ( apply @ SV16 @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK15_SY156 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ~ ( apply @ SV133 @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK15_SY156 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) ) )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[521]) ).
thf(587,plain,
! [SV134: $i,SV115: $i,SV36: $i,SV30: $i,SV16: $i] :
( ( ( ~ ( increasing @ SV16 @ SV30 @ SV36 @ SV115 @ SV134 ) )
= $true )
| ( ( ! [SY603: $i,SY604: $i,SY605: $i,SY606: $i] :
( ~ ( member @ SY603 @ SV30 )
| ~ ( member @ SY604 @ SV115 )
| ~ ( member @ SY605 @ SV30 )
| ~ ( member @ SY606 @ SV115 )
| ~ ( apply @ SV36 @ SY603 @ SY605 )
| ~ ( apply @ SV16 @ SY603 @ SY604 )
| ~ ( apply @ SV16 @ SY605 @ SY606 )
| ( apply @ SV134 @ SY604 @ SY606 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[522]) ).
thf(588,plain,
! [SV97: $i,SV70: $i,SV17: $i] :
( ( ( member @ SV17 @ SV70 )
= $false )
| ( ( ~ ( member @ SV17 @ SV97 ) )
= $true )
| ( ( member @ SV17 @ ( intersection @ SV70 @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(589,plain,
! [SV135: $i,SV17: $i] :
( ( ( ! [SY607: $i] :
~ ( member @ SV17 @ ( intersection @ SV135 @ SY607 ) ) )
= $true )
| ( ( member @ SV17 @ SV135 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[524]) ).
thf(590,plain,
! [SV155: $i,SV136: $i,SV17: $i] :
( ( ~ ( member @ SV17 @ ( intersection @ SV136 @ SV155 ) )
| ( member @ SV17 @ SV155 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(591,plain,
! [SV98: $i,SV71: $i,SV18: $i] :
( ( ( SV18 = SV71 )
= $true )
| ( ( SV18 = SV98 )
= $true )
| ( ( member @ SV18 @ ( unordered_pair @ SV71 @ SV98 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[526]) ).
thf(592,plain,
! [SV137: $i,SV18: $i] :
( ( ( ( SV18 != SV137 ) )
= $true )
| ( ( ! [SY609: $i] : ( member @ SV18 @ ( unordered_pair @ SV137 @ SY609 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[527]) ).
thf(593,plain,
! [SV138: $i,SV156: $i,SV18: $i] :
( ( ( SV18 != SV156 )
| ( member @ SV18 @ ( unordered_pair @ SV138 @ SV156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(594,plain,
! [SV99: $i,SV72: $i,SV19: $i] :
( ( ( injective @ SV19 @ SV72 @ SV99 )
= $false )
| ( ( ~ ( surjective @ SV19 @ SV72 @ SV99 ) )
= $true )
| ( ( one_to_one @ SV19 @ SV72 @ SV99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(595,plain,
! [SV157: $i,SV139: $i,SV19: $i] :
( ( ~ ( one_to_one @ SV19 @ SV139 @ SV157 )
| ( injective @ SV19 @ SV139 @ SV157 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(596,plain,
! [SV158: $i,SV140: $i,SV19: $i] :
( ( ~ ( one_to_one @ SV19 @ SV140 @ SV158 )
| ( surjective @ SV19 @ SV140 @ SV158 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(597,plain,
! [SV20: $i,SV46: $i,SV31: $i,SV73: $i,SV37: $i,SV159: $i] :
( ( ! [SY631: $i] :
( ~ ( member @ SV159 @ SV37 )
| ~ ( member @ SY631 @ SV73 )
| ! [SY632: $i] :
( ~ ( apply @ SV31 @ SV159 @ SY632 )
| ~ ( member @ SY632 @ SV46 )
| ~ ( apply @ SV20 @ SY632 @ SY631 ) )
| ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SV159 @ SY631 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(598,plain,
! [SV46: $i,SV31: $i,SV20: $i,SV73: $i,SV37: $i,SV160: $i] :
( ( ! [SY633: $i] :
( ~ ( member @ SV160 @ SV37 )
| ~ ( member @ SY633 @ SV73 )
| ~ ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SV160 @ SY633 )
| ~ ( ~ ~ ( ~ ( apply @ SV31 @ SV160 @ ( sK31_Y @ SY633 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) )
| ~ ( member @ ( sK31_Y @ SY633 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SV46 ) )
| ~ ( apply @ SV20 @ ( sK31_Y @ SY633 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SY633 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(599,plain,
! [SV47: $i,SV74: $i,SV116: $i] :
( ( ( member @ SV116 @ SV74 )
= $false )
| ( ( ~ ( member @ SV47 @ SV116 ) )
= $true )
| ( ( member @ SV47 @ ( sum @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[534]) ).
thf(600,plain,
! [SV48: $i,SV75: $i] :
( ( ( ~ ( member @ ( sK42_Y @ SV75 @ SV48 ) @ SV75 ) )
= $false )
| ( ( member @ SV48 @ ( sum @ SV75 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[535]) ).
thf(601,plain,
! [SV75: $i,SV48: $i] :
( ( ( ~ ( member @ SV48 @ ( sK42_Y @ SV75 @ SV48 ) ) )
= $false )
| ( ( member @ SV48 @ ( sum @ SV75 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[535]) ).
thf(602,plain,
! [SV49: $i,SV76: $i] :
( ( ( member @ ( sK41_Y @ SV76 @ SV49 ) @ SV76 )
= $true )
| ( ( member @ SV49 @ ( product @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[536]) ).
thf(603,plain,
! [SV76: $i,SV49: $i] :
( ( ( ~ ( member @ SV49 @ ( sK41_Y @ SV76 @ SV49 ) ) )
= $true )
| ( ( member @ SV49 @ ( product @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[537]) ).
thf(604,plain,
! [SV50: $i,SV77: $i,SV141: $i] :
( ( ( ~ ( member @ SV141 @ SV77 ) )
= $true )
| ( ( member @ SV50 @ SV141 )
= $true )
| ( ( member @ SV50 @ ( product @ SV77 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[538]) ).
thf(605,plain,
! [SV21: $i,SV78: $i,SV100: $i] :
( ( ( ~ ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
| ~ ! [SY560: $i] :
( ~ ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SY560 )
| ~ ( member @ SY560 @ SV100 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
| ~ ( member @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ( member @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) )
| ~ ( ( ( sK38_SY170 @ SV100 @ SV78 @ SV21 )
!= ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) ) ) ) )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(606,plain,
! [SV161: $i,SV142: $i,SV21: $i] :
( ( ~ ( maps @ SV21 @ SV142 @ SV161 )
| ! [SY634: $i] :
( ~ ( member @ SY634 @ SV142 )
| ~ ( ~ ( apply @ SV21 @ SY634 @ ( sK36_Y @ SY634 @ SV161 @ SV142 @ SV21 ) )
| ~ ( member @ ( sK36_Y @ SY634 @ SV161 @ SV142 @ SV21 ) @ SV161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(607,plain,
! [SV162: $i,SV143: $i,SV21: $i] :
( ( ~ ( maps @ SV21 @ SV143 @ SV162 )
| ! [SY635: $i,SY636: $i,SY637: $i] :
( ~ ( member @ SY635 @ SV143 )
| ~ ( member @ SY636 @ SV162 )
| ~ ( member @ SY637 @ SV162 )
| ~ ( apply @ SV21 @ SY635 @ SY636 )
| ~ ( apply @ SV21 @ SY635 @ SY637 )
| ( SY636 = SY637 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(608,plain,
! [SV51: $i,SV79: $i] :
( ( ( member @ ( sK27_X @ SV79 @ SV51 ) @ SV79 )
= $true )
| ( ( identity @ SV51 @ SV79 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[542]) ).
thf(609,plain,
! [SV79: $i,SV51: $i] :
( ( ( ~ ( apply @ SV51 @ ( sK27_X @ SV79 @ SV51 ) @ ( sK27_X @ SV79 @ SV51 ) ) )
= $true )
| ( ( identity @ SV51 @ SV79 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[543]) ).
thf(610,plain,
! [SV52: $i,SV80: $i,SV144: $i] :
( ( ( ~ ( member @ SV144 @ SV80 ) )
= $true )
| ( ( apply @ SV52 @ SV144 @ SV144 )
= $true )
| ( ( identity @ SV52 @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[544]) ).
thf(611,plain,
! [SV81: $i,SV22: $i,SV101: $i,SV163: $i,SV2: $i] :
( ( ( ~ ( apply @ SV2 @ SV163 @ SV101 )
| ~ ( member @ SV163 @ SV22 ) )
= $true )
| ( ( ~ ( member @ SV101 @ SV81 ) )
= $true )
| ( ( member @ SV101 @ ( image3 @ SV2 @ SV22 @ SV81 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(612,plain,
! [SV145: $i,SV22: $i,SV2: $i,SV164: $i] :
( ( ~ ( member @ SV164 @ ( image3 @ SV2 @ SV22 @ SV145 ) )
| ~ ( ~ ( apply @ SV2 @ ( sK18_X @ SV164 @ SV145 @ SV22 @ SV2 ) @ SV164 )
| ~ ( member @ ( sK18_X @ SV164 @ SV145 @ SV22 @ SV2 ) @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(613,plain,
! [SV146: $i,SV22: $i,SV2: $i,SV165: $i] :
( ( ~ ( member @ SV165 @ ( image3 @ SV2 @ SV22 @ SV146 ) )
| ( member @ SV165 @ SV146 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(614,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 )
| ~ ( member @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( member @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 ) )
| ~ ( member @ ( sK11_SY150 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( apply @ SV32 @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ( apply @ SV3 @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ( apply @ SV3 @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK11_SY150 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ~ ( apply @ SV117 @ ( sK11_SY150 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
= $false )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(615,plain,
! [SV118: $i,SV103: $i,SV32: $i,SV23: $i,SV3: $i] :
( ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV103 @ SV118 )
= $false )
| ( ( ! [SY587: $i,SY588: $i,SY589: $i,SY590: $i] :
( ~ ( member @ SY587 @ SV23 )
| ~ ( member @ SY588 @ SV103 )
| ~ ( member @ SY589 @ SV23 )
| ~ ( member @ SY590 @ SV103 )
| ~ ( apply @ SV32 @ SY587 @ SY589 )
| ~ ( apply @ SV3 @ SY587 @ SY588 )
| ~ ( apply @ SV3 @ SY589 @ SY590 )
| ( apply @ SV118 @ SY590 @ SY588 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(616,plain,
! [SV40: $i,SV55: $i] :
( ( ( member @ ( sK43_X @ SV55 @ SV40 ) @ SV55 )
= $false )
| ( ( subset @ SV40 @ SV55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[551]) ).
thf(617,plain,
! [SV56: $i,SV41: $i,SV119: $i] :
( ( ( member @ SV119 @ SV41 )
= $false )
| ( ( member @ SV119 @ SV56 )
= $true )
| ( ( subset @ SV41 @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(618,plain,
! [SV57: $i,SV82: $i,SV120: $i,SV4: $i] :
( ( ( apply @ SV4 @ SV120 @ SV82 )
= $false )
| ( ( ~ ( member @ SV120 @ SV57 ) )
= $true )
| ( ( member @ SV82 @ ( image2 @ SV4 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(619,plain,
! [SV58: $i,SV83: $i,SV4: $i] :
( ( ( ~ ( apply @ SV4 @ ( sK19_X @ SV83 @ SV58 @ SV4 ) @ SV83 ) )
= $false )
| ( ( member @ SV83 @ ( image2 @ SV4 @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[554]) ).
thf(620,plain,
! [SV4: $i,SV58: $i,SV83: $i] :
( ( ( ~ ( member @ ( sK19_X @ SV83 @ SV58 @ SV4 ) @ SV58 ) )
= $false )
| ( ( member @ SV83 @ ( image2 @ SV4 @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[554]) ).
thf(621,plain,
! [SV121: $i,SV147: $i,SV5: $i] :
( ( ( ~ ( member @ SV5 @ ( difference @ SV147 @ SV121 ) ) )
= $true )
| ( ( member @ SV5 @ SV147 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[556]) ).
thf(622,plain,
! [SV122: $i,SV166: $i,SV5: $i] :
( ( ( ~ ( member @ SV5 @ ( difference @ SV166 @ SV122 ) ) )
= $true )
| ( ( ~ ( member @ SV5 @ SV122 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(623,plain,
! [SV123: $i,SV6: $i] :
( ( ( member @ SV6 @ SV123 )
= $false )
| ( ( ! [SY593: $i] : ( member @ SV6 @ ( union @ SV123 @ SY593 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(624,plain,
! [SV124: $i,SV148: $i,SV6: $i] :
( ( ( ~ ( member @ SV6 @ SV148 ) )
= $true )
| ( ( member @ SV6 @ ( union @ SV124 @ SV148 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[560]) ).
thf(625,plain,
! [SV7: $i,SV24: $i,SV33: $i,SV104: $i,SV125: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 )
| ~ ( member @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
| ~ ( member @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 ) )
| ~ ( member @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
| ~ ( apply @ SV7 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ( apply @ SV7 @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ~ ( ~ ( ~ ( apply @ SV33 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
| ~ ( apply @ SV125 @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ( ( apply @ SV33 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
| ( apply @ SV125 @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) ) ) ) )
= $true )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[561]) ).
thf(626,plain,
! [SV167: $i,SV33: $i,SV24: $i,SV7: $i] :
( ( ! [SY638: $i] :
( ~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SY638 )
| ! [SY639: $i,SY640: $i] :
~ ( ~ ! [SY641: $i,SY642: $i] :
( ~ ( member @ SY639 @ SV24 )
| ~ ( member @ SY640 @ SV167 )
| ~ ( member @ SY641 @ SV24 )
| ~ ( member @ SY642 @ SV167 )
| ~ ( apply @ SV7 @ SY639 @ SY640 )
| ~ ( apply @ SV7 @ SY641 @ SY642 )
| ~ ( apply @ SV33 @ SY639 @ SY641 )
| ( apply @ SY638 @ SY640 @ SY642 ) )
| ~ ! [SY643: $i,SY644: $i] :
( ~ ( member @ SY639 @ SV24 )
| ~ ( member @ SY640 @ SV167 )
| ~ ( member @ SY643 @ SV24 )
| ~ ( member @ SY644 @ SV167 )
| ~ ( apply @ SV7 @ SY639 @ SY640 )
| ~ ( apply @ SV7 @ SY643 @ SY644 )
| ~ ( apply @ SY638 @ SY640 @ SY644 )
| ( apply @ SV33 @ SY639 @ SY643 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(627,plain,
! [SV33: $i,SV24: $i,SV7: $i] :
( ( ~ ! [SY440: $i] :
( ! [SY441: $i] :
~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SY440 @ SY441 )
| ( maps @ SV7 @ SV24 @ SY440 ) )
| ~ ! [SY442: $i] :
( ! [SY443: $i] :
~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SY442 @ SY443 )
| ( one_to_one @ SV7 @ SV24 @ SY442 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(628,plain,
! [SV8: $i,SV25: $i,SV86: $i,SV105: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) @ SV86 )
| ~ ( member @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) @ SV105 ) ) )
= $false )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV86 @ SV105 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[564]) ).
thf(629,plain,
! [SV8: $i,SV86: $i,SV105: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ( ~ ( apply @ SV25 @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) )
| ~ ( apply @ SV8 @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) ) )
| ~ ( ( apply @ SV25 @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) )
| ( apply @ SV8 @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) ) ) ) )
= $false )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV86 @ SV105 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[564]) ).
thf(630,plain,
! [SV8: $i,SV25: $i,SV106: $i,SV87: $i] :
( ( ( ~ ! [SY569: $i,SY570: $i] :
( ~ ( member @ SY569 @ SV87 )
| ~ ( member @ SY570 @ SV106 )
| ~ ( apply @ SV25 @ SY569 @ SY570 )
| ( apply @ SV8 @ SY570 @ SY569 ) )
| ~ ! [SY571: $i,SY572: $i] :
( ~ ( member @ SY571 @ SV87 )
| ~ ( member @ SY572 @ SV106 )
| ~ ( apply @ SV8 @ SY572 @ SY571 )
| ( apply @ SV25 @ SY571 @ SY572 ) ) )
= $false )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV87 @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(631,plain,
! [SV9: $i,SV34: $i,SV126: $i,SV26: $i,SV107: $i] :
( ( ( ~ ( member @ SV107 @ SV26 ) )
= $true )
| ( ( ~ ( member @ SV126 @ SV34 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV107 @ SV126 )
| ( apply @ ( inverse_function @ SV9 @ SV26 @ SV34 ) @ SV126 @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[566]) ).
thf(632,plain,
! [SV9: $i,SV34: $i,SV127: $i,SV26: $i,SV108: $i] :
( ( ( ~ ( member @ SV108 @ SV26 ) )
= $true )
| ( ( ~ ( member @ SV127 @ SV34 ) )
= $true )
| ( ( ~ ( apply @ ( inverse_function @ SV9 @ SV26 @ SV34 ) @ SV127 @ SV108 )
| ( apply @ SV9 @ SV108 @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[567]) ).
thf(633,plain,
! [SV61: $i,SV128: $i,SV88: $i,SV10: $i] :
( ( ( apply @ SV10 @ SV88 @ SV128 )
= $false )
| ( ( ~ ( member @ SV128 @ SV61 ) )
= $true )
| ( ( member @ SV88 @ ( inverse_image2 @ SV10 @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(634,plain,
! [SV62: $i,SV89: $i,SV10: $i] :
( ( ( ~ ( apply @ SV10 @ SV89 @ ( sK17_Y @ SV89 @ SV62 @ SV10 ) ) )
= $false )
| ( ( member @ SV89 @ ( inverse_image2 @ SV10 @ SV62 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[569]) ).
thf(635,plain,
! [SV10: $i,SV62: $i,SV89: $i] :
( ( ( ~ ( member @ ( sK17_Y @ SV89 @ SV62 @ SV10 ) @ SV62 ) )
= $false )
| ( ( member @ SV89 @ ( inverse_image2 @ SV10 @ SV62 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[569]) ).
thf(636,plain,
! [SV11: $i,SV63: $i,SV90: $i] :
( ( ( member @ ( sK23_Y @ SV90 @ SV63 @ SV11 ) @ SV90 )
= $true )
| ( ( surjective @ SV11 @ SV63 @ SV90 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[570]) ).
thf(637,plain,
! [SV63: $i,SV90: $i,SV11: $i] :
( ( ( ! [SY548: $i] :
( ~ ( apply @ SV11 @ SY548 @ ( sK23_Y @ SV90 @ SV63 @ SV11 ) )
| ~ ( member @ SY548 @ SV63 ) ) )
= $true )
| ( ( surjective @ SV11 @ SV63 @ SV90 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[571]) ).
thf(638,plain,
! [SV64: $i,SV11: $i,SV91: $i,SV149: $i] :
( ( ( ~ ( member @ SV149 @ SV91 ) )
= $true )
| ( ( ~ ( ~ ( apply @ SV11 @ ( sK22_E @ SV149 @ SV91 @ SV64 @ SV11 ) @ SV149 )
| ~ ( member @ ( sK22_E @ SV149 @ SV91 @ SV64 @ SV11 ) @ SV64 ) ) )
= $true )
| ( ( surjective @ SV11 @ SV64 @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[572]) ).
thf(639,plain,
! [SV92: $i,SV27: $i,SV168: $i,SV109: $i,SV12: $i] :
( ( ( ~ ( apply @ SV12 @ SV109 @ SV168 )
| ~ ( member @ SV168 @ SV27 ) )
= $true )
| ( ( ~ ( member @ SV109 @ SV92 ) )
= $true )
| ( ( member @ SV109 @ ( inverse_image3 @ SV12 @ SV27 @ SV92 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(640,plain,
! [SV150: $i,SV27: $i,SV12: $i,SV169: $i] :
( ( ~ ( member @ SV169 @ ( inverse_image3 @ SV12 @ SV27 @ SV150 ) )
| ~ ( ~ ( apply @ SV12 @ SV169 @ ( sK16_Y @ SV169 @ SV150 @ SV27 @ SV12 ) )
| ~ ( member @ ( sK16_Y @ SV169 @ SV150 @ SV27 @ SV12 ) @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(641,plain,
! [SV151: $i,SV27: $i,SV12: $i,SV170: $i] :
( ( ~ ( member @ SV170 @ ( inverse_image3 @ SV12 @ SV27 @ SV151 ) )
| ( member @ SV170 @ SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(642,plain,
! [SV13: $i,SV28: $i,SV93: $i,SV110: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ SV93 )
| ~ ( member @ ( sK29_SY162 @ SV110 @ SV93 @ SV28 @ SV13 ) @ SV110 ) )
| ~ ( member @ ( sK30_SY164 @ SV110 @ SV93 @ SV28 @ SV13 ) @ SV110 ) ) )
= $false )
| ( ( equal_maps @ SV13 @ SV28 @ SV93 @ SV110 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[576]) ).
thf(643,plain,
! [SV28: $i,SV93: $i,SV110: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( apply @ SV13 @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ ( sK29_SY162 @ SV110 @ SV93 @ SV28 @ SV13 ) )
| ~ ( apply @ SV28 @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ ( sK30_SY164 @ SV110 @ SV93 @ SV28 @ SV13 ) ) )
| ~ ( ( ( sK29_SY162 @ SV110 @ SV93 @ SV28 @ SV13 )
!= ( sK30_SY164 @ SV110 @ SV93 @ SV28 @ SV13 ) ) ) ) )
= $false )
| ( ( equal_maps @ SV13 @ SV28 @ SV93 @ SV110 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[576]) ).
thf(644,plain,
! [SV28: $i,SV13: $i,SV111: $i,SV94: $i,SV171: $i] :
( ( ( ! [SY645: $i,SY646: $i] :
( ~ ( member @ SV171 @ SV94 )
| ~ ( member @ SY645 @ SV111 )
| ~ ( member @ SY646 @ SV111 )
| ~ ( apply @ SV13 @ SV171 @ SY645 )
| ~ ( apply @ SV28 @ SV171 @ SY646 )
| ( SY645 = SY646 ) ) )
= $true )
| ( ( equal_maps @ SV13 @ SV28 @ SV94 @ SV111 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(645,plain,
! [SV14: $i,SV29: $i,SV35: $i,SV42: $i,SV129: $i,SV152: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV42 )
| ~ ( member @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV152 ) )
| ~ ~ ( ~ ( ! [SY623: $i] :
( ~ ( apply @ SV35 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY623 )
| ~ ( member @ SY623 @ SV129 )
| ~ ( apply @ SV29 @ SY623 @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ~ ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( apply @ SV35 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV129 ) )
| ~ ( apply @ SV29 @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) ) ) ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[578]) ).
thf(646,plain,
! [SV153: $i,SV130: $i,SV42: $i,SV35: $i,SV29: $i,SV14: $i] :
( ( ( ~ ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 ) )
= $true )
| ( ( ~ ( ~ ! [SY624: $i,SY625: $i] :
( ~ ( member @ SY624 @ SV42 )
| ~ ( member @ SY625 @ SV153 )
| ! [SY600: $i] :
( ~ ( apply @ SV35 @ SY624 @ SY600 )
| ~ ( member @ SY600 @ SV130 )
| ~ ( apply @ SV29 @ SY600 @ SY625 ) )
| ( apply @ SV14 @ SY624 @ SY625 ) )
| ~ ! [SY627: $i,SY628: $i] :
( ~ ( member @ SY627 @ SV42 )
| ~ ( member @ SY628 @ SV153 )
| ~ ( apply @ SV14 @ SY627 @ SY628 )
| ~ ( ~ ~ ( ~ ( apply @ SV35 @ SY627 @ ( sK32_Y @ SY628 @ SY627 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK32_Y @ SY628 @ SY627 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV130 ) )
| ~ ( apply @ SV29 @ ( sK32_Y @ SY628 @ SY627 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY628 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[579]) ).
thf(647,plain,
! [SV15: $i,SV67: $i,SV95: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK24_X1 @ SV95 @ SV67 @ SV15 ) @ SV67 )
| ~ ( member @ ( sK25_SY159 @ SV95 @ SV67 @ SV15 ) @ SV67 ) )
| ~ ( member @ ( sK26_SY161 @ SV95 @ SV67 @ SV15 ) @ SV95 ) ) )
= $true )
| ( ( injective @ SV15 @ SV67 @ SV95 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[580]) ).
thf(648,plain,
! [SV67: $i,SV95: $i,SV15: $i] :
( ( ( ~ ( ~ ~ ( ~ ( apply @ SV15 @ ( sK24_X1 @ SV95 @ SV67 @ SV15 ) @ ( sK26_SY161 @ SV95 @ SV67 @ SV15 ) )
| ~ ( apply @ SV15 @ ( sK25_SY159 @ SV95 @ SV67 @ SV15 ) @ ( sK26_SY161 @ SV95 @ SV67 @ SV15 ) ) )
| ~ ( ( ( sK24_X1 @ SV95 @ SV67 @ SV15 )
!= ( sK25_SY159 @ SV95 @ SV67 @ SV15 ) ) ) ) )
= $true )
| ( ( injective @ SV15 @ SV67 @ SV95 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[581]) ).
thf(649,plain,
! [SV15: $i,SV96: $i,SV172: $i,SV68: $i,SV154: $i] :
( ( ( ! [SY647: $i] :
( ~ ( member @ SV154 @ SV68 )
| ~ ( member @ SV172 @ SV68 )
| ~ ( member @ SY647 @ SV96 )
| ~ ( apply @ SV15 @ SV154 @ SY647 )
| ~ ( apply @ SV15 @ SV172 @ SY647 )
| ( SV154 = SV172 ) ) )
= $true )
| ( ( injective @ SV15 @ SV68 @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(650,plain,
! [SV131: $i,SV112: $i] :
( ( ( equal_set @ SV112 @ SV131 )
= $false )
| ( ( subset @ SV112 @ SV131 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[584]) ).
thf(651,plain,
! [SV132: $i,SV113: $i] :
( ( ( equal_set @ SV113 @ SV132 )
= $false )
| ( ( subset @ SV132 @ SV113 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(652,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 )
| ~ ( member @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( member @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 ) )
| ~ ( member @ ( sK15_SY156 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( apply @ SV36 @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ( apply @ SV16 @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ( apply @ SV16 @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK15_SY156 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ~ ( apply @ SV133 @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK15_SY156 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
= $false )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(653,plain,
! [SV134: $i,SV115: $i,SV36: $i,SV30: $i,SV16: $i] :
( ( ( increasing @ SV16 @ SV30 @ SV36 @ SV115 @ SV134 )
= $false )
| ( ( ! [SY603: $i,SY604: $i,SY605: $i,SY606: $i] :
( ~ ( member @ SY603 @ SV30 )
| ~ ( member @ SY604 @ SV115 )
| ~ ( member @ SY605 @ SV30 )
| ~ ( member @ SY606 @ SV115 )
| ~ ( apply @ SV36 @ SY603 @ SY605 )
| ~ ( apply @ SV16 @ SY603 @ SY604 )
| ~ ( apply @ SV16 @ SY605 @ SY606 )
| ( apply @ SV134 @ SY604 @ SY606 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[587]) ).
thf(654,plain,
! [SV70: $i,SV97: $i,SV17: $i] :
( ( ( member @ SV17 @ SV97 )
= $false )
| ( ( member @ SV17 @ SV70 )
= $false )
| ( ( member @ SV17 @ ( intersection @ SV70 @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[588]) ).
thf(655,plain,
! [SV173: $i,SV135: $i,SV17: $i] :
( ( ( ~ ( member @ SV17 @ ( intersection @ SV135 @ SV173 ) ) )
= $true )
| ( ( member @ SV17 @ SV135 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(656,plain,
! [SV155: $i,SV136: $i,SV17: $i] :
( ( ( ~ ( member @ SV17 @ ( intersection @ SV136 @ SV155 ) ) )
= $true )
| ( ( member @ SV17 @ SV155 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[590]) ).
thf(657,plain,
! [SV137: $i,SV18: $i] :
( ( ( SV18 = SV137 )
= $false )
| ( ( ! [SY609: $i] : ( member @ SV18 @ ( unordered_pair @ SV137 @ SY609 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[592]) ).
thf(658,plain,
! [SV138: $i,SV156: $i,SV18: $i] :
( ( ( ( SV18 != SV156 ) )
= $true )
| ( ( member @ SV18 @ ( unordered_pair @ SV138 @ SV156 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[593]) ).
thf(659,plain,
! [SV99: $i,SV72: $i,SV19: $i] :
( ( ( surjective @ SV19 @ SV72 @ SV99 )
= $false )
| ( ( injective @ SV19 @ SV72 @ SV99 )
= $false )
| ( ( one_to_one @ SV19 @ SV72 @ SV99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[594]) ).
thf(660,plain,
! [SV157: $i,SV139: $i,SV19: $i] :
( ( ( ~ ( one_to_one @ SV19 @ SV139 @ SV157 ) )
= $true )
| ( ( injective @ SV19 @ SV139 @ SV157 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[595]) ).
thf(661,plain,
! [SV158: $i,SV140: $i,SV19: $i] :
( ( ( ~ ( one_to_one @ SV19 @ SV140 @ SV158 ) )
= $true )
| ( ( surjective @ SV19 @ SV140 @ SV158 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[596]) ).
thf(662,plain,
! [SV20: $i,SV46: $i,SV31: $i,SV73: $i,SV174: $i,SV37: $i,SV159: $i] :
( ( ~ ( member @ SV159 @ SV37 )
| ~ ( member @ SV174 @ SV73 )
| ! [SY648: $i] :
( ~ ( apply @ SV31 @ SV159 @ SY648 )
| ~ ( member @ SY648 @ SV46 )
| ~ ( apply @ SV20 @ SY648 @ SV174 ) )
| ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SV159 @ SV174 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(663,plain,
! [SV46: $i,SV31: $i,SV20: $i,SV73: $i,SV175: $i,SV37: $i,SV160: $i] :
( ( ~ ( member @ SV160 @ SV37 )
| ~ ( member @ SV175 @ SV73 )
| ~ ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SV160 @ SV175 )
| ~ ( ~ ~ ( ~ ( apply @ SV31 @ SV160 @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) )
| ~ ( member @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SV46 ) )
| ~ ( apply @ SV20 @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(664,plain,
! [SV74: $i,SV116: $i,SV47: $i] :
( ( ( member @ SV47 @ SV116 )
= $false )
| ( ( member @ SV116 @ SV74 )
= $false )
| ( ( member @ SV47 @ ( sum @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[599]) ).
thf(665,plain,
! [SV48: $i,SV75: $i] :
( ( ( member @ ( sK42_Y @ SV75 @ SV48 ) @ SV75 )
= $true )
| ( ( member @ SV48 @ ( sum @ SV75 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[600]) ).
thf(666,plain,
! [SV75: $i,SV48: $i] :
( ( ( member @ SV48 @ ( sK42_Y @ SV75 @ SV48 ) )
= $true )
| ( ( member @ SV48 @ ( sum @ SV75 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[601]) ).
thf(667,plain,
! [SV76: $i,SV49: $i] :
( ( ( member @ SV49 @ ( sK41_Y @ SV76 @ SV49 ) )
= $false )
| ( ( member @ SV49 @ ( product @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[603]) ).
thf(668,plain,
! [SV50: $i,SV77: $i,SV141: $i] :
( ( ( member @ SV141 @ SV77 )
= $false )
| ( ( member @ SV50 @ SV141 )
= $true )
| ( ( member @ SV50 @ ( product @ SV77 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(669,plain,
! [SV21: $i,SV78: $i,SV100: $i] :
( ( ( ~ ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
| ~ ( member @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ( member @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) )
| ~ ( ( ( sK38_SY170 @ SV100 @ SV78 @ SV21 )
!= ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) ) ) ) )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[605]) ).
thf(670,plain,
! [SV78: $i,SV100: $i,SV21: $i] :
( ( ( ~ ! [SY560: $i] :
( ~ ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SY560 )
| ~ ( member @ SY560 @ SV100 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
| ~ ( member @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ( member @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) )
| ~ ( ( ( sK38_SY170 @ SV100 @ SV78 @ SV21 )
!= ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) ) ) ) )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[605]) ).
thf(671,plain,
! [SV161: $i,SV142: $i,SV21: $i] :
( ( ( ~ ( maps @ SV21 @ SV142 @ SV161 ) )
= $true )
| ( ( ! [SY634: $i] :
( ~ ( member @ SY634 @ SV142 )
| ~ ( ~ ( apply @ SV21 @ SY634 @ ( sK36_Y @ SY634 @ SV161 @ SV142 @ SV21 ) )
| ~ ( member @ ( sK36_Y @ SY634 @ SV161 @ SV142 @ SV21 ) @ SV161 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[606]) ).
thf(672,plain,
! [SV162: $i,SV143: $i,SV21: $i] :
( ( ( ~ ( maps @ SV21 @ SV143 @ SV162 ) )
= $true )
| ( ( ! [SY635: $i,SY636: $i,SY637: $i] :
( ~ ( member @ SY635 @ SV143 )
| ~ ( member @ SY636 @ SV162 )
| ~ ( member @ SY637 @ SV162 )
| ~ ( apply @ SV21 @ SY635 @ SY636 )
| ~ ( apply @ SV21 @ SY635 @ SY637 )
| ( SY636 = SY637 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[607]) ).
thf(673,plain,
! [SV79: $i,SV51: $i] :
( ( ( apply @ SV51 @ ( sK27_X @ SV79 @ SV51 ) @ ( sK27_X @ SV79 @ SV51 ) )
= $false )
| ( ( identity @ SV51 @ SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[609]) ).
thf(674,plain,
! [SV52: $i,SV80: $i,SV144: $i] :
( ( ( member @ SV144 @ SV80 )
= $false )
| ( ( apply @ SV52 @ SV144 @ SV144 )
= $true )
| ( ( identity @ SV52 @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[610]) ).
thf(675,plain,
! [SV81: $i,SV22: $i,SV101: $i,SV163: $i,SV2: $i] :
( ( ( ~ ( apply @ SV2 @ SV163 @ SV101 ) )
= $true )
| ( ( ~ ( member @ SV163 @ SV22 ) )
= $true )
| ( ( ~ ( member @ SV101 @ SV81 ) )
= $true )
| ( ( member @ SV101 @ ( image3 @ SV2 @ SV22 @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[611]) ).
thf(676,plain,
! [SV145: $i,SV22: $i,SV2: $i,SV164: $i] :
( ( ( ~ ( member @ SV164 @ ( image3 @ SV2 @ SV22 @ SV145 ) ) )
= $true )
| ( ( ~ ( ~ ( apply @ SV2 @ ( sK18_X @ SV164 @ SV145 @ SV22 @ SV2 ) @ SV164 )
| ~ ( member @ ( sK18_X @ SV164 @ SV145 @ SV22 @ SV2 ) @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[612]) ).
thf(677,plain,
! [SV146: $i,SV22: $i,SV2: $i,SV165: $i] :
( ( ( ~ ( member @ SV165 @ ( image3 @ SV2 @ SV22 @ SV146 ) ) )
= $true )
| ( ( member @ SV165 @ SV146 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[613]) ).
thf(678,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 )
| ~ ( member @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( member @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 ) )
| ~ ( member @ ( sK11_SY150 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( apply @ SV32 @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ( apply @ SV3 @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ( apply @ SV3 @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK11_SY150 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) ) )
= $false )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[614]) ).
thf(679,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ( ~ ~ ( apply @ SV117 @ ( sK11_SY150 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
= $false )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[614]) ).
thf(680,plain,
! [SV118: $i,SV3: $i,SV32: $i,SV103: $i,SV23: $i,SV176: $i] :
( ( ( ! [SY649: $i,SY650: $i,SY651: $i] :
( ~ ( member @ SV176 @ SV23 )
| ~ ( member @ SY649 @ SV103 )
| ~ ( member @ SY650 @ SV23 )
| ~ ( member @ SY651 @ SV103 )
| ~ ( apply @ SV32 @ SV176 @ SY650 )
| ~ ( apply @ SV3 @ SV176 @ SY649 )
| ~ ( apply @ SV3 @ SY650 @ SY651 )
| ( apply @ SV118 @ SY651 @ SY649 ) ) )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV103 @ SV118 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(681,plain,
! [SV82: $i,SV4: $i,SV57: $i,SV120: $i] :
( ( ( member @ SV120 @ SV57 )
= $false )
| ( ( apply @ SV4 @ SV120 @ SV82 )
= $false )
| ( ( member @ SV82 @ ( image2 @ SV4 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[618]) ).
thf(682,plain,
! [SV58: $i,SV83: $i,SV4: $i] :
( ( ( apply @ SV4 @ ( sK19_X @ SV83 @ SV58 @ SV4 ) @ SV83 )
= $true )
| ( ( member @ SV83 @ ( image2 @ SV4 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[619]) ).
thf(683,plain,
! [SV4: $i,SV58: $i,SV83: $i] :
( ( ( member @ ( sK19_X @ SV83 @ SV58 @ SV4 ) @ SV58 )
= $true )
| ( ( member @ SV83 @ ( image2 @ SV4 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[620]) ).
thf(684,plain,
! [SV121: $i,SV147: $i,SV5: $i] :
( ( ( member @ SV5 @ ( difference @ SV147 @ SV121 ) )
= $false )
| ( ( member @ SV5 @ SV147 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(685,plain,
! [SV122: $i,SV166: $i,SV5: $i] :
( ( ( member @ SV5 @ ( difference @ SV166 @ SV122 ) )
= $false )
| ( ( ~ ( member @ SV5 @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[622]) ).
thf(686,plain,
! [SV177: $i,SV123: $i,SV6: $i] :
( ( ( member @ SV6 @ ( union @ SV123 @ SV177 ) )
= $true )
| ( ( member @ SV6 @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(687,plain,
! [SV124: $i,SV148: $i,SV6: $i] :
( ( ( member @ SV6 @ SV148 )
= $false )
| ( ( member @ SV6 @ ( union @ SV124 @ SV148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[624]) ).
thf(688,plain,
! [SV7: $i,SV24: $i,SV33: $i,SV104: $i,SV125: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 )
| ~ ( member @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
| ~ ( member @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 ) )
| ~ ( member @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
| ~ ( apply @ SV7 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ( apply @ SV7 @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ~ ( ~ ( ~ ( apply @ SV33 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
| ~ ( apply @ SV125 @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ( ( apply @ SV33 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
| ( apply @ SV125 @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) ) ) )
= $false )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[625]) ).
thf(689,plain,
! [SV178: $i,SV167: $i,SV33: $i,SV24: $i,SV7: $i] :
( ( ~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
| ! [SY652: $i,SY653: $i] :
~ ( ~ ! [SY654: $i,SY655: $i] :
( ~ ( member @ SY652 @ SV24 )
| ~ ( member @ SY653 @ SV167 )
| ~ ( member @ SY654 @ SV24 )
| ~ ( member @ SY655 @ SV167 )
| ~ ( apply @ SV7 @ SY652 @ SY653 )
| ~ ( apply @ SV7 @ SY654 @ SY655 )
| ~ ( apply @ SV33 @ SY652 @ SY654 )
| ( apply @ SV178 @ SY653 @ SY655 ) )
| ~ ! [SY656: $i,SY657: $i] :
( ~ ( member @ SY652 @ SV24 )
| ~ ( member @ SY653 @ SV167 )
| ~ ( member @ SY656 @ SV24 )
| ~ ( member @ SY657 @ SV167 )
| ~ ( apply @ SV7 @ SY652 @ SY653 )
| ~ ( apply @ SV7 @ SY656 @ SY657 )
| ~ ( apply @ SV178 @ SY653 @ SY657 )
| ( apply @ SV33 @ SY652 @ SY656 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(690,plain,
! [SV33: $i,SV24: $i,SV7: $i] :
( ( ~ ! [SY440: $i] :
( ! [SY441: $i] :
~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SY440 @ SY441 )
| ( maps @ SV7 @ SV24 @ SY440 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[627]) ).
thf(691,plain,
! [SV33: $i,SV24: $i,SV7: $i] :
( ( ~ ! [SY442: $i] :
( ! [SY443: $i] :
~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SY442 @ SY443 )
| ( one_to_one @ SV7 @ SV24 @ SY442 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[627]) ).
thf(692,plain,
! [SV8: $i,SV25: $i,SV86: $i,SV105: $i] :
( ( ( ~ ( ~ ( member @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) @ SV86 )
| ~ ( member @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) @ SV105 ) ) )
= $true )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV86 @ SV105 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[628]) ).
thf(693,plain,
! [SV8: $i,SV86: $i,SV105: $i,SV25: $i] :
( ( ( ~ ( ~ ( ~ ( apply @ SV25 @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) )
| ~ ( apply @ SV8 @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) ) )
| ~ ( ( apply @ SV25 @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) )
| ( apply @ SV8 @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) ) ) ) )
= $true )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV86 @ SV105 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[629]) ).
thf(694,plain,
! [SV8: $i,SV25: $i,SV106: $i,SV87: $i] :
( ( ( ~ ! [SY569: $i,SY570: $i] :
( ~ ( member @ SY569 @ SV87 )
| ~ ( member @ SY570 @ SV106 )
| ~ ( apply @ SV25 @ SY569 @ SY570 )
| ( apply @ SV8 @ SY570 @ SY569 ) ) )
= $false )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV87 @ SV106 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[630]) ).
thf(695,plain,
! [SV25: $i,SV8: $i,SV106: $i,SV87: $i] :
( ( ( ~ ! [SY571: $i,SY572: $i] :
( ~ ( member @ SY571 @ SV87 )
| ~ ( member @ SY572 @ SV106 )
| ~ ( apply @ SV8 @ SY572 @ SY571 )
| ( apply @ SV25 @ SY571 @ SY572 ) ) )
= $false )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV87 @ SV106 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[630]) ).
thf(696,plain,
! [SV9: $i,SV34: $i,SV126: $i,SV26: $i,SV107: $i] :
( ( ( member @ SV107 @ SV26 )
= $false )
| ( ( ~ ( member @ SV126 @ SV34 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV107 @ SV126 )
| ( apply @ ( inverse_function @ SV9 @ SV26 @ SV34 ) @ SV126 @ SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[631]) ).
thf(697,plain,
! [SV9: $i,SV34: $i,SV127: $i,SV26: $i,SV108: $i] :
( ( ( member @ SV108 @ SV26 )
= $false )
| ( ( ~ ( member @ SV127 @ SV34 ) )
= $true )
| ( ( ~ ( apply @ ( inverse_function @ SV9 @ SV26 @ SV34 ) @ SV127 @ SV108 )
| ( apply @ SV9 @ SV108 @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[632]) ).
thf(698,plain,
! [SV88: $i,SV10: $i,SV61: $i,SV128: $i] :
( ( ( member @ SV128 @ SV61 )
= $false )
| ( ( apply @ SV10 @ SV88 @ SV128 )
= $false )
| ( ( member @ SV88 @ ( inverse_image2 @ SV10 @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[633]) ).
thf(699,plain,
! [SV62: $i,SV89: $i,SV10: $i] :
( ( ( apply @ SV10 @ SV89 @ ( sK17_Y @ SV89 @ SV62 @ SV10 ) )
= $true )
| ( ( member @ SV89 @ ( inverse_image2 @ SV10 @ SV62 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[634]) ).
thf(700,plain,
! [SV10: $i,SV62: $i,SV89: $i] :
( ( ( member @ ( sK17_Y @ SV89 @ SV62 @ SV10 ) @ SV62 )
= $true )
| ( ( member @ SV89 @ ( inverse_image2 @ SV10 @ SV62 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[635]) ).
thf(701,plain,
! [SV63: $i,SV90: $i,SV179: $i,SV11: $i] :
( ( ( ~ ( apply @ SV11 @ SV179 @ ( sK23_Y @ SV90 @ SV63 @ SV11 ) )
| ~ ( member @ SV179 @ SV63 ) )
= $true )
| ( ( surjective @ SV11 @ SV63 @ SV90 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(702,plain,
! [SV64: $i,SV11: $i,SV91: $i,SV149: $i] :
( ( ( member @ SV149 @ SV91 )
= $false )
| ( ( ~ ( ~ ( apply @ SV11 @ ( sK22_E @ SV149 @ SV91 @ SV64 @ SV11 ) @ SV149 )
| ~ ( member @ ( sK22_E @ SV149 @ SV91 @ SV64 @ SV11 ) @ SV64 ) ) )
= $true )
| ( ( surjective @ SV11 @ SV64 @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[638]) ).
thf(703,plain,
! [SV92: $i,SV27: $i,SV168: $i,SV109: $i,SV12: $i] :
( ( ( ~ ( apply @ SV12 @ SV109 @ SV168 ) )
= $true )
| ( ( ~ ( member @ SV168 @ SV27 ) )
= $true )
| ( ( ~ ( member @ SV109 @ SV92 ) )
= $true )
| ( ( member @ SV109 @ ( inverse_image3 @ SV12 @ SV27 @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[639]) ).
thf(704,plain,
! [SV150: $i,SV27: $i,SV12: $i,SV169: $i] :
( ( ( ~ ( member @ SV169 @ ( inverse_image3 @ SV12 @ SV27 @ SV150 ) ) )
= $true )
| ( ( ~ ( ~ ( apply @ SV12 @ SV169 @ ( sK16_Y @ SV169 @ SV150 @ SV27 @ SV12 ) )
| ~ ( member @ ( sK16_Y @ SV169 @ SV150 @ SV27 @ SV12 ) @ SV27 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[640]) ).
thf(705,plain,
! [SV151: $i,SV27: $i,SV12: $i,SV170: $i] :
( ( ( ~ ( member @ SV170 @ ( inverse_image3 @ SV12 @ SV27 @ SV151 ) ) )
= $true )
| ( ( member @ SV170 @ SV151 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[641]) ).
thf(706,plain,
! [SV13: $i,SV28: $i,SV93: $i,SV110: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ SV93 )
| ~ ( member @ ( sK29_SY162 @ SV110 @ SV93 @ SV28 @ SV13 ) @ SV110 ) )
| ~ ( member @ ( sK30_SY164 @ SV110 @ SV93 @ SV28 @ SV13 ) @ SV110 ) ) )
= $true )
| ( ( equal_maps @ SV13 @ SV28 @ SV93 @ SV110 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[642]) ).
thf(707,plain,
! [SV28: $i,SV93: $i,SV110: $i,SV13: $i] :
( ( ( ~ ( ~ ~ ( ~ ( apply @ SV13 @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ ( sK29_SY162 @ SV110 @ SV93 @ SV28 @ SV13 ) )
| ~ ( apply @ SV28 @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ ( sK30_SY164 @ SV110 @ SV93 @ SV28 @ SV13 ) ) )
| ~ ( ( ( sK29_SY162 @ SV110 @ SV93 @ SV28 @ SV13 )
!= ( sK30_SY164 @ SV110 @ SV93 @ SV28 @ SV13 ) ) ) ) )
= $true )
| ( ( equal_maps @ SV13 @ SV28 @ SV93 @ SV110 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[643]) ).
thf(708,plain,
! [SV28: $i,SV13: $i,SV111: $i,SV180: $i,SV94: $i,SV171: $i] :
( ( ( ! [SY658: $i] :
( ~ ( member @ SV171 @ SV94 )
| ~ ( member @ SV180 @ SV111 )
| ~ ( member @ SY658 @ SV111 )
| ~ ( apply @ SV13 @ SV171 @ SV180 )
| ~ ( apply @ SV28 @ SV171 @ SY658 )
| ( SV180 = SY658 ) ) )
= $true )
| ( ( equal_maps @ SV13 @ SV28 @ SV94 @ SV111 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(709,plain,
! [SV14: $i,SV29: $i,SV35: $i,SV42: $i,SV129: $i,SV152: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV42 )
| ~ ( member @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV152 ) )
| ~ ~ ( ~ ( ! [SY623: $i] :
( ~ ( apply @ SV35 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY623 )
| ~ ( member @ SY623 @ SV129 )
| ~ ( apply @ SV29 @ SY623 @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ~ ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( apply @ SV35 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV129 ) )
| ~ ( apply @ SV29 @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) ) ) )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[645]) ).
thf(710,plain,
! [SV153: $i,SV130: $i,SV42: $i,SV35: $i,SV29: $i,SV14: $i] :
( ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false )
| ( ( ~ ( ~ ! [SY624: $i,SY625: $i] :
( ~ ( member @ SY624 @ SV42 )
| ~ ( member @ SY625 @ SV153 )
| ! [SY600: $i] :
( ~ ( apply @ SV35 @ SY624 @ SY600 )
| ~ ( member @ SY600 @ SV130 )
| ~ ( apply @ SV29 @ SY600 @ SY625 ) )
| ( apply @ SV14 @ SY624 @ SY625 ) )
| ~ ! [SY627: $i,SY628: $i] :
( ~ ( member @ SY627 @ SV42 )
| ~ ( member @ SY628 @ SV153 )
| ~ ( apply @ SV14 @ SY627 @ SY628 )
| ~ ( ~ ~ ( ~ ( apply @ SV35 @ SY627 @ ( sK32_Y @ SY628 @ SY627 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK32_Y @ SY628 @ SY627 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV130 ) )
| ~ ( apply @ SV29 @ ( sK32_Y @ SY628 @ SY627 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY628 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[646]) ).
thf(711,plain,
! [SV15: $i,SV67: $i,SV95: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK24_X1 @ SV95 @ SV67 @ SV15 ) @ SV67 )
| ~ ( member @ ( sK25_SY159 @ SV95 @ SV67 @ SV15 ) @ SV67 ) )
| ~ ( member @ ( sK26_SY161 @ SV95 @ SV67 @ SV15 ) @ SV95 ) )
= $false )
| ( ( injective @ SV15 @ SV67 @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[647]) ).
thf(712,plain,
! [SV67: $i,SV95: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV15 @ ( sK24_X1 @ SV95 @ SV67 @ SV15 ) @ ( sK26_SY161 @ SV95 @ SV67 @ SV15 ) )
| ~ ( apply @ SV15 @ ( sK25_SY159 @ SV95 @ SV67 @ SV15 ) @ ( sK26_SY161 @ SV95 @ SV67 @ SV15 ) ) )
| ~ ( ( ( sK24_X1 @ SV95 @ SV67 @ SV15 )
!= ( sK25_SY159 @ SV95 @ SV67 @ SV15 ) ) ) )
= $false )
| ( ( injective @ SV15 @ SV67 @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[648]) ).
thf(713,plain,
! [SV15: $i,SV96: $i,SV181: $i,SV172: $i,SV68: $i,SV154: $i] :
( ( ( ~ ( member @ SV154 @ SV68 )
| ~ ( member @ SV172 @ SV68 )
| ~ ( member @ SV181 @ SV96 )
| ~ ( apply @ SV15 @ SV154 @ SV181 )
| ~ ( apply @ SV15 @ SV172 @ SV181 )
| ( SV154 = SV172 ) )
= $true )
| ( ( injective @ SV15 @ SV68 @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(714,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 )
| ~ ( member @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( member @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 ) )
| ~ ( member @ ( sK15_SY156 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( apply @ SV36 @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ( apply @ SV16 @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ( apply @ SV16 @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK15_SY156 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) ) )
= $false )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[652]) ).
thf(715,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ( ~ ~ ( apply @ SV133 @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK15_SY156 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
= $false )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[652]) ).
thf(716,plain,
! [SV134: $i,SV16: $i,SV36: $i,SV115: $i,SV30: $i,SV182: $i] :
( ( ( ! [SY659: $i,SY660: $i,SY661: $i] :
( ~ ( member @ SV182 @ SV30 )
| ~ ( member @ SY659 @ SV115 )
| ~ ( member @ SY660 @ SV30 )
| ~ ( member @ SY661 @ SV115 )
| ~ ( apply @ SV36 @ SV182 @ SY660 )
| ~ ( apply @ SV16 @ SV182 @ SY659 )
| ~ ( apply @ SV16 @ SY660 @ SY661 )
| ( apply @ SV134 @ SY659 @ SY661 ) ) )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV115 @ SV134 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(717,plain,
! [SV173: $i,SV135: $i,SV17: $i] :
( ( ( member @ SV17 @ ( intersection @ SV135 @ SV173 ) )
= $false )
| ( ( member @ SV17 @ SV135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[655]) ).
thf(718,plain,
! [SV155: $i,SV136: $i,SV17: $i] :
( ( ( member @ SV17 @ ( intersection @ SV136 @ SV155 ) )
= $false )
| ( ( member @ SV17 @ SV155 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[656]) ).
thf(719,plain,
! [SV183: $i,SV137: $i,SV18: $i] :
( ( ( member @ SV18 @ ( unordered_pair @ SV137 @ SV183 ) )
= $true )
| ( ( SV18 = SV137 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(720,plain,
! [SV138: $i,SV156: $i,SV18: $i] :
( ( ( SV18 = SV156 )
= $false )
| ( ( member @ SV18 @ ( unordered_pair @ SV138 @ SV156 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(721,plain,
! [SV157: $i,SV139: $i,SV19: $i] :
( ( ( one_to_one @ SV19 @ SV139 @ SV157 )
= $false )
| ( ( injective @ SV19 @ SV139 @ SV157 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[660]) ).
thf(722,plain,
! [SV158: $i,SV140: $i,SV19: $i] :
( ( ( one_to_one @ SV19 @ SV140 @ SV158 )
= $false )
| ( ( surjective @ SV19 @ SV140 @ SV158 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[661]) ).
thf(723,plain,
! [SV20: $i,SV46: $i,SV31: $i,SV73: $i,SV174: $i,SV37: $i,SV159: $i] :
( ( ( ~ ( member @ SV159 @ SV37 )
| ~ ( member @ SV174 @ SV73 ) )
= $true )
| ( ( ! [SY648: $i] :
( ~ ( apply @ SV31 @ SV159 @ SY648 )
| ~ ( member @ SY648 @ SV46 )
| ~ ( apply @ SV20 @ SY648 @ SV174 ) )
| ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SV159 @ SV174 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[662]) ).
thf(724,plain,
! [SV46: $i,SV31: $i,SV20: $i,SV73: $i,SV175: $i,SV37: $i,SV160: $i] :
( ( ( ~ ( member @ SV160 @ SV37 )
| ~ ( member @ SV175 @ SV73 ) )
= $true )
| ( ( ~ ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SV160 @ SV175 )
| ~ ( ~ ~ ( ~ ( apply @ SV31 @ SV160 @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) )
| ~ ( member @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SV46 ) )
| ~ ( apply @ SV20 @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SV175 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[663]) ).
thf(725,plain,
! [SV21: $i,SV78: $i,SV100: $i] :
( ( ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
| ~ ( member @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ( member @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) )
| ~ ( ( ( sK38_SY170 @ SV100 @ SV78 @ SV21 )
!= ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) ) ) ) )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[669]) ).
thf(726,plain,
! [SV78: $i,SV100: $i,SV21: $i] :
( ( ( ! [SY560: $i] :
( ~ ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SY560 )
| ~ ( member @ SY560 @ SV100 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
| ~ ( member @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ( member @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) )
| ~ ( ( ( sK38_SY170 @ SV100 @ SV78 @ SV21 )
!= ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) ) ) ) )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[670]) ).
thf(727,plain,
! [SV161: $i,SV142: $i,SV21: $i] :
( ( ( maps @ SV21 @ SV142 @ SV161 )
= $false )
| ( ( ! [SY634: $i] :
( ~ ( member @ SY634 @ SV142 )
| ~ ( ~ ( apply @ SV21 @ SY634 @ ( sK36_Y @ SY634 @ SV161 @ SV142 @ SV21 ) )
| ~ ( member @ ( sK36_Y @ SY634 @ SV161 @ SV142 @ SV21 ) @ SV161 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[671]) ).
thf(728,plain,
! [SV162: $i,SV143: $i,SV21: $i] :
( ( ( maps @ SV21 @ SV143 @ SV162 )
= $false )
| ( ( ! [SY635: $i,SY636: $i,SY637: $i] :
( ~ ( member @ SY635 @ SV143 )
| ~ ( member @ SY636 @ SV162 )
| ~ ( member @ SY637 @ SV162 )
| ~ ( apply @ SV21 @ SY635 @ SY636 )
| ~ ( apply @ SV21 @ SY635 @ SY637 )
| ( SY636 = SY637 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[672]) ).
thf(729,plain,
! [SV81: $i,SV22: $i,SV101: $i,SV163: $i,SV2: $i] :
( ( ( apply @ SV2 @ SV163 @ SV101 )
= $false )
| ( ( ~ ( member @ SV163 @ SV22 ) )
= $true )
| ( ( ~ ( member @ SV101 @ SV81 ) )
= $true )
| ( ( member @ SV101 @ ( image3 @ SV2 @ SV22 @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[675]) ).
thf(730,plain,
! [SV145: $i,SV22: $i,SV2: $i,SV164: $i] :
( ( ( member @ SV164 @ ( image3 @ SV2 @ SV22 @ SV145 ) )
= $false )
| ( ( ~ ( ~ ( apply @ SV2 @ ( sK18_X @ SV164 @ SV145 @ SV22 @ SV2 ) @ SV164 )
| ~ ( member @ ( sK18_X @ SV164 @ SV145 @ SV22 @ SV2 ) @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[676]) ).
thf(731,plain,
! [SV146: $i,SV22: $i,SV2: $i,SV165: $i] :
( ( ( member @ SV165 @ ( image3 @ SV2 @ SV22 @ SV146 ) )
= $false )
| ( ( member @ SV165 @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[677]) ).
thf(732,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 )
| ~ ( member @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( member @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 ) )
| ~ ( member @ ( sK11_SY150 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( apply @ SV32 @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ( apply @ SV3 @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ( apply @ SV3 @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK11_SY150 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) ) )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[678]) ).
thf(733,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ( ~ ( apply @ SV117 @ ( sK11_SY150 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[679]) ).
thf(734,plain,
! [SV118: $i,SV3: $i,SV32: $i,SV103: $i,SV184: $i,SV23: $i,SV176: $i] :
( ( ( ! [SY662: $i,SY663: $i] :
( ~ ( member @ SV176 @ SV23 )
| ~ ( member @ SV184 @ SV103 )
| ~ ( member @ SY662 @ SV23 )
| ~ ( member @ SY663 @ SV103 )
| ~ ( apply @ SV32 @ SV176 @ SY662 )
| ~ ( apply @ SV3 @ SV176 @ SV184 )
| ~ ( apply @ SV3 @ SY662 @ SY663 )
| ( apply @ SV118 @ SY663 @ SV184 ) ) )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV103 @ SV118 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(735,plain,
! [SV166: $i,SV122: $i,SV5: $i] :
( ( ( member @ SV5 @ SV122 )
= $false )
| ( ( member @ SV5 @ ( difference @ SV166 @ SV122 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[685]) ).
thf(736,plain,
! [SV7: $i,SV24: $i,SV33: $i,SV104: $i,SV125: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 )
| ~ ( member @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
| ~ ( member @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 ) )
| ~ ( member @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
| ~ ( apply @ SV7 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ( apply @ SV7 @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) ) )
= $false )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[688]) ).
thf(737,plain,
! [SV7: $i,SV24: $i,SV104: $i,SV125: $i,SV33: $i] :
( ( ( ~ ~ ( ~ ( ~ ( apply @ SV33 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
| ~ ( apply @ SV125 @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ( ( apply @ SV33 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
| ( apply @ SV125 @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) ) ) )
= $false )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[688]) ).
thf(738,plain,
! [SV178: $i,SV167: $i,SV33: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 ) )
= $true )
| ( ( ! [SY652: $i,SY653: $i] :
~ ( ~ ! [SY654: $i,SY655: $i] :
( ~ ( member @ SY652 @ SV24 )
| ~ ( member @ SY653 @ SV167 )
| ~ ( member @ SY654 @ SV24 )
| ~ ( member @ SY655 @ SV167 )
| ~ ( apply @ SV7 @ SY652 @ SY653 )
| ~ ( apply @ SV7 @ SY654 @ SY655 )
| ~ ( apply @ SV33 @ SY652 @ SY654 )
| ( apply @ SV178 @ SY653 @ SY655 ) )
| ~ ! [SY656: $i,SY657: $i] :
( ~ ( member @ SY652 @ SV24 )
| ~ ( member @ SY653 @ SV167 )
| ~ ( member @ SY656 @ SV24 )
| ~ ( member @ SY657 @ SV167 )
| ~ ( apply @ SV7 @ SY652 @ SY653 )
| ~ ( apply @ SV7 @ SY656 @ SY657 )
| ~ ( apply @ SV178 @ SY653 @ SY657 )
| ( apply @ SV33 @ SY652 @ SY656 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[689]) ).
thf(739,plain,
! [SV33: $i,SV24: $i,SV7: $i] :
( ( ! [SY440: $i] :
( ! [SY441: $i] :
~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SY440 @ SY441 )
| ( maps @ SV7 @ SV24 @ SY440 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[690]) ).
thf(740,plain,
! [SV33: $i,SV24: $i,SV7: $i] :
( ( ! [SY442: $i] :
( ! [SY443: $i] :
~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SY442 @ SY443 )
| ( one_to_one @ SV7 @ SV24 @ SY442 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[691]) ).
thf(741,plain,
! [SV8: $i,SV25: $i,SV86: $i,SV105: $i] :
( ( ( ~ ( member @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) @ SV86 )
| ~ ( member @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) @ SV105 ) )
= $false )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV86 @ SV105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[692]) ).
thf(742,plain,
! [SV8: $i,SV86: $i,SV105: $i,SV25: $i] :
( ( ( ~ ( ~ ( apply @ SV25 @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) )
| ~ ( apply @ SV8 @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) ) )
| ~ ( ( apply @ SV25 @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) )
| ( apply @ SV8 @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) ) ) )
= $false )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV86 @ SV105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[693]) ).
thf(743,plain,
! [SV8: $i,SV25: $i,SV106: $i,SV87: $i] :
( ( ( ! [SY569: $i,SY570: $i] :
( ~ ( member @ SY569 @ SV87 )
| ~ ( member @ SY570 @ SV106 )
| ~ ( apply @ SV25 @ SY569 @ SY570 )
| ( apply @ SV8 @ SY570 @ SY569 ) ) )
= $true )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV87 @ SV106 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[694]) ).
thf(744,plain,
! [SV25: $i,SV8: $i,SV106: $i,SV87: $i] :
( ( ( ! [SY571: $i,SY572: $i] :
( ~ ( member @ SY571 @ SV87 )
| ~ ( member @ SY572 @ SV106 )
| ~ ( apply @ SV8 @ SY572 @ SY571 )
| ( apply @ SV25 @ SY571 @ SY572 ) ) )
= $true )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV87 @ SV106 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[695]) ).
thf(745,plain,
! [SV9: $i,SV26: $i,SV107: $i,SV34: $i,SV126: $i] :
( ( ( member @ SV126 @ SV34 )
= $false )
| ( ( member @ SV107 @ SV26 )
= $false )
| ( ( ~ ( apply @ SV9 @ SV107 @ SV126 )
| ( apply @ ( inverse_function @ SV9 @ SV26 @ SV34 ) @ SV126 @ SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[696]) ).
thf(746,plain,
! [SV9: $i,SV26: $i,SV108: $i,SV34: $i,SV127: $i] :
( ( ( member @ SV127 @ SV34 )
= $false )
| ( ( member @ SV108 @ SV26 )
= $false )
| ( ( ~ ( apply @ ( inverse_function @ SV9 @ SV26 @ SV34 ) @ SV127 @ SV108 )
| ( apply @ SV9 @ SV108 @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[697]) ).
thf(747,plain,
! [SV63: $i,SV90: $i,SV179: $i,SV11: $i] :
( ( ( ~ ( apply @ SV11 @ SV179 @ ( sK23_Y @ SV90 @ SV63 @ SV11 ) ) )
= $true )
| ( ( ~ ( member @ SV179 @ SV63 ) )
= $true )
| ( ( surjective @ SV11 @ SV63 @ SV90 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[701]) ).
thf(748,plain,
! [SV64: $i,SV91: $i,SV149: $i,SV11: $i] :
( ( ( ~ ( apply @ SV11 @ ( sK22_E @ SV149 @ SV91 @ SV64 @ SV11 ) @ SV149 )
| ~ ( member @ ( sK22_E @ SV149 @ SV91 @ SV64 @ SV11 ) @ SV64 ) )
= $false )
| ( ( member @ SV149 @ SV91 )
= $false )
| ( ( surjective @ SV11 @ SV64 @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[702]) ).
thf(749,plain,
! [SV92: $i,SV27: $i,SV168: $i,SV109: $i,SV12: $i] :
( ( ( apply @ SV12 @ SV109 @ SV168 )
= $false )
| ( ( ~ ( member @ SV168 @ SV27 ) )
= $true )
| ( ( ~ ( member @ SV109 @ SV92 ) )
= $true )
| ( ( member @ SV109 @ ( inverse_image3 @ SV12 @ SV27 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[703]) ).
thf(750,plain,
! [SV150: $i,SV27: $i,SV12: $i,SV169: $i] :
( ( ( member @ SV169 @ ( inverse_image3 @ SV12 @ SV27 @ SV150 ) )
= $false )
| ( ( ~ ( ~ ( apply @ SV12 @ SV169 @ ( sK16_Y @ SV169 @ SV150 @ SV27 @ SV12 ) )
| ~ ( member @ ( sK16_Y @ SV169 @ SV150 @ SV27 @ SV12 ) @ SV27 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[704]) ).
thf(751,plain,
! [SV151: $i,SV27: $i,SV12: $i,SV170: $i] :
( ( ( member @ SV170 @ ( inverse_image3 @ SV12 @ SV27 @ SV151 ) )
= $false )
| ( ( member @ SV170 @ SV151 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[705]) ).
thf(752,plain,
! [SV13: $i,SV28: $i,SV93: $i,SV110: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ SV93 )
| ~ ( member @ ( sK29_SY162 @ SV110 @ SV93 @ SV28 @ SV13 ) @ SV110 ) )
| ~ ( member @ ( sK30_SY164 @ SV110 @ SV93 @ SV28 @ SV13 ) @ SV110 ) )
= $false )
| ( ( equal_maps @ SV13 @ SV28 @ SV93 @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[706]) ).
thf(753,plain,
! [SV28: $i,SV93: $i,SV110: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV13 @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ ( sK29_SY162 @ SV110 @ SV93 @ SV28 @ SV13 ) )
| ~ ( apply @ SV28 @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ ( sK30_SY164 @ SV110 @ SV93 @ SV28 @ SV13 ) ) )
| ~ ( ( ( sK29_SY162 @ SV110 @ SV93 @ SV28 @ SV13 )
!= ( sK30_SY164 @ SV110 @ SV93 @ SV28 @ SV13 ) ) ) )
= $false )
| ( ( equal_maps @ SV13 @ SV28 @ SV93 @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[707]) ).
thf(754,plain,
! [SV28: $i,SV13: $i,SV185: $i,SV111: $i,SV180: $i,SV94: $i,SV171: $i] :
( ( ( ~ ( member @ SV171 @ SV94 )
| ~ ( member @ SV180 @ SV111 )
| ~ ( member @ SV185 @ SV111 )
| ~ ( apply @ SV13 @ SV171 @ SV180 )
| ~ ( apply @ SV28 @ SV171 @ SV185 )
| ( SV180 = SV185 ) )
= $true )
| ( ( equal_maps @ SV13 @ SV28 @ SV94 @ SV111 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(755,plain,
! [SV14: $i,SV29: $i,SV35: $i,SV42: $i,SV129: $i,SV152: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV42 )
| ~ ( member @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV152 ) ) )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[709]) ).
thf(756,plain,
! [SV14: $i,SV29: $i,SV42: $i,SV129: $i,SV152: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ( ! [SY623: $i] :
( ~ ( apply @ SV35 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY623 )
| ~ ( member @ SY623 @ SV129 )
| ~ ( apply @ SV29 @ SY623 @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ~ ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( apply @ SV35 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV129 ) )
| ~ ( apply @ SV29 @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) ) ) )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[709]) ).
thf(757,plain,
! [SV14: $i,SV29: $i,SV130: $i,SV35: $i,SV153: $i,SV42: $i] :
( ( ( ~ ! [SY624: $i,SY625: $i] :
( ~ ( member @ SY624 @ SV42 )
| ~ ( member @ SY625 @ SV153 )
| ! [SY600: $i] :
( ~ ( apply @ SV35 @ SY624 @ SY600 )
| ~ ( member @ SY600 @ SV130 )
| ~ ( apply @ SV29 @ SY600 @ SY625 ) )
| ( apply @ SV14 @ SY624 @ SY625 ) )
| ~ ! [SY627: $i,SY628: $i] :
( ~ ( member @ SY627 @ SV42 )
| ~ ( member @ SY628 @ SV153 )
| ~ ( apply @ SV14 @ SY627 @ SY628 )
| ~ ( ~ ~ ( ~ ( apply @ SV35 @ SY627 @ ( sK32_Y @ SY628 @ SY627 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK32_Y @ SY628 @ SY627 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV130 ) )
| ~ ( apply @ SV29 @ ( sK32_Y @ SY628 @ SY627 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY628 ) ) ) )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[710]) ).
thf(758,plain,
! [SV15: $i,SV67: $i,SV95: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK24_X1 @ SV95 @ SV67 @ SV15 ) @ SV67 )
| ~ ( member @ ( sK25_SY159 @ SV95 @ SV67 @ SV15 ) @ SV67 ) ) )
= $false )
| ( ( injective @ SV15 @ SV67 @ SV95 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[711]) ).
thf(759,plain,
! [SV15: $i,SV67: $i,SV95: $i] :
( ( ( ~ ( member @ ( sK26_SY161 @ SV95 @ SV67 @ SV15 ) @ SV95 ) )
= $false )
| ( ( injective @ SV15 @ SV67 @ SV95 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[711]) ).
thf(760,plain,
! [SV67: $i,SV95: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV15 @ ( sK24_X1 @ SV95 @ SV67 @ SV15 ) @ ( sK26_SY161 @ SV95 @ SV67 @ SV15 ) )
| ~ ( apply @ SV15 @ ( sK25_SY159 @ SV95 @ SV67 @ SV15 ) @ ( sK26_SY161 @ SV95 @ SV67 @ SV15 ) ) ) )
= $false )
| ( ( injective @ SV15 @ SV67 @ SV95 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[712]) ).
thf(761,plain,
! [SV15: $i,SV67: $i,SV95: $i] :
( ( ( ~ ( ( ( sK24_X1 @ SV95 @ SV67 @ SV15 )
!= ( sK25_SY159 @ SV95 @ SV67 @ SV15 ) ) ) )
= $false )
| ( ( injective @ SV15 @ SV67 @ SV95 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[712]) ).
thf(762,plain,
! [SV15: $i,SV96: $i,SV181: $i,SV172: $i,SV68: $i,SV154: $i] :
( ( ( ~ ( member @ SV154 @ SV68 )
| ~ ( member @ SV172 @ SV68 )
| ~ ( member @ SV181 @ SV96 ) )
= $true )
| ( ( ~ ( apply @ SV15 @ SV154 @ SV181 )
| ~ ( apply @ SV15 @ SV172 @ SV181 )
| ( SV154 = SV172 ) )
= $true )
| ( ( injective @ SV15 @ SV68 @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[713]) ).
thf(763,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 )
| ~ ( member @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( member @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 ) )
| ~ ( member @ ( sK15_SY156 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( apply @ SV36 @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ( apply @ SV16 @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ( apply @ SV16 @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK15_SY156 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) ) )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[714]) ).
thf(764,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ( ~ ( apply @ SV133 @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK15_SY156 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[715]) ).
thf(765,plain,
! [SV134: $i,SV16: $i,SV36: $i,SV115: $i,SV186: $i,SV30: $i,SV182: $i] :
( ( ( ! [SY664: $i,SY665: $i] :
( ~ ( member @ SV182 @ SV30 )
| ~ ( member @ SV186 @ SV115 )
| ~ ( member @ SY664 @ SV30 )
| ~ ( member @ SY665 @ SV115 )
| ~ ( apply @ SV36 @ SV182 @ SY664 )
| ~ ( apply @ SV16 @ SV182 @ SV186 )
| ~ ( apply @ SV16 @ SY664 @ SY665 )
| ( apply @ SV134 @ SV186 @ SY665 ) ) )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV115 @ SV134 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(766,plain,
! [SV20: $i,SV46: $i,SV31: $i,SV73: $i,SV174: $i,SV37: $i,SV159: $i] :
( ( ( ~ ( member @ SV159 @ SV37 ) )
= $true )
| ( ( ~ ( member @ SV174 @ SV73 ) )
= $true )
| ( ( ! [SY648: $i] :
( ~ ( apply @ SV31 @ SV159 @ SY648 )
| ~ ( member @ SY648 @ SV46 )
| ~ ( apply @ SV20 @ SY648 @ SV174 ) )
| ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SV159 @ SV174 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[723]) ).
thf(767,plain,
! [SV46: $i,SV31: $i,SV20: $i,SV73: $i,SV175: $i,SV37: $i,SV160: $i] :
( ( ( ~ ( member @ SV160 @ SV37 ) )
= $true )
| ( ( ~ ( member @ SV175 @ SV73 ) )
= $true )
| ( ( ~ ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SV160 @ SV175 )
| ~ ( ~ ~ ( ~ ( apply @ SV31 @ SV160 @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) )
| ~ ( member @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SV46 ) )
| ~ ( apply @ SV20 @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SV175 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[724]) ).
thf(768,plain,
! [SV21: $i,SV78: $i,SV100: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
| ~ ( member @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ( member @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) )
| ~ ( ( ( sK38_SY170 @ SV100 @ SV78 @ SV21 )
!= ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) ) ) )
= $false )
| ( ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[725]) ).
thf(769,plain,
! [SV187: $i,SV78: $i,SV100: $i,SV21: $i] :
( ( ( ~ ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV187 )
| ~ ( member @ SV187 @ SV100 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
| ~ ( member @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ( member @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) )
| ~ ( ( ( sK38_SY170 @ SV100 @ SV78 @ SV21 )
!= ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) ) ) ) )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(770,plain,
! [SV161: $i,SV21: $i,SV142: $i,SV188: $i] :
( ( ( ~ ( member @ SV188 @ SV142 )
| ~ ( ~ ( apply @ SV21 @ SV188 @ ( sK36_Y @ SV188 @ SV161 @ SV142 @ SV21 ) )
| ~ ( member @ ( sK36_Y @ SV188 @ SV161 @ SV142 @ SV21 ) @ SV161 ) ) )
= $true )
| ( ( maps @ SV21 @ SV142 @ SV161 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(771,plain,
! [SV21: $i,SV162: $i,SV143: $i,SV189: $i] :
( ( ( ! [SY666: $i,SY667: $i] :
( ~ ( member @ SV189 @ SV143 )
| ~ ( member @ SY666 @ SV162 )
| ~ ( member @ SY667 @ SV162 )
| ~ ( apply @ SV21 @ SV189 @ SY666 )
| ~ ( apply @ SV21 @ SV189 @ SY667 )
| ( SY666 = SY667 ) ) )
= $true )
| ( ( maps @ SV21 @ SV143 @ SV162 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(772,plain,
! [SV81: $i,SV101: $i,SV2: $i,SV22: $i,SV163: $i] :
( ( ( member @ SV163 @ SV22 )
= $false )
| ( ( apply @ SV2 @ SV163 @ SV101 )
= $false )
| ( ( ~ ( member @ SV101 @ SV81 ) )
= $true )
| ( ( member @ SV101 @ ( image3 @ SV2 @ SV22 @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[729]) ).
thf(773,plain,
! [SV22: $i,SV145: $i,SV164: $i,SV2: $i] :
( ( ( ~ ( apply @ SV2 @ ( sK18_X @ SV164 @ SV145 @ SV22 @ SV2 ) @ SV164 )
| ~ ( member @ ( sK18_X @ SV164 @ SV145 @ SV22 @ SV2 ) @ SV22 ) )
= $false )
| ( ( member @ SV164 @ ( image3 @ SV2 @ SV22 @ SV145 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[730]) ).
thf(774,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 )
| ~ ( member @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( member @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 ) )
| ~ ( member @ ( sK11_SY150 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( apply @ SV32 @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ( apply @ SV3 @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ( apply @ SV3 @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK11_SY150 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
= $false )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[732]) ).
thf(775,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ( apply @ SV117 @ ( sK11_SY150 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) )
= $false )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[733]) ).
thf(776,plain,
! [SV118: $i,SV3: $i,SV32: $i,SV190: $i,SV103: $i,SV184: $i,SV23: $i,SV176: $i] :
( ( ( ! [SY668: $i] :
( ~ ( member @ SV176 @ SV23 )
| ~ ( member @ SV184 @ SV103 )
| ~ ( member @ SV190 @ SV23 )
| ~ ( member @ SY668 @ SV103 )
| ~ ( apply @ SV32 @ SV176 @ SV190 )
| ~ ( apply @ SV3 @ SV176 @ SV184 )
| ~ ( apply @ SV3 @ SV190 @ SY668 )
| ( apply @ SV118 @ SY668 @ SV184 ) ) )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV103 @ SV118 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(777,plain,
! [SV7: $i,SV24: $i,SV33: $i,SV104: $i,SV125: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 )
| ~ ( member @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
| ~ ( member @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 ) )
| ~ ( member @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
| ~ ( apply @ SV7 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ( apply @ SV7 @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) ) )
= $true )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[736]) ).
thf(778,plain,
! [SV7: $i,SV24: $i,SV104: $i,SV125: $i,SV33: $i] :
( ( ( ~ ( ~ ( ~ ( apply @ SV33 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
| ~ ( apply @ SV125 @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ( ( apply @ SV33 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
| ( apply @ SV125 @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) ) ) )
= $true )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[737]) ).
thf(779,plain,
! [SV178: $i,SV167: $i,SV33: $i,SV24: $i,SV7: $i] :
( ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false )
| ( ( ! [SY652: $i,SY653: $i] :
~ ( ~ ! [SY654: $i,SY655: $i] :
( ~ ( member @ SY652 @ SV24 )
| ~ ( member @ SY653 @ SV167 )
| ~ ( member @ SY654 @ SV24 )
| ~ ( member @ SY655 @ SV167 )
| ~ ( apply @ SV7 @ SY652 @ SY653 )
| ~ ( apply @ SV7 @ SY654 @ SY655 )
| ~ ( apply @ SV33 @ SY652 @ SY654 )
| ( apply @ SV178 @ SY653 @ SY655 ) )
| ~ ! [SY656: $i,SY657: $i] :
( ~ ( member @ SY652 @ SV24 )
| ~ ( member @ SY653 @ SV167 )
| ~ ( member @ SY656 @ SV24 )
| ~ ( member @ SY657 @ SV167 )
| ~ ( apply @ SV7 @ SY652 @ SY653 )
| ~ ( apply @ SV7 @ SY656 @ SY657 )
| ~ ( apply @ SV178 @ SY653 @ SY657 )
| ( apply @ SV33 @ SY652 @ SY656 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[738]) ).
thf(780,plain,
! [SV191: $i,SV33: $i,SV24: $i,SV7: $i] :
( ( ! [SY669: $i] :
~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SV191 @ SY669 )
| ( maps @ SV7 @ SV24 @ SV191 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(781,plain,
! [SV192: $i,SV33: $i,SV24: $i,SV7: $i] :
( ( ! [SY670: $i] :
~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SV192 @ SY670 )
| ( one_to_one @ SV7 @ SV24 @ SV192 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(782,plain,
! [SV8: $i,SV25: $i,SV86: $i,SV105: $i] :
( ( ( ~ ( member @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) @ SV86 ) )
= $false )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV86 @ SV105 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[741]) ).
thf(783,plain,
! [SV8: $i,SV25: $i,SV86: $i,SV105: $i] :
( ( ( ~ ( member @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) @ SV105 ) )
= $false )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV86 @ SV105 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[741]) ).
thf(784,plain,
! [SV8: $i,SV86: $i,SV105: $i,SV25: $i] :
( ( ( ~ ( ~ ( apply @ SV25 @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) )
| ~ ( apply @ SV8 @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) ) ) )
= $false )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV86 @ SV105 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[742]) ).
thf(785,plain,
! [SV8: $i,SV86: $i,SV105: $i,SV25: $i] :
( ( ( ~ ( ( apply @ SV25 @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) )
| ( apply @ SV8 @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) ) ) )
= $false )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV86 @ SV105 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[742]) ).
thf(786,plain,
! [SV8: $i,SV25: $i,SV106: $i,SV87: $i,SV193: $i] :
( ( ( ! [SY671: $i] :
( ~ ( member @ SV193 @ SV87 )
| ~ ( member @ SY671 @ SV106 )
| ~ ( apply @ SV25 @ SV193 @ SY671 )
| ( apply @ SV8 @ SY671 @ SV193 ) ) )
= $true )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV87 @ SV106 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(787,plain,
! [SV25: $i,SV8: $i,SV106: $i,SV87: $i,SV194: $i] :
( ( ( ! [SY672: $i] :
( ~ ( member @ SV194 @ SV87 )
| ~ ( member @ SY672 @ SV106 )
| ~ ( apply @ SV8 @ SY672 @ SV194 )
| ( apply @ SV25 @ SV194 @ SY672 ) ) )
= $true )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV87 @ SV106 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(788,plain,
! [SV34: $i,SV26: $i,SV126: $i,SV107: $i,SV9: $i] :
( ( ( ~ ( apply @ SV9 @ SV107 @ SV126 ) )
= $true )
| ( ( apply @ ( inverse_function @ SV9 @ SV26 @ SV34 ) @ SV126 @ SV107 )
= $true )
| ( ( member @ SV107 @ SV26 )
= $false )
| ( ( member @ SV126 @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[745]) ).
thf(789,plain,
! [SV108: $i,SV127: $i,SV34: $i,SV26: $i,SV9: $i] :
( ( ( ~ ( apply @ ( inverse_function @ SV9 @ SV26 @ SV34 ) @ SV127 @ SV108 ) )
= $true )
| ( ( apply @ SV9 @ SV108 @ SV127 )
= $true )
| ( ( member @ SV108 @ SV26 )
= $false )
| ( ( member @ SV127 @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[746]) ).
thf(790,plain,
! [SV63: $i,SV90: $i,SV179: $i,SV11: $i] :
( ( ( apply @ SV11 @ SV179 @ ( sK23_Y @ SV90 @ SV63 @ SV11 ) )
= $false )
| ( ( ~ ( member @ SV179 @ SV63 ) )
= $true )
| ( ( surjective @ SV11 @ SV63 @ SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[747]) ).
thf(791,plain,
! [SV64: $i,SV91: $i,SV149: $i,SV11: $i] :
( ( ( ~ ( apply @ SV11 @ ( sK22_E @ SV149 @ SV91 @ SV64 @ SV11 ) @ SV149 ) )
= $false )
| ( ( member @ SV149 @ SV91 )
= $false )
| ( ( surjective @ SV11 @ SV64 @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[748]) ).
thf(792,plain,
! [SV11: $i,SV64: $i,SV91: $i,SV149: $i] :
( ( ( ~ ( member @ ( sK22_E @ SV149 @ SV91 @ SV64 @ SV11 ) @ SV64 ) )
= $false )
| ( ( member @ SV149 @ SV91 )
= $false )
| ( ( surjective @ SV11 @ SV64 @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[748]) ).
thf(793,plain,
! [SV92: $i,SV109: $i,SV12: $i,SV27: $i,SV168: $i] :
( ( ( member @ SV168 @ SV27 )
= $false )
| ( ( apply @ SV12 @ SV109 @ SV168 )
= $false )
| ( ( ~ ( member @ SV109 @ SV92 ) )
= $true )
| ( ( member @ SV109 @ ( inverse_image3 @ SV12 @ SV27 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[749]) ).
thf(794,plain,
! [SV27: $i,SV150: $i,SV169: $i,SV12: $i] :
( ( ( ~ ( apply @ SV12 @ SV169 @ ( sK16_Y @ SV169 @ SV150 @ SV27 @ SV12 ) )
| ~ ( member @ ( sK16_Y @ SV169 @ SV150 @ SV27 @ SV12 ) @ SV27 ) )
= $false )
| ( ( member @ SV169 @ ( inverse_image3 @ SV12 @ SV27 @ SV150 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[750]) ).
thf(795,plain,
! [SV13: $i,SV28: $i,SV93: $i,SV110: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ SV93 )
| ~ ( member @ ( sK29_SY162 @ SV110 @ SV93 @ SV28 @ SV13 ) @ SV110 ) ) )
= $false )
| ( ( equal_maps @ SV13 @ SV28 @ SV93 @ SV110 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[752]) ).
thf(796,plain,
! [SV13: $i,SV28: $i,SV93: $i,SV110: $i] :
( ( ( ~ ( member @ ( sK30_SY164 @ SV110 @ SV93 @ SV28 @ SV13 ) @ SV110 ) )
= $false )
| ( ( equal_maps @ SV13 @ SV28 @ SV93 @ SV110 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[752]) ).
thf(797,plain,
! [SV28: $i,SV93: $i,SV110: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV13 @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ ( sK29_SY162 @ SV110 @ SV93 @ SV28 @ SV13 ) )
| ~ ( apply @ SV28 @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ ( sK30_SY164 @ SV110 @ SV93 @ SV28 @ SV13 ) ) ) )
= $false )
| ( ( equal_maps @ SV13 @ SV28 @ SV93 @ SV110 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[753]) ).
thf(798,plain,
! [SV13: $i,SV28: $i,SV93: $i,SV110: $i] :
( ( ( ~ ( ( ( sK29_SY162 @ SV110 @ SV93 @ SV28 @ SV13 )
!= ( sK30_SY164 @ SV110 @ SV93 @ SV28 @ SV13 ) ) ) )
= $false )
| ( ( equal_maps @ SV13 @ SV28 @ SV93 @ SV110 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[753]) ).
thf(799,plain,
! [SV28: $i,SV13: $i,SV185: $i,SV111: $i,SV180: $i,SV94: $i,SV171: $i] :
( ( ( ~ ( member @ SV171 @ SV94 )
| ~ ( member @ SV180 @ SV111 )
| ~ ( member @ SV185 @ SV111 ) )
= $true )
| ( ( ~ ( apply @ SV13 @ SV171 @ SV180 )
| ~ ( apply @ SV28 @ SV171 @ SV185 )
| ( SV180 = SV185 ) )
= $true )
| ( ( equal_maps @ SV13 @ SV28 @ SV94 @ SV111 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[754]) ).
thf(800,plain,
! [SV14: $i,SV29: $i,SV35: $i,SV42: $i,SV129: $i,SV152: $i] :
( ( ( ~ ( ~ ( member @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV42 )
| ~ ( member @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV152 ) ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[755]) ).
thf(801,plain,
! [SV14: $i,SV29: $i,SV42: $i,SV129: $i,SV152: $i,SV35: $i] :
( ( ( ~ ( ~ ( ! [SY623: $i] :
( ~ ( apply @ SV35 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY623 )
| ~ ( member @ SY623 @ SV129 )
| ~ ( apply @ SV29 @ SY623 @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ~ ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( apply @ SV35 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV129 ) )
| ~ ( apply @ SV29 @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) ) ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[756]) ).
thf(802,plain,
! [SV14: $i,SV29: $i,SV130: $i,SV35: $i,SV153: $i,SV42: $i] :
( ( ( ~ ! [SY624: $i,SY625: $i] :
( ~ ( member @ SY624 @ SV42 )
| ~ ( member @ SY625 @ SV153 )
| ! [SY600: $i] :
( ~ ( apply @ SV35 @ SY624 @ SY600 )
| ~ ( member @ SY600 @ SV130 )
| ~ ( apply @ SV29 @ SY600 @ SY625 ) )
| ( apply @ SV14 @ SY624 @ SY625 ) ) )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[757]) ).
thf(803,plain,
! [SV29: $i,SV130: $i,SV35: $i,SV14: $i,SV153: $i,SV42: $i] :
( ( ( ~ ! [SY627: $i,SY628: $i] :
( ~ ( member @ SY627 @ SV42 )
| ~ ( member @ SY628 @ SV153 )
| ~ ( apply @ SV14 @ SY627 @ SY628 )
| ~ ( ~ ~ ( ~ ( apply @ SV35 @ SY627 @ ( sK32_Y @ SY628 @ SY627 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK32_Y @ SY628 @ SY627 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV130 ) )
| ~ ( apply @ SV29 @ ( sK32_Y @ SY628 @ SY627 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY628 ) ) ) )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[757]) ).
thf(804,plain,
! [SV15: $i,SV67: $i,SV95: $i] :
( ( ( ~ ( ~ ( member @ ( sK24_X1 @ SV95 @ SV67 @ SV15 ) @ SV67 )
| ~ ( member @ ( sK25_SY159 @ SV95 @ SV67 @ SV15 ) @ SV67 ) ) )
= $true )
| ( ( injective @ SV15 @ SV67 @ SV95 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[758]) ).
thf(805,plain,
! [SV15: $i,SV67: $i,SV95: $i] :
( ( ( member @ ( sK26_SY161 @ SV95 @ SV67 @ SV15 ) @ SV95 )
= $true )
| ( ( injective @ SV15 @ SV67 @ SV95 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[759]) ).
thf(806,plain,
! [SV67: $i,SV95: $i,SV15: $i] :
( ( ( ~ ( ~ ( apply @ SV15 @ ( sK24_X1 @ SV95 @ SV67 @ SV15 ) @ ( sK26_SY161 @ SV95 @ SV67 @ SV15 ) )
| ~ ( apply @ SV15 @ ( sK25_SY159 @ SV95 @ SV67 @ SV15 ) @ ( sK26_SY161 @ SV95 @ SV67 @ SV15 ) ) ) )
= $true )
| ( ( injective @ SV15 @ SV67 @ SV95 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[760]) ).
thf(807,plain,
! [SV15: $i,SV67: $i,SV95: $i] :
( ( ( ( ( sK24_X1 @ SV95 @ SV67 @ SV15 )
!= ( sK25_SY159 @ SV95 @ SV67 @ SV15 ) ) )
= $true )
| ( ( injective @ SV15 @ SV67 @ SV95 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[761]) ).
thf(808,plain,
! [SV15: $i,SV96: $i,SV181: $i,SV172: $i,SV68: $i,SV154: $i] :
( ( ( ~ ( member @ SV154 @ SV68 )
| ~ ( member @ SV172 @ SV68 ) )
= $true )
| ( ( ~ ( member @ SV181 @ SV96 ) )
= $true )
| ( ( ~ ( apply @ SV15 @ SV154 @ SV181 )
| ~ ( apply @ SV15 @ SV172 @ SV181 )
| ( SV154 = SV172 ) )
= $true )
| ( ( injective @ SV15 @ SV68 @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[762]) ).
thf(809,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 )
| ~ ( member @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( member @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 ) )
| ~ ( member @ ( sK15_SY156 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( apply @ SV36 @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ( apply @ SV16 @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ( apply @ SV16 @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK15_SY156 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
= $false )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(810,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ( apply @ SV133 @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK15_SY156 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) )
= $false )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[764]) ).
thf(811,plain,
! [SV134: $i,SV16: $i,SV36: $i,SV195: $i,SV115: $i,SV186: $i,SV30: $i,SV182: $i] :
( ( ( ! [SY673: $i] :
( ~ ( member @ SV182 @ SV30 )
| ~ ( member @ SV186 @ SV115 )
| ~ ( member @ SV195 @ SV30 )
| ~ ( member @ SY673 @ SV115 )
| ~ ( apply @ SV36 @ SV182 @ SV195 )
| ~ ( apply @ SV16 @ SV182 @ SV186 )
| ~ ( apply @ SV16 @ SV195 @ SY673 )
| ( apply @ SV134 @ SV186 @ SY673 ) ) )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV115 @ SV134 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(812,plain,
! [SV20: $i,SV46: $i,SV31: $i,SV73: $i,SV174: $i,SV37: $i,SV159: $i] :
( ( ( member @ SV159 @ SV37 )
= $false )
| ( ( ~ ( member @ SV174 @ SV73 ) )
= $true )
| ( ( ! [SY648: $i] :
( ~ ( apply @ SV31 @ SV159 @ SY648 )
| ~ ( member @ SY648 @ SV46 )
| ~ ( apply @ SV20 @ SY648 @ SV174 ) )
| ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SV159 @ SV174 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[766]) ).
thf(813,plain,
! [SV46: $i,SV31: $i,SV20: $i,SV73: $i,SV175: $i,SV37: $i,SV160: $i] :
( ( ( member @ SV160 @ SV37 )
= $false )
| ( ( ~ ( member @ SV175 @ SV73 ) )
= $true )
| ( ( ~ ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SV160 @ SV175 )
| ~ ( ~ ~ ( ~ ( apply @ SV31 @ SV160 @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) )
| ~ ( member @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SV46 ) )
| ~ ( apply @ SV20 @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SV175 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[767]) ).
thf(814,plain,
! [SV21: $i,SV78: $i,SV100: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
| ~ ( member @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ( member @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) @ SV100 ) ) )
= $false )
| ( ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[768]) ).
thf(815,plain,
! [SV78: $i,SV100: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) )
| ~ ( ( ( sK38_SY170 @ SV100 @ SV78 @ SV21 )
!= ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) ) ) )
= $false )
| ( ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[768]) ).
thf(816,plain,
! [SV187: $i,SV78: $i,SV100: $i,SV21: $i] :
( ( ( ~ ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV187 ) )
= $true )
| ( ( ~ ( member @ SV187 @ SV100 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
| ~ ( member @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ( member @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) )
| ~ ( ( ( sK38_SY170 @ SV100 @ SV78 @ SV21 )
!= ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) ) ) ) )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[769]) ).
thf(817,plain,
! [SV161: $i,SV21: $i,SV142: $i,SV188: $i] :
( ( ( ~ ( member @ SV188 @ SV142 ) )
= $true )
| ( ( ~ ( ~ ( apply @ SV21 @ SV188 @ ( sK36_Y @ SV188 @ SV161 @ SV142 @ SV21 ) )
| ~ ( member @ ( sK36_Y @ SV188 @ SV161 @ SV142 @ SV21 ) @ SV161 ) ) )
= $true )
| ( ( maps @ SV21 @ SV142 @ SV161 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[770]) ).
thf(818,plain,
! [SV21: $i,SV162: $i,SV196: $i,SV143: $i,SV189: $i] :
( ( ( ! [SY674: $i] :
( ~ ( member @ SV189 @ SV143 )
| ~ ( member @ SV196 @ SV162 )
| ~ ( member @ SY674 @ SV162 )
| ~ ( apply @ SV21 @ SV189 @ SV196 )
| ~ ( apply @ SV21 @ SV189 @ SY674 )
| ( SV196 = SY674 ) ) )
= $true )
| ( ( maps @ SV21 @ SV143 @ SV162 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(819,plain,
! [SV22: $i,SV163: $i,SV2: $i,SV81: $i,SV101: $i] :
( ( ( member @ SV101 @ SV81 )
= $false )
| ( ( apply @ SV2 @ SV163 @ SV101 )
= $false )
| ( ( member @ SV163 @ SV22 )
= $false )
| ( ( member @ SV101 @ ( image3 @ SV2 @ SV22 @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[772]) ).
thf(820,plain,
! [SV22: $i,SV145: $i,SV164: $i,SV2: $i] :
( ( ( ~ ( apply @ SV2 @ ( sK18_X @ SV164 @ SV145 @ SV22 @ SV2 ) @ SV164 ) )
= $false )
| ( ( member @ SV164 @ ( image3 @ SV2 @ SV22 @ SV145 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[773]) ).
thf(821,plain,
! [SV2: $i,SV22: $i,SV145: $i,SV164: $i] :
( ( ( ~ ( member @ ( sK18_X @ SV164 @ SV145 @ SV22 @ SV2 ) @ SV22 ) )
= $false )
| ( ( member @ SV164 @ ( image3 @ SV2 @ SV22 @ SV145 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[773]) ).
thf(822,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 )
| ~ ( member @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( member @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 ) )
| ~ ( member @ ( sK11_SY150 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( apply @ SV32 @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ( apply @ SV3 @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) ) )
= $false )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[774]) ).
thf(823,plain,
! [SV23: $i,SV32: $i,SV102: $i,SV117: $i,SV3: $i] :
( ( ( ~ ( apply @ SV3 @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK11_SY150 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
= $false )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[774]) ).
thf(824,plain,
! [SV118: $i,SV3: $i,SV32: $i,SV197: $i,SV190: $i,SV103: $i,SV184: $i,SV23: $i,SV176: $i] :
( ( ( ~ ( member @ SV176 @ SV23 )
| ~ ( member @ SV184 @ SV103 )
| ~ ( member @ SV190 @ SV23 )
| ~ ( member @ SV197 @ SV103 )
| ~ ( apply @ SV32 @ SV176 @ SV190 )
| ~ ( apply @ SV3 @ SV176 @ SV184 )
| ~ ( apply @ SV3 @ SV190 @ SV197 )
| ( apply @ SV118 @ SV197 @ SV184 ) )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV103 @ SV118 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(825,plain,
! [SV7: $i,SV24: $i,SV33: $i,SV104: $i,SV125: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 )
| ~ ( member @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
| ~ ( member @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 ) )
| ~ ( member @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
| ~ ( apply @ SV7 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ( apply @ SV7 @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) )
= $false )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[777]) ).
thf(826,plain,
! [SV7: $i,SV24: $i,SV104: $i,SV125: $i,SV33: $i] :
( ( ( ~ ( ~ ( apply @ SV33 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
| ~ ( apply @ SV125 @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) )
| ~ ( ( apply @ SV33 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
| ( apply @ SV125 @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) ) )
= $false )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[778]) ).
thf(827,plain,
! [SV178: $i,SV33: $i,SV7: $i,SV167: $i,SV24: $i,SV198: $i] :
( ( ( ! [SY675: $i] :
~ ( ~ ! [SY676: $i,SY677: $i] :
( ~ ( member @ SV198 @ SV24 )
| ~ ( member @ SY675 @ SV167 )
| ~ ( member @ SY676 @ SV24 )
| ~ ( member @ SY677 @ SV167 )
| ~ ( apply @ SV7 @ SV198 @ SY675 )
| ~ ( apply @ SV7 @ SY676 @ SY677 )
| ~ ( apply @ SV33 @ SV198 @ SY676 )
| ( apply @ SV178 @ SY675 @ SY677 ) )
| ~ ! [SY678: $i,SY679: $i] :
( ~ ( member @ SV198 @ SV24 )
| ~ ( member @ SY675 @ SV167 )
| ~ ( member @ SY678 @ SV24 )
| ~ ( member @ SY679 @ SV167 )
| ~ ( apply @ SV7 @ SV198 @ SY675 )
| ~ ( apply @ SV7 @ SY678 @ SY679 )
| ~ ( apply @ SV178 @ SY675 @ SY679 )
| ( apply @ SV33 @ SV198 @ SY678 ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(828,plain,
! [SV191: $i,SV33: $i,SV24: $i,SV7: $i] :
( ( ( ! [SY669: $i] :
~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SV191 @ SY669 ) )
= $true )
| ( ( maps @ SV7 @ SV24 @ SV191 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[780]) ).
thf(829,plain,
! [SV192: $i,SV33: $i,SV24: $i,SV7: $i] :
( ( ( ! [SY670: $i] :
~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SV192 @ SY670 ) )
= $true )
| ( ( one_to_one @ SV7 @ SV24 @ SV192 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[781]) ).
thf(830,plain,
! [SV8: $i,SV25: $i,SV86: $i,SV105: $i] :
( ( ( member @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) @ SV86 )
= $true )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV86 @ SV105 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[782]) ).
thf(831,plain,
! [SV8: $i,SV25: $i,SV86: $i,SV105: $i] :
( ( ( member @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) @ SV105 )
= $true )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV86 @ SV105 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[783]) ).
thf(832,plain,
! [SV8: $i,SV86: $i,SV105: $i,SV25: $i] :
( ( ( ~ ( apply @ SV25 @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) )
| ~ ( apply @ SV8 @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) ) )
= $true )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV86 @ SV105 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[784]) ).
thf(833,plain,
! [SV8: $i,SV86: $i,SV105: $i,SV25: $i] :
( ( ( ( apply @ SV25 @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) )
| ( apply @ SV8 @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) ) )
= $true )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV86 @ SV105 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[785]) ).
thf(834,plain,
! [SV8: $i,SV25: $i,SV106: $i,SV199: $i,SV87: $i,SV193: $i] :
( ( ( ~ ( member @ SV193 @ SV87 )
| ~ ( member @ SV199 @ SV106 )
| ~ ( apply @ SV25 @ SV193 @ SV199 )
| ( apply @ SV8 @ SV199 @ SV193 ) )
= $true )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV87 @ SV106 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(835,plain,
! [SV25: $i,SV8: $i,SV106: $i,SV200: $i,SV87: $i,SV194: $i] :
( ( ( ~ ( member @ SV194 @ SV87 )
| ~ ( member @ SV200 @ SV106 )
| ~ ( apply @ SV8 @ SV200 @ SV194 )
| ( apply @ SV25 @ SV194 @ SV200 ) )
= $true )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV87 @ SV106 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(836,plain,
! [SV34: $i,SV26: $i,SV126: $i,SV107: $i,SV9: $i] :
( ( ( apply @ SV9 @ SV107 @ SV126 )
= $false )
| ( ( apply @ ( inverse_function @ SV9 @ SV26 @ SV34 ) @ SV126 @ SV107 )
= $true )
| ( ( member @ SV107 @ SV26 )
= $false )
| ( ( member @ SV126 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[788]) ).
thf(837,plain,
! [SV108: $i,SV127: $i,SV34: $i,SV26: $i,SV9: $i] :
( ( ( apply @ ( inverse_function @ SV9 @ SV26 @ SV34 ) @ SV127 @ SV108 )
= $false )
| ( ( apply @ SV9 @ SV108 @ SV127 )
= $true )
| ( ( member @ SV108 @ SV26 )
= $false )
| ( ( member @ SV127 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[789]) ).
thf(838,plain,
! [SV90: $i,SV11: $i,SV63: $i,SV179: $i] :
( ( ( member @ SV179 @ SV63 )
= $false )
| ( ( apply @ SV11 @ SV179 @ ( sK23_Y @ SV90 @ SV63 @ SV11 ) )
= $false )
| ( ( surjective @ SV11 @ SV63 @ SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[790]) ).
thf(839,plain,
! [SV64: $i,SV91: $i,SV149: $i,SV11: $i] :
( ( ( apply @ SV11 @ ( sK22_E @ SV149 @ SV91 @ SV64 @ SV11 ) @ SV149 )
= $true )
| ( ( member @ SV149 @ SV91 )
= $false )
| ( ( surjective @ SV11 @ SV64 @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[791]) ).
thf(840,plain,
! [SV11: $i,SV64: $i,SV91: $i,SV149: $i] :
( ( ( member @ ( sK22_E @ SV149 @ SV91 @ SV64 @ SV11 ) @ SV64 )
= $true )
| ( ( member @ SV149 @ SV91 )
= $false )
| ( ( surjective @ SV11 @ SV64 @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[792]) ).
thf(841,plain,
! [SV27: $i,SV168: $i,SV12: $i,SV92: $i,SV109: $i] :
( ( ( member @ SV109 @ SV92 )
= $false )
| ( ( apply @ SV12 @ SV109 @ SV168 )
= $false )
| ( ( member @ SV168 @ SV27 )
= $false )
| ( ( member @ SV109 @ ( inverse_image3 @ SV12 @ SV27 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[793]) ).
thf(842,plain,
! [SV27: $i,SV150: $i,SV169: $i,SV12: $i] :
( ( ( ~ ( apply @ SV12 @ SV169 @ ( sK16_Y @ SV169 @ SV150 @ SV27 @ SV12 ) ) )
= $false )
| ( ( member @ SV169 @ ( inverse_image3 @ SV12 @ SV27 @ SV150 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[794]) ).
thf(843,plain,
! [SV12: $i,SV27: $i,SV150: $i,SV169: $i] :
( ( ( ~ ( member @ ( sK16_Y @ SV169 @ SV150 @ SV27 @ SV12 ) @ SV27 ) )
= $false )
| ( ( member @ SV169 @ ( inverse_image3 @ SV12 @ SV27 @ SV150 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[794]) ).
thf(844,plain,
! [SV13: $i,SV28: $i,SV93: $i,SV110: $i] :
( ( ( ~ ( ~ ( member @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ SV93 )
| ~ ( member @ ( sK29_SY162 @ SV110 @ SV93 @ SV28 @ SV13 ) @ SV110 ) ) )
= $true )
| ( ( equal_maps @ SV13 @ SV28 @ SV93 @ SV110 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[795]) ).
thf(845,plain,
! [SV13: $i,SV28: $i,SV93: $i,SV110: $i] :
( ( ( member @ ( sK30_SY164 @ SV110 @ SV93 @ SV28 @ SV13 ) @ SV110 )
= $true )
| ( ( equal_maps @ SV13 @ SV28 @ SV93 @ SV110 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[796]) ).
thf(846,plain,
! [SV28: $i,SV93: $i,SV110: $i,SV13: $i] :
( ( ( ~ ( ~ ( apply @ SV13 @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ ( sK29_SY162 @ SV110 @ SV93 @ SV28 @ SV13 ) )
| ~ ( apply @ SV28 @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ ( sK30_SY164 @ SV110 @ SV93 @ SV28 @ SV13 ) ) ) )
= $true )
| ( ( equal_maps @ SV13 @ SV28 @ SV93 @ SV110 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[797]) ).
thf(847,plain,
! [SV13: $i,SV28: $i,SV93: $i,SV110: $i] :
( ( ( ( ( sK29_SY162 @ SV110 @ SV93 @ SV28 @ SV13 )
!= ( sK30_SY164 @ SV110 @ SV93 @ SV28 @ SV13 ) ) )
= $true )
| ( ( equal_maps @ SV13 @ SV28 @ SV93 @ SV110 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[798]) ).
thf(848,plain,
! [SV28: $i,SV13: $i,SV185: $i,SV111: $i,SV180: $i,SV94: $i,SV171: $i] :
( ( ( ~ ( member @ SV171 @ SV94 )
| ~ ( member @ SV180 @ SV111 ) )
= $true )
| ( ( ~ ( member @ SV185 @ SV111 ) )
= $true )
| ( ( ~ ( apply @ SV13 @ SV171 @ SV180 )
| ~ ( apply @ SV28 @ SV171 @ SV185 )
| ( SV180 = SV185 ) )
= $true )
| ( ( equal_maps @ SV13 @ SV28 @ SV94 @ SV111 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[799]) ).
thf(849,plain,
! [SV14: $i,SV29: $i,SV35: $i,SV42: $i,SV129: $i,SV152: $i] :
( ( ( ~ ( member @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV42 )
| ~ ( member @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV152 ) )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[800]) ).
thf(850,plain,
! [SV14: $i,SV29: $i,SV42: $i,SV129: $i,SV152: $i,SV35: $i] :
( ( ( ~ ( ! [SY623: $i] :
( ~ ( apply @ SV35 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY623 )
| ~ ( member @ SY623 @ SV129 )
| ~ ( apply @ SV29 @ SY623 @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ~ ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ~ ( ~ ( ~ ~ ( ~ ( apply @ SV35 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV129 ) )
| ~ ( apply @ SV29 @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) ) )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[801]) ).
thf(851,plain,
! [SV14: $i,SV29: $i,SV130: $i,SV35: $i,SV153: $i,SV42: $i] :
( ( ( ! [SY624: $i,SY625: $i] :
( ~ ( member @ SY624 @ SV42 )
| ~ ( member @ SY625 @ SV153 )
| ! [SY600: $i] :
( ~ ( apply @ SV35 @ SY624 @ SY600 )
| ~ ( member @ SY600 @ SV130 )
| ~ ( apply @ SV29 @ SY600 @ SY625 ) )
| ( apply @ SV14 @ SY624 @ SY625 ) ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[802]) ).
thf(852,plain,
! [SV29: $i,SV130: $i,SV35: $i,SV14: $i,SV153: $i,SV42: $i] :
( ( ( ! [SY627: $i,SY628: $i] :
( ~ ( member @ SY627 @ SV42 )
| ~ ( member @ SY628 @ SV153 )
| ~ ( apply @ SV14 @ SY627 @ SY628 )
| ~ ( ~ ~ ( ~ ( apply @ SV35 @ SY627 @ ( sK32_Y @ SY628 @ SY627 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK32_Y @ SY628 @ SY627 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV130 ) )
| ~ ( apply @ SV29 @ ( sK32_Y @ SY628 @ SY627 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY628 ) ) ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[803]) ).
thf(853,plain,
! [SV15: $i,SV67: $i,SV95: $i] :
( ( ( ~ ( member @ ( sK24_X1 @ SV95 @ SV67 @ SV15 ) @ SV67 )
| ~ ( member @ ( sK25_SY159 @ SV95 @ SV67 @ SV15 ) @ SV67 ) )
= $false )
| ( ( injective @ SV15 @ SV67 @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[804]) ).
thf(854,plain,
! [SV67: $i,SV95: $i,SV15: $i] :
( ( ( ~ ( apply @ SV15 @ ( sK24_X1 @ SV95 @ SV67 @ SV15 ) @ ( sK26_SY161 @ SV95 @ SV67 @ SV15 ) )
| ~ ( apply @ SV15 @ ( sK25_SY159 @ SV95 @ SV67 @ SV15 ) @ ( sK26_SY161 @ SV95 @ SV67 @ SV15 ) ) )
= $false )
| ( ( injective @ SV15 @ SV67 @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[806]) ).
thf(855,plain,
! [SV15: $i,SV67: $i,SV95: $i] :
( ( ( ( sK24_X1 @ SV95 @ SV67 @ SV15 )
= ( sK25_SY159 @ SV95 @ SV67 @ SV15 ) )
= $false )
| ( ( injective @ SV15 @ SV67 @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[807]) ).
thf(856,plain,
! [SV15: $i,SV96: $i,SV181: $i,SV172: $i,SV68: $i,SV154: $i] :
( ( ( ~ ( member @ SV154 @ SV68 ) )
= $true )
| ( ( ~ ( member @ SV172 @ SV68 ) )
= $true )
| ( ( ~ ( member @ SV181 @ SV96 ) )
= $true )
| ( ( ~ ( apply @ SV15 @ SV154 @ SV181 )
| ~ ( apply @ SV15 @ SV172 @ SV181 )
| ( SV154 = SV172 ) )
= $true )
| ( ( injective @ SV15 @ SV68 @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[808]) ).
thf(857,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 )
| ~ ( member @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( member @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 ) )
| ~ ( member @ ( sK15_SY156 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( apply @ SV36 @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ( apply @ SV16 @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) ) )
= $false )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[809]) ).
thf(858,plain,
! [SV30: $i,SV36: $i,SV114: $i,SV133: $i,SV16: $i] :
( ( ( ~ ( apply @ SV16 @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK15_SY156 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
= $false )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[809]) ).
thf(859,plain,
! [SV134: $i,SV16: $i,SV36: $i,SV201: $i,SV195: $i,SV115: $i,SV186: $i,SV30: $i,SV182: $i] :
( ( ( ~ ( member @ SV182 @ SV30 )
| ~ ( member @ SV186 @ SV115 )
| ~ ( member @ SV195 @ SV30 )
| ~ ( member @ SV201 @ SV115 )
| ~ ( apply @ SV36 @ SV182 @ SV195 )
| ~ ( apply @ SV16 @ SV182 @ SV186 )
| ~ ( apply @ SV16 @ SV195 @ SV201 )
| ( apply @ SV134 @ SV186 @ SV201 ) )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV115 @ SV134 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(860,plain,
! [SV20: $i,SV46: $i,SV31: $i,SV37: $i,SV159: $i,SV73: $i,SV174: $i] :
( ( ( member @ SV174 @ SV73 )
= $false )
| ( ( member @ SV159 @ SV37 )
= $false )
| ( ( ! [SY648: $i] :
( ~ ( apply @ SV31 @ SV159 @ SY648 )
| ~ ( member @ SY648 @ SV46 )
| ~ ( apply @ SV20 @ SY648 @ SV174 ) )
| ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SV159 @ SV174 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[812]) ).
thf(861,plain,
! [SV46: $i,SV31: $i,SV20: $i,SV37: $i,SV160: $i,SV73: $i,SV175: $i] :
( ( ( member @ SV175 @ SV73 )
= $false )
| ( ( member @ SV160 @ SV37 )
= $false )
| ( ( ~ ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SV160 @ SV175 )
| ~ ( ~ ~ ( ~ ( apply @ SV31 @ SV160 @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) )
| ~ ( member @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SV46 ) )
| ~ ( apply @ SV20 @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SV175 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[813]) ).
thf(862,plain,
! [SV21: $i,SV78: $i,SV100: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
| ~ ( member @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ( member @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) @ SV100 ) ) )
= $true )
| ( ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[814]) ).
thf(863,plain,
! [SV78: $i,SV100: $i,SV21: $i] :
( ( ( ~ ( ~ ~ ( ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) )
| ~ ( ( ( sK38_SY170 @ SV100 @ SV78 @ SV21 )
!= ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) ) ) )
= $true )
| ( ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[815]) ).
thf(864,plain,
! [SV187: $i,SV78: $i,SV100: $i,SV21: $i] :
( ( ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV187 )
= $false )
| ( ( ~ ( member @ SV187 @ SV100 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
| ~ ( member @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ( member @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) )
| ~ ( ( ( sK38_SY170 @ SV100 @ SV78 @ SV21 )
!= ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) ) ) ) )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[816]) ).
thf(865,plain,
! [SV161: $i,SV21: $i,SV142: $i,SV188: $i] :
( ( ( member @ SV188 @ SV142 )
= $false )
| ( ( ~ ( ~ ( apply @ SV21 @ SV188 @ ( sK36_Y @ SV188 @ SV161 @ SV142 @ SV21 ) )
| ~ ( member @ ( sK36_Y @ SV188 @ SV161 @ SV142 @ SV21 ) @ SV161 ) ) )
= $true )
| ( ( maps @ SV21 @ SV142 @ SV161 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[817]) ).
thf(866,plain,
! [SV21: $i,SV202: $i,SV162: $i,SV196: $i,SV143: $i,SV189: $i] :
( ( ( ~ ( member @ SV189 @ SV143 )
| ~ ( member @ SV196 @ SV162 )
| ~ ( member @ SV202 @ SV162 )
| ~ ( apply @ SV21 @ SV189 @ SV196 )
| ~ ( apply @ SV21 @ SV189 @ SV202 )
| ( SV196 = SV202 ) )
= $true )
| ( ( maps @ SV21 @ SV143 @ SV162 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(867,plain,
! [SV22: $i,SV145: $i,SV164: $i,SV2: $i] :
( ( ( apply @ SV2 @ ( sK18_X @ SV164 @ SV145 @ SV22 @ SV2 ) @ SV164 )
= $true )
| ( ( member @ SV164 @ ( image3 @ SV2 @ SV22 @ SV145 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[820]) ).
thf(868,plain,
! [SV2: $i,SV22: $i,SV145: $i,SV164: $i] :
( ( ( member @ ( sK18_X @ SV164 @ SV145 @ SV22 @ SV2 ) @ SV22 )
= $true )
| ( ( member @ SV164 @ ( image3 @ SV2 @ SV22 @ SV145 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[821]) ).
thf(869,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 )
| ~ ( member @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( member @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 ) )
| ~ ( member @ ( sK11_SY150 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( apply @ SV32 @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ( apply @ SV3 @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) ) )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[822]) ).
thf(870,plain,
! [SV23: $i,SV32: $i,SV102: $i,SV117: $i,SV3: $i] :
( ( ( apply @ SV3 @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK11_SY150 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[823]) ).
thf(871,plain,
! [SV118: $i,SV3: $i,SV32: $i,SV197: $i,SV190: $i,SV103: $i,SV184: $i,SV23: $i,SV176: $i] :
( ( ( ~ ( member @ SV176 @ SV23 )
| ~ ( member @ SV184 @ SV103 )
| ~ ( member @ SV190 @ SV23 )
| ~ ( member @ SV197 @ SV103 )
| ~ ( apply @ SV32 @ SV176 @ SV190 )
| ~ ( apply @ SV3 @ SV176 @ SV184 )
| ~ ( apply @ SV3 @ SV190 @ SV197 ) )
= $true )
| ( ( apply @ SV118 @ SV197 @ SV184 )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV103 @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[824]) ).
thf(872,plain,
! [SV7: $i,SV24: $i,SV33: $i,SV104: $i,SV125: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 )
| ~ ( member @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
| ~ ( member @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 ) )
| ~ ( member @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
| ~ ( apply @ SV7 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) ) )
= $false )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[825]) ).
thf(873,plain,
! [SV24: $i,SV33: $i,SV104: $i,SV125: $i,SV7: $i] :
( ( ( ~ ( apply @ SV7 @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) )
= $false )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[825]) ).
thf(874,plain,
! [SV7: $i,SV24: $i,SV104: $i,SV125: $i,SV33: $i] :
( ( ( ~ ( ~ ( apply @ SV33 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
| ~ ( apply @ SV125 @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) ) )
= $false )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[826]) ).
thf(875,plain,
! [SV7: $i,SV24: $i,SV104: $i,SV125: $i,SV33: $i] :
( ( ( ~ ( ( apply @ SV33 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
| ( apply @ SV125 @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) ) )
= $false )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[826]) ).
thf(876,plain,
! [SV178: $i,SV33: $i,SV7: $i,SV167: $i,SV203: $i,SV24: $i,SV198: $i] :
( ( ( ~ ( ~ ! [SY680: $i,SY681: $i] :
( ~ ( member @ SV198 @ SV24 )
| ~ ( member @ SV203 @ SV167 )
| ~ ( member @ SY680 @ SV24 )
| ~ ( member @ SY681 @ SV167 )
| ~ ( apply @ SV7 @ SV198 @ SV203 )
| ~ ( apply @ SV7 @ SY680 @ SY681 )
| ~ ( apply @ SV33 @ SV198 @ SY680 )
| ( apply @ SV178 @ SV203 @ SY681 ) )
| ~ ! [SY682: $i,SY683: $i] :
( ~ ( member @ SV198 @ SV24 )
| ~ ( member @ SV203 @ SV167 )
| ~ ( member @ SY682 @ SV24 )
| ~ ( member @ SY683 @ SV167 )
| ~ ( apply @ SV7 @ SV198 @ SV203 )
| ~ ( apply @ SV7 @ SY682 @ SY683 )
| ~ ( apply @ SV178 @ SV203 @ SY683 )
| ( apply @ SV33 @ SV198 @ SY682 ) ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(877,plain,
! [SV204: $i,SV191: $i,SV33: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SV191 @ SV204 ) )
= $true )
| ( ( maps @ SV7 @ SV24 @ SV191 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(878,plain,
! [SV205: $i,SV192: $i,SV33: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( isomorphism @ SV7 @ SV24 @ SV33 @ SV192 @ SV205 ) )
= $true )
| ( ( one_to_one @ SV7 @ SV24 @ SV192 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(879,plain,
! [SV8: $i,SV86: $i,SV105: $i,SV25: $i] :
( ( ( ~ ( apply @ SV25 @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) ) )
= $true )
| ( ( ~ ( apply @ SV8 @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) ) )
= $true )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV86 @ SV105 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[832]) ).
thf(880,plain,
! [SV8: $i,SV86: $i,SV105: $i,SV25: $i] :
( ( ( apply @ SV25 @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) )
= $true )
| ( ( apply @ SV8 @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) )
= $true )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV86 @ SV105 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[833]) ).
thf(881,plain,
! [SV8: $i,SV25: $i,SV106: $i,SV199: $i,SV87: $i,SV193: $i] :
( ( ( ~ ( member @ SV193 @ SV87 )
| ~ ( member @ SV199 @ SV106 ) )
= $true )
| ( ( ~ ( apply @ SV25 @ SV193 @ SV199 )
| ( apply @ SV8 @ SV199 @ SV193 ) )
= $true )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV87 @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[834]) ).
thf(882,plain,
! [SV25: $i,SV8: $i,SV106: $i,SV200: $i,SV87: $i,SV194: $i] :
( ( ( ~ ( member @ SV194 @ SV87 )
| ~ ( member @ SV200 @ SV106 ) )
= $true )
| ( ( ~ ( apply @ SV8 @ SV200 @ SV194 )
| ( apply @ SV25 @ SV194 @ SV200 ) )
= $true )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV87 @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[835]) ).
thf(883,plain,
! [SV27: $i,SV150: $i,SV169: $i,SV12: $i] :
( ( ( apply @ SV12 @ SV169 @ ( sK16_Y @ SV169 @ SV150 @ SV27 @ SV12 ) )
= $true )
| ( ( member @ SV169 @ ( inverse_image3 @ SV12 @ SV27 @ SV150 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[842]) ).
thf(884,plain,
! [SV12: $i,SV27: $i,SV150: $i,SV169: $i] :
( ( ( member @ ( sK16_Y @ SV169 @ SV150 @ SV27 @ SV12 ) @ SV27 )
= $true )
| ( ( member @ SV169 @ ( inverse_image3 @ SV12 @ SV27 @ SV150 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[843]) ).
thf(885,plain,
! [SV13: $i,SV28: $i,SV93: $i,SV110: $i] :
( ( ( ~ ( member @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ SV93 )
| ~ ( member @ ( sK29_SY162 @ SV110 @ SV93 @ SV28 @ SV13 ) @ SV110 ) )
= $false )
| ( ( equal_maps @ SV13 @ SV28 @ SV93 @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[844]) ).
thf(886,plain,
! [SV28: $i,SV93: $i,SV110: $i,SV13: $i] :
( ( ( ~ ( apply @ SV13 @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ ( sK29_SY162 @ SV110 @ SV93 @ SV28 @ SV13 ) )
| ~ ( apply @ SV28 @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ ( sK30_SY164 @ SV110 @ SV93 @ SV28 @ SV13 ) ) )
= $false )
| ( ( equal_maps @ SV13 @ SV28 @ SV93 @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[846]) ).
thf(887,plain,
! [SV13: $i,SV28: $i,SV93: $i,SV110: $i] :
( ( ( ( sK29_SY162 @ SV110 @ SV93 @ SV28 @ SV13 )
= ( sK30_SY164 @ SV110 @ SV93 @ SV28 @ SV13 ) )
= $false )
| ( ( equal_maps @ SV13 @ SV28 @ SV93 @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[847]) ).
thf(888,plain,
! [SV28: $i,SV13: $i,SV185: $i,SV111: $i,SV180: $i,SV94: $i,SV171: $i] :
( ( ( ~ ( member @ SV171 @ SV94 ) )
= $true )
| ( ( ~ ( member @ SV180 @ SV111 ) )
= $true )
| ( ( ~ ( member @ SV185 @ SV111 ) )
= $true )
| ( ( ~ ( apply @ SV13 @ SV171 @ SV180 )
| ~ ( apply @ SV28 @ SV171 @ SV185 )
| ( SV180 = SV185 ) )
= $true )
| ( ( equal_maps @ SV13 @ SV28 @ SV94 @ SV111 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[848]) ).
thf(889,plain,
! [SV14: $i,SV29: $i,SV35: $i,SV42: $i,SV129: $i,SV152: $i] :
( ( ( ~ ( member @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV42 ) )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[849]) ).
thf(890,plain,
! [SV14: $i,SV29: $i,SV35: $i,SV42: $i,SV129: $i,SV152: $i] :
( ( ( ~ ( member @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV152 ) )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[849]) ).
thf(891,plain,
! [SV14: $i,SV29: $i,SV42: $i,SV129: $i,SV152: $i,SV35: $i] :
( ( ( ~ ( ! [SY623: $i] :
( ~ ( apply @ SV35 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY623 )
| ~ ( member @ SY623 @ SV129 )
| ~ ( apply @ SV29 @ SY623 @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ~ ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) ) )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[850]) ).
thf(892,plain,
! [SV14: $i,SV29: $i,SV42: $i,SV129: $i,SV152: $i,SV35: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ~ ( apply @ SV35 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV129 ) )
| ~ ( apply @ SV29 @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) ) )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[850]) ).
thf(893,plain,
! [SV14: $i,SV29: $i,SV130: $i,SV35: $i,SV153: $i,SV42: $i,SV206: $i] :
( ( ( ! [SY684: $i] :
( ~ ( member @ SV206 @ SV42 )
| ~ ( member @ SY684 @ SV153 )
| ! [SY685: $i] :
( ~ ( apply @ SV35 @ SV206 @ SY685 )
| ~ ( member @ SY685 @ SV130 )
| ~ ( apply @ SV29 @ SY685 @ SY684 ) )
| ( apply @ SV14 @ SV206 @ SY684 ) ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(894,plain,
! [SV29: $i,SV130: $i,SV35: $i,SV14: $i,SV153: $i,SV42: $i,SV207: $i] :
( ( ( ! [SY686: $i] :
( ~ ( member @ SV207 @ SV42 )
| ~ ( member @ SY686 @ SV153 )
| ~ ( apply @ SV14 @ SV207 @ SY686 )
| ~ ( ~ ~ ( ~ ( apply @ SV35 @ SV207 @ ( sK32_Y @ SY686 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK32_Y @ SY686 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV130 ) )
| ~ ( apply @ SV29 @ ( sK32_Y @ SY686 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY686 ) ) ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(895,plain,
! [SV15: $i,SV67: $i,SV95: $i] :
( ( ( ~ ( member @ ( sK24_X1 @ SV95 @ SV67 @ SV15 ) @ SV67 ) )
= $false )
| ( ( injective @ SV15 @ SV67 @ SV95 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[853]) ).
thf(896,plain,
! [SV15: $i,SV67: $i,SV95: $i] :
( ( ( ~ ( member @ ( sK25_SY159 @ SV95 @ SV67 @ SV15 ) @ SV67 ) )
= $false )
| ( ( injective @ SV15 @ SV67 @ SV95 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[853]) ).
thf(897,plain,
! [SV67: $i,SV95: $i,SV15: $i] :
( ( ( ~ ( apply @ SV15 @ ( sK24_X1 @ SV95 @ SV67 @ SV15 ) @ ( sK26_SY161 @ SV95 @ SV67 @ SV15 ) ) )
= $false )
| ( ( injective @ SV15 @ SV67 @ SV95 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[854]) ).
thf(898,plain,
! [SV67: $i,SV95: $i,SV15: $i] :
( ( ( ~ ( apply @ SV15 @ ( sK25_SY159 @ SV95 @ SV67 @ SV15 ) @ ( sK26_SY161 @ SV95 @ SV67 @ SV15 ) ) )
= $false )
| ( ( injective @ SV15 @ SV67 @ SV95 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[854]) ).
thf(899,plain,
! [SV15: $i,SV96: $i,SV181: $i,SV172: $i,SV68: $i,SV154: $i] :
( ( ( member @ SV154 @ SV68 )
= $false )
| ( ( ~ ( member @ SV172 @ SV68 ) )
= $true )
| ( ( ~ ( member @ SV181 @ SV96 ) )
= $true )
| ( ( ~ ( apply @ SV15 @ SV154 @ SV181 )
| ~ ( apply @ SV15 @ SV172 @ SV181 )
| ( SV154 = SV172 ) )
= $true )
| ( ( injective @ SV15 @ SV68 @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[856]) ).
thf(900,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 )
| ~ ( member @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( member @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 ) )
| ~ ( member @ ( sK15_SY156 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( apply @ SV36 @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ( apply @ SV16 @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) ) )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[857]) ).
thf(901,plain,
! [SV30: $i,SV36: $i,SV114: $i,SV133: $i,SV16: $i] :
( ( ( apply @ SV16 @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK15_SY156 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[858]) ).
thf(902,plain,
! [SV134: $i,SV16: $i,SV36: $i,SV201: $i,SV195: $i,SV115: $i,SV186: $i,SV30: $i,SV182: $i] :
( ( ( ~ ( member @ SV182 @ SV30 )
| ~ ( member @ SV186 @ SV115 )
| ~ ( member @ SV195 @ SV30 )
| ~ ( member @ SV201 @ SV115 )
| ~ ( apply @ SV36 @ SV182 @ SV195 )
| ~ ( apply @ SV16 @ SV182 @ SV186 )
| ~ ( apply @ SV16 @ SV195 @ SV201 ) )
= $true )
| ( ( apply @ SV134 @ SV186 @ SV201 )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV115 @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[859]) ).
thf(903,plain,
! [SV73: $i,SV37: $i,SV174: $i,SV20: $i,SV46: $i,SV159: $i,SV31: $i] :
( ( ( ! [SY648: $i] :
( ~ ( apply @ SV31 @ SV159 @ SY648 )
| ~ ( member @ SY648 @ SV46 )
| ~ ( apply @ SV20 @ SY648 @ SV174 ) ) )
= $true )
| ( ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SV159 @ SV174 )
= $true )
| ( ( member @ SV159 @ SV37 )
= $false )
| ( ( member @ SV174 @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[860]) ).
thf(904,plain,
! [SV175: $i,SV160: $i,SV73: $i,SV46: $i,SV37: $i,SV31: $i,SV20: $i] :
( ( ( ~ ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SV160 @ SV175 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( apply @ SV31 @ SV160 @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) )
| ~ ( member @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SV46 ) )
| ~ ( apply @ SV20 @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SV175 ) ) )
= $true )
| ( ( member @ SV160 @ SV37 )
= $false )
| ( ( member @ SV175 @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[861]) ).
thf(905,plain,
! [SV21: $i,SV78: $i,SV100: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
| ~ ( member @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ( member @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
= $false )
| ( ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[862]) ).
thf(906,plain,
! [SV78: $i,SV100: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) )
| ~ ( ( ( sK38_SY170 @ SV100 @ SV78 @ SV21 )
!= ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) ) )
= $false )
| ( ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[863]) ).
thf(907,plain,
! [SV78: $i,SV21: $i,SV100: $i,SV187: $i] :
( ( ( member @ SV187 @ SV100 )
= $false )
| ( ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV187 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
| ~ ( member @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ( member @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) )
| ~ ( ( ( sK38_SY170 @ SV100 @ SV78 @ SV21 )
!= ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) ) ) ) )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[864]) ).
thf(908,plain,
! [SV142: $i,SV161: $i,SV188: $i,SV21: $i] :
( ( ( ~ ( apply @ SV21 @ SV188 @ ( sK36_Y @ SV188 @ SV161 @ SV142 @ SV21 ) )
| ~ ( member @ ( sK36_Y @ SV188 @ SV161 @ SV142 @ SV21 ) @ SV161 ) )
= $false )
| ( ( member @ SV188 @ SV142 )
= $false )
| ( ( maps @ SV21 @ SV142 @ SV161 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(909,plain,
! [SV21: $i,SV202: $i,SV162: $i,SV196: $i,SV143: $i,SV189: $i] :
( ( ( ~ ( member @ SV189 @ SV143 )
| ~ ( member @ SV196 @ SV162 )
| ~ ( member @ SV202 @ SV162 ) )
= $true )
| ( ( ~ ( apply @ SV21 @ SV189 @ SV196 )
| ~ ( apply @ SV21 @ SV189 @ SV202 )
| ( SV196 = SV202 ) )
= $true )
| ( ( maps @ SV21 @ SV143 @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[866]) ).
thf(910,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 )
| ~ ( member @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( member @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 ) )
| ~ ( member @ ( sK11_SY150 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( apply @ SV32 @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
| ~ ( apply @ SV3 @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
= $false )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[869]) ).
thf(911,plain,
! [SV118: $i,SV3: $i,SV32: $i,SV197: $i,SV190: $i,SV103: $i,SV184: $i,SV23: $i,SV176: $i] :
( ( ( ~ ( member @ SV176 @ SV23 )
| ~ ( member @ SV184 @ SV103 )
| ~ ( member @ SV190 @ SV23 )
| ~ ( member @ SV197 @ SV103 )
| ~ ( apply @ SV32 @ SV176 @ SV190 )
| ~ ( apply @ SV3 @ SV176 @ SV184 ) )
= $true )
| ( ( ~ ( apply @ SV3 @ SV190 @ SV197 ) )
= $true )
| ( ( apply @ SV118 @ SV197 @ SV184 )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV103 @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[871]) ).
thf(912,plain,
! [SV7: $i,SV24: $i,SV33: $i,SV104: $i,SV125: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 )
| ~ ( member @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
| ~ ( member @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 ) )
| ~ ( member @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
| ~ ( apply @ SV7 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) ) )
= $true )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[872]) ).
thf(913,plain,
! [SV24: $i,SV33: $i,SV104: $i,SV125: $i,SV7: $i] :
( ( ( apply @ SV7 @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
= $true )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[873]) ).
thf(914,plain,
! [SV7: $i,SV24: $i,SV104: $i,SV125: $i,SV33: $i] :
( ( ( ~ ( apply @ SV33 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
| ~ ( apply @ SV125 @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) )
= $true )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[874]) ).
thf(915,plain,
! [SV7: $i,SV24: $i,SV104: $i,SV125: $i,SV33: $i] :
( ( ( ( apply @ SV33 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
| ( apply @ SV125 @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) )
= $true )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[875]) ).
thf(916,plain,
! [SV178: $i,SV33: $i,SV7: $i,SV167: $i,SV203: $i,SV24: $i,SV198: $i] :
( ( ( ~ ! [SY680: $i,SY681: $i] :
( ~ ( member @ SV198 @ SV24 )
| ~ ( member @ SV203 @ SV167 )
| ~ ( member @ SY680 @ SV24 )
| ~ ( member @ SY681 @ SV167 )
| ~ ( apply @ SV7 @ SV198 @ SV203 )
| ~ ( apply @ SV7 @ SY680 @ SY681 )
| ~ ( apply @ SV33 @ SV198 @ SY680 )
| ( apply @ SV178 @ SV203 @ SY681 ) )
| ~ ! [SY682: $i,SY683: $i] :
( ~ ( member @ SV198 @ SV24 )
| ~ ( member @ SV203 @ SV167 )
| ~ ( member @ SY682 @ SV24 )
| ~ ( member @ SY683 @ SV167 )
| ~ ( apply @ SV7 @ SV198 @ SV203 )
| ~ ( apply @ SV7 @ SY682 @ SY683 )
| ~ ( apply @ SV178 @ SV203 @ SY683 )
| ( apply @ SV33 @ SV198 @ SY682 ) ) )
= $false )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[876]) ).
thf(917,plain,
! [SV204: $i,SV191: $i,SV33: $i,SV24: $i,SV7: $i] :
( ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV191 @ SV204 )
= $false )
| ( ( maps @ SV7 @ SV24 @ SV191 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(918,plain,
! [SV205: $i,SV192: $i,SV33: $i,SV24: $i,SV7: $i] :
( ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV192 @ SV205 )
= $false )
| ( ( one_to_one @ SV7 @ SV24 @ SV192 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[878]) ).
thf(919,plain,
! [SV8: $i,SV86: $i,SV105: $i,SV25: $i] :
( ( ( apply @ SV25 @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) )
= $false )
| ( ( ~ ( apply @ SV8 @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) ) )
= $true )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV86 @ SV105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[879]) ).
thf(920,plain,
! [SV8: $i,SV25: $i,SV106: $i,SV199: $i,SV87: $i,SV193: $i] :
( ( ( ~ ( member @ SV193 @ SV87 ) )
= $true )
| ( ( ~ ( member @ SV199 @ SV106 ) )
= $true )
| ( ( ~ ( apply @ SV25 @ SV193 @ SV199 )
| ( apply @ SV8 @ SV199 @ SV193 ) )
= $true )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV87 @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[881]) ).
thf(921,plain,
! [SV25: $i,SV8: $i,SV106: $i,SV200: $i,SV87: $i,SV194: $i] :
( ( ( ~ ( member @ SV194 @ SV87 ) )
= $true )
| ( ( ~ ( member @ SV200 @ SV106 ) )
= $true )
| ( ( ~ ( apply @ SV8 @ SV200 @ SV194 )
| ( apply @ SV25 @ SV194 @ SV200 ) )
= $true )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV87 @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[882]) ).
thf(922,plain,
! [SV13: $i,SV28: $i,SV93: $i,SV110: $i] :
( ( ( ~ ( member @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ SV93 ) )
= $false )
| ( ( equal_maps @ SV13 @ SV28 @ SV93 @ SV110 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[885]) ).
thf(923,plain,
! [SV13: $i,SV28: $i,SV93: $i,SV110: $i] :
( ( ( ~ ( member @ ( sK29_SY162 @ SV110 @ SV93 @ SV28 @ SV13 ) @ SV110 ) )
= $false )
| ( ( equal_maps @ SV13 @ SV28 @ SV93 @ SV110 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[885]) ).
thf(924,plain,
! [SV28: $i,SV93: $i,SV110: $i,SV13: $i] :
( ( ( ~ ( apply @ SV13 @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ ( sK29_SY162 @ SV110 @ SV93 @ SV28 @ SV13 ) ) )
= $false )
| ( ( equal_maps @ SV13 @ SV28 @ SV93 @ SV110 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[886]) ).
thf(925,plain,
! [SV13: $i,SV93: $i,SV110: $i,SV28: $i] :
( ( ( ~ ( apply @ SV28 @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ ( sK30_SY164 @ SV110 @ SV93 @ SV28 @ SV13 ) ) )
= $false )
| ( ( equal_maps @ SV13 @ SV28 @ SV93 @ SV110 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[886]) ).
thf(926,plain,
! [SV28: $i,SV13: $i,SV185: $i,SV111: $i,SV180: $i,SV94: $i,SV171: $i] :
( ( ( member @ SV171 @ SV94 )
= $false )
| ( ( ~ ( member @ SV180 @ SV111 ) )
= $true )
| ( ( ~ ( member @ SV185 @ SV111 ) )
= $true )
| ( ( ~ ( apply @ SV13 @ SV171 @ SV180 )
| ~ ( apply @ SV28 @ SV171 @ SV185 )
| ( SV180 = SV185 ) )
= $true )
| ( ( equal_maps @ SV13 @ SV28 @ SV94 @ SV111 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[888]) ).
thf(927,plain,
! [SV14: $i,SV29: $i,SV35: $i,SV42: $i,SV129: $i,SV152: $i] :
( ( ( member @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV42 )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[889]) ).
thf(928,plain,
! [SV14: $i,SV29: $i,SV35: $i,SV42: $i,SV129: $i,SV152: $i] :
( ( ( member @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV152 )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[890]) ).
thf(929,plain,
! [SV14: $i,SV29: $i,SV42: $i,SV129: $i,SV152: $i,SV35: $i] :
( ( ( ! [SY623: $i] :
( ~ ( apply @ SV35 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY623 )
| ~ ( member @ SY623 @ SV129 )
| ~ ( apply @ SV29 @ SY623 @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ~ ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[891]) ).
thf(930,plain,
! [SV14: $i,SV29: $i,SV42: $i,SV129: $i,SV152: $i,SV35: $i] :
( ( ( ~ ( ~ ~ ( ~ ( apply @ SV35 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV129 ) )
| ~ ( apply @ SV29 @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
| ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[892]) ).
thf(931,plain,
! [SV14: $i,SV29: $i,SV130: $i,SV35: $i,SV153: $i,SV208: $i,SV42: $i,SV206: $i] :
( ( ( ~ ( member @ SV206 @ SV42 )
| ~ ( member @ SV208 @ SV153 )
| ! [SY687: $i] :
( ~ ( apply @ SV35 @ SV206 @ SY687 )
| ~ ( member @ SY687 @ SV130 )
| ~ ( apply @ SV29 @ SY687 @ SV208 ) )
| ( apply @ SV14 @ SV206 @ SV208 ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(932,plain,
! [SV29: $i,SV130: $i,SV35: $i,SV14: $i,SV153: $i,SV209: $i,SV42: $i,SV207: $i] :
( ( ( ~ ( member @ SV207 @ SV42 )
| ~ ( member @ SV209 @ SV153 )
| ~ ( apply @ SV14 @ SV207 @ SV209 )
| ~ ( ~ ~ ( ~ ( apply @ SV35 @ SV207 @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV130 ) )
| ~ ( apply @ SV29 @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV209 ) ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(933,plain,
! [SV15: $i,SV67: $i,SV95: $i] :
( ( ( member @ ( sK24_X1 @ SV95 @ SV67 @ SV15 ) @ SV67 )
= $true )
| ( ( injective @ SV15 @ SV67 @ SV95 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[895]) ).
thf(934,plain,
! [SV15: $i,SV67: $i,SV95: $i] :
( ( ( member @ ( sK25_SY159 @ SV95 @ SV67 @ SV15 ) @ SV67 )
= $true )
| ( ( injective @ SV15 @ SV67 @ SV95 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[896]) ).
thf(935,plain,
! [SV67: $i,SV95: $i,SV15: $i] :
( ( ( apply @ SV15 @ ( sK24_X1 @ SV95 @ SV67 @ SV15 ) @ ( sK26_SY161 @ SV95 @ SV67 @ SV15 ) )
= $true )
| ( ( injective @ SV15 @ SV67 @ SV95 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[897]) ).
thf(936,plain,
! [SV67: $i,SV95: $i,SV15: $i] :
( ( ( apply @ SV15 @ ( sK25_SY159 @ SV95 @ SV67 @ SV15 ) @ ( sK26_SY161 @ SV95 @ SV67 @ SV15 ) )
= $true )
| ( ( injective @ SV15 @ SV67 @ SV95 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[898]) ).
thf(937,plain,
! [SV15: $i,SV96: $i,SV181: $i,SV154: $i,SV68: $i,SV172: $i] :
( ( ( member @ SV172 @ SV68 )
= $false )
| ( ( member @ SV154 @ SV68 )
= $false )
| ( ( ~ ( member @ SV181 @ SV96 ) )
= $true )
| ( ( ~ ( apply @ SV15 @ SV154 @ SV181 )
| ~ ( apply @ SV15 @ SV172 @ SV181 )
| ( SV154 = SV172 ) )
= $true )
| ( ( injective @ SV15 @ SV68 @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[899]) ).
thf(938,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 )
| ~ ( member @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( member @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 ) )
| ~ ( member @ ( sK15_SY156 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( apply @ SV36 @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
| ~ ( apply @ SV16 @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
= $false )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[900]) ).
thf(939,plain,
! [SV134: $i,SV16: $i,SV36: $i,SV201: $i,SV195: $i,SV115: $i,SV186: $i,SV30: $i,SV182: $i] :
( ( ( ~ ( member @ SV182 @ SV30 )
| ~ ( member @ SV186 @ SV115 )
| ~ ( member @ SV195 @ SV30 )
| ~ ( member @ SV201 @ SV115 )
| ~ ( apply @ SV36 @ SV182 @ SV195 )
| ~ ( apply @ SV16 @ SV182 @ SV186 ) )
= $true )
| ( ( ~ ( apply @ SV16 @ SV195 @ SV201 ) )
= $true )
| ( ( apply @ SV134 @ SV186 @ SV201 )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV115 @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[902]) ).
thf(940,plain,
! [SV73: $i,SV37: $i,SV174: $i,SV20: $i,SV46: $i,SV210: $i,SV159: $i,SV31: $i] :
( ( ( ~ ( apply @ SV31 @ SV159 @ SV210 )
| ~ ( member @ SV210 @ SV46 )
| ~ ( apply @ SV20 @ SV210 @ SV174 ) )
= $true )
| ( ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SV159 @ SV174 )
= $true )
| ( ( member @ SV159 @ SV37 )
= $false )
| ( ( member @ SV174 @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(941,plain,
! [SV175: $i,SV160: $i,SV73: $i,SV46: $i,SV37: $i,SV31: $i,SV20: $i] :
( ( ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SV160 @ SV175 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( apply @ SV31 @ SV160 @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) )
| ~ ( member @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SV46 ) )
| ~ ( apply @ SV20 @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SV175 ) ) )
= $true )
| ( ( member @ SV160 @ SV37 )
= $false )
| ( ( member @ SV175 @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[904]) ).
thf(942,plain,
! [SV21: $i,SV78: $i,SV100: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
| ~ ( member @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) @ SV100 ) ) )
= $false )
| ( ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[905]) ).
thf(943,plain,
! [SV21: $i,SV78: $i,SV100: $i] :
( ( ( ~ ( member @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
= $false )
| ( ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[905]) ).
thf(944,plain,
! [SV78: $i,SV100: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) ) )
= $false )
| ( ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[906]) ).
thf(945,plain,
! [SV21: $i,SV78: $i,SV100: $i] :
( ( ( ~ ( ( ( sK38_SY170 @ SV100 @ SV78 @ SV21 )
!= ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) ) )
= $false )
| ( ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[906]) ).
thf(946,plain,
! [SV187: $i,SV21: $i,SV78: $i,SV100: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
| ~ ( member @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ( member @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) )
| ~ ( ( ( sK38_SY170 @ SV100 @ SV78 @ SV21 )
!= ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) ) ) )
= $false )
| ( ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV187 )
= $false )
| ( ( member @ SV187 @ SV100 )
= $false )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[907]) ).
thf(947,plain,
! [SV142: $i,SV161: $i,SV188: $i,SV21: $i] :
( ( ( ~ ( apply @ SV21 @ SV188 @ ( sK36_Y @ SV188 @ SV161 @ SV142 @ SV21 ) ) )
= $false )
| ( ( member @ SV188 @ SV142 )
= $false )
| ( ( maps @ SV21 @ SV142 @ SV161 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[908]) ).
thf(948,plain,
! [SV21: $i,SV142: $i,SV161: $i,SV188: $i] :
( ( ( ~ ( member @ ( sK36_Y @ SV188 @ SV161 @ SV142 @ SV21 ) @ SV161 ) )
= $false )
| ( ( member @ SV188 @ SV142 )
= $false )
| ( ( maps @ SV21 @ SV142 @ SV161 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[908]) ).
thf(949,plain,
! [SV21: $i,SV202: $i,SV162: $i,SV196: $i,SV143: $i,SV189: $i] :
( ( ( ~ ( member @ SV189 @ SV143 )
| ~ ( member @ SV196 @ SV162 ) )
= $true )
| ( ( ~ ( member @ SV202 @ SV162 ) )
= $true )
| ( ( ~ ( apply @ SV21 @ SV189 @ SV196 )
| ~ ( apply @ SV21 @ SV189 @ SV202 )
| ( SV196 = SV202 ) )
= $true )
| ( ( maps @ SV21 @ SV143 @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[909]) ).
thf(950,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 )
| ~ ( member @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( member @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 ) )
| ~ ( member @ ( sK11_SY150 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( apply @ SV32 @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) ) )
= $false )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[910]) ).
thf(951,plain,
! [SV23: $i,SV32: $i,SV102: $i,SV117: $i,SV3: $i] :
( ( ( ~ ( apply @ SV3 @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
= $false )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[910]) ).
thf(952,plain,
! [SV118: $i,SV3: $i,SV32: $i,SV197: $i,SV190: $i,SV103: $i,SV184: $i,SV23: $i,SV176: $i] :
( ( ( ~ ( member @ SV176 @ SV23 )
| ~ ( member @ SV184 @ SV103 )
| ~ ( member @ SV190 @ SV23 )
| ~ ( member @ SV197 @ SV103 )
| ~ ( apply @ SV32 @ SV176 @ SV190 ) )
= $true )
| ( ( ~ ( apply @ SV3 @ SV176 @ SV184 ) )
= $true )
| ( ( ~ ( apply @ SV3 @ SV190 @ SV197 ) )
= $true )
| ( ( apply @ SV118 @ SV197 @ SV184 )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV103 @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[911]) ).
thf(953,plain,
! [SV7: $i,SV24: $i,SV33: $i,SV104: $i,SV125: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 )
| ~ ( member @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
| ~ ( member @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 ) )
| ~ ( member @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
| ~ ( apply @ SV7 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) )
= $false )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[912]) ).
thf(954,plain,
! [SV33: $i,SV125: $i,SV104: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( maps @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( apply @ SV7 @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[913]) ).
thf(955,plain,
! [SV7: $i,SV24: $i,SV104: $i,SV125: $i,SV33: $i] :
( ( ( ~ ( apply @ SV33 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) )
= $true )
| ( ( ~ ( apply @ SV125 @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) )
= $true )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[914]) ).
thf(956,plain,
! [SV7: $i,SV24: $i,SV104: $i,SV125: $i,SV33: $i] :
( ( ( apply @ SV33 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
= $true )
| ( ( apply @ SV125 @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
= $true )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[915]) ).
thf(957,plain,
! [SV178: $i,SV33: $i,SV7: $i,SV167: $i,SV203: $i,SV24: $i,SV198: $i] :
( ( ( ~ ! [SY680: $i,SY681: $i] :
( ~ ( member @ SV198 @ SV24 )
| ~ ( member @ SV203 @ SV167 )
| ~ ( member @ SY680 @ SV24 )
| ~ ( member @ SY681 @ SV167 )
| ~ ( apply @ SV7 @ SV198 @ SV203 )
| ~ ( apply @ SV7 @ SY680 @ SY681 )
| ~ ( apply @ SV33 @ SV198 @ SY680 )
| ( apply @ SV178 @ SV203 @ SY681 ) ) )
= $false )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[916]) ).
thf(958,plain,
! [SV33: $i,SV178: $i,SV7: $i,SV167: $i,SV203: $i,SV24: $i,SV198: $i] :
( ( ( ~ ! [SY682: $i,SY683: $i] :
( ~ ( member @ SV198 @ SV24 )
| ~ ( member @ SV203 @ SV167 )
| ~ ( member @ SY682 @ SV24 )
| ~ ( member @ SY683 @ SV167 )
| ~ ( apply @ SV7 @ SV198 @ SV203 )
| ~ ( apply @ SV7 @ SY682 @ SY683 )
| ~ ( apply @ SV178 @ SV203 @ SY683 )
| ( apply @ SV33 @ SV198 @ SY682 ) ) )
= $false )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[916]) ).
thf(959,plain,
! [SV25: $i,SV86: $i,SV105: $i,SV8: $i] :
( ( ( apply @ SV8 @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) )
= $false )
| ( ( apply @ SV25 @ ( sK20_X @ SV105 @ SV86 @ SV25 @ SV8 ) @ ( sK21_SY157 @ SV105 @ SV86 @ SV25 @ SV8 ) )
= $false )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV86 @ SV105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[919]) ).
thf(960,plain,
! [SV8: $i,SV25: $i,SV106: $i,SV199: $i,SV87: $i,SV193: $i] :
( ( ( member @ SV193 @ SV87 )
= $false )
| ( ( ~ ( member @ SV199 @ SV106 ) )
= $true )
| ( ( ~ ( apply @ SV25 @ SV193 @ SV199 )
| ( apply @ SV8 @ SV199 @ SV193 ) )
= $true )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV87 @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[920]) ).
thf(961,plain,
! [SV25: $i,SV8: $i,SV106: $i,SV200: $i,SV87: $i,SV194: $i] :
( ( ( member @ SV194 @ SV87 )
= $false )
| ( ( ~ ( member @ SV200 @ SV106 ) )
= $true )
| ( ( ~ ( apply @ SV8 @ SV200 @ SV194 )
| ( apply @ SV25 @ SV194 @ SV200 ) )
= $true )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV87 @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[921]) ).
thf(962,plain,
! [SV13: $i,SV28: $i,SV93: $i,SV110: $i] :
( ( ( member @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ SV93 )
= $true )
| ( ( equal_maps @ SV13 @ SV28 @ SV93 @ SV110 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[922]) ).
thf(963,plain,
! [SV13: $i,SV28: $i,SV93: $i,SV110: $i] :
( ( ( member @ ( sK29_SY162 @ SV110 @ SV93 @ SV28 @ SV13 ) @ SV110 )
= $true )
| ( ( equal_maps @ SV13 @ SV28 @ SV93 @ SV110 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[923]) ).
thf(964,plain,
! [SV28: $i,SV93: $i,SV110: $i,SV13: $i] :
( ( ( apply @ SV13 @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ ( sK29_SY162 @ SV110 @ SV93 @ SV28 @ SV13 ) )
= $true )
| ( ( equal_maps @ SV13 @ SV28 @ SV93 @ SV110 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[924]) ).
thf(965,plain,
! [SV13: $i,SV93: $i,SV110: $i,SV28: $i] :
( ( ( apply @ SV28 @ ( sK28_X @ SV110 @ SV93 @ SV28 @ SV13 ) @ ( sK30_SY164 @ SV110 @ SV93 @ SV28 @ SV13 ) )
= $true )
| ( ( equal_maps @ SV13 @ SV28 @ SV93 @ SV110 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[925]) ).
thf(966,plain,
! [SV28: $i,SV13: $i,SV185: $i,SV94: $i,SV171: $i,SV111: $i,SV180: $i] :
( ( ( member @ SV180 @ SV111 )
= $false )
| ( ( member @ SV171 @ SV94 )
= $false )
| ( ( ~ ( member @ SV185 @ SV111 ) )
= $true )
| ( ( ~ ( apply @ SV13 @ SV171 @ SV180 )
| ~ ( apply @ SV28 @ SV171 @ SV185 )
| ( SV180 = SV185 ) )
= $true )
| ( ( equal_maps @ SV13 @ SV28 @ SV94 @ SV111 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[926]) ).
thf(967,plain,
! [SV14: $i,SV29: $i,SV42: $i,SV129: $i,SV152: $i,SV35: $i] :
( ( ( ! [SY623: $i] :
( ~ ( apply @ SV35 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SY623 )
| ~ ( member @ SY623 @ SV129 )
| ~ ( apply @ SV29 @ SY623 @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) ) )
= $true )
| ( ( ~ ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[929]) ).
thf(968,plain,
! [SV14: $i,SV29: $i,SV42: $i,SV129: $i,SV152: $i,SV35: $i] :
( ( ( ~ ( ~ ~ ( ~ ( apply @ SV35 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV129 ) )
| ~ ( apply @ SV29 @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) ) )
= $true )
| ( ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[930]) ).
thf(969,plain,
! [SV14: $i,SV29: $i,SV130: $i,SV35: $i,SV153: $i,SV208: $i,SV42: $i,SV206: $i] :
( ( ( ~ ( member @ SV206 @ SV42 )
| ~ ( member @ SV208 @ SV153 ) )
= $true )
| ( ( ! [SY687: $i] :
( ~ ( apply @ SV35 @ SV206 @ SY687 )
| ~ ( member @ SY687 @ SV130 )
| ~ ( apply @ SV29 @ SY687 @ SV208 ) )
| ( apply @ SV14 @ SV206 @ SV208 ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[931]) ).
thf(970,plain,
! [SV29: $i,SV130: $i,SV35: $i,SV14: $i,SV153: $i,SV209: $i,SV42: $i,SV207: $i] :
( ( ( ~ ( member @ SV207 @ SV42 )
| ~ ( member @ SV209 @ SV153 ) )
= $true )
| ( ( ~ ( apply @ SV14 @ SV207 @ SV209 )
| ~ ( ~ ~ ( ~ ( apply @ SV35 @ SV207 @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV130 ) )
| ~ ( apply @ SV29 @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV209 ) ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[932]) ).
thf(971,plain,
! [SV15: $i,SV172: $i,SV68: $i,SV154: $i,SV96: $i,SV181: $i] :
( ( ( member @ SV181 @ SV96 )
= $false )
| ( ( member @ SV154 @ SV68 )
= $false )
| ( ( member @ SV172 @ SV68 )
= $false )
| ( ( ~ ( apply @ SV15 @ SV154 @ SV181 )
| ~ ( apply @ SV15 @ SV172 @ SV181 )
| ( SV154 = SV172 ) )
= $true )
| ( ( injective @ SV15 @ SV68 @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[937]) ).
thf(972,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 )
| ~ ( member @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( member @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 ) )
| ~ ( member @ ( sK15_SY156 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( apply @ SV36 @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) ) )
= $false )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[938]) ).
thf(973,plain,
! [SV30: $i,SV36: $i,SV114: $i,SV133: $i,SV16: $i] :
( ( ( ~ ( apply @ SV16 @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
= $false )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[938]) ).
thf(974,plain,
! [SV134: $i,SV16: $i,SV36: $i,SV201: $i,SV195: $i,SV115: $i,SV186: $i,SV30: $i,SV182: $i] :
( ( ( ~ ( member @ SV182 @ SV30 )
| ~ ( member @ SV186 @ SV115 )
| ~ ( member @ SV195 @ SV30 )
| ~ ( member @ SV201 @ SV115 )
| ~ ( apply @ SV36 @ SV182 @ SV195 ) )
= $true )
| ( ( ~ ( apply @ SV16 @ SV182 @ SV186 ) )
= $true )
| ( ( ~ ( apply @ SV16 @ SV195 @ SV201 ) )
= $true )
| ( ( apply @ SV134 @ SV186 @ SV201 )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV115 @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[939]) ).
thf(975,plain,
! [SV73: $i,SV37: $i,SV174: $i,SV20: $i,SV46: $i,SV210: $i,SV159: $i,SV31: $i] :
( ( ( ~ ( apply @ SV31 @ SV159 @ SV210 )
| ~ ( member @ SV210 @ SV46 ) )
= $true )
| ( ( ~ ( apply @ SV20 @ SV210 @ SV174 ) )
= $true )
| ( ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SV159 @ SV174 )
= $true )
| ( ( member @ SV159 @ SV37 )
= $false )
| ( ( member @ SV174 @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[940]) ).
thf(976,plain,
! [SV20: $i,SV37: $i,SV46: $i,SV73: $i,SV175: $i,SV160: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV31 @ SV160 @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) )
| ~ ( member @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SV46 ) )
| ~ ( apply @ SV20 @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SV175 ) )
= $false )
| ( ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SV160 @ SV175 )
= $false )
| ( ( member @ SV160 @ SV37 )
= $false )
| ( ( member @ SV175 @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[941]) ).
thf(977,plain,
! [SV21: $i,SV78: $i,SV100: $i] :
( ( ( ~ ( ~ ( member @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
| ~ ( member @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) @ SV100 ) ) )
= $true )
| ( ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[942]) ).
thf(978,plain,
! [SV21: $i,SV78: $i,SV100: $i] :
( ( ( member @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) @ SV100 )
= $true )
| ( ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[943]) ).
thf(979,plain,
! [SV78: $i,SV100: $i,SV21: $i] :
( ( ( ~ ( ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) ) )
= $true )
| ( ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[944]) ).
thf(980,plain,
! [SV21: $i,SV78: $i,SV100: $i] :
( ( ( ( ( sK38_SY170 @ SV100 @ SV78 @ SV21 )
!= ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) )
= $true )
| ( ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[945]) ).
thf(981,plain,
! [SV187: $i,SV21: $i,SV78: $i,SV100: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
| ~ ( member @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ( member @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) @ SV100 ) ) )
= $false )
| ( ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV187 )
= $false )
| ( ( member @ SV187 @ SV100 )
= $false )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[946]) ).
thf(982,plain,
! [SV187: $i,SV78: $i,SV100: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) )
| ~ ( ( ( sK38_SY170 @ SV100 @ SV78 @ SV21 )
!= ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) ) ) )
= $false )
| ( ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV187 )
= $false )
| ( ( member @ SV187 @ SV100 )
= $false )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[946]) ).
thf(983,plain,
! [SV142: $i,SV161: $i,SV188: $i,SV21: $i] :
( ( ( apply @ SV21 @ SV188 @ ( sK36_Y @ SV188 @ SV161 @ SV142 @ SV21 ) )
= $true )
| ( ( member @ SV188 @ SV142 )
= $false )
| ( ( maps @ SV21 @ SV142 @ SV161 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[947]) ).
thf(984,plain,
! [SV21: $i,SV142: $i,SV161: $i,SV188: $i] :
( ( ( member @ ( sK36_Y @ SV188 @ SV161 @ SV142 @ SV21 ) @ SV161 )
= $true )
| ( ( member @ SV188 @ SV142 )
= $false )
| ( ( maps @ SV21 @ SV142 @ SV161 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[948]) ).
thf(985,plain,
! [SV21: $i,SV202: $i,SV162: $i,SV196: $i,SV143: $i,SV189: $i] :
( ( ( ~ ( member @ SV189 @ SV143 ) )
= $true )
| ( ( ~ ( member @ SV196 @ SV162 ) )
= $true )
| ( ( ~ ( member @ SV202 @ SV162 ) )
= $true )
| ( ( ~ ( apply @ SV21 @ SV189 @ SV196 )
| ~ ( apply @ SV21 @ SV189 @ SV202 )
| ( SV196 = SV202 ) )
= $true )
| ( ( maps @ SV21 @ SV143 @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[949]) ).
thf(986,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 )
| ~ ( member @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( member @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 ) )
| ~ ( member @ ( sK11_SY150 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( apply @ SV32 @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) ) )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[950]) ).
thf(987,plain,
! [SV23: $i,SV32: $i,SV102: $i,SV117: $i,SV3: $i] :
( ( ( apply @ SV3 @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[951]) ).
thf(988,plain,
! [SV118: $i,SV3: $i,SV32: $i,SV197: $i,SV190: $i,SV103: $i,SV184: $i,SV23: $i,SV176: $i] :
( ( ( ~ ( member @ SV176 @ SV23 )
| ~ ( member @ SV184 @ SV103 )
| ~ ( member @ SV190 @ SV23 )
| ~ ( member @ SV197 @ SV103 ) )
= $true )
| ( ( ~ ( apply @ SV32 @ SV176 @ SV190 ) )
= $true )
| ( ( ~ ( apply @ SV3 @ SV176 @ SV184 ) )
= $true )
| ( ( ~ ( apply @ SV3 @ SV190 @ SV197 ) )
= $true )
| ( ( apply @ SV118 @ SV197 @ SV184 )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV103 @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[952]) ).
thf(989,plain,
! [SV7: $i,SV24: $i,SV33: $i,SV104: $i,SV125: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 )
| ~ ( member @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
| ~ ( member @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 ) )
| ~ ( member @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) ) )
= $false )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[953]) ).
thf(990,plain,
! [SV24: $i,SV33: $i,SV104: $i,SV125: $i,SV7: $i] :
( ( ( ~ ( apply @ SV7 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) )
= $false )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[953]) ).
thf(991,plain,
! [SV33: $i,SV125: $i,SV104: $i,SV24: $i,SV7: $i] :
( ( ( maps @ SV7 @ SV24 @ SV104 )
= $false )
| ( ( ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( apply @ SV7 @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[954]) ).
thf(992,plain,
! [SV7: $i,SV24: $i,SV104: $i,SV125: $i,SV33: $i] :
( ( ( apply @ SV33 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
= $false )
| ( ( ~ ( apply @ SV125 @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) ) )
= $true )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[955]) ).
thf(993,plain,
! [SV33: $i,SV125: $i,SV104: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( maps @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( apply @ SV125 @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
= $true )
| ( ( apply @ SV33 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[956]) ).
thf(994,plain,
! [SV178: $i,SV33: $i,SV7: $i,SV167: $i,SV203: $i,SV24: $i,SV198: $i] :
( ( ( ! [SY680: $i,SY681: $i] :
( ~ ( member @ SV198 @ SV24 )
| ~ ( member @ SV203 @ SV167 )
| ~ ( member @ SY680 @ SV24 )
| ~ ( member @ SY681 @ SV167 )
| ~ ( apply @ SV7 @ SV198 @ SV203 )
| ~ ( apply @ SV7 @ SY680 @ SY681 )
| ~ ( apply @ SV33 @ SV198 @ SY680 )
| ( apply @ SV178 @ SV203 @ SY681 ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[957]) ).
thf(995,plain,
! [SV33: $i,SV178: $i,SV7: $i,SV167: $i,SV203: $i,SV24: $i,SV198: $i] :
( ( ( ! [SY682: $i,SY683: $i] :
( ~ ( member @ SV198 @ SV24 )
| ~ ( member @ SV203 @ SV167 )
| ~ ( member @ SY682 @ SV24 )
| ~ ( member @ SY683 @ SV167 )
| ~ ( apply @ SV7 @ SV198 @ SV203 )
| ~ ( apply @ SV7 @ SY682 @ SY683 )
| ~ ( apply @ SV178 @ SV203 @ SY683 )
| ( apply @ SV33 @ SV198 @ SY682 ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[958]) ).
thf(996,plain,
! [SV8: $i,SV25: $i,SV87: $i,SV193: $i,SV106: $i,SV199: $i] :
( ( ( member @ SV199 @ SV106 )
= $false )
| ( ( member @ SV193 @ SV87 )
= $false )
| ( ( ~ ( apply @ SV25 @ SV193 @ SV199 )
| ( apply @ SV8 @ SV199 @ SV193 ) )
= $true )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV87 @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[960]) ).
thf(997,plain,
! [SV25: $i,SV8: $i,SV87: $i,SV194: $i,SV106: $i,SV200: $i] :
( ( ( member @ SV200 @ SV106 )
= $false )
| ( ( member @ SV194 @ SV87 )
= $false )
| ( ( ~ ( apply @ SV8 @ SV200 @ SV194 )
| ( apply @ SV25 @ SV194 @ SV200 ) )
= $true )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV87 @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[961]) ).
thf(998,plain,
! [SV28: $i,SV13: $i,SV180: $i,SV94: $i,SV171: $i,SV111: $i,SV185: $i] :
( ( ( member @ SV185 @ SV111 )
= $false )
| ( ( member @ SV171 @ SV94 )
= $false )
| ( ( member @ SV180 @ SV111 )
= $false )
| ( ( ~ ( apply @ SV13 @ SV171 @ SV180 )
| ~ ( apply @ SV28 @ SV171 @ SV185 )
| ( SV180 = SV185 ) )
= $true )
| ( ( equal_maps @ SV13 @ SV28 @ SV94 @ SV111 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(999,plain,
! [SV211: $i,SV14: $i,SV29: $i,SV42: $i,SV129: $i,SV152: $i,SV35: $i] :
( ( ( ~ ( apply @ SV35 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV211 )
| ~ ( member @ SV211 @ SV129 )
| ~ ( apply @ SV29 @ SV211 @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
= $true )
| ( ( ~ ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1000,plain,
! [SV14: $i,SV29: $i,SV42: $i,SV129: $i,SV152: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV35 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV129 ) )
| ~ ( apply @ SV29 @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
= $false )
| ( ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[968]) ).
thf(1001,plain,
! [SV14: $i,SV29: $i,SV130: $i,SV35: $i,SV153: $i,SV208: $i,SV42: $i,SV206: $i] :
( ( ( ~ ( member @ SV206 @ SV42 ) )
= $true )
| ( ( ~ ( member @ SV208 @ SV153 ) )
= $true )
| ( ( ! [SY687: $i] :
( ~ ( apply @ SV35 @ SV206 @ SY687 )
| ~ ( member @ SY687 @ SV130 )
| ~ ( apply @ SV29 @ SY687 @ SV208 ) )
| ( apply @ SV14 @ SV206 @ SV208 ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[969]) ).
thf(1002,plain,
! [SV29: $i,SV130: $i,SV35: $i,SV14: $i,SV153: $i,SV209: $i,SV42: $i,SV207: $i] :
( ( ( ~ ( member @ SV207 @ SV42 ) )
= $true )
| ( ( ~ ( member @ SV209 @ SV153 ) )
= $true )
| ( ( ~ ( apply @ SV14 @ SV207 @ SV209 )
| ~ ( ~ ~ ( ~ ( apply @ SV35 @ SV207 @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV130 ) )
| ~ ( apply @ SV29 @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV209 ) ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[970]) ).
thf(1003,plain,
! [SV96: $i,SV68: $i,SV172: $i,SV181: $i,SV154: $i,SV15: $i] :
( ( ( ~ ( apply @ SV15 @ SV154 @ SV181 )
| ~ ( apply @ SV15 @ SV172 @ SV181 ) )
= $true )
| ( ( SV154 = SV172 )
= $true )
| ( ( member @ SV172 @ SV68 )
= $false )
| ( ( member @ SV154 @ SV68 )
= $false )
| ( ( member @ SV181 @ SV96 )
= $false )
| ( ( injective @ SV15 @ SV68 @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[971]) ).
thf(1004,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 )
| ~ ( member @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( member @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 ) )
| ~ ( member @ ( sK15_SY156 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( apply @ SV36 @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) ) )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[972]) ).
thf(1005,plain,
! [SV30: $i,SV36: $i,SV114: $i,SV133: $i,SV16: $i] :
( ( ( apply @ SV16 @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[973]) ).
thf(1006,plain,
! [SV134: $i,SV16: $i,SV36: $i,SV201: $i,SV195: $i,SV115: $i,SV186: $i,SV30: $i,SV182: $i] :
( ( ( ~ ( member @ SV182 @ SV30 )
| ~ ( member @ SV186 @ SV115 )
| ~ ( member @ SV195 @ SV30 )
| ~ ( member @ SV201 @ SV115 ) )
= $true )
| ( ( ~ ( apply @ SV36 @ SV182 @ SV195 ) )
= $true )
| ( ( ~ ( apply @ SV16 @ SV182 @ SV186 ) )
= $true )
| ( ( ~ ( apply @ SV16 @ SV195 @ SV201 ) )
= $true )
| ( ( apply @ SV134 @ SV186 @ SV201 )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV115 @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[974]) ).
thf(1007,plain,
! [SV73: $i,SV37: $i,SV174: $i,SV20: $i,SV46: $i,SV210: $i,SV159: $i,SV31: $i] :
( ( ( ~ ( apply @ SV31 @ SV159 @ SV210 ) )
= $true )
| ( ( ~ ( member @ SV210 @ SV46 ) )
= $true )
| ( ( ~ ( apply @ SV20 @ SV210 @ SV174 ) )
= $true )
| ( ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SV159 @ SV174 )
= $true )
| ( ( member @ SV159 @ SV37 )
= $false )
| ( ( member @ SV174 @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[975]) ).
thf(1008,plain,
! [SV20: $i,SV37: $i,SV46: $i,SV73: $i,SV175: $i,SV160: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV31 @ SV160 @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) )
| ~ ( member @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SV46 ) ) )
= $false )
| ( ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SV160 @ SV175 )
= $false )
| ( ( member @ SV160 @ SV37 )
= $false )
| ( ( member @ SV175 @ SV73 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[976]) ).
thf(1009,plain,
! [SV31: $i,SV37: $i,SV46: $i,SV73: $i,SV160: $i,SV175: $i,SV20: $i] :
( ( ( ~ ( apply @ SV20 @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SV175 ) )
= $false )
| ( ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SV160 @ SV175 )
= $false )
| ( ( member @ SV160 @ SV37 )
= $false )
| ( ( member @ SV175 @ SV73 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[976]) ).
thf(1010,plain,
! [SV21: $i,SV78: $i,SV100: $i] :
( ( ( ~ ( member @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
| ~ ( member @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
= $false )
| ( ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[977]) ).
thf(1011,plain,
! [SV78: $i,SV100: $i,SV21: $i] :
( ( ( ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) )
= $false )
| ( ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[979]) ).
thf(1012,plain,
! [SV21: $i,SV78: $i,SV100: $i] :
( ( ( ( sK38_SY170 @ SV100 @ SV78 @ SV21 )
= ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) )
= $false )
| ( ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[980]) ).
thf(1013,plain,
! [SV187: $i,SV21: $i,SV78: $i,SV100: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
| ~ ( member @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ( member @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) @ SV100 ) ) )
= $true )
| ( ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV187 )
= $false )
| ( ( member @ SV187 @ SV100 )
= $false )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[981]) ).
thf(1014,plain,
! [SV187: $i,SV78: $i,SV100: $i,SV21: $i] :
( ( ( ~ ( ~ ~ ( ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) )
| ~ ( ( ( sK38_SY170 @ SV100 @ SV78 @ SV21 )
!= ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) ) ) )
= $true )
| ( ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV187 )
= $false )
| ( ( member @ SV187 @ SV100 )
= $false )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[982]) ).
thf(1015,plain,
! [SV21: $i,SV202: $i,SV162: $i,SV196: $i,SV143: $i,SV189: $i] :
( ( ( member @ SV189 @ SV143 )
= $false )
| ( ( ~ ( member @ SV196 @ SV162 ) )
= $true )
| ( ( ~ ( member @ SV202 @ SV162 ) )
= $true )
| ( ( ~ ( apply @ SV21 @ SV189 @ SV196 )
| ~ ( apply @ SV21 @ SV189 @ SV202 )
| ( SV196 = SV202 ) )
= $true )
| ( ( maps @ SV21 @ SV143 @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[985]) ).
thf(1016,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 )
| ~ ( member @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( member @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 ) )
| ~ ( member @ ( sK11_SY150 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( apply @ SV32 @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
= $false )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[986]) ).
thf(1017,plain,
! [SV118: $i,SV3: $i,SV32: $i,SV197: $i,SV190: $i,SV103: $i,SV184: $i,SV23: $i,SV176: $i] :
( ( ( ~ ( member @ SV176 @ SV23 )
| ~ ( member @ SV184 @ SV103 )
| ~ ( member @ SV190 @ SV23 ) )
= $true )
| ( ( ~ ( member @ SV197 @ SV103 ) )
= $true )
| ( ( ~ ( apply @ SV32 @ SV176 @ SV190 ) )
= $true )
| ( ( ~ ( apply @ SV3 @ SV176 @ SV184 ) )
= $true )
| ( ( ~ ( apply @ SV3 @ SV190 @ SV197 ) )
= $true )
| ( ( apply @ SV118 @ SV197 @ SV184 )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV103 @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[988]) ).
thf(1018,plain,
! [SV7: $i,SV24: $i,SV33: $i,SV104: $i,SV125: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 )
| ~ ( member @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
| ~ ( member @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 ) )
| ~ ( member @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) ) )
= $true )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[989]) ).
thf(1019,plain,
! [SV24: $i,SV33: $i,SV104: $i,SV125: $i,SV7: $i] :
( ( ( apply @ SV7 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
= $true )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[990]) ).
thf(1020,plain,
! [SV33: $i,SV125: $i,SV104: $i,SV24: $i,SV7: $i] :
( ( ( one_to_one @ SV7 @ SV24 @ SV104 )
= $false )
| ( ( maps @ SV7 @ SV24 @ SV104 )
= $false )
| ( ( apply @ SV7 @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[991]) ).
thf(1021,plain,
! [SV7: $i,SV24: $i,SV33: $i,SV104: $i,SV125: $i] :
( ( ( apply @ SV125 @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
= $false )
| ( ( apply @ SV33 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
= $false )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[992]) ).
thf(1022,plain,
! [SV33: $i,SV125: $i,SV104: $i,SV24: $i,SV7: $i] :
( ( ( maps @ SV7 @ SV24 @ SV104 )
= $false )
| ( ( ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( apply @ SV125 @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
= $true )
| ( ( apply @ SV33 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[993]) ).
thf(1023,plain,
! [SV178: $i,SV33: $i,SV7: $i,SV212: $i,SV167: $i,SV203: $i,SV24: $i,SV198: $i] :
( ( ( ! [SY688: $i] :
( ~ ( member @ SV198 @ SV24 )
| ~ ( member @ SV203 @ SV167 )
| ~ ( member @ SV212 @ SV24 )
| ~ ( member @ SY688 @ SV167 )
| ~ ( apply @ SV7 @ SV198 @ SV203 )
| ~ ( apply @ SV7 @ SV212 @ SY688 )
| ~ ( apply @ SV33 @ SV198 @ SV212 )
| ( apply @ SV178 @ SV203 @ SY688 ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1024,plain,
! [SV33: $i,SV178: $i,SV7: $i,SV213: $i,SV167: $i,SV203: $i,SV24: $i,SV198: $i] :
( ( ( ! [SY689: $i] :
( ~ ( member @ SV198 @ SV24 )
| ~ ( member @ SV203 @ SV167 )
| ~ ( member @ SV213 @ SV24 )
| ~ ( member @ SY689 @ SV167 )
| ~ ( apply @ SV7 @ SV198 @ SV203 )
| ~ ( apply @ SV7 @ SV213 @ SY689 )
| ~ ( apply @ SV178 @ SV203 @ SY689 )
| ( apply @ SV33 @ SV198 @ SV213 ) ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1025,plain,
! [SV106: $i,SV87: $i,SV8: $i,SV199: $i,SV193: $i,SV25: $i] :
( ( ( ~ ( apply @ SV25 @ SV193 @ SV199 ) )
= $true )
| ( ( apply @ SV8 @ SV199 @ SV193 )
= $true )
| ( ( member @ SV193 @ SV87 )
= $false )
| ( ( member @ SV199 @ SV106 )
= $false )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV87 @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[996]) ).
thf(1026,plain,
! [SV106: $i,SV87: $i,SV25: $i,SV194: $i,SV200: $i,SV8: $i] :
( ( ( ~ ( apply @ SV8 @ SV200 @ SV194 ) )
= $true )
| ( ( apply @ SV25 @ SV194 @ SV200 )
= $true )
| ( ( member @ SV194 @ SV87 )
= $false )
| ( ( member @ SV200 @ SV106 )
= $false )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV87 @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[997]) ).
thf(1027,plain,
! [SV94: $i,SV111: $i,SV185: $i,SV28: $i,SV180: $i,SV171: $i,SV13: $i] :
( ( ( ~ ( apply @ SV13 @ SV171 @ SV180 )
| ~ ( apply @ SV28 @ SV171 @ SV185 ) )
= $true )
| ( ( SV180 = SV185 )
= $true )
| ( ( member @ SV180 @ SV111 )
= $false )
| ( ( member @ SV171 @ SV94 )
= $false )
| ( ( member @ SV185 @ SV111 )
= $false )
| ( ( equal_maps @ SV13 @ SV28 @ SV94 @ SV111 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[998]) ).
thf(1028,plain,
! [SV211: $i,SV14: $i,SV29: $i,SV42: $i,SV129: $i,SV152: $i,SV35: $i] :
( ( ( ~ ( apply @ SV35 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV211 )
| ~ ( member @ SV211 @ SV129 ) )
= $true )
| ( ( ~ ( apply @ SV29 @ SV211 @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
= $true )
| ( ( ~ ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[999]) ).
thf(1029,plain,
! [SV14: $i,SV29: $i,SV42: $i,SV129: $i,SV152: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV35 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV129 ) ) )
= $false )
| ( ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1000]) ).
thf(1030,plain,
! [SV14: $i,SV35: $i,SV42: $i,SV129: $i,SV152: $i,SV29: $i] :
( ( ( ~ ( apply @ SV29 @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
= $false )
| ( ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1000]) ).
thf(1031,plain,
! [SV14: $i,SV29: $i,SV130: $i,SV35: $i,SV153: $i,SV208: $i,SV42: $i,SV206: $i] :
( ( ( member @ SV206 @ SV42 )
= $false )
| ( ( ~ ( member @ SV208 @ SV153 ) )
= $true )
| ( ( ! [SY687: $i] :
( ~ ( apply @ SV35 @ SV206 @ SY687 )
| ~ ( member @ SY687 @ SV130 )
| ~ ( apply @ SV29 @ SY687 @ SV208 ) )
| ( apply @ SV14 @ SV206 @ SV208 ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1001]) ).
thf(1032,plain,
! [SV29: $i,SV130: $i,SV35: $i,SV14: $i,SV153: $i,SV209: $i,SV42: $i,SV207: $i] :
( ( ( member @ SV207 @ SV42 )
= $false )
| ( ( ~ ( member @ SV209 @ SV153 ) )
= $true )
| ( ( ~ ( apply @ SV14 @ SV207 @ SV209 )
| ~ ( ~ ~ ( ~ ( apply @ SV35 @ SV207 @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV130 ) )
| ~ ( apply @ SV29 @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV209 ) ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1002]) ).
thf(1033,plain,
! [SV96: $i,SV68: $i,SV172: $i,SV181: $i,SV154: $i,SV15: $i] :
( ( ( ~ ( apply @ SV15 @ SV154 @ SV181 ) )
= $true )
| ( ( ~ ( apply @ SV15 @ SV172 @ SV181 ) )
= $true )
| ( ( SV154 = SV172 )
= $true )
| ( ( member @ SV172 @ SV68 )
= $false )
| ( ( member @ SV154 @ SV68 )
= $false )
| ( ( member @ SV181 @ SV96 )
= $false )
| ( ( injective @ SV15 @ SV68 @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1003]) ).
thf(1034,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 )
| ~ ( member @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( member @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 ) )
| ~ ( member @ ( sK15_SY156 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( apply @ SV36 @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
= $false )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1004]) ).
thf(1035,plain,
! [SV134: $i,SV16: $i,SV36: $i,SV201: $i,SV195: $i,SV115: $i,SV186: $i,SV30: $i,SV182: $i] :
( ( ( ~ ( member @ SV182 @ SV30 )
| ~ ( member @ SV186 @ SV115 )
| ~ ( member @ SV195 @ SV30 ) )
= $true )
| ( ( ~ ( member @ SV201 @ SV115 ) )
= $true )
| ( ( ~ ( apply @ SV36 @ SV182 @ SV195 ) )
= $true )
| ( ( ~ ( apply @ SV16 @ SV182 @ SV186 ) )
= $true )
| ( ( ~ ( apply @ SV16 @ SV195 @ SV201 ) )
= $true )
| ( ( apply @ SV134 @ SV186 @ SV201 )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV115 @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1006]) ).
thf(1036,plain,
! [SV73: $i,SV37: $i,SV174: $i,SV20: $i,SV46: $i,SV210: $i,SV159: $i,SV31: $i] :
( ( ( apply @ SV31 @ SV159 @ SV210 )
= $false )
| ( ( ~ ( member @ SV210 @ SV46 ) )
= $true )
| ( ( ~ ( apply @ SV20 @ SV210 @ SV174 ) )
= $true )
| ( ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SV159 @ SV174 )
= $true )
| ( ( member @ SV159 @ SV37 )
= $false )
| ( ( member @ SV174 @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1007]) ).
thf(1037,plain,
! [SV20: $i,SV37: $i,SV46: $i,SV73: $i,SV175: $i,SV160: $i,SV31: $i] :
( ( ( ~ ( ~ ( apply @ SV31 @ SV160 @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) )
| ~ ( member @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SV46 ) ) )
= $true )
| ( ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SV160 @ SV175 )
= $false )
| ( ( member @ SV160 @ SV37 )
= $false )
| ( ( member @ SV175 @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1008]) ).
thf(1038,plain,
! [SV31: $i,SV37: $i,SV46: $i,SV73: $i,SV160: $i,SV175: $i,SV20: $i] :
( ( ( apply @ SV20 @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SV175 )
= $true )
| ( ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SV160 @ SV175 )
= $false )
| ( ( member @ SV160 @ SV37 )
= $false )
| ( ( member @ SV175 @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1009]) ).
thf(1039,plain,
! [SV21: $i,SV78: $i,SV100: $i] :
( ( ( ~ ( member @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ SV78 ) )
= $false )
| ( ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1010]) ).
thf(1040,plain,
! [SV21: $i,SV78: $i,SV100: $i] :
( ( ( ~ ( member @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
= $false )
| ( ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1010]) ).
thf(1041,plain,
! [SV78: $i,SV100: $i,SV21: $i] :
( ( ( ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) ) )
= $false )
| ( ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1011]) ).
thf(1042,plain,
! [SV78: $i,SV100: $i,SV21: $i] :
( ( ( ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) )
= $false )
| ( ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1011]) ).
thf(1043,plain,
! [SV187: $i,SV21: $i,SV78: $i,SV100: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
| ~ ( member @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
| ~ ( member @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
= $false )
| ( ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV187 )
= $false )
| ( ( member @ SV187 @ SV100 )
= $false )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1013]) ).
thf(1044,plain,
! [SV187: $i,SV78: $i,SV100: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) )
| ~ ( ( ( sK38_SY170 @ SV100 @ SV78 @ SV21 )
!= ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) ) )
= $false )
| ( ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV187 )
= $false )
| ( ( member @ SV187 @ SV100 )
= $false )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1014]) ).
thf(1045,plain,
! [SV21: $i,SV202: $i,SV143: $i,SV189: $i,SV162: $i,SV196: $i] :
( ( ( member @ SV196 @ SV162 )
= $false )
| ( ( member @ SV189 @ SV143 )
= $false )
| ( ( ~ ( member @ SV202 @ SV162 ) )
= $true )
| ( ( ~ ( apply @ SV21 @ SV189 @ SV196 )
| ~ ( apply @ SV21 @ SV189 @ SV202 )
| ( SV196 = SV202 ) )
= $true )
| ( ( maps @ SV21 @ SV143 @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1046,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 )
| ~ ( member @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( member @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 ) )
| ~ ( member @ ( sK11_SY150 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) ) )
= $false )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1016]) ).
thf(1047,plain,
! [SV3: $i,SV23: $i,SV102: $i,SV117: $i,SV32: $i] :
( ( ( ~ ( apply @ SV32 @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) ) )
= $false )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1016]) ).
thf(1048,plain,
! [SV118: $i,SV3: $i,SV32: $i,SV197: $i,SV190: $i,SV103: $i,SV184: $i,SV23: $i,SV176: $i] :
( ( ( ~ ( member @ SV176 @ SV23 )
| ~ ( member @ SV184 @ SV103 ) )
= $true )
| ( ( ~ ( member @ SV190 @ SV23 ) )
= $true )
| ( ( ~ ( member @ SV197 @ SV103 ) )
= $true )
| ( ( ~ ( apply @ SV32 @ SV176 @ SV190 ) )
= $true )
| ( ( ~ ( apply @ SV3 @ SV176 @ SV184 ) )
= $true )
| ( ( ~ ( apply @ SV3 @ SV190 @ SV197 ) )
= $true )
| ( ( apply @ SV118 @ SV197 @ SV184 )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV103 @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1017]) ).
thf(1049,plain,
! [SV7: $i,SV24: $i,SV33: $i,SV104: $i,SV125: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 )
| ~ ( member @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
| ~ ( member @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 ) )
| ~ ( member @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
= $false )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1018]) ).
thf(1050,plain,
! [SV33: $i,SV125: $i,SV104: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( maps @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( apply @ SV7 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1019]) ).
thf(1051,plain,
! [SV125: $i,SV33: $i,SV104: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( maps @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( apply @ SV33 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
= $false )
| ( ( apply @ SV125 @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
= $false )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1021]) ).
thf(1052,plain,
! [SV33: $i,SV125: $i,SV104: $i,SV24: $i,SV7: $i] :
( ( ( one_to_one @ SV7 @ SV24 @ SV104 )
= $false )
| ( ( maps @ SV7 @ SV24 @ SV104 )
= $false )
| ( ( apply @ SV125 @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
= $true )
| ( ( apply @ SV33 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1053,plain,
! [SV178: $i,SV33: $i,SV7: $i,SV214: $i,SV212: $i,SV167: $i,SV203: $i,SV24: $i,SV198: $i] :
( ( ( ~ ( member @ SV198 @ SV24 )
| ~ ( member @ SV203 @ SV167 )
| ~ ( member @ SV212 @ SV24 )
| ~ ( member @ SV214 @ SV167 )
| ~ ( apply @ SV7 @ SV198 @ SV203 )
| ~ ( apply @ SV7 @ SV212 @ SV214 )
| ~ ( apply @ SV33 @ SV198 @ SV212 )
| ( apply @ SV178 @ SV203 @ SV214 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1054,plain,
! [SV33: $i,SV178: $i,SV7: $i,SV215: $i,SV213: $i,SV167: $i,SV203: $i,SV24: $i,SV198: $i] :
( ( ( ~ ( member @ SV198 @ SV24 )
| ~ ( member @ SV203 @ SV167 )
| ~ ( member @ SV213 @ SV24 )
| ~ ( member @ SV215 @ SV167 )
| ~ ( apply @ SV7 @ SV198 @ SV203 )
| ~ ( apply @ SV7 @ SV213 @ SV215 )
| ~ ( apply @ SV178 @ SV203 @ SV215 )
| ( apply @ SV33 @ SV198 @ SV213 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1055,plain,
! [SV106: $i,SV87: $i,SV8: $i,SV199: $i,SV193: $i,SV25: $i] :
( ( ( apply @ SV25 @ SV193 @ SV199 )
= $false )
| ( ( apply @ SV8 @ SV199 @ SV193 )
= $true )
| ( ( member @ SV193 @ SV87 )
= $false )
| ( ( member @ SV199 @ SV106 )
= $false )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV87 @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1025]) ).
thf(1056,plain,
! [SV106: $i,SV87: $i,SV25: $i,SV194: $i,SV200: $i,SV8: $i] :
( ( ( apply @ SV8 @ SV200 @ SV194 )
= $false )
| ( ( apply @ SV25 @ SV194 @ SV200 )
= $true )
| ( ( member @ SV194 @ SV87 )
= $false )
| ( ( member @ SV200 @ SV106 )
= $false )
| ( ( inverse_predicate @ SV8 @ SV25 @ SV87 @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1026]) ).
thf(1057,plain,
! [SV94: $i,SV111: $i,SV185: $i,SV28: $i,SV180: $i,SV171: $i,SV13: $i] :
( ( ( ~ ( apply @ SV13 @ SV171 @ SV180 ) )
= $true )
| ( ( ~ ( apply @ SV28 @ SV171 @ SV185 ) )
= $true )
| ( ( SV180 = SV185 )
= $true )
| ( ( member @ SV180 @ SV111 )
= $false )
| ( ( member @ SV171 @ SV94 )
= $false )
| ( ( member @ SV185 @ SV111 )
= $false )
| ( ( equal_maps @ SV13 @ SV28 @ SV94 @ SV111 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1027]) ).
thf(1058,plain,
! [SV211: $i,SV14: $i,SV29: $i,SV42: $i,SV129: $i,SV152: $i,SV35: $i] :
( ( ( ~ ( apply @ SV35 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV211 ) )
= $true )
| ( ( ~ ( member @ SV211 @ SV129 ) )
= $true )
| ( ( ~ ( apply @ SV29 @ SV211 @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
= $true )
| ( ( ~ ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1028]) ).
thf(1059,plain,
! [SV14: $i,SV29: $i,SV42: $i,SV129: $i,SV152: $i,SV35: $i] :
( ( ( ~ ( ~ ( apply @ SV35 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV129 ) ) )
= $true )
| ( ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1029]) ).
thf(1060,plain,
! [SV14: $i,SV35: $i,SV42: $i,SV129: $i,SV152: $i,SV29: $i] :
( ( ( apply @ SV29 @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) )
= $true )
| ( ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1030]) ).
thf(1061,plain,
! [SV14: $i,SV29: $i,SV130: $i,SV35: $i,SV42: $i,SV206: $i,SV153: $i,SV208: $i] :
( ( ( member @ SV208 @ SV153 )
= $false )
| ( ( member @ SV206 @ SV42 )
= $false )
| ( ( ! [SY687: $i] :
( ~ ( apply @ SV35 @ SV206 @ SY687 )
| ~ ( member @ SY687 @ SV130 )
| ~ ( apply @ SV29 @ SY687 @ SV208 ) )
| ( apply @ SV14 @ SV206 @ SV208 ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1031]) ).
thf(1062,plain,
! [SV29: $i,SV130: $i,SV35: $i,SV14: $i,SV42: $i,SV207: $i,SV153: $i,SV209: $i] :
( ( ( member @ SV209 @ SV153 )
= $false )
| ( ( member @ SV207 @ SV42 )
= $false )
| ( ( ~ ( apply @ SV14 @ SV207 @ SV209 )
| ~ ( ~ ~ ( ~ ( apply @ SV35 @ SV207 @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV130 ) )
| ~ ( apply @ SV29 @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV209 ) ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1032]) ).
thf(1063,plain,
! [SV96: $i,SV68: $i,SV172: $i,SV181: $i,SV154: $i,SV15: $i] :
( ( ( apply @ SV15 @ SV154 @ SV181 )
= $false )
| ( ( ~ ( apply @ SV15 @ SV172 @ SV181 ) )
= $true )
| ( ( SV154 = SV172 )
= $true )
| ( ( member @ SV172 @ SV68 )
= $false )
| ( ( member @ SV154 @ SV68 )
= $false )
| ( ( member @ SV181 @ SV96 )
= $false )
| ( ( injective @ SV15 @ SV68 @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1033]) ).
thf(1064,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 )
| ~ ( member @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( member @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 ) )
| ~ ( member @ ( sK15_SY156 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) ) )
= $false )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1034]) ).
thf(1065,plain,
! [SV16: $i,SV30: $i,SV114: $i,SV133: $i,SV36: $i] :
( ( ( ~ ( apply @ SV36 @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) ) )
= $false )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1034]) ).
thf(1066,plain,
! [SV134: $i,SV16: $i,SV36: $i,SV201: $i,SV195: $i,SV115: $i,SV186: $i,SV30: $i,SV182: $i] :
( ( ( ~ ( member @ SV182 @ SV30 )
| ~ ( member @ SV186 @ SV115 ) )
= $true )
| ( ( ~ ( member @ SV195 @ SV30 ) )
= $true )
| ( ( ~ ( member @ SV201 @ SV115 ) )
= $true )
| ( ( ~ ( apply @ SV36 @ SV182 @ SV195 ) )
= $true )
| ( ( ~ ( apply @ SV16 @ SV182 @ SV186 ) )
= $true )
| ( ( ~ ( apply @ SV16 @ SV195 @ SV201 ) )
= $true )
| ( ( apply @ SV134 @ SV186 @ SV201 )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV115 @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1035]) ).
thf(1067,plain,
! [SV73: $i,SV37: $i,SV174: $i,SV20: $i,SV159: $i,SV31: $i,SV46: $i,SV210: $i] :
( ( ( member @ SV210 @ SV46 )
= $false )
| ( ( apply @ SV31 @ SV159 @ SV210 )
= $false )
| ( ( ~ ( apply @ SV20 @ SV210 @ SV174 ) )
= $true )
| ( ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SV159 @ SV174 )
= $true )
| ( ( member @ SV159 @ SV37 )
= $false )
| ( ( member @ SV174 @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1036]) ).
thf(1068,plain,
! [SV20: $i,SV37: $i,SV46: $i,SV73: $i,SV175: $i,SV160: $i,SV31: $i] :
( ( ( ~ ( apply @ SV31 @ SV160 @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) )
| ~ ( member @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SV46 ) )
= $false )
| ( ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SV160 @ SV175 )
= $false )
| ( ( member @ SV160 @ SV37 )
= $false )
| ( ( member @ SV175 @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1037]) ).
thf(1069,plain,
! [SV21: $i,SV78: $i,SV100: $i] :
( ( ( member @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
= $true )
| ( ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1039]) ).
thf(1070,plain,
! [SV21: $i,SV78: $i,SV100: $i] :
( ( ( member @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) @ SV100 )
= $true )
| ( ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1040]) ).
thf(1071,plain,
! [SV78: $i,SV100: $i,SV21: $i] :
( ( ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) )
= $true )
| ( ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1041]) ).
thf(1072,plain,
! [SV78: $i,SV100: $i,SV21: $i] :
( ( ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) )
= $true )
| ( ( member @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
= $true )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1042]) ).
thf(1073,plain,
! [SV187: $i,SV21: $i,SV78: $i,SV100: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
| ~ ( member @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) @ SV100 ) ) )
= $false )
| ( ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV187 )
= $false )
| ( ( member @ SV187 @ SV100 )
= $false )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1043]) ).
thf(1074,plain,
! [SV187: $i,SV21: $i,SV78: $i,SV100: $i] :
( ( ( ~ ( member @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
= $false )
| ( ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV187 )
= $false )
| ( ( member @ SV187 @ SV100 )
= $false )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1043]) ).
thf(1075,plain,
! [SV187: $i,SV78: $i,SV100: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) ) )
= $false )
| ( ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV187 )
= $false )
| ( ( member @ SV187 @ SV100 )
= $false )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1044]) ).
thf(1076,plain,
! [SV187: $i,SV21: $i,SV78: $i,SV100: $i] :
( ( ( ~ ( ( ( sK38_SY170 @ SV100 @ SV78 @ SV21 )
!= ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) ) )
= $false )
| ( ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV187 )
= $false )
| ( ( member @ SV187 @ SV100 )
= $false )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1044]) ).
thf(1077,plain,
! [SV21: $i,SV196: $i,SV143: $i,SV189: $i,SV162: $i,SV202: $i] :
( ( ( member @ SV202 @ SV162 )
= $false )
| ( ( member @ SV189 @ SV143 )
= $false )
| ( ( member @ SV196 @ SV162 )
= $false )
| ( ( ~ ( apply @ SV21 @ SV189 @ SV196 )
| ~ ( apply @ SV21 @ SV189 @ SV202 )
| ( SV196 = SV202 ) )
= $true )
| ( ( maps @ SV21 @ SV143 @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1045]) ).
thf(1078,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 )
| ~ ( member @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( member @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 ) )
| ~ ( member @ ( sK11_SY150 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) ) )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1046]) ).
thf(1079,plain,
! [SV3: $i,SV23: $i,SV102: $i,SV117: $i,SV32: $i] :
( ( ( apply @ SV32 @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1047]) ).
thf(1080,plain,
! [SV118: $i,SV3: $i,SV32: $i,SV197: $i,SV190: $i,SV103: $i,SV184: $i,SV23: $i,SV176: $i] :
( ( ( ~ ( member @ SV176 @ SV23 ) )
= $true )
| ( ( ~ ( member @ SV184 @ SV103 ) )
= $true )
| ( ( ~ ( member @ SV190 @ SV23 ) )
= $true )
| ( ( ~ ( member @ SV197 @ SV103 ) )
= $true )
| ( ( ~ ( apply @ SV32 @ SV176 @ SV190 ) )
= $true )
| ( ( ~ ( apply @ SV3 @ SV176 @ SV184 ) )
= $true )
| ( ( ~ ( apply @ SV3 @ SV190 @ SV197 ) )
= $true )
| ( ( apply @ SV118 @ SV197 @ SV184 )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV103 @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1048]) ).
thf(1081,plain,
! [SV7: $i,SV24: $i,SV33: $i,SV104: $i,SV125: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 )
| ~ ( member @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
| ~ ( member @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 ) ) )
= $false )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1049]) ).
thf(1082,plain,
! [SV7: $i,SV24: $i,SV33: $i,SV104: $i,SV125: $i] :
( ( ( ~ ( member @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
= $false )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1049]) ).
thf(1083,plain,
! [SV33: $i,SV125: $i,SV104: $i,SV24: $i,SV7: $i] :
( ( ( maps @ SV7 @ SV24 @ SV104 )
= $false )
| ( ( ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( apply @ SV7 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1050]) ).
thf(1084,plain,
! [SV125: $i,SV33: $i,SV104: $i,SV24: $i,SV7: $i] :
( ( ( maps @ SV7 @ SV24 @ SV104 )
= $false )
| ( ( ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( apply @ SV33 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
= $false )
| ( ( apply @ SV125 @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
= $false )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1051]) ).
thf(1085,plain,
! [SV178: $i,SV33: $i,SV7: $i,SV214: $i,SV212: $i,SV167: $i,SV203: $i,SV24: $i,SV198: $i] :
( ( ( ~ ( member @ SV198 @ SV24 )
| ~ ( member @ SV203 @ SV167 )
| ~ ( member @ SV212 @ SV24 )
| ~ ( member @ SV214 @ SV167 )
| ~ ( apply @ SV7 @ SV198 @ SV203 )
| ~ ( apply @ SV7 @ SV212 @ SV214 ) )
= $true )
| ( ( ~ ( apply @ SV33 @ SV198 @ SV212 )
| ( apply @ SV178 @ SV203 @ SV214 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1053]) ).
thf(1086,plain,
! [SV33: $i,SV178: $i,SV7: $i,SV215: $i,SV213: $i,SV167: $i,SV203: $i,SV24: $i,SV198: $i] :
( ( ( ~ ( member @ SV198 @ SV24 )
| ~ ( member @ SV203 @ SV167 )
| ~ ( member @ SV213 @ SV24 )
| ~ ( member @ SV215 @ SV167 )
| ~ ( apply @ SV7 @ SV198 @ SV203 )
| ~ ( apply @ SV7 @ SV213 @ SV215 ) )
= $true )
| ( ( ~ ( apply @ SV178 @ SV203 @ SV215 )
| ( apply @ SV33 @ SV198 @ SV213 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1054]) ).
thf(1087,plain,
! [SV94: $i,SV111: $i,SV185: $i,SV28: $i,SV180: $i,SV171: $i,SV13: $i] :
( ( ( apply @ SV13 @ SV171 @ SV180 )
= $false )
| ( ( ~ ( apply @ SV28 @ SV171 @ SV185 ) )
= $true )
| ( ( SV180 = SV185 )
= $true )
| ( ( member @ SV180 @ SV111 )
= $false )
| ( ( member @ SV171 @ SV94 )
= $false )
| ( ( member @ SV185 @ SV111 )
= $false )
| ( ( equal_maps @ SV13 @ SV28 @ SV94 @ SV111 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1057]) ).
thf(1088,plain,
! [SV211: $i,SV14: $i,SV29: $i,SV42: $i,SV129: $i,SV152: $i,SV35: $i] :
( ( ( apply @ SV35 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV211 )
= $false )
| ( ( ~ ( member @ SV211 @ SV129 ) )
= $true )
| ( ( ~ ( apply @ SV29 @ SV211 @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
= $true )
| ( ( ~ ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1058]) ).
thf(1089,plain,
! [SV14: $i,SV29: $i,SV42: $i,SV129: $i,SV152: $i,SV35: $i] :
( ( ( ~ ( apply @ SV35 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV129 ) )
= $false )
| ( ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1059]) ).
thf(1090,plain,
! [SV153: $i,SV42: $i,SV14: $i,SV208: $i,SV29: $i,SV130: $i,SV206: $i,SV35: $i] :
( ( ( ! [SY687: $i] :
( ~ ( apply @ SV35 @ SV206 @ SY687 )
| ~ ( member @ SY687 @ SV130 )
| ~ ( apply @ SV29 @ SY687 @ SV208 ) ) )
= $true )
| ( ( apply @ SV14 @ SV206 @ SV208 )
= $true )
| ( ( member @ SV206 @ SV42 )
= $false )
| ( ( member @ SV208 @ SV153 )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1061]) ).
thf(1091,plain,
! [SV29: $i,SV42: $i,SV130: $i,SV153: $i,SV35: $i,SV209: $i,SV207: $i,SV14: $i] :
( ( ( ~ ( apply @ SV14 @ SV207 @ SV209 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( apply @ SV35 @ SV207 @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV130 ) )
| ~ ( apply @ SV29 @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV209 ) ) )
= $true )
| ( ( member @ SV207 @ SV42 )
= $false )
| ( ( member @ SV209 @ SV153 )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1062]) ).
thf(1092,plain,
! [SV96: $i,SV68: $i,SV154: $i,SV181: $i,SV172: $i,SV15: $i] :
( ( ( apply @ SV15 @ SV172 @ SV181 )
= $false )
| ( ( apply @ SV15 @ SV154 @ SV181 )
= $false )
| ( ( SV154 = SV172 )
= $true )
| ( ( member @ SV172 @ SV68 )
= $false )
| ( ( member @ SV154 @ SV68 )
= $false )
| ( ( member @ SV181 @ SV96 )
= $false )
| ( ( injective @ SV15 @ SV68 @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1063]) ).
thf(1093,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 )
| ~ ( member @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( member @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 ) )
| ~ ( member @ ( sK15_SY156 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) ) )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1064]) ).
thf(1094,plain,
! [SV16: $i,SV30: $i,SV114: $i,SV133: $i,SV36: $i] :
( ( ( apply @ SV36 @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1065]) ).
thf(1095,plain,
! [SV134: $i,SV16: $i,SV36: $i,SV201: $i,SV195: $i,SV115: $i,SV186: $i,SV30: $i,SV182: $i] :
( ( ( ~ ( member @ SV182 @ SV30 ) )
= $true )
| ( ( ~ ( member @ SV186 @ SV115 ) )
= $true )
| ( ( ~ ( member @ SV195 @ SV30 ) )
= $true )
| ( ( ~ ( member @ SV201 @ SV115 ) )
= $true )
| ( ( ~ ( apply @ SV36 @ SV182 @ SV195 ) )
= $true )
| ( ( ~ ( apply @ SV16 @ SV182 @ SV186 ) )
= $true )
| ( ( ~ ( apply @ SV16 @ SV195 @ SV201 ) )
= $true )
| ( ( apply @ SV134 @ SV186 @ SV201 )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV115 @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1066]) ).
thf(1096,plain,
! [SV73: $i,SV37: $i,SV46: $i,SV159: $i,SV31: $i,SV174: $i,SV210: $i,SV20: $i] :
( ( ( apply @ SV20 @ SV210 @ SV174 )
= $false )
| ( ( apply @ SV31 @ SV159 @ SV210 )
= $false )
| ( ( member @ SV210 @ SV46 )
= $false )
| ( ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SV159 @ SV174 )
= $true )
| ( ( member @ SV159 @ SV37 )
= $false )
| ( ( member @ SV174 @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1067]) ).
thf(1097,plain,
! [SV20: $i,SV37: $i,SV46: $i,SV73: $i,SV175: $i,SV160: $i,SV31: $i] :
( ( ( ~ ( apply @ SV31 @ SV160 @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) ) )
= $false )
| ( ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SV160 @ SV175 )
= $false )
| ( ( member @ SV160 @ SV37 )
= $false )
| ( ( member @ SV175 @ SV73 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1068]) ).
thf(1098,plain,
! [SV20: $i,SV31: $i,SV37: $i,SV46: $i,SV73: $i,SV160: $i,SV175: $i] :
( ( ( ~ ( member @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SV46 ) )
= $false )
| ( ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SV160 @ SV175 )
= $false )
| ( ( member @ SV160 @ SV37 )
= $false )
| ( ( member @ SV175 @ SV73 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1068]) ).
thf(1099,plain,
! [SV187: $i,SV21: $i,SV78: $i,SV100: $i] :
( ( ( ~ ( ~ ( member @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
| ~ ( member @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) @ SV100 ) ) )
= $true )
| ( ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV187 )
= $false )
| ( ( member @ SV187 @ SV100 )
= $false )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1073]) ).
thf(1100,plain,
! [SV187: $i,SV21: $i,SV78: $i,SV100: $i] :
( ( ( member @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) @ SV100 )
= $true )
| ( ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV187 )
= $false )
| ( ( member @ SV187 @ SV100 )
= $false )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1074]) ).
thf(1101,plain,
! [SV187: $i,SV78: $i,SV100: $i,SV21: $i] :
( ( ( ~ ( ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) ) )
= $true )
| ( ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV187 )
= $false )
| ( ( member @ SV187 @ SV100 )
= $false )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1075]) ).
thf(1102,plain,
! [SV187: $i,SV21: $i,SV78: $i,SV100: $i] :
( ( ( ( ( sK38_SY170 @ SV100 @ SV78 @ SV21 )
!= ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) )
= $true )
| ( ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV187 )
= $false )
| ( ( member @ SV187 @ SV100 )
= $false )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1076]) ).
thf(1103,plain,
! [SV143: $i,SV162: $i,SV202: $i,SV196: $i,SV189: $i,SV21: $i] :
( ( ( ~ ( apply @ SV21 @ SV189 @ SV196 )
| ~ ( apply @ SV21 @ SV189 @ SV202 ) )
= $true )
| ( ( SV196 = SV202 )
= $true )
| ( ( member @ SV196 @ SV162 )
= $false )
| ( ( member @ SV189 @ SV143 )
= $false )
| ( ( member @ SV202 @ SV162 )
= $false )
| ( ( maps @ SV21 @ SV143 @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1077]) ).
thf(1104,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 )
| ~ ( member @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( member @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 ) )
| ~ ( member @ ( sK11_SY150 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
= $false )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1078]) ).
thf(1105,plain,
! [SV118: $i,SV3: $i,SV32: $i,SV197: $i,SV190: $i,SV103: $i,SV184: $i,SV23: $i,SV176: $i] :
( ( ( member @ SV176 @ SV23 )
= $false )
| ( ( ~ ( member @ SV184 @ SV103 ) )
= $true )
| ( ( ~ ( member @ SV190 @ SV23 ) )
= $true )
| ( ( ~ ( member @ SV197 @ SV103 ) )
= $true )
| ( ( ~ ( apply @ SV32 @ SV176 @ SV190 ) )
= $true )
| ( ( ~ ( apply @ SV3 @ SV176 @ SV184 ) )
= $true )
| ( ( ~ ( apply @ SV3 @ SV190 @ SV197 ) )
= $true )
| ( ( apply @ SV118 @ SV197 @ SV184 )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV103 @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1080]) ).
thf(1106,plain,
! [SV7: $i,SV24: $i,SV33: $i,SV104: $i,SV125: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 )
| ~ ( member @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
| ~ ( member @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 ) ) )
= $true )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1081]) ).
thf(1107,plain,
! [SV7: $i,SV24: $i,SV33: $i,SV104: $i,SV125: $i] :
( ( ( member @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 )
= $true )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1082]) ).
thf(1108,plain,
! [SV33: $i,SV125: $i,SV104: $i,SV24: $i,SV7: $i] :
( ( ( one_to_one @ SV7 @ SV24 @ SV104 )
= $false )
| ( ( maps @ SV7 @ SV24 @ SV104 )
= $false )
| ( ( apply @ SV7 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1083]) ).
thf(1109,plain,
! [SV125: $i,SV33: $i,SV104: $i,SV24: $i,SV7: $i] :
( ( ( one_to_one @ SV7 @ SV24 @ SV104 )
= $false )
| ( ( maps @ SV7 @ SV24 @ SV104 )
= $false )
| ( ( apply @ SV33 @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
= $false )
| ( ( apply @ SV125 @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) )
= $false )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1084]) ).
thf(1110,plain,
! [SV178: $i,SV33: $i,SV7: $i,SV214: $i,SV212: $i,SV167: $i,SV203: $i,SV24: $i,SV198: $i] :
( ( ( ~ ( member @ SV198 @ SV24 )
| ~ ( member @ SV203 @ SV167 )
| ~ ( member @ SV212 @ SV24 )
| ~ ( member @ SV214 @ SV167 )
| ~ ( apply @ SV7 @ SV198 @ SV203 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV212 @ SV214 ) )
= $true )
| ( ( ~ ( apply @ SV33 @ SV198 @ SV212 )
| ( apply @ SV178 @ SV203 @ SV214 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1085]) ).
thf(1111,plain,
! [SV33: $i,SV178: $i,SV7: $i,SV215: $i,SV213: $i,SV167: $i,SV203: $i,SV24: $i,SV198: $i] :
( ( ( ~ ( member @ SV198 @ SV24 )
| ~ ( member @ SV203 @ SV167 )
| ~ ( member @ SV213 @ SV24 )
| ~ ( member @ SV215 @ SV167 )
| ~ ( apply @ SV7 @ SV198 @ SV203 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV213 @ SV215 ) )
= $true )
| ( ( ~ ( apply @ SV178 @ SV203 @ SV215 )
| ( apply @ SV33 @ SV198 @ SV213 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1086]) ).
thf(1112,plain,
! [SV94: $i,SV111: $i,SV180: $i,SV13: $i,SV185: $i,SV171: $i,SV28: $i] :
( ( ( apply @ SV28 @ SV171 @ SV185 )
= $false )
| ( ( apply @ SV13 @ SV171 @ SV180 )
= $false )
| ( ( SV180 = SV185 )
= $true )
| ( ( member @ SV180 @ SV111 )
= $false )
| ( ( member @ SV171 @ SV94 )
= $false )
| ( ( member @ SV185 @ SV111 )
= $false )
| ( ( equal_maps @ SV13 @ SV28 @ SV94 @ SV111 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1087]) ).
thf(1113,plain,
! [SV14: $i,SV29: $i,SV42: $i,SV152: $i,SV35: $i,SV129: $i,SV211: $i] :
( ( ( member @ SV211 @ SV129 )
= $false )
| ( ( apply @ SV35 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV211 )
= $false )
| ( ( ~ ( apply @ SV29 @ SV211 @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
= $true )
| ( ( ~ ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1088]) ).
thf(1114,plain,
! [SV14: $i,SV29: $i,SV42: $i,SV129: $i,SV152: $i,SV35: $i] :
( ( ( ~ ( apply @ SV35 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
= $false )
| ( ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1089]) ).
thf(1115,plain,
! [SV14: $i,SV29: $i,SV35: $i,SV42: $i,SV129: $i,SV152: $i] :
( ( ( ~ ( member @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV129 ) )
= $false )
| ( ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1089]) ).
thf(1116,plain,
! [SV153: $i,SV42: $i,SV14: $i,SV208: $i,SV29: $i,SV130: $i,SV216: $i,SV206: $i,SV35: $i] :
( ( ( ~ ( apply @ SV35 @ SV206 @ SV216 )
| ~ ( member @ SV216 @ SV130 )
| ~ ( apply @ SV29 @ SV216 @ SV208 ) )
= $true )
| ( ( apply @ SV14 @ SV206 @ SV208 )
= $true )
| ( ( member @ SV206 @ SV42 )
= $false )
| ( ( member @ SV208 @ SV153 )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1117,plain,
! [SV29: $i,SV42: $i,SV130: $i,SV153: $i,SV35: $i,SV209: $i,SV207: $i,SV14: $i] :
( ( ( apply @ SV14 @ SV207 @ SV209 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( apply @ SV35 @ SV207 @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV130 ) )
| ~ ( apply @ SV29 @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV209 ) ) )
= $true )
| ( ( member @ SV207 @ SV42 )
= $false )
| ( ( member @ SV209 @ SV153 )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1091]) ).
thf(1118,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 )
| ~ ( member @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( member @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 ) )
| ~ ( member @ ( sK15_SY156 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
= $false )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1093]) ).
thf(1119,plain,
! [SV134: $i,SV16: $i,SV36: $i,SV201: $i,SV195: $i,SV115: $i,SV186: $i,SV30: $i,SV182: $i] :
( ( ( member @ SV182 @ SV30 )
= $false )
| ( ( ~ ( member @ SV186 @ SV115 ) )
= $true )
| ( ( ~ ( member @ SV195 @ SV30 ) )
= $true )
| ( ( ~ ( member @ SV201 @ SV115 ) )
= $true )
| ( ( ~ ( apply @ SV36 @ SV182 @ SV195 ) )
= $true )
| ( ( ~ ( apply @ SV16 @ SV182 @ SV186 ) )
= $true )
| ( ( ~ ( apply @ SV16 @ SV195 @ SV201 ) )
= $true )
| ( ( apply @ SV134 @ SV186 @ SV201 )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV115 @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1095]) ).
thf(1120,plain,
! [SV20: $i,SV37: $i,SV46: $i,SV73: $i,SV175: $i,SV160: $i,SV31: $i] :
( ( ( apply @ SV31 @ SV160 @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) )
= $true )
| ( ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SV160 @ SV175 )
= $false )
| ( ( member @ SV160 @ SV37 )
= $false )
| ( ( member @ SV175 @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1097]) ).
thf(1121,plain,
! [SV20: $i,SV31: $i,SV37: $i,SV46: $i,SV73: $i,SV160: $i,SV175: $i] :
( ( ( member @ ( sK31_Y @ SV175 @ SV160 @ SV73 @ SV46 @ SV37 @ SV31 @ SV20 ) @ SV46 )
= $true )
| ( ( apply @ ( compose_function @ SV20 @ SV31 @ SV37 @ SV46 @ SV73 ) @ SV160 @ SV175 )
= $false )
| ( ( member @ SV160 @ SV37 )
= $false )
| ( ( member @ SV175 @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1098]) ).
thf(1122,plain,
! [SV187: $i,SV21: $i,SV78: $i,SV100: $i] :
( ( ( ~ ( member @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
| ~ ( member @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
= $false )
| ( ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV187 )
= $false )
| ( ( member @ SV187 @ SV100 )
= $false )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1099]) ).
thf(1123,plain,
! [SV187: $i,SV78: $i,SV100: $i,SV21: $i] :
( ( ( ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) )
| ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) )
= $false )
| ( ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV187 )
= $false )
| ( ( member @ SV187 @ SV100 )
= $false )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1101]) ).
thf(1124,plain,
! [SV187: $i,SV21: $i,SV78: $i,SV100: $i] :
( ( ( ( sK38_SY170 @ SV100 @ SV78 @ SV21 )
= ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) )
= $false )
| ( ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV187 )
= $false )
| ( ( member @ SV187 @ SV100 )
= $false )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1102]) ).
thf(1125,plain,
! [SV143: $i,SV162: $i,SV202: $i,SV196: $i,SV189: $i,SV21: $i] :
( ( ( ~ ( apply @ SV21 @ SV189 @ SV196 ) )
= $true )
| ( ( ~ ( apply @ SV21 @ SV189 @ SV202 ) )
= $true )
| ( ( SV196 = SV202 )
= $true )
| ( ( member @ SV196 @ SV162 )
= $false )
| ( ( member @ SV189 @ SV143 )
= $false )
| ( ( member @ SV202 @ SV162 )
= $false )
| ( ( maps @ SV21 @ SV143 @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1103]) ).
thf(1126,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 )
| ~ ( member @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( member @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 ) ) )
= $false )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1104]) ).
thf(1127,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ( ~ ( member @ ( sK11_SY150 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
= $false )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1104]) ).
thf(1128,plain,
! [SV118: $i,SV3: $i,SV32: $i,SV197: $i,SV190: $i,SV23: $i,SV176: $i,SV103: $i,SV184: $i] :
( ( ( member @ SV184 @ SV103 )
= $false )
| ( ( member @ SV176 @ SV23 )
= $false )
| ( ( ~ ( member @ SV190 @ SV23 ) )
= $true )
| ( ( ~ ( member @ SV197 @ SV103 ) )
= $true )
| ( ( ~ ( apply @ SV32 @ SV176 @ SV190 ) )
= $true )
| ( ( ~ ( apply @ SV3 @ SV176 @ SV184 ) )
= $true )
| ( ( ~ ( apply @ SV3 @ SV190 @ SV197 ) )
= $true )
| ( ( apply @ SV118 @ SV197 @ SV184 )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV103 @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1105]) ).
thf(1129,plain,
! [SV7: $i,SV24: $i,SV33: $i,SV104: $i,SV125: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 )
| ~ ( member @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
| ~ ( member @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 ) )
= $false )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1106]) ).
thf(1130,plain,
! [SV33: $i,SV125: $i,SV104: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( maps @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( member @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1107]) ).
thf(1131,plain,
! [SV178: $i,SV33: $i,SV7: $i,SV214: $i,SV212: $i,SV167: $i,SV203: $i,SV24: $i,SV198: $i] :
( ( ( ~ ( member @ SV198 @ SV24 )
| ~ ( member @ SV203 @ SV167 )
| ~ ( member @ SV212 @ SV24 )
| ~ ( member @ SV214 @ SV167 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV198 @ SV203 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV212 @ SV214 ) )
= $true )
| ( ( ~ ( apply @ SV33 @ SV198 @ SV212 )
| ( apply @ SV178 @ SV203 @ SV214 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1110]) ).
thf(1132,plain,
! [SV33: $i,SV178: $i,SV7: $i,SV215: $i,SV213: $i,SV167: $i,SV203: $i,SV24: $i,SV198: $i] :
( ( ( ~ ( member @ SV198 @ SV24 )
| ~ ( member @ SV203 @ SV167 )
| ~ ( member @ SV213 @ SV24 )
| ~ ( member @ SV215 @ SV167 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV198 @ SV203 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV213 @ SV215 ) )
= $true )
| ( ( ~ ( apply @ SV178 @ SV203 @ SV215 )
| ( apply @ SV33 @ SV198 @ SV213 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1111]) ).
thf(1133,plain,
! [SV14: $i,SV35: $i,SV42: $i,SV129: $i,SV152: $i,SV211: $i,SV29: $i] :
( ( ( apply @ SV29 @ SV211 @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) )
= $false )
| ( ( apply @ SV35 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV211 )
= $false )
| ( ( member @ SV211 @ SV129 )
= $false )
| ( ( ~ ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1113]) ).
thf(1134,plain,
! [SV14: $i,SV29: $i,SV42: $i,SV129: $i,SV152: $i,SV35: $i] :
( ( ( apply @ SV35 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) )
= $true )
| ( ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1114]) ).
thf(1135,plain,
! [SV14: $i,SV29: $i,SV35: $i,SV42: $i,SV129: $i,SV152: $i] :
( ( ( member @ ( sK35_SY169 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV129 )
= $true )
| ( ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) )
= $true )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1115]) ).
thf(1136,plain,
! [SV153: $i,SV42: $i,SV14: $i,SV208: $i,SV29: $i,SV130: $i,SV216: $i,SV206: $i,SV35: $i] :
( ( ( ~ ( apply @ SV35 @ SV206 @ SV216 )
| ~ ( member @ SV216 @ SV130 ) )
= $true )
| ( ( ~ ( apply @ SV29 @ SV216 @ SV208 ) )
= $true )
| ( ( apply @ SV14 @ SV206 @ SV208 )
= $true )
| ( ( member @ SV206 @ SV42 )
= $false )
| ( ( member @ SV208 @ SV153 )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1116]) ).
thf(1137,plain,
! [SV14: $i,SV29: $i,SV42: $i,SV130: $i,SV153: $i,SV209: $i,SV207: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV35 @ SV207 @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV130 ) )
| ~ ( apply @ SV29 @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV209 ) )
= $false )
| ( ( apply @ SV14 @ SV207 @ SV209 )
= $false )
| ( ( member @ SV207 @ SV42 )
= $false )
| ( ( member @ SV209 @ SV153 )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1117]) ).
thf(1138,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 )
| ~ ( member @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( member @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 ) ) )
= $false )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1118]) ).
thf(1139,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ( ~ ( member @ ( sK15_SY156 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
= $false )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1118]) ).
thf(1140,plain,
! [SV134: $i,SV16: $i,SV36: $i,SV201: $i,SV195: $i,SV30: $i,SV182: $i,SV115: $i,SV186: $i] :
( ( ( member @ SV186 @ SV115 )
= $false )
| ( ( member @ SV182 @ SV30 )
= $false )
| ( ( ~ ( member @ SV195 @ SV30 ) )
= $true )
| ( ( ~ ( member @ SV201 @ SV115 ) )
= $true )
| ( ( ~ ( apply @ SV36 @ SV182 @ SV195 ) )
= $true )
| ( ( ~ ( apply @ SV16 @ SV182 @ SV186 ) )
= $true )
| ( ( ~ ( apply @ SV16 @ SV195 @ SV201 ) )
= $true )
| ( ( apply @ SV134 @ SV186 @ SV201 )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV115 @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1119]) ).
thf(1141,plain,
! [SV187: $i,SV21: $i,SV78: $i,SV100: $i] :
( ( ( ~ ( member @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ SV78 ) )
= $false )
| ( ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV187 )
= $false )
| ( ( member @ SV187 @ SV100 )
= $false )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1122]) ).
thf(1142,plain,
! [SV187: $i,SV21: $i,SV78: $i,SV100: $i] :
( ( ( ~ ( member @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) @ SV100 ) )
= $false )
| ( ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV187 )
= $false )
| ( ( member @ SV187 @ SV100 )
= $false )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1122]) ).
thf(1143,plain,
! [SV187: $i,SV78: $i,SV100: $i,SV21: $i] :
( ( ( ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) ) )
= $false )
| ( ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV187 )
= $false )
| ( ( member @ SV187 @ SV100 )
= $false )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1123]) ).
thf(1144,plain,
! [SV187: $i,SV78: $i,SV100: $i,SV21: $i] :
( ( ( ~ ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) ) )
= $false )
| ( ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV187 )
= $false )
| ( ( member @ SV187 @ SV100 )
= $false )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1123]) ).
thf(1145,plain,
! [SV143: $i,SV162: $i,SV202: $i,SV196: $i,SV189: $i,SV21: $i] :
( ( ( apply @ SV21 @ SV189 @ SV196 )
= $false )
| ( ( ~ ( apply @ SV21 @ SV189 @ SV202 ) )
= $true )
| ( ( SV196 = SV202 )
= $true )
| ( ( member @ SV196 @ SV162 )
= $false )
| ( ( member @ SV189 @ SV143 )
= $false )
| ( ( member @ SV202 @ SV162 )
= $false )
| ( ( maps @ SV21 @ SV143 @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1125]) ).
thf(1146,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 )
| ~ ( member @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( member @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 ) ) )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1126]) ).
thf(1147,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ( member @ ( sK11_SY150 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1127]) ).
thf(1148,plain,
! [SV118: $i,SV3: $i,SV32: $i,SV197: $i,SV103: $i,SV184: $i,SV176: $i,SV23: $i,SV190: $i] :
( ( ( member @ SV190 @ SV23 )
= $false )
| ( ( member @ SV176 @ SV23 )
= $false )
| ( ( member @ SV184 @ SV103 )
= $false )
| ( ( ~ ( member @ SV197 @ SV103 ) )
= $true )
| ( ( ~ ( apply @ SV32 @ SV176 @ SV190 ) )
= $true )
| ( ( ~ ( apply @ SV3 @ SV176 @ SV184 ) )
= $true )
| ( ( ~ ( apply @ SV3 @ SV190 @ SV197 ) )
= $true )
| ( ( apply @ SV118 @ SV197 @ SV184 )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV103 @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1128]) ).
thf(1149,plain,
! [SV7: $i,SV24: $i,SV33: $i,SV104: $i,SV125: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 )
| ~ ( member @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) ) )
= $false )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1129]) ).
thf(1150,plain,
! [SV7: $i,SV24: $i,SV33: $i,SV104: $i,SV125: $i] :
( ( ( ~ ( member @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 ) )
= $false )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1129]) ).
thf(1151,plain,
! [SV33: $i,SV125: $i,SV104: $i,SV24: $i,SV7: $i] :
( ( ( maps @ SV7 @ SV24 @ SV104 )
= $false )
| ( ( ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( member @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1130]) ).
thf(1152,plain,
! [SV178: $i,SV33: $i,SV7: $i,SV214: $i,SV212: $i,SV167: $i,SV203: $i,SV24: $i,SV198: $i] :
( ( ( ~ ( member @ SV198 @ SV24 )
| ~ ( member @ SV203 @ SV167 )
| ~ ( member @ SV212 @ SV24 ) )
= $true )
| ( ( ~ ( member @ SV214 @ SV167 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV198 @ SV203 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV212 @ SV214 ) )
= $true )
| ( ( ~ ( apply @ SV33 @ SV198 @ SV212 )
| ( apply @ SV178 @ SV203 @ SV214 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1131]) ).
thf(1153,plain,
! [SV33: $i,SV178: $i,SV7: $i,SV215: $i,SV213: $i,SV167: $i,SV203: $i,SV24: $i,SV198: $i] :
( ( ( ~ ( member @ SV198 @ SV24 )
| ~ ( member @ SV203 @ SV167 )
| ~ ( member @ SV213 @ SV24 ) )
= $true )
| ( ( ~ ( member @ SV215 @ SV167 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV198 @ SV203 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV213 @ SV215 ) )
= $true )
| ( ( ~ ( apply @ SV178 @ SV203 @ SV215 )
| ( apply @ SV33 @ SV198 @ SV213 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1132]) ).
thf(1154,plain,
! [SV211: $i,SV29: $i,SV35: $i,SV42: $i,SV129: $i,SV152: $i,SV14: $i] :
( ( ( apply @ SV14 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) )
= $false )
| ( ( member @ SV211 @ SV129 )
= $false )
| ( ( apply @ SV35 @ ( sK33_X @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV211 )
= $false )
| ( ( apply @ SV29 @ SV211 @ ( sK34_SY165 @ SV152 @ SV129 @ SV42 @ SV35 @ SV29 @ SV14 ) )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV129 @ SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1133]) ).
thf(1155,plain,
! [SV153: $i,SV42: $i,SV14: $i,SV208: $i,SV29: $i,SV130: $i,SV216: $i,SV206: $i,SV35: $i] :
( ( ( ~ ( apply @ SV35 @ SV206 @ SV216 ) )
= $true )
| ( ( ~ ( member @ SV216 @ SV130 ) )
= $true )
| ( ( ~ ( apply @ SV29 @ SV216 @ SV208 ) )
= $true )
| ( ( apply @ SV14 @ SV206 @ SV208 )
= $true )
| ( ( member @ SV206 @ SV42 )
= $false )
| ( ( member @ SV208 @ SV153 )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1136]) ).
thf(1156,plain,
! [SV14: $i,SV29: $i,SV42: $i,SV130: $i,SV153: $i,SV209: $i,SV207: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV35 @ SV207 @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV130 ) ) )
= $false )
| ( ( apply @ SV14 @ SV207 @ SV209 )
= $false )
| ( ( member @ SV207 @ SV42 )
= $false )
| ( ( member @ SV209 @ SV153 )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1137]) ).
thf(1157,plain,
! [SV14: $i,SV35: $i,SV42: $i,SV130: $i,SV153: $i,SV207: $i,SV209: $i,SV29: $i] :
( ( ( ~ ( apply @ SV29 @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV209 ) )
= $false )
| ( ( apply @ SV14 @ SV207 @ SV209 )
= $false )
| ( ( member @ SV207 @ SV42 )
= $false )
| ( ( member @ SV209 @ SV153 )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1137]) ).
thf(1158,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 )
| ~ ( member @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( member @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 ) ) )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1138]) ).
thf(1159,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ( member @ ( sK15_SY156 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1139]) ).
thf(1160,plain,
! [SV134: $i,SV16: $i,SV36: $i,SV201: $i,SV115: $i,SV186: $i,SV182: $i,SV30: $i,SV195: $i] :
( ( ( member @ SV195 @ SV30 )
= $false )
| ( ( member @ SV182 @ SV30 )
= $false )
| ( ( member @ SV186 @ SV115 )
= $false )
| ( ( ~ ( member @ SV201 @ SV115 ) )
= $true )
| ( ( ~ ( apply @ SV36 @ SV182 @ SV195 ) )
= $true )
| ( ( ~ ( apply @ SV16 @ SV182 @ SV186 ) )
= $true )
| ( ( ~ ( apply @ SV16 @ SV195 @ SV201 ) )
= $true )
| ( ( apply @ SV134 @ SV186 @ SV201 )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV115 @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1140]) ).
thf(1161,plain,
! [SV187: $i,SV21: $i,SV78: $i,SV100: $i] :
( ( ( member @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ SV78 )
= $true )
| ( ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV187 )
= $false )
| ( ( member @ SV187 @ SV100 )
= $false )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1141]) ).
thf(1162,plain,
! [SV187: $i,SV21: $i,SV78: $i,SV100: $i] :
( ( ( member @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) @ SV100 )
= $true )
| ( ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV187 )
= $false )
| ( ( member @ SV187 @ SV100 )
= $false )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1142]) ).
thf(1163,plain,
! [SV187: $i,SV78: $i,SV100: $i,SV21: $i] :
( ( ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK38_SY170 @ SV100 @ SV78 @ SV21 ) )
= $true )
| ( ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV187 )
= $false )
| ( ( member @ SV187 @ SV100 )
= $false )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1143]) ).
thf(1164,plain,
! [SV187: $i,SV78: $i,SV100: $i,SV21: $i] :
( ( ( apply @ SV21 @ ( sK37_X @ SV100 @ SV78 @ SV21 ) @ ( sK39_SY172 @ SV100 @ SV78 @ SV21 ) )
= $true )
| ( ( apply @ SV21 @ ( sK40_X @ SV100 @ SV78 @ SV21 ) @ SV187 )
= $false )
| ( ( member @ SV187 @ SV100 )
= $false )
| ( ( maps @ SV21 @ SV78 @ SV100 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1144]) ).
thf(1165,plain,
! [SV143: $i,SV162: $i,SV196: $i,SV202: $i,SV189: $i,SV21: $i] :
( ( ( apply @ SV21 @ SV189 @ SV202 )
= $false )
| ( ( apply @ SV21 @ SV189 @ SV196 )
= $false )
| ( ( SV196 = SV202 )
= $true )
| ( ( member @ SV196 @ SV162 )
= $false )
| ( ( member @ SV189 @ SV143 )
= $false )
| ( ( member @ SV202 @ SV162 )
= $false )
| ( ( maps @ SV21 @ SV143 @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1145]) ).
thf(1166,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 )
| ~ ( member @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
| ~ ( member @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 ) )
= $false )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1146]) ).
thf(1167,plain,
! [SV118: $i,SV3: $i,SV32: $i,SV190: $i,SV23: $i,SV176: $i,SV184: $i,SV103: $i,SV197: $i] :
( ( ( member @ SV197 @ SV103 )
= $false )
| ( ( member @ SV184 @ SV103 )
= $false )
| ( ( member @ SV176 @ SV23 )
= $false )
| ( ( member @ SV190 @ SV23 )
= $false )
| ( ( ~ ( apply @ SV32 @ SV176 @ SV190 ) )
= $true )
| ( ( ~ ( apply @ SV3 @ SV176 @ SV184 ) )
= $true )
| ( ( ~ ( apply @ SV3 @ SV190 @ SV197 ) )
= $true )
| ( ( apply @ SV118 @ SV197 @ SV184 )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV103 @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1148]) ).
thf(1168,plain,
! [SV7: $i,SV24: $i,SV33: $i,SV104: $i,SV125: $i] :
( ( ( ~ ( ~ ( member @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 )
| ~ ( member @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) ) )
= $true )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1149]) ).
thf(1169,plain,
! [SV7: $i,SV24: $i,SV33: $i,SV104: $i,SV125: $i] :
( ( ( member @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 )
= $true )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1150]) ).
thf(1170,plain,
! [SV33: $i,SV125: $i,SV104: $i,SV24: $i,SV7: $i] :
( ( ( one_to_one @ SV7 @ SV24 @ SV104 )
= $false )
| ( ( maps @ SV7 @ SV24 @ SV104 )
= $false )
| ( ( member @ ( sK7_SY144 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1151]) ).
thf(1171,plain,
! [SV178: $i,SV33: $i,SV7: $i,SV214: $i,SV212: $i,SV167: $i,SV203: $i,SV24: $i,SV198: $i] :
( ( ( ~ ( member @ SV198 @ SV24 )
| ~ ( member @ SV203 @ SV167 ) )
= $true )
| ( ( ~ ( member @ SV212 @ SV24 ) )
= $true )
| ( ( ~ ( member @ SV214 @ SV167 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV198 @ SV203 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV212 @ SV214 ) )
= $true )
| ( ( ~ ( apply @ SV33 @ SV198 @ SV212 )
| ( apply @ SV178 @ SV203 @ SV214 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1152]) ).
thf(1172,plain,
! [SV33: $i,SV178: $i,SV7: $i,SV215: $i,SV213: $i,SV167: $i,SV203: $i,SV24: $i,SV198: $i] :
( ( ( ~ ( member @ SV198 @ SV24 )
| ~ ( member @ SV203 @ SV167 ) )
= $true )
| ( ( ~ ( member @ SV213 @ SV24 ) )
= $true )
| ( ( ~ ( member @ SV215 @ SV167 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV198 @ SV203 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV213 @ SV215 ) )
= $true )
| ( ( ~ ( apply @ SV178 @ SV203 @ SV215 )
| ( apply @ SV33 @ SV198 @ SV213 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1153]) ).
thf(1173,plain,
! [SV153: $i,SV42: $i,SV14: $i,SV208: $i,SV29: $i,SV130: $i,SV216: $i,SV206: $i,SV35: $i] :
( ( ( apply @ SV35 @ SV206 @ SV216 )
= $false )
| ( ( ~ ( member @ SV216 @ SV130 ) )
= $true )
| ( ( ~ ( apply @ SV29 @ SV216 @ SV208 ) )
= $true )
| ( ( apply @ SV14 @ SV206 @ SV208 )
= $true )
| ( ( member @ SV206 @ SV42 )
= $false )
| ( ( member @ SV208 @ SV153 )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1155]) ).
thf(1174,plain,
! [SV14: $i,SV29: $i,SV42: $i,SV130: $i,SV153: $i,SV209: $i,SV207: $i,SV35: $i] :
( ( ( ~ ( ~ ( apply @ SV35 @ SV207 @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV130 ) ) )
= $true )
| ( ( apply @ SV14 @ SV207 @ SV209 )
= $false )
| ( ( member @ SV207 @ SV42 )
= $false )
| ( ( member @ SV209 @ SV153 )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1156]) ).
thf(1175,plain,
! [SV14: $i,SV35: $i,SV42: $i,SV130: $i,SV153: $i,SV207: $i,SV209: $i,SV29: $i] :
( ( ( apply @ SV29 @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV209 )
= $true )
| ( ( apply @ SV14 @ SV207 @ SV209 )
= $false )
| ( ( member @ SV207 @ SV42 )
= $false )
| ( ( member @ SV209 @ SV153 )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1157]) ).
thf(1176,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 )
| ~ ( member @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
| ~ ( member @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 ) )
= $false )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1158]) ).
thf(1177,plain,
! [SV134: $i,SV16: $i,SV36: $i,SV195: $i,SV30: $i,SV182: $i,SV186: $i,SV115: $i,SV201: $i] :
( ( ( member @ SV201 @ SV115 )
= $false )
| ( ( member @ SV186 @ SV115 )
= $false )
| ( ( member @ SV182 @ SV30 )
= $false )
| ( ( member @ SV195 @ SV30 )
= $false )
| ( ( ~ ( apply @ SV36 @ SV182 @ SV195 ) )
= $true )
| ( ( ~ ( apply @ SV16 @ SV182 @ SV186 ) )
= $true )
| ( ( ~ ( apply @ SV16 @ SV195 @ SV201 ) )
= $true )
| ( ( apply @ SV134 @ SV186 @ SV201 )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV115 @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1160]) ).
thf(1178,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 )
| ~ ( member @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) ) )
= $false )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1166]) ).
thf(1179,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ( ~ ( member @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 ) )
= $false )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1166]) ).
thf(1180,plain,
! [SV118: $i,SV3: $i,SV197: $i,SV103: $i,SV184: $i,SV23: $i,SV190: $i,SV176: $i,SV32: $i] :
( ( ( apply @ SV32 @ SV176 @ SV190 )
= $false )
| ( ( member @ SV190 @ SV23 )
= $false )
| ( ( member @ SV176 @ SV23 )
= $false )
| ( ( member @ SV184 @ SV103 )
= $false )
| ( ( member @ SV197 @ SV103 )
= $false )
| ( ( ~ ( apply @ SV3 @ SV176 @ SV184 ) )
= $true )
| ( ( ~ ( apply @ SV3 @ SV190 @ SV197 ) )
= $true )
| ( ( apply @ SV118 @ SV197 @ SV184 )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV103 @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1167]) ).
thf(1181,plain,
! [SV7: $i,SV24: $i,SV33: $i,SV104: $i,SV125: $i] :
( ( ( ~ ( member @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 )
| ~ ( member @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
= $false )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1168]) ).
thf(1182,plain,
! [SV33: $i,SV125: $i,SV104: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( maps @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( member @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1169]) ).
thf(1183,plain,
! [SV178: $i,SV33: $i,SV7: $i,SV214: $i,SV212: $i,SV167: $i,SV203: $i,SV24: $i,SV198: $i] :
( ( ( ~ ( member @ SV198 @ SV24 ) )
= $true )
| ( ( ~ ( member @ SV203 @ SV167 ) )
= $true )
| ( ( ~ ( member @ SV212 @ SV24 ) )
= $true )
| ( ( ~ ( member @ SV214 @ SV167 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV198 @ SV203 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV212 @ SV214 ) )
= $true )
| ( ( ~ ( apply @ SV33 @ SV198 @ SV212 )
| ( apply @ SV178 @ SV203 @ SV214 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1171]) ).
thf(1184,plain,
! [SV33: $i,SV178: $i,SV7: $i,SV215: $i,SV213: $i,SV167: $i,SV203: $i,SV24: $i,SV198: $i] :
( ( ( ~ ( member @ SV198 @ SV24 ) )
= $true )
| ( ( ~ ( member @ SV203 @ SV167 ) )
= $true )
| ( ( ~ ( member @ SV213 @ SV24 ) )
= $true )
| ( ( ~ ( member @ SV215 @ SV167 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV198 @ SV203 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV213 @ SV215 ) )
= $true )
| ( ( ~ ( apply @ SV178 @ SV203 @ SV215 )
| ( apply @ SV33 @ SV198 @ SV213 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1172]) ).
thf(1185,plain,
! [SV153: $i,SV42: $i,SV14: $i,SV208: $i,SV29: $i,SV206: $i,SV35: $i,SV130: $i,SV216: $i] :
( ( ( member @ SV216 @ SV130 )
= $false )
| ( ( apply @ SV35 @ SV206 @ SV216 )
= $false )
| ( ( ~ ( apply @ SV29 @ SV216 @ SV208 ) )
= $true )
| ( ( apply @ SV14 @ SV206 @ SV208 )
= $true )
| ( ( member @ SV206 @ SV42 )
= $false )
| ( ( member @ SV208 @ SV153 )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1173]) ).
thf(1186,plain,
! [SV14: $i,SV29: $i,SV42: $i,SV130: $i,SV153: $i,SV209: $i,SV207: $i,SV35: $i] :
( ( ( ~ ( apply @ SV35 @ SV207 @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) )
| ~ ( member @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV130 ) )
= $false )
| ( ( apply @ SV14 @ SV207 @ SV209 )
= $false )
| ( ( member @ SV207 @ SV42 )
= $false )
| ( ( member @ SV209 @ SV153 )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1174]) ).
thf(1187,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 )
| ~ ( member @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) ) )
= $false )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1176]) ).
thf(1188,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ( ~ ( member @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 ) )
= $false )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1176]) ).
thf(1189,plain,
! [SV134: $i,SV16: $i,SV201: $i,SV115: $i,SV186: $i,SV30: $i,SV195: $i,SV182: $i,SV36: $i] :
( ( ( apply @ SV36 @ SV182 @ SV195 )
= $false )
| ( ( member @ SV195 @ SV30 )
= $false )
| ( ( member @ SV182 @ SV30 )
= $false )
| ( ( member @ SV186 @ SV115 )
= $false )
| ( ( member @ SV201 @ SV115 )
= $false )
| ( ( ~ ( apply @ SV16 @ SV182 @ SV186 ) )
= $true )
| ( ( ~ ( apply @ SV16 @ SV195 @ SV201 ) )
= $true )
| ( ( apply @ SV134 @ SV186 @ SV201 )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV115 @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1177]) ).
thf(1190,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ( ~ ( ~ ( member @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 )
| ~ ( member @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) ) )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1178]) ).
thf(1191,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ( member @ ( sK10_SY148 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1179]) ).
thf(1192,plain,
! [SV118: $i,SV32: $i,SV190: $i,SV23: $i,SV103: $i,SV197: $i,SV184: $i,SV176: $i,SV3: $i] :
( ( ( apply @ SV3 @ SV176 @ SV184 )
= $false )
| ( ( member @ SV197 @ SV103 )
= $false )
| ( ( member @ SV184 @ SV103 )
= $false )
| ( ( member @ SV176 @ SV23 )
= $false )
| ( ( member @ SV190 @ SV23 )
= $false )
| ( ( apply @ SV32 @ SV176 @ SV190 )
= $false )
| ( ( ~ ( apply @ SV3 @ SV190 @ SV197 ) )
= $true )
| ( ( apply @ SV118 @ SV197 @ SV184 )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV103 @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1180]) ).
thf(1193,plain,
! [SV7: $i,SV24: $i,SV33: $i,SV104: $i,SV125: $i] :
( ( ( ~ ( member @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 ) )
= $false )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1181]) ).
thf(1194,plain,
! [SV7: $i,SV24: $i,SV33: $i,SV104: $i,SV125: $i] :
( ( ( ~ ( member @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 ) )
= $false )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1181]) ).
thf(1195,plain,
! [SV33: $i,SV125: $i,SV104: $i,SV24: $i,SV7: $i] :
( ( ( maps @ SV7 @ SV24 @ SV104 )
= $false )
| ( ( ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( member @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1182]) ).
thf(1196,plain,
! [SV178: $i,SV33: $i,SV7: $i,SV214: $i,SV212: $i,SV167: $i,SV203: $i,SV24: $i,SV198: $i] :
( ( ( member @ SV198 @ SV24 )
= $false )
| ( ( ~ ( member @ SV203 @ SV167 ) )
= $true )
| ( ( ~ ( member @ SV212 @ SV24 ) )
= $true )
| ( ( ~ ( member @ SV214 @ SV167 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV198 @ SV203 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV212 @ SV214 ) )
= $true )
| ( ( ~ ( apply @ SV33 @ SV198 @ SV212 )
| ( apply @ SV178 @ SV203 @ SV214 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1183]) ).
thf(1197,plain,
! [SV33: $i,SV178: $i,SV7: $i,SV215: $i,SV213: $i,SV167: $i,SV203: $i,SV24: $i,SV198: $i] :
( ( ( member @ SV198 @ SV24 )
= $false )
| ( ( ~ ( member @ SV203 @ SV167 ) )
= $true )
| ( ( ~ ( member @ SV213 @ SV24 ) )
= $true )
| ( ( ~ ( member @ SV215 @ SV167 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV198 @ SV203 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV213 @ SV215 ) )
= $true )
| ( ( ~ ( apply @ SV178 @ SV203 @ SV215 )
| ( apply @ SV33 @ SV198 @ SV213 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1184]) ).
thf(1198,plain,
! [SV153: $i,SV42: $i,SV14: $i,SV130: $i,SV206: $i,SV35: $i,SV208: $i,SV216: $i,SV29: $i] :
( ( ( apply @ SV29 @ SV216 @ SV208 )
= $false )
| ( ( apply @ SV35 @ SV206 @ SV216 )
= $false )
| ( ( member @ SV216 @ SV130 )
= $false )
| ( ( apply @ SV14 @ SV206 @ SV208 )
= $true )
| ( ( member @ SV206 @ SV42 )
= $false )
| ( ( member @ SV208 @ SV153 )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1185]) ).
thf(1199,plain,
! [SV14: $i,SV29: $i,SV42: $i,SV130: $i,SV153: $i,SV209: $i,SV207: $i,SV35: $i] :
( ( ( ~ ( apply @ SV35 @ SV207 @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) ) )
= $false )
| ( ( apply @ SV14 @ SV207 @ SV209 )
= $false )
| ( ( member @ SV207 @ SV42 )
= $false )
| ( ( member @ SV209 @ SV153 )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1186]) ).
thf(1200,plain,
! [SV14: $i,SV29: $i,SV35: $i,SV42: $i,SV130: $i,SV153: $i,SV207: $i,SV209: $i] :
( ( ( ~ ( member @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV130 ) )
= $false )
| ( ( apply @ SV14 @ SV207 @ SV209 )
= $false )
| ( ( member @ SV207 @ SV42 )
= $false )
| ( ( member @ SV209 @ SV153 )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1186]) ).
thf(1201,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ( ~ ( ~ ( member @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 )
| ~ ( member @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) ) )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1187]) ).
thf(1202,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ( member @ ( sK14_SY154 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1188]) ).
thf(1203,plain,
! [SV134: $i,SV36: $i,SV195: $i,SV30: $i,SV115: $i,SV201: $i,SV186: $i,SV182: $i,SV16: $i] :
( ( ( apply @ SV16 @ SV182 @ SV186 )
= $false )
| ( ( member @ SV201 @ SV115 )
= $false )
| ( ( member @ SV186 @ SV115 )
= $false )
| ( ( member @ SV182 @ SV30 )
= $false )
| ( ( member @ SV195 @ SV30 )
= $false )
| ( ( apply @ SV36 @ SV182 @ SV195 )
= $false )
| ( ( ~ ( apply @ SV16 @ SV195 @ SV201 ) )
= $true )
| ( ( apply @ SV134 @ SV186 @ SV201 )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV115 @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1189]) ).
thf(1204,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ( ~ ( member @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 )
| ~ ( member @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
= $false )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1190]) ).
thf(1205,plain,
! [SV118: $i,SV103: $i,SV184: $i,SV23: $i,SV176: $i,SV32: $i,SV197: $i,SV190: $i,SV3: $i] :
( ( ( apply @ SV3 @ SV190 @ SV197 )
= $false )
| ( ( apply @ SV32 @ SV176 @ SV190 )
= $false )
| ( ( member @ SV190 @ SV23 )
= $false )
| ( ( member @ SV176 @ SV23 )
= $false )
| ( ( member @ SV184 @ SV103 )
= $false )
| ( ( member @ SV197 @ SV103 )
= $false )
| ( ( apply @ SV3 @ SV176 @ SV184 )
= $false )
| ( ( apply @ SV118 @ SV197 @ SV184 )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV103 @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1192]) ).
thf(1206,plain,
! [SV7: $i,SV24: $i,SV33: $i,SV104: $i,SV125: $i] :
( ( ( member @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 )
= $true )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1193]) ).
thf(1207,plain,
! [SV7: $i,SV24: $i,SV33: $i,SV104: $i,SV125: $i] :
( ( ( member @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 )
= $true )
| ( ( ~ ( maps @ SV7 @ SV24 @ SV104 )
| ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1194]) ).
thf(1208,plain,
! [SV33: $i,SV125: $i,SV104: $i,SV24: $i,SV7: $i] :
( ( ( one_to_one @ SV7 @ SV24 @ SV104 )
= $false )
| ( ( maps @ SV7 @ SV24 @ SV104 )
= $false )
| ( ( member @ ( sK6_SY142 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1195]) ).
thf(1209,plain,
! [SV178: $i,SV33: $i,SV7: $i,SV214: $i,SV212: $i,SV24: $i,SV198: $i,SV167: $i,SV203: $i] :
( ( ( member @ SV203 @ SV167 )
= $false )
| ( ( member @ SV198 @ SV24 )
= $false )
| ( ( ~ ( member @ SV212 @ SV24 ) )
= $true )
| ( ( ~ ( member @ SV214 @ SV167 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV198 @ SV203 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV212 @ SV214 ) )
= $true )
| ( ( ~ ( apply @ SV33 @ SV198 @ SV212 )
| ( apply @ SV178 @ SV203 @ SV214 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1196]) ).
thf(1210,plain,
! [SV33: $i,SV178: $i,SV7: $i,SV215: $i,SV213: $i,SV24: $i,SV198: $i,SV167: $i,SV203: $i] :
( ( ( member @ SV203 @ SV167 )
= $false )
| ( ( member @ SV198 @ SV24 )
= $false )
| ( ( ~ ( member @ SV213 @ SV24 ) )
= $true )
| ( ( ~ ( member @ SV215 @ SV167 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV198 @ SV203 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV213 @ SV215 ) )
= $true )
| ( ( ~ ( apply @ SV178 @ SV203 @ SV215 )
| ( apply @ SV33 @ SV198 @ SV213 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1197]) ).
thf(1211,plain,
! [SV14: $i,SV29: $i,SV42: $i,SV130: $i,SV153: $i,SV209: $i,SV207: $i,SV35: $i] :
( ( ( apply @ SV35 @ SV207 @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) )
= $true )
| ( ( apply @ SV14 @ SV207 @ SV209 )
= $false )
| ( ( member @ SV207 @ SV42 )
= $false )
| ( ( member @ SV209 @ SV153 )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1199]) ).
thf(1212,plain,
! [SV14: $i,SV29: $i,SV35: $i,SV42: $i,SV130: $i,SV153: $i,SV207: $i,SV209: $i] :
( ( ( member @ ( sK32_Y @ SV209 @ SV207 @ SV153 @ SV130 @ SV42 @ SV35 @ SV29 @ SV14 ) @ SV130 )
= $true )
| ( ( apply @ SV14 @ SV207 @ SV209 )
= $false )
| ( ( member @ SV207 @ SV42 )
= $false )
| ( ( member @ SV209 @ SV153 )
= $false )
| ( ( compose_predicate @ SV14 @ SV29 @ SV35 @ SV42 @ SV130 @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1200]) ).
thf(1213,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ( ~ ( member @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 )
| ~ ( member @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
= $false )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1201]) ).
thf(1214,plain,
! [SV134: $i,SV115: $i,SV186: $i,SV30: $i,SV182: $i,SV36: $i,SV201: $i,SV195: $i,SV16: $i] :
( ( ( apply @ SV16 @ SV195 @ SV201 )
= $false )
| ( ( apply @ SV36 @ SV182 @ SV195 )
= $false )
| ( ( member @ SV195 @ SV30 )
= $false )
| ( ( member @ SV182 @ SV30 )
= $false )
| ( ( member @ SV186 @ SV115 )
= $false )
| ( ( member @ SV201 @ SV115 )
= $false )
| ( ( apply @ SV16 @ SV182 @ SV186 )
= $false )
| ( ( apply @ SV134 @ SV186 @ SV201 )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV115 @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1203]) ).
thf(1215,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ( ~ ( member @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 ) )
= $false )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1204]) ).
thf(1216,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ( ~ ( member @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 ) )
= $false )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1204]) ).
thf(1217,plain,
! [SV33: $i,SV125: $i,SV104: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( maps @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( member @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1206]) ).
thf(1218,plain,
! [SV33: $i,SV125: $i,SV104: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( maps @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( member @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1207]) ).
thf(1219,plain,
! [SV178: $i,SV33: $i,SV7: $i,SV214: $i,SV167: $i,SV203: $i,SV198: $i,SV24: $i,SV212: $i] :
( ( ( member @ SV212 @ SV24 )
= $false )
| ( ( member @ SV198 @ SV24 )
= $false )
| ( ( member @ SV203 @ SV167 )
= $false )
| ( ( ~ ( member @ SV214 @ SV167 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV198 @ SV203 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV212 @ SV214 ) )
= $true )
| ( ( ~ ( apply @ SV33 @ SV198 @ SV212 )
| ( apply @ SV178 @ SV203 @ SV214 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1209]) ).
thf(1220,plain,
! [SV33: $i,SV178: $i,SV7: $i,SV215: $i,SV167: $i,SV203: $i,SV198: $i,SV24: $i,SV213: $i] :
( ( ( member @ SV213 @ SV24 )
= $false )
| ( ( member @ SV198 @ SV24 )
= $false )
| ( ( member @ SV203 @ SV167 )
= $false )
| ( ( ~ ( member @ SV215 @ SV167 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV198 @ SV203 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV213 @ SV215 ) )
= $true )
| ( ( ~ ( apply @ SV178 @ SV203 @ SV215 )
| ( apply @ SV33 @ SV198 @ SV213 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1210]) ).
thf(1221,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ( ~ ( member @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 ) )
= $false )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1213]) ).
thf(1222,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ( ~ ( member @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 ) )
= $false )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1213]) ).
thf(1223,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ( member @ ( sK8_X1 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV23 )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1215]) ).
thf(1224,plain,
! [SV3: $i,SV23: $i,SV32: $i,SV102: $i,SV117: $i] :
( ( ( member @ ( sK9_SY145 @ SV117 @ SV102 @ SV32 @ SV23 @ SV3 ) @ SV102 )
= $true )
| ( ( decreasing @ SV3 @ SV23 @ SV32 @ SV102 @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1216]) ).
thf(1225,plain,
! [SV33: $i,SV125: $i,SV104: $i,SV24: $i,SV7: $i] :
( ( ( maps @ SV7 @ SV24 @ SV104 )
= $false )
| ( ( ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( member @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1217]) ).
thf(1226,plain,
! [SV33: $i,SV125: $i,SV104: $i,SV24: $i,SV7: $i] :
( ( ( maps @ SV7 @ SV24 @ SV104 )
= $false )
| ( ( ~ ( one_to_one @ SV7 @ SV24 @ SV104 ) )
= $true )
| ( ( member @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1218]) ).
thf(1227,plain,
! [SV178: $i,SV33: $i,SV7: $i,SV212: $i,SV24: $i,SV198: $i,SV203: $i,SV167: $i,SV214: $i] :
( ( ( member @ SV214 @ SV167 )
= $false )
| ( ( member @ SV203 @ SV167 )
= $false )
| ( ( member @ SV198 @ SV24 )
= $false )
| ( ( member @ SV212 @ SV24 )
= $false )
| ( ( ~ ( apply @ SV7 @ SV198 @ SV203 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV212 @ SV214 ) )
= $true )
| ( ( ~ ( apply @ SV33 @ SV198 @ SV212 )
| ( apply @ SV178 @ SV203 @ SV214 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1219]) ).
thf(1228,plain,
! [SV33: $i,SV178: $i,SV7: $i,SV213: $i,SV24: $i,SV198: $i,SV203: $i,SV167: $i,SV215: $i] :
( ( ( member @ SV215 @ SV167 )
= $false )
| ( ( member @ SV203 @ SV167 )
= $false )
| ( ( member @ SV198 @ SV24 )
= $false )
| ( ( member @ SV213 @ SV24 )
= $false )
| ( ( ~ ( apply @ SV7 @ SV198 @ SV203 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV213 @ SV215 ) )
= $true )
| ( ( ~ ( apply @ SV178 @ SV203 @ SV215 )
| ( apply @ SV33 @ SV198 @ SV213 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1220]) ).
thf(1229,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ( member @ ( sK12_X1 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV30 )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1221]) ).
thf(1230,plain,
! [SV16: $i,SV30: $i,SV36: $i,SV114: $i,SV133: $i] :
( ( ( member @ ( sK13_SY151 @ SV133 @ SV114 @ SV36 @ SV30 @ SV16 ) @ SV114 )
= $true )
| ( ( increasing @ SV16 @ SV30 @ SV36 @ SV114 @ SV133 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1222]) ).
thf(1231,plain,
! [SV33: $i,SV125: $i,SV104: $i,SV24: $i,SV7: $i] :
( ( ( one_to_one @ SV7 @ SV24 @ SV104 )
= $false )
| ( ( maps @ SV7 @ SV24 @ SV104 )
= $false )
| ( ( member @ ( sK4_X1 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV24 )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1225]) ).
thf(1232,plain,
! [SV33: $i,SV125: $i,SV104: $i,SV24: $i,SV7: $i] :
( ( ( one_to_one @ SV7 @ SV24 @ SV104 )
= $false )
| ( ( maps @ SV7 @ SV24 @ SV104 )
= $false )
| ( ( member @ ( sK5_SY139 @ SV125 @ SV104 @ SV33 @ SV24 @ SV7 ) @ SV104 )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV104 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1226]) ).
thf(1233,plain,
! [SV178: $i,SV33: $i,SV214: $i,SV167: $i,SV24: $i,SV212: $i,SV203: $i,SV198: $i,SV7: $i] :
( ( ( apply @ SV7 @ SV198 @ SV203 )
= $false )
| ( ( member @ SV212 @ SV24 )
= $false )
| ( ( member @ SV198 @ SV24 )
= $false )
| ( ( member @ SV203 @ SV167 )
= $false )
| ( ( member @ SV214 @ SV167 )
= $false )
| ( ( ~ ( apply @ SV7 @ SV212 @ SV214 ) )
= $true )
| ( ( ~ ( apply @ SV33 @ SV198 @ SV212 )
| ( apply @ SV178 @ SV203 @ SV214 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1227]) ).
thf(1234,plain,
! [SV33: $i,SV178: $i,SV215: $i,SV167: $i,SV24: $i,SV213: $i,SV203: $i,SV198: $i,SV7: $i] :
( ( ( apply @ SV7 @ SV198 @ SV203 )
= $false )
| ( ( member @ SV213 @ SV24 )
= $false )
| ( ( member @ SV198 @ SV24 )
= $false )
| ( ( member @ SV203 @ SV167 )
= $false )
| ( ( member @ SV215 @ SV167 )
= $false )
| ( ( ~ ( apply @ SV7 @ SV213 @ SV215 ) )
= $true )
| ( ( ~ ( apply @ SV178 @ SV203 @ SV215 )
| ( apply @ SV33 @ SV198 @ SV213 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1228]) ).
thf(1235,plain,
! [SV178: $i,SV33: $i,SV24: $i,SV198: $i,SV203: $i,SV167: $i,SV214: $i,SV212: $i,SV7: $i] :
( ( ( apply @ SV7 @ SV212 @ SV214 )
= $false )
| ( ( member @ SV214 @ SV167 )
= $false )
| ( ( member @ SV203 @ SV167 )
= $false )
| ( ( member @ SV198 @ SV24 )
= $false )
| ( ( member @ SV212 @ SV24 )
= $false )
| ( ( apply @ SV7 @ SV198 @ SV203 )
= $false )
| ( ( ~ ( apply @ SV33 @ SV198 @ SV212 )
| ( apply @ SV178 @ SV203 @ SV214 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1233]) ).
thf(1236,plain,
! [SV33: $i,SV178: $i,SV24: $i,SV198: $i,SV203: $i,SV167: $i,SV215: $i,SV213: $i,SV7: $i] :
( ( ( apply @ SV7 @ SV213 @ SV215 )
= $false )
| ( ( member @ SV215 @ SV167 )
= $false )
| ( ( member @ SV203 @ SV167 )
= $false )
| ( ( member @ SV198 @ SV24 )
= $false )
| ( ( member @ SV213 @ SV24 )
= $false )
| ( ( apply @ SV7 @ SV198 @ SV203 )
= $false )
| ( ( ~ ( apply @ SV178 @ SV203 @ SV215 )
| ( apply @ SV33 @ SV198 @ SV213 ) )
= $true )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1234]) ).
thf(1237,plain,
! [SV167: $i,SV24: $i,SV7: $i,SV214: $i,SV203: $i,SV178: $i,SV212: $i,SV198: $i,SV33: $i] :
( ( ( ~ ( apply @ SV33 @ SV198 @ SV212 ) )
= $true )
| ( ( apply @ SV178 @ SV203 @ SV214 )
= $true )
| ( ( apply @ SV7 @ SV198 @ SV203 )
= $false )
| ( ( member @ SV212 @ SV24 )
= $false )
| ( ( member @ SV198 @ SV24 )
= $false )
| ( ( member @ SV203 @ SV167 )
= $false )
| ( ( member @ SV214 @ SV167 )
= $false )
| ( ( apply @ SV7 @ SV212 @ SV214 )
= $false )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1235]) ).
thf(1238,plain,
! [SV167: $i,SV24: $i,SV7: $i,SV213: $i,SV198: $i,SV33: $i,SV215: $i,SV203: $i,SV178: $i] :
( ( ( ~ ( apply @ SV178 @ SV203 @ SV215 ) )
= $true )
| ( ( apply @ SV33 @ SV198 @ SV213 )
= $true )
| ( ( apply @ SV7 @ SV198 @ SV203 )
= $false )
| ( ( member @ SV213 @ SV24 )
= $false )
| ( ( member @ SV198 @ SV24 )
= $false )
| ( ( member @ SV203 @ SV167 )
= $false )
| ( ( member @ SV215 @ SV167 )
= $false )
| ( ( apply @ SV7 @ SV213 @ SV215 )
= $false )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1236]) ).
thf(1239,plain,
! [SV167: $i,SV24: $i,SV7: $i,SV214: $i,SV203: $i,SV178: $i,SV212: $i,SV198: $i,SV33: $i] :
( ( ( apply @ SV33 @ SV198 @ SV212 )
= $false )
| ( ( apply @ SV178 @ SV203 @ SV214 )
= $true )
| ( ( apply @ SV7 @ SV198 @ SV203 )
= $false )
| ( ( member @ SV212 @ SV24 )
= $false )
| ( ( member @ SV198 @ SV24 )
= $false )
| ( ( member @ SV203 @ SV167 )
= $false )
| ( ( member @ SV214 @ SV167 )
= $false )
| ( ( apply @ SV7 @ SV212 @ SV214 )
= $false )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1237]) ).
thf(1240,plain,
! [SV167: $i,SV24: $i,SV7: $i,SV213: $i,SV198: $i,SV33: $i,SV215: $i,SV203: $i,SV178: $i] :
( ( ( apply @ SV178 @ SV203 @ SV215 )
= $false )
| ( ( apply @ SV33 @ SV198 @ SV213 )
= $true )
| ( ( apply @ SV7 @ SV198 @ SV203 )
= $false )
| ( ( member @ SV213 @ SV24 )
= $false )
| ( ( member @ SV198 @ SV24 )
= $false )
| ( ( member @ SV203 @ SV167 )
= $false )
| ( ( member @ SV215 @ SV167 )
= $false )
| ( ( apply @ SV7 @ SV213 @ SV215 )
= $false )
| ( ( isomorphism @ SV7 @ SV24 @ SV33 @ SV167 @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1238]) ).
thf(1241,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[121,1240,1239,1232,1231,1230,1229,1224,1223,1214,1212,1211,1208,1205,1202,1198,1191,1175,1170,1165,1164,1163,1162,1161,1159,1154,1147,1135,1134,1124,1121,1120,1112,1109,1108,1100,1096,1094,1092,1079,1072,1071,1070,1069,1060,1056,1055,1052,1038,1020,1012,1005,987,984,983,978,965,964,963,962,959,936,935,934,933,928,927,918,917,901,887,884,883,880,870,868,867,855,845,841,840,839,838,837,836,831,830,819,810,805,775,751,735,731,722,721,720,719,718,717,700,699,698,687,686,684,683,682,681,674,673,668,667,666,665,664,659,654,651,650,636,617,616,608,602,591,583,558,555,550,454,453,423,422,179,151]) ).
thf(1242,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1241]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET764+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 11 03:00:31 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.44
% 0.19/0.44 No.of.Axioms: 28
% 0.19/0.44
% 0.19/0.44 Length.of.Defs: 0
% 0.19/0.44
% 0.19/0.44 Contains.Choice.Funs: false
% 0.19/0.47 .
% 0.19/0.51 (rf:0,axioms:28,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:30,loop_count:0,foatp_calls:0,translation:fof_full).................................................................................................................................
% 1.23/1.56
% 1.23/1.56 ********************************
% 1.23/1.56 * All subproblems solved! *
% 1.23/1.56 ********************************
% 1.23/1.56 % SZS status Theorem for /export/starexec/sandbox/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:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:1241,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.91/2.08
% 1.91/2.08 %**** Beginning of derivation protocol ****
% 1.91/2.08 % SZS output start CNFRefutation
% See solution above
% 1.91/2.09
% 1.91/2.09 %**** End of derivation protocol ****
% 1.91/2.09 %**** no. of clauses in derivation: 1242 ****
% 1.91/2.09 %**** clause counter: 1241 ****
% 1.91/2.09
% 1.91/2.09 % SZS status Theorem for /export/starexec/sandbox/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:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:1241,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------