TSTP Solution File: SEU230+2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU230+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:08:44 EDT 2022
% Result : Theorem 235.02s 235.46s
% Output : CNFRefutation 239.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 204
% Syntax : Number of formulae : 2931 ( 849 unt; 120 typ; 0 def)
% Number of atoms : 33324 (11980 equ; 0 cnn)
% Maximal formula atoms : 15 ( 11 avg)
% Number of connectives : 81280 (13513 ~;13985 |; 592 &;52842 @)
% ( 152 <=>; 196 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 258 ( 258 >; 0 *; 0 +; 0 <<)
% Number of symbols : 123 ( 120 usr; 4 con; 0-5 aty)
% Number of variables : 10895 ( 0 ^10863 !; 32 ?;10895 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_are_equipotent,type,
are_equipotent: $i > $i > $o ).
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_cast_to_subset,type,
cast_to_subset: $i > $i ).
thf(tp_complements_of_subsets,type,
complements_of_subsets: $i > $i > $i ).
thf(tp_disjoint,type,
disjoint: $i > $i > $o ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_function_inverse,type,
function_inverse: $i > $i ).
thf(tp_identity_relation,type,
identity_relation: $i > $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_meet_of_subsets,type,
meet_of_subsets: $i > $i > $i ).
thf(tp_one_to_one,type,
one_to_one: $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_proper_subset,type,
proper_subset: $i > $i > $o ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_composition,type,
relation_composition: $i > $i > $i ).
thf(tp_relation_dom,type,
relation_dom: $i > $i ).
thf(tp_relation_dom_restriction,type,
relation_dom_restriction: $i > $i > $i ).
thf(tp_relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
thf(tp_relation_field,type,
relation_field: $i > $i ).
thf(tp_relation_image,type,
relation_image: $i > $i > $i ).
thf(tp_relation_inverse,type,
relation_inverse: $i > $i ).
thf(tp_relation_inverse_image,type,
relation_inverse_image: $i > $i > $i ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_relation_rng_restriction,type,
relation_rng_restriction: $i > $i > $i ).
thf(tp_sK10_SY3288,type,
sK10_SY3288: $i > $i > $i > $i ).
thf(tp_sK11_B,type,
sK11_B: $i > $i ).
thf(tp_sK12_SY3289,type,
sK12_SY3289: $i > $i ).
thf(tp_sK13_C,type,
sK13_C: $i > $i > $i ).
thf(tp_sK14_SY3290,type,
sK14_SY3290: $i > $i > $i ).
thf(tp_sK15_D,type,
sK15_D: $i > $i > $i > $i ).
thf(tp_sK16_C,type,
sK16_C: $i > $i > $i ).
thf(tp_sK17_SY3292,type,
sK17_SY3292: $i > $i > $i ).
thf(tp_sK18_D,type,
sK18_D: $i > $i > $i > $i ).
thf(tp_sK19_C,type,
sK19_C: $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_SY3294,type,
sK20_SY3294: $i > $i > $i ).
thf(tp_sK21_D,type,
sK21_D: $i > $i > $i > $i ).
thf(tp_sK22_D,type,
sK22_D: $i > $i > $i > $i ).
thf(tp_sK23_C,type,
sK23_C: $i > $i > $i ).
thf(tp_sK24_SY3296,type,
sK24_SY3296: $i > $i > $i ).
thf(tp_sK25_D,type,
sK25_D: $i > $i > $i > $i ).
thf(tp_sK26_C,type,
sK26_C: $i > $i > $i ).
thf(tp_sK27_SY3298,type,
sK27_SY3298: $i > $i > $i ).
thf(tp_sK28_D,type,
sK28_D: $i > $i > $i > $i ).
thf(tp_sK29_C,type,
sK29_C: $i > $i > $i ).
thf(tp_sK2_B,type,
sK2_B: $i > $i ).
thf(tp_sK30_C,type,
sK30_C: $i > $i > $i ).
thf(tp_sK31_SY3299,type,
sK31_SY3299: $i > $i > $i ).
thf(tp_sK32_E,type,
sK32_E: $i > $i > $i > $i > $i ).
thf(tp_sK33_SY3300,type,
sK33_SY3300: $i > $i > $i > $i > $i ).
thf(tp_sK34_D,type,
sK34_D: $i > $i > $i > $i ).
thf(tp_sK35_SY3303,type,
sK35_SY3303: $i > $i > $i > $i ).
thf(tp_sK36_SY3305,type,
sK36_SY3305: $i > $i > $i > $i ).
thf(tp_sK37_D,type,
sK37_D: $i > $i > $i > $i ).
thf(tp_sK38_D,type,
sK38_D: $i > $i > $i > $i ).
thf(tp_sK39_C,type,
sK39_C: $i > $i > $i ).
thf(tp_sK3_SY3278,type,
sK3_SY3278: $i > $i > $i ).
thf(tp_sK40_SY3306,type,
sK40_SY3306: $i > $i > $i ).
thf(tp_sK41_C,type,
sK41_C: $i > $i > $i ).
thf(tp_sK42_B,type,
sK42_B: $i > $i ).
thf(tp_sK43_C,type,
sK43_C: $i > $i > $i ).
thf(tp_sK44_D,type,
sK44_D: $i > $i > $i > $i ).
thf(tp_sK45_C,type,
sK45_C: $i > $i > $i ).
thf(tp_sK46_SY3307,type,
sK46_SY3307: $i > $i > $i ).
thf(tp_sK47_C,type,
sK47_C: $i > $i > $i ).
thf(tp_sK48_SY3309,type,
sK48_SY3309: $i > $i > $i ).
thf(tp_sK49_B,type,
sK49_B: $i > $i ).
thf(tp_sK4_C,type,
sK4_C: $i > $i > $i ).
thf(tp_sK50_E,type,
sK50_E: $i > $i > $i > $i > $i ).
thf(tp_sK51_E,type,
sK51_E: $i > $i > $i > $i > $i ).
thf(tp_sK52_D,type,
sK52_D: $i > $i > $i > $i ).
thf(tp_sK53_SY3313,type,
sK53_SY3313: $i > $i > $i > $i ).
thf(tp_sK54_E,type,
sK54_E: $i > $i > $i > $i > $i ).
thf(tp_sK55_D,type,
sK55_D: $i > $i > $i > $i ).
thf(tp_sK56_SY3315,type,
sK56_SY3315: $i > $i > $i > $i ).
thf(tp_sK57_D,type,
sK57_D: $i > $i > $i > $i ).
thf(tp_sK58_D,type,
sK58_D: $i > $i > $i > $i ).
thf(tp_sK59_SY3316,type,
sK59_SY3316: $i > $i > $i > $i ).
thf(tp_sK5_C,type,
sK5_C: $i > $i > $i ).
thf(tp_sK60_E,type,
sK60_E: $i > $i > $i > $i > $i ).
thf(tp_sK61_D,type,
sK61_D: $i > $i > $i > $i ).
thf(tp_sK62_SY3318,type,
sK62_SY3318: $i > $i > $i > $i ).
thf(tp_sK63_D,type,
sK63_D: $i > $i > $i > $i ).
thf(tp_sK64_SY3319,type,
sK64_SY3319: $i > $i > $i > $i ).
thf(tp_sK65_C,type,
sK65_C: $i > $i > $i ).
thf(tp_sK66_SY3320,type,
sK66_SY3320: $i > $i > $i ).
thf(tp_sK67_D,type,
sK67_D: $i > $i > $i > $i ).
thf(tp_sK68_B,type,
sK68_B: $i > $i ).
thf(tp_sK69_SY3321,type,
sK69_SY3321: $i > $i ).
thf(tp_sK6_D,type,
sK6_D: $i > $i > $i > $i ).
thf(tp_sK70_C,type,
sK70_C: $i > $i > $i ).
thf(tp_sK71_SY3322,type,
sK71_SY3322: $i > $i > $i ).
thf(tp_sK72_C,type,
sK72_C: $i > $i > $i ).
thf(tp_sK73_C,type,
sK73_C: $i > $i > $i ).
thf(tp_sK74_C,type,
sK74_C: $i > $i > $i ).
thf(tp_sK75_D,type,
sK75_D: $i > $i > $i > $i ).
thf(tp_sK76_D,type,
sK76_D: $i > $i > $i > $i ).
thf(tp_sK77_B,type,
sK77_B: $i > $i ).
thf(tp_sK78_C,type,
sK78_C: $i > $i > $i ).
thf(tp_sK7_F,type,
sK7_F: $i > $i > $i > $i > $i > $i ).
thf(tp_sK8_D,type,
sK8_D: $i > $i > $i > $i ).
thf(tp_sK9_SY3284,type,
sK9_SY3284: $i > $i > $i > $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(tp_set_meet,type,
set_meet: $i > $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subset_complement,type,
subset_complement: $i > $i > $i ).
thf(tp_subset_difference,type,
subset_difference: $i > $i > $i > $i ).
thf(tp_succ,type,
succ: $i > $i ).
thf(tp_union,type,
union: $i > $i ).
thf(tp_union_of_subsets,type,
union_of_subsets: $i > $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(tp_unordered_triple,type,
unordered_triple: $i > $i > $i > $i ).
thf(1,axiom,
! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
( ( subset @ E @ C )
=> ( in @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_tarski) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ( in @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_tarski) ).
thf(4,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(57,axiom,
! [A: $i] :
~ ( empty @ ( succ @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_ordinal1) ).
thf(98,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( powerset @ A ) ) )
=> ( ( C
= ( complements_of_subsets @ A @ B ) )
<=> ! [D: $i] :
( ( element @ D @ ( powerset @ A ) )
=> ( ( in @ D @ C )
<=> ( in @ ( subset_complement @ A @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_setfam_1) ).
thf(99,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_composition @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_1) ).
thf(100,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
<=> ! [B: $i,C: $i] :
( ( ( in @ B @ ( relation_dom @ A ) )
& ( in @ C @ ( relation_dom @ A ) )
& ( ( apply @ A @ B )
= ( apply @ A @ C ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
thf(102,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( B
= ( relation_inverse @ A ) )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ B )
<=> ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_relat_1) ).
thf(106,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
thf(107,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(109,axiom,
! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
thf(111,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
thf(112,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( ( in @ B @ ( relation_dom @ A ) )
=> ( ( C
= ( apply @ A @ B ) )
<=> ( in @ ( ordered_pair @ B @ C ) @ A ) ) )
& ( ~ ( in @ B @ ( relation_dom @ A ) )
=> ( ( C
= ( apply @ A @ B ) )
<=> ( C = empty_set ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(114,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(115,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_relat_1) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(118,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
thf(119,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
thf(120,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( A = B )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
<=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_relat_1) ).
thf(121,axiom,
! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(122,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(123,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
thf(124,axiom,
! [A: $i,B: $i] :
( ( ( A != empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ C @ D ) ) ) ) )
& ( ( A = empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ( B = empty_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_setfam_1) ).
thf(125,axiom,
! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_1) ).
thf(126,axiom,
! [A: $i] :
( ( succ @ A )
= ( set_union2 @ A @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( unordered_triple @ A @ B @ C ) )
<=> ! [E: $i] :
( ( in @ E @ D )
<=> ~ ( ( E != A )
& ( E != B )
& ( E != C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_enumset1) ).
thf(128,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_inverse_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ A )
& ( in @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_1) ).
thf(129,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ ( ordered_pair @ E @ D ) @ A )
& ( in @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_relat_1) ).
thf(130,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_inverse_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ ( relation_dom @ A ) )
& ( in @ ( apply @ A @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_funct_1) ).
thf(131,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_rng_restriction @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_relat_1) ).
thf(132,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ E @ ( relation_dom @ A ) )
& ( in @ E @ B )
& ( D
= ( apply @ A @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_funct_1) ).
thf(133,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_dom_restriction @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ( ( in @ D @ B )
& ( in @ ( ordered_pair @ D @ E ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_relat_1) ).
thf(135,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( B
= ( identity_relation @ A ) )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ B )
<=> ( ( in @ C @ A )
& ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_relat_1) ).
thf(143,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(148,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ ( relation_dom @ C ) )
& ( B
= ( apply @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_1) ).
thf(154,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_dom @ ( relation_dom_restriction @ C @ B ) ) )
<=> ( ( in @ A @ B )
& ( in @ A @ ( relation_dom @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_relat_1) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( relation @ D )
=> ( ( in @ ( ordered_pair @ A @ B ) @ ( relation_composition @ ( identity_relation @ C ) @ D ) )
<=> ( ( in @ A @ C )
& ( in @ ( ordered_pair @ A @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_relat_1) ).
thf(158,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ B @ A )
=> ( ( apply @ ( relation_dom_restriction @ C @ A ) @ B )
= ( apply @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funct_1) ).
thf(160,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
=> ( ( apply @ ( relation_dom_restriction @ C @ A ) @ B )
= ( apply @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_funct_1) ).
thf(163,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( B
= ( relation_dom_restriction @ C @ A ) )
<=> ( ( ( relation_dom @ B )
= ( set_intersection2 @ ( relation_dom @ C ) @ A ) )
& ! [D: $i] :
( ( in @ D @ ( relation_dom @ B ) )
=> ( ( apply @ B @ D )
= ( apply @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_1) ).
thf(164,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(171,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( ( one_to_one @ B )
& ( in @ A @ ( relation_rng @ B ) ) )
=> ( ( A
= ( apply @ B @ ( apply @ ( function_inverse @ B ) @ A ) ) )
& ( A
= ( apply @ ( relation_composition @ ( function_inverse @ B ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funct_1) ).
thf(172,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_relat_1) ).
thf(174,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).
thf(175,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ! [B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( B
= ( function_inverse @ A ) )
<=> ( ( ( relation_dom @ B )
= ( relation_rng @ A ) )
& ! [C: $i,D: $i] :
( ( ( ( in @ C @ ( relation_rng @ A ) )
& ( D
= ( apply @ B @ C ) ) )
=> ( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) )
& ( ( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) )
=> ( ( in @ C @ ( relation_rng @ A ) )
& ( D
= ( apply @ B @ C ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).
thf(176,axiom,
! [A: $i] :
( ( A != empty_set )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ A )
=> ( ~ ( in @ C @ B )
=> ( in @ C @ ( subset_complement @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).
thf(177,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(182,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_zfmisc_1) ).
thf(191,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(192,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( in @ B @ C )
& ( in @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(195,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(196,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(200,axiom,
! [A: $i,B: $i] :
( ( in @ B @ A )
=> ( ( apply @ ( identity_relation @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funct_1) ).
thf(201,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( B
= ( identity_relation @ A ) )
<=> ( ( ( relation_dom @ B )
= A )
& ! [C: $i] :
( ( in @ C @ A )
=> ( ( apply @ B @ C )
= C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
thf(204,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_field @ C ) )
& ( in @ B @ ( relation_field @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relat_1) ).
thf(209,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ A @ ( relation_dom @ B ) )
=> ( ( apply @ ( relation_composition @ B @ C ) @ A )
= ( apply @ C @ ( apply @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
thf(210,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
=> ( ( apply @ ( relation_composition @ C @ B ) @ A )
= ( apply @ B @ ( apply @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_1) ).
thf(212,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
<=> ( ( in @ A @ ( relation_dom @ C ) )
& ( in @ ( apply @ C @ A ) @ ( relation_dom @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_1) ).
thf(213,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_dom @ C ) )
& ( in @ B @ ( relation_rng @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
thf(221,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_inverse_image @ C @ B ) )
<=> ? [D: $i] :
( ( in @ D @ ( relation_rng @ C ) )
& ( in @ ( ordered_pair @ A @ D ) @ C )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t166_relat_1) ).
thf(229,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_image @ C @ B ) )
<=> ? [D: $i] :
( ( in @ D @ ( relation_dom @ C ) )
& ( in @ ( ordered_pair @ D @ A ) @ C )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_relat_1) ).
thf(231,axiom,
! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( powerset @ C ) @ B ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(239,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) )
<=> ( ( in @ A @ B )
& ( in @ A @ ( relation_rng @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_relat_1) ).
thf(241,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(242,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
<=> ( ( in @ B @ ( relation_dom @ C ) )
& ( in @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l82_funct_1) ).
thf(243,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l71_subset_1) ).
thf(244,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
thf(245,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(247,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_zfmisc_1) ).
thf(248,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_subset_1) ).
thf(250,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(251,axiom,
! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
thf(252,axiom,
! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l25_zfmisc_1) ).
thf(253,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l23_zfmisc_1) ).
thf(255,conjecture,
! [A: $i] : ( in @ A @ ( succ @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).
thf(256,negated_conjecture,
( ( ! [A: $i] : ( in @ A @ ( succ @ A ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[255]) ).
thf(257,plain,
( ( ! [A: $i] : ( in @ A @ ( succ @ A ) ) )
= $false ),
inference(unfold_def,[status(thm)],[256]) ).
thf(258,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
( ( subset @ E @ C )
=> ( in @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(259,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ( in @ D @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(260,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(261,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(262,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(263,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(264,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(265,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(266,plain,
( ( ! [A: $i] :
~ ( empty @ ( succ @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(267,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( powerset @ A ) ) )
=> ( ( C
= ( complements_of_subsets @ A @ B ) )
<=> ! [D: $i] :
( ( element @ D @ ( powerset @ A ) )
=> ( ( in @ D @ C )
<=> ( in @ ( subset_complement @ A @ D ) @ B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(268,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_composition @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(269,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
<=> ! [B: $i,C: $i] :
( ( ( in @ B @ ( relation_dom @ A ) )
& ( in @ C @ ( relation_dom @ A ) )
& ( ( apply @ A @ B )
= ( apply @ A @ C ) ) )
=> ( B = C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(270,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( B
= ( relation_inverse @ A ) )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ B )
<=> ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(271,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(272,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(273,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(274,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(275,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(276,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( ( in @ B @ ( relation_dom @ A ) )
=> ( ( C
= ( apply @ A @ B ) )
<=> ( in @ ( ordered_pair @ B @ C ) @ A ) ) )
& ( ~ ( in @ B @ ( relation_dom @ A ) )
=> ( ( C
= ( apply @ A @ B ) )
<=> ( C = empty_set ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(277,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(278,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(279,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(280,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(281,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(282,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(283,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(284,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( A = B )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
<=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(285,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(286,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(287,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(288,plain,
( ( ! [A: $i,B: $i] :
( ( ( A != empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ C @ D ) ) ) ) )
& ( ( A = empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ( B = empty_set ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(289,plain,
( ( ! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(290,plain,
( ( ! [A: $i] :
( ( succ @ A )
= ( set_union2 @ A @ ( singleton @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(291,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( unordered_triple @ A @ B @ C ) )
<=> ! [E: $i] :
( ( in @ E @ D )
<=> ~ ( ( E != A )
& ( E != B )
& ( E != C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(292,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_inverse_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ A )
& ( in @ E @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(293,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ ( ordered_pair @ E @ D ) @ A )
& ( in @ E @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(294,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_inverse_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ ( relation_dom @ A ) )
& ( in @ ( apply @ A @ D ) @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(295,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_rng_restriction @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(296,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ E @ ( relation_dom @ A ) )
& ( in @ E @ B )
& ( D
= ( apply @ A @ E ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(297,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_dom_restriction @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ( ( in @ D @ B )
& ( in @ ( ordered_pair @ D @ E ) @ A ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(298,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( B
= ( identity_relation @ A ) )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ B )
<=> ( ( in @ C @ A )
& ( C = D ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(299,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(300,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(301,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ ( relation_dom @ C ) )
& ( B
= ( apply @ C @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(302,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_dom @ ( relation_dom_restriction @ C @ B ) ) )
<=> ( ( in @ A @ B )
& ( in @ A @ ( relation_dom @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(303,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( relation @ D )
=> ( ( in @ ( ordered_pair @ A @ B ) @ ( relation_composition @ ( identity_relation @ C ) @ D ) )
<=> ( ( in @ A @ C )
& ( in @ ( ordered_pair @ A @ B ) @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(304,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ B @ A )
=> ( ( apply @ ( relation_dom_restriction @ C @ A ) @ B )
= ( apply @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(305,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
=> ( ( apply @ ( relation_dom_restriction @ C @ A ) @ B )
= ( apply @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(306,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( B
= ( relation_dom_restriction @ C @ A ) )
<=> ( ( ( relation_dom @ B )
= ( set_intersection2 @ ( relation_dom @ C ) @ A ) )
& ! [D: $i] :
( ( in @ D @ ( relation_dom @ B ) )
=> ( ( apply @ B @ D )
= ( apply @ C @ D ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(307,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(308,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( ( one_to_one @ B )
& ( in @ A @ ( relation_rng @ B ) ) )
=> ( ( A
= ( apply @ B @ ( apply @ ( function_inverse @ B ) @ A ) ) )
& ( A
= ( apply @ ( relation_composition @ ( function_inverse @ B ) @ B ) @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(309,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(310,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
& ( in @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(311,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ! [B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( B
= ( function_inverse @ A ) )
<=> ( ( ( relation_dom @ B )
= ( relation_rng @ A ) )
& ! [C: $i,D: $i] :
( ( ( ( in @ C @ ( relation_rng @ A ) )
& ( D
= ( apply @ B @ C ) ) )
=> ( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) )
& ( ( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) )
=> ( ( in @ C @ ( relation_rng @ A ) )
& ( D
= ( apply @ B @ C ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(312,plain,
( ( ! [A: $i] :
( ( A != empty_set )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ A )
=> ( ~ ( in @ C @ B )
=> ( in @ C @ ( subset_complement @ A @ B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(313,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(314,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(315,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(316,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( in @ B @ C )
& ( in @ C @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(317,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(318,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(319,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ A )
=> ( ( apply @ ( identity_relation @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(320,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( B
= ( identity_relation @ A ) )
<=> ( ( ( relation_dom @ B )
= A )
& ! [C: $i] :
( ( in @ C @ A )
=> ( ( apply @ B @ C )
= C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(321,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_field @ C ) )
& ( in @ B @ ( relation_field @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(322,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ A @ ( relation_dom @ B ) )
=> ( ( apply @ ( relation_composition @ B @ C ) @ A )
= ( apply @ C @ ( apply @ B @ A ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(323,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
=> ( ( apply @ ( relation_composition @ C @ B ) @ A )
= ( apply @ B @ ( apply @ C @ A ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(324,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
<=> ( ( in @ A @ ( relation_dom @ C ) )
& ( in @ ( apply @ C @ A ) @ ( relation_dom @ B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(325,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_dom @ C ) )
& ( in @ B @ ( relation_rng @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(326,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_inverse_image @ C @ B ) )
<=> ? [D: $i] :
( ( in @ D @ ( relation_rng @ C ) )
& ( in @ ( ordered_pair @ A @ D ) @ C )
& ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(327,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_image @ C @ B ) )
<=> ? [D: $i] :
( ( in @ D @ ( relation_dom @ C ) )
& ( in @ ( ordered_pair @ D @ A ) @ C )
& ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(328,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( powerset @ C ) @ B ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(329,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) )
<=> ( ( in @ A @ B )
& ( in @ A @ ( relation_rng @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(330,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(331,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
<=> ( ( in @ B @ ( relation_dom @ C ) )
& ( in @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(332,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(333,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(334,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(335,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(336,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(337,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(338,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(339,plain,
( ( ! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(340,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(341,plain,
( ( in @ sK1_A @ ( succ @ sK1_A ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[257]) ).
thf(342,plain,
( ( ~ ( in @ sK1_A @ ( succ @ sK1_A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[341]) ).
thf(343,plain,
( ( ! [A: $i] :
( ! [SY3276: $i] :
( ~ ( subset @ SY3276 @ ( sK2_B @ A ) )
| ( are_equipotent @ SY3276 @ ( sK2_B @ A ) )
| ( in @ SY3276 @ ( sK2_B @ A ) ) )
& ! [SY3277: $i] :
( ( ! [SY3282: $i] :
( ~ ( subset @ SY3282 @ SY3277 )
| ( in @ SY3282 @ ( sK3_SY3278 @ SY3277 @ A ) ) )
& ( in @ ( sK3_SY3278 @ SY3277 @ A ) @ ( sK2_B @ A ) ) )
| ~ ( in @ SY3277 @ ( sK2_B @ A ) ) )
& ! [SY3280: $i,SY3281: $i] :
( ~ ( in @ SY3280 @ ( sK2_B @ A ) )
| ~ ( subset @ SY3281 @ SY3280 )
| ( in @ SY3281 @ ( sK2_B @ A ) ) )
& ( in @ A @ ( sK2_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[258]) ).
thf(344,plain,
( ( ! [A: $i,B: $i] :
( ( ! [SY3283: $i] :
( ~ ( in @ SY3283 @ B )
| ~ ( in @ SY3283 @ ( sK4_C @ B @ A ) ) )
& ( in @ ( sK4_C @ B @ A ) @ B ) )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[259]) ).
thf(345,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[260]) ).
thf(346,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[261]) ).
thf(347,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[262]) ).
thf(348,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK5_C @ B @ A ) @ A )
| ~ ( in @ ( sK5_C @ B @ A ) @ B ) )
& ( ( in @ ( sK5_C @ B @ A ) @ A )
| ( in @ ( sK5_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[263]) ).
thf(349,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[264]) ).
thf(350,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[265]) ).
thf(351,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ! [C: $i] :
( ~ ( element @ C @ ( powerset @ ( powerset @ A ) ) )
| ( ( element @ ( sK6_D @ C @ B @ A ) @ ( powerset @ A ) )
& ( ~ ( in @ ( sK6_D @ C @ B @ A ) @ C )
| ~ ( in @ ( subset_complement @ A @ ( sK6_D @ C @ B @ A ) ) @ B ) )
& ( ( in @ ( sK6_D @ C @ B @ A ) @ C )
| ( in @ ( subset_complement @ A @ ( sK6_D @ C @ B @ A ) ) @ B ) ) )
| ( C
= ( complements_of_subsets @ A @ B ) ) )
& ! [C: $i] :
( ~ ( element @ C @ ( powerset @ ( powerset @ A ) ) )
| ( C
!= ( complements_of_subsets @ A @ B ) )
| ( ! [D: $i] :
( ~ ( element @ D @ ( powerset @ A ) )
| ~ ( in @ D @ C )
| ( in @ ( subset_complement @ A @ D ) @ B ) )
& ! [D: $i] :
( ~ ( element @ D @ ( powerset @ A ) )
| ~ ( in @ ( subset_complement @ A @ D ) @ B )
| ( in @ D @ C ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[267]) ).
thf(352,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ! [SY3287: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ C @ B @ A ) @ SY3287 ) @ A )
| ~ ( in @ ( ordered_pair @ SY3287 @ ( sK9_SY3284 @ C @ B @ A ) ) @ B ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ C @ B @ A ) @ ( sK9_SY3284 @ C @ B @ A ) ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK8_D @ C @ B @ A ) @ ( sK10_SY3288 @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK10_SY3288 @ C @ B @ A ) @ ( sK9_SY3284 @ C @ B @ A ) ) @ B ) )
| ( in @ ( ordered_pair @ ( sK8_D @ C @ B @ A ) @ ( sK9_SY3284 @ C @ B @ A ) ) @ C ) ) )
| ( C
= ( relation_composition @ A @ B ) ) )
& ! [C: $i] :
( ~ ( relation @ C )
| ( C
!= ( relation_composition @ A @ B ) )
| ( ! [D: $i,E: $i] :
( ! [F: $i] :
( ~ ( in @ ( ordered_pair @ D @ F ) @ A )
| ~ ( in @ ( ordered_pair @ F @ E ) @ B ) )
| ( in @ ( ordered_pair @ D @ E ) @ C ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( ( in @ ( ordered_pair @ D @ ( sK7_F @ E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK7_F @ E @ D @ C @ B @ A ) @ E ) @ B ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[268]) ).
thf(353,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ( in @ ( sK11_B @ A ) @ ( relation_dom @ A ) )
& ( in @ ( sK12_SY3289 @ A ) @ ( relation_dom @ A ) )
& ( ( apply @ A @ ( sK11_B @ A ) )
= ( apply @ A @ ( sK12_SY3289 @ A ) ) )
& ( ( sK11_B @ A )
!= ( sK12_SY3289 @ A ) ) )
| ( one_to_one @ A ) )
& ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ! [B: $i,C: $i] :
( ~ ( in @ B @ ( relation_dom @ A ) )
| ~ ( in @ C @ ( relation_dom @ A ) )
| ( ( apply @ A @ B )
!= ( apply @ A @ C ) )
| ( B = C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[269]) ).
thf(354,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK13_C @ B @ A ) @ ( sK14_SY3290 @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK14_SY3290 @ B @ A ) @ ( sK13_C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( sK13_C @ B @ A ) @ ( sK14_SY3290 @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK14_SY3290 @ B @ A ) @ ( sK13_C @ B @ A ) ) @ A ) ) )
| ( B
= ( relation_inverse @ A ) ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ( B
!= ( relation_inverse @ A ) )
| ( ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ B )
| ( in @ ( ordered_pair @ D @ C ) @ A ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ D @ C ) @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[270]) ).
thf(355,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY3291: $i] :
~ ( in @ ( ordered_pair @ SY3291 @ ( sK16_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK16_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK17_SY3292 @ B @ A ) @ ( sK16_C @ B @ A ) ) @ A )
| ( in @ ( sK16_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_rng @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_rng @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ D @ C ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ ( sK15_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[271]) ).
thf(356,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY3293: $i] :
( ( ( sK19_C @ B @ A )
!= ( apply @ A @ SY3293 ) )
| ~ ( in @ SY3293 @ ( relation_dom @ A ) ) )
| ~ ( in @ ( sK19_C @ B @ A ) @ B ) )
& ( ( ( ( sK19_C @ B @ A )
= ( apply @ A @ ( sK20_SY3294 @ B @ A ) ) )
& ( in @ ( sK20_SY3294 @ B @ A ) @ ( relation_dom @ A ) ) )
| ( in @ ( sK19_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_rng @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_rng @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
( ( C
!= ( apply @ A @ D ) )
| ~ ( in @ D @ ( relation_dom @ A ) ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( ( C
= ( apply @ A @ ( sK18_D @ C @ B @ A ) ) )
& ( in @ ( sK18_D @ C @ B @ A ) @ ( relation_dom @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[272]) ).
thf(357,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK21_D @ C @ B @ A ) @ A )
| ( in @ ( sK21_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK21_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK21_D @ C @ B @ A ) @ A )
| ( in @ ( sK21_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK21_D @ C @ B @ A ) @ B )
| ( in @ ( sK21_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_difference @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_difference @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ~ ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[273]) ).
thf(358,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY3295: $i] :
( ~ ( in @ ( sK23_C @ B @ A ) @ SY3295 )
| ~ ( in @ SY3295 @ A ) )
| ~ ( in @ ( sK23_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK23_C @ B @ A ) @ ( sK24_SY3296 @ B @ A ) )
& ( in @ ( sK24_SY3296 @ B @ A ) @ A ) )
| ( in @ ( sK23_C @ B @ A ) @ B ) ) )
| ( B
= ( union @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( union @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
( ~ ( in @ C @ D )
| ~ ( in @ D @ A ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( ( in @ C @ ( sK22_D @ C @ B @ A ) )
& ( in @ ( sK22_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[274]) ).
thf(359,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY3297: $i] :
~ ( in @ ( ordered_pair @ ( sK26_C @ B @ A ) @ SY3297 ) @ A )
| ~ ( in @ ( sK26_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK26_C @ B @ A ) @ ( sK27_SY3298 @ B @ A ) ) @ A )
| ( in @ ( sK26_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_dom @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_dom @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ C @ ( sK25_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[275]) ).
thf(360,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C
!= ( apply @ A @ B ) )
| ( in @ ( ordered_pair @ B @ C ) @ A ) ) )
& ! [B: $i] :
( ~ ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ~ ( in @ ( ordered_pair @ B @ C ) @ A )
| ( C
= ( apply @ A @ B ) ) ) )
& ! [B: $i] :
( ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C
!= ( apply @ A @ B ) )
| ( C = empty_set ) ) )
& ! [B: $i] :
( ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C != empty_set )
| ( C
= ( apply @ A @ B ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[276]) ).
thf(361,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK28_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK28_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK28_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK28_D @ C @ B @ A ) @ A )
| ( in @ ( sK28_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK28_D @ C @ B @ A ) @ B )
| ( in @ ( sK28_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_intersection2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_intersection2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ~ ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[277]) ).
thf(362,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK29_C @ B @ A ) @ A )
& ~ ( in @ ( sK29_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[278]) ).
thf(363,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( in @ ( ordered_pair @ ( sK30_C @ B @ A ) @ ( sK31_SY3299 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK30_C @ B @ A ) @ ( sK31_SY3299 @ B @ A ) ) @ B ) )
| ( subset @ A @ B ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[279]) ).
thf(364,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY3301: $i,SY3302: $i] :
( ~ ( in @ SY3301 @ A )
| ~ ( in @ SY3302 @ B )
| ( ( sK34_D @ C @ B @ A )
!= ( ordered_pair @ SY3301 @ SY3302 ) ) )
| ~ ( in @ ( sK34_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK35_SY3303 @ C @ B @ A ) @ A )
& ( in @ ( sK36_SY3305 @ C @ B @ A ) @ B )
& ( ( sK34_D @ C @ B @ A )
= ( ordered_pair @ ( sK35_SY3303 @ C @ B @ A ) @ ( sK36_SY3305 @ C @ B @ A ) ) ) )
| ( in @ ( sK34_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( cartesian_product2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( cartesian_product2 @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i,F: $i] :
( ~ ( in @ E @ A )
| ~ ( in @ F @ B )
| ( D
!= ( ordered_pair @ E @ F ) ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( sK32_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK33_SY3300 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK32_E @ D @ C @ B @ A ) @ ( sK33_SY3300 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[280]) ).
thf(365,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK37_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK37_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK37_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK37_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK37_D @ C @ B @ A ) @ C )
| ( in @ ( sK37_D @ C @ B @ A ) @ A )
| ( in @ ( sK37_D @ C @ B @ A ) @ B ) ) )
| ( C
= ( set_union2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A )
| ( in @ D @ B ) )
& ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[281]) ).
thf(366,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK38_D @ C @ B @ A ) @ C )
| ( ( sK38_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK38_D @ C @ B @ A ) @ C )
| ( ( sK38_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK38_D @ C @ B @ A ) @ C )
| ( ( sK38_D @ C @ B @ A )
= A )
| ( ( sK38_D @ C @ B @ A )
= B ) ) )
| ( C
= ( unordered_pair @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( unordered_pair @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( D = A )
| ( D = B ) )
& ! [D: $i] :
( ( D != A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ( D != B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[282]) ).
thf(367,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( in @ B @ A ) ) )
& ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( in @ B @ A )
| ( element @ B @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( empty @ B ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( empty @ B )
| ( element @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[283]) ).
thf(368,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK39_C @ B @ A ) @ ( sK40_SY3306 @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK39_C @ B @ A ) @ ( sK40_SY3306 @ B @ A ) ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK39_C @ B @ A ) @ ( sK40_SY3306 @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK39_C @ B @ A ) @ ( sK40_SY3306 @ B @ A ) ) @ B ) ) )
| ( A = B ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ( A != B )
| ( ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ B )
| ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[284]) ).
thf(369,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK41_C @ B @ A ) @ B )
| ~ ( subset @ ( sK41_C @ B @ A ) @ A ) )
& ( ( in @ ( sK41_C @ B @ A ) @ B )
| ( subset @ ( sK41_C @ B @ A ) @ A ) ) )
| ( B
= ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( in @ C @ B )
| ( subset @ C @ A ) )
& ! [C: $i] :
( ~ ( subset @ C @ A )
| ( in @ C @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[285]) ).
thf(370,plain,
( ( ! [A: $i] :
( ( in @ ( sK42_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[286]) ).
thf(371,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK43_C @ B @ A )
!= A )
| ~ ( in @ ( sK43_C @ B @ A ) @ B ) )
& ( ( ( sK43_C @ B @ A )
= A )
| ( in @ ( sK43_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[287]) ).
thf(372,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( ( ( ( in @ ( sK46_SY3307 @ B @ A ) @ A )
& ~ ( in @ ( sK45_C @ B @ A ) @ ( sK46_SY3307 @ B @ A ) ) )
| ~ ( in @ ( sK45_C @ B @ A ) @ B ) )
& ( ! [SY3308: $i] :
( ~ ( in @ SY3308 @ A )
| ( in @ ( sK45_C @ B @ A ) @ SY3308 ) )
| ( in @ ( sK45_C @ B @ A ) @ B ) ) )
| ( B
= ( set_meet @ A ) ) ) )
& ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( ! [C: $i] :
( ( ( in @ ( sK44_D @ C @ B @ A ) @ A )
& ~ ( in @ C @ ( sK44_D @ C @ B @ A ) ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ C @ D ) ) ) ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( B = empty_set ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
( ( B != empty_set )
| ( B
= ( set_meet @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[288]) ).
thf(373,plain,
( ( ! [A: $i] :
( ( ! [SY3310: $i,SY3311: $i] :
( ( sK49_B @ A )
!= ( ordered_pair @ SY3310 @ SY3311 ) )
& ( in @ ( sK49_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK47_C @ B @ A ) @ ( sK48_SY3309 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[289]) ).
thf(374,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( ~ ( in @ ( sK50_E @ D @ C @ B @ A ) @ D )
| ( ( sK50_E @ D @ C @ B @ A )
!= C ) )
& ( ~ ( in @ ( sK50_E @ D @ C @ B @ A ) @ D )
| ( ( sK50_E @ D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK50_E @ D @ C @ B @ A ) @ D )
| ( ( sK50_E @ D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK50_E @ D @ C @ B @ A ) @ D )
| ( ( sK50_E @ D @ C @ B @ A )
= C )
| ( ( sK50_E @ D @ C @ B @ A )
= A )
| ( ( sK50_E @ D @ C @ B @ A )
= B ) ) )
| ( D
= ( unordered_triple @ A @ B @ C ) ) )
& ! [C: $i,D: $i] :
( ( D
!= ( unordered_triple @ A @ B @ C ) )
| ( ! [E: $i] :
( ~ ( in @ E @ D )
| ( E = C )
| ( E = A )
| ( E = B ) )
& ! [E: $i] :
( ( E != C )
| ( in @ E @ D ) )
& ! [E: $i] :
( ( E != A )
| ( in @ E @ D ) )
& ! [E: $i] :
( ( E != B )
| ( in @ E @ D ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[291]) ).
thf(375,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY3312: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ C @ B @ A ) @ SY3312 ) @ A )
| ~ ( in @ SY3312 @ B ) )
| ~ ( in @ ( sK52_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK52_D @ C @ B @ A ) @ ( sK53_SY3313 @ C @ B @ A ) ) @ A )
& ( in @ ( sK53_SY3313 @ C @ B @ A ) @ B ) )
| ( in @ ( sK52_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( relation_inverse_image @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( relation_inverse_image @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ~ ( in @ E @ B ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( ordered_pair @ D @ ( sK51_E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( sK51_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[292]) ).
thf(376,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY3314: $i] :
( ~ ( in @ ( ordered_pair @ SY3314 @ ( sK55_D @ C @ B @ A ) ) @ A )
| ~ ( in @ SY3314 @ B ) )
| ~ ( in @ ( sK55_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK56_SY3315 @ C @ B @ A ) @ ( sK55_D @ C @ B @ A ) ) @ A )
& ( in @ ( sK56_SY3315 @ C @ B @ A ) @ B ) )
| ( in @ ( sK55_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( relation_image @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( relation_image @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i] :
( ~ ( in @ ( ordered_pair @ E @ D ) @ A )
| ~ ( in @ E @ B ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( ordered_pair @ ( sK54_E @ D @ C @ B @ A ) @ D ) @ A )
& ( in @ ( sK54_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[293]) ).
thf(377,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK57_D @ C @ B @ A ) @ ( relation_dom @ A ) )
| ~ ( in @ ( apply @ A @ ( sK57_D @ C @ B @ A ) ) @ B )
| ~ ( in @ ( sK57_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK57_D @ C @ B @ A ) @ ( relation_dom @ A ) )
| ( in @ ( sK57_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( apply @ A @ ( sK57_D @ C @ B @ A ) ) @ B )
| ( in @ ( sK57_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( relation_inverse_image @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( relation_inverse_image @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ ( relation_dom @ A ) )
| ~ ( in @ ( apply @ A @ D ) @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ ( relation_dom @ A ) ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ ( apply @ A @ D ) @ B ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[294]) ).
thf(378,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK59_SY3316 @ C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY3316 @ C @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY3316 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK59_SY3316 @ C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY3316 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY3316 @ C @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY3316 @ C @ B @ A ) ) @ C ) ) )
| ( C
= ( relation_rng_restriction @ A @ B ) ) )
& ! [C: $i] :
( ~ ( relation @ C )
| ( C
!= ( relation_rng_restriction @ A @ B ) )
| ( ! [D: $i,E: $i] :
( ~ ( in @ E @ A )
| ~ ( in @ ( ordered_pair @ D @ E ) @ B )
| ( in @ ( ordered_pair @ D @ E ) @ C ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ E @ A ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ ( ordered_pair @ D @ E ) @ B ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[295]) ).
thf(379,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY3317: $i] :
( ~ ( in @ SY3317 @ ( relation_dom @ A ) )
| ~ ( in @ SY3317 @ B )
| ( ( sK61_D @ C @ B @ A )
!= ( apply @ A @ SY3317 ) ) )
| ~ ( in @ ( sK61_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK62_SY3318 @ C @ B @ A ) @ ( relation_dom @ A ) )
& ( in @ ( sK62_SY3318 @ C @ B @ A ) @ B )
& ( ( sK61_D @ C @ B @ A )
= ( apply @ A @ ( sK62_SY3318 @ C @ B @ A ) ) ) )
| ( in @ ( sK61_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( relation_image @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( relation_image @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i] :
( ~ ( in @ E @ ( relation_dom @ A ) )
| ~ ( in @ E @ B )
| ( D
!= ( apply @ A @ E ) ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( sK60_E @ D @ C @ B @ A ) @ ( relation_dom @ A ) )
& ( in @ ( sK60_E @ D @ C @ B @ A ) @ B )
& ( D
= ( apply @ A @ ( sK60_E @ D @ C @ B @ A ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[296]) ).
thf(380,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK63_D @ C @ B @ A ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ C @ B @ A ) @ ( sK64_SY3319 @ C @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ C @ B @ A ) @ ( sK64_SY3319 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK63_D @ C @ B @ A ) @ B )
| ( in @ ( ordered_pair @ ( sK63_D @ C @ B @ A ) @ ( sK64_SY3319 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK63_D @ C @ B @ A ) @ ( sK64_SY3319 @ C @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK63_D @ C @ B @ A ) @ ( sK64_SY3319 @ C @ B @ A ) ) @ C ) ) )
| ( C
= ( relation_dom_restriction @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ( C
!= ( relation_dom_restriction @ A @ B ) )
| ( ! [D: $i,E: $i] :
( ~ ( in @ D @ B )
| ~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ( in @ ( ordered_pair @ D @ E ) @ C ) )
& ! [D: $i] :
( ! [E: $i] :
~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ D @ B ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ ( ordered_pair @ D @ E ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[297]) ).
thf(381,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( ( ( sK65_C @ B @ A )
!= ( sK66_SY3320 @ B @ A ) )
| ~ ( in @ ( sK65_C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ B @ A ) @ ( sK66_SY3320 @ B @ A ) ) @ B ) )
& ( ( ( sK65_C @ B @ A )
= ( sK66_SY3320 @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK65_C @ B @ A ) @ ( sK66_SY3320 @ B @ A ) ) @ B ) )
& ( ( in @ ( sK65_C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK65_C @ B @ A ) @ ( sK66_SY3320 @ B @ A ) ) @ B ) ) )
| ( B
= ( identity_relation @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( B
!= ( identity_relation @ A ) )
| ( ! [C: $i,D: $i] :
( ( C != D )
| ~ ( in @ C @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ B )
| ( C = D ) )
& ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ C @ D ) @ B )
| ( in @ C @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[298]) ).
thf(382,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[299]) ).
thf(383,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[300]) ).
thf(384,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ( B
!= ( apply @ C @ A ) )
| ~ ( in @ A @ ( relation_dom @ C ) )
| ( in @ ( ordered_pair @ A @ B ) @ C ) )
& ! [B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( B
= ( apply @ C @ A ) ) )
& ! [B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ A @ ( relation_dom @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[301]) ).
thf(385,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ B )
| ~ ( in @ A @ ( relation_dom @ C ) )
| ( in @ A @ ( relation_dom @ ( relation_dom_restriction @ C @ B ) ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ ( relation_dom_restriction @ C @ B ) ) )
| ( in @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ ( relation_dom_restriction @ C @ B ) ) )
| ( in @ A @ ( relation_dom @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[302]) ).
thf(386,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ~ ( relation @ D )
| ~ ( in @ A @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( relation_composition @ ( identity_relation @ C ) @ D ) ) )
& ! [C: $i,D: $i] :
( ~ ( relation @ D )
| ~ ( in @ ( ordered_pair @ A @ B ) @ ( relation_composition @ ( identity_relation @ C ) @ D ) )
| ( in @ A @ C ) )
& ! [C: $i,D: $i] :
( ~ ( relation @ D )
| ~ ( in @ ( ordered_pair @ A @ B ) @ ( relation_composition @ ( identity_relation @ C ) @ D ) )
| ( in @ ( ordered_pair @ A @ B ) @ D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[303]) ).
thf(387,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ B @ A )
| ( ( apply @ ( relation_dom_restriction @ C @ A ) @ B )
= ( apply @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[304]) ).
thf(388,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
| ( ( apply @ ( relation_dom_restriction @ C @ A ) @ B )
= ( apply @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[305]) ).
thf(389,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ( ( in @ ( sK67_D @ C @ B @ A ) @ ( relation_dom @ B ) )
& ( ( apply @ B @ ( sK67_D @ C @ B @ A ) )
!= ( apply @ C @ ( sK67_D @ C @ B @ A ) ) ) )
| ( ( relation_dom @ B )
!= ( set_intersection2 @ ( relation_dom @ C ) @ A ) )
| ( B
= ( relation_dom_restriction @ C @ A ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ( B
!= ( relation_dom_restriction @ C @ A ) )
| ! [D: $i] :
( ~ ( in @ D @ ( relation_dom @ B ) )
| ( ( apply @ B @ D )
= ( apply @ C @ D ) ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ( B
!= ( relation_dom_restriction @ C @ A ) )
| ( ( relation_dom @ B )
= ( set_intersection2 @ ( relation_dom @ C ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[306]) ).
thf(390,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
!= A )
| ~ ( in @ B @ A ) )
& ! [A: $i,B: $i] :
( ( in @ B @ A )
| ( ( set_difference @ A @ ( singleton @ B ) )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[307]) ).
thf(391,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ~ ( in @ A @ ( relation_rng @ B ) )
| ~ ( one_to_one @ B )
| ( A
= ( apply @ B @ ( apply @ ( function_inverse @ B ) @ A ) ) ) )
& ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ~ ( in @ A @ ( relation_rng @ B ) )
| ~ ( one_to_one @ B )
| ( A
= ( apply @ ( relation_composition @ ( function_inverse @ B ) @ B ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[308]) ).
thf(392,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK68_B @ A ) @ ( sK69_SY3321 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[309]) ).
thf(393,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( in @ B @ ( subset_complement @ A @ C ) )
| ~ ( in @ B @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[310]) ).
thf(394,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ! [B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ( ( ( sK71_SY3322 @ B @ A )
= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ( ( sK70_C @ B @ A )
= ( apply @ A @ ( sK71_SY3322 @ B @ A ) ) ) )
& ( ( ( sK71_SY3322 @ B @ A )
= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ( in @ ( sK71_SY3322 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( ( sK71_SY3322 @ B @ A )
= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ( ( sK71_SY3322 @ B @ A )
!= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ~ ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) ) )
& ( ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) )
| ( ( sK70_C @ B @ A )
= ( apply @ A @ ( sK71_SY3322 @ B @ A ) ) ) )
& ( ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) )
| ( in @ ( sK71_SY3322 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) )
| ( ( sK71_SY3322 @ B @ A )
!= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ~ ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) ) )
& ( ( ( sK70_C @ B @ A )
!= ( apply @ A @ ( sK71_SY3322 @ B @ A ) ) )
| ~ ( in @ ( sK71_SY3322 @ B @ A ) @ ( relation_dom @ A ) )
| ( ( sK70_C @ B @ A )
= ( apply @ A @ ( sK71_SY3322 @ B @ A ) ) ) )
& ( ( ( sK70_C @ B @ A )
!= ( apply @ A @ ( sK71_SY3322 @ B @ A ) ) )
| ~ ( in @ ( sK71_SY3322 @ B @ A ) @ ( relation_dom @ A ) )
| ( in @ ( sK71_SY3322 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( ( sK70_C @ B @ A )
!= ( apply @ A @ ( sK71_SY3322 @ B @ A ) ) )
| ~ ( in @ ( sK71_SY3322 @ B @ A ) @ ( relation_dom @ A ) )
| ( ( sK71_SY3322 @ B @ A )
!= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ~ ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) ) ) )
| ( ( relation_dom @ B )
!= ( relation_rng @ A ) )
| ( B
= ( function_inverse @ A ) ) )
& ! [B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( B
!= ( function_inverse @ A ) )
| ( ! [C: $i,D: $i] :
( ( D
!= ( apply @ B @ C ) )
| ~ ( in @ C @ ( relation_rng @ A ) )
| ( C
= ( apply @ A @ D ) ) )
& ! [C: $i,D: $i] :
( ( D
!= ( apply @ B @ C ) )
| ~ ( in @ C @ ( relation_rng @ A ) )
| ( in @ D @ ( relation_dom @ A ) ) )
& ! [C: $i,D: $i] :
( ( C
!= ( apply @ A @ D ) )
| ~ ( in @ D @ ( relation_dom @ A ) )
| ( D
= ( apply @ B @ C ) ) )
& ! [C: $i] :
( ! [D: $i] :
( ( C
!= ( apply @ A @ D ) )
| ~ ( in @ D @ ( relation_dom @ A ) ) )
| ( in @ C @ ( relation_rng @ A ) ) ) ) )
& ! [B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( B
!= ( function_inverse @ A ) )
| ( ( relation_dom @ B )
= ( relation_rng @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[311]) ).
thf(395,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( element @ C @ A )
| ( in @ C @ B )
| ( in @ C @ ( subset_complement @ A @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[312]) ).
thf(396,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK72_C @ B @ A ) @ ( set_intersection2 @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[313]) ).
thf(397,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[314]) ).
thf(398,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK73_C @ B @ A ) @ A )
& ( in @ ( sK73_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[315]) ).
thf(399,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ C )
| ~ ( in @ C @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[316]) ).
thf(400,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ C )
| ( subset @ ( unordered_pair @ A @ B ) @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ A @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[317]) ).
thf(401,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[318]) ).
thf(402,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ A )
| ( ( apply @ ( identity_relation @ A ) @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[319]) ).
thf(403,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ( in @ ( sK74_C @ B @ A ) @ A )
& ( ( apply @ B @ ( sK74_C @ B @ A ) )
!= ( sK74_C @ B @ A ) ) )
| ( ( relation_dom @ B )
!= A )
| ( B
= ( identity_relation @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( B
!= ( identity_relation @ A ) )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( ( apply @ B @ C )
= C ) ) )
& ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( B
!= ( identity_relation @ A ) )
| ( ( relation_dom @ B )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[320]) ).
thf(404,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ A @ ( relation_field @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ B @ ( relation_field @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[321]) ).
thf(405,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ B ) )
| ( ( apply @ ( relation_composition @ B @ C ) @ A )
= ( apply @ C @ ( apply @ B @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[322]) ).
thf(406,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
| ( ( apply @ ( relation_composition @ C @ B ) @ A )
= ( apply @ B @ ( apply @ C @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[323]) ).
thf(407,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ C ) )
| ~ ( in @ ( apply @ C @ A ) @ ( relation_dom @ B ) )
| ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
| ( in @ A @ ( relation_dom @ C ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
| ( in @ ( apply @ C @ A ) @ ( relation_dom @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[324]) ).
thf(408,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ A @ ( relation_dom @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ B @ ( relation_rng @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[325]) ).
thf(409,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ! [D: $i] :
( ~ ( in @ D @ ( relation_rng @ C ) )
| ~ ( in @ ( ordered_pair @ A @ D ) @ C )
| ~ ( in @ D @ B ) )
| ( in @ A @ ( relation_inverse_image @ C @ B ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_inverse_image @ C @ B ) )
| ( ( in @ ( sK75_D @ C @ B @ A ) @ ( relation_rng @ C ) )
& ( in @ ( ordered_pair @ A @ ( sK75_D @ C @ B @ A ) ) @ C )
& ( in @ ( sK75_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[326]) ).
thf(410,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ! [D: $i] :
( ~ ( in @ D @ ( relation_dom @ C ) )
| ~ ( in @ ( ordered_pair @ D @ A ) @ C )
| ~ ( in @ D @ B ) )
| ( in @ A @ ( relation_image @ C @ B ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_image @ C @ B ) )
| ( ( in @ ( sK76_D @ C @ B @ A ) @ ( relation_dom @ C ) )
& ( in @ ( ordered_pair @ ( sK76_D @ C @ B @ A ) @ A ) @ C )
& ( in @ ( sK76_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[327]) ).
thf(411,plain,
( ( ! [A: $i] :
( ! [SY3323: $i] :
( ~ ( subset @ SY3323 @ ( sK77_B @ A ) )
| ( are_equipotent @ SY3323 @ ( sK77_B @ A ) )
| ( in @ SY3323 @ ( sK77_B @ A ) ) )
& ! [SY3324: $i] :
( ~ ( in @ SY3324 @ ( sK77_B @ A ) )
| ( in @ ( powerset @ SY3324 ) @ ( sK77_B @ A ) ) )
& ! [SY3325: $i,SY3326: $i] :
( ~ ( in @ SY3325 @ ( sK77_B @ A ) )
| ~ ( subset @ SY3326 @ SY3325 )
| ( in @ SY3326 @ ( sK77_B @ A ) ) )
& ( in @ A @ ( sK77_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[328]) ).
thf(412,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ B )
| ~ ( in @ A @ ( relation_rng @ C ) )
| ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) )
| ( in @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) )
| ( in @ A @ ( relation_rng @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[329]) ).
thf(413,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) )
& ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ A @ C ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ B @ D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[330]) ).
thf(414,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ B @ ( relation_dom @ C ) )
| ~ ( in @ B @ A )
| ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) ) )
& ! [B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
| ( in @ B @ ( relation_dom @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
| ( in @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[331]) ).
thf(415,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK78_C @ B @ A ) @ A )
& ~ ( in @ ( sK78_C @ B @ A ) @ B ) )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[332]) ).
thf(416,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) )
& ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ A @ C ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ B @ D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[333]) ).
thf(417,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[334]) ).
thf(418,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[335]) ).
thf(419,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[336]) ).
thf(420,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[337]) ).
thf(421,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[338]) ).
thf(422,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[339]) ).
thf(423,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[340]) ).
thf(424,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(425,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(426,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(427,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(428,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[419]) ).
thf(429,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[418]) ).
thf(430,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(431,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) )
& ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ A @ C ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(432,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK78_C @ B @ A ) @ A )
& ~ ( in @ ( sK78_C @ B @ A ) @ B ) )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(433,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ B @ ( relation_dom @ C ) )
| ~ ( in @ B @ A )
| ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) ) )
& ! [B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
| ( in @ B @ ( relation_dom @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
| ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[414]) ).
thf(434,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) )
& ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ A @ C ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(435,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ B )
| ~ ( in @ A @ ( relation_rng @ C ) )
| ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) )
| ( in @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) )
| ( in @ A @ ( relation_rng @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(436,plain,
( ( ! [A: $i] :
( ! [SY3323: $i] :
( ~ ( subset @ SY3323 @ ( sK77_B @ A ) )
| ( are_equipotent @ SY3323 @ ( sK77_B @ A ) )
| ( in @ SY3323 @ ( sK77_B @ A ) ) )
& ! [SY3324: $i] :
( ~ ( in @ SY3324 @ ( sK77_B @ A ) )
| ( in @ ( powerset @ SY3324 ) @ ( sK77_B @ A ) ) )
& ! [SY3325: $i,SY3326: $i] :
( ~ ( in @ SY3325 @ ( sK77_B @ A ) )
| ~ ( subset @ SY3326 @ SY3325 )
| ( in @ SY3326 @ ( sK77_B @ A ) ) )
& ( in @ A @ ( sK77_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(437,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ! [D: $i] :
( ~ ( in @ D @ ( relation_dom @ C ) )
| ~ ( in @ ( ordered_pair @ D @ A ) @ C )
| ~ ( in @ D @ B ) )
| ( in @ A @ ( relation_image @ C @ B ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_image @ C @ B ) )
| ( ( in @ ( sK76_D @ C @ B @ A ) @ ( relation_dom @ C ) )
& ( in @ ( ordered_pair @ ( sK76_D @ C @ B @ A ) @ A ) @ C )
& ( in @ ( sK76_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(438,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ! [D: $i] :
( ~ ( in @ D @ ( relation_rng @ C ) )
| ~ ( in @ ( ordered_pair @ A @ D ) @ C )
| ~ ( in @ D @ B ) )
| ( in @ A @ ( relation_inverse_image @ C @ B ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_inverse_image @ C @ B ) )
| ( ( in @ ( sK75_D @ C @ B @ A ) @ ( relation_rng @ C ) )
& ( in @ ( ordered_pair @ A @ ( sK75_D @ C @ B @ A ) ) @ C )
& ( in @ ( sK75_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(439,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ A @ ( relation_dom @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ B @ ( relation_rng @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(440,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ C ) )
| ~ ( in @ ( apply @ C @ A ) @ ( relation_dom @ B ) )
| ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
| ( in @ A @ ( relation_dom @ C ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
| ( in @ ( apply @ C @ A ) @ ( relation_dom @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(441,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
| ( ( apply @ ( relation_composition @ C @ B ) @ A )
= ( apply @ B @ ( apply @ C @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[406]) ).
thf(442,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ B ) )
| ( ( apply @ ( relation_composition @ B @ C ) @ A )
= ( apply @ C @ ( apply @ B @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(443,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ A @ ( relation_field @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ B @ ( relation_field @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(444,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ( in @ ( sK74_C @ B @ A ) @ A )
& ( ( apply @ B @ ( sK74_C @ B @ A ) )
!= ( sK74_C @ B @ A ) ) )
| ( ( relation_dom @ B )
!= A )
| ( B
= ( identity_relation @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( B
!= ( identity_relation @ A ) )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( ( apply @ B @ C )
= C ) ) )
& ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( B
!= ( identity_relation @ A ) )
| ( ( relation_dom @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(445,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ A )
| ( ( apply @ ( identity_relation @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(446,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[401]) ).
thf(447,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ C )
| ( subset @ ( unordered_pair @ A @ B ) @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ A @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[400]) ).
thf(448,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ C )
| ~ ( in @ C @ A ) ) )
= $true ),
inference(copy,[status(thm)],[399]) ).
thf(449,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK73_C @ B @ A ) @ A )
& ( in @ ( sK73_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[398]) ).
thf(450,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[397]) ).
thf(451,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK72_C @ B @ A ) @ ( set_intersection2 @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(452,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( element @ C @ A )
| ( in @ C @ B )
| ( in @ C @ ( subset_complement @ A @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[395]) ).
thf(453,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ! [B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ( ( ( sK71_SY3322 @ B @ A )
= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ( ( sK70_C @ B @ A )
= ( apply @ A @ ( sK71_SY3322 @ B @ A ) ) ) )
& ( ( ( sK71_SY3322 @ B @ A )
= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ( in @ ( sK71_SY3322 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( ( sK71_SY3322 @ B @ A )
= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ( ( sK71_SY3322 @ B @ A )
!= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ~ ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) ) )
& ( ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) )
| ( ( sK70_C @ B @ A )
= ( apply @ A @ ( sK71_SY3322 @ B @ A ) ) ) )
& ( ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) )
| ( in @ ( sK71_SY3322 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) )
| ( ( sK71_SY3322 @ B @ A )
!= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ~ ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) ) )
& ( ( ( sK70_C @ B @ A )
!= ( apply @ A @ ( sK71_SY3322 @ B @ A ) ) )
| ~ ( in @ ( sK71_SY3322 @ B @ A ) @ ( relation_dom @ A ) )
| ( ( sK70_C @ B @ A )
= ( apply @ A @ ( sK71_SY3322 @ B @ A ) ) ) )
& ( ( ( sK70_C @ B @ A )
!= ( apply @ A @ ( sK71_SY3322 @ B @ A ) ) )
| ~ ( in @ ( sK71_SY3322 @ B @ A ) @ ( relation_dom @ A ) )
| ( in @ ( sK71_SY3322 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( ( sK70_C @ B @ A )
!= ( apply @ A @ ( sK71_SY3322 @ B @ A ) ) )
| ~ ( in @ ( sK71_SY3322 @ B @ A ) @ ( relation_dom @ A ) )
| ( ( sK71_SY3322 @ B @ A )
!= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ~ ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) ) ) )
| ( ( relation_dom @ B )
!= ( relation_rng @ A ) )
| ( B
= ( function_inverse @ A ) ) )
& ! [B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( B
!= ( function_inverse @ A ) )
| ( ! [C: $i,D: $i] :
( ( D
!= ( apply @ B @ C ) )
| ~ ( in @ C @ ( relation_rng @ A ) )
| ( C
= ( apply @ A @ D ) ) )
& ! [C: $i,D: $i] :
( ( D
!= ( apply @ B @ C ) )
| ~ ( in @ C @ ( relation_rng @ A ) )
| ( in @ D @ ( relation_dom @ A ) ) )
& ! [C: $i,D: $i] :
( ( C
!= ( apply @ A @ D ) )
| ~ ( in @ D @ ( relation_dom @ A ) )
| ( D
= ( apply @ B @ C ) ) )
& ! [C: $i] :
( ! [D: $i] :
( ( C
!= ( apply @ A @ D ) )
| ~ ( in @ D @ ( relation_dom @ A ) ) )
| ( in @ C @ ( relation_rng @ A ) ) ) ) )
& ! [B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( B
!= ( function_inverse @ A ) )
| ( ( relation_dom @ B )
= ( relation_rng @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[394]) ).
thf(454,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( in @ B @ ( subset_complement @ A @ C ) )
| ~ ( in @ B @ C ) ) )
= $true ),
inference(copy,[status(thm)],[393]) ).
thf(455,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK68_B @ A ) @ ( sK69_SY3321 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[392]) ).
thf(456,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ~ ( in @ A @ ( relation_rng @ B ) )
| ~ ( one_to_one @ B )
| ( A
= ( apply @ B @ ( apply @ ( function_inverse @ B ) @ A ) ) ) )
& ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ~ ( in @ A @ ( relation_rng @ B ) )
| ~ ( one_to_one @ B )
| ( A
= ( apply @ ( relation_composition @ ( function_inverse @ B ) @ B ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[391]) ).
thf(457,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
!= A )
| ~ ( in @ B @ A ) )
& ! [A: $i,B: $i] :
( ( in @ B @ A )
| ( ( set_difference @ A @ ( singleton @ B ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[390]) ).
thf(458,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ( ( in @ ( sK67_D @ C @ B @ A ) @ ( relation_dom @ B ) )
& ( ( apply @ B @ ( sK67_D @ C @ B @ A ) )
!= ( apply @ C @ ( sK67_D @ C @ B @ A ) ) ) )
| ( ( relation_dom @ B )
!= ( set_intersection2 @ ( relation_dom @ C ) @ A ) )
| ( B
= ( relation_dom_restriction @ C @ A ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ( B
!= ( relation_dom_restriction @ C @ A ) )
| ! [D: $i] :
( ~ ( in @ D @ ( relation_dom @ B ) )
| ( ( apply @ B @ D )
= ( apply @ C @ D ) ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ( B
!= ( relation_dom_restriction @ C @ A ) )
| ( ( relation_dom @ B )
= ( set_intersection2 @ ( relation_dom @ C ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(459,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
| ( ( apply @ ( relation_dom_restriction @ C @ A ) @ B )
= ( apply @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[388]) ).
thf(460,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ B @ A )
| ( ( apply @ ( relation_dom_restriction @ C @ A ) @ B )
= ( apply @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[387]) ).
thf(461,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ~ ( relation @ D )
| ~ ( in @ A @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( relation_composition @ ( identity_relation @ C ) @ D ) ) )
& ! [C: $i,D: $i] :
( ~ ( relation @ D )
| ~ ( in @ ( ordered_pair @ A @ B ) @ ( relation_composition @ ( identity_relation @ C ) @ D ) )
| ( in @ A @ C ) )
& ! [C: $i,D: $i] :
( ~ ( relation @ D )
| ~ ( in @ ( ordered_pair @ A @ B ) @ ( relation_composition @ ( identity_relation @ C ) @ D ) )
| ( in @ ( ordered_pair @ A @ B ) @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[386]) ).
thf(462,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ B )
| ~ ( in @ A @ ( relation_dom @ C ) )
| ( in @ A @ ( relation_dom @ ( relation_dom_restriction @ C @ B ) ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ ( relation_dom_restriction @ C @ B ) ) )
| ( in @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ ( relation_dom_restriction @ C @ B ) ) )
| ( in @ A @ ( relation_dom @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[385]) ).
thf(463,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ( B
!= ( apply @ C @ A ) )
| ~ ( in @ A @ ( relation_dom @ C ) )
| ( in @ ( ordered_pair @ A @ B ) @ C ) )
& ! [B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( B
= ( apply @ C @ A ) ) )
& ! [B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ A @ ( relation_dom @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[384]) ).
thf(464,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(465,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[382]) ).
thf(466,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( ( ( sK65_C @ B @ A )
!= ( sK66_SY3320 @ B @ A ) )
| ~ ( in @ ( sK65_C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ B @ A ) @ ( sK66_SY3320 @ B @ A ) ) @ B ) )
& ( ( ( sK65_C @ B @ A )
= ( sK66_SY3320 @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK65_C @ B @ A ) @ ( sK66_SY3320 @ B @ A ) ) @ B ) )
& ( ( in @ ( sK65_C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK65_C @ B @ A ) @ ( sK66_SY3320 @ B @ A ) ) @ B ) ) )
| ( B
= ( identity_relation @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( B
!= ( identity_relation @ A ) )
| ( ! [C: $i,D: $i] :
( ( C != D )
| ~ ( in @ C @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ B )
| ( C = D ) )
& ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ C @ D ) @ B )
| ( in @ C @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[381]) ).
thf(467,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK63_D @ C @ B @ A ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ C @ B @ A ) @ ( sK64_SY3319 @ C @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ C @ B @ A ) @ ( sK64_SY3319 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK63_D @ C @ B @ A ) @ B )
| ( in @ ( ordered_pair @ ( sK63_D @ C @ B @ A ) @ ( sK64_SY3319 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK63_D @ C @ B @ A ) @ ( sK64_SY3319 @ C @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK63_D @ C @ B @ A ) @ ( sK64_SY3319 @ C @ B @ A ) ) @ C ) ) )
| ( C
= ( relation_dom_restriction @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ( C
!= ( relation_dom_restriction @ A @ B ) )
| ( ! [D: $i,E: $i] :
( ~ ( in @ D @ B )
| ~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ( in @ ( ordered_pair @ D @ E ) @ C ) )
& ! [D: $i] :
( ! [E: $i] :
~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ D @ B ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ ( ordered_pair @ D @ E ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[380]) ).
thf(468,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY3317: $i] :
( ~ ( in @ SY3317 @ ( relation_dom @ A ) )
| ~ ( in @ SY3317 @ B )
| ( ( sK61_D @ C @ B @ A )
!= ( apply @ A @ SY3317 ) ) )
| ~ ( in @ ( sK61_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK62_SY3318 @ C @ B @ A ) @ ( relation_dom @ A ) )
& ( in @ ( sK62_SY3318 @ C @ B @ A ) @ B )
& ( ( sK61_D @ C @ B @ A )
= ( apply @ A @ ( sK62_SY3318 @ C @ B @ A ) ) ) )
| ( in @ ( sK61_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( relation_image @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( relation_image @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i] :
( ~ ( in @ E @ ( relation_dom @ A ) )
| ~ ( in @ E @ B )
| ( D
!= ( apply @ A @ E ) ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( sK60_E @ D @ C @ B @ A ) @ ( relation_dom @ A ) )
& ( in @ ( sK60_E @ D @ C @ B @ A ) @ B )
& ( D
= ( apply @ A @ ( sK60_E @ D @ C @ B @ A ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(469,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK59_SY3316 @ C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY3316 @ C @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY3316 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK59_SY3316 @ C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY3316 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY3316 @ C @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY3316 @ C @ B @ A ) ) @ C ) ) )
| ( C
= ( relation_rng_restriction @ A @ B ) ) )
& ! [C: $i] :
( ~ ( relation @ C )
| ( C
!= ( relation_rng_restriction @ A @ B ) )
| ( ! [D: $i,E: $i] :
( ~ ( in @ E @ A )
| ~ ( in @ ( ordered_pair @ D @ E ) @ B )
| ( in @ ( ordered_pair @ D @ E ) @ C ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ E @ A ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ ( ordered_pair @ D @ E ) @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[378]) ).
thf(470,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK57_D @ C @ B @ A ) @ ( relation_dom @ A ) )
| ~ ( in @ ( apply @ A @ ( sK57_D @ C @ B @ A ) ) @ B )
| ~ ( in @ ( sK57_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK57_D @ C @ B @ A ) @ ( relation_dom @ A ) )
| ( in @ ( sK57_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( apply @ A @ ( sK57_D @ C @ B @ A ) ) @ B )
| ( in @ ( sK57_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( relation_inverse_image @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( relation_inverse_image @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ ( relation_dom @ A ) )
| ~ ( in @ ( apply @ A @ D ) @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ ( relation_dom @ A ) ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ ( apply @ A @ D ) @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(471,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY3314: $i] :
( ~ ( in @ ( ordered_pair @ SY3314 @ ( sK55_D @ C @ B @ A ) ) @ A )
| ~ ( in @ SY3314 @ B ) )
| ~ ( in @ ( sK55_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK56_SY3315 @ C @ B @ A ) @ ( sK55_D @ C @ B @ A ) ) @ A )
& ( in @ ( sK56_SY3315 @ C @ B @ A ) @ B ) )
| ( in @ ( sK55_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( relation_image @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( relation_image @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i] :
( ~ ( in @ ( ordered_pair @ E @ D ) @ A )
| ~ ( in @ E @ B ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( ordered_pair @ ( sK54_E @ D @ C @ B @ A ) @ D ) @ A )
& ( in @ ( sK54_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(472,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY3312: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ C @ B @ A ) @ SY3312 ) @ A )
| ~ ( in @ SY3312 @ B ) )
| ~ ( in @ ( sK52_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK52_D @ C @ B @ A ) @ ( sK53_SY3313 @ C @ B @ A ) ) @ A )
& ( in @ ( sK53_SY3313 @ C @ B @ A ) @ B ) )
| ( in @ ( sK52_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( relation_inverse_image @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( relation_inverse_image @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ~ ( in @ E @ B ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( ordered_pair @ D @ ( sK51_E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( sK51_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(473,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( ~ ( in @ ( sK50_E @ D @ C @ B @ A ) @ D )
| ( ( sK50_E @ D @ C @ B @ A )
!= C ) )
& ( ~ ( in @ ( sK50_E @ D @ C @ B @ A ) @ D )
| ( ( sK50_E @ D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK50_E @ D @ C @ B @ A ) @ D )
| ( ( sK50_E @ D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK50_E @ D @ C @ B @ A ) @ D )
| ( ( sK50_E @ D @ C @ B @ A )
= C )
| ( ( sK50_E @ D @ C @ B @ A )
= A )
| ( ( sK50_E @ D @ C @ B @ A )
= B ) ) )
| ( D
= ( unordered_triple @ A @ B @ C ) ) )
& ! [C: $i,D: $i] :
( ( D
!= ( unordered_triple @ A @ B @ C ) )
| ( ! [E: $i] :
( ~ ( in @ E @ D )
| ( E = C )
| ( E = A )
| ( E = B ) )
& ! [E: $i] :
( ( E != C )
| ( in @ E @ D ) )
& ! [E: $i] :
( ( E != A )
| ( in @ E @ D ) )
& ! [E: $i] :
( ( E != B )
| ( in @ E @ D ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(474,plain,
( ( ! [A: $i] :
( ( succ @ A )
= ( set_union2 @ A @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[290]) ).
thf(475,plain,
( ( ! [A: $i] :
( ( ! [SY3310: $i,SY3311: $i] :
( ( sK49_B @ A )
!= ( ordered_pair @ SY3310 @ SY3311 ) )
& ( in @ ( sK49_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK47_C @ B @ A ) @ ( sK48_SY3309 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(476,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( ( ( ( in @ ( sK46_SY3307 @ B @ A ) @ A )
& ~ ( in @ ( sK45_C @ B @ A ) @ ( sK46_SY3307 @ B @ A ) ) )
| ~ ( in @ ( sK45_C @ B @ A ) @ B ) )
& ( ! [SY3308: $i] :
( ~ ( in @ SY3308 @ A )
| ( in @ ( sK45_C @ B @ A ) @ SY3308 ) )
| ( in @ ( sK45_C @ B @ A ) @ B ) ) )
| ( B
= ( set_meet @ A ) ) ) )
& ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( ! [C: $i] :
( ( ( in @ ( sK44_D @ C @ B @ A ) @ A )
& ~ ( in @ C @ ( sK44_D @ C @ B @ A ) ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ C @ D ) ) ) ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( B = empty_set ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
( ( B != empty_set )
| ( B
= ( set_meet @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(477,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK43_C @ B @ A )
!= A )
| ~ ( in @ ( sK43_C @ B @ A ) @ B ) )
& ( ( ( sK43_C @ B @ A )
= A )
| ( in @ ( sK43_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(478,plain,
( ( ! [A: $i] :
( ( in @ ( sK42_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(479,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK41_C @ B @ A ) @ B )
| ~ ( subset @ ( sK41_C @ B @ A ) @ A ) )
& ( ( in @ ( sK41_C @ B @ A ) @ B )
| ( subset @ ( sK41_C @ B @ A ) @ A ) ) )
| ( B
= ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( in @ C @ B )
| ( subset @ C @ A ) )
& ! [C: $i] :
( ~ ( subset @ C @ A )
| ( in @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(480,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK39_C @ B @ A ) @ ( sK40_SY3306 @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK39_C @ B @ A ) @ ( sK40_SY3306 @ B @ A ) ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK39_C @ B @ A ) @ ( sK40_SY3306 @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK39_C @ B @ A ) @ ( sK40_SY3306 @ B @ A ) ) @ B ) ) )
| ( A = B ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ( A != B )
| ( ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ B )
| ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(481,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( in @ B @ A ) ) )
& ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( in @ B @ A )
| ( element @ B @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( empty @ B ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( empty @ B )
| ( element @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(482,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK38_D @ C @ B @ A ) @ C )
| ( ( sK38_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK38_D @ C @ B @ A ) @ C )
| ( ( sK38_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK38_D @ C @ B @ A ) @ C )
| ( ( sK38_D @ C @ B @ A )
= A )
| ( ( sK38_D @ C @ B @ A )
= B ) ) )
| ( C
= ( unordered_pair @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( unordered_pair @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( D = A )
| ( D = B ) )
& ! [D: $i] :
( ( D != A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ( D != B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(483,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK37_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK37_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK37_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK37_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK37_D @ C @ B @ A ) @ C )
| ( in @ ( sK37_D @ C @ B @ A ) @ A )
| ( in @ ( sK37_D @ C @ B @ A ) @ B ) ) )
| ( C
= ( set_union2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A )
| ( in @ D @ B ) )
& ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(484,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY3301: $i,SY3302: $i] :
( ~ ( in @ SY3301 @ A )
| ~ ( in @ SY3302 @ B )
| ( ( sK34_D @ C @ B @ A )
!= ( ordered_pair @ SY3301 @ SY3302 ) ) )
| ~ ( in @ ( sK34_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK35_SY3303 @ C @ B @ A ) @ A )
& ( in @ ( sK36_SY3305 @ C @ B @ A ) @ B )
& ( ( sK34_D @ C @ B @ A )
= ( ordered_pair @ ( sK35_SY3303 @ C @ B @ A ) @ ( sK36_SY3305 @ C @ B @ A ) ) ) )
| ( in @ ( sK34_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( cartesian_product2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( cartesian_product2 @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i,F: $i] :
( ~ ( in @ E @ A )
| ~ ( in @ F @ B )
| ( D
!= ( ordered_pair @ E @ F ) ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( sK32_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK33_SY3300 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK32_E @ D @ C @ B @ A ) @ ( sK33_SY3300 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(485,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( in @ ( ordered_pair @ ( sK30_C @ B @ A ) @ ( sK31_SY3299 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK30_C @ B @ A ) @ ( sK31_SY3299 @ B @ A ) ) @ B ) )
| ( subset @ A @ B ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(486,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK29_C @ B @ A ) @ A )
& ~ ( in @ ( sK29_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(487,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK28_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK28_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK28_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK28_D @ C @ B @ A ) @ A )
| ( in @ ( sK28_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK28_D @ C @ B @ A ) @ B )
| ( in @ ( sK28_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_intersection2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_intersection2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ~ ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(488,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C
!= ( apply @ A @ B ) )
| ( in @ ( ordered_pair @ B @ C ) @ A ) ) )
& ! [B: $i] :
( ~ ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ~ ( in @ ( ordered_pair @ B @ C ) @ A )
| ( C
= ( apply @ A @ B ) ) ) )
& ! [B: $i] :
( ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C
!= ( apply @ A @ B ) )
| ( C = empty_set ) ) )
& ! [B: $i] :
( ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C != empty_set )
| ( C
= ( apply @ A @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(489,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY3297: $i] :
~ ( in @ ( ordered_pair @ ( sK26_C @ B @ A ) @ SY3297 ) @ A )
| ~ ( in @ ( sK26_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK26_C @ B @ A ) @ ( sK27_SY3298 @ B @ A ) ) @ A )
| ( in @ ( sK26_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_dom @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_dom @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ C @ ( sK25_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(490,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY3295: $i] :
( ~ ( in @ ( sK23_C @ B @ A ) @ SY3295 )
| ~ ( in @ SY3295 @ A ) )
| ~ ( in @ ( sK23_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK23_C @ B @ A ) @ ( sK24_SY3296 @ B @ A ) )
& ( in @ ( sK24_SY3296 @ B @ A ) @ A ) )
| ( in @ ( sK23_C @ B @ A ) @ B ) ) )
| ( B
= ( union @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( union @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
( ~ ( in @ C @ D )
| ~ ( in @ D @ A ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( ( in @ C @ ( sK22_D @ C @ B @ A ) )
& ( in @ ( sK22_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(491,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK21_D @ C @ B @ A ) @ A )
| ( in @ ( sK21_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK21_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK21_D @ C @ B @ A ) @ A )
| ( in @ ( sK21_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK21_D @ C @ B @ A ) @ B )
| ( in @ ( sK21_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_difference @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_difference @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ~ ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[357]) ).
thf(492,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY3293: $i] :
( ( ( sK19_C @ B @ A )
!= ( apply @ A @ SY3293 ) )
| ~ ( in @ SY3293 @ ( relation_dom @ A ) ) )
| ~ ( in @ ( sK19_C @ B @ A ) @ B ) )
& ( ( ( ( sK19_C @ B @ A )
= ( apply @ A @ ( sK20_SY3294 @ B @ A ) ) )
& ( in @ ( sK20_SY3294 @ B @ A ) @ ( relation_dom @ A ) ) )
| ( in @ ( sK19_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_rng @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_rng @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
( ( C
!= ( apply @ A @ D ) )
| ~ ( in @ D @ ( relation_dom @ A ) ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( ( C
= ( apply @ A @ ( sK18_D @ C @ B @ A ) ) )
& ( in @ ( sK18_D @ C @ B @ A ) @ ( relation_dom @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[356]) ).
thf(493,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY3291: $i] :
~ ( in @ ( ordered_pair @ SY3291 @ ( sK16_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK16_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK17_SY3292 @ B @ A ) @ ( sK16_C @ B @ A ) ) @ A )
| ( in @ ( sK16_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_rng @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_rng @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ D @ C ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ ( sK15_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[355]) ).
thf(494,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK13_C @ B @ A ) @ ( sK14_SY3290 @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK14_SY3290 @ B @ A ) @ ( sK13_C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( sK13_C @ B @ A ) @ ( sK14_SY3290 @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK14_SY3290 @ B @ A ) @ ( sK13_C @ B @ A ) ) @ A ) ) )
| ( B
= ( relation_inverse @ A ) ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ( B
!= ( relation_inverse @ A ) )
| ( ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ B )
| ( in @ ( ordered_pair @ D @ C ) @ A ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ D @ C ) @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[354]) ).
thf(495,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ( in @ ( sK11_B @ A ) @ ( relation_dom @ A ) )
& ( in @ ( sK12_SY3289 @ A ) @ ( relation_dom @ A ) )
& ( ( apply @ A @ ( sK11_B @ A ) )
= ( apply @ A @ ( sK12_SY3289 @ A ) ) )
& ( ( sK11_B @ A )
!= ( sK12_SY3289 @ A ) ) )
| ( one_to_one @ A ) )
& ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ! [B: $i,C: $i] :
( ~ ( in @ B @ ( relation_dom @ A ) )
| ~ ( in @ C @ ( relation_dom @ A ) )
| ( ( apply @ A @ B )
!= ( apply @ A @ C ) )
| ( B = C ) ) ) )
= $true ),
inference(copy,[status(thm)],[353]) ).
thf(496,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ! [SY3287: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ C @ B @ A ) @ SY3287 ) @ A )
| ~ ( in @ ( ordered_pair @ SY3287 @ ( sK9_SY3284 @ C @ B @ A ) ) @ B ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ C @ B @ A ) @ ( sK9_SY3284 @ C @ B @ A ) ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK8_D @ C @ B @ A ) @ ( sK10_SY3288 @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK10_SY3288 @ C @ B @ A ) @ ( sK9_SY3284 @ C @ B @ A ) ) @ B ) )
| ( in @ ( ordered_pair @ ( sK8_D @ C @ B @ A ) @ ( sK9_SY3284 @ C @ B @ A ) ) @ C ) ) )
| ( C
= ( relation_composition @ A @ B ) ) )
& ! [C: $i] :
( ~ ( relation @ C )
| ( C
!= ( relation_composition @ A @ B ) )
| ( ! [D: $i,E: $i] :
( ! [F: $i] :
( ~ ( in @ ( ordered_pair @ D @ F ) @ A )
| ~ ( in @ ( ordered_pair @ F @ E ) @ B ) )
| ( in @ ( ordered_pair @ D @ E ) @ C ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( ( in @ ( ordered_pair @ D @ ( sK7_F @ E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK7_F @ E @ D @ C @ B @ A ) @ E ) @ B ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[352]) ).
thf(497,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ! [C: $i] :
( ~ ( element @ C @ ( powerset @ ( powerset @ A ) ) )
| ( ( element @ ( sK6_D @ C @ B @ A ) @ ( powerset @ A ) )
& ( ~ ( in @ ( sK6_D @ C @ B @ A ) @ C )
| ~ ( in @ ( subset_complement @ A @ ( sK6_D @ C @ B @ A ) ) @ B ) )
& ( ( in @ ( sK6_D @ C @ B @ A ) @ C )
| ( in @ ( subset_complement @ A @ ( sK6_D @ C @ B @ A ) ) @ B ) ) )
| ( C
= ( complements_of_subsets @ A @ B ) ) )
& ! [C: $i] :
( ~ ( element @ C @ ( powerset @ ( powerset @ A ) ) )
| ( C
!= ( complements_of_subsets @ A @ B ) )
| ( ! [D: $i] :
( ~ ( element @ D @ ( powerset @ A ) )
| ~ ( in @ D @ C )
| ( in @ ( subset_complement @ A @ D ) @ B ) )
& ! [D: $i] :
( ~ ( element @ D @ ( powerset @ A ) )
| ~ ( in @ ( subset_complement @ A @ D ) @ B )
| ( in @ D @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[351]) ).
thf(498,plain,
( ( ! [A: $i] :
~ ( empty @ ( succ @ A ) ) )
= $true ),
inference(copy,[status(thm)],[266]) ).
thf(499,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[350]) ).
thf(500,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[349]) ).
thf(501,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK5_C @ B @ A ) @ A )
| ~ ( in @ ( sK5_C @ B @ A ) @ B ) )
& ( ( in @ ( sK5_C @ B @ A ) @ A )
| ( in @ ( sK5_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[348]) ).
thf(502,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[347]) ).
thf(503,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[346]) ).
thf(504,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[345]) ).
thf(505,plain,
( ( ! [A: $i,B: $i] :
( ( ! [SY3283: $i] :
( ~ ( in @ SY3283 @ B )
| ~ ( in @ SY3283 @ ( sK4_C @ B @ A ) ) )
& ( in @ ( sK4_C @ B @ A ) @ B ) )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[344]) ).
thf(506,plain,
( ( ! [A: $i] :
( ! [SY3276: $i] :
( ~ ( subset @ SY3276 @ ( sK2_B @ A ) )
| ( are_equipotent @ SY3276 @ ( sK2_B @ A ) )
| ( in @ SY3276 @ ( sK2_B @ A ) ) )
& ! [SY3277: $i] :
( ( ! [SY3282: $i] :
( ~ ( subset @ SY3282 @ SY3277 )
| ( in @ SY3282 @ ( sK3_SY3278 @ SY3277 @ A ) ) )
& ( in @ ( sK3_SY3278 @ SY3277 @ A ) @ ( sK2_B @ A ) ) )
| ~ ( in @ SY3277 @ ( sK2_B @ A ) ) )
& ! [SY3280: $i,SY3281: $i] :
( ~ ( in @ SY3280 @ ( sK2_B @ A ) )
| ~ ( subset @ SY3281 @ SY3280 )
| ( in @ SY3281 @ ( sK2_B @ A ) ) )
& ( in @ A @ ( sK2_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[343]) ).
thf(507,plain,
( ( ~ ( in @ sK1_A @ ( succ @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[342]) ).
thf(508,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK72_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[451]) ).
thf(509,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ ( sK59_SY3316 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SX2 @ SX1 @ SX0 ) @ ( sK59_SY3316 @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SX2 @ SX1 @ SX0 ) @ ( sK59_SY3316 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK59_SY3316 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK58_D @ SX2 @ SX1 @ SX0 ) @ ( sK59_SY3316 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SX2 @ SX1 @ SX0 ) @ ( sK59_SY3316 @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK58_D @ SX2 @ SX1 @ SX0 ) @ ( sK59_SY3316 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) ) ) )
| ( SX2
= ( relation_rng_restriction @ SX0 @ SX1 ) ) )
| ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ( SX2
!= ( relation_rng_restriction @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX1 )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ( in @ SX4 @ SX0 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[469]) ).
thf(510,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK29_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK29_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[486]) ).
thf(511,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX0 @ ( relation_dom @ SX2 ) )
| ( in @ SX0 @ ( relation_dom @ ( relation_dom_restriction @ SX2 @ SX1 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_dom @ ( relation_dom_restriction @ SX2 @ SX1 ) ) )
| ( in @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_dom @ ( relation_dom_restriction @ SX2 @ SX1 ) ) )
| ( in @ SX0 @ ( relation_dom @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[462]) ).
thf(512,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SX1 @ SX0 ) @ ( sK14_SY3290 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY3290 @ SX1 @ SX0 ) @ ( sK13_C @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SX1 @ SX0 ) @ ( sK14_SY3290 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK14_SY3290 @ SX1 @ SX0 ) @ ( sK13_C @ SX1 @ SX0 ) ) @ SX0 ) ) )
| ( SX1
= ( relation_inverse @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ( SX1
!= ( relation_inverse @ SX0 ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[494]) ).
thf(513,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ SX3 @ ( relation_dom @ SX0 ) )
| ~ ( in @ SX3 @ SX1 )
| ( ( sK61_D @ SX2 @ SX1 @ SX0 )
!= ( apply @ SX0 @ SX3 ) ) )
| ~ ( in @ ( sK61_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY3318 @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK62_SY3318 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( sK61_D @ SX2 @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK62_SY3318 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( in @ ( sK61_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ( SX2
= ( relation_image @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( relation_image @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
( ~ ( in @ SX4 @ ( relation_dom @ SX0 ) )
| ~ ( in @ SX4 @ SX1 )
| ( SX3
!= ( apply @ SX0 @ SX4 ) ) )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK60_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( SX3
!= ( apply @ SX0 @ ( sK60_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[468]) ).
thf(514,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ ( sK55_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ~ ( in @ ( sK55_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_SY3315 @ SX2 @ SX1 @ SX0 ) @ ( sK55_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK56_SY3315 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( in @ ( sK55_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ( SX2
= ( relation_image @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( relation_image @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX4 @ SX3 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ ( sK54_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[471]) ).
thf(515,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ~ ( in @ ( sK52_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SX2 @ SX1 @ SX0 ) @ ( sK53_SY3313 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK53_SY3313 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( in @ ( sK52_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ( SX2
= ( relation_inverse_image @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( relation_inverse_image @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ ( ordered_pair @ SX3 @ ( sK51_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK51_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[472]) ).
thf(516,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ ( sK63_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SX2 @ SX1 @ SX0 ) @ ( sK64_SY3319 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SX2 @ SX1 @ SX0 ) @ ( sK64_SY3319 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK63_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK63_D @ SX2 @ SX1 @ SX0 ) @ ( sK64_SY3319 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SX2 @ SX1 @ SX0 ) @ ( sK64_SY3319 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK63_D @ SX2 @ SX1 @ SX0 ) @ ( sK64_SY3319 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) ) ) )
| ( SX2
= ( relation_dom_restriction @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ( SX2
!= ( relation_dom_restriction @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ SX3 @ SX1 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ( in @ SX3 @ SX1 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[467]) ).
thf(517,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( relation_rng @ SX2 ) )
| ~ ( in @ ( ordered_pair @ SX0 @ SX3 ) @ SX2 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX0 @ ( relation_inverse_image @ SX2 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_inverse_image @ SX2 @ SX1 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK75_D @ SX2 @ SX1 @ SX0 ) @ ( relation_rng @ SX2 ) )
| ~ ( in @ ( ordered_pair @ SX0 @ ( sK75_D @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( in @ ( sK75_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[438]) ).
thf(518,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK65_C @ SX1 @ SX0 )
!= ( sK66_SY3320 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK65_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY3320 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK65_C @ SX1 @ SX0 )
= ( sK66_SY3320 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY3320 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK65_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY3320 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( SX2 = SX3 ) )
| ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[466]) ).
thf(519,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK50_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 )
| ( ( sK50_E @ SX3 @ SX2 @ SX1 @ SX0 )
!= SX2 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK50_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 )
| ( ( sK50_E @ SX3 @ SX2 @ SX1 @ SX0 )
!= SX0 ) )
| ~ ( ~ ( in @ ( sK50_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 )
| ( ( sK50_E @ SX3 @ SX2 @ SX1 @ SX0 )
!= SX1 ) ) ) )
| ~ ( ( in @ ( sK50_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 )
| ( ( sK50_E @ SX3 @ SX2 @ SX1 @ SX0 )
= SX2 )
| ( ( sK50_E @ SX3 @ SX2 @ SX1 @ SX0 )
= SX0 )
| ( ( sK50_E @ SX3 @ SX2 @ SX1 @ SX0 )
= SX1 ) ) )
| ( SX3
= ( unordered_triple @ SX0 @ SX1 @ SX2 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( SX3
!= ( unordered_triple @ SX0 @ SX1 @ SX2 ) )
| ~ ( ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( SX4 = SX2 )
| ( SX4 = SX0 )
| ( SX4 = SX1 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SX2 )
| ( in @ SX4 @ SX3 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SX0 )
| ( in @ SX4 @ SX3 ) )
| ~ ! [SX4: $i] :
( ( SX4 != SX1 )
| ( in @ SX4 @ SX3 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[473]) ).
thf(520,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX0 @ ( relation_field @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX1 @ ( relation_field @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443]) ).
thf(521,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ SX2 @ ( sK16_C @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK16_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_SY3292 @ SX1 @ SX0 ) @ ( sK16_C @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK16_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( relation_rng @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ( SX1
!= ( relation_rng @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ ( ordered_pair @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[493]) ).
thf(522,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX1 @ ( sK77_B @ SX0 ) )
| ( are_equipotent @ SX1 @ ( sK77_B @ SX0 ) )
| ( in @ SX1 @ ( sK77_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK77_B @ SX0 ) )
| ( in @ ( powerset @ SX1 ) @ ( sK77_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK77_B @ SX0 ) )
| ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK77_B @ SX0 ) ) )
| ~ ( in @ SX0 @ ( sK77_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[436]) ).
thf(523,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK41_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK41_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK41_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK41_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[479]) ).
thf(524,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[501]) ).
thf(525,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( in @ SX0 @ ( relation_rng @ SX1 ) )
| ~ ( one_to_one @ SX1 )
| ( SX0
= ( apply @ SX1 @ ( apply @ ( function_inverse @ SX1 ) @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( in @ SX0 @ ( relation_rng @ SX1 ) )
| ~ ( one_to_one @ SX1 )
| ( SX0
= ( apply @ ( relation_composition @ ( function_inverse @ SX1 ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456]) ).
thf(526,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_dom @ SX2 ) )
| ~ ( in @ ( apply @ SX2 @ SX0 ) @ ( relation_dom @ SX1 ) )
| ( in @ SX0 @ ( relation_dom @ ( relation_composition @ SX2 @ SX1 ) ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_dom @ ( relation_composition @ SX2 @ SX1 ) ) )
| ( in @ SX0 @ ( relation_dom @ SX2 ) ) )
| ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_dom @ ( relation_composition @ SX2 @ SX1 ) ) )
| ( in @ ( apply @ SX2 @ SX0 ) @ ( relation_dom @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[440]) ).
thf(527,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ ( powerset @ SX0 ) ) )
| ~ ( ~ ( element @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( subset_complement @ SX0 @ ( sK6_D @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( in @ ( subset_complement @ SX0 @ ( sK6_D @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX2
= ( complements_of_subsets @ SX0 @ SX1 ) ) )
| ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( SX2
!= ( complements_of_subsets @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( element @ SX3 @ ( powerset @ SX0 ) )
| ~ ( in @ SX3 @ SX2 )
| ( in @ ( subset_complement @ SX0 @ SX3 ) @ SX1 ) )
| ~ ! [SX3: $i] :
( ~ ( element @ SX3 @ ( powerset @ SX0 ) )
| ~ ( in @ ( subset_complement @ SX0 @ SX3 ) @ SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[497]) ).
thf(528,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ( SX1
!= ( apply @ SX2 @ SX0 ) )
| ~ ( in @ SX0 @ ( relation_dom @ SX2 ) )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( SX1
= ( apply @ SX2 @ SX0 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX0 @ ( relation_dom @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
thf(529,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX0 @ ( relation_rng @ SX2 ) )
| ( in @ SX0 @ ( relation_rng @ ( relation_rng_restriction @ SX1 @ SX2 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_rng @ ( relation_rng_restriction @ SX1 @ SX2 ) ) )
| ( in @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_rng @ ( relation_rng_restriction @ SX1 @ SX2 ) ) )
| ( in @ SX0 @ ( relation_rng @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[435]) ).
thf(530,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX1 @ ( sK2_B @ SX0 ) )
| ( are_equipotent @ SX1 @ ( sK2_B @ SX0 ) )
| ( in @ SX1 @ ( sK2_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK3_SY3278 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK3_SY3278 @ SX1 @ SX0 ) @ ( sK2_B @ SX0 ) ) )
| ~ ( in @ SX1 @ ( sK2_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK2_B @ SX0 ) )
| ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK2_B @ SX0 ) ) )
| ~ ( in @ SX0 @ ( sK2_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[506]) ).
thf(531,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK49_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK49_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK47_C @ SX1 @ SX0 ) @ ( sK48_SY3309 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[475]) ).
thf(532,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ( in @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[431]) ).
thf(533,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ ( sK26_C @ SX1 @ SX0 ) @ SX2 ) @ SX0 )
| ~ ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK26_C @ SX1 @ SX0 ) @ ( sK27_SY3298 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( relation_dom @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ( SX1
!= ( relation_dom @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ ( ordered_pair @ SX2 @ ( sK25_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[489]) ).
thf(534,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[481]) ).
thf(535,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( in @ ( sK42_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[478]) ).
thf(536,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK43_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK43_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK43_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK43_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[477]) ).
thf(537,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK74_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK74_C @ SX1 @ SX0 ) )
!= ( sK74_C @ SX1 @ SX0 ) ) ) )
| ( ( relation_dom @ SX1 )
!= SX0 )
| ( SX1
= ( identity_relation @ SX0 ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( ( apply @ SX1 @ SX2 )
= SX2 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[444]) ).
thf(538,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY3322 @ SX1 @ SX0 )
= ( apply @ SX1 @ ( sK70_C @ SX1 @ SX0 ) ) )
| ( ( sK70_C @ SX1 @ SX0 )
= ( apply @ SX0 @ ( sK71_SY3322 @ SX1 @ SX0 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SX1 @ SX0 )
= ( apply @ SX1 @ ( sK70_C @ SX1 @ SX0 ) ) )
| ( in @ ( sK71_SY3322 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SX1 @ SX0 )
= ( apply @ SX1 @ ( sK70_C @ SX1 @ SX0 ) ) )
| ( ( sK71_SY3322 @ SX1 @ SX0 )
!= ( apply @ SX1 @ ( sK70_C @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK70_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) )
| ( ( sK70_C @ SX1 @ SX0 )
= ( apply @ SX0 @ ( sK71_SY3322 @ SX1 @ SX0 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) )
| ( in @ ( sK71_SY3322 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) )
| ( ( sK71_SY3322 @ SX1 @ SX0 )
!= ( apply @ SX1 @ ( sK70_C @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK70_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK71_SY3322 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ( ( sK70_C @ SX1 @ SX0 )
= ( apply @ SX0 @ ( sK71_SY3322 @ SX1 @ SX0 ) ) ) )
| ~ ( ( ( sK70_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK71_SY3322 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ( in @ ( sK71_SY3322 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) ) )
| ~ ( ( ( sK70_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK71_SY3322 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ( ( sK71_SY3322 @ SX1 @ SX0 )
!= ( apply @ SX1 @ ( sK70_C @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK70_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) ) ) ) )
| ( ( relation_dom @ SX1 )
!= ( relation_rng @ SX0 ) )
| ( SX1
= ( function_inverse @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( function_inverse @ SX0 ) )
| ~ ( ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX3
!= ( apply @ SX1 @ SX2 ) )
| ~ ( in @ SX2 @ ( relation_rng @ SX0 ) )
| ( SX2
= ( apply @ SX0 @ SX3 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( SX3
!= ( apply @ SX1 @ SX2 ) )
| ~ ( in @ SX2 @ ( relation_rng @ SX0 ) )
| ( in @ SX3 @ ( relation_dom @ SX0 ) ) ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX2
!= ( apply @ SX0 @ SX3 ) )
| ~ ( in @ SX3 @ ( relation_dom @ SX0 ) )
| ( SX3
= ( apply @ SX1 @ SX2 ) ) )
| ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ( SX2
!= ( apply @ SX0 @ SX3 ) )
| ~ ( in @ SX3 @ ( relation_dom @ SX0 ) ) )
| ( in @ SX2 @ ( relation_rng @ SX0 ) ) ) ) ) )
| ~ ! [SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( function_inverse @ SX0 ) )
| ( ( relation_dom @ SX1 )
= ( relation_rng @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[453]) ).
thf(539,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ ( sK9_SY3284 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ ( sK9_SY3284 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ ( sK10_SY3288 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY3288 @ SX2 @ SX1 @ SX0 ) @ ( sK9_SY3284 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ ( sK9_SY3284 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) ) )
| ( SX2
= ( relation_composition @ SX0 @ SX1 ) ) )
| ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ( SX2
!= ( relation_composition @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i,SX4: $i] :
( ! [SX5: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX5 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX5 @ SX4 ) @ SX1 ) )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ~ ( ~ ( in @ ( ordered_pair @ SX3 @ ( sK7_F @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX4 ) @ SX1 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[496]) ).
thf(540,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX2 )
| ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[447]) ).
thf(541,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( relation @ SX3 )
| ~ ( in @ SX0 @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX3 )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( relation_composition @ ( identity_relation @ SX2 ) @ SX3 ) ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( relation @ SX3 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( relation_composition @ ( identity_relation @ SX2 ) @ SX3 ) )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( relation @ SX3 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( relation_composition @ ( identity_relation @ SX2 ) @ SX3 ) )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[461]) ).
thf(542,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( sK4_C @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[505]) ).
thf(543,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_B @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK12_SY3289 @ SX0 ) @ ( relation_dom @ SX0 ) ) )
| ( ( apply @ SX0 @ ( sK11_B @ SX0 ) )
!= ( apply @ SX0 @ ( sK12_SY3289 @ SX0 ) ) ) )
| ~ ( ( ( sK11_B @ SX0 )
!= ( sK12_SY3289 @ SX0 ) ) ) )
| ( one_to_one @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ~ ( in @ SX2 @ ( relation_dom @ SX0 ) )
| ( ( apply @ SX0 @ SX1 )
!= ( apply @ SX0 @ SX2 ) )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[495]) ).
thf(544,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK37_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK37_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ~ ( in @ ( sK37_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK37_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ( ( in @ ( sK37_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( in @ ( sK37_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK37_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX2
= ( set_union2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_union2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[483]) ).
thf(545,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457]) ).
thf(546,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK30_C @ SX1 @ SX0 ) @ ( sK31_SY3299 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( in @ ( ordered_pair @ ( sK30_C @ SX1 @ SX0 ) @ ( sK31_SY3299 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[485]) ).
thf(547,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK46_SY3307 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK45_C @ SX1 @ SX0 ) @ ( sK46_SY3307 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK45_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK45_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK45_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK44_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK44_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[476]) ).
thf(548,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK57_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( apply @ SX0 @ ( sK57_D @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( sK57_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK57_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ( in @ ( sK57_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ( in @ ( apply @ SX0 @ ( sK57_D @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( sK57_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( relation_inverse_image @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( relation_inverse_image @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( apply @ SX0 @ SX3 ) @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ ( apply @ SX0 @ SX3 ) @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[470]) ).
thf(549,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK28_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK28_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK28_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK28_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK28_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ( in @ ( sK28_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK28_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[487]) ).
thf(550,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[446]) ).
thf(551,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK21_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK21_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK21_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK21_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK21_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( in @ ( sK21_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK21_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( set_difference @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_difference @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( in @ SX3 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[491]) ).
thf(552,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ( ( sK19_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ SX2 ) )
| ~ ( in @ SX2 @ ( relation_dom @ SX0 ) ) )
| ~ ( in @ ( sK19_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ( ( sK19_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK20_SY3294 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK20_SY3294 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) )
| ( in @ ( sK19_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( relation_rng @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ( SX1
!= ( relation_rng @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ( SX2
!= ( apply @ SX0 @ SX3 ) )
| ~ ( in @ SX3 @ ( relation_dom @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ( SX2
!= ( apply @ SX0 @ ( sK18_D @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK18_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[492]) ).
thf(553,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK38_D @ SX2 @ SX1 @ SX0 )
!= SX0 ) )
| ~ ( ~ ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK38_D @ SX2 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ( ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK38_D @ SX2 @ SX1 @ SX0 )
= SX0 )
| ( ( sK38_D @ SX2 @ SX1 @ SX0 )
= SX1 ) ) )
| ( SX2
= ( unordered_pair @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( unordered_pair @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ( SX3 != SX0 )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[482]) ).
thf(554,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( ~ ( in @ ( sK67_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX1 ) )
| ~ ( ( ( apply @ SX1 @ ( sK67_D @ SX2 @ SX1 @ SX0 ) )
!= ( apply @ SX2 @ ( sK67_D @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ( ( relation_dom @ SX1 )
!= ( set_intersection2 @ ( relation_dom @ SX2 ) @ SX0 ) )
| ( SX1
= ( relation_dom_restriction @ SX2 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ( SX1
!= ( relation_dom_restriction @ SX2 @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( relation_dom @ SX1 ) )
| ( ( apply @ SX1 @ SX3 )
= ( apply @ SX2 @ SX3 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ( SX1
!= ( relation_dom_restriction @ SX2 @ SX0 ) )
| ( ( relation_dom @ SX1 )
= ( set_intersection2 @ ( relation_dom @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[458]) ).
thf(555,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_C @ SX1 @ SX0 ) @ ( sK40_SY3306 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK39_C @ SX1 @ SX0 ) @ ( sK40_SY3306 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK39_C @ SX1 @ SX0 ) @ ( sK40_SY3306 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK39_C @ SX1 @ SX0 ) @ ( sK40_SY3306 @ SX1 @ SX0 ) ) @ SX1 ) ) )
| ( SX0 = SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[480]) ).
thf(556,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK78_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK78_C @ SX1 @ SX0 ) @ SX1 ) )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[432]) ).
thf(557,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ ( sK24_SY3296 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK24_SY3296 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK22_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[490]) ).
thf(558,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ( in @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[434]) ).
thf(559,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( in @ SX1 @ ( relation_dom @ SX2 ) )
| ~ ( in @ SX1 @ SX0 )
| ( in @ SX1 @ ( relation_dom @ ( relation_dom_restriction @ SX2 @ SX0 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( in @ SX1 @ ( relation_dom @ ( relation_dom_restriction @ SX2 @ SX0 ) ) )
| ( in @ SX1 @ ( relation_dom @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( in @ SX1 @ ( relation_dom @ ( relation_dom_restriction @ SX2 @ SX0 ) ) )
| ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[433]) ).
thf(560,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i,SX4: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX4 @ SX1 )
| ( ( sK34_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ SX3 @ SX4 ) ) )
| ~ ( in @ ( sK34_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK35_SY3303 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK36_SY3305 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( sK34_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ ( sK35_SY3303 @ SX2 @ SX1 @ SX0 ) @ ( sK36_SY3305 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( in @ ( sK34_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ( SX2
= ( cartesian_product2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( cartesian_product2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i,SX5: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ~ ( ~ ( in @ ( sK32_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK33_SY3300 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( SX3
!= ( ordered_pair @ ( sK32_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK33_SY3300 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[484]) ).
thf(561,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK73_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK73_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(562,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( relation_dom @ SX2 ) )
| ~ ( in @ ( ordered_pair @ SX3 @ SX0 ) @ SX2 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX0 @ ( relation_image @ SX2 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_image @ SX2 @ SX1 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK76_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX2 ) )
| ~ ( in @ ( ordered_pair @ ( sK76_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) @ SX2 ) )
| ~ ( in @ ( sK76_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[437]) ).
thf(563,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX0 @ ( relation_dom @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX1 @ ( relation_rng @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[439]) ).
thf(564,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
( ( SX2
!= ( apply @ SX0 @ SX1 ) )
| ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ( SX2
= ( apply @ SX0 @ SX1 ) ) ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
( ( SX2
!= ( apply @ SX0 @ SX1 ) )
| ( SX2 = empty_set ) ) )
| ~ ! [SX1: $i] :
( ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
( ( SX2 != empty_set )
| ( SX2
= ( apply @ SX0 @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[488]) ).
thf(565,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[427]) ).
thf(566,plain,
! [SV1: $i] :
( ( ! [SY3327: $i] :
( ~ ( in @ SV1 @ SY3327 )
| ( ( set_union2 @ ( singleton @ SV1 ) @ SY3327 )
= SY3327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(567,plain,
! [SV2: $i] :
( ( ! [SY3328: $i] :
( ~ ( disjoint @ ( singleton @ SV2 ) @ SY3328 )
| ~ ( in @ SV2 @ SY3328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(568,plain,
! [SV3: $i] :
( ( ! [SY3329: $i] :
( ( in @ SV3 @ SY3329 )
| ( disjoint @ ( singleton @ SV3 ) @ SY3329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(569,plain,
! [SV4: $i] :
( ( ! [SY3330: $i] :
( ~ ( element @ SY3330 @ ( powerset @ SV4 ) )
| ! [SY3331: $i] :
( ~ ( in @ SY3331 @ SY3330 )
| ( in @ SY3331 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(570,plain,
! [SV5: $i] :
( ( ! [SY3332: $i] :
( ~ ( subset @ SV5 @ SY3332 )
| ! [SY3333: $i] :
( ( in @ SY3333 @ SV5 )
| ( subset @ SV5 @ ( set_difference @ SY3332 @ ( singleton @ SY3333 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(571,plain,
! [SV6: $i] :
( ( ! [SY3334: $i] :
( ~ ( in @ SV6 @ SY3334 )
| ( subset @ SV6 @ ( union @ SY3334 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(572,plain,
! [SV7: $i] :
( ( ! [SY3335: $i] :
( ~ ( function @ SY3335 )
| ~ ( relation @ SY3335 )
| ! [SY3336: $i] :
( ~ ( function @ SY3336 )
| ~ ( relation @ SY3336 )
| ~ ( in @ SV7 @ ( relation_dom @ ( relation_composition @ SY3336 @ SY3335 ) ) )
| ( ( apply @ ( relation_composition @ SY3336 @ SY3335 ) @ SV7 )
= ( apply @ SY3335 @ ( apply @ SY3336 @ SV7 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(573,plain,
! [SV8: $i] :
( ( ! [SY3337: $i] :
( ~ ( function @ SY3337 )
| ~ ( relation @ SY3337 )
| ! [SY3338: $i] :
( ~ ( function @ SY3338 )
| ~ ( relation @ SY3338 )
| ~ ( in @ SV8 @ ( relation_dom @ SY3337 ) )
| ( ( apply @ ( relation_composition @ SY3337 @ SY3338 ) @ SV8 )
= ( apply @ SY3338 @ ( apply @ SY3337 @ SV8 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(574,plain,
! [SV9: $i] :
( ( ! [SY3339: $i] :
( ~ ( in @ SY3339 @ SV9 )
| ( ( apply @ ( identity_relation @ SV9 ) @ SY3339 )
= SY3339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(575,plain,
! [SV10: $i] :
( ( ! [SY3340: $i,SY3341: $i] :
( ~ ( in @ SV10 @ SY3340 )
| ~ ( in @ SY3340 @ SY3341 )
| ~ ( in @ SY3341 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(576,plain,
! [SV11: $i] :
( ( ! [SY3342: $i] :
( ~ ( in @ SV11 @ SY3342 )
| ( ( set_union2 @ ( singleton @ SV11 ) @ SY3342 )
= SY3342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(577,plain,
! [SV12: $i] :
( ( ( SV12 = empty_set )
| ! [SY3343: $i] :
( ~ ( element @ SY3343 @ ( powerset @ SV12 ) )
| ! [SY3344: $i] :
( ~ ( element @ SY3344 @ SV12 )
| ( in @ SY3344 @ SY3343 )
| ( in @ SY3344 @ ( subset_complement @ SV12 @ SY3343 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(578,plain,
! [SV13: $i] :
( ( ! [SY3345: $i,SY3346: $i] :
( ~ ( element @ SY3346 @ ( powerset @ SV13 ) )
| ~ ( in @ SY3345 @ ( subset_complement @ SV13 @ SY3346 ) )
| ~ ( in @ SY3345 @ SY3346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(579,plain,
! [SV14: $i] :
( ( ~ ( relation @ SV14 )
| ( in @ ( ordered_pair @ ( sK68_B @ SV14 ) @ ( sK69_SY3321 @ SV14 ) ) @ SV14 )
| ( SV14 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(580,plain,
! [SV15: $i] :
( ( ! [SY3347: $i,SY3348: $i] :
( ~ ( function @ SY3348 )
| ~ ( relation @ SY3348 )
| ~ ( in @ SY3347 @ ( relation_dom @ ( relation_dom_restriction @ SY3348 @ SV15 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SY3348 @ SV15 ) @ SY3347 )
= ( apply @ SY3348 @ SY3347 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(581,plain,
! [SV16: $i] :
( ( ! [SY3349: $i,SY3350: $i] :
( ~ ( function @ SY3350 )
| ~ ( relation @ SY3350 )
| ~ ( in @ SY3349 @ SV16 )
| ( ( apply @ ( relation_dom_restriction @ SY3350 @ SV16 ) @ SY3349 )
= ( apply @ SY3350 @ SY3349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(582,plain,
! [SV17: $i] :
( ( ! [SY3351: $i] :
( ~ ( in @ SV17 @ SY3351 )
| ( subset @ SV17 @ ( union @ SY3351 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(583,plain,
! [SV18: $i] :
( ( ! [SY3352: $i] :
( ~ ( in @ SV18 @ SY3352 )
| ~ ( in @ SY3352 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(584,plain,
! [SV19: $i] :
( ( ( succ @ SV19 )
= ( set_union2 @ SV19 @ ( singleton @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(585,plain,
! [SV20: $i] :
( ( ~ ( empty @ ( succ @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(586,plain,
! [SV21: $i] :
( ( ! [SY3353: $i] :
( ~ ( in @ SV21 @ SY3353 )
| ( element @ SV21 @ SY3353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(587,plain,
! [SV22: $i] :
( ( ! [SY3354: $i] :
( ~ ( element @ SV22 @ SY3354 )
| ( empty @ SY3354 )
| ( in @ SV22 @ SY3354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(588,plain,
! [SV23: $i] :
( ( ! [SY3355: $i,SY3356: $i] :
( ~ ( element @ SY3355 @ ( powerset @ SY3356 ) )
| ~ ( in @ SV23 @ SY3355 )
| ( element @ SV23 @ SY3356 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(589,plain,
! [SV24: $i] :
( ( ! [SY3357: $i,SY3358: $i] :
( ~ ( element @ SY3357 @ ( powerset @ SY3358 ) )
| ~ ( in @ SV24 @ SY3357 )
| ~ ( empty @ SY3358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(590,plain,
! [SV25: $i] :
( ( ! [SY3359: $i] :
( ~ ( empty @ SY3359 )
| ~ ( in @ SV25 @ SY3359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(591,plain,
( ( in @ sK1_A @ ( succ @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(592,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK72_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(593,plain,
! [SV26: $i] :
( ( ! [SY3360: $i] :
( ~ ( relation @ SY3360 )
| ~ ( ~ ! [SY3361: $i] :
( ~ ( relation @ SY3361 )
| ~ ( ~ ( ~ ( in @ ( sK59_SY3316 @ SY3361 @ SY3360 @ SV26 ) @ SV26 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY3361 @ SY3360 @ SV26 ) @ ( sK59_SY3316 @ SY3361 @ SY3360 @ SV26 ) ) @ SY3360 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY3361 @ SY3360 @ SV26 ) @ ( sK59_SY3316 @ SY3361 @ SY3360 @ SV26 ) ) @ SY3361 ) )
| ~ ~ ( ~ ( ( in @ ( sK59_SY3316 @ SY3361 @ SY3360 @ SV26 ) @ SV26 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY3361 @ SY3360 @ SV26 ) @ ( sK59_SY3316 @ SY3361 @ SY3360 @ SV26 ) ) @ SY3361 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SY3361 @ SY3360 @ SV26 ) @ ( sK59_SY3316 @ SY3361 @ SY3360 @ SV26 ) ) @ SY3360 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY3361 @ SY3360 @ SV26 ) @ ( sK59_SY3316 @ SY3361 @ SY3360 @ SV26 ) ) @ SY3361 ) ) ) )
| ( SY3361
= ( relation_rng_restriction @ SV26 @ SY3360 ) ) )
| ~ ! [SY3362: $i] :
( ~ ( relation @ SY3362 )
| ( SY3362
!= ( relation_rng_restriction @ SV26 @ SY3360 ) )
| ~ ( ~ ! [SY3363: $i,SY3364: $i] :
( ~ ( in @ SY3364 @ SV26 )
| ~ ( in @ ( ordered_pair @ SY3363 @ SY3364 ) @ SY3360 )
| ( in @ ( ordered_pair @ SY3363 @ SY3364 ) @ SY3362 ) )
| ~ ~ ( ~ ! [SY3365: $i,SY3366: $i] :
( ~ ( in @ ( ordered_pair @ SY3365 @ SY3366 ) @ SY3362 )
| ( in @ SY3366 @ SV26 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3362 )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3360 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(594,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK29_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK29_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(595,plain,
! [SV27: $i] :
( ( ~ ( ~ ! [SY3369: $i,SY3370: $i] :
( ~ ( relation @ SY3370 )
| ~ ( in @ SV27 @ SY3369 )
| ~ ( in @ SV27 @ ( relation_dom @ SY3370 ) )
| ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SY3370 @ SY3369 ) ) ) )
| ~ ~ ( ~ ! [SY3371: $i,SY3372: $i] :
( ~ ( relation @ SY3372 )
| ~ ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SY3372 @ SY3371 ) ) )
| ( in @ SV27 @ SY3371 ) )
| ~ ! [SY3373: $i,SY3374: $i] :
( ~ ( relation @ SY3374 )
| ~ ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SY3374 @ SY3373 ) ) )
| ( in @ SV27 @ ( relation_dom @ SY3374 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(596,plain,
! [SV28: $i] :
( ( ~ ( relation @ SV28 )
| ~ ( ~ ! [SY3375: $i] :
( ~ ( relation @ SY3375 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SY3375 @ SV28 ) @ ( sK14_SY3290 @ SY3375 @ SV28 ) ) @ SY3375 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY3290 @ SY3375 @ SV28 ) @ ( sK13_C @ SY3375 @ SV28 ) ) @ SV28 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SY3375 @ SV28 ) @ ( sK14_SY3290 @ SY3375 @ SV28 ) ) @ SY3375 )
| ( in @ ( ordered_pair @ ( sK14_SY3290 @ SY3375 @ SV28 ) @ ( sK13_C @ SY3375 @ SV28 ) ) @ SV28 ) ) )
| ( SY3375
= ( relation_inverse @ SV28 ) ) )
| ~ ! [SY3376: $i] :
( ~ ( relation @ SY3376 )
| ( SY3376
!= ( relation_inverse @ SV28 ) )
| ~ ( ~ ! [SY3377: $i,SY3378: $i] :
( ~ ( in @ ( ordered_pair @ SY3377 @ SY3378 ) @ SY3376 )
| ( in @ ( ordered_pair @ SY3378 @ SY3377 ) @ SV28 ) )
| ~ ! [SY3379: $i,SY3380: $i] :
( ~ ( in @ ( ordered_pair @ SY3380 @ SY3379 ) @ SV28 )
| ( in @ ( ordered_pair @ SY3379 @ SY3380 ) @ SY3376 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(597,plain,
! [SV29: $i] :
( ( ~ ( function @ SV29 )
| ~ ( relation @ SV29 )
| ~ ( ~ ! [SY3381: $i,SY3382: $i] :
( ~ ( ~ ( ! [SY3383: $i] :
( ~ ( in @ SY3383 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3383 @ SY3381 )
| ( ( sK61_D @ SY3382 @ SY3381 @ SV29 )
!= ( apply @ SV29 @ SY3383 ) ) )
| ~ ( in @ ( sK61_D @ SY3382 @ SY3381 @ SV29 ) @ SY3382 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY3318 @ SY3382 @ SY3381 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK62_SY3318 @ SY3382 @ SY3381 @ SV29 ) @ SY3381 ) )
| ( ( sK61_D @ SY3382 @ SY3381 @ SV29 )
!= ( apply @ SV29 @ ( sK62_SY3318 @ SY3382 @ SY3381 @ SV29 ) ) ) )
| ( in @ ( sK61_D @ SY3382 @ SY3381 @ SV29 ) @ SY3382 ) ) )
| ( SY3382
= ( relation_image @ SV29 @ SY3381 ) ) )
| ~ ! [SY3384: $i,SY3385: $i] :
( ( SY3385
!= ( relation_image @ SV29 @ SY3384 ) )
| ~ ( ~ ! [SY3386: $i] :
( ! [SY3387: $i] :
( ~ ( in @ SY3387 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3387 @ SY3384 )
| ( SY3386
!= ( apply @ SV29 @ SY3387 ) ) )
| ( in @ SY3386 @ SY3385 ) )
| ~ ! [SY3388: $i] :
( ~ ( in @ SY3388 @ SY3385 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SY3388 @ SY3385 @ SY3384 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK60_E @ SY3388 @ SY3385 @ SY3384 @ SV29 ) @ SY3384 ) )
| ( SY3388
!= ( apply @ SV29 @ ( sK60_E @ SY3388 @ SY3385 @ SY3384 @ SV29 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(598,plain,
! [SV30: $i] :
( ( ~ ( relation @ SV30 )
| ~ ( ~ ! [SY3389: $i,SY3390: $i] :
( ~ ( ~ ( ! [SY3391: $i] :
( ~ ( in @ ( ordered_pair @ SY3391 @ ( sK55_D @ SY3390 @ SY3389 @ SV30 ) ) @ SV30 )
| ~ ( in @ SY3391 @ SY3389 ) )
| ~ ( in @ ( sK55_D @ SY3390 @ SY3389 @ SV30 ) @ SY3390 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_SY3315 @ SY3390 @ SY3389 @ SV30 ) @ ( sK55_D @ SY3390 @ SY3389 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK56_SY3315 @ SY3390 @ SY3389 @ SV30 ) @ SY3389 ) )
| ( in @ ( sK55_D @ SY3390 @ SY3389 @ SV30 ) @ SY3390 ) ) )
| ( SY3390
= ( relation_image @ SV30 @ SY3389 ) ) )
| ~ ! [SY3392: $i,SY3393: $i] :
( ( SY3393
!= ( relation_image @ SV30 @ SY3392 ) )
| ~ ( ~ ! [SY3394: $i] :
( ! [SY3395: $i] :
( ~ ( in @ ( ordered_pair @ SY3395 @ SY3394 ) @ SV30 )
| ~ ( in @ SY3395 @ SY3392 ) )
| ( in @ SY3394 @ SY3393 ) )
| ~ ! [SY3396: $i] :
( ~ ( in @ SY3396 @ SY3393 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SY3396 @ SY3393 @ SY3392 @ SV30 ) @ SY3396 ) @ SV30 )
| ~ ( in @ ( sK54_E @ SY3396 @ SY3393 @ SY3392 @ SV30 ) @ SY3392 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(599,plain,
! [SV31: $i] :
( ( ~ ( relation @ SV31 )
| ~ ( ~ ! [SY3397: $i,SY3398: $i] :
( ~ ( ~ ( ! [SY3399: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ SY3398 @ SY3397 @ SV31 ) @ SY3399 ) @ SV31 )
| ~ ( in @ SY3399 @ SY3397 ) )
| ~ ( in @ ( sK52_D @ SY3398 @ SY3397 @ SV31 ) @ SY3398 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SY3398 @ SY3397 @ SV31 ) @ ( sK53_SY3313 @ SY3398 @ SY3397 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( sK53_SY3313 @ SY3398 @ SY3397 @ SV31 ) @ SY3397 ) )
| ( in @ ( sK52_D @ SY3398 @ SY3397 @ SV31 ) @ SY3398 ) ) )
| ( SY3398
= ( relation_inverse_image @ SV31 @ SY3397 ) ) )
| ~ ! [SY3400: $i,SY3401: $i] :
( ( SY3401
!= ( relation_inverse_image @ SV31 @ SY3400 ) )
| ~ ( ~ ! [SY3402: $i] :
( ! [SY3403: $i] :
( ~ ( in @ ( ordered_pair @ SY3402 @ SY3403 ) @ SV31 )
| ~ ( in @ SY3403 @ SY3400 ) )
| ( in @ SY3402 @ SY3401 ) )
| ~ ! [SY3404: $i] :
( ~ ( in @ SY3404 @ SY3401 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3404 @ ( sK51_E @ SY3404 @ SY3401 @ SY3400 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( sK51_E @ SY3404 @ SY3401 @ SY3400 @ SV31 ) @ SY3400 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(600,plain,
! [SV32: $i] :
( ( ~ ( relation @ SV32 )
| ~ ( ~ ! [SY3405: $i,SY3406: $i] :
( ~ ( relation @ SY3406 )
| ~ ( ~ ( ~ ( in @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ SY3405 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ ( sK64_SY3319 @ SY3406 @ SY3405 @ SV32 ) ) @ SV32 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ ( sK64_SY3319 @ SY3406 @ SY3405 @ SV32 ) ) @ SY3406 ) )
| ~ ~ ( ~ ( ( in @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ SY3405 )
| ( in @ ( ordered_pair @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ ( sK64_SY3319 @ SY3406 @ SY3405 @ SV32 ) ) @ SY3406 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ ( sK64_SY3319 @ SY3406 @ SY3405 @ SV32 ) ) @ SV32 )
| ( in @ ( ordered_pair @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ ( sK64_SY3319 @ SY3406 @ SY3405 @ SV32 ) ) @ SY3406 ) ) ) )
| ( SY3406
= ( relation_dom_restriction @ SV32 @ SY3405 ) ) )
| ~ ! [SY3407: $i,SY3408: $i] :
( ~ ( relation @ SY3408 )
| ( SY3408
!= ( relation_dom_restriction @ SV32 @ SY3407 ) )
| ~ ( ~ ! [SY3409: $i,SY3410: $i] :
( ~ ( in @ SY3409 @ SY3407 )
| ~ ( in @ ( ordered_pair @ SY3409 @ SY3410 ) @ SV32 )
| ( in @ ( ordered_pair @ SY3409 @ SY3410 ) @ SY3408 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3408 )
| ( in @ SX3 @ SY3407 ) )
| ~ ! [SY3413: $i,SY3414: $i] :
( ~ ( in @ ( ordered_pair @ SY3413 @ SY3414 ) @ SY3408 )
| ( in @ ( ordered_pair @ SY3413 @ SY3414 ) @ SV32 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(601,plain,
! [SV33: $i] :
( ( ~ ( ~ ! [SY3415: $i,SY3416: $i] :
( ~ ( relation @ SY3416 )
| ! [SY3417: $i] :
( ~ ( in @ SY3417 @ ( relation_rng @ SY3416 ) )
| ~ ( in @ ( ordered_pair @ SV33 @ SY3417 ) @ SY3416 )
| ~ ( in @ SY3417 @ SY3415 ) )
| ( in @ SV33 @ ( relation_inverse_image @ SY3416 @ SY3415 ) ) )
| ~ ! [SY3418: $i,SY3419: $i] :
( ~ ( relation @ SY3419 )
| ~ ( in @ SV33 @ ( relation_inverse_image @ SY3419 @ SY3418 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK75_D @ SY3419 @ SY3418 @ SV33 ) @ ( relation_rng @ SY3419 ) )
| ~ ( in @ ( ordered_pair @ SV33 @ ( sK75_D @ SY3419 @ SY3418 @ SV33 ) ) @ SY3419 ) )
| ~ ( in @ ( sK75_D @ SY3419 @ SY3418 @ SV33 ) @ SY3418 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(602,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK65_C @ SX1 @ SX0 )
!= ( sK66_SY3320 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK65_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY3320 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK65_C @ SX1 @ SX0 )
= ( sK66_SY3320 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY3320 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK65_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY3320 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( SX2 = SX3 ) )
| ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(603,plain,
! [SV34: $i] :
( ( ! [SY3420: $i] :
~ ( ~ ! [SY3421: $i,SY3422: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK50_E @ SY3422 @ SY3421 @ SY3420 @ SV34 ) @ SY3422 )
| ( ( sK50_E @ SY3422 @ SY3421 @ SY3420 @ SV34 )
!= SY3421 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK50_E @ SY3422 @ SY3421 @ SY3420 @ SV34 ) @ SY3422 )
| ( ( sK50_E @ SY3422 @ SY3421 @ SY3420 @ SV34 )
!= SV34 ) )
| ~ ( ~ ( in @ ( sK50_E @ SY3422 @ SY3421 @ SY3420 @ SV34 ) @ SY3422 )
| ( ( sK50_E @ SY3422 @ SY3421 @ SY3420 @ SV34 )
!= SY3420 ) ) ) )
| ~ ( ( in @ ( sK50_E @ SY3422 @ SY3421 @ SY3420 @ SV34 ) @ SY3422 )
| ( ( sK50_E @ SY3422 @ SY3421 @ SY3420 @ SV34 )
= SY3421 )
| ( ( sK50_E @ SY3422 @ SY3421 @ SY3420 @ SV34 )
= SV34 )
| ( ( sK50_E @ SY3422 @ SY3421 @ SY3420 @ SV34 )
= SY3420 ) ) )
| ( SY3422
= ( unordered_triple @ SV34 @ SY3420 @ SY3421 ) ) )
| ~ ! [SY3423: $i,SY3424: $i] :
( ( SY3424
!= ( unordered_triple @ SV34 @ SY3420 @ SY3423 ) )
| ~ ( ~ ! [SY3425: $i] :
( ~ ( in @ SY3425 @ SY3424 )
| ( SY3425 = SY3423 )
| ( SY3425 = SV34 )
| ( SY3425 = SY3420 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SY3423 )
| ( in @ SX4 @ SY3424 ) )
| ~ ~ ( ~ ! [SY3427: $i] :
( ( SY3427 != SV34 )
| ( in @ SY3427 @ SY3424 ) )
| ~ ! [SX4: $i] :
( ( SX4 != SY3420 )
| ( in @ SX4 @ SY3424 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(604,plain,
! [SV35: $i] :
( ( ~ ( ~ ! [SY3429: $i,SY3430: $i] :
( ~ ( relation @ SY3430 )
| ~ ( in @ ( ordered_pair @ SV35 @ SY3429 ) @ SY3430 )
| ( in @ SV35 @ ( relation_field @ SY3430 ) ) )
| ~ ! [SY3431: $i,SY3432: $i] :
( ~ ( relation @ SY3432 )
| ~ ( in @ ( ordered_pair @ SV35 @ SY3431 ) @ SY3432 )
| ( in @ SY3431 @ ( relation_field @ SY3432 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(605,plain,
! [SV36: $i] :
( ( ~ ( relation @ SV36 )
| ~ ( ~ ! [SY3433: $i] :
( ~ ( ~ ( ! [SY3434: $i] :
~ ( in @ ( ordered_pair @ SY3434 @ ( sK16_C @ SY3433 @ SV36 ) ) @ SV36 )
| ~ ( in @ ( sK16_C @ SY3433 @ SV36 ) @ SY3433 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_SY3292 @ SY3433 @ SV36 ) @ ( sK16_C @ SY3433 @ SV36 ) ) @ SV36 )
| ( in @ ( sK16_C @ SY3433 @ SV36 ) @ SY3433 ) ) )
| ( SY3433
= ( relation_rng @ SV36 ) ) )
| ~ ! [SY3435: $i] :
( ( SY3435
!= ( relation_rng @ SV36 ) )
| ~ ( ~ ! [SY3436: $i] :
( ! [SY3437: $i] :
~ ( in @ ( ordered_pair @ SY3437 @ SY3436 ) @ SV36 )
| ( in @ SY3436 @ SY3435 ) )
| ~ ! [SY3438: $i] :
( ~ ( in @ SY3438 @ SY3435 )
| ( in @ ( ordered_pair @ ( sK15_D @ SY3438 @ SY3435 @ SV36 ) @ SY3438 ) @ SV36 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(606,plain,
! [SV37: $i] :
( ( ~ ( ~ ! [SY3439: $i] :
( ~ ( subset @ SY3439 @ ( sK77_B @ SV37 ) )
| ( are_equipotent @ SY3439 @ ( sK77_B @ SV37 ) )
| ( in @ SY3439 @ ( sK77_B @ SV37 ) ) )
| ~ ~ ( ~ ! [SY3440: $i] :
( ~ ( in @ SY3440 @ ( sK77_B @ SV37 ) )
| ( in @ ( powerset @ SY3440 ) @ ( sK77_B @ SV37 ) ) )
| ~ ~ ( ~ ! [SY3441: $i,SY3442: $i] :
( ~ ( in @ SY3441 @ ( sK77_B @ SV37 ) )
| ~ ( subset @ SY3442 @ SY3441 )
| ( in @ SY3442 @ ( sK77_B @ SV37 ) ) )
| ~ ( in @ SV37 @ ( sK77_B @ SV37 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(607,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK41_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK41_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK41_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK41_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(608,plain,
! [SV38: $i] :
( ( ! [SY3443: $i] :
( ~ ( ~ ( ~ ( in @ ( sK5_C @ SY3443 @ SV38 ) @ SV38 )
| ~ ( in @ ( sK5_C @ SY3443 @ SV38 ) @ SY3443 ) )
| ~ ( ( in @ ( sK5_C @ SY3443 @ SV38 ) @ SV38 )
| ( in @ ( sK5_C @ SY3443 @ SV38 ) @ SY3443 ) ) )
| ( SV38 = SY3443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(609,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( in @ SX0 @ ( relation_rng @ SX1 ) )
| ~ ( one_to_one @ SX1 )
| ( SX0
= ( apply @ SX1 @ ( apply @ ( function_inverse @ SX1 ) @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( in @ SX0 @ ( relation_rng @ SX1 ) )
| ~ ( one_to_one @ SX1 )
| ( SX0
= ( apply @ ( relation_composition @ ( function_inverse @ SX1 ) @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[525]) ).
thf(610,plain,
! [SV39: $i] :
( ( ! [SY3444: $i] :
( ~ ( function @ SY3444 )
| ~ ( relation @ SY3444 )
| ~ ( ~ ! [SY3445: $i] :
( ~ ( function @ SY3445 )
| ~ ( relation @ SY3445 )
| ~ ( in @ SV39 @ ( relation_dom @ SY3445 ) )
| ~ ( in @ ( apply @ SY3445 @ SV39 ) @ ( relation_dom @ SY3444 ) )
| ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3445 @ SY3444 ) ) ) )
| ~ ~ ( ~ ! [SY3446: $i] :
( ~ ( function @ SY3446 )
| ~ ( relation @ SY3446 )
| ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3446 @ SY3444 ) ) )
| ( in @ SV39 @ ( relation_dom @ SY3446 ) ) )
| ~ ! [SY3447: $i] :
( ~ ( function @ SY3447 )
| ~ ( relation @ SY3447 )
| ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3447 @ SY3444 ) ) )
| ( in @ ( apply @ SY3447 @ SV39 ) @ ( relation_dom @ SY3444 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(611,plain,
! [SV40: $i] :
( ( ! [SY3448: $i] :
( ~ ( element @ SY3448 @ ( powerset @ ( powerset @ SV40 ) ) )
| ~ ( ~ ! [SY3449: $i] :
( ~ ( element @ SY3449 @ ( powerset @ ( powerset @ SV40 ) ) )
| ~ ( ~ ( element @ ( sK6_D @ SY3449 @ SY3448 @ SV40 ) @ ( powerset @ SV40 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK6_D @ SY3449 @ SY3448 @ SV40 ) @ SY3449 )
| ~ ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SY3449 @ SY3448 @ SV40 ) ) @ SY3448 ) )
| ~ ( ( in @ ( sK6_D @ SY3449 @ SY3448 @ SV40 ) @ SY3449 )
| ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SY3449 @ SY3448 @ SV40 ) ) @ SY3448 ) ) ) )
| ( SY3449
= ( complements_of_subsets @ SV40 @ SY3448 ) ) )
| ~ ! [SY3450: $i] :
( ~ ( element @ SY3450 @ ( powerset @ ( powerset @ SV40 ) ) )
| ( SY3450
!= ( complements_of_subsets @ SV40 @ SY3448 ) )
| ~ ( ~ ! [SY3451: $i] :
( ~ ( element @ SY3451 @ ( powerset @ SV40 ) )
| ~ ( in @ SY3451 @ SY3450 )
| ( in @ ( subset_complement @ SV40 @ SY3451 ) @ SY3448 ) )
| ~ ! [SY3452: $i] :
( ~ ( element @ SY3452 @ ( powerset @ SV40 ) )
| ~ ( in @ ( subset_complement @ SV40 @ SY3452 ) @ SY3448 )
| ( in @ SY3452 @ SY3450 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(612,plain,
! [SV41: $i] :
( ( ~ ( ~ ! [SY3453: $i,SY3454: $i] :
( ~ ( function @ SY3454 )
| ~ ( relation @ SY3454 )
| ( SY3453
!= ( apply @ SY3454 @ SV41 ) )
| ~ ( in @ SV41 @ ( relation_dom @ SY3454 ) )
| ( in @ ( ordered_pair @ SV41 @ SY3453 ) @ SY3454 ) )
| ~ ~ ( ~ ! [SY3455: $i,SY3456: $i] :
( ~ ( function @ SY3456 )
| ~ ( relation @ SY3456 )
| ~ ( in @ ( ordered_pair @ SV41 @ SY3455 ) @ SY3456 )
| ( SY3455
= ( apply @ SY3456 @ SV41 ) ) )
| ~ ! [SY3457: $i,SY3458: $i] :
( ~ ( function @ SY3458 )
| ~ ( relation @ SY3458 )
| ~ ( in @ ( ordered_pair @ SV41 @ SY3457 ) @ SY3458 )
| ( in @ SV41 @ ( relation_dom @ SY3458 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(613,plain,
! [SV42: $i] :
( ( ~ ( ~ ! [SY3459: $i,SY3460: $i] :
( ~ ( relation @ SY3460 )
| ~ ( in @ SV42 @ SY3459 )
| ~ ( in @ SV42 @ ( relation_rng @ SY3460 ) )
| ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SY3459 @ SY3460 ) ) ) )
| ~ ~ ( ~ ! [SY3461: $i,SY3462: $i] :
( ~ ( relation @ SY3462 )
| ~ ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SY3461 @ SY3462 ) ) )
| ( in @ SV42 @ SY3461 ) )
| ~ ! [SY3463: $i,SY3464: $i] :
( ~ ( relation @ SY3464 )
| ~ ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SY3463 @ SY3464 ) ) )
| ( in @ SV42 @ ( relation_rng @ SY3464 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(614,plain,
! [SV43: $i] :
( ( ~ ( ~ ! [SY3465: $i] :
( ~ ( subset @ SY3465 @ ( sK2_B @ SV43 ) )
| ( are_equipotent @ SY3465 @ ( sK2_B @ SV43 ) )
| ( in @ SY3465 @ ( sK2_B @ SV43 ) ) )
| ~ ~ ( ~ ! [SY3466: $i] :
( ~ ( ~ ! [SY3467: $i] :
( ~ ( subset @ SY3467 @ SY3466 )
| ( in @ SY3467 @ ( sK3_SY3278 @ SY3466 @ SV43 ) ) )
| ~ ( in @ ( sK3_SY3278 @ SY3466 @ SV43 ) @ ( sK2_B @ SV43 ) ) )
| ~ ( in @ SY3466 @ ( sK2_B @ SV43 ) ) )
| ~ ~ ( ~ ! [SY3468: $i,SY3469: $i] :
( ~ ( in @ SY3468 @ ( sK2_B @ SV43 ) )
| ~ ( subset @ SY3469 @ SY3468 )
| ( in @ SY3469 @ ( sK2_B @ SV43 ) ) )
| ~ ( in @ SV43 @ ( sK2_B @ SV43 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(615,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK49_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK49_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK47_C @ SX1 @ SX0 ) @ ( sK48_SY3309 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(616,plain,
! [SV44: $i] :
( ( ! [SY3470: $i] :
~ ( ~ ! [SY3471: $i,SY3472: $i] :
( ~ ( in @ SV44 @ SY3471 )
| ~ ( in @ SY3470 @ SY3472 )
| ( in @ ( ordered_pair @ SV44 @ SY3470 ) @ ( cartesian_product2 @ SY3471 @ SY3472 ) ) )
| ~ ~ ( ~ ! [SY3473: $i] :
( ! [SY3474: $i] :
~ ( in @ ( ordered_pair @ SV44 @ SY3470 ) @ ( cartesian_product2 @ SY3473 @ SY3474 ) )
| ( in @ SV44 @ SY3473 ) )
| ~ ! [SY3475: $i,SY3476: $i] :
( ~ ( in @ ( ordered_pair @ SV44 @ SY3470 ) @ ( cartesian_product2 @ SY3475 @ SY3476 ) )
| ( in @ SY3470 @ SY3476 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(617,plain,
! [SV45: $i] :
( ( ~ ( relation @ SV45 )
| ~ ( ~ ! [SY3477: $i] :
( ~ ( ~ ( ! [SY3478: $i] :
~ ( in @ ( ordered_pair @ ( sK26_C @ SY3477 @ SV45 ) @ SY3478 ) @ SV45 )
| ~ ( in @ ( sK26_C @ SY3477 @ SV45 ) @ SY3477 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK26_C @ SY3477 @ SV45 ) @ ( sK27_SY3298 @ SY3477 @ SV45 ) ) @ SV45 )
| ( in @ ( sK26_C @ SY3477 @ SV45 ) @ SY3477 ) ) )
| ( SY3477
= ( relation_dom @ SV45 ) ) )
| ~ ! [SY3479: $i] :
( ( SY3479
!= ( relation_dom @ SV45 ) )
| ~ ( ~ ! [SY3480: $i] :
( ! [SY3481: $i] :
~ ( in @ ( ordered_pair @ SY3480 @ SY3481 ) @ SV45 )
| ( in @ SY3480 @ SY3479 ) )
| ~ ! [SY3482: $i] :
( ~ ( in @ SY3482 @ SY3479 )
| ( in @ ( ordered_pair @ SY3482 @ ( sK25_D @ SY3482 @ SY3479 @ SV45 ) ) @ SV45 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(618,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[534]) ).
thf(619,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK42_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[535]) ).
thf(620,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK43_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK43_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK43_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK43_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[536]) ).
thf(621,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK74_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK74_C @ SX1 @ SX0 ) )
!= ( sK74_C @ SX1 @ SX0 ) ) ) )
| ( ( relation_dom @ SX1 )
!= SX0 )
| ( SX1
= ( identity_relation @ SX0 ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( ( apply @ SX1 @ SX2 )
= SX2 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(622,plain,
! [SV46: $i] :
( ( ~ ( function @ SV46 )
| ~ ( relation @ SV46 )
| ~ ( one_to_one @ SV46 )
| ~ ( ~ ! [SY3483: $i] :
( ~ ( function @ SY3483 )
| ~ ( relation @ SY3483 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY3322 @ SY3483 @ SV46 )
= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ( ( sK70_C @ SY3483 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SY3483 @ SV46 )
= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SY3483 @ SV46 )
= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ( ( sK71_SY3322 @ SY3483 @ SV46 )
!= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK70_C @ SY3483 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK71_SY3322 @ SY3483 @ SV46 )
!= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY3483 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK70_C @ SY3483 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SY3483 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SY3483 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK71_SY3322 @ SY3483 @ SV46 )
!= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ( ( relation_dom @ SY3483 )
!= ( relation_rng @ SV46 ) )
| ( SY3483
= ( function_inverse @ SV46 ) ) )
| ~ ~ ( ~ ! [SY3484: $i] :
( ~ ( function @ SY3484 )
| ~ ( relation @ SY3484 )
| ( SY3484
!= ( function_inverse @ SV46 ) )
| ~ ( ~ ~ ( ~ ! [SY3485: $i,SY3486: $i] :
( ( SY3486
!= ( apply @ SY3484 @ SY3485 ) )
| ~ ( in @ SY3485 @ ( relation_rng @ SV46 ) )
| ( SY3485
= ( apply @ SV46 @ SY3486 ) ) )
| ~ ! [SY3487: $i,SY3488: $i] :
( ( SY3488
!= ( apply @ SY3484 @ SY3487 ) )
| ~ ( in @ SY3487 @ ( relation_rng @ SV46 ) )
| ( in @ SY3488 @ ( relation_dom @ SV46 ) ) ) )
| ~ ~ ( ~ ! [SY3489: $i,SY3490: $i] :
( ( SY3489
!= ( apply @ SV46 @ SY3490 ) )
| ~ ( in @ SY3490 @ ( relation_dom @ SV46 ) )
| ( SY3490
= ( apply @ SY3484 @ SY3489 ) ) )
| ~ ! [SY3491: $i] :
( ! [SY3492: $i] :
( ( SY3491
!= ( apply @ SV46 @ SY3492 ) )
| ~ ( in @ SY3492 @ ( relation_dom @ SV46 ) ) )
| ( in @ SY3491 @ ( relation_rng @ SV46 ) ) ) ) ) )
| ~ ! [SY3493: $i] :
( ~ ( function @ SY3493 )
| ~ ( relation @ SY3493 )
| ( SY3493
!= ( function_inverse @ SV46 ) )
| ( ( relation_dom @ SY3493 )
= ( relation_rng @ SV46 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(623,plain,
! [SV47: $i] :
( ( ~ ( relation @ SV47 )
| ! [SY3494: $i] :
( ~ ( relation @ SY3494 )
| ~ ( ~ ! [SY3495: $i] :
( ~ ( relation @ SY3495 )
| ~ ( ~ ( ! [SY3496: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY3495 @ SY3494 @ SV47 ) @ SY3496 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3496 @ ( sK9_SY3284 @ SY3495 @ SY3494 @ SV47 ) ) @ SY3494 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SY3495 @ SY3494 @ SV47 ) @ ( sK9_SY3284 @ SY3495 @ SY3494 @ SV47 ) ) @ SY3495 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY3495 @ SY3494 @ SV47 ) @ ( sK10_SY3288 @ SY3495 @ SY3494 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY3288 @ SY3495 @ SY3494 @ SV47 ) @ ( sK9_SY3284 @ SY3495 @ SY3494 @ SV47 ) ) @ SY3494 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SY3495 @ SY3494 @ SV47 ) @ ( sK9_SY3284 @ SY3495 @ SY3494 @ SV47 ) ) @ SY3495 ) ) )
| ( SY3495
= ( relation_composition @ SV47 @ SY3494 ) ) )
| ~ ! [SY3497: $i] :
( ~ ( relation @ SY3497 )
| ( SY3497
!= ( relation_composition @ SV47 @ SY3494 ) )
| ~ ( ~ ! [SY3498: $i,SY3499: $i] :
( ! [SY3500: $i] :
( ~ ( in @ ( ordered_pair @ SY3498 @ SY3500 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3500 @ SY3499 ) @ SY3494 ) )
| ( in @ ( ordered_pair @ SY3498 @ SY3499 ) @ SY3497 ) )
| ~ ! [SY3501: $i,SY3502: $i] :
( ~ ( in @ ( ordered_pair @ SY3501 @ SY3502 ) @ SY3497 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3501 @ ( sK7_F @ SY3502 @ SY3501 @ SY3497 @ SY3494 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY3502 @ SY3501 @ SY3497 @ SY3494 @ SV47 ) @ SY3502 ) @ SY3494 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(624,plain,
! [SV48: $i] :
( ( ~ ( ~ ! [SY3503: $i,SY3504: $i] :
( ~ ( in @ SV48 @ SY3504 )
| ~ ( in @ SY3503 @ SY3504 )
| ( subset @ ( unordered_pair @ SV48 @ SY3503 ) @ SY3504 ) )
| ~ ~ ( ~ ! [SY3505: $i,SY3506: $i] :
( ~ ( subset @ ( unordered_pair @ SV48 @ SY3505 ) @ SY3506 )
| ( in @ SV48 @ SY3506 ) )
| ~ ! [SY3507: $i,SY3508: $i] :
( ~ ( subset @ ( unordered_pair @ SV48 @ SY3507 ) @ SY3508 )
| ( in @ SY3507 @ SY3508 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(625,plain,
! [SV49: $i] :
( ( ! [SY3509: $i] :
~ ( ~ ! [SY3510: $i,SY3511: $i] :
( ~ ( relation @ SY3511 )
| ~ ( in @ SV49 @ SY3510 )
| ~ ( in @ ( ordered_pair @ SV49 @ SY3509 ) @ SY3511 )
| ( in @ ( ordered_pair @ SV49 @ SY3509 ) @ ( relation_composition @ ( identity_relation @ SY3510 ) @ SY3511 ) ) )
| ~ ~ ( ~ ! [SY3512: $i,SY3513: $i] :
( ~ ( relation @ SY3513 )
| ~ ( in @ ( ordered_pair @ SV49 @ SY3509 ) @ ( relation_composition @ ( identity_relation @ SY3512 ) @ SY3513 ) )
| ( in @ SV49 @ SY3512 ) )
| ~ ! [SY3514: $i,SY3515: $i] :
( ~ ( relation @ SY3515 )
| ~ ( in @ ( ordered_pair @ SV49 @ SY3509 ) @ ( relation_composition @ ( identity_relation @ SY3514 ) @ SY3515 ) )
| ( in @ ( ordered_pair @ SV49 @ SY3509 ) @ SY3515 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(626,plain,
! [SV50: $i] :
( ( ! [SY3516: $i] :
( ~ ( ~ ! [SY3517: $i] :
( ~ ( in @ SY3517 @ SY3516 )
| ~ ( in @ SY3517 @ ( sK4_C @ SY3516 @ SV50 ) ) )
| ~ ( in @ ( sK4_C @ SY3516 @ SV50 ) @ SY3516 ) )
| ~ ( in @ SV50 @ SY3516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(627,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_B @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK12_SY3289 @ SX0 ) @ ( relation_dom @ SX0 ) ) )
| ( ( apply @ SX0 @ ( sK11_B @ SX0 ) )
!= ( apply @ SX0 @ ( sK12_SY3289 @ SX0 ) ) ) )
| ~ ( ( ( sK11_B @ SX0 )
!= ( sK12_SY3289 @ SX0 ) ) ) )
| ( one_to_one @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ~ ( in @ SX2 @ ( relation_dom @ SX0 ) )
| ( ( apply @ SX0 @ SX1 )
!= ( apply @ SX0 @ SX2 ) )
| ( SX1 = SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(628,plain,
! [SV51: $i] :
( ( ~ ( ~ ! [SY3518: $i,SY3519: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK37_D @ SY3519 @ SY3518 @ SV51 ) @ SY3519 )
| ~ ( in @ ( sK37_D @ SY3519 @ SY3518 @ SV51 ) @ SV51 ) )
| ~ ( ~ ( in @ ( sK37_D @ SY3519 @ SY3518 @ SV51 ) @ SY3519 )
| ~ ( in @ ( sK37_D @ SY3519 @ SY3518 @ SV51 ) @ SY3518 ) ) )
| ~ ( ( in @ ( sK37_D @ SY3519 @ SY3518 @ SV51 ) @ SY3519 )
| ( in @ ( sK37_D @ SY3519 @ SY3518 @ SV51 ) @ SV51 )
| ( in @ ( sK37_D @ SY3519 @ SY3518 @ SV51 ) @ SY3518 ) ) )
| ( SY3519
= ( set_union2 @ SV51 @ SY3518 ) ) )
| ~ ! [SY3520: $i,SY3521: $i] :
( ( SY3521
!= ( set_union2 @ SV51 @ SY3520 ) )
| ~ ( ~ ! [SY3522: $i] :
( ~ ( in @ SY3522 @ SY3521 )
| ( in @ SY3522 @ SV51 )
| ( in @ SY3522 @ SY3520 ) )
| ~ ~ ( ~ ! [SY3523: $i] :
( ~ ( in @ SY3523 @ SV51 )
| ( in @ SY3523 @ SY3521 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY3520 )
| ( in @ SX3 @ SY3521 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(629,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[545]) ).
thf(630,plain,
! [SV52: $i] :
( ( ~ ( relation @ SV52 )
| ~ ( ~ ! [SY3525: $i] :
( ~ ( relation @ SY3525 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK30_C @ SY3525 @ SV52 ) @ ( sK31_SY3299 @ SY3525 @ SV52 ) ) @ SV52 )
| ~ ~ ( in @ ( ordered_pair @ ( sK30_C @ SY3525 @ SV52 ) @ ( sK31_SY3299 @ SY3525 @ SV52 ) ) @ SY3525 ) )
| ( subset @ SV52 @ SY3525 ) )
| ~ ! [SY3526: $i] :
( ~ ( relation @ SY3526 )
| ~ ( subset @ SV52 @ SY3526 )
| ! [SY3527: $i,SY3528: $i] :
( ~ ( in @ ( ordered_pair @ SY3527 @ SY3528 ) @ SV52 )
| ( in @ ( ordered_pair @ SY3527 @ SY3528 ) @ SY3526 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(631,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK46_SY3307 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK45_C @ SX1 @ SX0 ) @ ( sK46_SY3307 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK45_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK45_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK45_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK44_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK44_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(632,plain,
! [SV53: $i] :
( ( ~ ( function @ SV53 )
| ~ ( relation @ SV53 )
| ~ ( ~ ! [SY3529: $i,SY3530: $i] :
( ~ ( ~ ( ~ ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) ) @ SY3529 )
| ~ ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ SY3530 ) )
| ~ ~ ( ~ ( ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ SY3530 ) )
| ~ ( ( in @ ( apply @ SV53 @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) ) @ SY3529 )
| ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ SY3530 ) ) ) )
| ( SY3530
= ( relation_inverse_image @ SV53 @ SY3529 ) ) )
| ~ ! [SY3531: $i,SY3532: $i] :
( ( SY3532
!= ( relation_inverse_image @ SV53 @ SY3531 ) )
| ~ ( ~ ! [SY3533: $i] :
( ~ ( in @ SY3533 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SY3533 ) @ SY3531 )
| ( in @ SY3533 @ SY3532 ) )
| ~ ~ ( ~ ! [SY3534: $i] :
( ~ ( in @ SY3534 @ SY3532 )
| ( in @ SY3534 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY3535: $i] :
( ~ ( in @ SY3535 @ SY3532 )
| ( in @ ( apply @ SV53 @ SY3535 ) @ SY3531 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(633,plain,
! [SV54: $i] :
( ( ~ ( ~ ! [SY3536: $i,SY3537: $i] :
( ~ ( ~ ( ~ ( in @ ( sK28_D @ SY3537 @ SY3536 @ SV54 ) @ SV54 )
| ~ ( in @ ( sK28_D @ SY3537 @ SY3536 @ SV54 ) @ SY3536 )
| ~ ( in @ ( sK28_D @ SY3537 @ SY3536 @ SV54 ) @ SY3537 ) )
| ~ ~ ( ~ ( ( in @ ( sK28_D @ SY3537 @ SY3536 @ SV54 ) @ SV54 )
| ( in @ ( sK28_D @ SY3537 @ SY3536 @ SV54 ) @ SY3537 ) )
| ~ ( ( in @ ( sK28_D @ SY3537 @ SY3536 @ SV54 ) @ SY3536 )
| ( in @ ( sK28_D @ SY3537 @ SY3536 @ SV54 ) @ SY3537 ) ) ) )
| ( SY3537
= ( set_intersection2 @ SV54 @ SY3536 ) ) )
| ~ ! [SY3538: $i,SY3539: $i] :
( ( SY3539
!= ( set_intersection2 @ SV54 @ SY3538 ) )
| ~ ( ~ ! [SY3540: $i] :
( ~ ( in @ SY3540 @ SV54 )
| ~ ( in @ SY3540 @ SY3538 )
| ( in @ SY3540 @ SY3539 ) )
| ~ ~ ( ~ ! [SY3541: $i] :
( ~ ( in @ SY3541 @ SY3539 )
| ( in @ SY3541 @ SV54 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY3539 )
| ( in @ SX3 @ SY3538 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(634,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[550]) ).
thf(635,plain,
! [SV55: $i] :
( ( ~ ( ~ ! [SY3543: $i,SY3544: $i] :
( ~ ( ~ ( ~ ( in @ ( sK21_D @ SY3544 @ SY3543 @ SV55 ) @ SV55 )
| ( in @ ( sK21_D @ SY3544 @ SY3543 @ SV55 ) @ SY3543 )
| ~ ( in @ ( sK21_D @ SY3544 @ SY3543 @ SV55 ) @ SY3544 ) )
| ~ ~ ( ~ ( ( in @ ( sK21_D @ SY3544 @ SY3543 @ SV55 ) @ SV55 )
| ( in @ ( sK21_D @ SY3544 @ SY3543 @ SV55 ) @ SY3544 ) )
| ~ ( ~ ( in @ ( sK21_D @ SY3544 @ SY3543 @ SV55 ) @ SY3543 )
| ( in @ ( sK21_D @ SY3544 @ SY3543 @ SV55 ) @ SY3544 ) ) ) )
| ( SY3544
= ( set_difference @ SV55 @ SY3543 ) ) )
| ~ ! [SY3545: $i,SY3546: $i] :
( ( SY3546
!= ( set_difference @ SV55 @ SY3545 ) )
| ~ ( ~ ! [SY3547: $i] :
( ~ ( in @ SY3547 @ SV55 )
| ( in @ SY3547 @ SY3545 )
| ( in @ SY3547 @ SY3546 ) )
| ~ ~ ( ~ ! [SY3548: $i] :
( ~ ( in @ SY3548 @ SY3546 )
| ( in @ SY3548 @ SV55 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY3546 )
| ~ ( in @ SX3 @ SY3545 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(636,plain,
! [SV56: $i] :
( ( ~ ( function @ SV56 )
| ~ ( relation @ SV56 )
| ~ ( ~ ! [SY3550: $i] :
( ~ ( ~ ( ! [SY3551: $i] :
( ( ( sK19_C @ SY3550 @ SV56 )
!= ( apply @ SV56 @ SY3551 ) )
| ~ ( in @ SY3551 @ ( relation_dom @ SV56 ) ) )
| ~ ( in @ ( sK19_C @ SY3550 @ SV56 ) @ SY3550 ) )
| ~ ( ~ ( ( ( sK19_C @ SY3550 @ SV56 )
!= ( apply @ SV56 @ ( sK20_SY3294 @ SY3550 @ SV56 ) ) )
| ~ ( in @ ( sK20_SY3294 @ SY3550 @ SV56 ) @ ( relation_dom @ SV56 ) ) )
| ( in @ ( sK19_C @ SY3550 @ SV56 ) @ SY3550 ) ) )
| ( SY3550
= ( relation_rng @ SV56 ) ) )
| ~ ! [SY3552: $i] :
( ( SY3552
!= ( relation_rng @ SV56 ) )
| ~ ( ~ ! [SY3553: $i] :
( ! [SY3554: $i] :
( ( SY3553
!= ( apply @ SV56 @ SY3554 ) )
| ~ ( in @ SY3554 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY3553 @ SY3552 ) )
| ~ ! [SY3555: $i] :
( ~ ( in @ SY3555 @ SY3552 )
| ~ ( ( SY3555
!= ( apply @ SV56 @ ( sK18_D @ SY3555 @ SY3552 @ SV56 ) ) )
| ~ ( in @ ( sK18_D @ SY3555 @ SY3552 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(637,plain,
! [SV57: $i] :
( ( ~ ( ~ ! [SY3556: $i,SY3557: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK38_D @ SY3557 @ SY3556 @ SV57 ) @ SY3557 )
| ( ( sK38_D @ SY3557 @ SY3556 @ SV57 )
!= SV57 ) )
| ~ ( ~ ( in @ ( sK38_D @ SY3557 @ SY3556 @ SV57 ) @ SY3557 )
| ( ( sK38_D @ SY3557 @ SY3556 @ SV57 )
!= SY3556 ) ) )
| ~ ( ( in @ ( sK38_D @ SY3557 @ SY3556 @ SV57 ) @ SY3557 )
| ( ( sK38_D @ SY3557 @ SY3556 @ SV57 )
= SV57 )
| ( ( sK38_D @ SY3557 @ SY3556 @ SV57 )
= SY3556 ) ) )
| ( SY3557
= ( unordered_pair @ SV57 @ SY3556 ) ) )
| ~ ! [SY3558: $i,SY3559: $i] :
( ( SY3559
!= ( unordered_pair @ SV57 @ SY3558 ) )
| ~ ( ~ ! [SY3560: $i] :
( ~ ( in @ SY3560 @ SY3559 )
| ( SY3560 = SV57 )
| ( SY3560 = SY3558 ) )
| ~ ~ ( ~ ! [SY3561: $i] :
( ( SY3561 != SV57 )
| ( in @ SY3561 @ SY3559 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY3558 )
| ( in @ SX3 @ SY3559 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(638,plain,
! [SV58: $i] :
( ( ! [SY3563: $i] :
( ~ ( function @ SY3563 )
| ~ ( relation @ SY3563 )
| ~ ( ~ ! [SY3564: $i] :
( ~ ( function @ SY3564 )
| ~ ( relation @ SY3564 )
| ~ ( ~ ( in @ ( sK67_D @ SY3564 @ SY3563 @ SV58 ) @ ( relation_dom @ SY3563 ) )
| ~ ( ( ( apply @ SY3563 @ ( sK67_D @ SY3564 @ SY3563 @ SV58 ) )
!= ( apply @ SY3564 @ ( sK67_D @ SY3564 @ SY3563 @ SV58 ) ) ) ) )
| ( ( relation_dom @ SY3563 )
!= ( set_intersection2 @ ( relation_dom @ SY3564 ) @ SV58 ) )
| ( SY3563
= ( relation_dom_restriction @ SY3564 @ SV58 ) ) )
| ~ ~ ( ~ ! [SY3565: $i] :
( ~ ( function @ SY3565 )
| ~ ( relation @ SY3565 )
| ( SY3563
!= ( relation_dom_restriction @ SY3565 @ SV58 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( relation_dom @ SY3563 ) )
| ( ( apply @ SY3563 @ SX3 )
= ( apply @ SY3565 @ SX3 ) ) ) )
| ~ ! [SY3567: $i] :
( ~ ( function @ SY3567 )
| ~ ( relation @ SY3567 )
| ( SY3563
!= ( relation_dom_restriction @ SY3567 @ SV58 ) )
| ( ( relation_dom @ SY3563 )
= ( set_intersection2 @ ( relation_dom @ SY3567 ) @ SV58 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(639,plain,
! [SV59: $i] :
( ( ~ ( relation @ SV59 )
| ~ ( ~ ! [SY3568: $i] :
( ~ ( relation @ SY3568 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_C @ SY3568 @ SV59 ) @ ( sK40_SY3306 @ SY3568 @ SV59 ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK39_C @ SY3568 @ SV59 ) @ ( sK40_SY3306 @ SY3568 @ SV59 ) ) @ SY3568 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK39_C @ SY3568 @ SV59 ) @ ( sK40_SY3306 @ SY3568 @ SV59 ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK39_C @ SY3568 @ SV59 ) @ ( sK40_SY3306 @ SY3568 @ SV59 ) ) @ SY3568 ) ) )
| ( SV59 = SY3568 ) )
| ~ ! [SY3569: $i] :
( ~ ( relation @ SY3569 )
| ( SV59 != SY3569 )
| ~ ( ~ ! [SY3570: $i,SY3571: $i] :
( ~ ( in @ ( ordered_pair @ SY3570 @ SY3571 ) @ SV59 )
| ( in @ ( ordered_pair @ SY3570 @ SY3571 ) @ SY3569 ) )
| ~ ! [SY3572: $i,SY3573: $i] :
( ~ ( in @ ( ordered_pair @ SY3572 @ SY3573 ) @ SY3569 )
| ( in @ ( ordered_pair @ SY3572 @ SY3573 ) @ SV59 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(640,plain,
! [SV60: $i] :
( ( ! [SY3574: $i] :
( ~ ( ~ ( in @ ( sK78_C @ SY3574 @ SV60 ) @ SV60 )
| ~ ~ ( in @ ( sK78_C @ SY3574 @ SV60 ) @ SY3574 ) )
| ( element @ SV60 @ ( powerset @ SY3574 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(641,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ ( sK24_SY3296 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK24_SY3296 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK22_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[557]) ).
thf(642,plain,
! [SV61: $i] :
( ( ! [SY3575: $i] :
~ ( ~ ! [SY3576: $i,SY3577: $i] :
( ~ ( in @ SV61 @ SY3576 )
| ~ ( in @ SY3575 @ SY3577 )
| ( in @ ( ordered_pair @ SV61 @ SY3575 ) @ ( cartesian_product2 @ SY3576 @ SY3577 ) ) )
| ~ ~ ( ~ ! [SY3578: $i] :
( ! [SY3579: $i] :
~ ( in @ ( ordered_pair @ SV61 @ SY3575 ) @ ( cartesian_product2 @ SY3578 @ SY3579 ) )
| ( in @ SV61 @ SY3578 ) )
| ~ ! [SY3580: $i,SY3581: $i] :
( ~ ( in @ ( ordered_pair @ SV61 @ SY3575 ) @ ( cartesian_product2 @ SY3580 @ SY3581 ) )
| ( in @ SY3575 @ SY3581 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(643,plain,
! [SV62: $i] :
( ( ~ ( ~ ! [SY3582: $i,SY3583: $i] :
( ~ ( function @ SY3583 )
| ~ ( relation @ SY3583 )
| ~ ( in @ SY3582 @ ( relation_dom @ SY3583 ) )
| ~ ( in @ SY3582 @ SV62 )
| ( in @ SY3582 @ ( relation_dom @ ( relation_dom_restriction @ SY3583 @ SV62 ) ) ) )
| ~ ~ ( ~ ! [SY3584: $i,SY3585: $i] :
( ~ ( function @ SY3585 )
| ~ ( relation @ SY3585 )
| ~ ( in @ SY3584 @ ( relation_dom @ ( relation_dom_restriction @ SY3585 @ SV62 ) ) )
| ( in @ SY3584 @ ( relation_dom @ SY3585 ) ) )
| ~ ! [SY3586: $i,SY3587: $i] :
( ~ ( function @ SY3587 )
| ~ ( relation @ SY3587 )
| ~ ( in @ SY3586 @ ( relation_dom @ ( relation_dom_restriction @ SY3587 @ SV62 ) ) )
| ( in @ SY3586 @ SV62 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(644,plain,
! [SV63: $i] :
( ( ~ ( ~ ! [SY3588: $i,SY3589: $i] :
( ~ ( ~ ( ! [SY3590: $i,SY3591: $i] :
( ~ ( in @ SY3590 @ SV63 )
| ~ ( in @ SY3591 @ SY3588 )
| ( ( sK34_D @ SY3589 @ SY3588 @ SV63 )
!= ( ordered_pair @ SY3590 @ SY3591 ) ) )
| ~ ( in @ ( sK34_D @ SY3589 @ SY3588 @ SV63 ) @ SY3589 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK35_SY3303 @ SY3589 @ SY3588 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK36_SY3305 @ SY3589 @ SY3588 @ SV63 ) @ SY3588 ) )
| ( ( sK34_D @ SY3589 @ SY3588 @ SV63 )
!= ( ordered_pair @ ( sK35_SY3303 @ SY3589 @ SY3588 @ SV63 ) @ ( sK36_SY3305 @ SY3589 @ SY3588 @ SV63 ) ) ) )
| ( in @ ( sK34_D @ SY3589 @ SY3588 @ SV63 ) @ SY3589 ) ) )
| ( SY3589
= ( cartesian_product2 @ SV63 @ SY3588 ) ) )
| ~ ! [SY3592: $i,SY3593: $i] :
( ( SY3593
!= ( cartesian_product2 @ SV63 @ SY3592 ) )
| ~ ( ~ ! [SY3594: $i] :
( ! [SY3595: $i,SY3596: $i] :
( ~ ( in @ SY3595 @ SV63 )
| ~ ( in @ SY3596 @ SY3592 )
| ( SY3594
!= ( ordered_pair @ SY3595 @ SY3596 ) ) )
| ( in @ SY3594 @ SY3593 ) )
| ~ ! [SY3597: $i] :
( ~ ( in @ SY3597 @ SY3593 )
| ~ ( ~ ~ ( ~ ( in @ ( sK32_E @ SY3597 @ SY3593 @ SY3592 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK33_SY3300 @ SY3597 @ SY3593 @ SY3592 @ SV63 ) @ SY3592 ) )
| ( SY3597
!= ( ordered_pair @ ( sK32_E @ SY3597 @ SY3593 @ SY3592 @ SV63 ) @ ( sK33_SY3300 @ SY3597 @ SY3593 @ SY3592 @ SV63 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(645,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK73_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK73_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(646,plain,
! [SV64: $i] :
( ( ~ ( ~ ! [SY3598: $i,SY3599: $i] :
( ~ ( relation @ SY3599 )
| ! [SY3600: $i] :
( ~ ( in @ SY3600 @ ( relation_dom @ SY3599 ) )
| ~ ( in @ ( ordered_pair @ SY3600 @ SV64 ) @ SY3599 )
| ~ ( in @ SY3600 @ SY3598 ) )
| ( in @ SV64 @ ( relation_image @ SY3599 @ SY3598 ) ) )
| ~ ! [SY3601: $i,SY3602: $i] :
( ~ ( relation @ SY3602 )
| ~ ( in @ SV64 @ ( relation_image @ SY3602 @ SY3601 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK76_D @ SY3602 @ SY3601 @ SV64 ) @ ( relation_dom @ SY3602 ) )
| ~ ( in @ ( ordered_pair @ ( sK76_D @ SY3602 @ SY3601 @ SV64 ) @ SV64 ) @ SY3602 ) )
| ~ ( in @ ( sK76_D @ SY3602 @ SY3601 @ SV64 ) @ SY3601 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(647,plain,
! [SV65: $i] :
( ( ~ ( ~ ! [SY3603: $i,SY3604: $i] :
( ~ ( relation @ SY3604 )
| ~ ( in @ ( ordered_pair @ SV65 @ SY3603 ) @ SY3604 )
| ( in @ SV65 @ ( relation_dom @ SY3604 ) ) )
| ~ ! [SY3605: $i,SY3606: $i] :
( ~ ( relation @ SY3606 )
| ~ ( in @ ( ordered_pair @ SV65 @ SY3605 ) @ SY3606 )
| ( in @ SY3605 @ ( relation_rng @ SY3606 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(648,plain,
! [SV66: $i] :
( ( ~ ( function @ SV66 )
| ~ ( relation @ SV66 )
| ~ ( ~ ~ ( ~ ! [SY3607: $i] :
( ~ ( in @ SY3607 @ ( relation_dom @ SV66 ) )
| ! [SY3608: $i] :
( ( SY3608
!= ( apply @ SV66 @ SY3607 ) )
| ( in @ ( ordered_pair @ SY3607 @ SY3608 ) @ SV66 ) ) )
| ~ ! [SY3609: $i] :
( ~ ( in @ SY3609 @ ( relation_dom @ SV66 ) )
| ! [SY3610: $i] :
( ~ ( in @ ( ordered_pair @ SY3609 @ SY3610 ) @ SV66 )
| ( SY3610
= ( apply @ SV66 @ SY3609 ) ) ) ) )
| ~ ~ ( ~ ! [SY3611: $i] :
( ( in @ SY3611 @ ( relation_dom @ SV66 ) )
| ! [SY3612: $i] :
( ( SY3612
!= ( apply @ SV66 @ SY3611 ) )
| ( SY3612 = empty_set ) ) )
| ~ ! [SY3613: $i] :
( ( in @ SY3613 @ ( relation_dom @ SV66 ) )
| ! [SY3614: $i] :
( ( SY3614 != empty_set )
| ( SY3614
= ( apply @ SV66 @ SY3613 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(649,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(650,plain,
! [SV67: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV67 )
| ( ( set_union2 @ ( singleton @ SV1 ) @ SV67 )
= SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(651,plain,
! [SV68: $i,SV2: $i] :
( ( ~ ( disjoint @ ( singleton @ SV2 ) @ SV68 )
| ~ ( in @ SV2 @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(652,plain,
! [SV69: $i,SV3: $i] :
( ( ( in @ SV3 @ SV69 )
| ( disjoint @ ( singleton @ SV3 ) @ SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(653,plain,
! [SV4: $i,SV70: $i] :
( ( ~ ( element @ SV70 @ ( powerset @ SV4 ) )
| ! [SY3615: $i] :
( ~ ( in @ SY3615 @ SV70 )
| ( in @ SY3615 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(654,plain,
! [SV71: $i,SV5: $i] :
( ( ~ ( subset @ SV5 @ SV71 )
| ! [SY3616: $i] :
( ( in @ SY3616 @ SV5 )
| ( subset @ SV5 @ ( set_difference @ SV71 @ ( singleton @ SY3616 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(655,plain,
! [SV72: $i,SV6: $i] :
( ( ~ ( in @ SV6 @ SV72 )
| ( subset @ SV6 @ ( union @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(656,plain,
! [SV7: $i,SV73: $i] :
( ( ~ ( function @ SV73 )
| ~ ( relation @ SV73 )
| ! [SY3617: $i] :
( ~ ( function @ SY3617 )
| ~ ( relation @ SY3617 )
| ~ ( in @ SV7 @ ( relation_dom @ ( relation_composition @ SY3617 @ SV73 ) ) )
| ( ( apply @ ( relation_composition @ SY3617 @ SV73 ) @ SV7 )
= ( apply @ SV73 @ ( apply @ SY3617 @ SV7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(657,plain,
! [SV8: $i,SV74: $i] :
( ( ~ ( function @ SV74 )
| ~ ( relation @ SV74 )
| ! [SY3618: $i] :
( ~ ( function @ SY3618 )
| ~ ( relation @ SY3618 )
| ~ ( in @ SV8 @ ( relation_dom @ SV74 ) )
| ( ( apply @ ( relation_composition @ SV74 @ SY3618 ) @ SV8 )
= ( apply @ SY3618 @ ( apply @ SV74 @ SV8 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(658,plain,
! [SV9: $i,SV75: $i] :
( ( ~ ( in @ SV75 @ SV9 )
| ( ( apply @ ( identity_relation @ SV9 ) @ SV75 )
= SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(659,plain,
! [SV76: $i,SV10: $i] :
( ( ! [SY3619: $i] :
( ~ ( in @ SV10 @ SV76 )
| ~ ( in @ SV76 @ SY3619 )
| ~ ( in @ SY3619 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(660,plain,
! [SV77: $i,SV11: $i] :
( ( ~ ( in @ SV11 @ SV77 )
| ( ( set_union2 @ ( singleton @ SV11 ) @ SV77 )
= SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(661,plain,
! [SV12: $i] :
( ( ( SV12 = empty_set )
= $true )
| ( ( ! [SY3343: $i] :
( ~ ( element @ SY3343 @ ( powerset @ SV12 ) )
| ! [SY3344: $i] :
( ~ ( element @ SY3344 @ SV12 )
| ( in @ SY3344 @ SY3343 )
| ( in @ SY3344 @ ( subset_complement @ SV12 @ SY3343 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[577]) ).
thf(662,plain,
! [SV78: $i,SV13: $i] :
( ( ! [SY3620: $i] :
( ~ ( element @ SY3620 @ ( powerset @ SV13 ) )
| ~ ( in @ SV78 @ ( subset_complement @ SV13 @ SY3620 ) )
| ~ ( in @ SV78 @ SY3620 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(663,plain,
! [SV14: $i] :
( ( ( ~ ( relation @ SV14 ) )
= $true )
| ( ( ( in @ ( ordered_pair @ ( sK68_B @ SV14 ) @ ( sK69_SY3321 @ SV14 ) ) @ SV14 )
| ( SV14 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[579]) ).
thf(664,plain,
! [SV15: $i,SV79: $i] :
( ( ! [SY3621: $i] :
( ~ ( function @ SY3621 )
| ~ ( relation @ SY3621 )
| ~ ( in @ SV79 @ ( relation_dom @ ( relation_dom_restriction @ SY3621 @ SV15 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SY3621 @ SV15 ) @ SV79 )
= ( apply @ SY3621 @ SV79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(665,plain,
! [SV16: $i,SV80: $i] :
( ( ! [SY3622: $i] :
( ~ ( function @ SY3622 )
| ~ ( relation @ SY3622 )
| ~ ( in @ SV80 @ SV16 )
| ( ( apply @ ( relation_dom_restriction @ SY3622 @ SV16 ) @ SV80 )
= ( apply @ SY3622 @ SV80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(666,plain,
! [SV81: $i,SV17: $i] :
( ( ~ ( in @ SV17 @ SV81 )
| ( subset @ SV17 @ ( union @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(667,plain,
! [SV82: $i,SV18: $i] :
( ( ~ ( in @ SV18 @ SV82 )
| ~ ( in @ SV82 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(668,plain,
! [SV20: $i] :
( ( empty @ ( succ @ SV20 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(669,plain,
! [SV83: $i,SV21: $i] :
( ( ~ ( in @ SV21 @ SV83 )
| ( element @ SV21 @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(670,plain,
! [SV84: $i,SV22: $i] :
( ( ~ ( element @ SV22 @ SV84 )
| ( empty @ SV84 )
| ( in @ SV22 @ SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(671,plain,
! [SV23: $i,SV85: $i] :
( ( ! [SY3623: $i] :
( ~ ( element @ SV85 @ ( powerset @ SY3623 ) )
| ~ ( in @ SV23 @ SV85 )
| ( element @ SV23 @ SY3623 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(672,plain,
! [SV24: $i,SV86: $i] :
( ( ! [SY3624: $i] :
( ~ ( element @ SV86 @ ( powerset @ SY3624 ) )
| ~ ( in @ SV24 @ SV86 )
| ~ ( empty @ SY3624 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(673,plain,
! [SV25: $i,SV87: $i] :
( ( ~ ( empty @ SV87 )
| ~ ( in @ SV25 @ SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(674,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK72_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[592]) ).
thf(675,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[592]) ).
thf(676,plain,
! [SV26: $i,SV88: $i] :
( ( ~ ( relation @ SV88 )
| ~ ( ~ ! [SY3625: $i] :
( ~ ( relation @ SY3625 )
| ~ ( ~ ( ~ ( in @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) @ SV26 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY3625 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) ) @ SV88 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY3625 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) ) @ SY3625 ) )
| ~ ~ ( ~ ( ( in @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) @ SV26 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY3625 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) ) @ SY3625 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SY3625 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) ) @ SV88 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY3625 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) ) @ SY3625 ) ) ) )
| ( SY3625
= ( relation_rng_restriction @ SV26 @ SV88 ) ) )
| ~ ! [SY3626: $i] :
( ~ ( relation @ SY3626 )
| ( SY3626
!= ( relation_rng_restriction @ SV26 @ SV88 ) )
| ~ ( ~ ! [SY3627: $i,SY3628: $i] :
( ~ ( in @ SY3628 @ SV26 )
| ~ ( in @ ( ordered_pair @ SY3627 @ SY3628 ) @ SV88 )
| ( in @ ( ordered_pair @ SY3627 @ SY3628 ) @ SY3626 ) )
| ~ ~ ( ~ ! [SY3365: $i,SY3366: $i] :
( ~ ( in @ ( ordered_pair @ SY3365 @ SY3366 ) @ SY3626 )
| ( in @ SY3366 @ SV26 ) )
| ~ ! [SY3631: $i,SY3632: $i] :
( ~ ( in @ ( ordered_pair @ SY3631 @ SY3632 ) @ SY3626 )
| ( in @ ( ordered_pair @ SY3631 @ SY3632 ) @ SV88 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(677,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK29_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK29_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[594]) ).
thf(678,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[594]) ).
thf(679,plain,
! [SV27: $i] :
( ( ~ ! [SY3369: $i,SY3370: $i] :
( ~ ( relation @ SY3370 )
| ~ ( in @ SV27 @ SY3369 )
| ~ ( in @ SV27 @ ( relation_dom @ SY3370 ) )
| ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SY3370 @ SY3369 ) ) ) )
| ~ ~ ( ~ ! [SY3371: $i,SY3372: $i] :
( ~ ( relation @ SY3372 )
| ~ ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SY3372 @ SY3371 ) ) )
| ( in @ SV27 @ SY3371 ) )
| ~ ! [SY3373: $i,SY3374: $i] :
( ~ ( relation @ SY3374 )
| ~ ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SY3374 @ SY3373 ) ) )
| ( in @ SV27 @ ( relation_dom @ SY3374 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[595]) ).
thf(680,plain,
! [SV28: $i] :
( ( ( ~ ( relation @ SV28 ) )
= $true )
| ( ( ~ ( ~ ! [SY3375: $i] :
( ~ ( relation @ SY3375 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SY3375 @ SV28 ) @ ( sK14_SY3290 @ SY3375 @ SV28 ) ) @ SY3375 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY3290 @ SY3375 @ SV28 ) @ ( sK13_C @ SY3375 @ SV28 ) ) @ SV28 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SY3375 @ SV28 ) @ ( sK14_SY3290 @ SY3375 @ SV28 ) ) @ SY3375 )
| ( in @ ( ordered_pair @ ( sK14_SY3290 @ SY3375 @ SV28 ) @ ( sK13_C @ SY3375 @ SV28 ) ) @ SV28 ) ) )
| ( SY3375
= ( relation_inverse @ SV28 ) ) )
| ~ ! [SY3376: $i] :
( ~ ( relation @ SY3376 )
| ( SY3376
!= ( relation_inverse @ SV28 ) )
| ~ ( ~ ! [SY3377: $i,SY3378: $i] :
( ~ ( in @ ( ordered_pair @ SY3377 @ SY3378 ) @ SY3376 )
| ( in @ ( ordered_pair @ SY3378 @ SY3377 ) @ SV28 ) )
| ~ ! [SY3379: $i,SY3380: $i] :
( ~ ( in @ ( ordered_pair @ SY3380 @ SY3379 ) @ SV28 )
| ( in @ ( ordered_pair @ SY3379 @ SY3380 ) @ SY3376 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[596]) ).
thf(681,plain,
! [SV29: $i] :
( ( ( ~ ( function @ SV29 )
| ~ ( relation @ SV29 ) )
= $true )
| ( ( ~ ( ~ ! [SY3381: $i,SY3382: $i] :
( ~ ( ~ ( ! [SY3383: $i] :
( ~ ( in @ SY3383 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3383 @ SY3381 )
| ( ( sK61_D @ SY3382 @ SY3381 @ SV29 )
!= ( apply @ SV29 @ SY3383 ) ) )
| ~ ( in @ ( sK61_D @ SY3382 @ SY3381 @ SV29 ) @ SY3382 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY3318 @ SY3382 @ SY3381 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK62_SY3318 @ SY3382 @ SY3381 @ SV29 ) @ SY3381 ) )
| ( ( sK61_D @ SY3382 @ SY3381 @ SV29 )
!= ( apply @ SV29 @ ( sK62_SY3318 @ SY3382 @ SY3381 @ SV29 ) ) ) )
| ( in @ ( sK61_D @ SY3382 @ SY3381 @ SV29 ) @ SY3382 ) ) )
| ( SY3382
= ( relation_image @ SV29 @ SY3381 ) ) )
| ~ ! [SY3384: $i,SY3385: $i] :
( ( SY3385
!= ( relation_image @ SV29 @ SY3384 ) )
| ~ ( ~ ! [SY3386: $i] :
( ! [SY3387: $i] :
( ~ ( in @ SY3387 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3387 @ SY3384 )
| ( SY3386
!= ( apply @ SV29 @ SY3387 ) ) )
| ( in @ SY3386 @ SY3385 ) )
| ~ ! [SY3388: $i] :
( ~ ( in @ SY3388 @ SY3385 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SY3388 @ SY3385 @ SY3384 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK60_E @ SY3388 @ SY3385 @ SY3384 @ SV29 ) @ SY3384 ) )
| ( SY3388
!= ( apply @ SV29 @ ( sK60_E @ SY3388 @ SY3385 @ SY3384 @ SV29 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[597]) ).
thf(682,plain,
! [SV30: $i] :
( ( ( ~ ( relation @ SV30 ) )
= $true )
| ( ( ~ ( ~ ! [SY3389: $i,SY3390: $i] :
( ~ ( ~ ( ! [SY3391: $i] :
( ~ ( in @ ( ordered_pair @ SY3391 @ ( sK55_D @ SY3390 @ SY3389 @ SV30 ) ) @ SV30 )
| ~ ( in @ SY3391 @ SY3389 ) )
| ~ ( in @ ( sK55_D @ SY3390 @ SY3389 @ SV30 ) @ SY3390 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_SY3315 @ SY3390 @ SY3389 @ SV30 ) @ ( sK55_D @ SY3390 @ SY3389 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK56_SY3315 @ SY3390 @ SY3389 @ SV30 ) @ SY3389 ) )
| ( in @ ( sK55_D @ SY3390 @ SY3389 @ SV30 ) @ SY3390 ) ) )
| ( SY3390
= ( relation_image @ SV30 @ SY3389 ) ) )
| ~ ! [SY3392: $i,SY3393: $i] :
( ( SY3393
!= ( relation_image @ SV30 @ SY3392 ) )
| ~ ( ~ ! [SY3394: $i] :
( ! [SY3395: $i] :
( ~ ( in @ ( ordered_pair @ SY3395 @ SY3394 ) @ SV30 )
| ~ ( in @ SY3395 @ SY3392 ) )
| ( in @ SY3394 @ SY3393 ) )
| ~ ! [SY3396: $i] :
( ~ ( in @ SY3396 @ SY3393 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SY3396 @ SY3393 @ SY3392 @ SV30 ) @ SY3396 ) @ SV30 )
| ~ ( in @ ( sK54_E @ SY3396 @ SY3393 @ SY3392 @ SV30 ) @ SY3392 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[598]) ).
thf(683,plain,
! [SV31: $i] :
( ( ( ~ ( relation @ SV31 ) )
= $true )
| ( ( ~ ( ~ ! [SY3397: $i,SY3398: $i] :
( ~ ( ~ ( ! [SY3399: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ SY3398 @ SY3397 @ SV31 ) @ SY3399 ) @ SV31 )
| ~ ( in @ SY3399 @ SY3397 ) )
| ~ ( in @ ( sK52_D @ SY3398 @ SY3397 @ SV31 ) @ SY3398 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SY3398 @ SY3397 @ SV31 ) @ ( sK53_SY3313 @ SY3398 @ SY3397 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( sK53_SY3313 @ SY3398 @ SY3397 @ SV31 ) @ SY3397 ) )
| ( in @ ( sK52_D @ SY3398 @ SY3397 @ SV31 ) @ SY3398 ) ) )
| ( SY3398
= ( relation_inverse_image @ SV31 @ SY3397 ) ) )
| ~ ! [SY3400: $i,SY3401: $i] :
( ( SY3401
!= ( relation_inverse_image @ SV31 @ SY3400 ) )
| ~ ( ~ ! [SY3402: $i] :
( ! [SY3403: $i] :
( ~ ( in @ ( ordered_pair @ SY3402 @ SY3403 ) @ SV31 )
| ~ ( in @ SY3403 @ SY3400 ) )
| ( in @ SY3402 @ SY3401 ) )
| ~ ! [SY3404: $i] :
( ~ ( in @ SY3404 @ SY3401 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3404 @ ( sK51_E @ SY3404 @ SY3401 @ SY3400 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( sK51_E @ SY3404 @ SY3401 @ SY3400 @ SV31 ) @ SY3400 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[599]) ).
thf(684,plain,
! [SV32: $i] :
( ( ( ~ ( relation @ SV32 ) )
= $true )
| ( ( ~ ( ~ ! [SY3405: $i,SY3406: $i] :
( ~ ( relation @ SY3406 )
| ~ ( ~ ( ~ ( in @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ SY3405 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ ( sK64_SY3319 @ SY3406 @ SY3405 @ SV32 ) ) @ SV32 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ ( sK64_SY3319 @ SY3406 @ SY3405 @ SV32 ) ) @ SY3406 ) )
| ~ ~ ( ~ ( ( in @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ SY3405 )
| ( in @ ( ordered_pair @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ ( sK64_SY3319 @ SY3406 @ SY3405 @ SV32 ) ) @ SY3406 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ ( sK64_SY3319 @ SY3406 @ SY3405 @ SV32 ) ) @ SV32 )
| ( in @ ( ordered_pair @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ ( sK64_SY3319 @ SY3406 @ SY3405 @ SV32 ) ) @ SY3406 ) ) ) )
| ( SY3406
= ( relation_dom_restriction @ SV32 @ SY3405 ) ) )
| ~ ! [SY3407: $i,SY3408: $i] :
( ~ ( relation @ SY3408 )
| ( SY3408
!= ( relation_dom_restriction @ SV32 @ SY3407 ) )
| ~ ( ~ ! [SY3409: $i,SY3410: $i] :
( ~ ( in @ SY3409 @ SY3407 )
| ~ ( in @ ( ordered_pair @ SY3409 @ SY3410 ) @ SV32 )
| ( in @ ( ordered_pair @ SY3409 @ SY3410 ) @ SY3408 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3408 )
| ( in @ SX3 @ SY3407 ) )
| ~ ! [SY3413: $i,SY3414: $i] :
( ~ ( in @ ( ordered_pair @ SY3413 @ SY3414 ) @ SY3408 )
| ( in @ ( ordered_pair @ SY3413 @ SY3414 ) @ SV32 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[600]) ).
thf(685,plain,
! [SV33: $i] :
( ( ~ ! [SY3415: $i,SY3416: $i] :
( ~ ( relation @ SY3416 )
| ! [SY3417: $i] :
( ~ ( in @ SY3417 @ ( relation_rng @ SY3416 ) )
| ~ ( in @ ( ordered_pair @ SV33 @ SY3417 ) @ SY3416 )
| ~ ( in @ SY3417 @ SY3415 ) )
| ( in @ SV33 @ ( relation_inverse_image @ SY3416 @ SY3415 ) ) )
| ~ ! [SY3418: $i,SY3419: $i] :
( ~ ( relation @ SY3419 )
| ~ ( in @ SV33 @ ( relation_inverse_image @ SY3419 @ SY3418 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK75_D @ SY3419 @ SY3418 @ SV33 ) @ ( relation_rng @ SY3419 ) )
| ~ ( in @ ( ordered_pair @ SV33 @ ( sK75_D @ SY3419 @ SY3418 @ SV33 ) ) @ SY3419 ) )
| ~ ( in @ ( sK75_D @ SY3419 @ SY3418 @ SV33 ) @ SY3418 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[601]) ).
thf(686,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK65_C @ SX1 @ SX0 )
!= ( sK66_SY3320 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK65_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY3320 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK65_C @ SX1 @ SX0 )
= ( sK66_SY3320 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY3320 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK65_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY3320 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[602]) ).
thf(687,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( SX2 = SX3 ) )
| ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[602]) ).
thf(688,plain,
! [SV34: $i,SV89: $i] :
( ( ~ ( ~ ! [SY3633: $i,SY3634: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 ) @ SY3634 )
| ( ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 )
!= SY3633 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 ) @ SY3634 )
| ( ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 )
!= SV34 ) )
| ~ ( ~ ( in @ ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 ) @ SY3634 )
| ( ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 )
!= SV89 ) ) ) )
| ~ ( ( in @ ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 ) @ SY3634 )
| ( ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 )
= SY3633 )
| ( ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 )
= SV34 )
| ( ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 )
= SV89 ) ) )
| ( SY3634
= ( unordered_triple @ SV34 @ SV89 @ SY3633 ) ) )
| ~ ! [SY3635: $i,SY3636: $i] :
( ( SY3636
!= ( unordered_triple @ SV34 @ SV89 @ SY3635 ) )
| ~ ( ~ ! [SY3637: $i] :
( ~ ( in @ SY3637 @ SY3636 )
| ( SY3637 = SY3635 )
| ( SY3637 = SV34 )
| ( SY3637 = SV89 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SY3635 )
| ( in @ SX4 @ SY3636 ) )
| ~ ~ ( ~ ! [SY3427: $i] :
( ( SY3427 != SV34 )
| ( in @ SY3427 @ SY3636 ) )
| ~ ! [SY3640: $i] :
( ( SY3640 != SV89 )
| ( in @ SY3640 @ SY3636 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(689,plain,
! [SV35: $i] :
( ( ~ ! [SY3429: $i,SY3430: $i] :
( ~ ( relation @ SY3430 )
| ~ ( in @ ( ordered_pair @ SV35 @ SY3429 ) @ SY3430 )
| ( in @ SV35 @ ( relation_field @ SY3430 ) ) )
| ~ ! [SY3431: $i,SY3432: $i] :
( ~ ( relation @ SY3432 )
| ~ ( in @ ( ordered_pair @ SV35 @ SY3431 ) @ SY3432 )
| ( in @ SY3431 @ ( relation_field @ SY3432 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(690,plain,
! [SV36: $i] :
( ( ( ~ ( relation @ SV36 ) )
= $true )
| ( ( ~ ( ~ ! [SY3433: $i] :
( ~ ( ~ ( ! [SY3434: $i] :
~ ( in @ ( ordered_pair @ SY3434 @ ( sK16_C @ SY3433 @ SV36 ) ) @ SV36 )
| ~ ( in @ ( sK16_C @ SY3433 @ SV36 ) @ SY3433 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_SY3292 @ SY3433 @ SV36 ) @ ( sK16_C @ SY3433 @ SV36 ) ) @ SV36 )
| ( in @ ( sK16_C @ SY3433 @ SV36 ) @ SY3433 ) ) )
| ( SY3433
= ( relation_rng @ SV36 ) ) )
| ~ ! [SY3435: $i] :
( ( SY3435
!= ( relation_rng @ SV36 ) )
| ~ ( ~ ! [SY3436: $i] :
( ! [SY3437: $i] :
~ ( in @ ( ordered_pair @ SY3437 @ SY3436 ) @ SV36 )
| ( in @ SY3436 @ SY3435 ) )
| ~ ! [SY3438: $i] :
( ~ ( in @ SY3438 @ SY3435 )
| ( in @ ( ordered_pair @ ( sK15_D @ SY3438 @ SY3435 @ SV36 ) @ SY3438 ) @ SV36 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[605]) ).
thf(691,plain,
! [SV37: $i] :
( ( ~ ! [SY3439: $i] :
( ~ ( subset @ SY3439 @ ( sK77_B @ SV37 ) )
| ( are_equipotent @ SY3439 @ ( sK77_B @ SV37 ) )
| ( in @ SY3439 @ ( sK77_B @ SV37 ) ) )
| ~ ~ ( ~ ! [SY3440: $i] :
( ~ ( in @ SY3440 @ ( sK77_B @ SV37 ) )
| ( in @ ( powerset @ SY3440 ) @ ( sK77_B @ SV37 ) ) )
| ~ ~ ( ~ ! [SY3441: $i,SY3442: $i] :
( ~ ( in @ SY3441 @ ( sK77_B @ SV37 ) )
| ~ ( subset @ SY3442 @ SY3441 )
| ( in @ SY3442 @ ( sK77_B @ SV37 ) ) )
| ~ ( in @ SV37 @ ( sK77_B @ SV37 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[606]) ).
thf(692,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK41_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK41_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK41_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK41_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[607]) ).
thf(693,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[607]) ).
thf(694,plain,
! [SV38: $i,SV90: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK5_C @ SV90 @ SV38 ) @ SV38 )
| ~ ( in @ ( sK5_C @ SV90 @ SV38 ) @ SV90 ) )
| ~ ( ( in @ ( sK5_C @ SV90 @ SV38 ) @ SV38 )
| ( in @ ( sK5_C @ SV90 @ SV38 ) @ SV90 ) ) )
| ( SV38 = SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(695,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( in @ SX0 @ ( relation_rng @ SX1 ) )
| ~ ( one_to_one @ SX1 )
| ( SX0
= ( apply @ SX1 @ ( apply @ ( function_inverse @ SX1 ) @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[609]) ).
thf(696,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( in @ SX0 @ ( relation_rng @ SX1 ) )
| ~ ( one_to_one @ SX1 )
| ( SX0
= ( apply @ ( relation_composition @ ( function_inverse @ SX1 ) @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[609]) ).
thf(697,plain,
! [SV39: $i,SV91: $i] :
( ( ~ ( function @ SV91 )
| ~ ( relation @ SV91 )
| ~ ( ~ ! [SY3641: $i] :
( ~ ( function @ SY3641 )
| ~ ( relation @ SY3641 )
| ~ ( in @ SV39 @ ( relation_dom @ SY3641 ) )
| ~ ( in @ ( apply @ SY3641 @ SV39 ) @ ( relation_dom @ SV91 ) )
| ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3641 @ SV91 ) ) ) )
| ~ ~ ( ~ ! [SY3642: $i] :
( ~ ( function @ SY3642 )
| ~ ( relation @ SY3642 )
| ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3642 @ SV91 ) ) )
| ( in @ SV39 @ ( relation_dom @ SY3642 ) ) )
| ~ ! [SY3643: $i] :
( ~ ( function @ SY3643 )
| ~ ( relation @ SY3643 )
| ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3643 @ SV91 ) ) )
| ( in @ ( apply @ SY3643 @ SV39 ) @ ( relation_dom @ SV91 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(698,plain,
! [SV40: $i,SV92: $i] :
( ( ~ ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
| ~ ( ~ ! [SY3644: $i] :
( ~ ( element @ SY3644 @ ( powerset @ ( powerset @ SV40 ) ) )
| ~ ( ~ ( element @ ( sK6_D @ SY3644 @ SV92 @ SV40 ) @ ( powerset @ SV40 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK6_D @ SY3644 @ SV92 @ SV40 ) @ SY3644 )
| ~ ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SY3644 @ SV92 @ SV40 ) ) @ SV92 ) )
| ~ ( ( in @ ( sK6_D @ SY3644 @ SV92 @ SV40 ) @ SY3644 )
| ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SY3644 @ SV92 @ SV40 ) ) @ SV92 ) ) ) )
| ( SY3644
= ( complements_of_subsets @ SV40 @ SV92 ) ) )
| ~ ! [SY3645: $i] :
( ~ ( element @ SY3645 @ ( powerset @ ( powerset @ SV40 ) ) )
| ( SY3645
!= ( complements_of_subsets @ SV40 @ SV92 ) )
| ~ ( ~ ! [SY3646: $i] :
( ~ ( element @ SY3646 @ ( powerset @ SV40 ) )
| ~ ( in @ SY3646 @ SY3645 )
| ( in @ ( subset_complement @ SV40 @ SY3646 ) @ SV92 ) )
| ~ ! [SY3647: $i] :
( ~ ( element @ SY3647 @ ( powerset @ SV40 ) )
| ~ ( in @ ( subset_complement @ SV40 @ SY3647 ) @ SV92 )
| ( in @ SY3647 @ SY3645 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(699,plain,
! [SV41: $i] :
( ( ~ ! [SY3453: $i,SY3454: $i] :
( ~ ( function @ SY3454 )
| ~ ( relation @ SY3454 )
| ( SY3453
!= ( apply @ SY3454 @ SV41 ) )
| ~ ( in @ SV41 @ ( relation_dom @ SY3454 ) )
| ( in @ ( ordered_pair @ SV41 @ SY3453 ) @ SY3454 ) )
| ~ ~ ( ~ ! [SY3455: $i,SY3456: $i] :
( ~ ( function @ SY3456 )
| ~ ( relation @ SY3456 )
| ~ ( in @ ( ordered_pair @ SV41 @ SY3455 ) @ SY3456 )
| ( SY3455
= ( apply @ SY3456 @ SV41 ) ) )
| ~ ! [SY3457: $i,SY3458: $i] :
( ~ ( function @ SY3458 )
| ~ ( relation @ SY3458 )
| ~ ( in @ ( ordered_pair @ SV41 @ SY3457 ) @ SY3458 )
| ( in @ SV41 @ ( relation_dom @ SY3458 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[612]) ).
thf(700,plain,
! [SV42: $i] :
( ( ~ ! [SY3459: $i,SY3460: $i] :
( ~ ( relation @ SY3460 )
| ~ ( in @ SV42 @ SY3459 )
| ~ ( in @ SV42 @ ( relation_rng @ SY3460 ) )
| ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SY3459 @ SY3460 ) ) ) )
| ~ ~ ( ~ ! [SY3461: $i,SY3462: $i] :
( ~ ( relation @ SY3462 )
| ~ ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SY3461 @ SY3462 ) ) )
| ( in @ SV42 @ SY3461 ) )
| ~ ! [SY3463: $i,SY3464: $i] :
( ~ ( relation @ SY3464 )
| ~ ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SY3463 @ SY3464 ) ) )
| ( in @ SV42 @ ( relation_rng @ SY3464 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[613]) ).
thf(701,plain,
! [SV43: $i] :
( ( ~ ! [SY3465: $i] :
( ~ ( subset @ SY3465 @ ( sK2_B @ SV43 ) )
| ( are_equipotent @ SY3465 @ ( sK2_B @ SV43 ) )
| ( in @ SY3465 @ ( sK2_B @ SV43 ) ) )
| ~ ~ ( ~ ! [SY3466: $i] :
( ~ ( ~ ! [SY3467: $i] :
( ~ ( subset @ SY3467 @ SY3466 )
| ( in @ SY3467 @ ( sK3_SY3278 @ SY3466 @ SV43 ) ) )
| ~ ( in @ ( sK3_SY3278 @ SY3466 @ SV43 ) @ ( sK2_B @ SV43 ) ) )
| ~ ( in @ SY3466 @ ( sK2_B @ SV43 ) ) )
| ~ ~ ( ~ ! [SY3468: $i,SY3469: $i] :
( ~ ( in @ SY3468 @ ( sK2_B @ SV43 ) )
| ~ ( subset @ SY3469 @ SY3468 )
| ( in @ SY3469 @ ( sK2_B @ SV43 ) ) )
| ~ ( in @ SV43 @ ( sK2_B @ SV43 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[614]) ).
thf(702,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK49_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK49_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[615]) ).
thf(703,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK47_C @ SX1 @ SX0 ) @ ( sK48_SY3309 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[615]) ).
thf(704,plain,
! [SV93: $i,SV44: $i] :
( ( ~ ( ~ ! [SY3648: $i,SY3649: $i] :
( ~ ( in @ SV44 @ SY3648 )
| ~ ( in @ SV93 @ SY3649 )
| ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SY3648 @ SY3649 ) ) )
| ~ ~ ( ~ ! [SY3650: $i] :
( ! [SY3651: $i] :
~ ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SY3650 @ SY3651 ) )
| ( in @ SV44 @ SY3650 ) )
| ~ ! [SY3652: $i,SY3653: $i] :
( ~ ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SY3652 @ SY3653 ) )
| ( in @ SV93 @ SY3653 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(705,plain,
! [SV45: $i] :
( ( ( ~ ( relation @ SV45 ) )
= $true )
| ( ( ~ ( ~ ! [SY3477: $i] :
( ~ ( ~ ( ! [SY3478: $i] :
~ ( in @ ( ordered_pair @ ( sK26_C @ SY3477 @ SV45 ) @ SY3478 ) @ SV45 )
| ~ ( in @ ( sK26_C @ SY3477 @ SV45 ) @ SY3477 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK26_C @ SY3477 @ SV45 ) @ ( sK27_SY3298 @ SY3477 @ SV45 ) ) @ SV45 )
| ( in @ ( sK26_C @ SY3477 @ SV45 ) @ SY3477 ) ) )
| ( SY3477
= ( relation_dom @ SV45 ) ) )
| ~ ! [SY3479: $i] :
( ( SY3479
!= ( relation_dom @ SV45 ) )
| ~ ( ~ ! [SY3480: $i] :
( ! [SY3481: $i] :
~ ( in @ ( ordered_pair @ SY3480 @ SY3481 ) @ SV45 )
| ( in @ SY3480 @ SY3479 ) )
| ~ ! [SY3482: $i] :
( ~ ( in @ SY3482 @ SY3479 )
| ( in @ ( ordered_pair @ SY3482 @ ( sK25_D @ SY3482 @ SY3479 @ SV45 ) ) @ SV45 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[617]) ).
thf(706,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[618]) ).
thf(707,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[618]) ).
thf(708,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK42_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[619]) ).
thf(709,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[619]) ).
thf(710,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK43_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK43_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK43_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK43_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[620]) ).
thf(711,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[620]) ).
thf(712,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK74_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK74_C @ SX1 @ SX0 ) )
!= ( sK74_C @ SX1 @ SX0 ) ) ) )
| ( ( relation_dom @ SX1 )
!= SX0 )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[621]) ).
thf(713,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( ( apply @ SX1 @ SX2 )
= SX2 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[621]) ).
thf(714,plain,
! [SV46: $i] :
( ( ( ~ ( function @ SV46 )
| ~ ( relation @ SV46 ) )
= $true )
| ( ( ~ ( one_to_one @ SV46 )
| ~ ( ~ ! [SY3483: $i] :
( ~ ( function @ SY3483 )
| ~ ( relation @ SY3483 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY3322 @ SY3483 @ SV46 )
= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ( ( sK70_C @ SY3483 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SY3483 @ SV46 )
= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SY3483 @ SV46 )
= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ( ( sK71_SY3322 @ SY3483 @ SV46 )
!= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK70_C @ SY3483 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK71_SY3322 @ SY3483 @ SV46 )
!= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY3483 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK70_C @ SY3483 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SY3483 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SY3483 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK71_SY3322 @ SY3483 @ SV46 )
!= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ( ( relation_dom @ SY3483 )
!= ( relation_rng @ SV46 ) )
| ( SY3483
= ( function_inverse @ SV46 ) ) )
| ~ ~ ( ~ ! [SY3484: $i] :
( ~ ( function @ SY3484 )
| ~ ( relation @ SY3484 )
| ( SY3484
!= ( function_inverse @ SV46 ) )
| ~ ( ~ ~ ( ~ ! [SY3485: $i,SY3486: $i] :
( ( SY3486
!= ( apply @ SY3484 @ SY3485 ) )
| ~ ( in @ SY3485 @ ( relation_rng @ SV46 ) )
| ( SY3485
= ( apply @ SV46 @ SY3486 ) ) )
| ~ ! [SY3487: $i,SY3488: $i] :
( ( SY3488
!= ( apply @ SY3484 @ SY3487 ) )
| ~ ( in @ SY3487 @ ( relation_rng @ SV46 ) )
| ( in @ SY3488 @ ( relation_dom @ SV46 ) ) ) )
| ~ ~ ( ~ ! [SY3489: $i,SY3490: $i] :
( ( SY3489
!= ( apply @ SV46 @ SY3490 ) )
| ~ ( in @ SY3490 @ ( relation_dom @ SV46 ) )
| ( SY3490
= ( apply @ SY3484 @ SY3489 ) ) )
| ~ ! [SY3491: $i] :
( ! [SY3492: $i] :
( ( SY3491
!= ( apply @ SV46 @ SY3492 ) )
| ~ ( in @ SY3492 @ ( relation_dom @ SV46 ) ) )
| ( in @ SY3491 @ ( relation_rng @ SV46 ) ) ) ) ) )
| ~ ! [SY3493: $i] :
( ~ ( function @ SY3493 )
| ~ ( relation @ SY3493 )
| ( SY3493
!= ( function_inverse @ SV46 ) )
| ( ( relation_dom @ SY3493 )
= ( relation_rng @ SV46 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[622]) ).
thf(715,plain,
! [SV47: $i] :
( ( ( ~ ( relation @ SV47 ) )
= $true )
| ( ( ! [SY3494: $i] :
( ~ ( relation @ SY3494 )
| ~ ( ~ ! [SY3495: $i] :
( ~ ( relation @ SY3495 )
| ~ ( ~ ( ! [SY3496: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY3495 @ SY3494 @ SV47 ) @ SY3496 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3496 @ ( sK9_SY3284 @ SY3495 @ SY3494 @ SV47 ) ) @ SY3494 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SY3495 @ SY3494 @ SV47 ) @ ( sK9_SY3284 @ SY3495 @ SY3494 @ SV47 ) ) @ SY3495 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY3495 @ SY3494 @ SV47 ) @ ( sK10_SY3288 @ SY3495 @ SY3494 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY3288 @ SY3495 @ SY3494 @ SV47 ) @ ( sK9_SY3284 @ SY3495 @ SY3494 @ SV47 ) ) @ SY3494 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SY3495 @ SY3494 @ SV47 ) @ ( sK9_SY3284 @ SY3495 @ SY3494 @ SV47 ) ) @ SY3495 ) ) )
| ( SY3495
= ( relation_composition @ SV47 @ SY3494 ) ) )
| ~ ! [SY3497: $i] :
( ~ ( relation @ SY3497 )
| ( SY3497
!= ( relation_composition @ SV47 @ SY3494 ) )
| ~ ( ~ ! [SY3498: $i,SY3499: $i] :
( ! [SY3500: $i] :
( ~ ( in @ ( ordered_pair @ SY3498 @ SY3500 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3500 @ SY3499 ) @ SY3494 ) )
| ( in @ ( ordered_pair @ SY3498 @ SY3499 ) @ SY3497 ) )
| ~ ! [SY3501: $i,SY3502: $i] :
( ~ ( in @ ( ordered_pair @ SY3501 @ SY3502 ) @ SY3497 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3501 @ ( sK7_F @ SY3502 @ SY3501 @ SY3497 @ SY3494 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY3502 @ SY3501 @ SY3497 @ SY3494 @ SV47 ) @ SY3502 ) @ SY3494 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[623]) ).
thf(716,plain,
! [SV48: $i] :
( ( ~ ! [SY3503: $i,SY3504: $i] :
( ~ ( in @ SV48 @ SY3504 )
| ~ ( in @ SY3503 @ SY3504 )
| ( subset @ ( unordered_pair @ SV48 @ SY3503 ) @ SY3504 ) )
| ~ ~ ( ~ ! [SY3505: $i,SY3506: $i] :
( ~ ( subset @ ( unordered_pair @ SV48 @ SY3505 ) @ SY3506 )
| ( in @ SV48 @ SY3506 ) )
| ~ ! [SY3507: $i,SY3508: $i] :
( ~ ( subset @ ( unordered_pair @ SV48 @ SY3507 ) @ SY3508 )
| ( in @ SY3507 @ SY3508 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[624]) ).
thf(717,plain,
! [SV94: $i,SV49: $i] :
( ( ~ ( ~ ! [SY3654: $i,SY3655: $i] :
( ~ ( relation @ SY3655 )
| ~ ( in @ SV49 @ SY3654 )
| ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ SY3655 )
| ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SY3654 ) @ SY3655 ) ) )
| ~ ~ ( ~ ! [SY3656: $i,SY3657: $i] :
( ~ ( relation @ SY3657 )
| ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SY3656 ) @ SY3657 ) )
| ( in @ SV49 @ SY3656 ) )
| ~ ! [SY3658: $i,SY3659: $i] :
( ~ ( relation @ SY3659 )
| ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SY3658 ) @ SY3659 ) )
| ( in @ ( ordered_pair @ SV49 @ SV94 ) @ SY3659 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(718,plain,
! [SV50: $i,SV95: $i] :
( ( ~ ( ~ ! [SY3660: $i] :
( ~ ( in @ SY3660 @ SV95 )
| ~ ( in @ SY3660 @ ( sK4_C @ SV95 @ SV50 ) ) )
| ~ ( in @ ( sK4_C @ SV95 @ SV50 ) @ SV95 ) )
| ~ ( in @ SV50 @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(719,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_B @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK12_SY3289 @ SX0 ) @ ( relation_dom @ SX0 ) ) )
| ( ( apply @ SX0 @ ( sK11_B @ SX0 ) )
!= ( apply @ SX0 @ ( sK12_SY3289 @ SX0 ) ) ) )
| ~ ( ( ( sK11_B @ SX0 )
!= ( sK12_SY3289 @ SX0 ) ) ) )
| ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[627]) ).
thf(720,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ~ ( in @ SX2 @ ( relation_dom @ SX0 ) )
| ( ( apply @ SX0 @ SX1 )
!= ( apply @ SX0 @ SX2 ) )
| ( SX1 = SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[627]) ).
thf(721,plain,
! [SV51: $i] :
( ( ~ ! [SY3518: $i,SY3519: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK37_D @ SY3519 @ SY3518 @ SV51 ) @ SY3519 )
| ~ ( in @ ( sK37_D @ SY3519 @ SY3518 @ SV51 ) @ SV51 ) )
| ~ ( ~ ( in @ ( sK37_D @ SY3519 @ SY3518 @ SV51 ) @ SY3519 )
| ~ ( in @ ( sK37_D @ SY3519 @ SY3518 @ SV51 ) @ SY3518 ) ) )
| ~ ( ( in @ ( sK37_D @ SY3519 @ SY3518 @ SV51 ) @ SY3519 )
| ( in @ ( sK37_D @ SY3519 @ SY3518 @ SV51 ) @ SV51 )
| ( in @ ( sK37_D @ SY3519 @ SY3518 @ SV51 ) @ SY3518 ) ) )
| ( SY3519
= ( set_union2 @ SV51 @ SY3518 ) ) )
| ~ ! [SY3520: $i,SY3521: $i] :
( ( SY3521
!= ( set_union2 @ SV51 @ SY3520 ) )
| ~ ( ~ ! [SY3522: $i] :
( ~ ( in @ SY3522 @ SY3521 )
| ( in @ SY3522 @ SV51 )
| ( in @ SY3522 @ SY3520 ) )
| ~ ~ ( ~ ! [SY3523: $i] :
( ~ ( in @ SY3523 @ SV51 )
| ( in @ SY3523 @ SY3521 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY3520 )
| ( in @ SX3 @ SY3521 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[628]) ).
thf(722,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[629]) ).
thf(723,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[629]) ).
thf(724,plain,
! [SV52: $i] :
( ( ( ~ ( relation @ SV52 ) )
= $true )
| ( ( ~ ( ~ ! [SY3525: $i] :
( ~ ( relation @ SY3525 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK30_C @ SY3525 @ SV52 ) @ ( sK31_SY3299 @ SY3525 @ SV52 ) ) @ SV52 )
| ~ ~ ( in @ ( ordered_pair @ ( sK30_C @ SY3525 @ SV52 ) @ ( sK31_SY3299 @ SY3525 @ SV52 ) ) @ SY3525 ) )
| ( subset @ SV52 @ SY3525 ) )
| ~ ! [SY3526: $i] :
( ~ ( relation @ SY3526 )
| ~ ( subset @ SV52 @ SY3526 )
| ! [SY3527: $i,SY3528: $i] :
( ~ ( in @ ( ordered_pair @ SY3527 @ SY3528 ) @ SV52 )
| ( in @ ( ordered_pair @ SY3527 @ SY3528 ) @ SY3526 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[630]) ).
thf(725,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK46_SY3307 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK45_C @ SX1 @ SX0 ) @ ( sK46_SY3307 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK45_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK45_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK45_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK44_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK44_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[631]) ).
thf(726,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[631]) ).
thf(727,plain,
! [SV53: $i] :
( ( ( ~ ( function @ SV53 )
| ~ ( relation @ SV53 ) )
= $true )
| ( ( ~ ( ~ ! [SY3529: $i,SY3530: $i] :
( ~ ( ~ ( ~ ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) ) @ SY3529 )
| ~ ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ SY3530 ) )
| ~ ~ ( ~ ( ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ SY3530 ) )
| ~ ( ( in @ ( apply @ SV53 @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) ) @ SY3529 )
| ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ SY3530 ) ) ) )
| ( SY3530
= ( relation_inverse_image @ SV53 @ SY3529 ) ) )
| ~ ! [SY3531: $i,SY3532: $i] :
( ( SY3532
!= ( relation_inverse_image @ SV53 @ SY3531 ) )
| ~ ( ~ ! [SY3533: $i] :
( ~ ( in @ SY3533 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SY3533 ) @ SY3531 )
| ( in @ SY3533 @ SY3532 ) )
| ~ ~ ( ~ ! [SY3534: $i] :
( ~ ( in @ SY3534 @ SY3532 )
| ( in @ SY3534 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY3535: $i] :
( ~ ( in @ SY3535 @ SY3532 )
| ( in @ ( apply @ SV53 @ SY3535 ) @ SY3531 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[632]) ).
thf(728,plain,
! [SV54: $i] :
( ( ~ ! [SY3536: $i,SY3537: $i] :
( ~ ( ~ ( ~ ( in @ ( sK28_D @ SY3537 @ SY3536 @ SV54 ) @ SV54 )
| ~ ( in @ ( sK28_D @ SY3537 @ SY3536 @ SV54 ) @ SY3536 )
| ~ ( in @ ( sK28_D @ SY3537 @ SY3536 @ SV54 ) @ SY3537 ) )
| ~ ~ ( ~ ( ( in @ ( sK28_D @ SY3537 @ SY3536 @ SV54 ) @ SV54 )
| ( in @ ( sK28_D @ SY3537 @ SY3536 @ SV54 ) @ SY3537 ) )
| ~ ( ( in @ ( sK28_D @ SY3537 @ SY3536 @ SV54 ) @ SY3536 )
| ( in @ ( sK28_D @ SY3537 @ SY3536 @ SV54 ) @ SY3537 ) ) ) )
| ( SY3537
= ( set_intersection2 @ SV54 @ SY3536 ) ) )
| ~ ! [SY3538: $i,SY3539: $i] :
( ( SY3539
!= ( set_intersection2 @ SV54 @ SY3538 ) )
| ~ ( ~ ! [SY3540: $i] :
( ~ ( in @ SY3540 @ SV54 )
| ~ ( in @ SY3540 @ SY3538 )
| ( in @ SY3540 @ SY3539 ) )
| ~ ~ ( ~ ! [SY3541: $i] :
( ~ ( in @ SY3541 @ SY3539 )
| ( in @ SY3541 @ SV54 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY3539 )
| ( in @ SX3 @ SY3538 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[633]) ).
thf(729,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[634]) ).
thf(730,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[634]) ).
thf(731,plain,
! [SV55: $i] :
( ( ~ ! [SY3543: $i,SY3544: $i] :
( ~ ( ~ ( ~ ( in @ ( sK21_D @ SY3544 @ SY3543 @ SV55 ) @ SV55 )
| ( in @ ( sK21_D @ SY3544 @ SY3543 @ SV55 ) @ SY3543 )
| ~ ( in @ ( sK21_D @ SY3544 @ SY3543 @ SV55 ) @ SY3544 ) )
| ~ ~ ( ~ ( ( in @ ( sK21_D @ SY3544 @ SY3543 @ SV55 ) @ SV55 )
| ( in @ ( sK21_D @ SY3544 @ SY3543 @ SV55 ) @ SY3544 ) )
| ~ ( ~ ( in @ ( sK21_D @ SY3544 @ SY3543 @ SV55 ) @ SY3543 )
| ( in @ ( sK21_D @ SY3544 @ SY3543 @ SV55 ) @ SY3544 ) ) ) )
| ( SY3544
= ( set_difference @ SV55 @ SY3543 ) ) )
| ~ ! [SY3545: $i,SY3546: $i] :
( ( SY3546
!= ( set_difference @ SV55 @ SY3545 ) )
| ~ ( ~ ! [SY3547: $i] :
( ~ ( in @ SY3547 @ SV55 )
| ( in @ SY3547 @ SY3545 )
| ( in @ SY3547 @ SY3546 ) )
| ~ ~ ( ~ ! [SY3548: $i] :
( ~ ( in @ SY3548 @ SY3546 )
| ( in @ SY3548 @ SV55 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY3546 )
| ~ ( in @ SX3 @ SY3545 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[635]) ).
thf(732,plain,
! [SV56: $i] :
( ( ( ~ ( function @ SV56 )
| ~ ( relation @ SV56 ) )
= $true )
| ( ( ~ ( ~ ! [SY3550: $i] :
( ~ ( ~ ( ! [SY3551: $i] :
( ( ( sK19_C @ SY3550 @ SV56 )
!= ( apply @ SV56 @ SY3551 ) )
| ~ ( in @ SY3551 @ ( relation_dom @ SV56 ) ) )
| ~ ( in @ ( sK19_C @ SY3550 @ SV56 ) @ SY3550 ) )
| ~ ( ~ ( ( ( sK19_C @ SY3550 @ SV56 )
!= ( apply @ SV56 @ ( sK20_SY3294 @ SY3550 @ SV56 ) ) )
| ~ ( in @ ( sK20_SY3294 @ SY3550 @ SV56 ) @ ( relation_dom @ SV56 ) ) )
| ( in @ ( sK19_C @ SY3550 @ SV56 ) @ SY3550 ) ) )
| ( SY3550
= ( relation_rng @ SV56 ) ) )
| ~ ! [SY3552: $i] :
( ( SY3552
!= ( relation_rng @ SV56 ) )
| ~ ( ~ ! [SY3553: $i] :
( ! [SY3554: $i] :
( ( SY3553
!= ( apply @ SV56 @ SY3554 ) )
| ~ ( in @ SY3554 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY3553 @ SY3552 ) )
| ~ ! [SY3555: $i] :
( ~ ( in @ SY3555 @ SY3552 )
| ~ ( ( SY3555
!= ( apply @ SV56 @ ( sK18_D @ SY3555 @ SY3552 @ SV56 ) ) )
| ~ ( in @ ( sK18_D @ SY3555 @ SY3552 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[636]) ).
thf(733,plain,
! [SV57: $i] :
( ( ~ ! [SY3556: $i,SY3557: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK38_D @ SY3557 @ SY3556 @ SV57 ) @ SY3557 )
| ( ( sK38_D @ SY3557 @ SY3556 @ SV57 )
!= SV57 ) )
| ~ ( ~ ( in @ ( sK38_D @ SY3557 @ SY3556 @ SV57 ) @ SY3557 )
| ( ( sK38_D @ SY3557 @ SY3556 @ SV57 )
!= SY3556 ) ) )
| ~ ( ( in @ ( sK38_D @ SY3557 @ SY3556 @ SV57 ) @ SY3557 )
| ( ( sK38_D @ SY3557 @ SY3556 @ SV57 )
= SV57 )
| ( ( sK38_D @ SY3557 @ SY3556 @ SV57 )
= SY3556 ) ) )
| ( SY3557
= ( unordered_pair @ SV57 @ SY3556 ) ) )
| ~ ! [SY3558: $i,SY3559: $i] :
( ( SY3559
!= ( unordered_pair @ SV57 @ SY3558 ) )
| ~ ( ~ ! [SY3560: $i] :
( ~ ( in @ SY3560 @ SY3559 )
| ( SY3560 = SV57 )
| ( SY3560 = SY3558 ) )
| ~ ~ ( ~ ! [SY3561: $i] :
( ( SY3561 != SV57 )
| ( in @ SY3561 @ SY3559 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY3558 )
| ( in @ SX3 @ SY3559 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[637]) ).
thf(734,plain,
! [SV58: $i,SV96: $i] :
( ( ~ ( function @ SV96 )
| ~ ( relation @ SV96 )
| ~ ( ~ ! [SY3661: $i] :
( ~ ( function @ SY3661 )
| ~ ( relation @ SY3661 )
| ~ ( ~ ( in @ ( sK67_D @ SY3661 @ SV96 @ SV58 ) @ ( relation_dom @ SV96 ) )
| ~ ( ( ( apply @ SV96 @ ( sK67_D @ SY3661 @ SV96 @ SV58 ) )
!= ( apply @ SY3661 @ ( sK67_D @ SY3661 @ SV96 @ SV58 ) ) ) ) )
| ( ( relation_dom @ SV96 )
!= ( set_intersection2 @ ( relation_dom @ SY3661 ) @ SV58 ) )
| ( SV96
= ( relation_dom_restriction @ SY3661 @ SV58 ) ) )
| ~ ~ ( ~ ! [SY3662: $i] :
( ~ ( function @ SY3662 )
| ~ ( relation @ SY3662 )
| ( SV96
!= ( relation_dom_restriction @ SY3662 @ SV58 ) )
| ! [SY3663: $i] :
( ~ ( in @ SY3663 @ ( relation_dom @ SV96 ) )
| ( ( apply @ SV96 @ SY3663 )
= ( apply @ SY3662 @ SY3663 ) ) ) )
| ~ ! [SY3664: $i] :
( ~ ( function @ SY3664 )
| ~ ( relation @ SY3664 )
| ( SV96
!= ( relation_dom_restriction @ SY3664 @ SV58 ) )
| ( ( relation_dom @ SV96 )
= ( set_intersection2 @ ( relation_dom @ SY3664 ) @ SV58 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(735,plain,
! [SV59: $i] :
( ( ( ~ ( relation @ SV59 ) )
= $true )
| ( ( ~ ( ~ ! [SY3568: $i] :
( ~ ( relation @ SY3568 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_C @ SY3568 @ SV59 ) @ ( sK40_SY3306 @ SY3568 @ SV59 ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK39_C @ SY3568 @ SV59 ) @ ( sK40_SY3306 @ SY3568 @ SV59 ) ) @ SY3568 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK39_C @ SY3568 @ SV59 ) @ ( sK40_SY3306 @ SY3568 @ SV59 ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK39_C @ SY3568 @ SV59 ) @ ( sK40_SY3306 @ SY3568 @ SV59 ) ) @ SY3568 ) ) )
| ( SV59 = SY3568 ) )
| ~ ! [SY3569: $i] :
( ~ ( relation @ SY3569 )
| ( SV59 != SY3569 )
| ~ ( ~ ! [SY3570: $i,SY3571: $i] :
( ~ ( in @ ( ordered_pair @ SY3570 @ SY3571 ) @ SV59 )
| ( in @ ( ordered_pair @ SY3570 @ SY3571 ) @ SY3569 ) )
| ~ ! [SY3572: $i,SY3573: $i] :
( ~ ( in @ ( ordered_pair @ SY3572 @ SY3573 ) @ SY3569 )
| ( in @ ( ordered_pair @ SY3572 @ SY3573 ) @ SV59 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[639]) ).
thf(736,plain,
! [SV60: $i,SV97: $i] :
( ( ~ ( ~ ( in @ ( sK78_C @ SV97 @ SV60 ) @ SV60 )
| ~ ~ ( in @ ( sK78_C @ SV97 @ SV60 ) @ SV97 ) )
| ( element @ SV60 @ ( powerset @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(737,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ ( sK24_SY3296 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK24_SY3296 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[641]) ).
thf(738,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK22_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[641]) ).
thf(739,plain,
! [SV98: $i,SV61: $i] :
( ( ~ ( ~ ! [SY3665: $i,SY3666: $i] :
( ~ ( in @ SV61 @ SY3665 )
| ~ ( in @ SV98 @ SY3666 )
| ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SY3665 @ SY3666 ) ) )
| ~ ~ ( ~ ! [SY3667: $i] :
( ! [SY3668: $i] :
~ ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SY3667 @ SY3668 ) )
| ( in @ SV61 @ SY3667 ) )
| ~ ! [SY3669: $i,SY3670: $i] :
( ~ ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SY3669 @ SY3670 ) )
| ( in @ SV98 @ SY3670 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(740,plain,
! [SV62: $i] :
( ( ~ ! [SY3582: $i,SY3583: $i] :
( ~ ( function @ SY3583 )
| ~ ( relation @ SY3583 )
| ~ ( in @ SY3582 @ ( relation_dom @ SY3583 ) )
| ~ ( in @ SY3582 @ SV62 )
| ( in @ SY3582 @ ( relation_dom @ ( relation_dom_restriction @ SY3583 @ SV62 ) ) ) )
| ~ ~ ( ~ ! [SY3584: $i,SY3585: $i] :
( ~ ( function @ SY3585 )
| ~ ( relation @ SY3585 )
| ~ ( in @ SY3584 @ ( relation_dom @ ( relation_dom_restriction @ SY3585 @ SV62 ) ) )
| ( in @ SY3584 @ ( relation_dom @ SY3585 ) ) )
| ~ ! [SY3586: $i,SY3587: $i] :
( ~ ( function @ SY3587 )
| ~ ( relation @ SY3587 )
| ~ ( in @ SY3586 @ ( relation_dom @ ( relation_dom_restriction @ SY3587 @ SV62 ) ) )
| ( in @ SY3586 @ SV62 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[643]) ).
thf(741,plain,
! [SV63: $i] :
( ( ~ ! [SY3588: $i,SY3589: $i] :
( ~ ( ~ ( ! [SY3590: $i,SY3591: $i] :
( ~ ( in @ SY3590 @ SV63 )
| ~ ( in @ SY3591 @ SY3588 )
| ( ( sK34_D @ SY3589 @ SY3588 @ SV63 )
!= ( ordered_pair @ SY3590 @ SY3591 ) ) )
| ~ ( in @ ( sK34_D @ SY3589 @ SY3588 @ SV63 ) @ SY3589 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK35_SY3303 @ SY3589 @ SY3588 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK36_SY3305 @ SY3589 @ SY3588 @ SV63 ) @ SY3588 ) )
| ( ( sK34_D @ SY3589 @ SY3588 @ SV63 )
!= ( ordered_pair @ ( sK35_SY3303 @ SY3589 @ SY3588 @ SV63 ) @ ( sK36_SY3305 @ SY3589 @ SY3588 @ SV63 ) ) ) )
| ( in @ ( sK34_D @ SY3589 @ SY3588 @ SV63 ) @ SY3589 ) ) )
| ( SY3589
= ( cartesian_product2 @ SV63 @ SY3588 ) ) )
| ~ ! [SY3592: $i,SY3593: $i] :
( ( SY3593
!= ( cartesian_product2 @ SV63 @ SY3592 ) )
| ~ ( ~ ! [SY3594: $i] :
( ! [SY3595: $i,SY3596: $i] :
( ~ ( in @ SY3595 @ SV63 )
| ~ ( in @ SY3596 @ SY3592 )
| ( SY3594
!= ( ordered_pair @ SY3595 @ SY3596 ) ) )
| ( in @ SY3594 @ SY3593 ) )
| ~ ! [SY3597: $i] :
( ~ ( in @ SY3597 @ SY3593 )
| ~ ( ~ ~ ( ~ ( in @ ( sK32_E @ SY3597 @ SY3593 @ SY3592 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK33_SY3300 @ SY3597 @ SY3593 @ SY3592 @ SV63 ) @ SY3592 ) )
| ( SY3597
!= ( ordered_pair @ ( sK32_E @ SY3597 @ SY3593 @ SY3592 @ SV63 ) @ ( sK33_SY3300 @ SY3597 @ SY3593 @ SY3592 @ SV63 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[644]) ).
thf(742,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK73_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK73_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[645]) ).
thf(743,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[645]) ).
thf(744,plain,
! [SV64: $i] :
( ( ~ ! [SY3598: $i,SY3599: $i] :
( ~ ( relation @ SY3599 )
| ! [SY3600: $i] :
( ~ ( in @ SY3600 @ ( relation_dom @ SY3599 ) )
| ~ ( in @ ( ordered_pair @ SY3600 @ SV64 ) @ SY3599 )
| ~ ( in @ SY3600 @ SY3598 ) )
| ( in @ SV64 @ ( relation_image @ SY3599 @ SY3598 ) ) )
| ~ ! [SY3601: $i,SY3602: $i] :
( ~ ( relation @ SY3602 )
| ~ ( in @ SV64 @ ( relation_image @ SY3602 @ SY3601 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK76_D @ SY3602 @ SY3601 @ SV64 ) @ ( relation_dom @ SY3602 ) )
| ~ ( in @ ( ordered_pair @ ( sK76_D @ SY3602 @ SY3601 @ SV64 ) @ SV64 ) @ SY3602 ) )
| ~ ( in @ ( sK76_D @ SY3602 @ SY3601 @ SV64 ) @ SY3601 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[646]) ).
thf(745,plain,
! [SV65: $i] :
( ( ~ ! [SY3603: $i,SY3604: $i] :
( ~ ( relation @ SY3604 )
| ~ ( in @ ( ordered_pair @ SV65 @ SY3603 ) @ SY3604 )
| ( in @ SV65 @ ( relation_dom @ SY3604 ) ) )
| ~ ! [SY3605: $i,SY3606: $i] :
( ~ ( relation @ SY3606 )
| ~ ( in @ ( ordered_pair @ SV65 @ SY3605 ) @ SY3606 )
| ( in @ SY3605 @ ( relation_rng @ SY3606 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[647]) ).
thf(746,plain,
! [SV66: $i] :
( ( ( ~ ( function @ SV66 )
| ~ ( relation @ SV66 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY3607: $i] :
( ~ ( in @ SY3607 @ ( relation_dom @ SV66 ) )
| ! [SY3608: $i] :
( ( SY3608
!= ( apply @ SV66 @ SY3607 ) )
| ( in @ ( ordered_pair @ SY3607 @ SY3608 ) @ SV66 ) ) )
| ~ ! [SY3609: $i] :
( ~ ( in @ SY3609 @ ( relation_dom @ SV66 ) )
| ! [SY3610: $i] :
( ~ ( in @ ( ordered_pair @ SY3609 @ SY3610 ) @ SV66 )
| ( SY3610
= ( apply @ SV66 @ SY3609 ) ) ) ) )
| ~ ~ ( ~ ! [SY3611: $i] :
( ( in @ SY3611 @ ( relation_dom @ SV66 ) )
| ! [SY3612: $i] :
( ( SY3612
!= ( apply @ SV66 @ SY3611 ) )
| ( SY3612 = empty_set ) ) )
| ~ ! [SY3613: $i] :
( ( in @ SY3613 @ ( relation_dom @ SV66 ) )
| ! [SY3614: $i] :
( ( SY3614 != empty_set )
| ( SY3614
= ( apply @ SV66 @ SY3613 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[648]) ).
thf(747,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[649]) ).
thf(748,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[649]) ).
thf(749,plain,
! [SV67: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV67 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV1 ) @ SV67 )
= SV67 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[650]) ).
thf(750,plain,
! [SV68: $i,SV2: $i] :
( ( ( ~ ( disjoint @ ( singleton @ SV2 ) @ SV68 ) )
= $true )
| ( ( ~ ( in @ SV2 @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[651]) ).
thf(751,plain,
! [SV69: $i,SV3: $i] :
( ( ( in @ SV3 @ SV69 )
= $true )
| ( ( disjoint @ ( singleton @ SV3 ) @ SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[652]) ).
thf(752,plain,
! [SV4: $i,SV70: $i] :
( ( ( ~ ( element @ SV70 @ ( powerset @ SV4 ) ) )
= $true )
| ( ( ! [SY3615: $i] :
( ~ ( in @ SY3615 @ SV70 )
| ( in @ SY3615 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[653]) ).
thf(753,plain,
! [SV71: $i,SV5: $i] :
( ( ( ~ ( subset @ SV5 @ SV71 ) )
= $true )
| ( ( ! [SY3616: $i] :
( ( in @ SY3616 @ SV5 )
| ( subset @ SV5 @ ( set_difference @ SV71 @ ( singleton @ SY3616 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[654]) ).
thf(754,plain,
! [SV72: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV72 ) )
= $true )
| ( ( subset @ SV6 @ ( union @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[655]) ).
thf(755,plain,
! [SV7: $i,SV73: $i] :
( ( ( ~ ( function @ SV73 )
| ~ ( relation @ SV73 ) )
= $true )
| ( ( ! [SY3617: $i] :
( ~ ( function @ SY3617 )
| ~ ( relation @ SY3617 )
| ~ ( in @ SV7 @ ( relation_dom @ ( relation_composition @ SY3617 @ SV73 ) ) )
| ( ( apply @ ( relation_composition @ SY3617 @ SV73 ) @ SV7 )
= ( apply @ SV73 @ ( apply @ SY3617 @ SV7 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[656]) ).
thf(756,plain,
! [SV8: $i,SV74: $i] :
( ( ( ~ ( function @ SV74 )
| ~ ( relation @ SV74 ) )
= $true )
| ( ( ! [SY3618: $i] :
( ~ ( function @ SY3618 )
| ~ ( relation @ SY3618 )
| ~ ( in @ SV8 @ ( relation_dom @ SV74 ) )
| ( ( apply @ ( relation_composition @ SV74 @ SY3618 ) @ SV8 )
= ( apply @ SY3618 @ ( apply @ SV74 @ SV8 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[657]) ).
thf(757,plain,
! [SV9: $i,SV75: $i] :
( ( ( ~ ( in @ SV75 @ SV9 ) )
= $true )
| ( ( ( apply @ ( identity_relation @ SV9 ) @ SV75 )
= SV75 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[658]) ).
thf(758,plain,
! [SV99: $i,SV76: $i,SV10: $i] :
( ( ~ ( in @ SV10 @ SV76 )
| ~ ( in @ SV76 @ SV99 )
| ~ ( in @ SV99 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(759,plain,
! [SV77: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ SV77 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV11 ) @ SV77 )
= SV77 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[660]) ).
thf(760,plain,
! [SV12: $i,SV100: $i] :
( ( ( ~ ( element @ SV100 @ ( powerset @ SV12 ) )
| ! [SY3671: $i] :
( ~ ( element @ SY3671 @ SV12 )
| ( in @ SY3671 @ SV100 )
| ( in @ SY3671 @ ( subset_complement @ SV12 @ SV100 ) ) ) )
= $true )
| ( ( SV12 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(761,plain,
! [SV78: $i,SV13: $i,SV101: $i] :
( ( ~ ( element @ SV101 @ ( powerset @ SV13 ) )
| ~ ( in @ SV78 @ ( subset_complement @ SV13 @ SV101 ) )
| ~ ( in @ SV78 @ SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(762,plain,
! [SV14: $i] :
( ( ( relation @ SV14 )
= $false )
| ( ( ( in @ ( ordered_pair @ ( sK68_B @ SV14 ) @ ( sK69_SY3321 @ SV14 ) ) @ SV14 )
| ( SV14 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[663]) ).
thf(763,plain,
! [SV15: $i,SV79: $i,SV102: $i] :
( ( ~ ( function @ SV102 )
| ~ ( relation @ SV102 )
| ~ ( in @ SV79 @ ( relation_dom @ ( relation_dom_restriction @ SV102 @ SV15 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SV102 @ SV15 ) @ SV79 )
= ( apply @ SV102 @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(764,plain,
! [SV16: $i,SV80: $i,SV103: $i] :
( ( ~ ( function @ SV103 )
| ~ ( relation @ SV103 )
| ~ ( in @ SV80 @ SV16 )
| ( ( apply @ ( relation_dom_restriction @ SV103 @ SV16 ) @ SV80 )
= ( apply @ SV103 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(765,plain,
! [SV81: $i,SV17: $i] :
( ( ( ~ ( in @ SV17 @ SV81 ) )
= $true )
| ( ( subset @ SV17 @ ( union @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[666]) ).
thf(766,plain,
! [SV82: $i,SV18: $i] :
( ( ( ~ ( in @ SV18 @ SV82 ) )
= $true )
| ( ( ~ ( in @ SV82 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[667]) ).
thf(767,plain,
! [SV83: $i,SV21: $i] :
( ( ( ~ ( in @ SV21 @ SV83 ) )
= $true )
| ( ( element @ SV21 @ SV83 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[669]) ).
thf(768,plain,
! [SV84: $i,SV22: $i] :
( ( ( ~ ( element @ SV22 @ SV84 ) )
= $true )
| ( ( ( empty @ SV84 )
| ( in @ SV22 @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[670]) ).
thf(769,plain,
! [SV23: $i,SV104: $i,SV85: $i] :
( ( ~ ( element @ SV85 @ ( powerset @ SV104 ) )
| ~ ( in @ SV23 @ SV85 )
| ( element @ SV23 @ SV104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(770,plain,
! [SV24: $i,SV105: $i,SV86: $i] :
( ( ~ ( element @ SV86 @ ( powerset @ SV105 ) )
| ~ ( in @ SV24 @ SV86 )
| ~ ( empty @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(771,plain,
! [SV25: $i,SV87: $i] :
( ( ( ~ ( empty @ SV87 ) )
= $true )
| ( ( ~ ( in @ SV25 @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[673]) ).
thf(772,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK72_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[674]) ).
thf(773,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[675]) ).
thf(774,plain,
! [SV26: $i,SV88: $i] :
( ( ( ~ ( relation @ SV88 ) )
= $true )
| ( ( ~ ( ~ ! [SY3625: $i] :
( ~ ( relation @ SY3625 )
| ~ ( ~ ( ~ ( in @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) @ SV26 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY3625 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) ) @ SV88 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY3625 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) ) @ SY3625 ) )
| ~ ~ ( ~ ( ( in @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) @ SV26 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY3625 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) ) @ SY3625 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SY3625 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) ) @ SV88 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY3625 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) ) @ SY3625 ) ) ) )
| ( SY3625
= ( relation_rng_restriction @ SV26 @ SV88 ) ) )
| ~ ! [SY3626: $i] :
( ~ ( relation @ SY3626 )
| ( SY3626
!= ( relation_rng_restriction @ SV26 @ SV88 ) )
| ~ ( ~ ! [SY3627: $i,SY3628: $i] :
( ~ ( in @ SY3628 @ SV26 )
| ~ ( in @ ( ordered_pair @ SY3627 @ SY3628 ) @ SV88 )
| ( in @ ( ordered_pair @ SY3627 @ SY3628 ) @ SY3626 ) )
| ~ ~ ( ~ ! [SY3365: $i,SY3366: $i] :
( ~ ( in @ ( ordered_pair @ SY3365 @ SY3366 ) @ SY3626 )
| ( in @ SY3366 @ SV26 ) )
| ~ ! [SY3631: $i,SY3632: $i] :
( ~ ( in @ ( ordered_pair @ SY3631 @ SY3632 ) @ SY3626 )
| ( in @ ( ordered_pair @ SY3631 @ SY3632 ) @ SV88 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[676]) ).
thf(775,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK29_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK29_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[677]) ).
thf(776,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[678]) ).
thf(777,plain,
! [SV27: $i] :
( ( ~ ! [SY3369: $i,SY3370: $i] :
( ~ ( relation @ SY3370 )
| ~ ( in @ SV27 @ SY3369 )
| ~ ( in @ SV27 @ ( relation_dom @ SY3370 ) )
| ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SY3370 @ SY3369 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[679]) ).
thf(778,plain,
! [SV27: $i] :
( ( ~ ~ ( ~ ! [SY3371: $i,SY3372: $i] :
( ~ ( relation @ SY3372 )
| ~ ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SY3372 @ SY3371 ) ) )
| ( in @ SV27 @ SY3371 ) )
| ~ ! [SY3373: $i,SY3374: $i] :
( ~ ( relation @ SY3374 )
| ~ ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SY3374 @ SY3373 ) ) )
| ( in @ SV27 @ ( relation_dom @ SY3374 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[679]) ).
thf(779,plain,
! [SV28: $i] :
( ( ( relation @ SV28 )
= $false )
| ( ( ~ ( ~ ! [SY3375: $i] :
( ~ ( relation @ SY3375 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SY3375 @ SV28 ) @ ( sK14_SY3290 @ SY3375 @ SV28 ) ) @ SY3375 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY3290 @ SY3375 @ SV28 ) @ ( sK13_C @ SY3375 @ SV28 ) ) @ SV28 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SY3375 @ SV28 ) @ ( sK14_SY3290 @ SY3375 @ SV28 ) ) @ SY3375 )
| ( in @ ( ordered_pair @ ( sK14_SY3290 @ SY3375 @ SV28 ) @ ( sK13_C @ SY3375 @ SV28 ) ) @ SV28 ) ) )
| ( SY3375
= ( relation_inverse @ SV28 ) ) )
| ~ ! [SY3376: $i] :
( ~ ( relation @ SY3376 )
| ( SY3376
!= ( relation_inverse @ SV28 ) )
| ~ ( ~ ! [SY3377: $i,SY3378: $i] :
( ~ ( in @ ( ordered_pair @ SY3377 @ SY3378 ) @ SY3376 )
| ( in @ ( ordered_pair @ SY3378 @ SY3377 ) @ SV28 ) )
| ~ ! [SY3379: $i,SY3380: $i] :
( ~ ( in @ ( ordered_pair @ SY3380 @ SY3379 ) @ SV28 )
| ( in @ ( ordered_pair @ SY3379 @ SY3380 ) @ SY3376 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[680]) ).
thf(780,plain,
! [SV29: $i] :
( ( ( ~ ( function @ SV29 ) )
= $true )
| ( ( ~ ( relation @ SV29 ) )
= $true )
| ( ( ~ ( ~ ! [SY3381: $i,SY3382: $i] :
( ~ ( ~ ( ! [SY3383: $i] :
( ~ ( in @ SY3383 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3383 @ SY3381 )
| ( ( sK61_D @ SY3382 @ SY3381 @ SV29 )
!= ( apply @ SV29 @ SY3383 ) ) )
| ~ ( in @ ( sK61_D @ SY3382 @ SY3381 @ SV29 ) @ SY3382 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY3318 @ SY3382 @ SY3381 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK62_SY3318 @ SY3382 @ SY3381 @ SV29 ) @ SY3381 ) )
| ( ( sK61_D @ SY3382 @ SY3381 @ SV29 )
!= ( apply @ SV29 @ ( sK62_SY3318 @ SY3382 @ SY3381 @ SV29 ) ) ) )
| ( in @ ( sK61_D @ SY3382 @ SY3381 @ SV29 ) @ SY3382 ) ) )
| ( SY3382
= ( relation_image @ SV29 @ SY3381 ) ) )
| ~ ! [SY3384: $i,SY3385: $i] :
( ( SY3385
!= ( relation_image @ SV29 @ SY3384 ) )
| ~ ( ~ ! [SY3386: $i] :
( ! [SY3387: $i] :
( ~ ( in @ SY3387 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3387 @ SY3384 )
| ( SY3386
!= ( apply @ SV29 @ SY3387 ) ) )
| ( in @ SY3386 @ SY3385 ) )
| ~ ! [SY3388: $i] :
( ~ ( in @ SY3388 @ SY3385 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SY3388 @ SY3385 @ SY3384 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK60_E @ SY3388 @ SY3385 @ SY3384 @ SV29 ) @ SY3384 ) )
| ( SY3388
!= ( apply @ SV29 @ ( sK60_E @ SY3388 @ SY3385 @ SY3384 @ SV29 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[681]) ).
thf(781,plain,
! [SV30: $i] :
( ( ( relation @ SV30 )
= $false )
| ( ( ~ ( ~ ! [SY3389: $i,SY3390: $i] :
( ~ ( ~ ( ! [SY3391: $i] :
( ~ ( in @ ( ordered_pair @ SY3391 @ ( sK55_D @ SY3390 @ SY3389 @ SV30 ) ) @ SV30 )
| ~ ( in @ SY3391 @ SY3389 ) )
| ~ ( in @ ( sK55_D @ SY3390 @ SY3389 @ SV30 ) @ SY3390 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_SY3315 @ SY3390 @ SY3389 @ SV30 ) @ ( sK55_D @ SY3390 @ SY3389 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK56_SY3315 @ SY3390 @ SY3389 @ SV30 ) @ SY3389 ) )
| ( in @ ( sK55_D @ SY3390 @ SY3389 @ SV30 ) @ SY3390 ) ) )
| ( SY3390
= ( relation_image @ SV30 @ SY3389 ) ) )
| ~ ! [SY3392: $i,SY3393: $i] :
( ( SY3393
!= ( relation_image @ SV30 @ SY3392 ) )
| ~ ( ~ ! [SY3394: $i] :
( ! [SY3395: $i] :
( ~ ( in @ ( ordered_pair @ SY3395 @ SY3394 ) @ SV30 )
| ~ ( in @ SY3395 @ SY3392 ) )
| ( in @ SY3394 @ SY3393 ) )
| ~ ! [SY3396: $i] :
( ~ ( in @ SY3396 @ SY3393 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SY3396 @ SY3393 @ SY3392 @ SV30 ) @ SY3396 ) @ SV30 )
| ~ ( in @ ( sK54_E @ SY3396 @ SY3393 @ SY3392 @ SV30 ) @ SY3392 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[682]) ).
thf(782,plain,
! [SV31: $i] :
( ( ( relation @ SV31 )
= $false )
| ( ( ~ ( ~ ! [SY3397: $i,SY3398: $i] :
( ~ ( ~ ( ! [SY3399: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ SY3398 @ SY3397 @ SV31 ) @ SY3399 ) @ SV31 )
| ~ ( in @ SY3399 @ SY3397 ) )
| ~ ( in @ ( sK52_D @ SY3398 @ SY3397 @ SV31 ) @ SY3398 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SY3398 @ SY3397 @ SV31 ) @ ( sK53_SY3313 @ SY3398 @ SY3397 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( sK53_SY3313 @ SY3398 @ SY3397 @ SV31 ) @ SY3397 ) )
| ( in @ ( sK52_D @ SY3398 @ SY3397 @ SV31 ) @ SY3398 ) ) )
| ( SY3398
= ( relation_inverse_image @ SV31 @ SY3397 ) ) )
| ~ ! [SY3400: $i,SY3401: $i] :
( ( SY3401
!= ( relation_inverse_image @ SV31 @ SY3400 ) )
| ~ ( ~ ! [SY3402: $i] :
( ! [SY3403: $i] :
( ~ ( in @ ( ordered_pair @ SY3402 @ SY3403 ) @ SV31 )
| ~ ( in @ SY3403 @ SY3400 ) )
| ( in @ SY3402 @ SY3401 ) )
| ~ ! [SY3404: $i] :
( ~ ( in @ SY3404 @ SY3401 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3404 @ ( sK51_E @ SY3404 @ SY3401 @ SY3400 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( sK51_E @ SY3404 @ SY3401 @ SY3400 @ SV31 ) @ SY3400 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[683]) ).
thf(783,plain,
! [SV32: $i] :
( ( ( relation @ SV32 )
= $false )
| ( ( ~ ( ~ ! [SY3405: $i,SY3406: $i] :
( ~ ( relation @ SY3406 )
| ~ ( ~ ( ~ ( in @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ SY3405 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ ( sK64_SY3319 @ SY3406 @ SY3405 @ SV32 ) ) @ SV32 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ ( sK64_SY3319 @ SY3406 @ SY3405 @ SV32 ) ) @ SY3406 ) )
| ~ ~ ( ~ ( ( in @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ SY3405 )
| ( in @ ( ordered_pair @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ ( sK64_SY3319 @ SY3406 @ SY3405 @ SV32 ) ) @ SY3406 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ ( sK64_SY3319 @ SY3406 @ SY3405 @ SV32 ) ) @ SV32 )
| ( in @ ( ordered_pair @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ ( sK64_SY3319 @ SY3406 @ SY3405 @ SV32 ) ) @ SY3406 ) ) ) )
| ( SY3406
= ( relation_dom_restriction @ SV32 @ SY3405 ) ) )
| ~ ! [SY3407: $i,SY3408: $i] :
( ~ ( relation @ SY3408 )
| ( SY3408
!= ( relation_dom_restriction @ SV32 @ SY3407 ) )
| ~ ( ~ ! [SY3409: $i,SY3410: $i] :
( ~ ( in @ SY3409 @ SY3407 )
| ~ ( in @ ( ordered_pair @ SY3409 @ SY3410 ) @ SV32 )
| ( in @ ( ordered_pair @ SY3409 @ SY3410 ) @ SY3408 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3408 )
| ( in @ SX3 @ SY3407 ) )
| ~ ! [SY3413: $i,SY3414: $i] :
( ~ ( in @ ( ordered_pair @ SY3413 @ SY3414 ) @ SY3408 )
| ( in @ ( ordered_pair @ SY3413 @ SY3414 ) @ SV32 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[684]) ).
thf(784,plain,
! [SV33: $i] :
( ( ~ ! [SY3415: $i,SY3416: $i] :
( ~ ( relation @ SY3416 )
| ! [SY3417: $i] :
( ~ ( in @ SY3417 @ ( relation_rng @ SY3416 ) )
| ~ ( in @ ( ordered_pair @ SV33 @ SY3417 ) @ SY3416 )
| ~ ( in @ SY3417 @ SY3415 ) )
| ( in @ SV33 @ ( relation_inverse_image @ SY3416 @ SY3415 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[685]) ).
thf(785,plain,
! [SV33: $i] :
( ( ~ ! [SY3418: $i,SY3419: $i] :
( ~ ( relation @ SY3419 )
| ~ ( in @ SV33 @ ( relation_inverse_image @ SY3419 @ SY3418 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK75_D @ SY3419 @ SY3418 @ SV33 ) @ ( relation_rng @ SY3419 ) )
| ~ ( in @ ( ordered_pair @ SV33 @ ( sK75_D @ SY3419 @ SY3418 @ SV33 ) ) @ SY3419 ) )
| ~ ( in @ ( sK75_D @ SY3419 @ SY3418 @ SV33 ) @ SY3418 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[685]) ).
thf(786,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK65_C @ SX1 @ SX0 )
!= ( sK66_SY3320 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK65_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY3320 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK65_C @ SX1 @ SX0 )
= ( sK66_SY3320 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY3320 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK65_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY3320 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[686]) ).
thf(787,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( SX2 = SX3 ) )
| ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[687]) ).
thf(788,plain,
! [SV34: $i,SV89: $i] :
( ( ~ ! [SY3633: $i,SY3634: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 ) @ SY3634 )
| ( ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 )
!= SY3633 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 ) @ SY3634 )
| ( ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 )
!= SV34 ) )
| ~ ( ~ ( in @ ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 ) @ SY3634 )
| ( ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 )
!= SV89 ) ) ) )
| ~ ( ( in @ ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 ) @ SY3634 )
| ( ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 )
= SY3633 )
| ( ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 )
= SV34 )
| ( ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 )
= SV89 ) ) )
| ( SY3634
= ( unordered_triple @ SV34 @ SV89 @ SY3633 ) ) )
| ~ ! [SY3635: $i,SY3636: $i] :
( ( SY3636
!= ( unordered_triple @ SV34 @ SV89 @ SY3635 ) )
| ~ ( ~ ! [SY3637: $i] :
( ~ ( in @ SY3637 @ SY3636 )
| ( SY3637 = SY3635 )
| ( SY3637 = SV34 )
| ( SY3637 = SV89 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SY3635 )
| ( in @ SX4 @ SY3636 ) )
| ~ ~ ( ~ ! [SY3427: $i] :
( ( SY3427 != SV34 )
| ( in @ SY3427 @ SY3636 ) )
| ~ ! [SY3640: $i] :
( ( SY3640 != SV89 )
| ( in @ SY3640 @ SY3636 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[688]) ).
thf(789,plain,
! [SV35: $i] :
( ( ~ ! [SY3429: $i,SY3430: $i] :
( ~ ( relation @ SY3430 )
| ~ ( in @ ( ordered_pair @ SV35 @ SY3429 ) @ SY3430 )
| ( in @ SV35 @ ( relation_field @ SY3430 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[689]) ).
thf(790,plain,
! [SV35: $i] :
( ( ~ ! [SY3431: $i,SY3432: $i] :
( ~ ( relation @ SY3432 )
| ~ ( in @ ( ordered_pair @ SV35 @ SY3431 ) @ SY3432 )
| ( in @ SY3431 @ ( relation_field @ SY3432 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[689]) ).
thf(791,plain,
! [SV36: $i] :
( ( ( relation @ SV36 )
= $false )
| ( ( ~ ( ~ ! [SY3433: $i] :
( ~ ( ~ ( ! [SY3434: $i] :
~ ( in @ ( ordered_pair @ SY3434 @ ( sK16_C @ SY3433 @ SV36 ) ) @ SV36 )
| ~ ( in @ ( sK16_C @ SY3433 @ SV36 ) @ SY3433 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_SY3292 @ SY3433 @ SV36 ) @ ( sK16_C @ SY3433 @ SV36 ) ) @ SV36 )
| ( in @ ( sK16_C @ SY3433 @ SV36 ) @ SY3433 ) ) )
| ( SY3433
= ( relation_rng @ SV36 ) ) )
| ~ ! [SY3435: $i] :
( ( SY3435
!= ( relation_rng @ SV36 ) )
| ~ ( ~ ! [SY3436: $i] :
( ! [SY3437: $i] :
~ ( in @ ( ordered_pair @ SY3437 @ SY3436 ) @ SV36 )
| ( in @ SY3436 @ SY3435 ) )
| ~ ! [SY3438: $i] :
( ~ ( in @ SY3438 @ SY3435 )
| ( in @ ( ordered_pair @ ( sK15_D @ SY3438 @ SY3435 @ SV36 ) @ SY3438 ) @ SV36 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[690]) ).
thf(792,plain,
! [SV37: $i] :
( ( ~ ! [SY3439: $i] :
( ~ ( subset @ SY3439 @ ( sK77_B @ SV37 ) )
| ( are_equipotent @ SY3439 @ ( sK77_B @ SV37 ) )
| ( in @ SY3439 @ ( sK77_B @ SV37 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[691]) ).
thf(793,plain,
! [SV37: $i] :
( ( ~ ~ ( ~ ! [SY3440: $i] :
( ~ ( in @ SY3440 @ ( sK77_B @ SV37 ) )
| ( in @ ( powerset @ SY3440 ) @ ( sK77_B @ SV37 ) ) )
| ~ ~ ( ~ ! [SY3441: $i,SY3442: $i] :
( ~ ( in @ SY3441 @ ( sK77_B @ SV37 ) )
| ~ ( subset @ SY3442 @ SY3441 )
| ( in @ SY3442 @ ( sK77_B @ SV37 ) ) )
| ~ ( in @ SV37 @ ( sK77_B @ SV37 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[691]) ).
thf(794,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK41_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK41_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK41_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK41_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[692]) ).
thf(795,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[693]) ).
thf(796,plain,
! [SV38: $i,SV90: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK5_C @ SV90 @ SV38 ) @ SV38 )
| ~ ( in @ ( sK5_C @ SV90 @ SV38 ) @ SV90 ) )
| ~ ( ( in @ ( sK5_C @ SV90 @ SV38 ) @ SV38 )
| ( in @ ( sK5_C @ SV90 @ SV38 ) @ SV90 ) ) ) )
= $true )
| ( ( SV38 = SV90 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[694]) ).
thf(797,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( in @ SX0 @ ( relation_rng @ SX1 ) )
| ~ ( one_to_one @ SX1 )
| ( SX0
= ( apply @ SX1 @ ( apply @ ( function_inverse @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[695]) ).
thf(798,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( in @ SX0 @ ( relation_rng @ SX1 ) )
| ~ ( one_to_one @ SX1 )
| ( SX0
= ( apply @ ( relation_composition @ ( function_inverse @ SX1 ) @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[696]) ).
thf(799,plain,
! [SV39: $i,SV91: $i] :
( ( ( ~ ( function @ SV91 )
| ~ ( relation @ SV91 ) )
= $true )
| ( ( ~ ( ~ ! [SY3641: $i] :
( ~ ( function @ SY3641 )
| ~ ( relation @ SY3641 )
| ~ ( in @ SV39 @ ( relation_dom @ SY3641 ) )
| ~ ( in @ ( apply @ SY3641 @ SV39 ) @ ( relation_dom @ SV91 ) )
| ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3641 @ SV91 ) ) ) )
| ~ ~ ( ~ ! [SY3642: $i] :
( ~ ( function @ SY3642 )
| ~ ( relation @ SY3642 )
| ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3642 @ SV91 ) ) )
| ( in @ SV39 @ ( relation_dom @ SY3642 ) ) )
| ~ ! [SY3643: $i] :
( ~ ( function @ SY3643 )
| ~ ( relation @ SY3643 )
| ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3643 @ SV91 ) ) )
| ( in @ ( apply @ SY3643 @ SV39 ) @ ( relation_dom @ SV91 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[697]) ).
thf(800,plain,
! [SV40: $i,SV92: $i] :
( ( ( ~ ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3644: $i] :
( ~ ( element @ SY3644 @ ( powerset @ ( powerset @ SV40 ) ) )
| ~ ( ~ ( element @ ( sK6_D @ SY3644 @ SV92 @ SV40 ) @ ( powerset @ SV40 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK6_D @ SY3644 @ SV92 @ SV40 ) @ SY3644 )
| ~ ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SY3644 @ SV92 @ SV40 ) ) @ SV92 ) )
| ~ ( ( in @ ( sK6_D @ SY3644 @ SV92 @ SV40 ) @ SY3644 )
| ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SY3644 @ SV92 @ SV40 ) ) @ SV92 ) ) ) )
| ( SY3644
= ( complements_of_subsets @ SV40 @ SV92 ) ) )
| ~ ! [SY3645: $i] :
( ~ ( element @ SY3645 @ ( powerset @ ( powerset @ SV40 ) ) )
| ( SY3645
!= ( complements_of_subsets @ SV40 @ SV92 ) )
| ~ ( ~ ! [SY3646: $i] :
( ~ ( element @ SY3646 @ ( powerset @ SV40 ) )
| ~ ( in @ SY3646 @ SY3645 )
| ( in @ ( subset_complement @ SV40 @ SY3646 ) @ SV92 ) )
| ~ ! [SY3647: $i] :
( ~ ( element @ SY3647 @ ( powerset @ SV40 ) )
| ~ ( in @ ( subset_complement @ SV40 @ SY3647 ) @ SV92 )
| ( in @ SY3647 @ SY3645 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[698]) ).
thf(801,plain,
! [SV41: $i] :
( ( ~ ! [SY3453: $i,SY3454: $i] :
( ~ ( function @ SY3454 )
| ~ ( relation @ SY3454 )
| ( SY3453
!= ( apply @ SY3454 @ SV41 ) )
| ~ ( in @ SV41 @ ( relation_dom @ SY3454 ) )
| ( in @ ( ordered_pair @ SV41 @ SY3453 ) @ SY3454 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[699]) ).
thf(802,plain,
! [SV41: $i] :
( ( ~ ~ ( ~ ! [SY3455: $i,SY3456: $i] :
( ~ ( function @ SY3456 )
| ~ ( relation @ SY3456 )
| ~ ( in @ ( ordered_pair @ SV41 @ SY3455 ) @ SY3456 )
| ( SY3455
= ( apply @ SY3456 @ SV41 ) ) )
| ~ ! [SY3457: $i,SY3458: $i] :
( ~ ( function @ SY3458 )
| ~ ( relation @ SY3458 )
| ~ ( in @ ( ordered_pair @ SV41 @ SY3457 ) @ SY3458 )
| ( in @ SV41 @ ( relation_dom @ SY3458 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[699]) ).
thf(803,plain,
! [SV42: $i] :
( ( ~ ! [SY3459: $i,SY3460: $i] :
( ~ ( relation @ SY3460 )
| ~ ( in @ SV42 @ SY3459 )
| ~ ( in @ SV42 @ ( relation_rng @ SY3460 ) )
| ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SY3459 @ SY3460 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[700]) ).
thf(804,plain,
! [SV42: $i] :
( ( ~ ~ ( ~ ! [SY3461: $i,SY3462: $i] :
( ~ ( relation @ SY3462 )
| ~ ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SY3461 @ SY3462 ) ) )
| ( in @ SV42 @ SY3461 ) )
| ~ ! [SY3463: $i,SY3464: $i] :
( ~ ( relation @ SY3464 )
| ~ ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SY3463 @ SY3464 ) ) )
| ( in @ SV42 @ ( relation_rng @ SY3464 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[700]) ).
thf(805,plain,
! [SV43: $i] :
( ( ~ ! [SY3465: $i] :
( ~ ( subset @ SY3465 @ ( sK2_B @ SV43 ) )
| ( are_equipotent @ SY3465 @ ( sK2_B @ SV43 ) )
| ( in @ SY3465 @ ( sK2_B @ SV43 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[701]) ).
thf(806,plain,
! [SV43: $i] :
( ( ~ ~ ( ~ ! [SY3466: $i] :
( ~ ( ~ ! [SY3467: $i] :
( ~ ( subset @ SY3467 @ SY3466 )
| ( in @ SY3467 @ ( sK3_SY3278 @ SY3466 @ SV43 ) ) )
| ~ ( in @ ( sK3_SY3278 @ SY3466 @ SV43 ) @ ( sK2_B @ SV43 ) ) )
| ~ ( in @ SY3466 @ ( sK2_B @ SV43 ) ) )
| ~ ~ ( ~ ! [SY3468: $i,SY3469: $i] :
( ~ ( in @ SY3468 @ ( sK2_B @ SV43 ) )
| ~ ( subset @ SY3469 @ SY3468 )
| ( in @ SY3469 @ ( sK2_B @ SV43 ) ) )
| ~ ( in @ SV43 @ ( sK2_B @ SV43 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[701]) ).
thf(807,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK49_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK49_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[702]) ).
thf(808,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK47_C @ SX1 @ SX0 ) @ ( sK48_SY3309 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[703]) ).
thf(809,plain,
! [SV93: $i,SV44: $i] :
( ( ~ ! [SY3648: $i,SY3649: $i] :
( ~ ( in @ SV44 @ SY3648 )
| ~ ( in @ SV93 @ SY3649 )
| ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SY3648 @ SY3649 ) ) )
| ~ ~ ( ~ ! [SY3650: $i] :
( ! [SY3651: $i] :
~ ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SY3650 @ SY3651 ) )
| ( in @ SV44 @ SY3650 ) )
| ~ ! [SY3652: $i,SY3653: $i] :
( ~ ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SY3652 @ SY3653 ) )
| ( in @ SV93 @ SY3653 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[704]) ).
thf(810,plain,
! [SV45: $i] :
( ( ( relation @ SV45 )
= $false )
| ( ( ~ ( ~ ! [SY3477: $i] :
( ~ ( ~ ( ! [SY3478: $i] :
~ ( in @ ( ordered_pair @ ( sK26_C @ SY3477 @ SV45 ) @ SY3478 ) @ SV45 )
| ~ ( in @ ( sK26_C @ SY3477 @ SV45 ) @ SY3477 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK26_C @ SY3477 @ SV45 ) @ ( sK27_SY3298 @ SY3477 @ SV45 ) ) @ SV45 )
| ( in @ ( sK26_C @ SY3477 @ SV45 ) @ SY3477 ) ) )
| ( SY3477
= ( relation_dom @ SV45 ) ) )
| ~ ! [SY3479: $i] :
( ( SY3479
!= ( relation_dom @ SV45 ) )
| ~ ( ~ ! [SY3480: $i] :
( ! [SY3481: $i] :
~ ( in @ ( ordered_pair @ SY3480 @ SY3481 ) @ SV45 )
| ( in @ SY3480 @ SY3479 ) )
| ~ ! [SY3482: $i] :
( ~ ( in @ SY3482 @ SY3479 )
| ( in @ ( ordered_pair @ SY3482 @ ( sK25_D @ SY3482 @ SY3479 @ SV45 ) ) @ SV45 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[705]) ).
thf(811,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[706]) ).
thf(812,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[707]) ).
thf(813,plain,
( ( ! [SX0: $i] :
( ( in @ ( sK42_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[708]) ).
thf(814,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[709]) ).
thf(815,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK43_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK43_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK43_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK43_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[710]) ).
thf(816,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[711]) ).
thf(817,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK74_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK74_C @ SX1 @ SX0 ) )
!= ( sK74_C @ SX1 @ SX0 ) ) ) )
| ( ( relation_dom @ SX1 )
!= SX0 )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[712]) ).
thf(818,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( ( apply @ SX1 @ SX2 )
= SX2 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[713]) ).
thf(819,plain,
! [SV46: $i] :
( ( ( ~ ( function @ SV46 ) )
= $true )
| ( ( ~ ( relation @ SV46 ) )
= $true )
| ( ( ~ ( one_to_one @ SV46 )
| ~ ( ~ ! [SY3483: $i] :
( ~ ( function @ SY3483 )
| ~ ( relation @ SY3483 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY3322 @ SY3483 @ SV46 )
= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ( ( sK70_C @ SY3483 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SY3483 @ SV46 )
= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SY3483 @ SV46 )
= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ( ( sK71_SY3322 @ SY3483 @ SV46 )
!= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK70_C @ SY3483 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK71_SY3322 @ SY3483 @ SV46 )
!= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY3483 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK70_C @ SY3483 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SY3483 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SY3483 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK71_SY3322 @ SY3483 @ SV46 )
!= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ( ( relation_dom @ SY3483 )
!= ( relation_rng @ SV46 ) )
| ( SY3483
= ( function_inverse @ SV46 ) ) )
| ~ ~ ( ~ ! [SY3484: $i] :
( ~ ( function @ SY3484 )
| ~ ( relation @ SY3484 )
| ( SY3484
!= ( function_inverse @ SV46 ) )
| ~ ( ~ ~ ( ~ ! [SY3485: $i,SY3486: $i] :
( ( SY3486
!= ( apply @ SY3484 @ SY3485 ) )
| ~ ( in @ SY3485 @ ( relation_rng @ SV46 ) )
| ( SY3485
= ( apply @ SV46 @ SY3486 ) ) )
| ~ ! [SY3487: $i,SY3488: $i] :
( ( SY3488
!= ( apply @ SY3484 @ SY3487 ) )
| ~ ( in @ SY3487 @ ( relation_rng @ SV46 ) )
| ( in @ SY3488 @ ( relation_dom @ SV46 ) ) ) )
| ~ ~ ( ~ ! [SY3489: $i,SY3490: $i] :
( ( SY3489
!= ( apply @ SV46 @ SY3490 ) )
| ~ ( in @ SY3490 @ ( relation_dom @ SV46 ) )
| ( SY3490
= ( apply @ SY3484 @ SY3489 ) ) )
| ~ ! [SY3491: $i] :
( ! [SY3492: $i] :
( ( SY3491
!= ( apply @ SV46 @ SY3492 ) )
| ~ ( in @ SY3492 @ ( relation_dom @ SV46 ) ) )
| ( in @ SY3491 @ ( relation_rng @ SV46 ) ) ) ) ) )
| ~ ! [SY3493: $i] :
( ~ ( function @ SY3493 )
| ~ ( relation @ SY3493 )
| ( SY3493
!= ( function_inverse @ SV46 ) )
| ( ( relation_dom @ SY3493 )
= ( relation_rng @ SV46 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[714]) ).
thf(820,plain,
! [SV47: $i] :
( ( ( relation @ SV47 )
= $false )
| ( ( ! [SY3494: $i] :
( ~ ( relation @ SY3494 )
| ~ ( ~ ! [SY3495: $i] :
( ~ ( relation @ SY3495 )
| ~ ( ~ ( ! [SY3496: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY3495 @ SY3494 @ SV47 ) @ SY3496 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3496 @ ( sK9_SY3284 @ SY3495 @ SY3494 @ SV47 ) ) @ SY3494 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SY3495 @ SY3494 @ SV47 ) @ ( sK9_SY3284 @ SY3495 @ SY3494 @ SV47 ) ) @ SY3495 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY3495 @ SY3494 @ SV47 ) @ ( sK10_SY3288 @ SY3495 @ SY3494 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY3288 @ SY3495 @ SY3494 @ SV47 ) @ ( sK9_SY3284 @ SY3495 @ SY3494 @ SV47 ) ) @ SY3494 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SY3495 @ SY3494 @ SV47 ) @ ( sK9_SY3284 @ SY3495 @ SY3494 @ SV47 ) ) @ SY3495 ) ) )
| ( SY3495
= ( relation_composition @ SV47 @ SY3494 ) ) )
| ~ ! [SY3497: $i] :
( ~ ( relation @ SY3497 )
| ( SY3497
!= ( relation_composition @ SV47 @ SY3494 ) )
| ~ ( ~ ! [SY3498: $i,SY3499: $i] :
( ! [SY3500: $i] :
( ~ ( in @ ( ordered_pair @ SY3498 @ SY3500 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3500 @ SY3499 ) @ SY3494 ) )
| ( in @ ( ordered_pair @ SY3498 @ SY3499 ) @ SY3497 ) )
| ~ ! [SY3501: $i,SY3502: $i] :
( ~ ( in @ ( ordered_pair @ SY3501 @ SY3502 ) @ SY3497 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3501 @ ( sK7_F @ SY3502 @ SY3501 @ SY3497 @ SY3494 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY3502 @ SY3501 @ SY3497 @ SY3494 @ SV47 ) @ SY3502 ) @ SY3494 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[715]) ).
thf(821,plain,
! [SV48: $i] :
( ( ~ ! [SY3503: $i,SY3504: $i] :
( ~ ( in @ SV48 @ SY3504 )
| ~ ( in @ SY3503 @ SY3504 )
| ( subset @ ( unordered_pair @ SV48 @ SY3503 ) @ SY3504 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[716]) ).
thf(822,plain,
! [SV48: $i] :
( ( ~ ~ ( ~ ! [SY3505: $i,SY3506: $i] :
( ~ ( subset @ ( unordered_pair @ SV48 @ SY3505 ) @ SY3506 )
| ( in @ SV48 @ SY3506 ) )
| ~ ! [SY3507: $i,SY3508: $i] :
( ~ ( subset @ ( unordered_pair @ SV48 @ SY3507 ) @ SY3508 )
| ( in @ SY3507 @ SY3508 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[716]) ).
thf(823,plain,
! [SV94: $i,SV49: $i] :
( ( ~ ! [SY3654: $i,SY3655: $i] :
( ~ ( relation @ SY3655 )
| ~ ( in @ SV49 @ SY3654 )
| ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ SY3655 )
| ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SY3654 ) @ SY3655 ) ) )
| ~ ~ ( ~ ! [SY3656: $i,SY3657: $i] :
( ~ ( relation @ SY3657 )
| ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SY3656 ) @ SY3657 ) )
| ( in @ SV49 @ SY3656 ) )
| ~ ! [SY3658: $i,SY3659: $i] :
( ~ ( relation @ SY3659 )
| ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SY3658 ) @ SY3659 ) )
| ( in @ ( ordered_pair @ SV49 @ SV94 ) @ SY3659 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[717]) ).
thf(824,plain,
! [SV50: $i,SV95: $i] :
( ( ( ~ ( ~ ! [SY3660: $i] :
( ~ ( in @ SY3660 @ SV95 )
| ~ ( in @ SY3660 @ ( sK4_C @ SV95 @ SV50 ) ) )
| ~ ( in @ ( sK4_C @ SV95 @ SV50 ) @ SV95 ) ) )
= $true )
| ( ( ~ ( in @ SV50 @ SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[718]) ).
thf(825,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_B @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK12_SY3289 @ SX0 ) @ ( relation_dom @ SX0 ) ) )
| ( ( apply @ SX0 @ ( sK11_B @ SX0 ) )
!= ( apply @ SX0 @ ( sK12_SY3289 @ SX0 ) ) ) )
| ~ ( ( ( sK11_B @ SX0 )
!= ( sK12_SY3289 @ SX0 ) ) ) )
| ( one_to_one @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[719]) ).
thf(826,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ~ ( in @ SX2 @ ( relation_dom @ SX0 ) )
| ( ( apply @ SX0 @ SX1 )
!= ( apply @ SX0 @ SX2 ) )
| ( SX1 = SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[720]) ).
thf(827,plain,
! [SV51: $i] :
( ( ~ ! [SY3518: $i,SY3519: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK37_D @ SY3519 @ SY3518 @ SV51 ) @ SY3519 )
| ~ ( in @ ( sK37_D @ SY3519 @ SY3518 @ SV51 ) @ SV51 ) )
| ~ ( ~ ( in @ ( sK37_D @ SY3519 @ SY3518 @ SV51 ) @ SY3519 )
| ~ ( in @ ( sK37_D @ SY3519 @ SY3518 @ SV51 ) @ SY3518 ) ) )
| ~ ( ( in @ ( sK37_D @ SY3519 @ SY3518 @ SV51 ) @ SY3519 )
| ( in @ ( sK37_D @ SY3519 @ SY3518 @ SV51 ) @ SV51 )
| ( in @ ( sK37_D @ SY3519 @ SY3518 @ SV51 ) @ SY3518 ) ) )
| ( SY3519
= ( set_union2 @ SV51 @ SY3518 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[721]) ).
thf(828,plain,
! [SV51: $i] :
( ( ~ ! [SY3520: $i,SY3521: $i] :
( ( SY3521
!= ( set_union2 @ SV51 @ SY3520 ) )
| ~ ( ~ ! [SY3522: $i] :
( ~ ( in @ SY3522 @ SY3521 )
| ( in @ SY3522 @ SV51 )
| ( in @ SY3522 @ SY3520 ) )
| ~ ~ ( ~ ! [SY3523: $i] :
( ~ ( in @ SY3523 @ SV51 )
| ( in @ SY3523 @ SY3521 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY3520 )
| ( in @ SX3 @ SY3521 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[721]) ).
thf(829,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[722]) ).
thf(830,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[723]) ).
thf(831,plain,
! [SV52: $i] :
( ( ( relation @ SV52 )
= $false )
| ( ( ~ ( ~ ! [SY3525: $i] :
( ~ ( relation @ SY3525 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK30_C @ SY3525 @ SV52 ) @ ( sK31_SY3299 @ SY3525 @ SV52 ) ) @ SV52 )
| ~ ~ ( in @ ( ordered_pair @ ( sK30_C @ SY3525 @ SV52 ) @ ( sK31_SY3299 @ SY3525 @ SV52 ) ) @ SY3525 ) )
| ( subset @ SV52 @ SY3525 ) )
| ~ ! [SY3526: $i] :
( ~ ( relation @ SY3526 )
| ~ ( subset @ SV52 @ SY3526 )
| ! [SY3527: $i,SY3528: $i] :
( ~ ( in @ ( ordered_pair @ SY3527 @ SY3528 ) @ SV52 )
| ( in @ ( ordered_pair @ SY3527 @ SY3528 ) @ SY3526 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[724]) ).
thf(832,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK46_SY3307 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK45_C @ SX1 @ SX0 ) @ ( sK46_SY3307 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK45_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK45_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK45_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK44_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK44_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[725]) ).
thf(833,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[726]) ).
thf(834,plain,
! [SV53: $i] :
( ( ( ~ ( function @ SV53 ) )
= $true )
| ( ( ~ ( relation @ SV53 ) )
= $true )
| ( ( ~ ( ~ ! [SY3529: $i,SY3530: $i] :
( ~ ( ~ ( ~ ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) ) @ SY3529 )
| ~ ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ SY3530 ) )
| ~ ~ ( ~ ( ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ SY3530 ) )
| ~ ( ( in @ ( apply @ SV53 @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) ) @ SY3529 )
| ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ SY3530 ) ) ) )
| ( SY3530
= ( relation_inverse_image @ SV53 @ SY3529 ) ) )
| ~ ! [SY3531: $i,SY3532: $i] :
( ( SY3532
!= ( relation_inverse_image @ SV53 @ SY3531 ) )
| ~ ( ~ ! [SY3533: $i] :
( ~ ( in @ SY3533 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SY3533 ) @ SY3531 )
| ( in @ SY3533 @ SY3532 ) )
| ~ ~ ( ~ ! [SY3534: $i] :
( ~ ( in @ SY3534 @ SY3532 )
| ( in @ SY3534 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY3535: $i] :
( ~ ( in @ SY3535 @ SY3532 )
| ( in @ ( apply @ SV53 @ SY3535 ) @ SY3531 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[727]) ).
thf(835,plain,
! [SV54: $i] :
( ( ~ ! [SY3536: $i,SY3537: $i] :
( ~ ( ~ ( ~ ( in @ ( sK28_D @ SY3537 @ SY3536 @ SV54 ) @ SV54 )
| ~ ( in @ ( sK28_D @ SY3537 @ SY3536 @ SV54 ) @ SY3536 )
| ~ ( in @ ( sK28_D @ SY3537 @ SY3536 @ SV54 ) @ SY3537 ) )
| ~ ~ ( ~ ( ( in @ ( sK28_D @ SY3537 @ SY3536 @ SV54 ) @ SV54 )
| ( in @ ( sK28_D @ SY3537 @ SY3536 @ SV54 ) @ SY3537 ) )
| ~ ( ( in @ ( sK28_D @ SY3537 @ SY3536 @ SV54 ) @ SY3536 )
| ( in @ ( sK28_D @ SY3537 @ SY3536 @ SV54 ) @ SY3537 ) ) ) )
| ( SY3537
= ( set_intersection2 @ SV54 @ SY3536 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[728]) ).
thf(836,plain,
! [SV54: $i] :
( ( ~ ! [SY3538: $i,SY3539: $i] :
( ( SY3539
!= ( set_intersection2 @ SV54 @ SY3538 ) )
| ~ ( ~ ! [SY3540: $i] :
( ~ ( in @ SY3540 @ SV54 )
| ~ ( in @ SY3540 @ SY3538 )
| ( in @ SY3540 @ SY3539 ) )
| ~ ~ ( ~ ! [SY3541: $i] :
( ~ ( in @ SY3541 @ SY3539 )
| ( in @ SY3541 @ SV54 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY3539 )
| ( in @ SX3 @ SY3538 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[728]) ).
thf(837,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[729]) ).
thf(838,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[730]) ).
thf(839,plain,
! [SV55: $i] :
( ( ~ ! [SY3543: $i,SY3544: $i] :
( ~ ( ~ ( ~ ( in @ ( sK21_D @ SY3544 @ SY3543 @ SV55 ) @ SV55 )
| ( in @ ( sK21_D @ SY3544 @ SY3543 @ SV55 ) @ SY3543 )
| ~ ( in @ ( sK21_D @ SY3544 @ SY3543 @ SV55 ) @ SY3544 ) )
| ~ ~ ( ~ ( ( in @ ( sK21_D @ SY3544 @ SY3543 @ SV55 ) @ SV55 )
| ( in @ ( sK21_D @ SY3544 @ SY3543 @ SV55 ) @ SY3544 ) )
| ~ ( ~ ( in @ ( sK21_D @ SY3544 @ SY3543 @ SV55 ) @ SY3543 )
| ( in @ ( sK21_D @ SY3544 @ SY3543 @ SV55 ) @ SY3544 ) ) ) )
| ( SY3544
= ( set_difference @ SV55 @ SY3543 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[731]) ).
thf(840,plain,
! [SV55: $i] :
( ( ~ ! [SY3545: $i,SY3546: $i] :
( ( SY3546
!= ( set_difference @ SV55 @ SY3545 ) )
| ~ ( ~ ! [SY3547: $i] :
( ~ ( in @ SY3547 @ SV55 )
| ( in @ SY3547 @ SY3545 )
| ( in @ SY3547 @ SY3546 ) )
| ~ ~ ( ~ ! [SY3548: $i] :
( ~ ( in @ SY3548 @ SY3546 )
| ( in @ SY3548 @ SV55 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY3546 )
| ~ ( in @ SX3 @ SY3545 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[731]) ).
thf(841,plain,
! [SV56: $i] :
( ( ( ~ ( function @ SV56 ) )
= $true )
| ( ( ~ ( relation @ SV56 ) )
= $true )
| ( ( ~ ( ~ ! [SY3550: $i] :
( ~ ( ~ ( ! [SY3551: $i] :
( ( ( sK19_C @ SY3550 @ SV56 )
!= ( apply @ SV56 @ SY3551 ) )
| ~ ( in @ SY3551 @ ( relation_dom @ SV56 ) ) )
| ~ ( in @ ( sK19_C @ SY3550 @ SV56 ) @ SY3550 ) )
| ~ ( ~ ( ( ( sK19_C @ SY3550 @ SV56 )
!= ( apply @ SV56 @ ( sK20_SY3294 @ SY3550 @ SV56 ) ) )
| ~ ( in @ ( sK20_SY3294 @ SY3550 @ SV56 ) @ ( relation_dom @ SV56 ) ) )
| ( in @ ( sK19_C @ SY3550 @ SV56 ) @ SY3550 ) ) )
| ( SY3550
= ( relation_rng @ SV56 ) ) )
| ~ ! [SY3552: $i] :
( ( SY3552
!= ( relation_rng @ SV56 ) )
| ~ ( ~ ! [SY3553: $i] :
( ! [SY3554: $i] :
( ( SY3553
!= ( apply @ SV56 @ SY3554 ) )
| ~ ( in @ SY3554 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY3553 @ SY3552 ) )
| ~ ! [SY3555: $i] :
( ~ ( in @ SY3555 @ SY3552 )
| ~ ( ( SY3555
!= ( apply @ SV56 @ ( sK18_D @ SY3555 @ SY3552 @ SV56 ) ) )
| ~ ( in @ ( sK18_D @ SY3555 @ SY3552 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[732]) ).
thf(842,plain,
! [SV57: $i] :
( ( ~ ! [SY3556: $i,SY3557: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK38_D @ SY3557 @ SY3556 @ SV57 ) @ SY3557 )
| ( ( sK38_D @ SY3557 @ SY3556 @ SV57 )
!= SV57 ) )
| ~ ( ~ ( in @ ( sK38_D @ SY3557 @ SY3556 @ SV57 ) @ SY3557 )
| ( ( sK38_D @ SY3557 @ SY3556 @ SV57 )
!= SY3556 ) ) )
| ~ ( ( in @ ( sK38_D @ SY3557 @ SY3556 @ SV57 ) @ SY3557 )
| ( ( sK38_D @ SY3557 @ SY3556 @ SV57 )
= SV57 )
| ( ( sK38_D @ SY3557 @ SY3556 @ SV57 )
= SY3556 ) ) )
| ( SY3557
= ( unordered_pair @ SV57 @ SY3556 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[733]) ).
thf(843,plain,
! [SV57: $i] :
( ( ~ ! [SY3558: $i,SY3559: $i] :
( ( SY3559
!= ( unordered_pair @ SV57 @ SY3558 ) )
| ~ ( ~ ! [SY3560: $i] :
( ~ ( in @ SY3560 @ SY3559 )
| ( SY3560 = SV57 )
| ( SY3560 = SY3558 ) )
| ~ ~ ( ~ ! [SY3561: $i] :
( ( SY3561 != SV57 )
| ( in @ SY3561 @ SY3559 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY3558 )
| ( in @ SX3 @ SY3559 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[733]) ).
thf(844,plain,
! [SV58: $i,SV96: $i] :
( ( ( ~ ( function @ SV96 )
| ~ ( relation @ SV96 ) )
= $true )
| ( ( ~ ( ~ ! [SY3661: $i] :
( ~ ( function @ SY3661 )
| ~ ( relation @ SY3661 )
| ~ ( ~ ( in @ ( sK67_D @ SY3661 @ SV96 @ SV58 ) @ ( relation_dom @ SV96 ) )
| ~ ( ( ( apply @ SV96 @ ( sK67_D @ SY3661 @ SV96 @ SV58 ) )
!= ( apply @ SY3661 @ ( sK67_D @ SY3661 @ SV96 @ SV58 ) ) ) ) )
| ( ( relation_dom @ SV96 )
!= ( set_intersection2 @ ( relation_dom @ SY3661 ) @ SV58 ) )
| ( SV96
= ( relation_dom_restriction @ SY3661 @ SV58 ) ) )
| ~ ~ ( ~ ! [SY3662: $i] :
( ~ ( function @ SY3662 )
| ~ ( relation @ SY3662 )
| ( SV96
!= ( relation_dom_restriction @ SY3662 @ SV58 ) )
| ! [SY3663: $i] :
( ~ ( in @ SY3663 @ ( relation_dom @ SV96 ) )
| ( ( apply @ SV96 @ SY3663 )
= ( apply @ SY3662 @ SY3663 ) ) ) )
| ~ ! [SY3664: $i] :
( ~ ( function @ SY3664 )
| ~ ( relation @ SY3664 )
| ( SV96
!= ( relation_dom_restriction @ SY3664 @ SV58 ) )
| ( ( relation_dom @ SV96 )
= ( set_intersection2 @ ( relation_dom @ SY3664 ) @ SV58 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[734]) ).
thf(845,plain,
! [SV59: $i] :
( ( ( relation @ SV59 )
= $false )
| ( ( ~ ( ~ ! [SY3568: $i] :
( ~ ( relation @ SY3568 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_C @ SY3568 @ SV59 ) @ ( sK40_SY3306 @ SY3568 @ SV59 ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK39_C @ SY3568 @ SV59 ) @ ( sK40_SY3306 @ SY3568 @ SV59 ) ) @ SY3568 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK39_C @ SY3568 @ SV59 ) @ ( sK40_SY3306 @ SY3568 @ SV59 ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK39_C @ SY3568 @ SV59 ) @ ( sK40_SY3306 @ SY3568 @ SV59 ) ) @ SY3568 ) ) )
| ( SV59 = SY3568 ) )
| ~ ! [SY3569: $i] :
( ~ ( relation @ SY3569 )
| ( SV59 != SY3569 )
| ~ ( ~ ! [SY3570: $i,SY3571: $i] :
( ~ ( in @ ( ordered_pair @ SY3570 @ SY3571 ) @ SV59 )
| ( in @ ( ordered_pair @ SY3570 @ SY3571 ) @ SY3569 ) )
| ~ ! [SY3572: $i,SY3573: $i] :
( ~ ( in @ ( ordered_pair @ SY3572 @ SY3573 ) @ SY3569 )
| ( in @ ( ordered_pair @ SY3572 @ SY3573 ) @ SV59 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[735]) ).
thf(846,plain,
! [SV60: $i,SV97: $i] :
( ( ( ~ ( ~ ( in @ ( sK78_C @ SV97 @ SV60 ) @ SV60 )
| ~ ~ ( in @ ( sK78_C @ SV97 @ SV60 ) @ SV97 ) ) )
= $true )
| ( ( element @ SV60 @ ( powerset @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[736]) ).
thf(847,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ ( sK24_SY3296 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK24_SY3296 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[737]) ).
thf(848,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK22_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[738]) ).
thf(849,plain,
! [SV98: $i,SV61: $i] :
( ( ~ ! [SY3665: $i,SY3666: $i] :
( ~ ( in @ SV61 @ SY3665 )
| ~ ( in @ SV98 @ SY3666 )
| ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SY3665 @ SY3666 ) ) )
| ~ ~ ( ~ ! [SY3667: $i] :
( ! [SY3668: $i] :
~ ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SY3667 @ SY3668 ) )
| ( in @ SV61 @ SY3667 ) )
| ~ ! [SY3669: $i,SY3670: $i] :
( ~ ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SY3669 @ SY3670 ) )
| ( in @ SV98 @ SY3670 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[739]) ).
thf(850,plain,
! [SV62: $i] :
( ( ~ ! [SY3582: $i,SY3583: $i] :
( ~ ( function @ SY3583 )
| ~ ( relation @ SY3583 )
| ~ ( in @ SY3582 @ ( relation_dom @ SY3583 ) )
| ~ ( in @ SY3582 @ SV62 )
| ( in @ SY3582 @ ( relation_dom @ ( relation_dom_restriction @ SY3583 @ SV62 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[740]) ).
thf(851,plain,
! [SV62: $i] :
( ( ~ ~ ( ~ ! [SY3584: $i,SY3585: $i] :
( ~ ( function @ SY3585 )
| ~ ( relation @ SY3585 )
| ~ ( in @ SY3584 @ ( relation_dom @ ( relation_dom_restriction @ SY3585 @ SV62 ) ) )
| ( in @ SY3584 @ ( relation_dom @ SY3585 ) ) )
| ~ ! [SY3586: $i,SY3587: $i] :
( ~ ( function @ SY3587 )
| ~ ( relation @ SY3587 )
| ~ ( in @ SY3586 @ ( relation_dom @ ( relation_dom_restriction @ SY3587 @ SV62 ) ) )
| ( in @ SY3586 @ SV62 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[740]) ).
thf(852,plain,
! [SV63: $i] :
( ( ~ ! [SY3588: $i,SY3589: $i] :
( ~ ( ~ ( ! [SY3590: $i,SY3591: $i] :
( ~ ( in @ SY3590 @ SV63 )
| ~ ( in @ SY3591 @ SY3588 )
| ( ( sK34_D @ SY3589 @ SY3588 @ SV63 )
!= ( ordered_pair @ SY3590 @ SY3591 ) ) )
| ~ ( in @ ( sK34_D @ SY3589 @ SY3588 @ SV63 ) @ SY3589 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK35_SY3303 @ SY3589 @ SY3588 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK36_SY3305 @ SY3589 @ SY3588 @ SV63 ) @ SY3588 ) )
| ( ( sK34_D @ SY3589 @ SY3588 @ SV63 )
!= ( ordered_pair @ ( sK35_SY3303 @ SY3589 @ SY3588 @ SV63 ) @ ( sK36_SY3305 @ SY3589 @ SY3588 @ SV63 ) ) ) )
| ( in @ ( sK34_D @ SY3589 @ SY3588 @ SV63 ) @ SY3589 ) ) )
| ( SY3589
= ( cartesian_product2 @ SV63 @ SY3588 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[741]) ).
thf(853,plain,
! [SV63: $i] :
( ( ~ ! [SY3592: $i,SY3593: $i] :
( ( SY3593
!= ( cartesian_product2 @ SV63 @ SY3592 ) )
| ~ ( ~ ! [SY3594: $i] :
( ! [SY3595: $i,SY3596: $i] :
( ~ ( in @ SY3595 @ SV63 )
| ~ ( in @ SY3596 @ SY3592 )
| ( SY3594
!= ( ordered_pair @ SY3595 @ SY3596 ) ) )
| ( in @ SY3594 @ SY3593 ) )
| ~ ! [SY3597: $i] :
( ~ ( in @ SY3597 @ SY3593 )
| ~ ( ~ ~ ( ~ ( in @ ( sK32_E @ SY3597 @ SY3593 @ SY3592 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK33_SY3300 @ SY3597 @ SY3593 @ SY3592 @ SV63 ) @ SY3592 ) )
| ( SY3597
!= ( ordered_pair @ ( sK32_E @ SY3597 @ SY3593 @ SY3592 @ SV63 ) @ ( sK33_SY3300 @ SY3597 @ SY3593 @ SY3592 @ SV63 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[741]) ).
thf(854,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK73_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK73_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[742]) ).
thf(855,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[743]) ).
thf(856,plain,
! [SV64: $i] :
( ( ~ ! [SY3598: $i,SY3599: $i] :
( ~ ( relation @ SY3599 )
| ! [SY3600: $i] :
( ~ ( in @ SY3600 @ ( relation_dom @ SY3599 ) )
| ~ ( in @ ( ordered_pair @ SY3600 @ SV64 ) @ SY3599 )
| ~ ( in @ SY3600 @ SY3598 ) )
| ( in @ SV64 @ ( relation_image @ SY3599 @ SY3598 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[744]) ).
thf(857,plain,
! [SV64: $i] :
( ( ~ ! [SY3601: $i,SY3602: $i] :
( ~ ( relation @ SY3602 )
| ~ ( in @ SV64 @ ( relation_image @ SY3602 @ SY3601 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK76_D @ SY3602 @ SY3601 @ SV64 ) @ ( relation_dom @ SY3602 ) )
| ~ ( in @ ( ordered_pair @ ( sK76_D @ SY3602 @ SY3601 @ SV64 ) @ SV64 ) @ SY3602 ) )
| ~ ( in @ ( sK76_D @ SY3602 @ SY3601 @ SV64 ) @ SY3601 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[744]) ).
thf(858,plain,
! [SV65: $i] :
( ( ~ ! [SY3603: $i,SY3604: $i] :
( ~ ( relation @ SY3604 )
| ~ ( in @ ( ordered_pair @ SV65 @ SY3603 ) @ SY3604 )
| ( in @ SV65 @ ( relation_dom @ SY3604 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[745]) ).
thf(859,plain,
! [SV65: $i] :
( ( ~ ! [SY3605: $i,SY3606: $i] :
( ~ ( relation @ SY3606 )
| ~ ( in @ ( ordered_pair @ SV65 @ SY3605 ) @ SY3606 )
| ( in @ SY3605 @ ( relation_rng @ SY3606 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[745]) ).
thf(860,plain,
! [SV66: $i] :
( ( ( ~ ( function @ SV66 ) )
= $true )
| ( ( ~ ( relation @ SV66 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY3607: $i] :
( ~ ( in @ SY3607 @ ( relation_dom @ SV66 ) )
| ! [SY3608: $i] :
( ( SY3608
!= ( apply @ SV66 @ SY3607 ) )
| ( in @ ( ordered_pair @ SY3607 @ SY3608 ) @ SV66 ) ) )
| ~ ! [SY3609: $i] :
( ~ ( in @ SY3609 @ ( relation_dom @ SV66 ) )
| ! [SY3610: $i] :
( ~ ( in @ ( ordered_pair @ SY3609 @ SY3610 ) @ SV66 )
| ( SY3610
= ( apply @ SV66 @ SY3609 ) ) ) ) )
| ~ ~ ( ~ ! [SY3611: $i] :
( ( in @ SY3611 @ ( relation_dom @ SV66 ) )
| ! [SY3612: $i] :
( ( SY3612
!= ( apply @ SV66 @ SY3611 ) )
| ( SY3612 = empty_set ) ) )
| ~ ! [SY3613: $i] :
( ( in @ SY3613 @ ( relation_dom @ SV66 ) )
| ! [SY3614: $i] :
( ( SY3614 != empty_set )
| ( SY3614
= ( apply @ SV66 @ SY3613 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[746]) ).
thf(861,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[747]) ).
thf(862,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[748]) ).
thf(863,plain,
! [SV67: $i,SV1: $i] :
( ( ( in @ SV1 @ SV67 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV1 ) @ SV67 )
= SV67 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[749]) ).
thf(864,plain,
! [SV68: $i,SV2: $i] :
( ( ( disjoint @ ( singleton @ SV2 ) @ SV68 )
= $false )
| ( ( ~ ( in @ SV2 @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[750]) ).
thf(865,plain,
! [SV4: $i,SV70: $i] :
( ( ( element @ SV70 @ ( powerset @ SV4 ) )
= $false )
| ( ( ! [SY3615: $i] :
( ~ ( in @ SY3615 @ SV70 )
| ( in @ SY3615 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[752]) ).
thf(866,plain,
! [SV71: $i,SV5: $i] :
( ( ( subset @ SV5 @ SV71 )
= $false )
| ( ( ! [SY3616: $i] :
( ( in @ SY3616 @ SV5 )
| ( subset @ SV5 @ ( set_difference @ SV71 @ ( singleton @ SY3616 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[753]) ).
thf(867,plain,
! [SV72: $i,SV6: $i] :
( ( ( in @ SV6 @ SV72 )
= $false )
| ( ( subset @ SV6 @ ( union @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[754]) ).
thf(868,plain,
! [SV7: $i,SV73: $i] :
( ( ( ~ ( function @ SV73 ) )
= $true )
| ( ( ~ ( relation @ SV73 ) )
= $true )
| ( ( ! [SY3617: $i] :
( ~ ( function @ SY3617 )
| ~ ( relation @ SY3617 )
| ~ ( in @ SV7 @ ( relation_dom @ ( relation_composition @ SY3617 @ SV73 ) ) )
| ( ( apply @ ( relation_composition @ SY3617 @ SV73 ) @ SV7 )
= ( apply @ SV73 @ ( apply @ SY3617 @ SV7 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[755]) ).
thf(869,plain,
! [SV8: $i,SV74: $i] :
( ( ( ~ ( function @ SV74 ) )
= $true )
| ( ( ~ ( relation @ SV74 ) )
= $true )
| ( ( ! [SY3618: $i] :
( ~ ( function @ SY3618 )
| ~ ( relation @ SY3618 )
| ~ ( in @ SV8 @ ( relation_dom @ SV74 ) )
| ( ( apply @ ( relation_composition @ SV74 @ SY3618 ) @ SV8 )
= ( apply @ SY3618 @ ( apply @ SV74 @ SV8 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[756]) ).
thf(870,plain,
! [SV9: $i,SV75: $i] :
( ( ( in @ SV75 @ SV9 )
= $false )
| ( ( ( apply @ ( identity_relation @ SV9 ) @ SV75 )
= SV75 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[757]) ).
thf(871,plain,
! [SV99: $i,SV76: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV76 )
| ~ ( in @ SV76 @ SV99 ) )
= $true )
| ( ( ~ ( in @ SV99 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[758]) ).
thf(872,plain,
! [SV77: $i,SV11: $i] :
( ( ( in @ SV11 @ SV77 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV11 ) @ SV77 )
= SV77 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[759]) ).
thf(873,plain,
! [SV12: $i,SV100: $i] :
( ( ( ~ ( element @ SV100 @ ( powerset @ SV12 ) ) )
= $true )
| ( ( ! [SY3671: $i] :
( ~ ( element @ SY3671 @ SV12 )
| ( in @ SY3671 @ SV100 )
| ( in @ SY3671 @ ( subset_complement @ SV12 @ SV100 ) ) ) )
= $true )
| ( ( SV12 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[760]) ).
thf(874,plain,
! [SV78: $i,SV13: $i,SV101: $i] :
( ( ( ~ ( element @ SV101 @ ( powerset @ SV13 ) ) )
= $true )
| ( ( ~ ( in @ SV78 @ ( subset_complement @ SV13 @ SV101 ) )
| ~ ( in @ SV78 @ SV101 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[761]) ).
thf(875,plain,
! [SV14: $i] :
( ( ( in @ ( ordered_pair @ ( sK68_B @ SV14 ) @ ( sK69_SY3321 @ SV14 ) ) @ SV14 )
= $true )
| ( ( SV14 = empty_set )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[762]) ).
thf(876,plain,
! [SV15: $i,SV79: $i,SV102: $i] :
( ( ( ~ ( function @ SV102 )
| ~ ( relation @ SV102 ) )
= $true )
| ( ( ~ ( in @ SV79 @ ( relation_dom @ ( relation_dom_restriction @ SV102 @ SV15 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SV102 @ SV15 ) @ SV79 )
= ( apply @ SV102 @ SV79 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[763]) ).
thf(877,plain,
! [SV16: $i,SV80: $i,SV103: $i] :
( ( ( ~ ( function @ SV103 )
| ~ ( relation @ SV103 ) )
= $true )
| ( ( ~ ( in @ SV80 @ SV16 )
| ( ( apply @ ( relation_dom_restriction @ SV103 @ SV16 ) @ SV80 )
= ( apply @ SV103 @ SV80 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[764]) ).
thf(878,plain,
! [SV81: $i,SV17: $i] :
( ( ( in @ SV17 @ SV81 )
= $false )
| ( ( subset @ SV17 @ ( union @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[765]) ).
thf(879,plain,
! [SV82: $i,SV18: $i] :
( ( ( in @ SV18 @ SV82 )
= $false )
| ( ( ~ ( in @ SV82 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[766]) ).
thf(880,plain,
! [SV83: $i,SV21: $i] :
( ( ( in @ SV21 @ SV83 )
= $false )
| ( ( element @ SV21 @ SV83 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[767]) ).
thf(881,plain,
! [SV84: $i,SV22: $i] :
( ( ( element @ SV22 @ SV84 )
= $false )
| ( ( ( empty @ SV84 )
| ( in @ SV22 @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[768]) ).
thf(882,plain,
! [SV23: $i,SV104: $i,SV85: $i] :
( ( ( ~ ( element @ SV85 @ ( powerset @ SV104 ) )
| ~ ( in @ SV23 @ SV85 ) )
= $true )
| ( ( element @ SV23 @ SV104 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[769]) ).
thf(883,plain,
! [SV24: $i,SV105: $i,SV86: $i] :
( ( ( ~ ( element @ SV86 @ ( powerset @ SV105 ) )
| ~ ( in @ SV24 @ SV86 ) )
= $true )
| ( ( ~ ( empty @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[770]) ).
thf(884,plain,
! [SV25: $i,SV87: $i] :
( ( ( empty @ SV87 )
= $false )
| ( ( ~ ( in @ SV25 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[771]) ).
thf(885,plain,
! [SV106: $i] :
( ( ! [SY3672: $i] :
( ( disjoint @ SV106 @ SY3672 )
| ( in @ ( sK72_C @ SY3672 @ SV106 ) @ ( set_intersection2 @ SV106 @ SY3672 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(886,plain,
! [SV107: $i] :
( ( ! [SY3673: $i] :
( ! [SY3674: $i] :
~ ( in @ SY3674 @ ( set_intersection2 @ SV107 @ SY3673 ) )
| ~ ( disjoint @ SV107 @ SY3673 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(887,plain,
! [SV26: $i,SV88: $i] :
( ( ( relation @ SV88 )
= $false )
| ( ( ~ ( ~ ! [SY3625: $i] :
( ~ ( relation @ SY3625 )
| ~ ( ~ ( ~ ( in @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) @ SV26 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY3625 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) ) @ SV88 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY3625 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) ) @ SY3625 ) )
| ~ ~ ( ~ ( ( in @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) @ SV26 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY3625 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) ) @ SY3625 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SY3625 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) ) @ SV88 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY3625 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) ) @ SY3625 ) ) ) )
| ( SY3625
= ( relation_rng_restriction @ SV26 @ SV88 ) ) )
| ~ ! [SY3626: $i] :
( ~ ( relation @ SY3626 )
| ( SY3626
!= ( relation_rng_restriction @ SV26 @ SV88 ) )
| ~ ( ~ ! [SY3627: $i,SY3628: $i] :
( ~ ( in @ SY3628 @ SV26 )
| ~ ( in @ ( ordered_pair @ SY3627 @ SY3628 ) @ SV88 )
| ( in @ ( ordered_pair @ SY3627 @ SY3628 ) @ SY3626 ) )
| ~ ~ ( ~ ! [SY3365: $i,SY3366: $i] :
( ~ ( in @ ( ordered_pair @ SY3365 @ SY3366 ) @ SY3626 )
| ( in @ SY3366 @ SV26 ) )
| ~ ! [SY3631: $i,SY3632: $i] :
( ~ ( in @ ( ordered_pair @ SY3631 @ SY3632 ) @ SY3626 )
| ( in @ ( ordered_pair @ SY3631 @ SY3632 ) @ SV88 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[774]) ).
thf(888,plain,
! [SV108: $i] :
( ( ! [SY3675: $i] :
( ~ ( ~ ( in @ ( sK29_C @ SY3675 @ SV108 ) @ SV108 )
| ~ ~ ( in @ ( sK29_C @ SY3675 @ SV108 ) @ SY3675 ) )
| ( subset @ SV108 @ SY3675 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(889,plain,
! [SV109: $i] :
( ( ! [SY3676: $i] :
( ~ ( subset @ SV109 @ SY3676 )
| ! [SY3677: $i] :
( ~ ( in @ SY3677 @ SV109 )
| ( in @ SY3677 @ SY3676 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(890,plain,
! [SV27: $i] :
( ( ! [SY3369: $i,SY3370: $i] :
( ~ ( relation @ SY3370 )
| ~ ( in @ SV27 @ SY3369 )
| ~ ( in @ SV27 @ ( relation_dom @ SY3370 ) )
| ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SY3370 @ SY3369 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[777]) ).
thf(891,plain,
! [SV27: $i] :
( ( ~ ( ~ ! [SY3371: $i,SY3372: $i] :
( ~ ( relation @ SY3372 )
| ~ ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SY3372 @ SY3371 ) ) )
| ( in @ SV27 @ SY3371 ) )
| ~ ! [SY3373: $i,SY3374: $i] :
( ~ ( relation @ SY3374 )
| ~ ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SY3374 @ SY3373 ) ) )
| ( in @ SV27 @ ( relation_dom @ SY3374 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[778]) ).
thf(892,plain,
! [SV28: $i] :
( ( ( ~ ! [SY3375: $i] :
( ~ ( relation @ SY3375 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SY3375 @ SV28 ) @ ( sK14_SY3290 @ SY3375 @ SV28 ) ) @ SY3375 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY3290 @ SY3375 @ SV28 ) @ ( sK13_C @ SY3375 @ SV28 ) ) @ SV28 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SY3375 @ SV28 ) @ ( sK14_SY3290 @ SY3375 @ SV28 ) ) @ SY3375 )
| ( in @ ( ordered_pair @ ( sK14_SY3290 @ SY3375 @ SV28 ) @ ( sK13_C @ SY3375 @ SV28 ) ) @ SV28 ) ) )
| ( SY3375
= ( relation_inverse @ SV28 ) ) )
| ~ ! [SY3376: $i] :
( ~ ( relation @ SY3376 )
| ( SY3376
!= ( relation_inverse @ SV28 ) )
| ~ ( ~ ! [SY3377: $i,SY3378: $i] :
( ~ ( in @ ( ordered_pair @ SY3377 @ SY3378 ) @ SY3376 )
| ( in @ ( ordered_pair @ SY3378 @ SY3377 ) @ SV28 ) )
| ~ ! [SY3379: $i,SY3380: $i] :
( ~ ( in @ ( ordered_pair @ SY3380 @ SY3379 ) @ SV28 )
| ( in @ ( ordered_pair @ SY3379 @ SY3380 ) @ SY3376 ) ) ) ) )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[779]) ).
thf(893,plain,
! [SV29: $i] :
( ( ( function @ SV29 )
= $false )
| ( ( ~ ( relation @ SV29 ) )
= $true )
| ( ( ~ ( ~ ! [SY3381: $i,SY3382: $i] :
( ~ ( ~ ( ! [SY3383: $i] :
( ~ ( in @ SY3383 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3383 @ SY3381 )
| ( ( sK61_D @ SY3382 @ SY3381 @ SV29 )
!= ( apply @ SV29 @ SY3383 ) ) )
| ~ ( in @ ( sK61_D @ SY3382 @ SY3381 @ SV29 ) @ SY3382 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY3318 @ SY3382 @ SY3381 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK62_SY3318 @ SY3382 @ SY3381 @ SV29 ) @ SY3381 ) )
| ( ( sK61_D @ SY3382 @ SY3381 @ SV29 )
!= ( apply @ SV29 @ ( sK62_SY3318 @ SY3382 @ SY3381 @ SV29 ) ) ) )
| ( in @ ( sK61_D @ SY3382 @ SY3381 @ SV29 ) @ SY3382 ) ) )
| ( SY3382
= ( relation_image @ SV29 @ SY3381 ) ) )
| ~ ! [SY3384: $i,SY3385: $i] :
( ( SY3385
!= ( relation_image @ SV29 @ SY3384 ) )
| ~ ( ~ ! [SY3386: $i] :
( ! [SY3387: $i] :
( ~ ( in @ SY3387 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3387 @ SY3384 )
| ( SY3386
!= ( apply @ SV29 @ SY3387 ) ) )
| ( in @ SY3386 @ SY3385 ) )
| ~ ! [SY3388: $i] :
( ~ ( in @ SY3388 @ SY3385 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SY3388 @ SY3385 @ SY3384 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK60_E @ SY3388 @ SY3385 @ SY3384 @ SV29 ) @ SY3384 ) )
| ( SY3388
!= ( apply @ SV29 @ ( sK60_E @ SY3388 @ SY3385 @ SY3384 @ SV29 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[780]) ).
thf(894,plain,
! [SV30: $i] :
( ( ( ~ ! [SY3389: $i,SY3390: $i] :
( ~ ( ~ ( ! [SY3391: $i] :
( ~ ( in @ ( ordered_pair @ SY3391 @ ( sK55_D @ SY3390 @ SY3389 @ SV30 ) ) @ SV30 )
| ~ ( in @ SY3391 @ SY3389 ) )
| ~ ( in @ ( sK55_D @ SY3390 @ SY3389 @ SV30 ) @ SY3390 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_SY3315 @ SY3390 @ SY3389 @ SV30 ) @ ( sK55_D @ SY3390 @ SY3389 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK56_SY3315 @ SY3390 @ SY3389 @ SV30 ) @ SY3389 ) )
| ( in @ ( sK55_D @ SY3390 @ SY3389 @ SV30 ) @ SY3390 ) ) )
| ( SY3390
= ( relation_image @ SV30 @ SY3389 ) ) )
| ~ ! [SY3392: $i,SY3393: $i] :
( ( SY3393
!= ( relation_image @ SV30 @ SY3392 ) )
| ~ ( ~ ! [SY3394: $i] :
( ! [SY3395: $i] :
( ~ ( in @ ( ordered_pair @ SY3395 @ SY3394 ) @ SV30 )
| ~ ( in @ SY3395 @ SY3392 ) )
| ( in @ SY3394 @ SY3393 ) )
| ~ ! [SY3396: $i] :
( ~ ( in @ SY3396 @ SY3393 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SY3396 @ SY3393 @ SY3392 @ SV30 ) @ SY3396 ) @ SV30 )
| ~ ( in @ ( sK54_E @ SY3396 @ SY3393 @ SY3392 @ SV30 ) @ SY3392 ) ) ) ) ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[781]) ).
thf(895,plain,
! [SV31: $i] :
( ( ( ~ ! [SY3397: $i,SY3398: $i] :
( ~ ( ~ ( ! [SY3399: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ SY3398 @ SY3397 @ SV31 ) @ SY3399 ) @ SV31 )
| ~ ( in @ SY3399 @ SY3397 ) )
| ~ ( in @ ( sK52_D @ SY3398 @ SY3397 @ SV31 ) @ SY3398 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SY3398 @ SY3397 @ SV31 ) @ ( sK53_SY3313 @ SY3398 @ SY3397 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( sK53_SY3313 @ SY3398 @ SY3397 @ SV31 ) @ SY3397 ) )
| ( in @ ( sK52_D @ SY3398 @ SY3397 @ SV31 ) @ SY3398 ) ) )
| ( SY3398
= ( relation_inverse_image @ SV31 @ SY3397 ) ) )
| ~ ! [SY3400: $i,SY3401: $i] :
( ( SY3401
!= ( relation_inverse_image @ SV31 @ SY3400 ) )
| ~ ( ~ ! [SY3402: $i] :
( ! [SY3403: $i] :
( ~ ( in @ ( ordered_pair @ SY3402 @ SY3403 ) @ SV31 )
| ~ ( in @ SY3403 @ SY3400 ) )
| ( in @ SY3402 @ SY3401 ) )
| ~ ! [SY3404: $i] :
( ~ ( in @ SY3404 @ SY3401 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3404 @ ( sK51_E @ SY3404 @ SY3401 @ SY3400 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( sK51_E @ SY3404 @ SY3401 @ SY3400 @ SV31 ) @ SY3400 ) ) ) ) ) )
= $false )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[782]) ).
thf(896,plain,
! [SV32: $i] :
( ( ( ~ ! [SY3405: $i,SY3406: $i] :
( ~ ( relation @ SY3406 )
| ~ ( ~ ( ~ ( in @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ SY3405 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ ( sK64_SY3319 @ SY3406 @ SY3405 @ SV32 ) ) @ SV32 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ ( sK64_SY3319 @ SY3406 @ SY3405 @ SV32 ) ) @ SY3406 ) )
| ~ ~ ( ~ ( ( in @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ SY3405 )
| ( in @ ( ordered_pair @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ ( sK64_SY3319 @ SY3406 @ SY3405 @ SV32 ) ) @ SY3406 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ ( sK64_SY3319 @ SY3406 @ SY3405 @ SV32 ) ) @ SV32 )
| ( in @ ( ordered_pair @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ ( sK64_SY3319 @ SY3406 @ SY3405 @ SV32 ) ) @ SY3406 ) ) ) )
| ( SY3406
= ( relation_dom_restriction @ SV32 @ SY3405 ) ) )
| ~ ! [SY3407: $i,SY3408: $i] :
( ~ ( relation @ SY3408 )
| ( SY3408
!= ( relation_dom_restriction @ SV32 @ SY3407 ) )
| ~ ( ~ ! [SY3409: $i,SY3410: $i] :
( ~ ( in @ SY3409 @ SY3407 )
| ~ ( in @ ( ordered_pair @ SY3409 @ SY3410 ) @ SV32 )
| ( in @ ( ordered_pair @ SY3409 @ SY3410 ) @ SY3408 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3408 )
| ( in @ SX3 @ SY3407 ) )
| ~ ! [SY3413: $i,SY3414: $i] :
( ~ ( in @ ( ordered_pair @ SY3413 @ SY3414 ) @ SY3408 )
| ( in @ ( ordered_pair @ SY3413 @ SY3414 ) @ SV32 ) ) ) ) ) )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[783]) ).
thf(897,plain,
! [SV33: $i] :
( ( ! [SY3415: $i,SY3416: $i] :
( ~ ( relation @ SY3416 )
| ! [SY3417: $i] :
( ~ ( in @ SY3417 @ ( relation_rng @ SY3416 ) )
| ~ ( in @ ( ordered_pair @ SV33 @ SY3417 ) @ SY3416 )
| ~ ( in @ SY3417 @ SY3415 ) )
| ( in @ SV33 @ ( relation_inverse_image @ SY3416 @ SY3415 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[784]) ).
thf(898,plain,
! [SV33: $i] :
( ( ! [SY3418: $i,SY3419: $i] :
( ~ ( relation @ SY3419 )
| ~ ( in @ SV33 @ ( relation_inverse_image @ SY3419 @ SY3418 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK75_D @ SY3419 @ SY3418 @ SV33 ) @ ( relation_rng @ SY3419 ) )
| ~ ( in @ ( ordered_pair @ SV33 @ ( sK75_D @ SY3419 @ SY3418 @ SV33 ) ) @ SY3419 ) )
| ~ ( in @ ( sK75_D @ SY3419 @ SY3418 @ SV33 ) @ SY3418 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[785]) ).
thf(899,plain,
! [SV110: $i] :
( ( ! [SY3678: $i] :
( ~ ( relation @ SY3678 )
| ~ ( ~ ( ( ( sK65_C @ SY3678 @ SV110 )
!= ( sK66_SY3320 @ SY3678 @ SV110 ) )
| ~ ( in @ ( sK65_C @ SY3678 @ SV110 ) @ SV110 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SY3678 @ SV110 ) @ ( sK66_SY3320 @ SY3678 @ SV110 ) ) @ SY3678 ) )
| ~ ~ ( ~ ( ( ( sK65_C @ SY3678 @ SV110 )
= ( sK66_SY3320 @ SY3678 @ SV110 ) )
| ( in @ ( ordered_pair @ ( sK65_C @ SY3678 @ SV110 ) @ ( sK66_SY3320 @ SY3678 @ SV110 ) ) @ SY3678 ) )
| ~ ( ( in @ ( sK65_C @ SY3678 @ SV110 ) @ SV110 )
| ( in @ ( ordered_pair @ ( sK65_C @ SY3678 @ SV110 ) @ ( sK66_SY3320 @ SY3678 @ SV110 ) ) @ SY3678 ) ) ) )
| ( SY3678
= ( identity_relation @ SV110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(900,plain,
! [SV111: $i] :
( ( ! [SY3679: $i] :
( ~ ( relation @ SY3679 )
| ( SY3679
!= ( identity_relation @ SV111 ) )
| ~ ( ~ ! [SY3680: $i,SY3681: $i] :
( ( SY3680 != SY3681 )
| ~ ( in @ SY3680 @ SV111 )
| ( in @ ( ordered_pair @ SY3680 @ SY3681 ) @ SY3679 ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SY3679 )
| ( SX2 = SX3 ) )
| ~ ! [SY3684: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SY3684 @ SX3 ) @ SY3679 )
| ( in @ SY3684 @ SV111 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(901,plain,
! [SV34: $i,SV89: $i] :
( ( ~ ! [SY3633: $i,SY3634: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 ) @ SY3634 )
| ( ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 )
!= SY3633 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 ) @ SY3634 )
| ( ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 )
!= SV34 ) )
| ~ ( ~ ( in @ ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 ) @ SY3634 )
| ( ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 )
!= SV89 ) ) ) )
| ~ ( ( in @ ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 ) @ SY3634 )
| ( ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 )
= SY3633 )
| ( ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 )
= SV34 )
| ( ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 )
= SV89 ) ) )
| ( SY3634
= ( unordered_triple @ SV34 @ SV89 @ SY3633 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[788]) ).
thf(902,plain,
! [SV89: $i,SV34: $i] :
( ( ~ ! [SY3635: $i,SY3636: $i] :
( ( SY3636
!= ( unordered_triple @ SV34 @ SV89 @ SY3635 ) )
| ~ ( ~ ! [SY3637: $i] :
( ~ ( in @ SY3637 @ SY3636 )
| ( SY3637 = SY3635 )
| ( SY3637 = SV34 )
| ( SY3637 = SV89 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SY3635 )
| ( in @ SX4 @ SY3636 ) )
| ~ ~ ( ~ ! [SY3427: $i] :
( ( SY3427 != SV34 )
| ( in @ SY3427 @ SY3636 ) )
| ~ ! [SY3640: $i] :
( ( SY3640 != SV89 )
| ( in @ SY3640 @ SY3636 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[788]) ).
thf(903,plain,
! [SV35: $i] :
( ( ! [SY3429: $i,SY3430: $i] :
( ~ ( relation @ SY3430 )
| ~ ( in @ ( ordered_pair @ SV35 @ SY3429 ) @ SY3430 )
| ( in @ SV35 @ ( relation_field @ SY3430 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[789]) ).
thf(904,plain,
! [SV35: $i] :
( ( ! [SY3431: $i,SY3432: $i] :
( ~ ( relation @ SY3432 )
| ~ ( in @ ( ordered_pair @ SV35 @ SY3431 ) @ SY3432 )
| ( in @ SY3431 @ ( relation_field @ SY3432 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[790]) ).
thf(905,plain,
! [SV36: $i] :
( ( ( ~ ! [SY3433: $i] :
( ~ ( ~ ( ! [SY3434: $i] :
~ ( in @ ( ordered_pair @ SY3434 @ ( sK16_C @ SY3433 @ SV36 ) ) @ SV36 )
| ~ ( in @ ( sK16_C @ SY3433 @ SV36 ) @ SY3433 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_SY3292 @ SY3433 @ SV36 ) @ ( sK16_C @ SY3433 @ SV36 ) ) @ SV36 )
| ( in @ ( sK16_C @ SY3433 @ SV36 ) @ SY3433 ) ) )
| ( SY3433
= ( relation_rng @ SV36 ) ) )
| ~ ! [SY3435: $i] :
( ( SY3435
!= ( relation_rng @ SV36 ) )
| ~ ( ~ ! [SY3436: $i] :
( ! [SY3437: $i] :
~ ( in @ ( ordered_pair @ SY3437 @ SY3436 ) @ SV36 )
| ( in @ SY3436 @ SY3435 ) )
| ~ ! [SY3438: $i] :
( ~ ( in @ SY3438 @ SY3435 )
| ( in @ ( ordered_pair @ ( sK15_D @ SY3438 @ SY3435 @ SV36 ) @ SY3438 ) @ SV36 ) ) ) ) )
= $false )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[791]) ).
thf(906,plain,
! [SV37: $i] :
( ( ! [SY3439: $i] :
( ~ ( subset @ SY3439 @ ( sK77_B @ SV37 ) )
| ( are_equipotent @ SY3439 @ ( sK77_B @ SV37 ) )
| ( in @ SY3439 @ ( sK77_B @ SV37 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[792]) ).
thf(907,plain,
! [SV37: $i] :
( ( ~ ( ~ ! [SY3440: $i] :
( ~ ( in @ SY3440 @ ( sK77_B @ SV37 ) )
| ( in @ ( powerset @ SY3440 ) @ ( sK77_B @ SV37 ) ) )
| ~ ~ ( ~ ! [SY3441: $i,SY3442: $i] :
( ~ ( in @ SY3441 @ ( sK77_B @ SV37 ) )
| ~ ( subset @ SY3442 @ SY3441 )
| ( in @ SY3442 @ ( sK77_B @ SV37 ) ) )
| ~ ( in @ SV37 @ ( sK77_B @ SV37 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[793]) ).
thf(908,plain,
! [SV112: $i] :
( ( ! [SY3686: $i] :
( ~ ( ~ ( ~ ( in @ ( sK41_C @ SY3686 @ SV112 ) @ SY3686 )
| ~ ( subset @ ( sK41_C @ SY3686 @ SV112 ) @ SV112 ) )
| ~ ( ( in @ ( sK41_C @ SY3686 @ SV112 ) @ SY3686 )
| ( subset @ ( sK41_C @ SY3686 @ SV112 ) @ SV112 ) ) )
| ( SY3686
= ( powerset @ SV112 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(909,plain,
! [SV113: $i] :
( ( ! [SY3687: $i] :
( ( SY3687
!= ( powerset @ SV113 ) )
| ~ ( ~ ! [SY3688: $i] :
( ~ ( in @ SY3688 @ SY3687 )
| ( subset @ SY3688 @ SV113 ) )
| ~ ! [SY3689: $i] :
( ~ ( subset @ SY3689 @ SV113 )
| ( in @ SY3689 @ SY3687 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(910,plain,
! [SV38: $i,SV90: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_C @ SV90 @ SV38 ) @ SV38 )
| ~ ( in @ ( sK5_C @ SV90 @ SV38 ) @ SV90 ) )
| ~ ( ( in @ ( sK5_C @ SV90 @ SV38 ) @ SV38 )
| ( in @ ( sK5_C @ SV90 @ SV38 ) @ SV90 ) ) )
= $false )
| ( ( SV38 = SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[796]) ).
thf(911,plain,
! [SV114: $i] :
( ( ! [SY3690: $i] :
( ~ ( function @ SY3690 )
| ~ ( relation @ SY3690 )
| ~ ( in @ SV114 @ ( relation_rng @ SY3690 ) )
| ~ ( one_to_one @ SY3690 )
| ( SV114
= ( apply @ SY3690 @ ( apply @ ( function_inverse @ SY3690 ) @ SV114 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(912,plain,
! [SV115: $i] :
( ( ! [SY3691: $i] :
( ~ ( function @ SY3691 )
| ~ ( relation @ SY3691 )
| ~ ( in @ SV115 @ ( relation_rng @ SY3691 ) )
| ~ ( one_to_one @ SY3691 )
| ( SV115
= ( apply @ ( relation_composition @ ( function_inverse @ SY3691 ) @ SY3691 ) @ SV115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(913,plain,
! [SV39: $i,SV91: $i] :
( ( ( ~ ( function @ SV91 ) )
= $true )
| ( ( ~ ( relation @ SV91 ) )
= $true )
| ( ( ~ ( ~ ! [SY3641: $i] :
( ~ ( function @ SY3641 )
| ~ ( relation @ SY3641 )
| ~ ( in @ SV39 @ ( relation_dom @ SY3641 ) )
| ~ ( in @ ( apply @ SY3641 @ SV39 ) @ ( relation_dom @ SV91 ) )
| ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3641 @ SV91 ) ) ) )
| ~ ~ ( ~ ! [SY3642: $i] :
( ~ ( function @ SY3642 )
| ~ ( relation @ SY3642 )
| ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3642 @ SV91 ) ) )
| ( in @ SV39 @ ( relation_dom @ SY3642 ) ) )
| ~ ! [SY3643: $i] :
( ~ ( function @ SY3643 )
| ~ ( relation @ SY3643 )
| ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3643 @ SV91 ) ) )
| ( in @ ( apply @ SY3643 @ SV39 ) @ ( relation_dom @ SV91 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[799]) ).
thf(914,plain,
! [SV40: $i,SV92: $i] :
( ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY3644: $i] :
( ~ ( element @ SY3644 @ ( powerset @ ( powerset @ SV40 ) ) )
| ~ ( ~ ( element @ ( sK6_D @ SY3644 @ SV92 @ SV40 ) @ ( powerset @ SV40 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK6_D @ SY3644 @ SV92 @ SV40 ) @ SY3644 )
| ~ ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SY3644 @ SV92 @ SV40 ) ) @ SV92 ) )
| ~ ( ( in @ ( sK6_D @ SY3644 @ SV92 @ SV40 ) @ SY3644 )
| ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SY3644 @ SV92 @ SV40 ) ) @ SV92 ) ) ) )
| ( SY3644
= ( complements_of_subsets @ SV40 @ SV92 ) ) )
| ~ ! [SY3645: $i] :
( ~ ( element @ SY3645 @ ( powerset @ ( powerset @ SV40 ) ) )
| ( SY3645
!= ( complements_of_subsets @ SV40 @ SV92 ) )
| ~ ( ~ ! [SY3646: $i] :
( ~ ( element @ SY3646 @ ( powerset @ SV40 ) )
| ~ ( in @ SY3646 @ SY3645 )
| ( in @ ( subset_complement @ SV40 @ SY3646 ) @ SV92 ) )
| ~ ! [SY3647: $i] :
( ~ ( element @ SY3647 @ ( powerset @ SV40 ) )
| ~ ( in @ ( subset_complement @ SV40 @ SY3647 ) @ SV92 )
| ( in @ SY3647 @ SY3645 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[800]) ).
thf(915,plain,
! [SV41: $i] :
( ( ! [SY3453: $i,SY3454: $i] :
( ~ ( function @ SY3454 )
| ~ ( relation @ SY3454 )
| ( SY3453
!= ( apply @ SY3454 @ SV41 ) )
| ~ ( in @ SV41 @ ( relation_dom @ SY3454 ) )
| ( in @ ( ordered_pair @ SV41 @ SY3453 ) @ SY3454 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[801]) ).
thf(916,plain,
! [SV41: $i] :
( ( ~ ( ~ ! [SY3455: $i,SY3456: $i] :
( ~ ( function @ SY3456 )
| ~ ( relation @ SY3456 )
| ~ ( in @ ( ordered_pair @ SV41 @ SY3455 ) @ SY3456 )
| ( SY3455
= ( apply @ SY3456 @ SV41 ) ) )
| ~ ! [SY3457: $i,SY3458: $i] :
( ~ ( function @ SY3458 )
| ~ ( relation @ SY3458 )
| ~ ( in @ ( ordered_pair @ SV41 @ SY3457 ) @ SY3458 )
| ( in @ SV41 @ ( relation_dom @ SY3458 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[802]) ).
thf(917,plain,
! [SV42: $i] :
( ( ! [SY3459: $i,SY3460: $i] :
( ~ ( relation @ SY3460 )
| ~ ( in @ SV42 @ SY3459 )
| ~ ( in @ SV42 @ ( relation_rng @ SY3460 ) )
| ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SY3459 @ SY3460 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[803]) ).
thf(918,plain,
! [SV42: $i] :
( ( ~ ( ~ ! [SY3461: $i,SY3462: $i] :
( ~ ( relation @ SY3462 )
| ~ ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SY3461 @ SY3462 ) ) )
| ( in @ SV42 @ SY3461 ) )
| ~ ! [SY3463: $i,SY3464: $i] :
( ~ ( relation @ SY3464 )
| ~ ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SY3463 @ SY3464 ) ) )
| ( in @ SV42 @ ( relation_rng @ SY3464 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[804]) ).
thf(919,plain,
! [SV43: $i] :
( ( ! [SY3465: $i] :
( ~ ( subset @ SY3465 @ ( sK2_B @ SV43 ) )
| ( are_equipotent @ SY3465 @ ( sK2_B @ SV43 ) )
| ( in @ SY3465 @ ( sK2_B @ SV43 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[805]) ).
thf(920,plain,
! [SV43: $i] :
( ( ~ ( ~ ! [SY3466: $i] :
( ~ ( ~ ! [SY3467: $i] :
( ~ ( subset @ SY3467 @ SY3466 )
| ( in @ SY3467 @ ( sK3_SY3278 @ SY3466 @ SV43 ) ) )
| ~ ( in @ ( sK3_SY3278 @ SY3466 @ SV43 ) @ ( sK2_B @ SV43 ) ) )
| ~ ( in @ SY3466 @ ( sK2_B @ SV43 ) ) )
| ~ ~ ( ~ ! [SY3468: $i,SY3469: $i] :
( ~ ( in @ SY3468 @ ( sK2_B @ SV43 ) )
| ~ ( subset @ SY3469 @ SY3468 )
| ( in @ SY3469 @ ( sK2_B @ SV43 ) ) )
| ~ ( in @ SV43 @ ( sK2_B @ SV43 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[806]) ).
thf(921,plain,
! [SV116: $i] :
( ( ~ ( ~ ! [SY3692: $i,SY3693: $i] :
( ( sK49_B @ SV116 )
!= ( ordered_pair @ SY3692 @ SY3693 ) )
| ~ ( in @ ( sK49_B @ SV116 ) @ SV116 ) )
| ( relation @ SV116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(922,plain,
! [SV117: $i] :
( ( ~ ( relation @ SV117 )
| ! [SY3694: $i] :
( ( SY3694
= ( ordered_pair @ ( sK47_C @ SY3694 @ SV117 ) @ ( sK48_SY3309 @ SY3694 @ SV117 ) ) )
| ~ ( in @ SY3694 @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(923,plain,
! [SV93: $i,SV44: $i] :
( ( ~ ! [SY3648: $i,SY3649: $i] :
( ~ ( in @ SV44 @ SY3648 )
| ~ ( in @ SV93 @ SY3649 )
| ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SY3648 @ SY3649 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[809]) ).
thf(924,plain,
! [SV93: $i,SV44: $i] :
( ( ~ ~ ( ~ ! [SY3650: $i] :
( ! [SY3651: $i] :
~ ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SY3650 @ SY3651 ) )
| ( in @ SV44 @ SY3650 ) )
| ~ ! [SY3652: $i,SY3653: $i] :
( ~ ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SY3652 @ SY3653 ) )
| ( in @ SV93 @ SY3653 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[809]) ).
thf(925,plain,
! [SV45: $i] :
( ( ( ~ ! [SY3477: $i] :
( ~ ( ~ ( ! [SY3478: $i] :
~ ( in @ ( ordered_pair @ ( sK26_C @ SY3477 @ SV45 ) @ SY3478 ) @ SV45 )
| ~ ( in @ ( sK26_C @ SY3477 @ SV45 ) @ SY3477 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK26_C @ SY3477 @ SV45 ) @ ( sK27_SY3298 @ SY3477 @ SV45 ) ) @ SV45 )
| ( in @ ( sK26_C @ SY3477 @ SV45 ) @ SY3477 ) ) )
| ( SY3477
= ( relation_dom @ SV45 ) ) )
| ~ ! [SY3479: $i] :
( ( SY3479
!= ( relation_dom @ SV45 ) )
| ~ ( ~ ! [SY3480: $i] :
( ! [SY3481: $i] :
~ ( in @ ( ordered_pair @ SY3480 @ SY3481 ) @ SV45 )
| ( in @ SY3480 @ SY3479 ) )
| ~ ! [SY3482: $i] :
( ~ ( in @ SY3482 @ SY3479 )
| ( in @ ( ordered_pair @ SY3482 @ ( sK25_D @ SY3482 @ SY3479 @ SV45 ) ) @ SV45 ) ) ) ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[810]) ).
thf(926,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[811]) ).
thf(927,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[812]) ).
thf(928,plain,
! [SV118: $i] :
( ( ( in @ ( sK42_B @ SV118 ) @ SV118 )
| ( SV118 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(929,plain,
! [SV119: $i] :
( ( ( SV119 != empty_set )
| ! [SY3695: $i] :
~ ( in @ SY3695 @ SV119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(930,plain,
! [SV120: $i] :
( ( ! [SY3696: $i] :
( ~ ( ~ ( ( ( sK43_C @ SY3696 @ SV120 )
!= SV120 )
| ~ ( in @ ( sK43_C @ SY3696 @ SV120 ) @ SY3696 ) )
| ~ ( ( ( sK43_C @ SY3696 @ SV120 )
= SV120 )
| ( in @ ( sK43_C @ SY3696 @ SV120 ) @ SY3696 ) ) )
| ( SY3696
= ( singleton @ SV120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(931,plain,
! [SV121: $i] :
( ( ! [SY3697: $i] :
( ( SY3697
!= ( singleton @ SV121 ) )
| ~ ( ~ ! [SY3698: $i] :
( ( SY3698 != SV121 )
| ( in @ SY3698 @ SY3697 ) )
| ~ ! [SY3699: $i] :
( ~ ( in @ SY3699 @ SY3697 )
| ( SY3699 = SV121 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(932,plain,
! [SV122: $i] :
( ( ! [SY3700: $i] :
( ~ ( function @ SY3700 )
| ~ ( relation @ SY3700 )
| ~ ( ~ ( in @ ( sK74_C @ SY3700 @ SV122 ) @ SV122 )
| ~ ( ( ( apply @ SY3700 @ ( sK74_C @ SY3700 @ SV122 ) )
!= ( sK74_C @ SY3700 @ SV122 ) ) ) )
| ( ( relation_dom @ SY3700 )
!= SV122 )
| ( SY3700
= ( identity_relation @ SV122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(933,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( ( apply @ SX1 @ SX2 )
= SX2 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[818]) ).
thf(934,plain,
! [SV46: $i] :
( ( ( function @ SV46 )
= $false )
| ( ( ~ ( relation @ SV46 ) )
= $true )
| ( ( ~ ( one_to_one @ SV46 )
| ~ ( ~ ! [SY3483: $i] :
( ~ ( function @ SY3483 )
| ~ ( relation @ SY3483 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY3322 @ SY3483 @ SV46 )
= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ( ( sK70_C @ SY3483 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SY3483 @ SV46 )
= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SY3483 @ SV46 )
= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ( ( sK71_SY3322 @ SY3483 @ SV46 )
!= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK70_C @ SY3483 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK71_SY3322 @ SY3483 @ SV46 )
!= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY3483 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK70_C @ SY3483 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SY3483 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SY3483 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK71_SY3322 @ SY3483 @ SV46 )
!= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ( ( relation_dom @ SY3483 )
!= ( relation_rng @ SV46 ) )
| ( SY3483
= ( function_inverse @ SV46 ) ) )
| ~ ~ ( ~ ! [SY3484: $i] :
( ~ ( function @ SY3484 )
| ~ ( relation @ SY3484 )
| ( SY3484
!= ( function_inverse @ SV46 ) )
| ~ ( ~ ~ ( ~ ! [SY3485: $i,SY3486: $i] :
( ( SY3486
!= ( apply @ SY3484 @ SY3485 ) )
| ~ ( in @ SY3485 @ ( relation_rng @ SV46 ) )
| ( SY3485
= ( apply @ SV46 @ SY3486 ) ) )
| ~ ! [SY3487: $i,SY3488: $i] :
( ( SY3488
!= ( apply @ SY3484 @ SY3487 ) )
| ~ ( in @ SY3487 @ ( relation_rng @ SV46 ) )
| ( in @ SY3488 @ ( relation_dom @ SV46 ) ) ) )
| ~ ~ ( ~ ! [SY3489: $i,SY3490: $i] :
( ( SY3489
!= ( apply @ SV46 @ SY3490 ) )
| ~ ( in @ SY3490 @ ( relation_dom @ SV46 ) )
| ( SY3490
= ( apply @ SY3484 @ SY3489 ) ) )
| ~ ! [SY3491: $i] :
( ! [SY3492: $i] :
( ( SY3491
!= ( apply @ SV46 @ SY3492 ) )
| ~ ( in @ SY3492 @ ( relation_dom @ SV46 ) ) )
| ( in @ SY3491 @ ( relation_rng @ SV46 ) ) ) ) ) )
| ~ ! [SY3493: $i] :
( ~ ( function @ SY3493 )
| ~ ( relation @ SY3493 )
| ( SY3493
!= ( function_inverse @ SV46 ) )
| ( ( relation_dom @ SY3493 )
= ( relation_rng @ SV46 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[819]) ).
thf(935,plain,
! [SV47: $i,SV123: $i] :
( ( ( ~ ( relation @ SV123 )
| ~ ( ~ ! [SY3701: $i] :
( ~ ( relation @ SY3701 )
| ~ ( ~ ( ! [SY3702: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY3701 @ SV123 @ SV47 ) @ SY3702 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3702 @ ( sK9_SY3284 @ SY3701 @ SV123 @ SV47 ) ) @ SV123 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SY3701 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SY3701 @ SV123 @ SV47 ) ) @ SY3701 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY3701 @ SV123 @ SV47 ) @ ( sK10_SY3288 @ SY3701 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY3288 @ SY3701 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SY3701 @ SV123 @ SV47 ) ) @ SV123 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SY3701 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SY3701 @ SV123 @ SV47 ) ) @ SY3701 ) ) )
| ( SY3701
= ( relation_composition @ SV47 @ SV123 ) ) )
| ~ ! [SY3703: $i] :
( ~ ( relation @ SY3703 )
| ( SY3703
!= ( relation_composition @ SV47 @ SV123 ) )
| ~ ( ~ ! [SY3704: $i,SY3705: $i] :
( ! [SY3706: $i] :
( ~ ( in @ ( ordered_pair @ SY3704 @ SY3706 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3706 @ SY3705 ) @ SV123 ) )
| ( in @ ( ordered_pair @ SY3704 @ SY3705 ) @ SY3703 ) )
| ~ ! [SY3707: $i,SY3708: $i] :
( ~ ( in @ ( ordered_pair @ SY3707 @ SY3708 ) @ SY3703 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3707 @ ( sK7_F @ SY3708 @ SY3707 @ SY3703 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY3708 @ SY3707 @ SY3703 @ SV123 @ SV47 ) @ SY3708 ) @ SV123 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(936,plain,
! [SV48: $i] :
( ( ! [SY3503: $i,SY3504: $i] :
( ~ ( in @ SV48 @ SY3504 )
| ~ ( in @ SY3503 @ SY3504 )
| ( subset @ ( unordered_pair @ SV48 @ SY3503 ) @ SY3504 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[821]) ).
thf(937,plain,
! [SV48: $i] :
( ( ~ ( ~ ! [SY3505: $i,SY3506: $i] :
( ~ ( subset @ ( unordered_pair @ SV48 @ SY3505 ) @ SY3506 )
| ( in @ SV48 @ SY3506 ) )
| ~ ! [SY3507: $i,SY3508: $i] :
( ~ ( subset @ ( unordered_pair @ SV48 @ SY3507 ) @ SY3508 )
| ( in @ SY3507 @ SY3508 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[822]) ).
thf(938,plain,
! [SV94: $i,SV49: $i] :
( ( ~ ! [SY3654: $i,SY3655: $i] :
( ~ ( relation @ SY3655 )
| ~ ( in @ SV49 @ SY3654 )
| ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ SY3655 )
| ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SY3654 ) @ SY3655 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[823]) ).
thf(939,plain,
! [SV94: $i,SV49: $i] :
( ( ~ ~ ( ~ ! [SY3656: $i,SY3657: $i] :
( ~ ( relation @ SY3657 )
| ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SY3656 ) @ SY3657 ) )
| ( in @ SV49 @ SY3656 ) )
| ~ ! [SY3658: $i,SY3659: $i] :
( ~ ( relation @ SY3659 )
| ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SY3658 ) @ SY3659 ) )
| ( in @ ( ordered_pair @ SV49 @ SV94 ) @ SY3659 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[823]) ).
thf(940,plain,
! [SV50: $i,SV95: $i] :
( ( ( ~ ! [SY3660: $i] :
( ~ ( in @ SY3660 @ SV95 )
| ~ ( in @ SY3660 @ ( sK4_C @ SV95 @ SV50 ) ) )
| ~ ( in @ ( sK4_C @ SV95 @ SV50 ) @ SV95 ) )
= $false )
| ( ( ~ ( in @ SV50 @ SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[824]) ).
thf(941,plain,
! [SV124: $i] :
( ( ~ ( function @ SV124 )
| ~ ( relation @ SV124 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_B @ SV124 ) @ ( relation_dom @ SV124 ) )
| ~ ( in @ ( sK12_SY3289 @ SV124 ) @ ( relation_dom @ SV124 ) ) )
| ( ( apply @ SV124 @ ( sK11_B @ SV124 ) )
!= ( apply @ SV124 @ ( sK12_SY3289 @ SV124 ) ) ) )
| ~ ( ( ( sK11_B @ SV124 )
!= ( sK12_SY3289 @ SV124 ) ) ) )
| ( one_to_one @ SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(942,plain,
! [SV125: $i] :
( ( ~ ( function @ SV125 )
| ~ ( relation @ SV125 )
| ~ ( one_to_one @ SV125 )
| ! [SY3709: $i,SY3710: $i] :
( ~ ( in @ SY3709 @ ( relation_dom @ SV125 ) )
| ~ ( in @ SY3710 @ ( relation_dom @ SV125 ) )
| ( ( apply @ SV125 @ SY3709 )
!= ( apply @ SV125 @ SY3710 ) )
| ( SY3709 = SY3710 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(943,plain,
! [SV51: $i] :
( ( ! [SY3518: $i,SY3519: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK37_D @ SY3519 @ SY3518 @ SV51 ) @ SY3519 )
| ~ ( in @ ( sK37_D @ SY3519 @ SY3518 @ SV51 ) @ SV51 ) )
| ~ ( ~ ( in @ ( sK37_D @ SY3519 @ SY3518 @ SV51 ) @ SY3519 )
| ~ ( in @ ( sK37_D @ SY3519 @ SY3518 @ SV51 ) @ SY3518 ) ) )
| ~ ( ( in @ ( sK37_D @ SY3519 @ SY3518 @ SV51 ) @ SY3519 )
| ( in @ ( sK37_D @ SY3519 @ SY3518 @ SV51 ) @ SV51 )
| ( in @ ( sK37_D @ SY3519 @ SY3518 @ SV51 ) @ SY3518 ) ) )
| ( SY3519
= ( set_union2 @ SV51 @ SY3518 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[827]) ).
thf(944,plain,
! [SV51: $i] :
( ( ! [SY3520: $i,SY3521: $i] :
( ( SY3521
!= ( set_union2 @ SV51 @ SY3520 ) )
| ~ ( ~ ! [SY3522: $i] :
( ~ ( in @ SY3522 @ SY3521 )
| ( in @ SY3522 @ SV51 )
| ( in @ SY3522 @ SY3520 ) )
| ~ ~ ( ~ ! [SY3523: $i] :
( ~ ( in @ SY3523 @ SV51 )
| ( in @ SY3523 @ SY3521 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY3520 )
| ( in @ SX3 @ SY3521 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[828]) ).
thf(945,plain,
! [SV126: $i] :
( ( ! [SY3711: $i] :
( ( ( set_difference @ SV126 @ ( singleton @ SY3711 ) )
!= SV126 )
| ~ ( in @ SY3711 @ SV126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(946,plain,
! [SV127: $i] :
( ( ! [SY3712: $i] :
( ( in @ SY3712 @ SV127 )
| ( ( set_difference @ SV127 @ ( singleton @ SY3712 ) )
= SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(947,plain,
! [SV52: $i] :
( ( ( ~ ! [SY3525: $i] :
( ~ ( relation @ SY3525 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK30_C @ SY3525 @ SV52 ) @ ( sK31_SY3299 @ SY3525 @ SV52 ) ) @ SV52 )
| ~ ~ ( in @ ( ordered_pair @ ( sK30_C @ SY3525 @ SV52 ) @ ( sK31_SY3299 @ SY3525 @ SV52 ) ) @ SY3525 ) )
| ( subset @ SV52 @ SY3525 ) )
| ~ ! [SY3526: $i] :
( ~ ( relation @ SY3526 )
| ~ ( subset @ SV52 @ SY3526 )
| ! [SY3527: $i,SY3528: $i] :
( ~ ( in @ ( ordered_pair @ SY3527 @ SY3528 ) @ SV52 )
| ( in @ ( ordered_pair @ SY3527 @ SY3528 ) @ SY3526 ) ) ) )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[831]) ).
thf(948,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK46_SY3307 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK45_C @ SX1 @ SX0 ) @ ( sK46_SY3307 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK45_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK45_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK45_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK44_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK44_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[832]) ).
thf(949,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[833]) ).
thf(950,plain,
! [SV53: $i] :
( ( ( function @ SV53 )
= $false )
| ( ( ~ ( relation @ SV53 ) )
= $true )
| ( ( ~ ( ~ ! [SY3529: $i,SY3530: $i] :
( ~ ( ~ ( ~ ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) ) @ SY3529 )
| ~ ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ SY3530 ) )
| ~ ~ ( ~ ( ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ SY3530 ) )
| ~ ( ( in @ ( apply @ SV53 @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) ) @ SY3529 )
| ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ SY3530 ) ) ) )
| ( SY3530
= ( relation_inverse_image @ SV53 @ SY3529 ) ) )
| ~ ! [SY3531: $i,SY3532: $i] :
( ( SY3532
!= ( relation_inverse_image @ SV53 @ SY3531 ) )
| ~ ( ~ ! [SY3533: $i] :
( ~ ( in @ SY3533 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SY3533 ) @ SY3531 )
| ( in @ SY3533 @ SY3532 ) )
| ~ ~ ( ~ ! [SY3534: $i] :
( ~ ( in @ SY3534 @ SY3532 )
| ( in @ SY3534 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY3535: $i] :
( ~ ( in @ SY3535 @ SY3532 )
| ( in @ ( apply @ SV53 @ SY3535 ) @ SY3531 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(951,plain,
! [SV54: $i] :
( ( ! [SY3536: $i,SY3537: $i] :
( ~ ( ~ ( ~ ( in @ ( sK28_D @ SY3537 @ SY3536 @ SV54 ) @ SV54 )
| ~ ( in @ ( sK28_D @ SY3537 @ SY3536 @ SV54 ) @ SY3536 )
| ~ ( in @ ( sK28_D @ SY3537 @ SY3536 @ SV54 ) @ SY3537 ) )
| ~ ~ ( ~ ( ( in @ ( sK28_D @ SY3537 @ SY3536 @ SV54 ) @ SV54 )
| ( in @ ( sK28_D @ SY3537 @ SY3536 @ SV54 ) @ SY3537 ) )
| ~ ( ( in @ ( sK28_D @ SY3537 @ SY3536 @ SV54 ) @ SY3536 )
| ( in @ ( sK28_D @ SY3537 @ SY3536 @ SV54 ) @ SY3537 ) ) ) )
| ( SY3537
= ( set_intersection2 @ SV54 @ SY3536 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[835]) ).
thf(952,plain,
! [SV54: $i] :
( ( ! [SY3538: $i,SY3539: $i] :
( ( SY3539
!= ( set_intersection2 @ SV54 @ SY3538 ) )
| ~ ( ~ ! [SY3540: $i] :
( ~ ( in @ SY3540 @ SV54 )
| ~ ( in @ SY3540 @ SY3538 )
| ( in @ SY3540 @ SY3539 ) )
| ~ ~ ( ~ ! [SY3541: $i] :
( ~ ( in @ SY3541 @ SY3539 )
| ( in @ SY3541 @ SV54 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY3539 )
| ( in @ SX3 @ SY3538 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[836]) ).
thf(953,plain,
! [SV128: $i] :
( ( ! [SY3713: $i] :
( ~ ( in @ SV128 @ SY3713 )
| ( subset @ ( singleton @ SV128 ) @ SY3713 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(954,plain,
! [SV129: $i] :
( ( ! [SY3714: $i] :
( ~ ( subset @ ( singleton @ SV129 ) @ SY3714 )
| ( in @ SV129 @ SY3714 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(955,plain,
! [SV55: $i] :
( ( ! [SY3543: $i,SY3544: $i] :
( ~ ( ~ ( ~ ( in @ ( sK21_D @ SY3544 @ SY3543 @ SV55 ) @ SV55 )
| ( in @ ( sK21_D @ SY3544 @ SY3543 @ SV55 ) @ SY3543 )
| ~ ( in @ ( sK21_D @ SY3544 @ SY3543 @ SV55 ) @ SY3544 ) )
| ~ ~ ( ~ ( ( in @ ( sK21_D @ SY3544 @ SY3543 @ SV55 ) @ SV55 )
| ( in @ ( sK21_D @ SY3544 @ SY3543 @ SV55 ) @ SY3544 ) )
| ~ ( ~ ( in @ ( sK21_D @ SY3544 @ SY3543 @ SV55 ) @ SY3543 )
| ( in @ ( sK21_D @ SY3544 @ SY3543 @ SV55 ) @ SY3544 ) ) ) )
| ( SY3544
= ( set_difference @ SV55 @ SY3543 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[839]) ).
thf(956,plain,
! [SV55: $i] :
( ( ! [SY3545: $i,SY3546: $i] :
( ( SY3546
!= ( set_difference @ SV55 @ SY3545 ) )
| ~ ( ~ ! [SY3547: $i] :
( ~ ( in @ SY3547 @ SV55 )
| ( in @ SY3547 @ SY3545 )
| ( in @ SY3547 @ SY3546 ) )
| ~ ~ ( ~ ! [SY3548: $i] :
( ~ ( in @ SY3548 @ SY3546 )
| ( in @ SY3548 @ SV55 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY3546 )
| ~ ( in @ SX3 @ SY3545 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[840]) ).
thf(957,plain,
! [SV56: $i] :
( ( ( function @ SV56 )
= $false )
| ( ( ~ ( relation @ SV56 ) )
= $true )
| ( ( ~ ( ~ ! [SY3550: $i] :
( ~ ( ~ ( ! [SY3551: $i] :
( ( ( sK19_C @ SY3550 @ SV56 )
!= ( apply @ SV56 @ SY3551 ) )
| ~ ( in @ SY3551 @ ( relation_dom @ SV56 ) ) )
| ~ ( in @ ( sK19_C @ SY3550 @ SV56 ) @ SY3550 ) )
| ~ ( ~ ( ( ( sK19_C @ SY3550 @ SV56 )
!= ( apply @ SV56 @ ( sK20_SY3294 @ SY3550 @ SV56 ) ) )
| ~ ( in @ ( sK20_SY3294 @ SY3550 @ SV56 ) @ ( relation_dom @ SV56 ) ) )
| ( in @ ( sK19_C @ SY3550 @ SV56 ) @ SY3550 ) ) )
| ( SY3550
= ( relation_rng @ SV56 ) ) )
| ~ ! [SY3552: $i] :
( ( SY3552
!= ( relation_rng @ SV56 ) )
| ~ ( ~ ! [SY3553: $i] :
( ! [SY3554: $i] :
( ( SY3553
!= ( apply @ SV56 @ SY3554 ) )
| ~ ( in @ SY3554 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY3553 @ SY3552 ) )
| ~ ! [SY3555: $i] :
( ~ ( in @ SY3555 @ SY3552 )
| ~ ( ( SY3555
!= ( apply @ SV56 @ ( sK18_D @ SY3555 @ SY3552 @ SV56 ) ) )
| ~ ( in @ ( sK18_D @ SY3555 @ SY3552 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[841]) ).
thf(958,plain,
! [SV57: $i] :
( ( ! [SY3556: $i,SY3557: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK38_D @ SY3557 @ SY3556 @ SV57 ) @ SY3557 )
| ( ( sK38_D @ SY3557 @ SY3556 @ SV57 )
!= SV57 ) )
| ~ ( ~ ( in @ ( sK38_D @ SY3557 @ SY3556 @ SV57 ) @ SY3557 )
| ( ( sK38_D @ SY3557 @ SY3556 @ SV57 )
!= SY3556 ) ) )
| ~ ( ( in @ ( sK38_D @ SY3557 @ SY3556 @ SV57 ) @ SY3557 )
| ( ( sK38_D @ SY3557 @ SY3556 @ SV57 )
= SV57 )
| ( ( sK38_D @ SY3557 @ SY3556 @ SV57 )
= SY3556 ) ) )
| ( SY3557
= ( unordered_pair @ SV57 @ SY3556 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[842]) ).
thf(959,plain,
! [SV57: $i] :
( ( ! [SY3558: $i,SY3559: $i] :
( ( SY3559
!= ( unordered_pair @ SV57 @ SY3558 ) )
| ~ ( ~ ! [SY3560: $i] :
( ~ ( in @ SY3560 @ SY3559 )
| ( SY3560 = SV57 )
| ( SY3560 = SY3558 ) )
| ~ ~ ( ~ ! [SY3561: $i] :
( ( SY3561 != SV57 )
| ( in @ SY3561 @ SY3559 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY3558 )
| ( in @ SX3 @ SY3559 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[843]) ).
thf(960,plain,
! [SV58: $i,SV96: $i] :
( ( ( ~ ( function @ SV96 ) )
= $true )
| ( ( ~ ( relation @ SV96 ) )
= $true )
| ( ( ~ ( ~ ! [SY3661: $i] :
( ~ ( function @ SY3661 )
| ~ ( relation @ SY3661 )
| ~ ( ~ ( in @ ( sK67_D @ SY3661 @ SV96 @ SV58 ) @ ( relation_dom @ SV96 ) )
| ~ ( ( ( apply @ SV96 @ ( sK67_D @ SY3661 @ SV96 @ SV58 ) )
!= ( apply @ SY3661 @ ( sK67_D @ SY3661 @ SV96 @ SV58 ) ) ) ) )
| ( ( relation_dom @ SV96 )
!= ( set_intersection2 @ ( relation_dom @ SY3661 ) @ SV58 ) )
| ( SV96
= ( relation_dom_restriction @ SY3661 @ SV58 ) ) )
| ~ ~ ( ~ ! [SY3662: $i] :
( ~ ( function @ SY3662 )
| ~ ( relation @ SY3662 )
| ( SV96
!= ( relation_dom_restriction @ SY3662 @ SV58 ) )
| ! [SY3663: $i] :
( ~ ( in @ SY3663 @ ( relation_dom @ SV96 ) )
| ( ( apply @ SV96 @ SY3663 )
= ( apply @ SY3662 @ SY3663 ) ) ) )
| ~ ! [SY3664: $i] :
( ~ ( function @ SY3664 )
| ~ ( relation @ SY3664 )
| ( SV96
!= ( relation_dom_restriction @ SY3664 @ SV58 ) )
| ( ( relation_dom @ SV96 )
= ( set_intersection2 @ ( relation_dom @ SY3664 ) @ SV58 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[844]) ).
thf(961,plain,
! [SV59: $i] :
( ( ( ~ ! [SY3568: $i] :
( ~ ( relation @ SY3568 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_C @ SY3568 @ SV59 ) @ ( sK40_SY3306 @ SY3568 @ SV59 ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK39_C @ SY3568 @ SV59 ) @ ( sK40_SY3306 @ SY3568 @ SV59 ) ) @ SY3568 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK39_C @ SY3568 @ SV59 ) @ ( sK40_SY3306 @ SY3568 @ SV59 ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK39_C @ SY3568 @ SV59 ) @ ( sK40_SY3306 @ SY3568 @ SV59 ) ) @ SY3568 ) ) )
| ( SV59 = SY3568 ) )
| ~ ! [SY3569: $i] :
( ~ ( relation @ SY3569 )
| ( SV59 != SY3569 )
| ~ ( ~ ! [SY3570: $i,SY3571: $i] :
( ~ ( in @ ( ordered_pair @ SY3570 @ SY3571 ) @ SV59 )
| ( in @ ( ordered_pair @ SY3570 @ SY3571 ) @ SY3569 ) )
| ~ ! [SY3572: $i,SY3573: $i] :
( ~ ( in @ ( ordered_pair @ SY3572 @ SY3573 ) @ SY3569 )
| ( in @ ( ordered_pair @ SY3572 @ SY3573 ) @ SV59 ) ) ) ) )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[845]) ).
thf(962,plain,
! [SV60: $i,SV97: $i] :
( ( ( ~ ( in @ ( sK78_C @ SV97 @ SV60 ) @ SV60 )
| ~ ~ ( in @ ( sK78_C @ SV97 @ SV60 ) @ SV97 ) )
= $false )
| ( ( element @ SV60 @ ( powerset @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[846]) ).
thf(963,plain,
! [SV130: $i] :
( ( ! [SY3715: $i] :
( ~ ( ~ ( ! [SY3716: $i] :
( ~ ( in @ ( sK23_C @ SY3715 @ SV130 ) @ SY3716 )
| ~ ( in @ SY3716 @ SV130 ) )
| ~ ( in @ ( sK23_C @ SY3715 @ SV130 ) @ SY3715 ) )
| ~ ( ~ ( ~ ( in @ ( sK23_C @ SY3715 @ SV130 ) @ ( sK24_SY3296 @ SY3715 @ SV130 ) )
| ~ ( in @ ( sK24_SY3296 @ SY3715 @ SV130 ) @ SV130 ) )
| ( in @ ( sK23_C @ SY3715 @ SV130 ) @ SY3715 ) ) )
| ( SY3715
= ( union @ SV130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(964,plain,
! [SV131: $i] :
( ( ! [SY3717: $i] :
( ( SY3717
!= ( union @ SV131 ) )
| ~ ( ~ ! [SY3718: $i] :
( ! [SY3719: $i] :
( ~ ( in @ SY3718 @ SY3719 )
| ~ ( in @ SY3719 @ SV131 ) )
| ( in @ SY3718 @ SY3717 ) )
| ~ ! [SY3720: $i] :
( ~ ( in @ SY3720 @ SY3717 )
| ~ ( ~ ( in @ SY3720 @ ( sK22_D @ SY3720 @ SY3717 @ SV131 ) )
| ~ ( in @ ( sK22_D @ SY3720 @ SY3717 @ SV131 ) @ SV131 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(965,plain,
! [SV98: $i,SV61: $i] :
( ( ~ ! [SY3665: $i,SY3666: $i] :
( ~ ( in @ SV61 @ SY3665 )
| ~ ( in @ SV98 @ SY3666 )
| ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SY3665 @ SY3666 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[849]) ).
thf(966,plain,
! [SV98: $i,SV61: $i] :
( ( ~ ~ ( ~ ! [SY3667: $i] :
( ! [SY3668: $i] :
~ ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SY3667 @ SY3668 ) )
| ( in @ SV61 @ SY3667 ) )
| ~ ! [SY3669: $i,SY3670: $i] :
( ~ ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SY3669 @ SY3670 ) )
| ( in @ SV98 @ SY3670 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[849]) ).
thf(967,plain,
! [SV62: $i] :
( ( ! [SY3582: $i,SY3583: $i] :
( ~ ( function @ SY3583 )
| ~ ( relation @ SY3583 )
| ~ ( in @ SY3582 @ ( relation_dom @ SY3583 ) )
| ~ ( in @ SY3582 @ SV62 )
| ( in @ SY3582 @ ( relation_dom @ ( relation_dom_restriction @ SY3583 @ SV62 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[850]) ).
thf(968,plain,
! [SV62: $i] :
( ( ~ ( ~ ! [SY3584: $i,SY3585: $i] :
( ~ ( function @ SY3585 )
| ~ ( relation @ SY3585 )
| ~ ( in @ SY3584 @ ( relation_dom @ ( relation_dom_restriction @ SY3585 @ SV62 ) ) )
| ( in @ SY3584 @ ( relation_dom @ SY3585 ) ) )
| ~ ! [SY3586: $i,SY3587: $i] :
( ~ ( function @ SY3587 )
| ~ ( relation @ SY3587 )
| ~ ( in @ SY3586 @ ( relation_dom @ ( relation_dom_restriction @ SY3587 @ SV62 ) ) )
| ( in @ SY3586 @ SV62 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[851]) ).
thf(969,plain,
! [SV63: $i] :
( ( ! [SY3588: $i,SY3589: $i] :
( ~ ( ~ ( ! [SY3590: $i,SY3591: $i] :
( ~ ( in @ SY3590 @ SV63 )
| ~ ( in @ SY3591 @ SY3588 )
| ( ( sK34_D @ SY3589 @ SY3588 @ SV63 )
!= ( ordered_pair @ SY3590 @ SY3591 ) ) )
| ~ ( in @ ( sK34_D @ SY3589 @ SY3588 @ SV63 ) @ SY3589 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK35_SY3303 @ SY3589 @ SY3588 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK36_SY3305 @ SY3589 @ SY3588 @ SV63 ) @ SY3588 ) )
| ( ( sK34_D @ SY3589 @ SY3588 @ SV63 )
!= ( ordered_pair @ ( sK35_SY3303 @ SY3589 @ SY3588 @ SV63 ) @ ( sK36_SY3305 @ SY3589 @ SY3588 @ SV63 ) ) ) )
| ( in @ ( sK34_D @ SY3589 @ SY3588 @ SV63 ) @ SY3589 ) ) )
| ( SY3589
= ( cartesian_product2 @ SV63 @ SY3588 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[852]) ).
thf(970,plain,
! [SV63: $i] :
( ( ! [SY3592: $i,SY3593: $i] :
( ( SY3593
!= ( cartesian_product2 @ SV63 @ SY3592 ) )
| ~ ( ~ ! [SY3594: $i] :
( ! [SY3595: $i,SY3596: $i] :
( ~ ( in @ SY3595 @ SV63 )
| ~ ( in @ SY3596 @ SY3592 )
| ( SY3594
!= ( ordered_pair @ SY3595 @ SY3596 ) ) )
| ( in @ SY3594 @ SY3593 ) )
| ~ ! [SY3597: $i] :
( ~ ( in @ SY3597 @ SY3593 )
| ~ ( ~ ~ ( ~ ( in @ ( sK32_E @ SY3597 @ SY3593 @ SY3592 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK33_SY3300 @ SY3597 @ SY3593 @ SY3592 @ SV63 ) @ SY3592 ) )
| ( SY3597
!= ( ordered_pair @ ( sK32_E @ SY3597 @ SY3593 @ SY3592 @ SV63 ) @ ( sK33_SY3300 @ SY3597 @ SY3593 @ SY3592 @ SV63 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[853]) ).
thf(971,plain,
! [SV132: $i] :
( ( ! [SY3721: $i] :
( ( disjoint @ SV132 @ SY3721 )
| ~ ( ~ ( in @ ( sK73_C @ SY3721 @ SV132 ) @ SV132 )
| ~ ( in @ ( sK73_C @ SY3721 @ SV132 ) @ SY3721 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(972,plain,
! [SV133: $i] :
( ( ! [SY3722: $i] :
( ! [SY3723: $i] :
( ~ ( in @ SY3723 @ SV133 )
| ~ ( in @ SY3723 @ SY3722 ) )
| ~ ( disjoint @ SV133 @ SY3722 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(973,plain,
! [SV64: $i] :
( ( ! [SY3598: $i,SY3599: $i] :
( ~ ( relation @ SY3599 )
| ! [SY3600: $i] :
( ~ ( in @ SY3600 @ ( relation_dom @ SY3599 ) )
| ~ ( in @ ( ordered_pair @ SY3600 @ SV64 ) @ SY3599 )
| ~ ( in @ SY3600 @ SY3598 ) )
| ( in @ SV64 @ ( relation_image @ SY3599 @ SY3598 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[856]) ).
thf(974,plain,
! [SV64: $i] :
( ( ! [SY3601: $i,SY3602: $i] :
( ~ ( relation @ SY3602 )
| ~ ( in @ SV64 @ ( relation_image @ SY3602 @ SY3601 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK76_D @ SY3602 @ SY3601 @ SV64 ) @ ( relation_dom @ SY3602 ) )
| ~ ( in @ ( ordered_pair @ ( sK76_D @ SY3602 @ SY3601 @ SV64 ) @ SV64 ) @ SY3602 ) )
| ~ ( in @ ( sK76_D @ SY3602 @ SY3601 @ SV64 ) @ SY3601 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[857]) ).
thf(975,plain,
! [SV65: $i] :
( ( ! [SY3603: $i,SY3604: $i] :
( ~ ( relation @ SY3604 )
| ~ ( in @ ( ordered_pair @ SV65 @ SY3603 ) @ SY3604 )
| ( in @ SV65 @ ( relation_dom @ SY3604 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[858]) ).
thf(976,plain,
! [SV65: $i] :
( ( ! [SY3605: $i,SY3606: $i] :
( ~ ( relation @ SY3606 )
| ~ ( in @ ( ordered_pair @ SV65 @ SY3605 ) @ SY3606 )
| ( in @ SY3605 @ ( relation_rng @ SY3606 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[859]) ).
thf(977,plain,
! [SV66: $i] :
( ( ( function @ SV66 )
= $false )
| ( ( ~ ( relation @ SV66 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY3607: $i] :
( ~ ( in @ SY3607 @ ( relation_dom @ SV66 ) )
| ! [SY3608: $i] :
( ( SY3608
!= ( apply @ SV66 @ SY3607 ) )
| ( in @ ( ordered_pair @ SY3607 @ SY3608 ) @ SV66 ) ) )
| ~ ! [SY3609: $i] :
( ~ ( in @ SY3609 @ ( relation_dom @ SV66 ) )
| ! [SY3610: $i] :
( ~ ( in @ ( ordered_pair @ SY3609 @ SY3610 ) @ SV66 )
| ( SY3610
= ( apply @ SV66 @ SY3609 ) ) ) ) )
| ~ ~ ( ~ ! [SY3611: $i] :
( ( in @ SY3611 @ ( relation_dom @ SV66 ) )
| ! [SY3612: $i] :
( ( SY3612
!= ( apply @ SV66 @ SY3611 ) )
| ( SY3612 = empty_set ) ) )
| ~ ! [SY3613: $i] :
( ( in @ SY3613 @ ( relation_dom @ SV66 ) )
| ! [SY3614: $i] :
( ( SY3614 != empty_set )
| ( SY3614
= ( apply @ SV66 @ SY3613 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(978,plain,
! [SV134: $i] :
( ( ! [SY3724: $i] :
( ~ ( in @ SV134 @ SY3724 )
| ( subset @ ( singleton @ SV134 ) @ SY3724 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(979,plain,
! [SV135: $i] :
( ( ! [SY3725: $i] :
( ~ ( subset @ ( singleton @ SV135 ) @ SY3725 )
| ( in @ SV135 @ SY3725 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(980,plain,
! [SV68: $i,SV2: $i] :
( ( ( in @ SV2 @ SV68 )
= $false )
| ( ( disjoint @ ( singleton @ SV2 ) @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[864]) ).
thf(981,plain,
! [SV4: $i,SV70: $i,SV136: $i] :
( ( ( ~ ( in @ SV136 @ SV70 )
| ( in @ SV136 @ SV4 ) )
= $true )
| ( ( element @ SV70 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(982,plain,
! [SV71: $i,SV5: $i,SV137: $i] :
( ( ( ( in @ SV137 @ SV5 )
| ( subset @ SV5 @ ( set_difference @ SV71 @ ( singleton @ SV137 ) ) ) )
= $true )
| ( ( subset @ SV5 @ SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(983,plain,
! [SV7: $i,SV73: $i] :
( ( ( function @ SV73 )
= $false )
| ( ( ~ ( relation @ SV73 ) )
= $true )
| ( ( ! [SY3617: $i] :
( ~ ( function @ SY3617 )
| ~ ( relation @ SY3617 )
| ~ ( in @ SV7 @ ( relation_dom @ ( relation_composition @ SY3617 @ SV73 ) ) )
| ( ( apply @ ( relation_composition @ SY3617 @ SV73 ) @ SV7 )
= ( apply @ SV73 @ ( apply @ SY3617 @ SV7 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[868]) ).
thf(984,plain,
! [SV8: $i,SV74: $i] :
( ( ( function @ SV74 )
= $false )
| ( ( ~ ( relation @ SV74 ) )
= $true )
| ( ( ! [SY3618: $i] :
( ~ ( function @ SY3618 )
| ~ ( relation @ SY3618 )
| ~ ( in @ SV8 @ ( relation_dom @ SV74 ) )
| ( ( apply @ ( relation_composition @ SV74 @ SY3618 ) @ SV8 )
= ( apply @ SY3618 @ ( apply @ SV74 @ SV8 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[869]) ).
thf(985,plain,
! [SV99: $i,SV76: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV76 ) )
= $true )
| ( ( ~ ( in @ SV76 @ SV99 ) )
= $true )
| ( ( ~ ( in @ SV99 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[871]) ).
thf(986,plain,
! [SV12: $i,SV100: $i] :
( ( ( element @ SV100 @ ( powerset @ SV12 ) )
= $false )
| ( ( ! [SY3671: $i] :
( ~ ( element @ SY3671 @ SV12 )
| ( in @ SY3671 @ SV100 )
| ( in @ SY3671 @ ( subset_complement @ SV12 @ SV100 ) ) ) )
= $true )
| ( ( SV12 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[873]) ).
thf(987,plain,
! [SV78: $i,SV13: $i,SV101: $i] :
( ( ( element @ SV101 @ ( powerset @ SV13 ) )
= $false )
| ( ( ~ ( in @ SV78 @ ( subset_complement @ SV13 @ SV101 ) )
| ~ ( in @ SV78 @ SV101 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[874]) ).
thf(988,plain,
! [SV15: $i,SV79: $i,SV102: $i] :
( ( ( ~ ( function @ SV102 ) )
= $true )
| ( ( ~ ( relation @ SV102 ) )
= $true )
| ( ( ~ ( in @ SV79 @ ( relation_dom @ ( relation_dom_restriction @ SV102 @ SV15 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SV102 @ SV15 ) @ SV79 )
= ( apply @ SV102 @ SV79 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[876]) ).
thf(989,plain,
! [SV16: $i,SV80: $i,SV103: $i] :
( ( ( ~ ( function @ SV103 ) )
= $true )
| ( ( ~ ( relation @ SV103 ) )
= $true )
| ( ( ~ ( in @ SV80 @ SV16 )
| ( ( apply @ ( relation_dom_restriction @ SV103 @ SV16 ) @ SV80 )
= ( apply @ SV103 @ SV80 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[877]) ).
thf(990,plain,
! [SV18: $i,SV82: $i] :
( ( ( in @ SV82 @ SV18 )
= $false )
| ( ( in @ SV18 @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[879]) ).
thf(991,plain,
! [SV22: $i,SV84: $i] :
( ( ( empty @ SV84 )
= $true )
| ( ( in @ SV22 @ SV84 )
= $true )
| ( ( element @ SV22 @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[881]) ).
thf(992,plain,
! [SV23: $i,SV104: $i,SV85: $i] :
( ( ( ~ ( element @ SV85 @ ( powerset @ SV104 ) ) )
= $true )
| ( ( ~ ( in @ SV23 @ SV85 ) )
= $true )
| ( ( element @ SV23 @ SV104 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[882]) ).
thf(993,plain,
! [SV24: $i,SV105: $i,SV86: $i] :
( ( ( ~ ( element @ SV86 @ ( powerset @ SV105 ) ) )
= $true )
| ( ( ~ ( in @ SV24 @ SV86 ) )
= $true )
| ( ( ~ ( empty @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[883]) ).
thf(994,plain,
! [SV87: $i,SV25: $i] :
( ( ( in @ SV25 @ SV87 )
= $false )
| ( ( empty @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[884]) ).
thf(995,plain,
! [SV138: $i,SV106: $i] :
( ( ( disjoint @ SV106 @ SV138 )
| ( in @ ( sK72_C @ SV138 @ SV106 ) @ ( set_intersection2 @ SV106 @ SV138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[885]) ).
thf(996,plain,
! [SV139: $i,SV107: $i] :
( ( ! [SY3726: $i] :
~ ( in @ SY3726 @ ( set_intersection2 @ SV107 @ SV139 ) )
| ~ ( disjoint @ SV107 @ SV139 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(997,plain,
! [SV26: $i,SV88: $i] :
( ( ( ~ ! [SY3625: $i] :
( ~ ( relation @ SY3625 )
| ~ ( ~ ( ~ ( in @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) @ SV26 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY3625 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) ) @ SV88 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY3625 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) ) @ SY3625 ) )
| ~ ~ ( ~ ( ( in @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) @ SV26 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY3625 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) ) @ SY3625 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SY3625 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) ) @ SV88 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY3625 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) ) @ SY3625 ) ) ) )
| ( SY3625
= ( relation_rng_restriction @ SV26 @ SV88 ) ) )
| ~ ! [SY3626: $i] :
( ~ ( relation @ SY3626 )
| ( SY3626
!= ( relation_rng_restriction @ SV26 @ SV88 ) )
| ~ ( ~ ! [SY3627: $i,SY3628: $i] :
( ~ ( in @ SY3628 @ SV26 )
| ~ ( in @ ( ordered_pair @ SY3627 @ SY3628 ) @ SV88 )
| ( in @ ( ordered_pair @ SY3627 @ SY3628 ) @ SY3626 ) )
| ~ ~ ( ~ ! [SY3365: $i,SY3366: $i] :
( ~ ( in @ ( ordered_pair @ SY3365 @ SY3366 ) @ SY3626 )
| ( in @ SY3366 @ SV26 ) )
| ~ ! [SY3631: $i,SY3632: $i] :
( ~ ( in @ ( ordered_pair @ SY3631 @ SY3632 ) @ SY3626 )
| ( in @ ( ordered_pair @ SY3631 @ SY3632 ) @ SV88 ) ) ) ) ) )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[887]) ).
thf(998,plain,
! [SV108: $i,SV140: $i] :
( ( ~ ( ~ ( in @ ( sK29_C @ SV140 @ SV108 ) @ SV108 )
| ~ ~ ( in @ ( sK29_C @ SV140 @ SV108 ) @ SV140 ) )
| ( subset @ SV108 @ SV140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[888]) ).
thf(999,plain,
! [SV141: $i,SV109: $i] :
( ( ~ ( subset @ SV109 @ SV141 )
| ! [SY3727: $i] :
( ~ ( in @ SY3727 @ SV109 )
| ( in @ SY3727 @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(1000,plain,
! [SV142: $i,SV27: $i] :
( ( ! [SY3728: $i] :
( ~ ( relation @ SY3728 )
| ~ ( in @ SV27 @ SV142 )
| ~ ( in @ SV27 @ ( relation_dom @ SY3728 ) )
| ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SY3728 @ SV142 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(1001,plain,
! [SV27: $i] :
( ( ~ ! [SY3371: $i,SY3372: $i] :
( ~ ( relation @ SY3372 )
| ~ ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SY3372 @ SY3371 ) ) )
| ( in @ SV27 @ SY3371 ) )
| ~ ! [SY3373: $i,SY3374: $i] :
( ~ ( relation @ SY3374 )
| ~ ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SY3374 @ SY3373 ) ) )
| ( in @ SV27 @ ( relation_dom @ SY3374 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[891]) ).
thf(1002,plain,
! [SV28: $i] :
( ( ( ~ ! [SY3375: $i] :
( ~ ( relation @ SY3375 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SY3375 @ SV28 ) @ ( sK14_SY3290 @ SY3375 @ SV28 ) ) @ SY3375 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY3290 @ SY3375 @ SV28 ) @ ( sK13_C @ SY3375 @ SV28 ) ) @ SV28 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SY3375 @ SV28 ) @ ( sK14_SY3290 @ SY3375 @ SV28 ) ) @ SY3375 )
| ( in @ ( ordered_pair @ ( sK14_SY3290 @ SY3375 @ SV28 ) @ ( sK13_C @ SY3375 @ SV28 ) ) @ SV28 ) ) )
| ( SY3375
= ( relation_inverse @ SV28 ) ) ) )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[892]) ).
thf(1003,plain,
! [SV28: $i] :
( ( ( ~ ! [SY3376: $i] :
( ~ ( relation @ SY3376 )
| ( SY3376
!= ( relation_inverse @ SV28 ) )
| ~ ( ~ ! [SY3377: $i,SY3378: $i] :
( ~ ( in @ ( ordered_pair @ SY3377 @ SY3378 ) @ SY3376 )
| ( in @ ( ordered_pair @ SY3378 @ SY3377 ) @ SV28 ) )
| ~ ! [SY3379: $i,SY3380: $i] :
( ~ ( in @ ( ordered_pair @ SY3380 @ SY3379 ) @ SV28 )
| ( in @ ( ordered_pair @ SY3379 @ SY3380 ) @ SY3376 ) ) ) ) )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[892]) ).
thf(1004,plain,
! [SV29: $i] :
( ( ( relation @ SV29 )
= $false )
| ( ( function @ SV29 )
= $false )
| ( ( ~ ( ~ ! [SY3381: $i,SY3382: $i] :
( ~ ( ~ ( ! [SY3383: $i] :
( ~ ( in @ SY3383 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3383 @ SY3381 )
| ( ( sK61_D @ SY3382 @ SY3381 @ SV29 )
!= ( apply @ SV29 @ SY3383 ) ) )
| ~ ( in @ ( sK61_D @ SY3382 @ SY3381 @ SV29 ) @ SY3382 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY3318 @ SY3382 @ SY3381 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK62_SY3318 @ SY3382 @ SY3381 @ SV29 ) @ SY3381 ) )
| ( ( sK61_D @ SY3382 @ SY3381 @ SV29 )
!= ( apply @ SV29 @ ( sK62_SY3318 @ SY3382 @ SY3381 @ SV29 ) ) ) )
| ( in @ ( sK61_D @ SY3382 @ SY3381 @ SV29 ) @ SY3382 ) ) )
| ( SY3382
= ( relation_image @ SV29 @ SY3381 ) ) )
| ~ ! [SY3384: $i,SY3385: $i] :
( ( SY3385
!= ( relation_image @ SV29 @ SY3384 ) )
| ~ ( ~ ! [SY3386: $i] :
( ! [SY3387: $i] :
( ~ ( in @ SY3387 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3387 @ SY3384 )
| ( SY3386
!= ( apply @ SV29 @ SY3387 ) ) )
| ( in @ SY3386 @ SY3385 ) )
| ~ ! [SY3388: $i] :
( ~ ( in @ SY3388 @ SY3385 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SY3388 @ SY3385 @ SY3384 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK60_E @ SY3388 @ SY3385 @ SY3384 @ SV29 ) @ SY3384 ) )
| ( SY3388
!= ( apply @ SV29 @ ( sK60_E @ SY3388 @ SY3385 @ SY3384 @ SV29 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[893]) ).
thf(1005,plain,
! [SV30: $i] :
( ( ( ~ ! [SY3389: $i,SY3390: $i] :
( ~ ( ~ ( ! [SY3391: $i] :
( ~ ( in @ ( ordered_pair @ SY3391 @ ( sK55_D @ SY3390 @ SY3389 @ SV30 ) ) @ SV30 )
| ~ ( in @ SY3391 @ SY3389 ) )
| ~ ( in @ ( sK55_D @ SY3390 @ SY3389 @ SV30 ) @ SY3390 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_SY3315 @ SY3390 @ SY3389 @ SV30 ) @ ( sK55_D @ SY3390 @ SY3389 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK56_SY3315 @ SY3390 @ SY3389 @ SV30 ) @ SY3389 ) )
| ( in @ ( sK55_D @ SY3390 @ SY3389 @ SV30 ) @ SY3390 ) ) )
| ( SY3390
= ( relation_image @ SV30 @ SY3389 ) ) ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[894]) ).
thf(1006,plain,
! [SV30: $i] :
( ( ( ~ ! [SY3392: $i,SY3393: $i] :
( ( SY3393
!= ( relation_image @ SV30 @ SY3392 ) )
| ~ ( ~ ! [SY3394: $i] :
( ! [SY3395: $i] :
( ~ ( in @ ( ordered_pair @ SY3395 @ SY3394 ) @ SV30 )
| ~ ( in @ SY3395 @ SY3392 ) )
| ( in @ SY3394 @ SY3393 ) )
| ~ ! [SY3396: $i] :
( ~ ( in @ SY3396 @ SY3393 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SY3396 @ SY3393 @ SY3392 @ SV30 ) @ SY3396 ) @ SV30 )
| ~ ( in @ ( sK54_E @ SY3396 @ SY3393 @ SY3392 @ SV30 ) @ SY3392 ) ) ) ) ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[894]) ).
thf(1007,plain,
! [SV31: $i] :
( ( ( ~ ! [SY3397: $i,SY3398: $i] :
( ~ ( ~ ( ! [SY3399: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ SY3398 @ SY3397 @ SV31 ) @ SY3399 ) @ SV31 )
| ~ ( in @ SY3399 @ SY3397 ) )
| ~ ( in @ ( sK52_D @ SY3398 @ SY3397 @ SV31 ) @ SY3398 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SY3398 @ SY3397 @ SV31 ) @ ( sK53_SY3313 @ SY3398 @ SY3397 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( sK53_SY3313 @ SY3398 @ SY3397 @ SV31 ) @ SY3397 ) )
| ( in @ ( sK52_D @ SY3398 @ SY3397 @ SV31 ) @ SY3398 ) ) )
| ( SY3398
= ( relation_inverse_image @ SV31 @ SY3397 ) ) ) )
= $false )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[895]) ).
thf(1008,plain,
! [SV31: $i] :
( ( ( ~ ! [SY3400: $i,SY3401: $i] :
( ( SY3401
!= ( relation_inverse_image @ SV31 @ SY3400 ) )
| ~ ( ~ ! [SY3402: $i] :
( ! [SY3403: $i] :
( ~ ( in @ ( ordered_pair @ SY3402 @ SY3403 ) @ SV31 )
| ~ ( in @ SY3403 @ SY3400 ) )
| ( in @ SY3402 @ SY3401 ) )
| ~ ! [SY3404: $i] :
( ~ ( in @ SY3404 @ SY3401 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3404 @ ( sK51_E @ SY3404 @ SY3401 @ SY3400 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( sK51_E @ SY3404 @ SY3401 @ SY3400 @ SV31 ) @ SY3400 ) ) ) ) ) )
= $false )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[895]) ).
thf(1009,plain,
! [SV32: $i] :
( ( ( ~ ! [SY3405: $i,SY3406: $i] :
( ~ ( relation @ SY3406 )
| ~ ( ~ ( ~ ( in @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ SY3405 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ ( sK64_SY3319 @ SY3406 @ SY3405 @ SV32 ) ) @ SV32 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ ( sK64_SY3319 @ SY3406 @ SY3405 @ SV32 ) ) @ SY3406 ) )
| ~ ~ ( ~ ( ( in @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ SY3405 )
| ( in @ ( ordered_pair @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ ( sK64_SY3319 @ SY3406 @ SY3405 @ SV32 ) ) @ SY3406 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ ( sK64_SY3319 @ SY3406 @ SY3405 @ SV32 ) ) @ SV32 )
| ( in @ ( ordered_pair @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ ( sK64_SY3319 @ SY3406 @ SY3405 @ SV32 ) ) @ SY3406 ) ) ) )
| ( SY3406
= ( relation_dom_restriction @ SV32 @ SY3405 ) ) ) )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[896]) ).
thf(1010,plain,
! [SV32: $i] :
( ( ( ~ ! [SY3407: $i,SY3408: $i] :
( ~ ( relation @ SY3408 )
| ( SY3408
!= ( relation_dom_restriction @ SV32 @ SY3407 ) )
| ~ ( ~ ! [SY3409: $i,SY3410: $i] :
( ~ ( in @ SY3409 @ SY3407 )
| ~ ( in @ ( ordered_pair @ SY3409 @ SY3410 ) @ SV32 )
| ( in @ ( ordered_pair @ SY3409 @ SY3410 ) @ SY3408 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3408 )
| ( in @ SX3 @ SY3407 ) )
| ~ ! [SY3413: $i,SY3414: $i] :
( ~ ( in @ ( ordered_pair @ SY3413 @ SY3414 ) @ SY3408 )
| ( in @ ( ordered_pair @ SY3413 @ SY3414 ) @ SV32 ) ) ) ) ) )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[896]) ).
thf(1011,plain,
! [SV143: $i,SV33: $i] :
( ( ! [SY3729: $i] :
( ~ ( relation @ SY3729 )
| ! [SY3730: $i] :
( ~ ( in @ SY3730 @ ( relation_rng @ SY3729 ) )
| ~ ( in @ ( ordered_pair @ SV33 @ SY3730 ) @ SY3729 )
| ~ ( in @ SY3730 @ SV143 ) )
| ( in @ SV33 @ ( relation_inverse_image @ SY3729 @ SV143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(1012,plain,
! [SV144: $i,SV33: $i] :
( ( ! [SY3731: $i] :
( ~ ( relation @ SY3731 )
| ~ ( in @ SV33 @ ( relation_inverse_image @ SY3731 @ SV144 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK75_D @ SY3731 @ SV144 @ SV33 ) @ ( relation_rng @ SY3731 ) )
| ~ ( in @ ( ordered_pair @ SV33 @ ( sK75_D @ SY3731 @ SV144 @ SV33 ) ) @ SY3731 ) )
| ~ ( in @ ( sK75_D @ SY3731 @ SV144 @ SV33 ) @ SV144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(1013,plain,
! [SV110: $i,SV145: $i] :
( ( ~ ( relation @ SV145 )
| ~ ( ~ ( ( ( sK65_C @ SV145 @ SV110 )
!= ( sK66_SY3320 @ SV145 @ SV110 ) )
| ~ ( in @ ( sK65_C @ SV145 @ SV110 ) @ SV110 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 ) )
| ~ ~ ( ~ ( ( ( sK65_C @ SV145 @ SV110 )
= ( sK66_SY3320 @ SV145 @ SV110 ) )
| ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 ) )
| ~ ( ( in @ ( sK65_C @ SV145 @ SV110 ) @ SV110 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 ) ) ) )
| ( SV145
= ( identity_relation @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(1014,plain,
! [SV111: $i,SV146: $i] :
( ( ~ ( relation @ SV146 )
| ( SV146
!= ( identity_relation @ SV111 ) )
| ~ ( ~ ! [SY3732: $i,SY3733: $i] :
( ( SY3732 != SY3733 )
| ~ ( in @ SY3732 @ SV111 )
| ( in @ ( ordered_pair @ SY3732 @ SY3733 ) @ SV146 ) )
| ~ ~ ( ~ ! [SY3734: $i,SY3735: $i] :
( ~ ( in @ ( ordered_pair @ SY3734 @ SY3735 ) @ SV146 )
| ( SY3734 = SY3735 ) )
| ~ ! [SY3736: $i] :
( ! [SY3737: $i] :
~ ( in @ ( ordered_pair @ SY3736 @ SY3737 ) @ SV146 )
| ( in @ SY3736 @ SV111 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(1015,plain,
! [SV34: $i,SV89: $i] :
( ( ! [SY3633: $i,SY3634: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 ) @ SY3634 )
| ( ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 )
!= SY3633 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 ) @ SY3634 )
| ( ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 )
!= SV34 ) )
| ~ ( ~ ( in @ ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 ) @ SY3634 )
| ( ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 )
!= SV89 ) ) ) )
| ~ ( ( in @ ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 ) @ SY3634 )
| ( ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 )
= SY3633 )
| ( ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 )
= SV34 )
| ( ( sK50_E @ SY3634 @ SY3633 @ SV89 @ SV34 )
= SV89 ) ) )
| ( SY3634
= ( unordered_triple @ SV34 @ SV89 @ SY3633 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[901]) ).
thf(1016,plain,
! [SV89: $i,SV34: $i] :
( ( ! [SY3635: $i,SY3636: $i] :
( ( SY3636
!= ( unordered_triple @ SV34 @ SV89 @ SY3635 ) )
| ~ ( ~ ! [SY3637: $i] :
( ~ ( in @ SY3637 @ SY3636 )
| ( SY3637 = SY3635 )
| ( SY3637 = SV34 )
| ( SY3637 = SV89 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SY3635 )
| ( in @ SX4 @ SY3636 ) )
| ~ ~ ( ~ ! [SY3427: $i] :
( ( SY3427 != SV34 )
| ( in @ SY3427 @ SY3636 ) )
| ~ ! [SY3640: $i] :
( ( SY3640 != SV89 )
| ( in @ SY3640 @ SY3636 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[902]) ).
thf(1017,plain,
! [SV147: $i,SV35: $i] :
( ( ! [SY3738: $i] :
( ~ ( relation @ SY3738 )
| ~ ( in @ ( ordered_pair @ SV35 @ SV147 ) @ SY3738 )
| ( in @ SV35 @ ( relation_field @ SY3738 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(1018,plain,
! [SV148: $i,SV35: $i] :
( ( ! [SY3739: $i] :
( ~ ( relation @ SY3739 )
| ~ ( in @ ( ordered_pair @ SV35 @ SV148 ) @ SY3739 )
| ( in @ SV148 @ ( relation_field @ SY3739 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[904]) ).
thf(1019,plain,
! [SV36: $i] :
( ( ( ~ ! [SY3433: $i] :
( ~ ( ~ ( ! [SY3434: $i] :
~ ( in @ ( ordered_pair @ SY3434 @ ( sK16_C @ SY3433 @ SV36 ) ) @ SV36 )
| ~ ( in @ ( sK16_C @ SY3433 @ SV36 ) @ SY3433 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_SY3292 @ SY3433 @ SV36 ) @ ( sK16_C @ SY3433 @ SV36 ) ) @ SV36 )
| ( in @ ( sK16_C @ SY3433 @ SV36 ) @ SY3433 ) ) )
| ( SY3433
= ( relation_rng @ SV36 ) ) ) )
= $false )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[905]) ).
thf(1020,plain,
! [SV36: $i] :
( ( ( ~ ! [SY3435: $i] :
( ( SY3435
!= ( relation_rng @ SV36 ) )
| ~ ( ~ ! [SY3436: $i] :
( ! [SY3437: $i] :
~ ( in @ ( ordered_pair @ SY3437 @ SY3436 ) @ SV36 )
| ( in @ SY3436 @ SY3435 ) )
| ~ ! [SY3438: $i] :
( ~ ( in @ SY3438 @ SY3435 )
| ( in @ ( ordered_pair @ ( sK15_D @ SY3438 @ SY3435 @ SV36 ) @ SY3438 ) @ SV36 ) ) ) ) )
= $false )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[905]) ).
thf(1021,plain,
! [SV37: $i,SV149: $i] :
( ( ~ ( subset @ SV149 @ ( sK77_B @ SV37 ) )
| ( are_equipotent @ SV149 @ ( sK77_B @ SV37 ) )
| ( in @ SV149 @ ( sK77_B @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(1022,plain,
! [SV37: $i] :
( ( ~ ! [SY3440: $i] :
( ~ ( in @ SY3440 @ ( sK77_B @ SV37 ) )
| ( in @ ( powerset @ SY3440 ) @ ( sK77_B @ SV37 ) ) )
| ~ ~ ( ~ ! [SY3441: $i,SY3442: $i] :
( ~ ( in @ SY3441 @ ( sK77_B @ SV37 ) )
| ~ ( subset @ SY3442 @ SY3441 )
| ( in @ SY3442 @ ( sK77_B @ SV37 ) ) )
| ~ ( in @ SV37 @ ( sK77_B @ SV37 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[907]) ).
thf(1023,plain,
! [SV112: $i,SV150: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK41_C @ SV150 @ SV112 ) @ SV150 )
| ~ ( subset @ ( sK41_C @ SV150 @ SV112 ) @ SV112 ) )
| ~ ( ( in @ ( sK41_C @ SV150 @ SV112 ) @ SV150 )
| ( subset @ ( sK41_C @ SV150 @ SV112 ) @ SV112 ) ) )
| ( SV150
= ( powerset @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(1024,plain,
! [SV113: $i,SV151: $i] :
( ( ( SV151
!= ( powerset @ SV113 ) )
| ~ ( ~ ! [SY3740: $i] :
( ~ ( in @ SY3740 @ SV151 )
| ( subset @ SY3740 @ SV113 ) )
| ~ ! [SY3741: $i] :
( ~ ( subset @ SY3741 @ SV113 )
| ( in @ SY3741 @ SV151 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(1025,plain,
! [SV38: $i,SV90: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_C @ SV90 @ SV38 ) @ SV38 )
| ~ ( in @ ( sK5_C @ SV90 @ SV38 ) @ SV90 ) ) )
= $false )
| ( ( SV38 = SV90 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[910]) ).
thf(1026,plain,
! [SV38: $i,SV90: $i] :
( ( ( ~ ( ( in @ ( sK5_C @ SV90 @ SV38 ) @ SV38 )
| ( in @ ( sK5_C @ SV90 @ SV38 ) @ SV90 ) ) )
= $false )
| ( ( SV38 = SV90 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[910]) ).
thf(1027,plain,
! [SV114: $i,SV152: $i] :
( ( ~ ( function @ SV152 )
| ~ ( relation @ SV152 )
| ~ ( in @ SV114 @ ( relation_rng @ SV152 ) )
| ~ ( one_to_one @ SV152 )
| ( SV114
= ( apply @ SV152 @ ( apply @ ( function_inverse @ SV152 ) @ SV114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(1028,plain,
! [SV115: $i,SV153: $i] :
( ( ~ ( function @ SV153 )
| ~ ( relation @ SV153 )
| ~ ( in @ SV115 @ ( relation_rng @ SV153 ) )
| ~ ( one_to_one @ SV153 )
| ( SV115
= ( apply @ ( relation_composition @ ( function_inverse @ SV153 ) @ SV153 ) @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[912]) ).
thf(1029,plain,
! [SV39: $i,SV91: $i] :
( ( ( function @ SV91 )
= $false )
| ( ( ~ ( relation @ SV91 ) )
= $true )
| ( ( ~ ( ~ ! [SY3641: $i] :
( ~ ( function @ SY3641 )
| ~ ( relation @ SY3641 )
| ~ ( in @ SV39 @ ( relation_dom @ SY3641 ) )
| ~ ( in @ ( apply @ SY3641 @ SV39 ) @ ( relation_dom @ SV91 ) )
| ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3641 @ SV91 ) ) ) )
| ~ ~ ( ~ ! [SY3642: $i] :
( ~ ( function @ SY3642 )
| ~ ( relation @ SY3642 )
| ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3642 @ SV91 ) ) )
| ( in @ SV39 @ ( relation_dom @ SY3642 ) ) )
| ~ ! [SY3643: $i] :
( ~ ( function @ SY3643 )
| ~ ( relation @ SY3643 )
| ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3643 @ SV91 ) ) )
| ( in @ ( apply @ SY3643 @ SV39 ) @ ( relation_dom @ SV91 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[913]) ).
thf(1030,plain,
! [SV92: $i,SV40: $i] :
( ( ( ~ ! [SY3644: $i] :
( ~ ( element @ SY3644 @ ( powerset @ ( powerset @ SV40 ) ) )
| ~ ( ~ ( element @ ( sK6_D @ SY3644 @ SV92 @ SV40 ) @ ( powerset @ SV40 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK6_D @ SY3644 @ SV92 @ SV40 ) @ SY3644 )
| ~ ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SY3644 @ SV92 @ SV40 ) ) @ SV92 ) )
| ~ ( ( in @ ( sK6_D @ SY3644 @ SV92 @ SV40 ) @ SY3644 )
| ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SY3644 @ SV92 @ SV40 ) ) @ SV92 ) ) ) )
| ( SY3644
= ( complements_of_subsets @ SV40 @ SV92 ) ) )
| ~ ! [SY3645: $i] :
( ~ ( element @ SY3645 @ ( powerset @ ( powerset @ SV40 ) ) )
| ( SY3645
!= ( complements_of_subsets @ SV40 @ SV92 ) )
| ~ ( ~ ! [SY3646: $i] :
( ~ ( element @ SY3646 @ ( powerset @ SV40 ) )
| ~ ( in @ SY3646 @ SY3645 )
| ( in @ ( subset_complement @ SV40 @ SY3646 ) @ SV92 ) )
| ~ ! [SY3647: $i] :
( ~ ( element @ SY3647 @ ( powerset @ SV40 ) )
| ~ ( in @ ( subset_complement @ SV40 @ SY3647 ) @ SV92 )
| ( in @ SY3647 @ SY3645 ) ) ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[914]) ).
thf(1031,plain,
! [SV41: $i,SV154: $i] :
( ( ! [SY3742: $i] :
( ~ ( function @ SY3742 )
| ~ ( relation @ SY3742 )
| ( SV154
!= ( apply @ SY3742 @ SV41 ) )
| ~ ( in @ SV41 @ ( relation_dom @ SY3742 ) )
| ( in @ ( ordered_pair @ SV41 @ SV154 ) @ SY3742 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1032,plain,
! [SV41: $i] :
( ( ~ ! [SY3455: $i,SY3456: $i] :
( ~ ( function @ SY3456 )
| ~ ( relation @ SY3456 )
| ~ ( in @ ( ordered_pair @ SV41 @ SY3455 ) @ SY3456 )
| ( SY3455
= ( apply @ SY3456 @ SV41 ) ) )
| ~ ! [SY3457: $i,SY3458: $i] :
( ~ ( function @ SY3458 )
| ~ ( relation @ SY3458 )
| ~ ( in @ ( ordered_pair @ SV41 @ SY3457 ) @ SY3458 )
| ( in @ SV41 @ ( relation_dom @ SY3458 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[916]) ).
thf(1033,plain,
! [SV155: $i,SV42: $i] :
( ( ! [SY3743: $i] :
( ~ ( relation @ SY3743 )
| ~ ( in @ SV42 @ SV155 )
| ~ ( in @ SV42 @ ( relation_rng @ SY3743 ) )
| ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SV155 @ SY3743 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(1034,plain,
! [SV42: $i] :
( ( ~ ! [SY3461: $i,SY3462: $i] :
( ~ ( relation @ SY3462 )
| ~ ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SY3461 @ SY3462 ) ) )
| ( in @ SV42 @ SY3461 ) )
| ~ ! [SY3463: $i,SY3464: $i] :
( ~ ( relation @ SY3464 )
| ~ ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SY3463 @ SY3464 ) ) )
| ( in @ SV42 @ ( relation_rng @ SY3464 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[918]) ).
thf(1035,plain,
! [SV43: $i,SV156: $i] :
( ( ~ ( subset @ SV156 @ ( sK2_B @ SV43 ) )
| ( are_equipotent @ SV156 @ ( sK2_B @ SV43 ) )
| ( in @ SV156 @ ( sK2_B @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1036,plain,
! [SV43: $i] :
( ( ~ ! [SY3466: $i] :
( ~ ( ~ ! [SY3467: $i] :
( ~ ( subset @ SY3467 @ SY3466 )
| ( in @ SY3467 @ ( sK3_SY3278 @ SY3466 @ SV43 ) ) )
| ~ ( in @ ( sK3_SY3278 @ SY3466 @ SV43 ) @ ( sK2_B @ SV43 ) ) )
| ~ ( in @ SY3466 @ ( sK2_B @ SV43 ) ) )
| ~ ~ ( ~ ! [SY3468: $i,SY3469: $i] :
( ~ ( in @ SY3468 @ ( sK2_B @ SV43 ) )
| ~ ( subset @ SY3469 @ SY3468 )
| ( in @ SY3469 @ ( sK2_B @ SV43 ) ) )
| ~ ( in @ SV43 @ ( sK2_B @ SV43 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[920]) ).
thf(1037,plain,
! [SV116: $i] :
( ( ( ~ ( ~ ! [SY3692: $i,SY3693: $i] :
( ( sK49_B @ SV116 )
!= ( ordered_pair @ SY3692 @ SY3693 ) )
| ~ ( in @ ( sK49_B @ SV116 ) @ SV116 ) ) )
= $true )
| ( ( relation @ SV116 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[921]) ).
thf(1038,plain,
! [SV117: $i] :
( ( ( ~ ( relation @ SV117 ) )
= $true )
| ( ( ! [SY3694: $i] :
( ( SY3694
= ( ordered_pair @ ( sK47_C @ SY3694 @ SV117 ) @ ( sK48_SY3309 @ SY3694 @ SV117 ) ) )
| ~ ( in @ SY3694 @ SV117 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[922]) ).
thf(1039,plain,
! [SV93: $i,SV44: $i] :
( ( ! [SY3648: $i,SY3649: $i] :
( ~ ( in @ SV44 @ SY3648 )
| ~ ( in @ SV93 @ SY3649 )
| ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SY3648 @ SY3649 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[923]) ).
thf(1040,plain,
! [SV93: $i,SV44: $i] :
( ( ~ ( ~ ! [SY3650: $i] :
( ! [SY3651: $i] :
~ ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SY3650 @ SY3651 ) )
| ( in @ SV44 @ SY3650 ) )
| ~ ! [SY3652: $i,SY3653: $i] :
( ~ ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SY3652 @ SY3653 ) )
| ( in @ SV93 @ SY3653 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[924]) ).
thf(1041,plain,
! [SV45: $i] :
( ( ( ~ ! [SY3477: $i] :
( ~ ( ~ ( ! [SY3478: $i] :
~ ( in @ ( ordered_pair @ ( sK26_C @ SY3477 @ SV45 ) @ SY3478 ) @ SV45 )
| ~ ( in @ ( sK26_C @ SY3477 @ SV45 ) @ SY3477 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK26_C @ SY3477 @ SV45 ) @ ( sK27_SY3298 @ SY3477 @ SV45 ) ) @ SV45 )
| ( in @ ( sK26_C @ SY3477 @ SV45 ) @ SY3477 ) ) )
| ( SY3477
= ( relation_dom @ SV45 ) ) ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[925]) ).
thf(1042,plain,
! [SV45: $i] :
( ( ( ~ ! [SY3479: $i] :
( ( SY3479
!= ( relation_dom @ SV45 ) )
| ~ ( ~ ! [SY3480: $i] :
( ! [SY3481: $i] :
~ ( in @ ( ordered_pair @ SY3480 @ SY3481 ) @ SV45 )
| ( in @ SY3480 @ SY3479 ) )
| ~ ! [SY3482: $i] :
( ~ ( in @ SY3482 @ SY3479 )
| ( in @ ( ordered_pair @ SY3482 @ ( sK25_D @ SY3482 @ SY3479 @ SV45 ) ) @ SV45 ) ) ) ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[925]) ).
thf(1043,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[926]) ).
thf(1044,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[926]) ).
thf(1045,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[927]) ).
thf(1046,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[927]) ).
thf(1047,plain,
! [SV118: $i] :
( ( ( in @ ( sK42_B @ SV118 ) @ SV118 )
= $true )
| ( ( SV118 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[928]) ).
thf(1048,plain,
! [SV119: $i] :
( ( ( ( SV119 != empty_set ) )
= $true )
| ( ( ! [SY3695: $i] :
~ ( in @ SY3695 @ SV119 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[929]) ).
thf(1049,plain,
! [SV120: $i,SV157: $i] :
( ( ~ ( ~ ( ( ( sK43_C @ SV157 @ SV120 )
!= SV120 )
| ~ ( in @ ( sK43_C @ SV157 @ SV120 ) @ SV157 ) )
| ~ ( ( ( sK43_C @ SV157 @ SV120 )
= SV120 )
| ( in @ ( sK43_C @ SV157 @ SV120 ) @ SV157 ) ) )
| ( SV157
= ( singleton @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(1050,plain,
! [SV121: $i,SV158: $i] :
( ( ( SV158
!= ( singleton @ SV121 ) )
| ~ ( ~ ! [SY3744: $i] :
( ( SY3744 != SV121 )
| ( in @ SY3744 @ SV158 ) )
| ~ ! [SY3745: $i] :
( ~ ( in @ SY3745 @ SV158 )
| ( SY3745 = SV121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1051,plain,
! [SV122: $i,SV159: $i] :
( ( ~ ( function @ SV159 )
| ~ ( relation @ SV159 )
| ~ ( ~ ( in @ ( sK74_C @ SV159 @ SV122 ) @ SV122 )
| ~ ( ( ( apply @ SV159 @ ( sK74_C @ SV159 @ SV122 ) )
!= ( sK74_C @ SV159 @ SV122 ) ) ) )
| ( ( relation_dom @ SV159 )
!= SV122 )
| ( SV159
= ( identity_relation @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1052,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( ( apply @ SX1 @ SX2 )
= SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[933]) ).
thf(1053,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[933]) ).
thf(1054,plain,
! [SV46: $i] :
( ( ( relation @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( ~ ( one_to_one @ SV46 )
| ~ ( ~ ! [SY3483: $i] :
( ~ ( function @ SY3483 )
| ~ ( relation @ SY3483 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY3322 @ SY3483 @ SV46 )
= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ( ( sK70_C @ SY3483 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SY3483 @ SV46 )
= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SY3483 @ SV46 )
= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ( ( sK71_SY3322 @ SY3483 @ SV46 )
!= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK70_C @ SY3483 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK71_SY3322 @ SY3483 @ SV46 )
!= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY3483 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK70_C @ SY3483 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SY3483 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SY3483 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK71_SY3322 @ SY3483 @ SV46 )
!= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ( ( relation_dom @ SY3483 )
!= ( relation_rng @ SV46 ) )
| ( SY3483
= ( function_inverse @ SV46 ) ) )
| ~ ~ ( ~ ! [SY3484: $i] :
( ~ ( function @ SY3484 )
| ~ ( relation @ SY3484 )
| ( SY3484
!= ( function_inverse @ SV46 ) )
| ~ ( ~ ~ ( ~ ! [SY3485: $i,SY3486: $i] :
( ( SY3486
!= ( apply @ SY3484 @ SY3485 ) )
| ~ ( in @ SY3485 @ ( relation_rng @ SV46 ) )
| ( SY3485
= ( apply @ SV46 @ SY3486 ) ) )
| ~ ! [SY3487: $i,SY3488: $i] :
( ( SY3488
!= ( apply @ SY3484 @ SY3487 ) )
| ~ ( in @ SY3487 @ ( relation_rng @ SV46 ) )
| ( in @ SY3488 @ ( relation_dom @ SV46 ) ) ) )
| ~ ~ ( ~ ! [SY3489: $i,SY3490: $i] :
( ( SY3489
!= ( apply @ SV46 @ SY3490 ) )
| ~ ( in @ SY3490 @ ( relation_dom @ SV46 ) )
| ( SY3490
= ( apply @ SY3484 @ SY3489 ) ) )
| ~ ! [SY3491: $i] :
( ! [SY3492: $i] :
( ( SY3491
!= ( apply @ SV46 @ SY3492 ) )
| ~ ( in @ SY3492 @ ( relation_dom @ SV46 ) ) )
| ( in @ SY3491 @ ( relation_rng @ SV46 ) ) ) ) ) )
| ~ ! [SY3493: $i] :
( ~ ( function @ SY3493 )
| ~ ( relation @ SY3493 )
| ( SY3493
!= ( function_inverse @ SV46 ) )
| ( ( relation_dom @ SY3493 )
= ( relation_rng @ SV46 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[934]) ).
thf(1055,plain,
! [SV47: $i,SV123: $i] :
( ( ( ~ ( relation @ SV123 ) )
= $true )
| ( ( ~ ( ~ ! [SY3701: $i] :
( ~ ( relation @ SY3701 )
| ~ ( ~ ( ! [SY3702: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY3701 @ SV123 @ SV47 ) @ SY3702 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3702 @ ( sK9_SY3284 @ SY3701 @ SV123 @ SV47 ) ) @ SV123 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SY3701 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SY3701 @ SV123 @ SV47 ) ) @ SY3701 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY3701 @ SV123 @ SV47 ) @ ( sK10_SY3288 @ SY3701 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY3288 @ SY3701 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SY3701 @ SV123 @ SV47 ) ) @ SV123 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SY3701 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SY3701 @ SV123 @ SV47 ) ) @ SY3701 ) ) )
| ( SY3701
= ( relation_composition @ SV47 @ SV123 ) ) )
| ~ ! [SY3703: $i] :
( ~ ( relation @ SY3703 )
| ( SY3703
!= ( relation_composition @ SV47 @ SV123 ) )
| ~ ( ~ ! [SY3704: $i,SY3705: $i] :
( ! [SY3706: $i] :
( ~ ( in @ ( ordered_pair @ SY3704 @ SY3706 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3706 @ SY3705 ) @ SV123 ) )
| ( in @ ( ordered_pair @ SY3704 @ SY3705 ) @ SY3703 ) )
| ~ ! [SY3707: $i,SY3708: $i] :
( ~ ( in @ ( ordered_pair @ SY3707 @ SY3708 ) @ SY3703 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3707 @ ( sK7_F @ SY3708 @ SY3707 @ SY3703 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY3708 @ SY3707 @ SY3703 @ SV123 @ SV47 ) @ SY3708 ) @ SV123 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[935]) ).
thf(1056,plain,
! [SV160: $i,SV48: $i] :
( ( ! [SY3746: $i] :
( ~ ( in @ SV48 @ SY3746 )
| ~ ( in @ SV160 @ SY3746 )
| ( subset @ ( unordered_pair @ SV48 @ SV160 ) @ SY3746 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1057,plain,
! [SV48: $i] :
( ( ~ ! [SY3505: $i,SY3506: $i] :
( ~ ( subset @ ( unordered_pair @ SV48 @ SY3505 ) @ SY3506 )
| ( in @ SV48 @ SY3506 ) )
| ~ ! [SY3507: $i,SY3508: $i] :
( ~ ( subset @ ( unordered_pair @ SV48 @ SY3507 ) @ SY3508 )
| ( in @ SY3507 @ SY3508 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[937]) ).
thf(1058,plain,
! [SV94: $i,SV49: $i] :
( ( ! [SY3654: $i,SY3655: $i] :
( ~ ( relation @ SY3655 )
| ~ ( in @ SV49 @ SY3654 )
| ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ SY3655 )
| ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SY3654 ) @ SY3655 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[938]) ).
thf(1059,plain,
! [SV94: $i,SV49: $i] :
( ( ~ ( ~ ! [SY3656: $i,SY3657: $i] :
( ~ ( relation @ SY3657 )
| ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SY3656 ) @ SY3657 ) )
| ( in @ SV49 @ SY3656 ) )
| ~ ! [SY3658: $i,SY3659: $i] :
( ~ ( relation @ SY3659 )
| ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SY3658 ) @ SY3659 ) )
| ( in @ ( ordered_pair @ SV49 @ SV94 ) @ SY3659 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[939]) ).
thf(1060,plain,
! [SV50: $i,SV95: $i] :
( ( ( ~ ! [SY3660: $i] :
( ~ ( in @ SY3660 @ SV95 )
| ~ ( in @ SY3660 @ ( sK4_C @ SV95 @ SV50 ) ) ) )
= $false )
| ( ( ~ ( in @ SV50 @ SV95 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[940]) ).
thf(1061,plain,
! [SV50: $i,SV95: $i] :
( ( ( ~ ( in @ ( sK4_C @ SV95 @ SV50 ) @ SV95 ) )
= $false )
| ( ( ~ ( in @ SV50 @ SV95 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[940]) ).
thf(1062,plain,
! [SV124: $i] :
( ( ( ~ ( function @ SV124 )
| ~ ( relation @ SV124 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_B @ SV124 ) @ ( relation_dom @ SV124 ) )
| ~ ( in @ ( sK12_SY3289 @ SV124 ) @ ( relation_dom @ SV124 ) ) )
| ( ( apply @ SV124 @ ( sK11_B @ SV124 ) )
!= ( apply @ SV124 @ ( sK12_SY3289 @ SV124 ) ) ) )
| ~ ( ( ( sK11_B @ SV124 )
!= ( sK12_SY3289 @ SV124 ) ) ) )
| ( one_to_one @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[941]) ).
thf(1063,plain,
! [SV125: $i] :
( ( ( ~ ( function @ SV125 )
| ~ ( relation @ SV125 ) )
= $true )
| ( ( ~ ( one_to_one @ SV125 )
| ! [SY3709: $i,SY3710: $i] :
( ~ ( in @ SY3709 @ ( relation_dom @ SV125 ) )
| ~ ( in @ SY3710 @ ( relation_dom @ SV125 ) )
| ( ( apply @ SV125 @ SY3709 )
!= ( apply @ SV125 @ SY3710 ) )
| ( SY3709 = SY3710 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[942]) ).
thf(1064,plain,
! [SV51: $i,SV161: $i] :
( ( ! [SY3747: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK37_D @ SY3747 @ SV161 @ SV51 ) @ SY3747 )
| ~ ( in @ ( sK37_D @ SY3747 @ SV161 @ SV51 ) @ SV51 ) )
| ~ ( ~ ( in @ ( sK37_D @ SY3747 @ SV161 @ SV51 ) @ SY3747 )
| ~ ( in @ ( sK37_D @ SY3747 @ SV161 @ SV51 ) @ SV161 ) ) )
| ~ ( ( in @ ( sK37_D @ SY3747 @ SV161 @ SV51 ) @ SY3747 )
| ( in @ ( sK37_D @ SY3747 @ SV161 @ SV51 ) @ SV51 )
| ( in @ ( sK37_D @ SY3747 @ SV161 @ SV51 ) @ SV161 ) ) )
| ( SY3747
= ( set_union2 @ SV51 @ SV161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1065,plain,
! [SV162: $i,SV51: $i] :
( ( ! [SY3748: $i] :
( ( SY3748
!= ( set_union2 @ SV51 @ SV162 ) )
| ~ ( ~ ! [SY3749: $i] :
( ~ ( in @ SY3749 @ SY3748 )
| ( in @ SY3749 @ SV51 )
| ( in @ SY3749 @ SV162 ) )
| ~ ~ ( ~ ! [SY3523: $i] :
( ~ ( in @ SY3523 @ SV51 )
| ( in @ SY3523 @ SY3748 ) )
| ~ ! [SY3751: $i] :
( ~ ( in @ SY3751 @ SV162 )
| ( in @ SY3751 @ SY3748 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(1066,plain,
! [SV163: $i,SV126: $i] :
( ( ( ( set_difference @ SV126 @ ( singleton @ SV163 ) )
!= SV126 )
| ~ ( in @ SV163 @ SV126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1067,plain,
! [SV127: $i,SV164: $i] :
( ( ( in @ SV164 @ SV127 )
| ( ( set_difference @ SV127 @ ( singleton @ SV164 ) )
= SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(1068,plain,
! [SV52: $i] :
( ( ( ~ ! [SY3525: $i] :
( ~ ( relation @ SY3525 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK30_C @ SY3525 @ SV52 ) @ ( sK31_SY3299 @ SY3525 @ SV52 ) ) @ SV52 )
| ~ ~ ( in @ ( ordered_pair @ ( sK30_C @ SY3525 @ SV52 ) @ ( sK31_SY3299 @ SY3525 @ SV52 ) ) @ SY3525 ) )
| ( subset @ SV52 @ SY3525 ) ) )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[947]) ).
thf(1069,plain,
! [SV52: $i] :
( ( ( ~ ! [SY3526: $i] :
( ~ ( relation @ SY3526 )
| ~ ( subset @ SV52 @ SY3526 )
| ! [SY3527: $i,SY3528: $i] :
( ~ ( in @ ( ordered_pair @ SY3527 @ SY3528 ) @ SV52 )
| ( in @ ( ordered_pair @ SY3527 @ SY3528 ) @ SY3526 ) ) ) )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[947]) ).
thf(1070,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK46_SY3307 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK45_C @ SX1 @ SX0 ) @ ( sK46_SY3307 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK45_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK45_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK45_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[948]) ).
thf(1071,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK44_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK44_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[948]) ).
thf(1072,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[949]) ).
thf(1073,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[949]) ).
thf(1074,plain,
! [SV53: $i] :
( ( ( relation @ SV53 )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( ~ ( ~ ! [SY3529: $i,SY3530: $i] :
( ~ ( ~ ( ~ ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) ) @ SY3529 )
| ~ ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ SY3530 ) )
| ~ ~ ( ~ ( ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ SY3530 ) )
| ~ ( ( in @ ( apply @ SV53 @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) ) @ SY3529 )
| ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ SY3530 ) ) ) )
| ( SY3530
= ( relation_inverse_image @ SV53 @ SY3529 ) ) )
| ~ ! [SY3531: $i,SY3532: $i] :
( ( SY3532
!= ( relation_inverse_image @ SV53 @ SY3531 ) )
| ~ ( ~ ! [SY3533: $i] :
( ~ ( in @ SY3533 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SY3533 ) @ SY3531 )
| ( in @ SY3533 @ SY3532 ) )
| ~ ~ ( ~ ! [SY3534: $i] :
( ~ ( in @ SY3534 @ SY3532 )
| ( in @ SY3534 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY3535: $i] :
( ~ ( in @ SY3535 @ SY3532 )
| ( in @ ( apply @ SV53 @ SY3535 ) @ SY3531 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[950]) ).
thf(1075,plain,
! [SV54: $i,SV165: $i] :
( ( ! [SY3752: $i] :
( ~ ( ~ ( ~ ( in @ ( sK28_D @ SY3752 @ SV165 @ SV54 ) @ SV54 )
| ~ ( in @ ( sK28_D @ SY3752 @ SV165 @ SV54 ) @ SV165 )
| ~ ( in @ ( sK28_D @ SY3752 @ SV165 @ SV54 ) @ SY3752 ) )
| ~ ~ ( ~ ( ( in @ ( sK28_D @ SY3752 @ SV165 @ SV54 ) @ SV54 )
| ( in @ ( sK28_D @ SY3752 @ SV165 @ SV54 ) @ SY3752 ) )
| ~ ( ( in @ ( sK28_D @ SY3752 @ SV165 @ SV54 ) @ SV165 )
| ( in @ ( sK28_D @ SY3752 @ SV165 @ SV54 ) @ SY3752 ) ) ) )
| ( SY3752
= ( set_intersection2 @ SV54 @ SV165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1076,plain,
! [SV166: $i,SV54: $i] :
( ( ! [SY3753: $i] :
( ( SY3753
!= ( set_intersection2 @ SV54 @ SV166 ) )
| ~ ( ~ ! [SY3754: $i] :
( ~ ( in @ SY3754 @ SV54 )
| ~ ( in @ SY3754 @ SV166 )
| ( in @ SY3754 @ SY3753 ) )
| ~ ~ ( ~ ! [SY3541: $i] :
( ~ ( in @ SY3541 @ SY3753 )
| ( in @ SY3541 @ SV54 ) )
| ~ ! [SY3756: $i] :
( ~ ( in @ SY3756 @ SY3753 )
| ( in @ SY3756 @ SV166 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1077,plain,
! [SV167: $i,SV128: $i] :
( ( ~ ( in @ SV128 @ SV167 )
| ( subset @ ( singleton @ SV128 ) @ SV167 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1078,plain,
! [SV168: $i,SV129: $i] :
( ( ~ ( subset @ ( singleton @ SV129 ) @ SV168 )
| ( in @ SV129 @ SV168 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1079,plain,
! [SV55: $i,SV169: $i] :
( ( ! [SY3757: $i] :
( ~ ( ~ ( ~ ( in @ ( sK21_D @ SY3757 @ SV169 @ SV55 ) @ SV55 )
| ( in @ ( sK21_D @ SY3757 @ SV169 @ SV55 ) @ SV169 )
| ~ ( in @ ( sK21_D @ SY3757 @ SV169 @ SV55 ) @ SY3757 ) )
| ~ ~ ( ~ ( ( in @ ( sK21_D @ SY3757 @ SV169 @ SV55 ) @ SV55 )
| ( in @ ( sK21_D @ SY3757 @ SV169 @ SV55 ) @ SY3757 ) )
| ~ ( ~ ( in @ ( sK21_D @ SY3757 @ SV169 @ SV55 ) @ SV169 )
| ( in @ ( sK21_D @ SY3757 @ SV169 @ SV55 ) @ SY3757 ) ) ) )
| ( SY3757
= ( set_difference @ SV55 @ SV169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1080,plain,
! [SV170: $i,SV55: $i] :
( ( ! [SY3758: $i] :
( ( SY3758
!= ( set_difference @ SV55 @ SV170 ) )
| ~ ( ~ ! [SY3759: $i] :
( ~ ( in @ SY3759 @ SV55 )
| ( in @ SY3759 @ SV170 )
| ( in @ SY3759 @ SY3758 ) )
| ~ ~ ( ~ ! [SY3548: $i] :
( ~ ( in @ SY3548 @ SY3758 )
| ( in @ SY3548 @ SV55 ) )
| ~ ! [SY3761: $i] :
( ~ ( in @ SY3761 @ SY3758 )
| ~ ( in @ SY3761 @ SV170 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1081,plain,
! [SV56: $i] :
( ( ( relation @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( ~ ( ~ ! [SY3550: $i] :
( ~ ( ~ ( ! [SY3551: $i] :
( ( ( sK19_C @ SY3550 @ SV56 )
!= ( apply @ SV56 @ SY3551 ) )
| ~ ( in @ SY3551 @ ( relation_dom @ SV56 ) ) )
| ~ ( in @ ( sK19_C @ SY3550 @ SV56 ) @ SY3550 ) )
| ~ ( ~ ( ( ( sK19_C @ SY3550 @ SV56 )
!= ( apply @ SV56 @ ( sK20_SY3294 @ SY3550 @ SV56 ) ) )
| ~ ( in @ ( sK20_SY3294 @ SY3550 @ SV56 ) @ ( relation_dom @ SV56 ) ) )
| ( in @ ( sK19_C @ SY3550 @ SV56 ) @ SY3550 ) ) )
| ( SY3550
= ( relation_rng @ SV56 ) ) )
| ~ ! [SY3552: $i] :
( ( SY3552
!= ( relation_rng @ SV56 ) )
| ~ ( ~ ! [SY3553: $i] :
( ! [SY3554: $i] :
( ( SY3553
!= ( apply @ SV56 @ SY3554 ) )
| ~ ( in @ SY3554 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY3553 @ SY3552 ) )
| ~ ! [SY3555: $i] :
( ~ ( in @ SY3555 @ SY3552 )
| ~ ( ( SY3555
!= ( apply @ SV56 @ ( sK18_D @ SY3555 @ SY3552 @ SV56 ) ) )
| ~ ( in @ ( sK18_D @ SY3555 @ SY3552 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[957]) ).
thf(1082,plain,
! [SV57: $i,SV171: $i] :
( ( ! [SY3762: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK38_D @ SY3762 @ SV171 @ SV57 ) @ SY3762 )
| ( ( sK38_D @ SY3762 @ SV171 @ SV57 )
!= SV57 ) )
| ~ ( ~ ( in @ ( sK38_D @ SY3762 @ SV171 @ SV57 ) @ SY3762 )
| ( ( sK38_D @ SY3762 @ SV171 @ SV57 )
!= SV171 ) ) )
| ~ ( ( in @ ( sK38_D @ SY3762 @ SV171 @ SV57 ) @ SY3762 )
| ( ( sK38_D @ SY3762 @ SV171 @ SV57 )
= SV57 )
| ( ( sK38_D @ SY3762 @ SV171 @ SV57 )
= SV171 ) ) )
| ( SY3762
= ( unordered_pair @ SV57 @ SV171 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1083,plain,
! [SV172: $i,SV57: $i] :
( ( ! [SY3763: $i] :
( ( SY3763
!= ( unordered_pair @ SV57 @ SV172 ) )
| ~ ( ~ ! [SY3764: $i] :
( ~ ( in @ SY3764 @ SY3763 )
| ( SY3764 = SV57 )
| ( SY3764 = SV172 ) )
| ~ ~ ( ~ ! [SY3561: $i] :
( ( SY3561 != SV57 )
| ( in @ SY3561 @ SY3763 ) )
| ~ ! [SY3766: $i] :
( ( SY3766 != SV172 )
| ( in @ SY3766 @ SY3763 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1084,plain,
! [SV58: $i,SV96: $i] :
( ( ( function @ SV96 )
= $false )
| ( ( ~ ( relation @ SV96 ) )
= $true )
| ( ( ~ ( ~ ! [SY3661: $i] :
( ~ ( function @ SY3661 )
| ~ ( relation @ SY3661 )
| ~ ( ~ ( in @ ( sK67_D @ SY3661 @ SV96 @ SV58 ) @ ( relation_dom @ SV96 ) )
| ~ ( ( ( apply @ SV96 @ ( sK67_D @ SY3661 @ SV96 @ SV58 ) )
!= ( apply @ SY3661 @ ( sK67_D @ SY3661 @ SV96 @ SV58 ) ) ) ) )
| ( ( relation_dom @ SV96 )
!= ( set_intersection2 @ ( relation_dom @ SY3661 ) @ SV58 ) )
| ( SV96
= ( relation_dom_restriction @ SY3661 @ SV58 ) ) )
| ~ ~ ( ~ ! [SY3662: $i] :
( ~ ( function @ SY3662 )
| ~ ( relation @ SY3662 )
| ( SV96
!= ( relation_dom_restriction @ SY3662 @ SV58 ) )
| ! [SY3663: $i] :
( ~ ( in @ SY3663 @ ( relation_dom @ SV96 ) )
| ( ( apply @ SV96 @ SY3663 )
= ( apply @ SY3662 @ SY3663 ) ) ) )
| ~ ! [SY3664: $i] :
( ~ ( function @ SY3664 )
| ~ ( relation @ SY3664 )
| ( SV96
!= ( relation_dom_restriction @ SY3664 @ SV58 ) )
| ( ( relation_dom @ SV96 )
= ( set_intersection2 @ ( relation_dom @ SY3664 ) @ SV58 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[960]) ).
thf(1085,plain,
! [SV59: $i] :
( ( ( ~ ! [SY3568: $i] :
( ~ ( relation @ SY3568 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_C @ SY3568 @ SV59 ) @ ( sK40_SY3306 @ SY3568 @ SV59 ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK39_C @ SY3568 @ SV59 ) @ ( sK40_SY3306 @ SY3568 @ SV59 ) ) @ SY3568 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK39_C @ SY3568 @ SV59 ) @ ( sK40_SY3306 @ SY3568 @ SV59 ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK39_C @ SY3568 @ SV59 ) @ ( sK40_SY3306 @ SY3568 @ SV59 ) ) @ SY3568 ) ) )
| ( SV59 = SY3568 ) ) )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[961]) ).
thf(1086,plain,
! [SV59: $i] :
( ( ( ~ ! [SY3569: $i] :
( ~ ( relation @ SY3569 )
| ( SV59 != SY3569 )
| ~ ( ~ ! [SY3570: $i,SY3571: $i] :
( ~ ( in @ ( ordered_pair @ SY3570 @ SY3571 ) @ SV59 )
| ( in @ ( ordered_pair @ SY3570 @ SY3571 ) @ SY3569 ) )
| ~ ! [SY3572: $i,SY3573: $i] :
( ~ ( in @ ( ordered_pair @ SY3572 @ SY3573 ) @ SY3569 )
| ( in @ ( ordered_pair @ SY3572 @ SY3573 ) @ SV59 ) ) ) ) )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[961]) ).
thf(1087,plain,
! [SV60: $i,SV97: $i] :
( ( ( ~ ( in @ ( sK78_C @ SV97 @ SV60 ) @ SV60 ) )
= $false )
| ( ( element @ SV60 @ ( powerset @ SV97 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[962]) ).
thf(1088,plain,
! [SV60: $i,SV97: $i] :
( ( ( ~ ~ ( in @ ( sK78_C @ SV97 @ SV60 ) @ SV97 ) )
= $false )
| ( ( element @ SV60 @ ( powerset @ SV97 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[962]) ).
thf(1089,plain,
! [SV130: $i,SV173: $i] :
( ( ~ ( ~ ( ! [SY3767: $i] :
( ~ ( in @ ( sK23_C @ SV173 @ SV130 ) @ SY3767 )
| ~ ( in @ SY3767 @ SV130 ) )
| ~ ( in @ ( sK23_C @ SV173 @ SV130 ) @ SV173 ) )
| ~ ( ~ ( ~ ( in @ ( sK23_C @ SV173 @ SV130 ) @ ( sK24_SY3296 @ SV173 @ SV130 ) )
| ~ ( in @ ( sK24_SY3296 @ SV173 @ SV130 ) @ SV130 ) )
| ( in @ ( sK23_C @ SV173 @ SV130 ) @ SV173 ) ) )
| ( SV173
= ( union @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[963]) ).
thf(1090,plain,
! [SV131: $i,SV174: $i] :
( ( ( SV174
!= ( union @ SV131 ) )
| ~ ( ~ ! [SY3768: $i] :
( ! [SY3719: $i] :
( ~ ( in @ SY3768 @ SY3719 )
| ~ ( in @ SY3719 @ SV131 ) )
| ( in @ SY3768 @ SV174 ) )
| ~ ! [SY3770: $i] :
( ~ ( in @ SY3770 @ SV174 )
| ~ ( ~ ( in @ SY3770 @ ( sK22_D @ SY3770 @ SV174 @ SV131 ) )
| ~ ( in @ ( sK22_D @ SY3770 @ SV174 @ SV131 ) @ SV131 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1091,plain,
! [SV98: $i,SV61: $i] :
( ( ! [SY3665: $i,SY3666: $i] :
( ~ ( in @ SV61 @ SY3665 )
| ~ ( in @ SV98 @ SY3666 )
| ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SY3665 @ SY3666 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[965]) ).
thf(1092,plain,
! [SV98: $i,SV61: $i] :
( ( ~ ( ~ ! [SY3667: $i] :
( ! [SY3668: $i] :
~ ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SY3667 @ SY3668 ) )
| ( in @ SV61 @ SY3667 ) )
| ~ ! [SY3669: $i,SY3670: $i] :
( ~ ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SY3669 @ SY3670 ) )
| ( in @ SV98 @ SY3670 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[966]) ).
thf(1093,plain,
! [SV62: $i,SV175: $i] :
( ( ! [SY3771: $i] :
( ~ ( function @ SY3771 )
| ~ ( relation @ SY3771 )
| ~ ( in @ SV175 @ ( relation_dom @ SY3771 ) )
| ~ ( in @ SV175 @ SV62 )
| ( in @ SV175 @ ( relation_dom @ ( relation_dom_restriction @ SY3771 @ SV62 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1094,plain,
! [SV62: $i] :
( ( ~ ! [SY3584: $i,SY3585: $i] :
( ~ ( function @ SY3585 )
| ~ ( relation @ SY3585 )
| ~ ( in @ SY3584 @ ( relation_dom @ ( relation_dom_restriction @ SY3585 @ SV62 ) ) )
| ( in @ SY3584 @ ( relation_dom @ SY3585 ) ) )
| ~ ! [SY3586: $i,SY3587: $i] :
( ~ ( function @ SY3587 )
| ~ ( relation @ SY3587 )
| ~ ( in @ SY3586 @ ( relation_dom @ ( relation_dom_restriction @ SY3587 @ SV62 ) ) )
| ( in @ SY3586 @ SV62 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[968]) ).
thf(1095,plain,
! [SV176: $i,SV63: $i] :
( ( ! [SY3772: $i] :
( ~ ( ~ ( ! [SY3773: $i,SY3774: $i] :
( ~ ( in @ SY3773 @ SV63 )
| ~ ( in @ SY3774 @ SV176 )
| ( ( sK34_D @ SY3772 @ SV176 @ SV63 )
!= ( ordered_pair @ SY3773 @ SY3774 ) ) )
| ~ ( in @ ( sK34_D @ SY3772 @ SV176 @ SV63 ) @ SY3772 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK35_SY3303 @ SY3772 @ SV176 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK36_SY3305 @ SY3772 @ SV176 @ SV63 ) @ SV176 ) )
| ( ( sK34_D @ SY3772 @ SV176 @ SV63 )
!= ( ordered_pair @ ( sK35_SY3303 @ SY3772 @ SV176 @ SV63 ) @ ( sK36_SY3305 @ SY3772 @ SV176 @ SV63 ) ) ) )
| ( in @ ( sK34_D @ SY3772 @ SV176 @ SV63 ) @ SY3772 ) ) )
| ( SY3772
= ( cartesian_product2 @ SV63 @ SV176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1096,plain,
! [SV177: $i,SV63: $i] :
( ( ! [SY3775: $i] :
( ( SY3775
!= ( cartesian_product2 @ SV63 @ SV177 ) )
| ~ ( ~ ! [SY3776: $i] :
( ! [SY3777: $i,SY3778: $i] :
( ~ ( in @ SY3777 @ SV63 )
| ~ ( in @ SY3778 @ SV177 )
| ( SY3776
!= ( ordered_pair @ SY3777 @ SY3778 ) ) )
| ( in @ SY3776 @ SY3775 ) )
| ~ ! [SY3779: $i] :
( ~ ( in @ SY3779 @ SY3775 )
| ~ ( ~ ~ ( ~ ( in @ ( sK32_E @ SY3779 @ SY3775 @ SV177 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK33_SY3300 @ SY3779 @ SY3775 @ SV177 @ SV63 ) @ SV177 ) )
| ( SY3779
!= ( ordered_pair @ ( sK32_E @ SY3779 @ SY3775 @ SV177 @ SV63 ) @ ( sK33_SY3300 @ SY3779 @ SY3775 @ SV177 @ SV63 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1097,plain,
! [SV178: $i,SV132: $i] :
( ( ( disjoint @ SV132 @ SV178 )
| ~ ( ~ ( in @ ( sK73_C @ SV178 @ SV132 ) @ SV132 )
| ~ ( in @ ( sK73_C @ SV178 @ SV132 ) @ SV178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1098,plain,
! [SV179: $i,SV133: $i] :
( ( ! [SY3780: $i] :
( ~ ( in @ SY3780 @ SV133 )
| ~ ( in @ SY3780 @ SV179 ) )
| ~ ( disjoint @ SV133 @ SV179 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1099,plain,
! [SV180: $i,SV64: $i] :
( ( ! [SY3781: $i] :
( ~ ( relation @ SY3781 )
| ! [SY3782: $i] :
( ~ ( in @ SY3782 @ ( relation_dom @ SY3781 ) )
| ~ ( in @ ( ordered_pair @ SY3782 @ SV64 ) @ SY3781 )
| ~ ( in @ SY3782 @ SV180 ) )
| ( in @ SV64 @ ( relation_image @ SY3781 @ SV180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1100,plain,
! [SV181: $i,SV64: $i] :
( ( ! [SY3783: $i] :
( ~ ( relation @ SY3783 )
| ~ ( in @ SV64 @ ( relation_image @ SY3783 @ SV181 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK76_D @ SY3783 @ SV181 @ SV64 ) @ ( relation_dom @ SY3783 ) )
| ~ ( in @ ( ordered_pair @ ( sK76_D @ SY3783 @ SV181 @ SV64 ) @ SV64 ) @ SY3783 ) )
| ~ ( in @ ( sK76_D @ SY3783 @ SV181 @ SV64 ) @ SV181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1101,plain,
! [SV182: $i,SV65: $i] :
( ( ! [SY3784: $i] :
( ~ ( relation @ SY3784 )
| ~ ( in @ ( ordered_pair @ SV65 @ SV182 ) @ SY3784 )
| ( in @ SV65 @ ( relation_dom @ SY3784 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1102,plain,
! [SV183: $i,SV65: $i] :
( ( ! [SY3785: $i] :
( ~ ( relation @ SY3785 )
| ~ ( in @ ( ordered_pair @ SV65 @ SV183 ) @ SY3785 )
| ( in @ SV183 @ ( relation_rng @ SY3785 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1103,plain,
! [SV66: $i] :
( ( ( relation @ SV66 )
= $false )
| ( ( function @ SV66 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY3607: $i] :
( ~ ( in @ SY3607 @ ( relation_dom @ SV66 ) )
| ! [SY3608: $i] :
( ( SY3608
!= ( apply @ SV66 @ SY3607 ) )
| ( in @ ( ordered_pair @ SY3607 @ SY3608 ) @ SV66 ) ) )
| ~ ! [SY3609: $i] :
( ~ ( in @ SY3609 @ ( relation_dom @ SV66 ) )
| ! [SY3610: $i] :
( ~ ( in @ ( ordered_pair @ SY3609 @ SY3610 ) @ SV66 )
| ( SY3610
= ( apply @ SV66 @ SY3609 ) ) ) ) )
| ~ ~ ( ~ ! [SY3611: $i] :
( ( in @ SY3611 @ ( relation_dom @ SV66 ) )
| ! [SY3612: $i] :
( ( SY3612
!= ( apply @ SV66 @ SY3611 ) )
| ( SY3612 = empty_set ) ) )
| ~ ! [SY3613: $i] :
( ( in @ SY3613 @ ( relation_dom @ SV66 ) )
| ! [SY3614: $i] :
( ( SY3614 != empty_set )
| ( SY3614
= ( apply @ SV66 @ SY3613 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[977]) ).
thf(1104,plain,
! [SV184: $i,SV134: $i] :
( ( ~ ( in @ SV134 @ SV184 )
| ( subset @ ( singleton @ SV134 ) @ SV184 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1105,plain,
! [SV185: $i,SV135: $i] :
( ( ~ ( subset @ ( singleton @ SV135 ) @ SV185 )
| ( in @ SV135 @ SV185 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1106,plain,
! [SV4: $i,SV70: $i,SV136: $i] :
( ( ( ~ ( in @ SV136 @ SV70 ) )
= $true )
| ( ( in @ SV136 @ SV4 )
= $true )
| ( ( element @ SV70 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[981]) ).
thf(1107,plain,
! [SV71: $i,SV5: $i,SV137: $i] :
( ( ( in @ SV137 @ SV5 )
= $true )
| ( ( subset @ SV5 @ ( set_difference @ SV71 @ ( singleton @ SV137 ) ) )
= $true )
| ( ( subset @ SV5 @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[982]) ).
thf(1108,plain,
! [SV7: $i,SV73: $i] :
( ( ( relation @ SV73 )
= $false )
| ( ( function @ SV73 )
= $false )
| ( ( ! [SY3617: $i] :
( ~ ( function @ SY3617 )
| ~ ( relation @ SY3617 )
| ~ ( in @ SV7 @ ( relation_dom @ ( relation_composition @ SY3617 @ SV73 ) ) )
| ( ( apply @ ( relation_composition @ SY3617 @ SV73 ) @ SV7 )
= ( apply @ SV73 @ ( apply @ SY3617 @ SV7 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[983]) ).
thf(1109,plain,
! [SV8: $i,SV74: $i] :
( ( ( relation @ SV74 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( ! [SY3618: $i] :
( ~ ( function @ SY3618 )
| ~ ( relation @ SY3618 )
| ~ ( in @ SV8 @ ( relation_dom @ SV74 ) )
| ( ( apply @ ( relation_composition @ SV74 @ SY3618 ) @ SV8 )
= ( apply @ SY3618 @ ( apply @ SV74 @ SV8 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[984]) ).
thf(1110,plain,
! [SV99: $i,SV76: $i,SV10: $i] :
( ( ( in @ SV10 @ SV76 )
= $false )
| ( ( ~ ( in @ SV76 @ SV99 ) )
= $true )
| ( ( ~ ( in @ SV99 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[985]) ).
thf(1111,plain,
! [SV100: $i,SV12: $i,SV186: $i] :
( ( ( ~ ( element @ SV186 @ SV12 )
| ( in @ SV186 @ SV100 )
| ( in @ SV186 @ ( subset_complement @ SV12 @ SV100 ) ) )
= $true )
| ( ( element @ SV100 @ ( powerset @ SV12 ) )
= $false )
| ( ( SV12 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1112,plain,
! [SV101: $i,SV13: $i,SV78: $i] :
( ( ( ~ ( in @ SV78 @ ( subset_complement @ SV13 @ SV101 ) ) )
= $true )
| ( ( ~ ( in @ SV78 @ SV101 ) )
= $true )
| ( ( element @ SV101 @ ( powerset @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[987]) ).
thf(1113,plain,
! [SV15: $i,SV79: $i,SV102: $i] :
( ( ( function @ SV102 )
= $false )
| ( ( ~ ( relation @ SV102 ) )
= $true )
| ( ( ~ ( in @ SV79 @ ( relation_dom @ ( relation_dom_restriction @ SV102 @ SV15 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SV102 @ SV15 ) @ SV79 )
= ( apply @ SV102 @ SV79 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[988]) ).
thf(1114,plain,
! [SV16: $i,SV80: $i,SV103: $i] :
( ( ( function @ SV103 )
= $false )
| ( ( ~ ( relation @ SV103 ) )
= $true )
| ( ( ~ ( in @ SV80 @ SV16 )
| ( ( apply @ ( relation_dom_restriction @ SV103 @ SV16 ) @ SV80 )
= ( apply @ SV103 @ SV80 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(1115,plain,
! [SV23: $i,SV104: $i,SV85: $i] :
( ( ( element @ SV85 @ ( powerset @ SV104 ) )
= $false )
| ( ( ~ ( in @ SV23 @ SV85 ) )
= $true )
| ( ( element @ SV23 @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[992]) ).
thf(1116,plain,
! [SV24: $i,SV105: $i,SV86: $i] :
( ( ( element @ SV86 @ ( powerset @ SV105 ) )
= $false )
| ( ( ~ ( in @ SV24 @ SV86 ) )
= $true )
| ( ( ~ ( empty @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[993]) ).
thf(1117,plain,
! [SV138: $i,SV106: $i] :
( ( ( disjoint @ SV106 @ SV138 )
= $true )
| ( ( in @ ( sK72_C @ SV138 @ SV106 ) @ ( set_intersection2 @ SV106 @ SV138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[995]) ).
thf(1118,plain,
! [SV139: $i,SV107: $i] :
( ( ( ! [SY3726: $i] :
~ ( in @ SY3726 @ ( set_intersection2 @ SV107 @ SV139 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV107 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[996]) ).
thf(1119,plain,
! [SV26: $i,SV88: $i] :
( ( ( ~ ! [SY3625: $i] :
( ~ ( relation @ SY3625 )
| ~ ( ~ ( ~ ( in @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) @ SV26 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY3625 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) ) @ SV88 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY3625 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) ) @ SY3625 ) )
| ~ ~ ( ~ ( ( in @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) @ SV26 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY3625 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) ) @ SY3625 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SY3625 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) ) @ SV88 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY3625 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) ) @ SY3625 ) ) ) )
| ( SY3625
= ( relation_rng_restriction @ SV26 @ SV88 ) ) ) )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[997]) ).
thf(1120,plain,
! [SV88: $i,SV26: $i] :
( ( ( ~ ! [SY3626: $i] :
( ~ ( relation @ SY3626 )
| ( SY3626
!= ( relation_rng_restriction @ SV26 @ SV88 ) )
| ~ ( ~ ! [SY3627: $i,SY3628: $i] :
( ~ ( in @ SY3628 @ SV26 )
| ~ ( in @ ( ordered_pair @ SY3627 @ SY3628 ) @ SV88 )
| ( in @ ( ordered_pair @ SY3627 @ SY3628 ) @ SY3626 ) )
| ~ ~ ( ~ ! [SY3365: $i,SY3366: $i] :
( ~ ( in @ ( ordered_pair @ SY3365 @ SY3366 ) @ SY3626 )
| ( in @ SY3366 @ SV26 ) )
| ~ ! [SY3631: $i,SY3632: $i] :
( ~ ( in @ ( ordered_pair @ SY3631 @ SY3632 ) @ SY3626 )
| ( in @ ( ordered_pair @ SY3631 @ SY3632 ) @ SV88 ) ) ) ) ) )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[997]) ).
thf(1121,plain,
! [SV108: $i,SV140: $i] :
( ( ( ~ ( ~ ( in @ ( sK29_C @ SV140 @ SV108 ) @ SV108 )
| ~ ~ ( in @ ( sK29_C @ SV140 @ SV108 ) @ SV140 ) ) )
= $true )
| ( ( subset @ SV108 @ SV140 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[998]) ).
thf(1122,plain,
! [SV141: $i,SV109: $i] :
( ( ( ~ ( subset @ SV109 @ SV141 ) )
= $true )
| ( ( ! [SY3727: $i] :
( ~ ( in @ SY3727 @ SV109 )
| ( in @ SY3727 @ SV141 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[999]) ).
thf(1123,plain,
! [SV142: $i,SV27: $i,SV187: $i] :
( ( ~ ( relation @ SV187 )
| ~ ( in @ SV27 @ SV142 )
| ~ ( in @ SV27 @ ( relation_dom @ SV187 ) )
| ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SV187 @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1124,plain,
! [SV27: $i] :
( ( ~ ! [SY3371: $i,SY3372: $i] :
( ~ ( relation @ SY3372 )
| ~ ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SY3372 @ SY3371 ) ) )
| ( in @ SV27 @ SY3371 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1001]) ).
thf(1125,plain,
! [SV27: $i] :
( ( ~ ! [SY3373: $i,SY3374: $i] :
( ~ ( relation @ SY3374 )
| ~ ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SY3374 @ SY3373 ) ) )
| ( in @ SV27 @ ( relation_dom @ SY3374 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1001]) ).
thf(1126,plain,
! [SV28: $i] :
( ( ( ! [SY3375: $i] :
( ~ ( relation @ SY3375 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SY3375 @ SV28 ) @ ( sK14_SY3290 @ SY3375 @ SV28 ) ) @ SY3375 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY3290 @ SY3375 @ SV28 ) @ ( sK13_C @ SY3375 @ SV28 ) ) @ SV28 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SY3375 @ SV28 ) @ ( sK14_SY3290 @ SY3375 @ SV28 ) ) @ SY3375 )
| ( in @ ( ordered_pair @ ( sK14_SY3290 @ SY3375 @ SV28 ) @ ( sK13_C @ SY3375 @ SV28 ) ) @ SV28 ) ) )
| ( SY3375
= ( relation_inverse @ SV28 ) ) ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1002]) ).
thf(1127,plain,
! [SV28: $i] :
( ( ( ! [SY3376: $i] :
( ~ ( relation @ SY3376 )
| ( SY3376
!= ( relation_inverse @ SV28 ) )
| ~ ( ~ ! [SY3377: $i,SY3378: $i] :
( ~ ( in @ ( ordered_pair @ SY3377 @ SY3378 ) @ SY3376 )
| ( in @ ( ordered_pair @ SY3378 @ SY3377 ) @ SV28 ) )
| ~ ! [SY3379: $i,SY3380: $i] :
( ~ ( in @ ( ordered_pair @ SY3380 @ SY3379 ) @ SV28 )
| ( in @ ( ordered_pair @ SY3379 @ SY3380 ) @ SY3376 ) ) ) ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1003]) ).
thf(1128,plain,
! [SV29: $i] :
( ( ( ~ ! [SY3381: $i,SY3382: $i] :
( ~ ( ~ ( ! [SY3383: $i] :
( ~ ( in @ SY3383 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3383 @ SY3381 )
| ( ( sK61_D @ SY3382 @ SY3381 @ SV29 )
!= ( apply @ SV29 @ SY3383 ) ) )
| ~ ( in @ ( sK61_D @ SY3382 @ SY3381 @ SV29 ) @ SY3382 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY3318 @ SY3382 @ SY3381 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK62_SY3318 @ SY3382 @ SY3381 @ SV29 ) @ SY3381 ) )
| ( ( sK61_D @ SY3382 @ SY3381 @ SV29 )
!= ( apply @ SV29 @ ( sK62_SY3318 @ SY3382 @ SY3381 @ SV29 ) ) ) )
| ( in @ ( sK61_D @ SY3382 @ SY3381 @ SV29 ) @ SY3382 ) ) )
| ( SY3382
= ( relation_image @ SV29 @ SY3381 ) ) )
| ~ ! [SY3384: $i,SY3385: $i] :
( ( SY3385
!= ( relation_image @ SV29 @ SY3384 ) )
| ~ ( ~ ! [SY3386: $i] :
( ! [SY3387: $i] :
( ~ ( in @ SY3387 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3387 @ SY3384 )
| ( SY3386
!= ( apply @ SV29 @ SY3387 ) ) )
| ( in @ SY3386 @ SY3385 ) )
| ~ ! [SY3388: $i] :
( ~ ( in @ SY3388 @ SY3385 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SY3388 @ SY3385 @ SY3384 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK60_E @ SY3388 @ SY3385 @ SY3384 @ SV29 ) @ SY3384 ) )
| ( SY3388
!= ( apply @ SV29 @ ( sK60_E @ SY3388 @ SY3385 @ SY3384 @ SV29 ) ) ) ) ) ) ) )
= $false )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1004]) ).
thf(1129,plain,
! [SV30: $i] :
( ( ( ! [SY3389: $i,SY3390: $i] :
( ~ ( ~ ( ! [SY3391: $i] :
( ~ ( in @ ( ordered_pair @ SY3391 @ ( sK55_D @ SY3390 @ SY3389 @ SV30 ) ) @ SV30 )
| ~ ( in @ SY3391 @ SY3389 ) )
| ~ ( in @ ( sK55_D @ SY3390 @ SY3389 @ SV30 ) @ SY3390 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_SY3315 @ SY3390 @ SY3389 @ SV30 ) @ ( sK55_D @ SY3390 @ SY3389 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK56_SY3315 @ SY3390 @ SY3389 @ SV30 ) @ SY3389 ) )
| ( in @ ( sK55_D @ SY3390 @ SY3389 @ SV30 ) @ SY3390 ) ) )
| ( SY3390
= ( relation_image @ SV30 @ SY3389 ) ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1005]) ).
thf(1130,plain,
! [SV30: $i] :
( ( ( ! [SY3392: $i,SY3393: $i] :
( ( SY3393
!= ( relation_image @ SV30 @ SY3392 ) )
| ~ ( ~ ! [SY3394: $i] :
( ! [SY3395: $i] :
( ~ ( in @ ( ordered_pair @ SY3395 @ SY3394 ) @ SV30 )
| ~ ( in @ SY3395 @ SY3392 ) )
| ( in @ SY3394 @ SY3393 ) )
| ~ ! [SY3396: $i] :
( ~ ( in @ SY3396 @ SY3393 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SY3396 @ SY3393 @ SY3392 @ SV30 ) @ SY3396 ) @ SV30 )
| ~ ( in @ ( sK54_E @ SY3396 @ SY3393 @ SY3392 @ SV30 ) @ SY3392 ) ) ) ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1006]) ).
thf(1131,plain,
! [SV31: $i] :
( ( ( ! [SY3397: $i,SY3398: $i] :
( ~ ( ~ ( ! [SY3399: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ SY3398 @ SY3397 @ SV31 ) @ SY3399 ) @ SV31 )
| ~ ( in @ SY3399 @ SY3397 ) )
| ~ ( in @ ( sK52_D @ SY3398 @ SY3397 @ SV31 ) @ SY3398 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SY3398 @ SY3397 @ SV31 ) @ ( sK53_SY3313 @ SY3398 @ SY3397 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( sK53_SY3313 @ SY3398 @ SY3397 @ SV31 ) @ SY3397 ) )
| ( in @ ( sK52_D @ SY3398 @ SY3397 @ SV31 ) @ SY3398 ) ) )
| ( SY3398
= ( relation_inverse_image @ SV31 @ SY3397 ) ) ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1007]) ).
thf(1132,plain,
! [SV31: $i] :
( ( ( ! [SY3400: $i,SY3401: $i] :
( ( SY3401
!= ( relation_inverse_image @ SV31 @ SY3400 ) )
| ~ ( ~ ! [SY3402: $i] :
( ! [SY3403: $i] :
( ~ ( in @ ( ordered_pair @ SY3402 @ SY3403 ) @ SV31 )
| ~ ( in @ SY3403 @ SY3400 ) )
| ( in @ SY3402 @ SY3401 ) )
| ~ ! [SY3404: $i] :
( ~ ( in @ SY3404 @ SY3401 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3404 @ ( sK51_E @ SY3404 @ SY3401 @ SY3400 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( sK51_E @ SY3404 @ SY3401 @ SY3400 @ SV31 ) @ SY3400 ) ) ) ) ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1008]) ).
thf(1133,plain,
! [SV32: $i] :
( ( ( ! [SY3405: $i,SY3406: $i] :
( ~ ( relation @ SY3406 )
| ~ ( ~ ( ~ ( in @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ SY3405 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ ( sK64_SY3319 @ SY3406 @ SY3405 @ SV32 ) ) @ SV32 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ ( sK64_SY3319 @ SY3406 @ SY3405 @ SV32 ) ) @ SY3406 ) )
| ~ ~ ( ~ ( ( in @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ SY3405 )
| ( in @ ( ordered_pair @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ ( sK64_SY3319 @ SY3406 @ SY3405 @ SV32 ) ) @ SY3406 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ ( sK64_SY3319 @ SY3406 @ SY3405 @ SV32 ) ) @ SV32 )
| ( in @ ( ordered_pair @ ( sK63_D @ SY3406 @ SY3405 @ SV32 ) @ ( sK64_SY3319 @ SY3406 @ SY3405 @ SV32 ) ) @ SY3406 ) ) ) )
| ( SY3406
= ( relation_dom_restriction @ SV32 @ SY3405 ) ) ) )
= $true )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1009]) ).
thf(1134,plain,
! [SV32: $i] :
( ( ( ! [SY3407: $i,SY3408: $i] :
( ~ ( relation @ SY3408 )
| ( SY3408
!= ( relation_dom_restriction @ SV32 @ SY3407 ) )
| ~ ( ~ ! [SY3409: $i,SY3410: $i] :
( ~ ( in @ SY3409 @ SY3407 )
| ~ ( in @ ( ordered_pair @ SY3409 @ SY3410 ) @ SV32 )
| ( in @ ( ordered_pair @ SY3409 @ SY3410 ) @ SY3408 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3408 )
| ( in @ SX3 @ SY3407 ) )
| ~ ! [SY3413: $i,SY3414: $i] :
( ~ ( in @ ( ordered_pair @ SY3413 @ SY3414 ) @ SY3408 )
| ( in @ ( ordered_pair @ SY3413 @ SY3414 ) @ SV32 ) ) ) ) ) )
= $true )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1010]) ).
thf(1135,plain,
! [SV143: $i,SV33: $i,SV188: $i] :
( ( ~ ( relation @ SV188 )
| ! [SY3786: $i] :
( ~ ( in @ SY3786 @ ( relation_rng @ SV188 ) )
| ~ ( in @ ( ordered_pair @ SV33 @ SY3786 ) @ SV188 )
| ~ ( in @ SY3786 @ SV143 ) )
| ( in @ SV33 @ ( relation_inverse_image @ SV188 @ SV143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1136,plain,
! [SV144: $i,SV33: $i,SV189: $i] :
( ( ~ ( relation @ SV189 )
| ~ ( in @ SV33 @ ( relation_inverse_image @ SV189 @ SV144 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK75_D @ SV189 @ SV144 @ SV33 ) @ ( relation_rng @ SV189 ) )
| ~ ( in @ ( ordered_pair @ SV33 @ ( sK75_D @ SV189 @ SV144 @ SV33 ) ) @ SV189 ) )
| ~ ( in @ ( sK75_D @ SV189 @ SV144 @ SV33 ) @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1137,plain,
! [SV110: $i,SV145: $i] :
( ( ( ~ ( relation @ SV145 ) )
= $true )
| ( ( ~ ( ~ ( ( ( sK65_C @ SV145 @ SV110 )
!= ( sK66_SY3320 @ SV145 @ SV110 ) )
| ~ ( in @ ( sK65_C @ SV145 @ SV110 ) @ SV110 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 ) )
| ~ ~ ( ~ ( ( ( sK65_C @ SV145 @ SV110 )
= ( sK66_SY3320 @ SV145 @ SV110 ) )
| ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 ) )
| ~ ( ( in @ ( sK65_C @ SV145 @ SV110 ) @ SV110 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 ) ) ) )
| ( SV145
= ( identity_relation @ SV110 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1013]) ).
thf(1138,plain,
! [SV111: $i,SV146: $i] :
( ( ( ~ ( relation @ SV146 ) )
= $true )
| ( ( ( SV146
!= ( identity_relation @ SV111 ) )
| ~ ( ~ ! [SY3732: $i,SY3733: $i] :
( ( SY3732 != SY3733 )
| ~ ( in @ SY3732 @ SV111 )
| ( in @ ( ordered_pair @ SY3732 @ SY3733 ) @ SV146 ) )
| ~ ~ ( ~ ! [SY3734: $i,SY3735: $i] :
( ~ ( in @ ( ordered_pair @ SY3734 @ SY3735 ) @ SV146 )
| ( SY3734 = SY3735 ) )
| ~ ! [SY3736: $i] :
( ! [SY3737: $i] :
~ ( in @ ( ordered_pair @ SY3736 @ SY3737 ) @ SV146 )
| ( in @ SY3736 @ SV111 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1014]) ).
thf(1139,plain,
! [SV34: $i,SV89: $i,SV190: $i] :
( ( ! [SY3787: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK50_E @ SY3787 @ SV190 @ SV89 @ SV34 ) @ SY3787 )
| ( ( sK50_E @ SY3787 @ SV190 @ SV89 @ SV34 )
!= SV190 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK50_E @ SY3787 @ SV190 @ SV89 @ SV34 ) @ SY3787 )
| ( ( sK50_E @ SY3787 @ SV190 @ SV89 @ SV34 )
!= SV34 ) )
| ~ ( ~ ( in @ ( sK50_E @ SY3787 @ SV190 @ SV89 @ SV34 ) @ SY3787 )
| ( ( sK50_E @ SY3787 @ SV190 @ SV89 @ SV34 )
!= SV89 ) ) ) )
| ~ ( ( in @ ( sK50_E @ SY3787 @ SV190 @ SV89 @ SV34 ) @ SY3787 )
| ( ( sK50_E @ SY3787 @ SV190 @ SV89 @ SV34 )
= SV190 )
| ( ( sK50_E @ SY3787 @ SV190 @ SV89 @ SV34 )
= SV34 )
| ( ( sK50_E @ SY3787 @ SV190 @ SV89 @ SV34 )
= SV89 ) ) )
| ( SY3787
= ( unordered_triple @ SV34 @ SV89 @ SV190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1140,plain,
! [SV191: $i,SV89: $i,SV34: $i] :
( ( ! [SY3788: $i] :
( ( SY3788
!= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
| ~ ( ~ ! [SY3789: $i] :
( ~ ( in @ SY3789 @ SY3788 )
| ( SY3789 = SV191 )
| ( SY3789 = SV34 )
| ( SY3789 = SV89 ) )
| ~ ~ ( ~ ! [SY3790: $i] :
( ( SY3790 != SV191 )
| ( in @ SY3790 @ SY3788 ) )
| ~ ~ ( ~ ! [SY3427: $i] :
( ( SY3427 != SV34 )
| ( in @ SY3427 @ SY3788 ) )
| ~ ! [SY3640: $i] :
( ( SY3640 != SV89 )
| ( in @ SY3640 @ SY3788 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1141,plain,
! [SV147: $i,SV35: $i,SV192: $i] :
( ( ~ ( relation @ SV192 )
| ~ ( in @ ( ordered_pair @ SV35 @ SV147 ) @ SV192 )
| ( in @ SV35 @ ( relation_field @ SV192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1142,plain,
! [SV148: $i,SV35: $i,SV193: $i] :
( ( ~ ( relation @ SV193 )
| ~ ( in @ ( ordered_pair @ SV35 @ SV148 ) @ SV193 )
| ( in @ SV148 @ ( relation_field @ SV193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1143,plain,
! [SV36: $i] :
( ( ( ! [SY3433: $i] :
( ~ ( ~ ( ! [SY3434: $i] :
~ ( in @ ( ordered_pair @ SY3434 @ ( sK16_C @ SY3433 @ SV36 ) ) @ SV36 )
| ~ ( in @ ( sK16_C @ SY3433 @ SV36 ) @ SY3433 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_SY3292 @ SY3433 @ SV36 ) @ ( sK16_C @ SY3433 @ SV36 ) ) @ SV36 )
| ( in @ ( sK16_C @ SY3433 @ SV36 ) @ SY3433 ) ) )
| ( SY3433
= ( relation_rng @ SV36 ) ) ) )
= $true )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1019]) ).
thf(1144,plain,
! [SV36: $i] :
( ( ( ! [SY3435: $i] :
( ( SY3435
!= ( relation_rng @ SV36 ) )
| ~ ( ~ ! [SY3436: $i] :
( ! [SY3437: $i] :
~ ( in @ ( ordered_pair @ SY3437 @ SY3436 ) @ SV36 )
| ( in @ SY3436 @ SY3435 ) )
| ~ ! [SY3438: $i] :
( ~ ( in @ SY3438 @ SY3435 )
| ( in @ ( ordered_pair @ ( sK15_D @ SY3438 @ SY3435 @ SV36 ) @ SY3438 ) @ SV36 ) ) ) ) )
= $true )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1020]) ).
thf(1145,plain,
! [SV37: $i,SV149: $i] :
( ( ( ~ ( subset @ SV149 @ ( sK77_B @ SV37 ) )
| ( are_equipotent @ SV149 @ ( sK77_B @ SV37 ) ) )
= $true )
| ( ( in @ SV149 @ ( sK77_B @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1021]) ).
thf(1146,plain,
! [SV37: $i] :
( ( ~ ! [SY3440: $i] :
( ~ ( in @ SY3440 @ ( sK77_B @ SV37 ) )
| ( in @ ( powerset @ SY3440 ) @ ( sK77_B @ SV37 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1022]) ).
thf(1147,plain,
! [SV37: $i] :
( ( ~ ~ ( ~ ! [SY3441: $i,SY3442: $i] :
( ~ ( in @ SY3441 @ ( sK77_B @ SV37 ) )
| ~ ( subset @ SY3442 @ SY3441 )
| ( in @ SY3442 @ ( sK77_B @ SV37 ) ) )
| ~ ( in @ SV37 @ ( sK77_B @ SV37 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1022]) ).
thf(1148,plain,
! [SV112: $i,SV150: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK41_C @ SV150 @ SV112 ) @ SV150 )
| ~ ( subset @ ( sK41_C @ SV150 @ SV112 ) @ SV112 ) )
| ~ ( ( in @ ( sK41_C @ SV150 @ SV112 ) @ SV150 )
| ( subset @ ( sK41_C @ SV150 @ SV112 ) @ SV112 ) ) ) )
= $true )
| ( ( SV150
= ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1023]) ).
thf(1149,plain,
! [SV113: $i,SV151: $i] :
( ( ( ( SV151
!= ( powerset @ SV113 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3740: $i] :
( ~ ( in @ SY3740 @ SV151 )
| ( subset @ SY3740 @ SV113 ) )
| ~ ! [SY3741: $i] :
( ~ ( subset @ SY3741 @ SV113 )
| ( in @ SY3741 @ SV151 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1024]) ).
thf(1150,plain,
! [SV38: $i,SV90: $i] :
( ( ( ~ ( in @ ( sK5_C @ SV90 @ SV38 ) @ SV38 )
| ~ ( in @ ( sK5_C @ SV90 @ SV38 ) @ SV90 ) )
= $true )
| ( ( SV38 = SV90 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1025]) ).
thf(1151,plain,
! [SV38: $i,SV90: $i] :
( ( ( ( in @ ( sK5_C @ SV90 @ SV38 ) @ SV38 )
| ( in @ ( sK5_C @ SV90 @ SV38 ) @ SV90 ) )
= $true )
| ( ( SV38 = SV90 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1026]) ).
thf(1152,plain,
! [SV114: $i,SV152: $i] :
( ( ( ~ ( function @ SV152 )
| ~ ( relation @ SV152 ) )
= $true )
| ( ( ~ ( in @ SV114 @ ( relation_rng @ SV152 ) )
| ~ ( one_to_one @ SV152 )
| ( SV114
= ( apply @ SV152 @ ( apply @ ( function_inverse @ SV152 ) @ SV114 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1027]) ).
thf(1153,plain,
! [SV115: $i,SV153: $i] :
( ( ( ~ ( function @ SV153 )
| ~ ( relation @ SV153 ) )
= $true )
| ( ( ~ ( in @ SV115 @ ( relation_rng @ SV153 ) )
| ~ ( one_to_one @ SV153 )
| ( SV115
= ( apply @ ( relation_composition @ ( function_inverse @ SV153 ) @ SV153 ) @ SV115 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1028]) ).
thf(1154,plain,
! [SV39: $i,SV91: $i] :
( ( ( relation @ SV91 )
= $false )
| ( ( function @ SV91 )
= $false )
| ( ( ~ ( ~ ! [SY3641: $i] :
( ~ ( function @ SY3641 )
| ~ ( relation @ SY3641 )
| ~ ( in @ SV39 @ ( relation_dom @ SY3641 ) )
| ~ ( in @ ( apply @ SY3641 @ SV39 ) @ ( relation_dom @ SV91 ) )
| ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3641 @ SV91 ) ) ) )
| ~ ~ ( ~ ! [SY3642: $i] :
( ~ ( function @ SY3642 )
| ~ ( relation @ SY3642 )
| ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3642 @ SV91 ) ) )
| ( in @ SV39 @ ( relation_dom @ SY3642 ) ) )
| ~ ! [SY3643: $i] :
( ~ ( function @ SY3643 )
| ~ ( relation @ SY3643 )
| ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3643 @ SV91 ) ) )
| ( in @ ( apply @ SY3643 @ SV39 ) @ ( relation_dom @ SV91 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1029]) ).
thf(1155,plain,
! [SV92: $i,SV40: $i] :
( ( ( ~ ! [SY3644: $i] :
( ~ ( element @ SY3644 @ ( powerset @ ( powerset @ SV40 ) ) )
| ~ ( ~ ( element @ ( sK6_D @ SY3644 @ SV92 @ SV40 ) @ ( powerset @ SV40 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK6_D @ SY3644 @ SV92 @ SV40 ) @ SY3644 )
| ~ ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SY3644 @ SV92 @ SV40 ) ) @ SV92 ) )
| ~ ( ( in @ ( sK6_D @ SY3644 @ SV92 @ SV40 ) @ SY3644 )
| ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SY3644 @ SV92 @ SV40 ) ) @ SV92 ) ) ) )
| ( SY3644
= ( complements_of_subsets @ SV40 @ SV92 ) ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1030]) ).
thf(1156,plain,
! [SV92: $i,SV40: $i] :
( ( ( ~ ! [SY3645: $i] :
( ~ ( element @ SY3645 @ ( powerset @ ( powerset @ SV40 ) ) )
| ( SY3645
!= ( complements_of_subsets @ SV40 @ SV92 ) )
| ~ ( ~ ! [SY3646: $i] :
( ~ ( element @ SY3646 @ ( powerset @ SV40 ) )
| ~ ( in @ SY3646 @ SY3645 )
| ( in @ ( subset_complement @ SV40 @ SY3646 ) @ SV92 ) )
| ~ ! [SY3647: $i] :
( ~ ( element @ SY3647 @ ( powerset @ SV40 ) )
| ~ ( in @ ( subset_complement @ SV40 @ SY3647 ) @ SV92 )
| ( in @ SY3647 @ SY3645 ) ) ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1030]) ).
thf(1157,plain,
! [SV41: $i,SV154: $i,SV194: $i] :
( ( ~ ( function @ SV194 )
| ~ ( relation @ SV194 )
| ( SV154
!= ( apply @ SV194 @ SV41 ) )
| ~ ( in @ SV41 @ ( relation_dom @ SV194 ) )
| ( in @ ( ordered_pair @ SV41 @ SV154 ) @ SV194 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1158,plain,
! [SV41: $i] :
( ( ~ ! [SY3455: $i,SY3456: $i] :
( ~ ( function @ SY3456 )
| ~ ( relation @ SY3456 )
| ~ ( in @ ( ordered_pair @ SV41 @ SY3455 ) @ SY3456 )
| ( SY3455
= ( apply @ SY3456 @ SV41 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1032]) ).
thf(1159,plain,
! [SV41: $i] :
( ( ~ ! [SY3457: $i,SY3458: $i] :
( ~ ( function @ SY3458 )
| ~ ( relation @ SY3458 )
| ~ ( in @ ( ordered_pair @ SV41 @ SY3457 ) @ SY3458 )
| ( in @ SV41 @ ( relation_dom @ SY3458 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1032]) ).
thf(1160,plain,
! [SV155: $i,SV42: $i,SV195: $i] :
( ( ~ ( relation @ SV195 )
| ~ ( in @ SV42 @ SV155 )
| ~ ( in @ SV42 @ ( relation_rng @ SV195 ) )
| ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SV155 @ SV195 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1161,plain,
! [SV42: $i] :
( ( ~ ! [SY3461: $i,SY3462: $i] :
( ~ ( relation @ SY3462 )
| ~ ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SY3461 @ SY3462 ) ) )
| ( in @ SV42 @ SY3461 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1034]) ).
thf(1162,plain,
! [SV42: $i] :
( ( ~ ! [SY3463: $i,SY3464: $i] :
( ~ ( relation @ SY3464 )
| ~ ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SY3463 @ SY3464 ) ) )
| ( in @ SV42 @ ( relation_rng @ SY3464 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1034]) ).
thf(1163,plain,
! [SV43: $i,SV156: $i] :
( ( ( ~ ( subset @ SV156 @ ( sK2_B @ SV43 ) )
| ( are_equipotent @ SV156 @ ( sK2_B @ SV43 ) ) )
= $true )
| ( ( in @ SV156 @ ( sK2_B @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1035]) ).
thf(1164,plain,
! [SV43: $i] :
( ( ~ ! [SY3466: $i] :
( ~ ( ~ ! [SY3467: $i] :
( ~ ( subset @ SY3467 @ SY3466 )
| ( in @ SY3467 @ ( sK3_SY3278 @ SY3466 @ SV43 ) ) )
| ~ ( in @ ( sK3_SY3278 @ SY3466 @ SV43 ) @ ( sK2_B @ SV43 ) ) )
| ~ ( in @ SY3466 @ ( sK2_B @ SV43 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1036]) ).
thf(1165,plain,
! [SV43: $i] :
( ( ~ ~ ( ~ ! [SY3468: $i,SY3469: $i] :
( ~ ( in @ SY3468 @ ( sK2_B @ SV43 ) )
| ~ ( subset @ SY3469 @ SY3468 )
| ( in @ SY3469 @ ( sK2_B @ SV43 ) ) )
| ~ ( in @ SV43 @ ( sK2_B @ SV43 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1036]) ).
thf(1166,plain,
! [SV116: $i] :
( ( ( ~ ! [SY3692: $i,SY3693: $i] :
( ( sK49_B @ SV116 )
!= ( ordered_pair @ SY3692 @ SY3693 ) )
| ~ ( in @ ( sK49_B @ SV116 ) @ SV116 ) )
= $false )
| ( ( relation @ SV116 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1037]) ).
thf(1167,plain,
! [SV117: $i] :
( ( ( relation @ SV117 )
= $false )
| ( ( ! [SY3694: $i] :
( ( SY3694
= ( ordered_pair @ ( sK47_C @ SY3694 @ SV117 ) @ ( sK48_SY3309 @ SY3694 @ SV117 ) ) )
| ~ ( in @ SY3694 @ SV117 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1038]) ).
thf(1168,plain,
! [SV93: $i,SV196: $i,SV44: $i] :
( ( ! [SY3793: $i] :
( ~ ( in @ SV44 @ SV196 )
| ~ ( in @ SV93 @ SY3793 )
| ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SV196 @ SY3793 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1169,plain,
! [SV93: $i,SV44: $i] :
( ( ~ ! [SY3650: $i] :
( ! [SY3651: $i] :
~ ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SY3650 @ SY3651 ) )
| ( in @ SV44 @ SY3650 ) )
| ~ ! [SY3652: $i,SY3653: $i] :
( ~ ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SY3652 @ SY3653 ) )
| ( in @ SV93 @ SY3653 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1040]) ).
thf(1170,plain,
! [SV45: $i] :
( ( ( ! [SY3477: $i] :
( ~ ( ~ ( ! [SY3478: $i] :
~ ( in @ ( ordered_pair @ ( sK26_C @ SY3477 @ SV45 ) @ SY3478 ) @ SV45 )
| ~ ( in @ ( sK26_C @ SY3477 @ SV45 ) @ SY3477 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK26_C @ SY3477 @ SV45 ) @ ( sK27_SY3298 @ SY3477 @ SV45 ) ) @ SV45 )
| ( in @ ( sK26_C @ SY3477 @ SV45 ) @ SY3477 ) ) )
| ( SY3477
= ( relation_dom @ SV45 ) ) ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1041]) ).
thf(1171,plain,
! [SV45: $i] :
( ( ( ! [SY3479: $i] :
( ( SY3479
!= ( relation_dom @ SV45 ) )
| ~ ( ~ ! [SY3480: $i] :
( ! [SY3481: $i] :
~ ( in @ ( ordered_pair @ SY3480 @ SY3481 ) @ SV45 )
| ( in @ SY3480 @ SY3479 ) )
| ~ ! [SY3482: $i] :
( ~ ( in @ SY3482 @ SY3479 )
| ( in @ ( ordered_pair @ SY3482 @ ( sK25_D @ SY3482 @ SY3479 @ SV45 ) ) @ SV45 ) ) ) ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1042]) ).
thf(1172,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1043]) ).
thf(1173,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1044]) ).
thf(1174,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1045]) ).
thf(1175,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1046]) ).
thf(1176,plain,
! [SV119: $i] :
( ( ( SV119 = empty_set )
= $false )
| ( ( ! [SY3695: $i] :
~ ( in @ SY3695 @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1048]) ).
thf(1177,plain,
! [SV120: $i,SV157: $i] :
( ( ( ~ ( ~ ( ( ( sK43_C @ SV157 @ SV120 )
!= SV120 )
| ~ ( in @ ( sK43_C @ SV157 @ SV120 ) @ SV157 ) )
| ~ ( ( ( sK43_C @ SV157 @ SV120 )
= SV120 )
| ( in @ ( sK43_C @ SV157 @ SV120 ) @ SV157 ) ) ) )
= $true )
| ( ( SV157
= ( singleton @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1049]) ).
thf(1178,plain,
! [SV121: $i,SV158: $i] :
( ( ( ( SV158
!= ( singleton @ SV121 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3744: $i] :
( ( SY3744 != SV121 )
| ( in @ SY3744 @ SV158 ) )
| ~ ! [SY3745: $i] :
( ~ ( in @ SY3745 @ SV158 )
| ( SY3745 = SV121 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1050]) ).
thf(1179,plain,
! [SV122: $i,SV159: $i] :
( ( ( ~ ( function @ SV159 )
| ~ ( relation @ SV159 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK74_C @ SV159 @ SV122 ) @ SV122 )
| ~ ( ( ( apply @ SV159 @ ( sK74_C @ SV159 @ SV122 ) )
!= ( sK74_C @ SV159 @ SV122 ) ) ) )
| ( ( relation_dom @ SV159 )
!= SV122 )
| ( SV159
= ( identity_relation @ SV122 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1051]) ).
thf(1180,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( ( apply @ SX1 @ SX2 )
= SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1052]) ).
thf(1181,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1053]) ).
thf(1182,plain,
! [SV46: $i] :
( ( ( ~ ( one_to_one @ SV46 ) )
= $true )
| ( ( ~ ( ~ ! [SY3483: $i] :
( ~ ( function @ SY3483 )
| ~ ( relation @ SY3483 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY3322 @ SY3483 @ SV46 )
= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ( ( sK70_C @ SY3483 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SY3483 @ SV46 )
= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SY3483 @ SV46 )
= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ( ( sK71_SY3322 @ SY3483 @ SV46 )
!= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK70_C @ SY3483 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK71_SY3322 @ SY3483 @ SV46 )
!= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY3483 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK70_C @ SY3483 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SY3483 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SY3483 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK71_SY3322 @ SY3483 @ SV46 )
!= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ( ( relation_dom @ SY3483 )
!= ( relation_rng @ SV46 ) )
| ( SY3483
= ( function_inverse @ SV46 ) ) )
| ~ ~ ( ~ ! [SY3484: $i] :
( ~ ( function @ SY3484 )
| ~ ( relation @ SY3484 )
| ( SY3484
!= ( function_inverse @ SV46 ) )
| ~ ( ~ ~ ( ~ ! [SY3485: $i,SY3486: $i] :
( ( SY3486
!= ( apply @ SY3484 @ SY3485 ) )
| ~ ( in @ SY3485 @ ( relation_rng @ SV46 ) )
| ( SY3485
= ( apply @ SV46 @ SY3486 ) ) )
| ~ ! [SY3487: $i,SY3488: $i] :
( ( SY3488
!= ( apply @ SY3484 @ SY3487 ) )
| ~ ( in @ SY3487 @ ( relation_rng @ SV46 ) )
| ( in @ SY3488 @ ( relation_dom @ SV46 ) ) ) )
| ~ ~ ( ~ ! [SY3489: $i,SY3490: $i] :
( ( SY3489
!= ( apply @ SV46 @ SY3490 ) )
| ~ ( in @ SY3490 @ ( relation_dom @ SV46 ) )
| ( SY3490
= ( apply @ SY3484 @ SY3489 ) ) )
| ~ ! [SY3491: $i] :
( ! [SY3492: $i] :
( ( SY3491
!= ( apply @ SV46 @ SY3492 ) )
| ~ ( in @ SY3492 @ ( relation_dom @ SV46 ) ) )
| ( in @ SY3491 @ ( relation_rng @ SV46 ) ) ) ) ) )
| ~ ! [SY3493: $i] :
( ~ ( function @ SY3493 )
| ~ ( relation @ SY3493 )
| ( SY3493
!= ( function_inverse @ SV46 ) )
| ( ( relation_dom @ SY3493 )
= ( relation_rng @ SV46 ) ) ) ) ) )
= $true )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1054]) ).
thf(1183,plain,
! [SV47: $i,SV123: $i] :
( ( ( relation @ SV123 )
= $false )
| ( ( ~ ( ~ ! [SY3701: $i] :
( ~ ( relation @ SY3701 )
| ~ ( ~ ( ! [SY3702: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY3701 @ SV123 @ SV47 ) @ SY3702 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3702 @ ( sK9_SY3284 @ SY3701 @ SV123 @ SV47 ) ) @ SV123 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SY3701 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SY3701 @ SV123 @ SV47 ) ) @ SY3701 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY3701 @ SV123 @ SV47 ) @ ( sK10_SY3288 @ SY3701 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY3288 @ SY3701 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SY3701 @ SV123 @ SV47 ) ) @ SV123 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SY3701 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SY3701 @ SV123 @ SV47 ) ) @ SY3701 ) ) )
| ( SY3701
= ( relation_composition @ SV47 @ SV123 ) ) )
| ~ ! [SY3703: $i] :
( ~ ( relation @ SY3703 )
| ( SY3703
!= ( relation_composition @ SV47 @ SV123 ) )
| ~ ( ~ ! [SY3704: $i,SY3705: $i] :
( ! [SY3706: $i] :
( ~ ( in @ ( ordered_pair @ SY3704 @ SY3706 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3706 @ SY3705 ) @ SV123 ) )
| ( in @ ( ordered_pair @ SY3704 @ SY3705 ) @ SY3703 ) )
| ~ ! [SY3707: $i,SY3708: $i] :
( ~ ( in @ ( ordered_pair @ SY3707 @ SY3708 ) @ SY3703 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3707 @ ( sK7_F @ SY3708 @ SY3707 @ SY3703 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY3708 @ SY3707 @ SY3703 @ SV123 @ SV47 ) @ SY3708 ) @ SV123 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1055]) ).
thf(1184,plain,
! [SV160: $i,SV197: $i,SV48: $i] :
( ( ~ ( in @ SV48 @ SV197 )
| ~ ( in @ SV160 @ SV197 )
| ( subset @ ( unordered_pair @ SV48 @ SV160 ) @ SV197 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1185,plain,
! [SV48: $i] :
( ( ~ ! [SY3505: $i,SY3506: $i] :
( ~ ( subset @ ( unordered_pair @ SV48 @ SY3505 ) @ SY3506 )
| ( in @ SV48 @ SY3506 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1057]) ).
thf(1186,plain,
! [SV48: $i] :
( ( ~ ! [SY3507: $i,SY3508: $i] :
( ~ ( subset @ ( unordered_pair @ SV48 @ SY3507 ) @ SY3508 )
| ( in @ SY3507 @ SY3508 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1057]) ).
thf(1187,plain,
! [SV94: $i,SV198: $i,SV49: $i] :
( ( ! [SY3794: $i] :
( ~ ( relation @ SY3794 )
| ~ ( in @ SV49 @ SV198 )
| ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ SY3794 )
| ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SV198 ) @ SY3794 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1188,plain,
! [SV94: $i,SV49: $i] :
( ( ~ ! [SY3656: $i,SY3657: $i] :
( ~ ( relation @ SY3657 )
| ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SY3656 ) @ SY3657 ) )
| ( in @ SV49 @ SY3656 ) )
| ~ ! [SY3658: $i,SY3659: $i] :
( ~ ( relation @ SY3659 )
| ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SY3658 ) @ SY3659 ) )
| ( in @ ( ordered_pair @ SV49 @ SV94 ) @ SY3659 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1059]) ).
thf(1189,plain,
! [SV50: $i,SV95: $i] :
( ( ( ! [SY3660: $i] :
( ~ ( in @ SY3660 @ SV95 )
| ~ ( in @ SY3660 @ ( sK4_C @ SV95 @ SV50 ) ) ) )
= $true )
| ( ( ~ ( in @ SV50 @ SV95 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1060]) ).
thf(1190,plain,
! [SV50: $i,SV95: $i] :
( ( ( in @ ( sK4_C @ SV95 @ SV50 ) @ SV95 )
= $true )
| ( ( ~ ( in @ SV50 @ SV95 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1061]) ).
thf(1191,plain,
! [SV124: $i] :
( ( ( ~ ( function @ SV124 ) )
= $true )
| ( ( ~ ( relation @ SV124 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_B @ SV124 ) @ ( relation_dom @ SV124 ) )
| ~ ( in @ ( sK12_SY3289 @ SV124 ) @ ( relation_dom @ SV124 ) ) )
| ( ( apply @ SV124 @ ( sK11_B @ SV124 ) )
!= ( apply @ SV124 @ ( sK12_SY3289 @ SV124 ) ) ) )
| ~ ( ( ( sK11_B @ SV124 )
!= ( sK12_SY3289 @ SV124 ) ) ) )
| ( one_to_one @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1062]) ).
thf(1192,plain,
! [SV125: $i] :
( ( ( ~ ( function @ SV125 ) )
= $true )
| ( ( ~ ( relation @ SV125 ) )
= $true )
| ( ( ~ ( one_to_one @ SV125 )
| ! [SY3709: $i,SY3710: $i] :
( ~ ( in @ SY3709 @ ( relation_dom @ SV125 ) )
| ~ ( in @ SY3710 @ ( relation_dom @ SV125 ) )
| ( ( apply @ SV125 @ SY3709 )
!= ( apply @ SV125 @ SY3710 ) )
| ( SY3709 = SY3710 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1063]) ).
thf(1193,plain,
! [SV51: $i,SV161: $i,SV199: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV199 )
| ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV51 ) )
| ~ ( ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV199 )
| ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV161 ) ) )
| ~ ( ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV199 )
| ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV51 )
| ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV161 ) ) )
| ( SV199
= ( set_union2 @ SV51 @ SV161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1194,plain,
! [SV162: $i,SV51: $i,SV200: $i] :
( ( ( SV200
!= ( set_union2 @ SV51 @ SV162 ) )
| ~ ( ~ ! [SY3795: $i] :
( ~ ( in @ SY3795 @ SV200 )
| ( in @ SY3795 @ SV51 )
| ( in @ SY3795 @ SV162 ) )
| ~ ~ ( ~ ! [SY3796: $i] :
( ~ ( in @ SY3796 @ SV51 )
| ( in @ SY3796 @ SV200 ) )
| ~ ! [SY3797: $i] :
( ~ ( in @ SY3797 @ SV162 )
| ( in @ SY3797 @ SV200 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1065]) ).
thf(1195,plain,
! [SV163: $i,SV126: $i] :
( ( ( ( ( set_difference @ SV126 @ ( singleton @ SV163 ) )
!= SV126 ) )
= $true )
| ( ( ~ ( in @ SV163 @ SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1066]) ).
thf(1196,plain,
! [SV127: $i,SV164: $i] :
( ( ( in @ SV164 @ SV127 )
= $true )
| ( ( ( set_difference @ SV127 @ ( singleton @ SV164 ) )
= SV127 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1067]) ).
thf(1197,plain,
! [SV52: $i] :
( ( ( ! [SY3525: $i] :
( ~ ( relation @ SY3525 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK30_C @ SY3525 @ SV52 ) @ ( sK31_SY3299 @ SY3525 @ SV52 ) ) @ SV52 )
| ~ ~ ( in @ ( ordered_pair @ ( sK30_C @ SY3525 @ SV52 ) @ ( sK31_SY3299 @ SY3525 @ SV52 ) ) @ SY3525 ) )
| ( subset @ SV52 @ SY3525 ) ) )
= $true )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1068]) ).
thf(1198,plain,
! [SV52: $i] :
( ( ( ! [SY3526: $i] :
( ~ ( relation @ SY3526 )
| ~ ( subset @ SV52 @ SY3526 )
| ! [SY3527: $i,SY3528: $i] :
( ~ ( in @ ( ordered_pair @ SY3527 @ SY3528 ) @ SV52 )
| ( in @ ( ordered_pair @ SY3527 @ SY3528 ) @ SY3526 ) ) ) )
= $true )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1069]) ).
thf(1199,plain,
( ( ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK46_SY3307 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK45_C @ SX1 @ SX0 ) @ ( sK46_SY3307 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK45_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK45_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK45_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1070]) ).
thf(1200,plain,
( ( ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK44_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK44_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1071]) ).
thf(1201,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1072]) ).
thf(1202,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1073]) ).
thf(1203,plain,
! [SV53: $i] :
( ( ( ~ ! [SY3529: $i,SY3530: $i] :
( ~ ( ~ ( ~ ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) ) @ SY3529 )
| ~ ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ SY3530 ) )
| ~ ~ ( ~ ( ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ SY3530 ) )
| ~ ( ( in @ ( apply @ SV53 @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) ) @ SY3529 )
| ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ SY3530 ) ) ) )
| ( SY3530
= ( relation_inverse_image @ SV53 @ SY3529 ) ) )
| ~ ! [SY3531: $i,SY3532: $i] :
( ( SY3532
!= ( relation_inverse_image @ SV53 @ SY3531 ) )
| ~ ( ~ ! [SY3533: $i] :
( ~ ( in @ SY3533 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SY3533 ) @ SY3531 )
| ( in @ SY3533 @ SY3532 ) )
| ~ ~ ( ~ ! [SY3534: $i] :
( ~ ( in @ SY3534 @ SY3532 )
| ( in @ SY3534 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY3535: $i] :
( ~ ( in @ SY3535 @ SY3532 )
| ( in @ ( apply @ SV53 @ SY3535 ) @ SY3531 ) ) ) ) ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1074]) ).
thf(1204,plain,
! [SV54: $i,SV165: $i,SV201: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV54 )
| ~ ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV165 )
| ~ ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV201 ) )
| ~ ~ ( ~ ( ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV54 )
| ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV201 ) )
| ~ ( ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV165 )
| ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV201 ) ) ) )
| ( SV201
= ( set_intersection2 @ SV54 @ SV165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1205,plain,
! [SV166: $i,SV54: $i,SV202: $i] :
( ( ( SV202
!= ( set_intersection2 @ SV54 @ SV166 ) )
| ~ ( ~ ! [SY3798: $i] :
( ~ ( in @ SY3798 @ SV54 )
| ~ ( in @ SY3798 @ SV166 )
| ( in @ SY3798 @ SV202 ) )
| ~ ~ ( ~ ! [SY3799: $i] :
( ~ ( in @ SY3799 @ SV202 )
| ( in @ SY3799 @ SV54 ) )
| ~ ! [SY3800: $i] :
( ~ ( in @ SY3800 @ SV202 )
| ( in @ SY3800 @ SV166 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1206,plain,
! [SV167: $i,SV128: $i] :
( ( ( ~ ( in @ SV128 @ SV167 ) )
= $true )
| ( ( subset @ ( singleton @ SV128 ) @ SV167 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1077]) ).
thf(1207,plain,
! [SV168: $i,SV129: $i] :
( ( ( ~ ( subset @ ( singleton @ SV129 ) @ SV168 ) )
= $true )
| ( ( in @ SV129 @ SV168 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1078]) ).
thf(1208,plain,
! [SV55: $i,SV169: $i,SV203: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV55 )
| ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV169 )
| ~ ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV203 ) )
| ~ ~ ( ~ ( ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV55 )
| ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV203 ) )
| ~ ( ~ ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV169 )
| ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV203 ) ) ) )
| ( SV203
= ( set_difference @ SV55 @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1209,plain,
! [SV170: $i,SV55: $i,SV204: $i] :
( ( ( SV204
!= ( set_difference @ SV55 @ SV170 ) )
| ~ ( ~ ! [SY3801: $i] :
( ~ ( in @ SY3801 @ SV55 )
| ( in @ SY3801 @ SV170 )
| ( in @ SY3801 @ SV204 ) )
| ~ ~ ( ~ ! [SY3802: $i] :
( ~ ( in @ SY3802 @ SV204 )
| ( in @ SY3802 @ SV55 ) )
| ~ ! [SY3803: $i] :
( ~ ( in @ SY3803 @ SV204 )
| ~ ( in @ SY3803 @ SV170 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1210,plain,
! [SV56: $i] :
( ( ( ~ ! [SY3550: $i] :
( ~ ( ~ ( ! [SY3551: $i] :
( ( ( sK19_C @ SY3550 @ SV56 )
!= ( apply @ SV56 @ SY3551 ) )
| ~ ( in @ SY3551 @ ( relation_dom @ SV56 ) ) )
| ~ ( in @ ( sK19_C @ SY3550 @ SV56 ) @ SY3550 ) )
| ~ ( ~ ( ( ( sK19_C @ SY3550 @ SV56 )
!= ( apply @ SV56 @ ( sK20_SY3294 @ SY3550 @ SV56 ) ) )
| ~ ( in @ ( sK20_SY3294 @ SY3550 @ SV56 ) @ ( relation_dom @ SV56 ) ) )
| ( in @ ( sK19_C @ SY3550 @ SV56 ) @ SY3550 ) ) )
| ( SY3550
= ( relation_rng @ SV56 ) ) )
| ~ ! [SY3552: $i] :
( ( SY3552
!= ( relation_rng @ SV56 ) )
| ~ ( ~ ! [SY3553: $i] :
( ! [SY3554: $i] :
( ( SY3553
!= ( apply @ SV56 @ SY3554 ) )
| ~ ( in @ SY3554 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY3553 @ SY3552 ) )
| ~ ! [SY3555: $i] :
( ~ ( in @ SY3555 @ SY3552 )
| ~ ( ( SY3555
!= ( apply @ SV56 @ ( sK18_D @ SY3555 @ SY3552 @ SV56 ) ) )
| ~ ( in @ ( sK18_D @ SY3555 @ SY3552 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) ) ) ) )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1081]) ).
thf(1211,plain,
! [SV57: $i,SV171: $i,SV205: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK38_D @ SV205 @ SV171 @ SV57 ) @ SV205 )
| ( ( sK38_D @ SV205 @ SV171 @ SV57 )
!= SV57 ) )
| ~ ( ~ ( in @ ( sK38_D @ SV205 @ SV171 @ SV57 ) @ SV205 )
| ( ( sK38_D @ SV205 @ SV171 @ SV57 )
!= SV171 ) ) )
| ~ ( ( in @ ( sK38_D @ SV205 @ SV171 @ SV57 ) @ SV205 )
| ( ( sK38_D @ SV205 @ SV171 @ SV57 )
= SV57 )
| ( ( sK38_D @ SV205 @ SV171 @ SV57 )
= SV171 ) ) )
| ( SV205
= ( unordered_pair @ SV57 @ SV171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1212,plain,
! [SV172: $i,SV57: $i,SV206: $i] :
( ( ( SV206
!= ( unordered_pair @ SV57 @ SV172 ) )
| ~ ( ~ ! [SY3804: $i] :
( ~ ( in @ SY3804 @ SV206 )
| ( SY3804 = SV57 )
| ( SY3804 = SV172 ) )
| ~ ~ ( ~ ! [SY3805: $i] :
( ( SY3805 != SV57 )
| ( in @ SY3805 @ SV206 ) )
| ~ ! [SY3806: $i] :
( ( SY3806 != SV172 )
| ( in @ SY3806 @ SV206 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1213,plain,
! [SV58: $i,SV96: $i] :
( ( ( relation @ SV96 )
= $false )
| ( ( function @ SV96 )
= $false )
| ( ( ~ ( ~ ! [SY3661: $i] :
( ~ ( function @ SY3661 )
| ~ ( relation @ SY3661 )
| ~ ( ~ ( in @ ( sK67_D @ SY3661 @ SV96 @ SV58 ) @ ( relation_dom @ SV96 ) )
| ~ ( ( ( apply @ SV96 @ ( sK67_D @ SY3661 @ SV96 @ SV58 ) )
!= ( apply @ SY3661 @ ( sK67_D @ SY3661 @ SV96 @ SV58 ) ) ) ) )
| ( ( relation_dom @ SV96 )
!= ( set_intersection2 @ ( relation_dom @ SY3661 ) @ SV58 ) )
| ( SV96
= ( relation_dom_restriction @ SY3661 @ SV58 ) ) )
| ~ ~ ( ~ ! [SY3662: $i] :
( ~ ( function @ SY3662 )
| ~ ( relation @ SY3662 )
| ( SV96
!= ( relation_dom_restriction @ SY3662 @ SV58 ) )
| ! [SY3663: $i] :
( ~ ( in @ SY3663 @ ( relation_dom @ SV96 ) )
| ( ( apply @ SV96 @ SY3663 )
= ( apply @ SY3662 @ SY3663 ) ) ) )
| ~ ! [SY3664: $i] :
( ~ ( function @ SY3664 )
| ~ ( relation @ SY3664 )
| ( SV96
!= ( relation_dom_restriction @ SY3664 @ SV58 ) )
| ( ( relation_dom @ SV96 )
= ( set_intersection2 @ ( relation_dom @ SY3664 ) @ SV58 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1084]) ).
thf(1214,plain,
! [SV59: $i] :
( ( ( ! [SY3568: $i] :
( ~ ( relation @ SY3568 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_C @ SY3568 @ SV59 ) @ ( sK40_SY3306 @ SY3568 @ SV59 ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK39_C @ SY3568 @ SV59 ) @ ( sK40_SY3306 @ SY3568 @ SV59 ) ) @ SY3568 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK39_C @ SY3568 @ SV59 ) @ ( sK40_SY3306 @ SY3568 @ SV59 ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK39_C @ SY3568 @ SV59 ) @ ( sK40_SY3306 @ SY3568 @ SV59 ) ) @ SY3568 ) ) )
| ( SV59 = SY3568 ) ) )
= $true )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1085]) ).
thf(1215,plain,
! [SV59: $i] :
( ( ( ! [SY3569: $i] :
( ~ ( relation @ SY3569 )
| ( SV59 != SY3569 )
| ~ ( ~ ! [SY3570: $i,SY3571: $i] :
( ~ ( in @ ( ordered_pair @ SY3570 @ SY3571 ) @ SV59 )
| ( in @ ( ordered_pair @ SY3570 @ SY3571 ) @ SY3569 ) )
| ~ ! [SY3572: $i,SY3573: $i] :
( ~ ( in @ ( ordered_pair @ SY3572 @ SY3573 ) @ SY3569 )
| ( in @ ( ordered_pair @ SY3572 @ SY3573 ) @ SV59 ) ) ) ) )
= $true )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1086]) ).
thf(1216,plain,
! [SV60: $i,SV97: $i] :
( ( ( in @ ( sK78_C @ SV97 @ SV60 ) @ SV60 )
= $true )
| ( ( element @ SV60 @ ( powerset @ SV97 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1087]) ).
thf(1217,plain,
! [SV60: $i,SV97: $i] :
( ( ( ~ ( in @ ( sK78_C @ SV97 @ SV60 ) @ SV97 ) )
= $true )
| ( ( element @ SV60 @ ( powerset @ SV97 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1088]) ).
thf(1218,plain,
! [SV130: $i,SV173: $i] :
( ( ( ~ ( ~ ( ! [SY3767: $i] :
( ~ ( in @ ( sK23_C @ SV173 @ SV130 ) @ SY3767 )
| ~ ( in @ SY3767 @ SV130 ) )
| ~ ( in @ ( sK23_C @ SV173 @ SV130 ) @ SV173 ) )
| ~ ( ~ ( ~ ( in @ ( sK23_C @ SV173 @ SV130 ) @ ( sK24_SY3296 @ SV173 @ SV130 ) )
| ~ ( in @ ( sK24_SY3296 @ SV173 @ SV130 ) @ SV130 ) )
| ( in @ ( sK23_C @ SV173 @ SV130 ) @ SV173 ) ) ) )
= $true )
| ( ( SV173
= ( union @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1089]) ).
thf(1219,plain,
! [SV131: $i,SV174: $i] :
( ( ( ( SV174
!= ( union @ SV131 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3768: $i] :
( ! [SY3719: $i] :
( ~ ( in @ SY3768 @ SY3719 )
| ~ ( in @ SY3719 @ SV131 ) )
| ( in @ SY3768 @ SV174 ) )
| ~ ! [SY3770: $i] :
( ~ ( in @ SY3770 @ SV174 )
| ~ ( ~ ( in @ SY3770 @ ( sK22_D @ SY3770 @ SV174 @ SV131 ) )
| ~ ( in @ ( sK22_D @ SY3770 @ SV174 @ SV131 ) @ SV131 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1090]) ).
thf(1220,plain,
! [SV98: $i,SV207: $i,SV61: $i] :
( ( ! [SY3807: $i] :
( ~ ( in @ SV61 @ SV207 )
| ~ ( in @ SV98 @ SY3807 )
| ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SV207 @ SY3807 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1221,plain,
! [SV98: $i,SV61: $i] :
( ( ~ ! [SY3667: $i] :
( ! [SY3668: $i] :
~ ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SY3667 @ SY3668 ) )
| ( in @ SV61 @ SY3667 ) )
| ~ ! [SY3669: $i,SY3670: $i] :
( ~ ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SY3669 @ SY3670 ) )
| ( in @ SV98 @ SY3670 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1092]) ).
thf(1222,plain,
! [SV62: $i,SV175: $i,SV208: $i] :
( ( ~ ( function @ SV208 )
| ~ ( relation @ SV208 )
| ~ ( in @ SV175 @ ( relation_dom @ SV208 ) )
| ~ ( in @ SV175 @ SV62 )
| ( in @ SV175 @ ( relation_dom @ ( relation_dom_restriction @ SV208 @ SV62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1093]) ).
thf(1223,plain,
! [SV62: $i] :
( ( ~ ! [SY3584: $i,SY3585: $i] :
( ~ ( function @ SY3585 )
| ~ ( relation @ SY3585 )
| ~ ( in @ SY3584 @ ( relation_dom @ ( relation_dom_restriction @ SY3585 @ SV62 ) ) )
| ( in @ SY3584 @ ( relation_dom @ SY3585 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1094]) ).
thf(1224,plain,
! [SV62: $i] :
( ( ~ ! [SY3586: $i,SY3587: $i] :
( ~ ( function @ SY3587 )
| ~ ( relation @ SY3587 )
| ~ ( in @ SY3586 @ ( relation_dom @ ( relation_dom_restriction @ SY3587 @ SV62 ) ) )
| ( in @ SY3586 @ SV62 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1094]) ).
thf(1225,plain,
! [SV209: $i,SV176: $i,SV63: $i] :
( ( ~ ( ~ ( ! [SY3808: $i,SY3809: $i] :
( ~ ( in @ SY3808 @ SV63 )
| ~ ( in @ SY3809 @ SV176 )
| ( ( sK34_D @ SV209 @ SV176 @ SV63 )
!= ( ordered_pair @ SY3808 @ SY3809 ) ) )
| ~ ( in @ ( sK34_D @ SV209 @ SV176 @ SV63 ) @ SV209 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK35_SY3303 @ SV209 @ SV176 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK36_SY3305 @ SV209 @ SV176 @ SV63 ) @ SV176 ) )
| ( ( sK34_D @ SV209 @ SV176 @ SV63 )
!= ( ordered_pair @ ( sK35_SY3303 @ SV209 @ SV176 @ SV63 ) @ ( sK36_SY3305 @ SV209 @ SV176 @ SV63 ) ) ) )
| ( in @ ( sK34_D @ SV209 @ SV176 @ SV63 ) @ SV209 ) ) )
| ( SV209
= ( cartesian_product2 @ SV63 @ SV176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1226,plain,
! [SV177: $i,SV63: $i,SV210: $i] :
( ( ( SV210
!= ( cartesian_product2 @ SV63 @ SV177 ) )
| ~ ( ~ ! [SY3810: $i] :
( ! [SY3777: $i,SY3778: $i] :
( ~ ( in @ SY3777 @ SV63 )
| ~ ( in @ SY3778 @ SV177 )
| ( SY3810
!= ( ordered_pair @ SY3777 @ SY3778 ) ) )
| ( in @ SY3810 @ SV210 ) )
| ~ ! [SY3813: $i] :
( ~ ( in @ SY3813 @ SV210 )
| ~ ( ~ ~ ( ~ ( in @ ( sK32_E @ SY3813 @ SV210 @ SV177 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK33_SY3300 @ SY3813 @ SV210 @ SV177 @ SV63 ) @ SV177 ) )
| ( SY3813
!= ( ordered_pair @ ( sK32_E @ SY3813 @ SV210 @ SV177 @ SV63 ) @ ( sK33_SY3300 @ SY3813 @ SV210 @ SV177 @ SV63 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1227,plain,
! [SV178: $i,SV132: $i] :
( ( ( disjoint @ SV132 @ SV178 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK73_C @ SV178 @ SV132 ) @ SV132 )
| ~ ( in @ ( sK73_C @ SV178 @ SV132 ) @ SV178 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1097]) ).
thf(1228,plain,
! [SV179: $i,SV133: $i] :
( ( ( ! [SY3780: $i] :
( ~ ( in @ SY3780 @ SV133 )
| ~ ( in @ SY3780 @ SV179 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV133 @ SV179 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1098]) ).
thf(1229,plain,
! [SV180: $i,SV64: $i,SV211: $i] :
( ( ~ ( relation @ SV211 )
| ! [SY3814: $i] :
( ~ ( in @ SY3814 @ ( relation_dom @ SV211 ) )
| ~ ( in @ ( ordered_pair @ SY3814 @ SV64 ) @ SV211 )
| ~ ( in @ SY3814 @ SV180 ) )
| ( in @ SV64 @ ( relation_image @ SV211 @ SV180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1230,plain,
! [SV181: $i,SV64: $i,SV212: $i] :
( ( ~ ( relation @ SV212 )
| ~ ( in @ SV64 @ ( relation_image @ SV212 @ SV181 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK76_D @ SV212 @ SV181 @ SV64 ) @ ( relation_dom @ SV212 ) )
| ~ ( in @ ( ordered_pair @ ( sK76_D @ SV212 @ SV181 @ SV64 ) @ SV64 ) @ SV212 ) )
| ~ ( in @ ( sK76_D @ SV212 @ SV181 @ SV64 ) @ SV181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1231,plain,
! [SV182: $i,SV65: $i,SV213: $i] :
( ( ~ ( relation @ SV213 )
| ~ ( in @ ( ordered_pair @ SV65 @ SV182 ) @ SV213 )
| ( in @ SV65 @ ( relation_dom @ SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1232,plain,
! [SV183: $i,SV65: $i,SV214: $i] :
( ( ~ ( relation @ SV214 )
| ~ ( in @ ( ordered_pair @ SV65 @ SV183 ) @ SV214 )
| ( in @ SV183 @ ( relation_rng @ SV214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1233,plain,
! [SV66: $i] :
( ( ( ~ ~ ( ~ ! [SY3607: $i] :
( ~ ( in @ SY3607 @ ( relation_dom @ SV66 ) )
| ! [SY3608: $i] :
( ( SY3608
!= ( apply @ SV66 @ SY3607 ) )
| ( in @ ( ordered_pair @ SY3607 @ SY3608 ) @ SV66 ) ) )
| ~ ! [SY3609: $i] :
( ~ ( in @ SY3609 @ ( relation_dom @ SV66 ) )
| ! [SY3610: $i] :
( ~ ( in @ ( ordered_pair @ SY3609 @ SY3610 ) @ SV66 )
| ( SY3610
= ( apply @ SV66 @ SY3609 ) ) ) ) )
| ~ ~ ( ~ ! [SY3611: $i] :
( ( in @ SY3611 @ ( relation_dom @ SV66 ) )
| ! [SY3612: $i] :
( ( SY3612
!= ( apply @ SV66 @ SY3611 ) )
| ( SY3612 = empty_set ) ) )
| ~ ! [SY3613: $i] :
( ( in @ SY3613 @ ( relation_dom @ SV66 ) )
| ! [SY3614: $i] :
( ( SY3614 != empty_set )
| ( SY3614
= ( apply @ SV66 @ SY3613 ) ) ) ) ) )
= $false )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1103]) ).
thf(1234,plain,
! [SV184: $i,SV134: $i] :
( ( ( ~ ( in @ SV134 @ SV184 ) )
= $true )
| ( ( subset @ ( singleton @ SV134 ) @ SV184 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1104]) ).
thf(1235,plain,
! [SV185: $i,SV135: $i] :
( ( ( ~ ( subset @ ( singleton @ SV135 ) @ SV185 ) )
= $true )
| ( ( in @ SV135 @ SV185 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1105]) ).
thf(1236,plain,
! [SV4: $i,SV70: $i,SV136: $i] :
( ( ( in @ SV136 @ SV70 )
= $false )
| ( ( in @ SV136 @ SV4 )
= $true )
| ( ( element @ SV70 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1106]) ).
thf(1237,plain,
! [SV73: $i,SV7: $i,SV215: $i] :
( ( ( ~ ( function @ SV215 )
| ~ ( relation @ SV215 )
| ~ ( in @ SV7 @ ( relation_dom @ ( relation_composition @ SV215 @ SV73 ) ) )
| ( ( apply @ ( relation_composition @ SV215 @ SV73 ) @ SV7 )
= ( apply @ SV73 @ ( apply @ SV215 @ SV7 ) ) ) )
= $true )
| ( ( function @ SV73 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1238,plain,
! [SV74: $i,SV8: $i,SV216: $i] :
( ( ( ~ ( function @ SV216 )
| ~ ( relation @ SV216 )
| ~ ( in @ SV8 @ ( relation_dom @ SV74 ) )
| ( ( apply @ ( relation_composition @ SV74 @ SV216 ) @ SV8 )
= ( apply @ SV216 @ ( apply @ SV74 @ SV8 ) ) ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1239,plain,
! [SV10: $i,SV99: $i,SV76: $i] :
( ( ( in @ SV76 @ SV99 )
= $false )
| ( ( in @ SV10 @ SV76 )
= $false )
| ( ( ~ ( in @ SV99 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1110]) ).
thf(1240,plain,
! [SV100: $i,SV12: $i,SV186: $i] :
( ( ( ~ ( element @ SV186 @ SV12 ) )
= $true )
| ( ( ( in @ SV186 @ SV100 )
| ( in @ SV186 @ ( subset_complement @ SV12 @ SV100 ) ) )
= $true )
| ( ( element @ SV100 @ ( powerset @ SV12 ) )
= $false )
| ( ( SV12 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1111]) ).
thf(1241,plain,
! [SV101: $i,SV13: $i,SV78: $i] :
( ( ( in @ SV78 @ ( subset_complement @ SV13 @ SV101 ) )
= $false )
| ( ( ~ ( in @ SV78 @ SV101 ) )
= $true )
| ( ( element @ SV101 @ ( powerset @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1112]) ).
thf(1242,plain,
! [SV15: $i,SV79: $i,SV102: $i] :
( ( ( relation @ SV102 )
= $false )
| ( ( function @ SV102 )
= $false )
| ( ( ~ ( in @ SV79 @ ( relation_dom @ ( relation_dom_restriction @ SV102 @ SV15 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SV102 @ SV15 ) @ SV79 )
= ( apply @ SV102 @ SV79 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1113]) ).
thf(1243,plain,
! [SV16: $i,SV80: $i,SV103: $i] :
( ( ( relation @ SV103 )
= $false )
| ( ( function @ SV103 )
= $false )
| ( ( ~ ( in @ SV80 @ SV16 )
| ( ( apply @ ( relation_dom_restriction @ SV103 @ SV16 ) @ SV80 )
= ( apply @ SV103 @ SV80 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1114]) ).
thf(1244,plain,
! [SV104: $i,SV85: $i,SV23: $i] :
( ( ( in @ SV23 @ SV85 )
= $false )
| ( ( element @ SV85 @ ( powerset @ SV104 ) )
= $false )
| ( ( element @ SV23 @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1115]) ).
thf(1245,plain,
! [SV105: $i,SV86: $i,SV24: $i] :
( ( ( in @ SV24 @ SV86 )
= $false )
| ( ( element @ SV86 @ ( powerset @ SV105 ) )
= $false )
| ( ( ~ ( empty @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1116]) ).
thf(1246,plain,
! [SV139: $i,SV107: $i,SV217: $i] :
( ( ( ~ ( in @ SV217 @ ( set_intersection2 @ SV107 @ SV139 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV107 @ SV139 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1247,plain,
! [SV26: $i,SV88: $i] :
( ( ( ! [SY3625: $i] :
( ~ ( relation @ SY3625 )
| ~ ( ~ ( ~ ( in @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) @ SV26 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY3625 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) ) @ SV88 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY3625 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) ) @ SY3625 ) )
| ~ ~ ( ~ ( ( in @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) @ SV26 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY3625 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) ) @ SY3625 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SY3625 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) ) @ SV88 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY3625 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SY3625 @ SV88 @ SV26 ) ) @ SY3625 ) ) ) )
| ( SY3625
= ( relation_rng_restriction @ SV26 @ SV88 ) ) ) )
= $true )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1119]) ).
thf(1248,plain,
! [SV88: $i,SV26: $i] :
( ( ( ! [SY3626: $i] :
( ~ ( relation @ SY3626 )
| ( SY3626
!= ( relation_rng_restriction @ SV26 @ SV88 ) )
| ~ ( ~ ! [SY3627: $i,SY3628: $i] :
( ~ ( in @ SY3628 @ SV26 )
| ~ ( in @ ( ordered_pair @ SY3627 @ SY3628 ) @ SV88 )
| ( in @ ( ordered_pair @ SY3627 @ SY3628 ) @ SY3626 ) )
| ~ ~ ( ~ ! [SY3365: $i,SY3366: $i] :
( ~ ( in @ ( ordered_pair @ SY3365 @ SY3366 ) @ SY3626 )
| ( in @ SY3366 @ SV26 ) )
| ~ ! [SY3631: $i,SY3632: $i] :
( ~ ( in @ ( ordered_pair @ SY3631 @ SY3632 ) @ SY3626 )
| ( in @ ( ordered_pair @ SY3631 @ SY3632 ) @ SV88 ) ) ) ) ) )
= $true )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1120]) ).
thf(1249,plain,
! [SV108: $i,SV140: $i] :
( ( ( ~ ( in @ ( sK29_C @ SV140 @ SV108 ) @ SV108 )
| ~ ~ ( in @ ( sK29_C @ SV140 @ SV108 ) @ SV140 ) )
= $false )
| ( ( subset @ SV108 @ SV140 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1121]) ).
thf(1250,plain,
! [SV141: $i,SV109: $i] :
( ( ( subset @ SV109 @ SV141 )
= $false )
| ( ( ! [SY3727: $i] :
( ~ ( in @ SY3727 @ SV109 )
| ( in @ SY3727 @ SV141 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1122]) ).
thf(1251,plain,
! [SV142: $i,SV27: $i,SV187: $i] :
( ( ( ~ ( relation @ SV187 ) )
= $true )
| ( ( ~ ( in @ SV27 @ SV142 )
| ~ ( in @ SV27 @ ( relation_dom @ SV187 ) )
| ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SV187 @ SV142 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1123]) ).
thf(1252,plain,
! [SV27: $i] :
( ( ! [SY3371: $i,SY3372: $i] :
( ~ ( relation @ SY3372 )
| ~ ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SY3372 @ SY3371 ) ) )
| ( in @ SV27 @ SY3371 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1124]) ).
thf(1253,plain,
! [SV27: $i] :
( ( ! [SY3373: $i,SY3374: $i] :
( ~ ( relation @ SY3374 )
| ~ ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SY3374 @ SY3373 ) ) )
| ( in @ SV27 @ ( relation_dom @ SY3374 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1125]) ).
thf(1254,plain,
! [SV28: $i,SV218: $i] :
( ( ( ~ ( relation @ SV218 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV218 @ SV28 ) @ ( sK14_SY3290 @ SV218 @ SV28 ) ) @ SV218 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY3290 @ SV218 @ SV28 ) @ ( sK13_C @ SV218 @ SV28 ) ) @ SV28 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SV218 @ SV28 ) @ ( sK14_SY3290 @ SV218 @ SV28 ) ) @ SV218 )
| ( in @ ( ordered_pair @ ( sK14_SY3290 @ SV218 @ SV28 ) @ ( sK13_C @ SV218 @ SV28 ) ) @ SV28 ) ) )
| ( SV218
= ( relation_inverse @ SV28 ) ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1255,plain,
! [SV28: $i,SV219: $i] :
( ( ( ~ ( relation @ SV219 )
| ( SV219
!= ( relation_inverse @ SV28 ) )
| ~ ( ~ ! [SY3815: $i,SY3816: $i] :
( ~ ( in @ ( ordered_pair @ SY3815 @ SY3816 ) @ SV219 )
| ( in @ ( ordered_pair @ SY3816 @ SY3815 ) @ SV28 ) )
| ~ ! [SY3817: $i,SY3818: $i] :
( ~ ( in @ ( ordered_pair @ SY3818 @ SY3817 ) @ SV28 )
| ( in @ ( ordered_pair @ SY3817 @ SY3818 ) @ SV219 ) ) ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1256,plain,
! [SV29: $i] :
( ( ( ~ ! [SY3381: $i,SY3382: $i] :
( ~ ( ~ ( ! [SY3383: $i] :
( ~ ( in @ SY3383 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3383 @ SY3381 )
| ( ( sK61_D @ SY3382 @ SY3381 @ SV29 )
!= ( apply @ SV29 @ SY3383 ) ) )
| ~ ( in @ ( sK61_D @ SY3382 @ SY3381 @ SV29 ) @ SY3382 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY3318 @ SY3382 @ SY3381 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK62_SY3318 @ SY3382 @ SY3381 @ SV29 ) @ SY3381 ) )
| ( ( sK61_D @ SY3382 @ SY3381 @ SV29 )
!= ( apply @ SV29 @ ( sK62_SY3318 @ SY3382 @ SY3381 @ SV29 ) ) ) )
| ( in @ ( sK61_D @ SY3382 @ SY3381 @ SV29 ) @ SY3382 ) ) )
| ( SY3382
= ( relation_image @ SV29 @ SY3381 ) ) ) )
= $false )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1128]) ).
thf(1257,plain,
! [SV29: $i] :
( ( ( ~ ! [SY3384: $i,SY3385: $i] :
( ( SY3385
!= ( relation_image @ SV29 @ SY3384 ) )
| ~ ( ~ ! [SY3386: $i] :
( ! [SY3387: $i] :
( ~ ( in @ SY3387 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3387 @ SY3384 )
| ( SY3386
!= ( apply @ SV29 @ SY3387 ) ) )
| ( in @ SY3386 @ SY3385 ) )
| ~ ! [SY3388: $i] :
( ~ ( in @ SY3388 @ SY3385 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SY3388 @ SY3385 @ SY3384 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK60_E @ SY3388 @ SY3385 @ SY3384 @ SV29 ) @ SY3384 ) )
| ( SY3388
!= ( apply @ SV29 @ ( sK60_E @ SY3388 @ SY3385 @ SY3384 @ SV29 ) ) ) ) ) ) ) )
= $false )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1128]) ).
thf(1258,plain,
! [SV30: $i,SV220: $i] :
( ( ( ! [SY3819: $i] :
( ~ ( ~ ( ! [SY3820: $i] :
( ~ ( in @ ( ordered_pair @ SY3820 @ ( sK55_D @ SY3819 @ SV220 @ SV30 ) ) @ SV30 )
| ~ ( in @ SY3820 @ SV220 ) )
| ~ ( in @ ( sK55_D @ SY3819 @ SV220 @ SV30 ) @ SY3819 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_SY3315 @ SY3819 @ SV220 @ SV30 ) @ ( sK55_D @ SY3819 @ SV220 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK56_SY3315 @ SY3819 @ SV220 @ SV30 ) @ SV220 ) )
| ( in @ ( sK55_D @ SY3819 @ SV220 @ SV30 ) @ SY3819 ) ) )
| ( SY3819
= ( relation_image @ SV30 @ SV220 ) ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1259,plain,
! [SV221: $i,SV30: $i] :
( ( ( ! [SY3821: $i] :
( ( SY3821
!= ( relation_image @ SV30 @ SV221 ) )
| ~ ( ~ ! [SY3822: $i] :
( ! [SY3823: $i] :
( ~ ( in @ ( ordered_pair @ SY3823 @ SY3822 ) @ SV30 )
| ~ ( in @ SY3823 @ SV221 ) )
| ( in @ SY3822 @ SY3821 ) )
| ~ ! [SY3824: $i] :
( ~ ( in @ SY3824 @ SY3821 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SY3824 @ SY3821 @ SV221 @ SV30 ) @ SY3824 ) @ SV30 )
| ~ ( in @ ( sK54_E @ SY3824 @ SY3821 @ SV221 @ SV30 ) @ SV221 ) ) ) ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1260,plain,
! [SV31: $i,SV222: $i] :
( ( ( ! [SY3825: $i] :
( ~ ( ~ ( ! [SY3826: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ SY3825 @ SV222 @ SV31 ) @ SY3826 ) @ SV31 )
| ~ ( in @ SY3826 @ SV222 ) )
| ~ ( in @ ( sK52_D @ SY3825 @ SV222 @ SV31 ) @ SY3825 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SY3825 @ SV222 @ SV31 ) @ ( sK53_SY3313 @ SY3825 @ SV222 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( sK53_SY3313 @ SY3825 @ SV222 @ SV31 ) @ SV222 ) )
| ( in @ ( sK52_D @ SY3825 @ SV222 @ SV31 ) @ SY3825 ) ) )
| ( SY3825
= ( relation_inverse_image @ SV31 @ SV222 ) ) ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1261,plain,
! [SV223: $i,SV31: $i] :
( ( ( ! [SY3827: $i] :
( ( SY3827
!= ( relation_inverse_image @ SV31 @ SV223 ) )
| ~ ( ~ ! [SY3828: $i] :
( ! [SY3829: $i] :
( ~ ( in @ ( ordered_pair @ SY3828 @ SY3829 ) @ SV31 )
| ~ ( in @ SY3829 @ SV223 ) )
| ( in @ SY3828 @ SY3827 ) )
| ~ ! [SY3830: $i] :
( ~ ( in @ SY3830 @ SY3827 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3830 @ ( sK51_E @ SY3830 @ SY3827 @ SV223 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( sK51_E @ SY3830 @ SY3827 @ SV223 @ SV31 ) @ SV223 ) ) ) ) ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1262,plain,
! [SV32: $i,SV224: $i] :
( ( ( ! [SY3831: $i] :
( ~ ( relation @ SY3831 )
| ~ ( ~ ( ~ ( in @ ( sK63_D @ SY3831 @ SV224 @ SV32 ) @ SV224 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SY3831 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SY3831 @ SV224 @ SV32 ) ) @ SV32 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SY3831 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SY3831 @ SV224 @ SV32 ) ) @ SY3831 ) )
| ~ ~ ( ~ ( ( in @ ( sK63_D @ SY3831 @ SV224 @ SV32 ) @ SV224 )
| ( in @ ( ordered_pair @ ( sK63_D @ SY3831 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SY3831 @ SV224 @ SV32 ) ) @ SY3831 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SY3831 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SY3831 @ SV224 @ SV32 ) ) @ SV32 )
| ( in @ ( ordered_pair @ ( sK63_D @ SY3831 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SY3831 @ SV224 @ SV32 ) ) @ SY3831 ) ) ) )
| ( SY3831
= ( relation_dom_restriction @ SV32 @ SV224 ) ) ) )
= $true )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1263,plain,
! [SV225: $i,SV32: $i] :
( ( ( ! [SY3832: $i] :
( ~ ( relation @ SY3832 )
| ( SY3832
!= ( relation_dom_restriction @ SV32 @ SV225 ) )
| ~ ( ~ ! [SY3833: $i,SY3834: $i] :
( ~ ( in @ SY3833 @ SV225 )
| ~ ( in @ ( ordered_pair @ SY3833 @ SY3834 ) @ SV32 )
| ( in @ ( ordered_pair @ SY3833 @ SY3834 ) @ SY3832 ) )
| ~ ~ ( ~ ! [SY3835: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SY3835 @ SX4 ) @ SY3832 )
| ( in @ SY3835 @ SV225 ) )
| ~ ! [SY3413: $i,SY3414: $i] :
( ~ ( in @ ( ordered_pair @ SY3413 @ SY3414 ) @ SY3832 )
| ( in @ ( ordered_pair @ SY3413 @ SY3414 ) @ SV32 ) ) ) ) ) )
= $true )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1264,plain,
! [SV143: $i,SV33: $i,SV188: $i] :
( ( ( ~ ( relation @ SV188 ) )
= $true )
| ( ( ! [SY3786: $i] :
( ~ ( in @ SY3786 @ ( relation_rng @ SV188 ) )
| ~ ( in @ ( ordered_pair @ SV33 @ SY3786 ) @ SV188 )
| ~ ( in @ SY3786 @ SV143 ) )
| ( in @ SV33 @ ( relation_inverse_image @ SV188 @ SV143 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1135]) ).
thf(1265,plain,
! [SV144: $i,SV33: $i,SV189: $i] :
( ( ( ~ ( relation @ SV189 ) )
= $true )
| ( ( ~ ( in @ SV33 @ ( relation_inverse_image @ SV189 @ SV144 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK75_D @ SV189 @ SV144 @ SV33 ) @ ( relation_rng @ SV189 ) )
| ~ ( in @ ( ordered_pair @ SV33 @ ( sK75_D @ SV189 @ SV144 @ SV33 ) ) @ SV189 ) )
| ~ ( in @ ( sK75_D @ SV189 @ SV144 @ SV33 ) @ SV144 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1136]) ).
thf(1266,plain,
! [SV110: $i,SV145: $i] :
( ( ( relation @ SV145 )
= $false )
| ( ( ~ ( ~ ( ( ( sK65_C @ SV145 @ SV110 )
!= ( sK66_SY3320 @ SV145 @ SV110 ) )
| ~ ( in @ ( sK65_C @ SV145 @ SV110 ) @ SV110 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 ) )
| ~ ~ ( ~ ( ( ( sK65_C @ SV145 @ SV110 )
= ( sK66_SY3320 @ SV145 @ SV110 ) )
| ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 ) )
| ~ ( ( in @ ( sK65_C @ SV145 @ SV110 ) @ SV110 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 ) ) ) )
| ( SV145
= ( identity_relation @ SV110 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1137]) ).
thf(1267,plain,
! [SV111: $i,SV146: $i] :
( ( ( relation @ SV146 )
= $false )
| ( ( ( SV146
!= ( identity_relation @ SV111 ) )
| ~ ( ~ ! [SY3732: $i,SY3733: $i] :
( ( SY3732 != SY3733 )
| ~ ( in @ SY3732 @ SV111 )
| ( in @ ( ordered_pair @ SY3732 @ SY3733 ) @ SV146 ) )
| ~ ~ ( ~ ! [SY3734: $i,SY3735: $i] :
( ~ ( in @ ( ordered_pair @ SY3734 @ SY3735 ) @ SV146 )
| ( SY3734 = SY3735 ) )
| ~ ! [SY3736: $i] :
( ! [SY3737: $i] :
~ ( in @ ( ordered_pair @ SY3736 @ SY3737 ) @ SV146 )
| ( in @ SY3736 @ SV111 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1138]) ).
thf(1268,plain,
! [SV34: $i,SV89: $i,SV190: $i,SV226: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV190 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV34 ) )
| ~ ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV89 ) ) ) )
| ~ ( ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
= SV190 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
= SV34 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
= SV89 ) ) )
| ( SV226
= ( unordered_triple @ SV34 @ SV89 @ SV190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1139]) ).
thf(1269,plain,
! [SV191: $i,SV89: $i,SV34: $i,SV227: $i] :
( ( ( SV227
!= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
| ~ ( ~ ! [SY3839: $i] :
( ~ ( in @ SY3839 @ SV227 )
| ( SY3839 = SV191 )
| ( SY3839 = SV34 )
| ( SY3839 = SV89 ) )
| ~ ~ ( ~ ! [SY3840: $i] :
( ( SY3840 != SV191 )
| ( in @ SY3840 @ SV227 ) )
| ~ ~ ( ~ ! [SY3841: $i] :
( ( SY3841 != SV34 )
| ( in @ SY3841 @ SV227 ) )
| ~ ! [SY3842: $i] :
( ( SY3842 != SV89 )
| ( in @ SY3842 @ SV227 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1270,plain,
! [SV147: $i,SV35: $i,SV192: $i] :
( ( ( ~ ( relation @ SV192 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV35 @ SV147 ) @ SV192 )
| ( in @ SV35 @ ( relation_field @ SV192 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1141]) ).
thf(1271,plain,
! [SV148: $i,SV35: $i,SV193: $i] :
( ( ( ~ ( relation @ SV193 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV35 @ SV148 ) @ SV193 )
| ( in @ SV148 @ ( relation_field @ SV193 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1142]) ).
thf(1272,plain,
! [SV36: $i,SV228: $i] :
( ( ( ~ ( ~ ( ! [SY3843: $i] :
~ ( in @ ( ordered_pair @ SY3843 @ ( sK16_C @ SV228 @ SV36 ) ) @ SV36 )
| ~ ( in @ ( sK16_C @ SV228 @ SV36 ) @ SV228 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_SY3292 @ SV228 @ SV36 ) @ ( sK16_C @ SV228 @ SV36 ) ) @ SV36 )
| ( in @ ( sK16_C @ SV228 @ SV36 ) @ SV228 ) ) )
| ( SV228
= ( relation_rng @ SV36 ) ) )
= $true )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1273,plain,
! [SV36: $i,SV229: $i] :
( ( ( ( SV229
!= ( relation_rng @ SV36 ) )
| ~ ( ~ ! [SY3844: $i] :
( ! [SY3437: $i] :
~ ( in @ ( ordered_pair @ SY3437 @ SY3844 ) @ SV36 )
| ( in @ SY3844 @ SV229 ) )
| ~ ! [SY3846: $i] :
( ~ ( in @ SY3846 @ SV229 )
| ( in @ ( ordered_pair @ ( sK15_D @ SY3846 @ SV229 @ SV36 ) @ SY3846 ) @ SV36 ) ) ) )
= $true )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1274,plain,
! [SV37: $i,SV149: $i] :
( ( ( ~ ( subset @ SV149 @ ( sK77_B @ SV37 ) ) )
= $true )
| ( ( are_equipotent @ SV149 @ ( sK77_B @ SV37 ) )
= $true )
| ( ( in @ SV149 @ ( sK77_B @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1145]) ).
thf(1275,plain,
! [SV37: $i] :
( ( ! [SY3440: $i] :
( ~ ( in @ SY3440 @ ( sK77_B @ SV37 ) )
| ( in @ ( powerset @ SY3440 ) @ ( sK77_B @ SV37 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1146]) ).
thf(1276,plain,
! [SV37: $i] :
( ( ~ ( ~ ! [SY3441: $i,SY3442: $i] :
( ~ ( in @ SY3441 @ ( sK77_B @ SV37 ) )
| ~ ( subset @ SY3442 @ SY3441 )
| ( in @ SY3442 @ ( sK77_B @ SV37 ) ) )
| ~ ( in @ SV37 @ ( sK77_B @ SV37 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1147]) ).
thf(1277,plain,
! [SV112: $i,SV150: $i] :
( ( ( ~ ( ~ ( in @ ( sK41_C @ SV150 @ SV112 ) @ SV150 )
| ~ ( subset @ ( sK41_C @ SV150 @ SV112 ) @ SV112 ) )
| ~ ( ( in @ ( sK41_C @ SV150 @ SV112 ) @ SV150 )
| ( subset @ ( sK41_C @ SV150 @ SV112 ) @ SV112 ) ) )
= $false )
| ( ( SV150
= ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1148]) ).
thf(1278,plain,
! [SV113: $i,SV151: $i] :
( ( ( SV151
= ( powerset @ SV113 ) )
= $false )
| ( ( ~ ( ~ ! [SY3740: $i] :
( ~ ( in @ SY3740 @ SV151 )
| ( subset @ SY3740 @ SV113 ) )
| ~ ! [SY3741: $i] :
( ~ ( subset @ SY3741 @ SV113 )
| ( in @ SY3741 @ SV151 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1149]) ).
thf(1279,plain,
! [SV38: $i,SV90: $i] :
( ( ( ~ ( in @ ( sK5_C @ SV90 @ SV38 ) @ SV38 ) )
= $true )
| ( ( ~ ( in @ ( sK5_C @ SV90 @ SV38 ) @ SV90 ) )
= $true )
| ( ( SV38 = SV90 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1150]) ).
thf(1280,plain,
! [SV38: $i,SV90: $i] :
( ( ( in @ ( sK5_C @ SV90 @ SV38 ) @ SV38 )
= $true )
| ( ( in @ ( sK5_C @ SV90 @ SV38 ) @ SV90 )
= $true )
| ( ( SV38 = SV90 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1151]) ).
thf(1281,plain,
! [SV114: $i,SV152: $i] :
( ( ( ~ ( function @ SV152 ) )
= $true )
| ( ( ~ ( relation @ SV152 ) )
= $true )
| ( ( ~ ( in @ SV114 @ ( relation_rng @ SV152 ) )
| ~ ( one_to_one @ SV152 )
| ( SV114
= ( apply @ SV152 @ ( apply @ ( function_inverse @ SV152 ) @ SV114 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1152]) ).
thf(1282,plain,
! [SV115: $i,SV153: $i] :
( ( ( ~ ( function @ SV153 ) )
= $true )
| ( ( ~ ( relation @ SV153 ) )
= $true )
| ( ( ~ ( in @ SV115 @ ( relation_rng @ SV153 ) )
| ~ ( one_to_one @ SV153 )
| ( SV115
= ( apply @ ( relation_composition @ ( function_inverse @ SV153 ) @ SV153 ) @ SV115 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1153]) ).
thf(1283,plain,
! [SV91: $i,SV39: $i] :
( ( ( ~ ! [SY3641: $i] :
( ~ ( function @ SY3641 )
| ~ ( relation @ SY3641 )
| ~ ( in @ SV39 @ ( relation_dom @ SY3641 ) )
| ~ ( in @ ( apply @ SY3641 @ SV39 ) @ ( relation_dom @ SV91 ) )
| ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3641 @ SV91 ) ) ) )
| ~ ~ ( ~ ! [SY3642: $i] :
( ~ ( function @ SY3642 )
| ~ ( relation @ SY3642 )
| ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3642 @ SV91 ) ) )
| ( in @ SV39 @ ( relation_dom @ SY3642 ) ) )
| ~ ! [SY3643: $i] :
( ~ ( function @ SY3643 )
| ~ ( relation @ SY3643 )
| ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3643 @ SV91 ) ) )
| ( in @ ( apply @ SY3643 @ SV39 ) @ ( relation_dom @ SV91 ) ) ) ) )
= $false )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1154]) ).
thf(1284,plain,
! [SV92: $i,SV40: $i] :
( ( ( ! [SY3644: $i] :
( ~ ( element @ SY3644 @ ( powerset @ ( powerset @ SV40 ) ) )
| ~ ( ~ ( element @ ( sK6_D @ SY3644 @ SV92 @ SV40 ) @ ( powerset @ SV40 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK6_D @ SY3644 @ SV92 @ SV40 ) @ SY3644 )
| ~ ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SY3644 @ SV92 @ SV40 ) ) @ SV92 ) )
| ~ ( ( in @ ( sK6_D @ SY3644 @ SV92 @ SV40 ) @ SY3644 )
| ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SY3644 @ SV92 @ SV40 ) ) @ SV92 ) ) ) )
| ( SY3644
= ( complements_of_subsets @ SV40 @ SV92 ) ) ) )
= $true )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1155]) ).
thf(1285,plain,
! [SV92: $i,SV40: $i] :
( ( ( ! [SY3645: $i] :
( ~ ( element @ SY3645 @ ( powerset @ ( powerset @ SV40 ) ) )
| ( SY3645
!= ( complements_of_subsets @ SV40 @ SV92 ) )
| ~ ( ~ ! [SY3646: $i] :
( ~ ( element @ SY3646 @ ( powerset @ SV40 ) )
| ~ ( in @ SY3646 @ SY3645 )
| ( in @ ( subset_complement @ SV40 @ SY3646 ) @ SV92 ) )
| ~ ! [SY3647: $i] :
( ~ ( element @ SY3647 @ ( powerset @ SV40 ) )
| ~ ( in @ ( subset_complement @ SV40 @ SY3647 ) @ SV92 )
| ( in @ SY3647 @ SY3645 ) ) ) ) )
= $true )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1156]) ).
thf(1286,plain,
! [SV41: $i,SV154: $i,SV194: $i] :
( ( ( ~ ( function @ SV194 )
| ~ ( relation @ SV194 ) )
= $true )
| ( ( ( SV154
!= ( apply @ SV194 @ SV41 ) )
| ~ ( in @ SV41 @ ( relation_dom @ SV194 ) )
| ( in @ ( ordered_pair @ SV41 @ SV154 ) @ SV194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1157]) ).
thf(1287,plain,
! [SV41: $i] :
( ( ! [SY3455: $i,SY3456: $i] :
( ~ ( function @ SY3456 )
| ~ ( relation @ SY3456 )
| ~ ( in @ ( ordered_pair @ SV41 @ SY3455 ) @ SY3456 )
| ( SY3455
= ( apply @ SY3456 @ SV41 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1158]) ).
thf(1288,plain,
! [SV41: $i] :
( ( ! [SY3457: $i,SY3458: $i] :
( ~ ( function @ SY3458 )
| ~ ( relation @ SY3458 )
| ~ ( in @ ( ordered_pair @ SV41 @ SY3457 ) @ SY3458 )
| ( in @ SV41 @ ( relation_dom @ SY3458 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1159]) ).
thf(1289,plain,
! [SV155: $i,SV42: $i,SV195: $i] :
( ( ( ~ ( relation @ SV195 ) )
= $true )
| ( ( ~ ( in @ SV42 @ SV155 )
| ~ ( in @ SV42 @ ( relation_rng @ SV195 ) )
| ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SV155 @ SV195 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1160]) ).
thf(1290,plain,
! [SV42: $i] :
( ( ! [SY3461: $i,SY3462: $i] :
( ~ ( relation @ SY3462 )
| ~ ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SY3461 @ SY3462 ) ) )
| ( in @ SV42 @ SY3461 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1161]) ).
thf(1291,plain,
! [SV42: $i] :
( ( ! [SY3463: $i,SY3464: $i] :
( ~ ( relation @ SY3464 )
| ~ ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SY3463 @ SY3464 ) ) )
| ( in @ SV42 @ ( relation_rng @ SY3464 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1162]) ).
thf(1292,plain,
! [SV43: $i,SV156: $i] :
( ( ( ~ ( subset @ SV156 @ ( sK2_B @ SV43 ) ) )
= $true )
| ( ( are_equipotent @ SV156 @ ( sK2_B @ SV43 ) )
= $true )
| ( ( in @ SV156 @ ( sK2_B @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1163]) ).
thf(1293,plain,
! [SV43: $i] :
( ( ! [SY3466: $i] :
( ~ ( ~ ! [SY3467: $i] :
( ~ ( subset @ SY3467 @ SY3466 )
| ( in @ SY3467 @ ( sK3_SY3278 @ SY3466 @ SV43 ) ) )
| ~ ( in @ ( sK3_SY3278 @ SY3466 @ SV43 ) @ ( sK2_B @ SV43 ) ) )
| ~ ( in @ SY3466 @ ( sK2_B @ SV43 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1164]) ).
thf(1294,plain,
! [SV43: $i] :
( ( ~ ( ~ ! [SY3468: $i,SY3469: $i] :
( ~ ( in @ SY3468 @ ( sK2_B @ SV43 ) )
| ~ ( subset @ SY3469 @ SY3468 )
| ( in @ SY3469 @ ( sK2_B @ SV43 ) ) )
| ~ ( in @ SV43 @ ( sK2_B @ SV43 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1165]) ).
thf(1295,plain,
! [SV116: $i] :
( ( ( ~ ! [SY3692: $i,SY3693: $i] :
( ( sK49_B @ SV116 )
!= ( ordered_pair @ SY3692 @ SY3693 ) ) )
= $false )
| ( ( relation @ SV116 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1166]) ).
thf(1296,plain,
! [SV116: $i] :
( ( ( ~ ( in @ ( sK49_B @ SV116 ) @ SV116 ) )
= $false )
| ( ( relation @ SV116 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1166]) ).
thf(1297,plain,
! [SV117: $i,SV230: $i] :
( ( ( ( SV230
= ( ordered_pair @ ( sK47_C @ SV230 @ SV117 ) @ ( sK48_SY3309 @ SV230 @ SV117 ) ) )
| ~ ( in @ SV230 @ SV117 ) )
= $true )
| ( ( relation @ SV117 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1167]) ).
thf(1298,plain,
! [SV231: $i,SV93: $i,SV196: $i,SV44: $i] :
( ( ~ ( in @ SV44 @ SV196 )
| ~ ( in @ SV93 @ SV231 )
| ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SV196 @ SV231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1168]) ).
thf(1299,plain,
! [SV93: $i,SV44: $i] :
( ( ~ ! [SY3650: $i] :
( ! [SY3651: $i] :
~ ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SY3650 @ SY3651 ) )
| ( in @ SV44 @ SY3650 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1169]) ).
thf(1300,plain,
! [SV93: $i,SV44: $i] :
( ( ~ ! [SY3652: $i,SY3653: $i] :
( ~ ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SY3652 @ SY3653 ) )
| ( in @ SV93 @ SY3653 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1169]) ).
thf(1301,plain,
! [SV45: $i,SV232: $i] :
( ( ( ~ ( ~ ( ! [SY3847: $i] :
~ ( in @ ( ordered_pair @ ( sK26_C @ SV232 @ SV45 ) @ SY3847 ) @ SV45 )
| ~ ( in @ ( sK26_C @ SV232 @ SV45 ) @ SV232 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK26_C @ SV232 @ SV45 ) @ ( sK27_SY3298 @ SV232 @ SV45 ) ) @ SV45 )
| ( in @ ( sK26_C @ SV232 @ SV45 ) @ SV232 ) ) )
| ( SV232
= ( relation_dom @ SV45 ) ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1170]) ).
thf(1302,plain,
! [SV45: $i,SV233: $i] :
( ( ( ( SV233
!= ( relation_dom @ SV45 ) )
| ~ ( ~ ! [SY3848: $i] :
( ! [SY3481: $i] :
~ ( in @ ( ordered_pair @ SY3848 @ SY3481 ) @ SV45 )
| ( in @ SY3848 @ SV233 ) )
| ~ ! [SY3850: $i] :
( ~ ( in @ SY3850 @ SV233 )
| ( in @ ( ordered_pair @ SY3850 @ ( sK25_D @ SY3850 @ SV233 @ SV45 ) ) @ SV45 ) ) ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1171]) ).
thf(1303,plain,
! [SV234: $i] :
( ( ( empty @ SV234 )
| ! [SY3851: $i] :
( ~ ( element @ SY3851 @ SV234 )
| ( in @ SY3851 @ SV234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1172]) ).
thf(1304,plain,
! [SV235: $i] :
( ( ( empty @ SV235 )
| ! [SY3852: $i] :
( ~ ( in @ SY3852 @ SV235 )
| ( element @ SY3852 @ SV235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1305,plain,
! [SV236: $i] :
( ( ~ ( empty @ SV236 )
| ! [SY3853: $i] :
( ~ ( element @ SY3853 @ SV236 )
| ( empty @ SY3853 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1306,plain,
! [SV237: $i] :
( ( ~ ( empty @ SV237 )
| ! [SY3854: $i] :
( ~ ( empty @ SY3854 )
| ( element @ SY3854 @ SV237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1307,plain,
! [SV119: $i,SV238: $i] :
( ( ( ~ ( in @ SV238 @ SV119 ) )
= $true )
| ( ( SV119 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1176]) ).
thf(1308,plain,
! [SV120: $i,SV157: $i] :
( ( ( ~ ( ( ( sK43_C @ SV157 @ SV120 )
!= SV120 )
| ~ ( in @ ( sK43_C @ SV157 @ SV120 ) @ SV157 ) )
| ~ ( ( ( sK43_C @ SV157 @ SV120 )
= SV120 )
| ( in @ ( sK43_C @ SV157 @ SV120 ) @ SV157 ) ) )
= $false )
| ( ( SV157
= ( singleton @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1177]) ).
thf(1309,plain,
! [SV121: $i,SV158: $i] :
( ( ( SV158
= ( singleton @ SV121 ) )
= $false )
| ( ( ~ ( ~ ! [SY3744: $i] :
( ( SY3744 != SV121 )
| ( in @ SY3744 @ SV158 ) )
| ~ ! [SY3745: $i] :
( ~ ( in @ SY3745 @ SV158 )
| ( SY3745 = SV121 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1178]) ).
thf(1310,plain,
! [SV122: $i,SV159: $i] :
( ( ( ~ ( function @ SV159 ) )
= $true )
| ( ( ~ ( relation @ SV159 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK74_C @ SV159 @ SV122 ) @ SV122 )
| ~ ( ( ( apply @ SV159 @ ( sK74_C @ SV159 @ SV122 ) )
!= ( sK74_C @ SV159 @ SV122 ) ) ) )
| ( ( relation_dom @ SV159 )
!= SV122 )
| ( SV159
= ( identity_relation @ SV122 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1179]) ).
thf(1311,plain,
! [SV239: $i] :
( ( ! [SY3855: $i] :
( ~ ( function @ SY3855 )
| ~ ( relation @ SY3855 )
| ( SY3855
!= ( identity_relation @ SV239 ) )
| ! [SY3856: $i] :
( ~ ( in @ SY3856 @ SV239 )
| ( ( apply @ SY3855 @ SY3856 )
= SY3856 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1180]) ).
thf(1312,plain,
! [SV240: $i] :
( ( ! [SY3857: $i] :
( ~ ( function @ SY3857 )
| ~ ( relation @ SY3857 )
| ( SY3857
!= ( identity_relation @ SV240 ) )
| ( ( relation_dom @ SY3857 )
= SV240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1313,plain,
! [SV46: $i] :
( ( ( one_to_one @ SV46 )
= $false )
| ( ( ~ ( ~ ! [SY3483: $i] :
( ~ ( function @ SY3483 )
| ~ ( relation @ SY3483 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY3322 @ SY3483 @ SV46 )
= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ( ( sK70_C @ SY3483 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SY3483 @ SV46 )
= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SY3483 @ SV46 )
= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ( ( sK71_SY3322 @ SY3483 @ SV46 )
!= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK70_C @ SY3483 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK71_SY3322 @ SY3483 @ SV46 )
!= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY3483 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK70_C @ SY3483 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SY3483 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SY3483 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK71_SY3322 @ SY3483 @ SV46 )
!= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ( ( relation_dom @ SY3483 )
!= ( relation_rng @ SV46 ) )
| ( SY3483
= ( function_inverse @ SV46 ) ) )
| ~ ~ ( ~ ! [SY3484: $i] :
( ~ ( function @ SY3484 )
| ~ ( relation @ SY3484 )
| ( SY3484
!= ( function_inverse @ SV46 ) )
| ~ ( ~ ~ ( ~ ! [SY3485: $i,SY3486: $i] :
( ( SY3486
!= ( apply @ SY3484 @ SY3485 ) )
| ~ ( in @ SY3485 @ ( relation_rng @ SV46 ) )
| ( SY3485
= ( apply @ SV46 @ SY3486 ) ) )
| ~ ! [SY3487: $i,SY3488: $i] :
( ( SY3488
!= ( apply @ SY3484 @ SY3487 ) )
| ~ ( in @ SY3487 @ ( relation_rng @ SV46 ) )
| ( in @ SY3488 @ ( relation_dom @ SV46 ) ) ) )
| ~ ~ ( ~ ! [SY3489: $i,SY3490: $i] :
( ( SY3489
!= ( apply @ SV46 @ SY3490 ) )
| ~ ( in @ SY3490 @ ( relation_dom @ SV46 ) )
| ( SY3490
= ( apply @ SY3484 @ SY3489 ) ) )
| ~ ! [SY3491: $i] :
( ! [SY3492: $i] :
( ( SY3491
!= ( apply @ SV46 @ SY3492 ) )
| ~ ( in @ SY3492 @ ( relation_dom @ SV46 ) ) )
| ( in @ SY3491 @ ( relation_rng @ SV46 ) ) ) ) ) )
| ~ ! [SY3493: $i] :
( ~ ( function @ SY3493 )
| ~ ( relation @ SY3493 )
| ( SY3493
!= ( function_inverse @ SV46 ) )
| ( ( relation_dom @ SY3493 )
= ( relation_rng @ SV46 ) ) ) ) ) )
= $true )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1182]) ).
thf(1314,plain,
! [SV47: $i,SV123: $i] :
( ( ( ~ ! [SY3701: $i] :
( ~ ( relation @ SY3701 )
| ~ ( ~ ( ! [SY3702: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY3701 @ SV123 @ SV47 ) @ SY3702 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3702 @ ( sK9_SY3284 @ SY3701 @ SV123 @ SV47 ) ) @ SV123 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SY3701 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SY3701 @ SV123 @ SV47 ) ) @ SY3701 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY3701 @ SV123 @ SV47 ) @ ( sK10_SY3288 @ SY3701 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY3288 @ SY3701 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SY3701 @ SV123 @ SV47 ) ) @ SV123 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SY3701 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SY3701 @ SV123 @ SV47 ) ) @ SY3701 ) ) )
| ( SY3701
= ( relation_composition @ SV47 @ SV123 ) ) )
| ~ ! [SY3703: $i] :
( ~ ( relation @ SY3703 )
| ( SY3703
!= ( relation_composition @ SV47 @ SV123 ) )
| ~ ( ~ ! [SY3704: $i,SY3705: $i] :
( ! [SY3706: $i] :
( ~ ( in @ ( ordered_pair @ SY3704 @ SY3706 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3706 @ SY3705 ) @ SV123 ) )
| ( in @ ( ordered_pair @ SY3704 @ SY3705 ) @ SY3703 ) )
| ~ ! [SY3707: $i,SY3708: $i] :
( ~ ( in @ ( ordered_pair @ SY3707 @ SY3708 ) @ SY3703 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3707 @ ( sK7_F @ SY3708 @ SY3707 @ SY3703 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY3708 @ SY3707 @ SY3703 @ SV123 @ SV47 ) @ SY3708 ) @ SV123 ) ) ) ) ) )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1183]) ).
thf(1315,plain,
! [SV160: $i,SV197: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ SV197 )
| ~ ( in @ SV160 @ SV197 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV48 @ SV160 ) @ SV197 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1184]) ).
thf(1316,plain,
! [SV48: $i] :
( ( ! [SY3505: $i,SY3506: $i] :
( ~ ( subset @ ( unordered_pair @ SV48 @ SY3505 ) @ SY3506 )
| ( in @ SV48 @ SY3506 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1185]) ).
thf(1317,plain,
! [SV48: $i] :
( ( ! [SY3507: $i,SY3508: $i] :
( ~ ( subset @ ( unordered_pair @ SV48 @ SY3507 ) @ SY3508 )
| ( in @ SY3507 @ SY3508 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1186]) ).
thf(1318,plain,
! [SV94: $i,SV198: $i,SV49: $i,SV241: $i] :
( ( ~ ( relation @ SV241 )
| ~ ( in @ SV49 @ SV198 )
| ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ SV241 )
| ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SV198 ) @ SV241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1187]) ).
thf(1319,plain,
! [SV94: $i,SV49: $i] :
( ( ~ ! [SY3656: $i,SY3657: $i] :
( ~ ( relation @ SY3657 )
| ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SY3656 ) @ SY3657 ) )
| ( in @ SV49 @ SY3656 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1188]) ).
thf(1320,plain,
! [SV94: $i,SV49: $i] :
( ( ~ ! [SY3658: $i,SY3659: $i] :
( ~ ( relation @ SY3659 )
| ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SY3658 ) @ SY3659 ) )
| ( in @ ( ordered_pair @ SV49 @ SV94 ) @ SY3659 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1188]) ).
thf(1321,plain,
! [SV50: $i,SV95: $i,SV242: $i] :
( ( ( ~ ( in @ SV242 @ SV95 )
| ~ ( in @ SV242 @ ( sK4_C @ SV95 @ SV50 ) ) )
= $true )
| ( ( ~ ( in @ SV50 @ SV95 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1322,plain,
! [SV95: $i,SV50: $i] :
( ( ( in @ SV50 @ SV95 )
= $false )
| ( ( in @ ( sK4_C @ SV95 @ SV50 ) @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1190]) ).
thf(1323,plain,
! [SV124: $i] :
( ( ( function @ SV124 )
= $false )
| ( ( ~ ( relation @ SV124 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_B @ SV124 ) @ ( relation_dom @ SV124 ) )
| ~ ( in @ ( sK12_SY3289 @ SV124 ) @ ( relation_dom @ SV124 ) ) )
| ( ( apply @ SV124 @ ( sK11_B @ SV124 ) )
!= ( apply @ SV124 @ ( sK12_SY3289 @ SV124 ) ) ) )
| ~ ( ( ( sK11_B @ SV124 )
!= ( sK12_SY3289 @ SV124 ) ) ) )
| ( one_to_one @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1191]) ).
thf(1324,plain,
! [SV125: $i] :
( ( ( function @ SV125 )
= $false )
| ( ( ~ ( relation @ SV125 ) )
= $true )
| ( ( ~ ( one_to_one @ SV125 )
| ! [SY3709: $i,SY3710: $i] :
( ~ ( in @ SY3709 @ ( relation_dom @ SV125 ) )
| ~ ( in @ SY3710 @ ( relation_dom @ SV125 ) )
| ( ( apply @ SV125 @ SY3709 )
!= ( apply @ SV125 @ SY3710 ) )
| ( SY3709 = SY3710 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1192]) ).
thf(1325,plain,
! [SV51: $i,SV161: $i,SV199: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV199 )
| ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV51 ) )
| ~ ( ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV199 )
| ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV161 ) ) )
| ~ ( ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV199 )
| ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV51 )
| ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV161 ) ) ) )
= $true )
| ( ( SV199
= ( set_union2 @ SV51 @ SV161 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1193]) ).
thf(1326,plain,
! [SV162: $i,SV51: $i,SV200: $i] :
( ( ( ( SV200
!= ( set_union2 @ SV51 @ SV162 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3795: $i] :
( ~ ( in @ SY3795 @ SV200 )
| ( in @ SY3795 @ SV51 )
| ( in @ SY3795 @ SV162 ) )
| ~ ~ ( ~ ! [SY3796: $i] :
( ~ ( in @ SY3796 @ SV51 )
| ( in @ SY3796 @ SV200 ) )
| ~ ! [SY3797: $i] :
( ~ ( in @ SY3797 @ SV162 )
| ( in @ SY3797 @ SV200 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1194]) ).
thf(1327,plain,
! [SV163: $i,SV126: $i] :
( ( ( ( set_difference @ SV126 @ ( singleton @ SV163 ) )
= SV126 )
= $false )
| ( ( ~ ( in @ SV163 @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1195]) ).
thf(1328,plain,
! [SV52: $i,SV243: $i] :
( ( ( ~ ( relation @ SV243 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK30_C @ SV243 @ SV52 ) @ ( sK31_SY3299 @ SV243 @ SV52 ) ) @ SV52 )
| ~ ~ ( in @ ( ordered_pair @ ( sK30_C @ SV243 @ SV52 ) @ ( sK31_SY3299 @ SV243 @ SV52 ) ) @ SV243 ) )
| ( subset @ SV52 @ SV243 ) )
= $true )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1329,plain,
! [SV52: $i,SV244: $i] :
( ( ( ~ ( relation @ SV244 )
| ~ ( subset @ SV52 @ SV244 )
| ! [SY3858: $i,SY3859: $i] :
( ~ ( in @ ( ordered_pair @ SY3858 @ SY3859 ) @ SV52 )
| ( in @ ( ordered_pair @ SY3858 @ SY3859 ) @ SV244 ) ) )
= $true )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1330,plain,
! [SV245: $i] :
( ( ( SV245 = empty_set )
| ! [SY3860: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK46_SY3307 @ SY3860 @ SV245 ) @ SV245 )
| ~ ~ ( in @ ( sK45_C @ SY3860 @ SV245 ) @ ( sK46_SY3307 @ SY3860 @ SV245 ) ) )
| ~ ( in @ ( sK45_C @ SY3860 @ SV245 ) @ SY3860 ) )
| ~ ( ! [SY3861: $i] :
( ~ ( in @ SY3861 @ SV245 )
| ( in @ ( sK45_C @ SY3860 @ SV245 ) @ SY3861 ) )
| ( in @ ( sK45_C @ SY3860 @ SV245 ) @ SY3860 ) ) )
| ( SY3860
= ( set_meet @ SV245 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1199]) ).
thf(1331,plain,
! [SV246: $i] :
( ( ( SV246 = empty_set )
| ! [SY3862: $i] :
( ( SY3862
!= ( set_meet @ SV246 ) )
| ~ ( ~ ! [SY3863: $i] :
( ~ ( ~ ( in @ ( sK44_D @ SY3863 @ SY3862 @ SV246 ) @ SV246 )
| ~ ~ ( in @ SY3863 @ ( sK44_D @ SY3863 @ SY3862 @ SV246 ) ) )
| ( in @ SY3863 @ SY3862 ) )
| ~ ! [SY3864: $i] :
( ~ ( in @ SY3864 @ SY3862 )
| ! [SY3865: $i] :
( ~ ( in @ SY3865 @ SV246 )
| ( in @ SY3864 @ SY3865 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1332,plain,
! [SV247: $i] :
( ( ( SV247 != empty_set )
| ! [SY3866: $i] :
( ( SY3866
!= ( set_meet @ SV247 ) )
| ( SY3866 = empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1333,plain,
! [SV248: $i] :
( ( ( SV248 != empty_set )
| ! [SY3867: $i] :
( ( SY3867 != empty_set )
| ( SY3867
= ( set_meet @ SV248 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1202]) ).
thf(1334,plain,
! [SV53: $i] :
( ( ( ~ ! [SY3529: $i,SY3530: $i] :
( ~ ( ~ ( ~ ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) ) @ SY3529 )
| ~ ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ SY3530 ) )
| ~ ~ ( ~ ( ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ SY3530 ) )
| ~ ( ( in @ ( apply @ SV53 @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) ) @ SY3529 )
| ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ SY3530 ) ) ) )
| ( SY3530
= ( relation_inverse_image @ SV53 @ SY3529 ) ) ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1203]) ).
thf(1335,plain,
! [SV53: $i] :
( ( ( ~ ! [SY3531: $i,SY3532: $i] :
( ( SY3532
!= ( relation_inverse_image @ SV53 @ SY3531 ) )
| ~ ( ~ ! [SY3533: $i] :
( ~ ( in @ SY3533 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SY3533 ) @ SY3531 )
| ( in @ SY3533 @ SY3532 ) )
| ~ ~ ( ~ ! [SY3534: $i] :
( ~ ( in @ SY3534 @ SY3532 )
| ( in @ SY3534 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY3535: $i] :
( ~ ( in @ SY3535 @ SY3532 )
| ( in @ ( apply @ SV53 @ SY3535 ) @ SY3531 ) ) ) ) ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1203]) ).
thf(1336,plain,
! [SV54: $i,SV165: $i,SV201: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV54 )
| ~ ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV165 )
| ~ ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV201 ) )
| ~ ~ ( ~ ( ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV54 )
| ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV201 ) )
| ~ ( ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV165 )
| ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV201 ) ) ) ) )
= $true )
| ( ( SV201
= ( set_intersection2 @ SV54 @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1204]) ).
thf(1337,plain,
! [SV166: $i,SV54: $i,SV202: $i] :
( ( ( ( SV202
!= ( set_intersection2 @ SV54 @ SV166 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3798: $i] :
( ~ ( in @ SY3798 @ SV54 )
| ~ ( in @ SY3798 @ SV166 )
| ( in @ SY3798 @ SV202 ) )
| ~ ~ ( ~ ! [SY3799: $i] :
( ~ ( in @ SY3799 @ SV202 )
| ( in @ SY3799 @ SV54 ) )
| ~ ! [SY3800: $i] :
( ~ ( in @ SY3800 @ SV202 )
| ( in @ SY3800 @ SV166 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1205]) ).
thf(1338,plain,
! [SV167: $i,SV128: $i] :
( ( ( in @ SV128 @ SV167 )
= $false )
| ( ( subset @ ( singleton @ SV128 ) @ SV167 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1206]) ).
thf(1339,plain,
! [SV168: $i,SV129: $i] :
( ( ( subset @ ( singleton @ SV129 ) @ SV168 )
= $false )
| ( ( in @ SV129 @ SV168 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1207]) ).
thf(1340,plain,
! [SV55: $i,SV169: $i,SV203: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV55 )
| ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV169 )
| ~ ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV203 ) )
| ~ ~ ( ~ ( ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV55 )
| ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV203 ) )
| ~ ( ~ ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV169 )
| ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV203 ) ) ) ) )
= $true )
| ( ( SV203
= ( set_difference @ SV55 @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1208]) ).
thf(1341,plain,
! [SV170: $i,SV55: $i,SV204: $i] :
( ( ( ( SV204
!= ( set_difference @ SV55 @ SV170 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3801: $i] :
( ~ ( in @ SY3801 @ SV55 )
| ( in @ SY3801 @ SV170 )
| ( in @ SY3801 @ SV204 ) )
| ~ ~ ( ~ ! [SY3802: $i] :
( ~ ( in @ SY3802 @ SV204 )
| ( in @ SY3802 @ SV55 ) )
| ~ ! [SY3803: $i] :
( ~ ( in @ SY3803 @ SV204 )
| ~ ( in @ SY3803 @ SV170 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1209]) ).
thf(1342,plain,
! [SV56: $i] :
( ( ( ~ ! [SY3550: $i] :
( ~ ( ~ ( ! [SY3551: $i] :
( ( ( sK19_C @ SY3550 @ SV56 )
!= ( apply @ SV56 @ SY3551 ) )
| ~ ( in @ SY3551 @ ( relation_dom @ SV56 ) ) )
| ~ ( in @ ( sK19_C @ SY3550 @ SV56 ) @ SY3550 ) )
| ~ ( ~ ( ( ( sK19_C @ SY3550 @ SV56 )
!= ( apply @ SV56 @ ( sK20_SY3294 @ SY3550 @ SV56 ) ) )
| ~ ( in @ ( sK20_SY3294 @ SY3550 @ SV56 ) @ ( relation_dom @ SV56 ) ) )
| ( in @ ( sK19_C @ SY3550 @ SV56 ) @ SY3550 ) ) )
| ( SY3550
= ( relation_rng @ SV56 ) ) ) )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1210]) ).
thf(1343,plain,
! [SV56: $i] :
( ( ( ~ ! [SY3552: $i] :
( ( SY3552
!= ( relation_rng @ SV56 ) )
| ~ ( ~ ! [SY3553: $i] :
( ! [SY3554: $i] :
( ( SY3553
!= ( apply @ SV56 @ SY3554 ) )
| ~ ( in @ SY3554 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY3553 @ SY3552 ) )
| ~ ! [SY3555: $i] :
( ~ ( in @ SY3555 @ SY3552 )
| ~ ( ( SY3555
!= ( apply @ SV56 @ ( sK18_D @ SY3555 @ SY3552 @ SV56 ) ) )
| ~ ( in @ ( sK18_D @ SY3555 @ SY3552 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) ) ) ) )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1210]) ).
thf(1344,plain,
! [SV57: $i,SV171: $i,SV205: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK38_D @ SV205 @ SV171 @ SV57 ) @ SV205 )
| ( ( sK38_D @ SV205 @ SV171 @ SV57 )
!= SV57 ) )
| ~ ( ~ ( in @ ( sK38_D @ SV205 @ SV171 @ SV57 ) @ SV205 )
| ( ( sK38_D @ SV205 @ SV171 @ SV57 )
!= SV171 ) ) )
| ~ ( ( in @ ( sK38_D @ SV205 @ SV171 @ SV57 ) @ SV205 )
| ( ( sK38_D @ SV205 @ SV171 @ SV57 )
= SV57 )
| ( ( sK38_D @ SV205 @ SV171 @ SV57 )
= SV171 ) ) ) )
= $true )
| ( ( SV205
= ( unordered_pair @ SV57 @ SV171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1211]) ).
thf(1345,plain,
! [SV172: $i,SV57: $i,SV206: $i] :
( ( ( ( SV206
!= ( unordered_pair @ SV57 @ SV172 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3804: $i] :
( ~ ( in @ SY3804 @ SV206 )
| ( SY3804 = SV57 )
| ( SY3804 = SV172 ) )
| ~ ~ ( ~ ! [SY3805: $i] :
( ( SY3805 != SV57 )
| ( in @ SY3805 @ SV206 ) )
| ~ ! [SY3806: $i] :
( ( SY3806 != SV172 )
| ( in @ SY3806 @ SV206 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1212]) ).
thf(1346,plain,
! [SV58: $i,SV96: $i] :
( ( ( ~ ! [SY3661: $i] :
( ~ ( function @ SY3661 )
| ~ ( relation @ SY3661 )
| ~ ( ~ ( in @ ( sK67_D @ SY3661 @ SV96 @ SV58 ) @ ( relation_dom @ SV96 ) )
| ~ ( ( ( apply @ SV96 @ ( sK67_D @ SY3661 @ SV96 @ SV58 ) )
!= ( apply @ SY3661 @ ( sK67_D @ SY3661 @ SV96 @ SV58 ) ) ) ) )
| ( ( relation_dom @ SV96 )
!= ( set_intersection2 @ ( relation_dom @ SY3661 ) @ SV58 ) )
| ( SV96
= ( relation_dom_restriction @ SY3661 @ SV58 ) ) )
| ~ ~ ( ~ ! [SY3662: $i] :
( ~ ( function @ SY3662 )
| ~ ( relation @ SY3662 )
| ( SV96
!= ( relation_dom_restriction @ SY3662 @ SV58 ) )
| ! [SY3663: $i] :
( ~ ( in @ SY3663 @ ( relation_dom @ SV96 ) )
| ( ( apply @ SV96 @ SY3663 )
= ( apply @ SY3662 @ SY3663 ) ) ) )
| ~ ! [SY3664: $i] :
( ~ ( function @ SY3664 )
| ~ ( relation @ SY3664 )
| ( SV96
!= ( relation_dom_restriction @ SY3664 @ SV58 ) )
| ( ( relation_dom @ SV96 )
= ( set_intersection2 @ ( relation_dom @ SY3664 ) @ SV58 ) ) ) ) )
= $false )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1213]) ).
thf(1347,plain,
! [SV59: $i,SV249: $i] :
( ( ( ~ ( relation @ SV249 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV249 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV249 ) ) )
| ( SV59 = SV249 ) )
= $true )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1348,plain,
! [SV59: $i,SV250: $i] :
( ( ( ~ ( relation @ SV250 )
| ( SV59 != SV250 )
| ~ ( ~ ! [SY3868: $i,SY3869: $i] :
( ~ ( in @ ( ordered_pair @ SY3868 @ SY3869 ) @ SV59 )
| ( in @ ( ordered_pair @ SY3868 @ SY3869 ) @ SV250 ) )
| ~ ! [SY3870: $i,SY3871: $i] :
( ~ ( in @ ( ordered_pair @ SY3870 @ SY3871 ) @ SV250 )
| ( in @ ( ordered_pair @ SY3870 @ SY3871 ) @ SV59 ) ) ) )
= $true )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1349,plain,
! [SV60: $i,SV97: $i] :
( ( ( in @ ( sK78_C @ SV97 @ SV60 ) @ SV97 )
= $false )
| ( ( element @ SV60 @ ( powerset @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1217]) ).
thf(1350,plain,
! [SV130: $i,SV173: $i] :
( ( ( ~ ( ! [SY3767: $i] :
( ~ ( in @ ( sK23_C @ SV173 @ SV130 ) @ SY3767 )
| ~ ( in @ SY3767 @ SV130 ) )
| ~ ( in @ ( sK23_C @ SV173 @ SV130 ) @ SV173 ) )
| ~ ( ~ ( ~ ( in @ ( sK23_C @ SV173 @ SV130 ) @ ( sK24_SY3296 @ SV173 @ SV130 ) )
| ~ ( in @ ( sK24_SY3296 @ SV173 @ SV130 ) @ SV130 ) )
| ( in @ ( sK23_C @ SV173 @ SV130 ) @ SV173 ) ) )
= $false )
| ( ( SV173
= ( union @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1218]) ).
thf(1351,plain,
! [SV131: $i,SV174: $i] :
( ( ( SV174
= ( union @ SV131 ) )
= $false )
| ( ( ~ ( ~ ! [SY3768: $i] :
( ! [SY3719: $i] :
( ~ ( in @ SY3768 @ SY3719 )
| ~ ( in @ SY3719 @ SV131 ) )
| ( in @ SY3768 @ SV174 ) )
| ~ ! [SY3770: $i] :
( ~ ( in @ SY3770 @ SV174 )
| ~ ( ~ ( in @ SY3770 @ ( sK22_D @ SY3770 @ SV174 @ SV131 ) )
| ~ ( in @ ( sK22_D @ SY3770 @ SV174 @ SV131 ) @ SV131 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1219]) ).
thf(1352,plain,
! [SV251: $i,SV98: $i,SV207: $i,SV61: $i] :
( ( ~ ( in @ SV61 @ SV207 )
| ~ ( in @ SV98 @ SV251 )
| ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SV207 @ SV251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1220]) ).
thf(1353,plain,
! [SV98: $i,SV61: $i] :
( ( ~ ! [SY3667: $i] :
( ! [SY3668: $i] :
~ ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SY3667 @ SY3668 ) )
| ( in @ SV61 @ SY3667 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1221]) ).
thf(1354,plain,
! [SV98: $i,SV61: $i] :
( ( ~ ! [SY3669: $i,SY3670: $i] :
( ~ ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SY3669 @ SY3670 ) )
| ( in @ SV98 @ SY3670 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1221]) ).
thf(1355,plain,
! [SV62: $i,SV175: $i,SV208: $i] :
( ( ( ~ ( function @ SV208 )
| ~ ( relation @ SV208 ) )
= $true )
| ( ( ~ ( in @ SV175 @ ( relation_dom @ SV208 ) )
| ~ ( in @ SV175 @ SV62 )
| ( in @ SV175 @ ( relation_dom @ ( relation_dom_restriction @ SV208 @ SV62 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1222]) ).
thf(1356,plain,
! [SV62: $i] :
( ( ! [SY3584: $i,SY3585: $i] :
( ~ ( function @ SY3585 )
| ~ ( relation @ SY3585 )
| ~ ( in @ SY3584 @ ( relation_dom @ ( relation_dom_restriction @ SY3585 @ SV62 ) ) )
| ( in @ SY3584 @ ( relation_dom @ SY3585 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1223]) ).
thf(1357,plain,
! [SV62: $i] :
( ( ! [SY3586: $i,SY3587: $i] :
( ~ ( function @ SY3587 )
| ~ ( relation @ SY3587 )
| ~ ( in @ SY3586 @ ( relation_dom @ ( relation_dom_restriction @ SY3587 @ SV62 ) ) )
| ( in @ SY3586 @ SV62 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1224]) ).
thf(1358,plain,
! [SV209: $i,SV176: $i,SV63: $i] :
( ( ( ~ ( ~ ( ! [SY3808: $i,SY3809: $i] :
( ~ ( in @ SY3808 @ SV63 )
| ~ ( in @ SY3809 @ SV176 )
| ( ( sK34_D @ SV209 @ SV176 @ SV63 )
!= ( ordered_pair @ SY3808 @ SY3809 ) ) )
| ~ ( in @ ( sK34_D @ SV209 @ SV176 @ SV63 ) @ SV209 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK35_SY3303 @ SV209 @ SV176 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK36_SY3305 @ SV209 @ SV176 @ SV63 ) @ SV176 ) )
| ( ( sK34_D @ SV209 @ SV176 @ SV63 )
!= ( ordered_pair @ ( sK35_SY3303 @ SV209 @ SV176 @ SV63 ) @ ( sK36_SY3305 @ SV209 @ SV176 @ SV63 ) ) ) )
| ( in @ ( sK34_D @ SV209 @ SV176 @ SV63 ) @ SV209 ) ) ) )
= $true )
| ( ( SV209
= ( cartesian_product2 @ SV63 @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1225]) ).
thf(1359,plain,
! [SV177: $i,SV63: $i,SV210: $i] :
( ( ( ( SV210
!= ( cartesian_product2 @ SV63 @ SV177 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3810: $i] :
( ! [SY3777: $i,SY3778: $i] :
( ~ ( in @ SY3777 @ SV63 )
| ~ ( in @ SY3778 @ SV177 )
| ( SY3810
!= ( ordered_pair @ SY3777 @ SY3778 ) ) )
| ( in @ SY3810 @ SV210 ) )
| ~ ! [SY3813: $i] :
( ~ ( in @ SY3813 @ SV210 )
| ~ ( ~ ~ ( ~ ( in @ ( sK32_E @ SY3813 @ SV210 @ SV177 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK33_SY3300 @ SY3813 @ SV210 @ SV177 @ SV63 ) @ SV177 ) )
| ( SY3813
!= ( ordered_pair @ ( sK32_E @ SY3813 @ SV210 @ SV177 @ SV63 ) @ ( sK33_SY3300 @ SY3813 @ SV210 @ SV177 @ SV63 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1226]) ).
thf(1360,plain,
! [SV132: $i,SV178: $i] :
( ( ( ~ ( in @ ( sK73_C @ SV178 @ SV132 ) @ SV132 )
| ~ ( in @ ( sK73_C @ SV178 @ SV132 ) @ SV178 ) )
= $false )
| ( ( disjoint @ SV132 @ SV178 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1227]) ).
thf(1361,plain,
! [SV179: $i,SV133: $i,SV252: $i] :
( ( ( ~ ( in @ SV252 @ SV133 )
| ~ ( in @ SV252 @ SV179 ) )
= $true )
| ( ( ~ ( disjoint @ SV133 @ SV179 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1228]) ).
thf(1362,plain,
! [SV180: $i,SV64: $i,SV211: $i] :
( ( ( ~ ( relation @ SV211 ) )
= $true )
| ( ( ! [SY3814: $i] :
( ~ ( in @ SY3814 @ ( relation_dom @ SV211 ) )
| ~ ( in @ ( ordered_pair @ SY3814 @ SV64 ) @ SV211 )
| ~ ( in @ SY3814 @ SV180 ) )
| ( in @ SV64 @ ( relation_image @ SV211 @ SV180 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1229]) ).
thf(1363,plain,
! [SV181: $i,SV64: $i,SV212: $i] :
( ( ( ~ ( relation @ SV212 ) )
= $true )
| ( ( ~ ( in @ SV64 @ ( relation_image @ SV212 @ SV181 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK76_D @ SV212 @ SV181 @ SV64 ) @ ( relation_dom @ SV212 ) )
| ~ ( in @ ( ordered_pair @ ( sK76_D @ SV212 @ SV181 @ SV64 ) @ SV64 ) @ SV212 ) )
| ~ ( in @ ( sK76_D @ SV212 @ SV181 @ SV64 ) @ SV181 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1230]) ).
thf(1364,plain,
! [SV182: $i,SV65: $i,SV213: $i] :
( ( ( ~ ( relation @ SV213 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV65 @ SV182 ) @ SV213 )
| ( in @ SV65 @ ( relation_dom @ SV213 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1231]) ).
thf(1365,plain,
! [SV183: $i,SV65: $i,SV214: $i] :
( ( ( ~ ( relation @ SV214 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV65 @ SV183 ) @ SV214 )
| ( in @ SV183 @ ( relation_rng @ SV214 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1232]) ).
thf(1366,plain,
! [SV66: $i] :
( ( ( ~ ~ ( ~ ! [SY3607: $i] :
( ~ ( in @ SY3607 @ ( relation_dom @ SV66 ) )
| ! [SY3608: $i] :
( ( SY3608
!= ( apply @ SV66 @ SY3607 ) )
| ( in @ ( ordered_pair @ SY3607 @ SY3608 ) @ SV66 ) ) )
| ~ ! [SY3609: $i] :
( ~ ( in @ SY3609 @ ( relation_dom @ SV66 ) )
| ! [SY3610: $i] :
( ~ ( in @ ( ordered_pair @ SY3609 @ SY3610 ) @ SV66 )
| ( SY3610
= ( apply @ SV66 @ SY3609 ) ) ) ) ) )
= $false )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1233]) ).
thf(1367,plain,
! [SV66: $i] :
( ( ( ~ ~ ( ~ ! [SY3611: $i] :
( ( in @ SY3611 @ ( relation_dom @ SV66 ) )
| ! [SY3612: $i] :
( ( SY3612
!= ( apply @ SV66 @ SY3611 ) )
| ( SY3612 = empty_set ) ) )
| ~ ! [SY3613: $i] :
( ( in @ SY3613 @ ( relation_dom @ SV66 ) )
| ! [SY3614: $i] :
( ( SY3614 != empty_set )
| ( SY3614
= ( apply @ SV66 @ SY3613 ) ) ) ) ) )
= $false )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1233]) ).
thf(1368,plain,
! [SV184: $i,SV134: $i] :
( ( ( in @ SV134 @ SV184 )
= $false )
| ( ( subset @ ( singleton @ SV134 ) @ SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1234]) ).
thf(1369,plain,
! [SV185: $i,SV135: $i] :
( ( ( subset @ ( singleton @ SV135 ) @ SV185 )
= $false )
| ( ( in @ SV135 @ SV185 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1235]) ).
thf(1370,plain,
! [SV73: $i,SV7: $i,SV215: $i] :
( ( ( ~ ( function @ SV215 )
| ~ ( relation @ SV215 ) )
= $true )
| ( ( ~ ( in @ SV7 @ ( relation_dom @ ( relation_composition @ SV215 @ SV73 ) ) )
| ( ( apply @ ( relation_composition @ SV215 @ SV73 ) @ SV7 )
= ( apply @ SV73 @ ( apply @ SV215 @ SV7 ) ) ) )
= $true )
| ( ( function @ SV73 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1237]) ).
thf(1371,plain,
! [SV74: $i,SV8: $i,SV216: $i] :
( ( ( ~ ( function @ SV216 )
| ~ ( relation @ SV216 ) )
= $true )
| ( ( ~ ( in @ SV8 @ ( relation_dom @ SV74 ) )
| ( ( apply @ ( relation_composition @ SV74 @ SV216 ) @ SV8 )
= ( apply @ SV216 @ ( apply @ SV74 @ SV8 ) ) ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1238]) ).
thf(1372,plain,
! [SV76: $i,SV10: $i,SV99: $i] :
( ( ( in @ SV99 @ SV10 )
= $false )
| ( ( in @ SV10 @ SV76 )
= $false )
| ( ( in @ SV76 @ SV99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1239]) ).
thf(1373,plain,
! [SV100: $i,SV12: $i,SV186: $i] :
( ( ( element @ SV186 @ SV12 )
= $false )
| ( ( ( in @ SV186 @ SV100 )
| ( in @ SV186 @ ( subset_complement @ SV12 @ SV100 ) ) )
= $true )
| ( ( element @ SV100 @ ( powerset @ SV12 ) )
= $false )
| ( ( SV12 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1240]) ).
thf(1374,plain,
! [SV13: $i,SV101: $i,SV78: $i] :
( ( ( in @ SV78 @ SV101 )
= $false )
| ( ( in @ SV78 @ ( subset_complement @ SV13 @ SV101 ) )
= $false )
| ( ( element @ SV101 @ ( powerset @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1241]) ).
thf(1375,plain,
! [SV15: $i,SV102: $i,SV79: $i] :
( ( ( ~ ( in @ SV79 @ ( relation_dom @ ( relation_dom_restriction @ SV102 @ SV15 ) ) ) )
= $true )
| ( ( ( apply @ ( relation_dom_restriction @ SV102 @ SV15 ) @ SV79 )
= ( apply @ SV102 @ SV79 ) )
= $true )
| ( ( function @ SV102 )
= $false )
| ( ( relation @ SV102 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1242]) ).
thf(1376,plain,
! [SV103: $i,SV16: $i,SV80: $i] :
( ( ( ~ ( in @ SV80 @ SV16 ) )
= $true )
| ( ( ( apply @ ( relation_dom_restriction @ SV103 @ SV16 ) @ SV80 )
= ( apply @ SV103 @ SV80 ) )
= $true )
| ( ( function @ SV103 )
= $false )
| ( ( relation @ SV103 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1243]) ).
thf(1377,plain,
! [SV24: $i,SV86: $i,SV105: $i] :
( ( ( empty @ SV105 )
= $false )
| ( ( element @ SV86 @ ( powerset @ SV105 ) )
= $false )
| ( ( in @ SV24 @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1245]) ).
thf(1378,plain,
! [SV139: $i,SV107: $i,SV217: $i] :
( ( ( in @ SV217 @ ( set_intersection2 @ SV107 @ SV139 ) )
= $false )
| ( ( ~ ( disjoint @ SV107 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1246]) ).
thf(1379,plain,
! [SV26: $i,SV88: $i,SV253: $i] :
( ( ( ~ ( relation @ SV253 )
| ~ ( ~ ( ~ ( in @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) @ SV26 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV88 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 ) )
| ~ ~ ( ~ ( ( in @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) @ SV26 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV88 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 ) ) ) )
| ( SV253
= ( relation_rng_restriction @ SV26 @ SV88 ) ) )
= $true )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1380,plain,
! [SV88: $i,SV26: $i,SV254: $i] :
( ( ( ~ ( relation @ SV254 )
| ( SV254
!= ( relation_rng_restriction @ SV26 @ SV88 ) )
| ~ ( ~ ! [SY3872: $i,SY3873: $i] :
( ~ ( in @ SY3873 @ SV26 )
| ~ ( in @ ( ordered_pair @ SY3872 @ SY3873 ) @ SV88 )
| ( in @ ( ordered_pair @ SY3872 @ SY3873 ) @ SV254 ) )
| ~ ~ ( ~ ! [SY3874: $i,SY3875: $i] :
( ~ ( in @ ( ordered_pair @ SY3874 @ SY3875 ) @ SV254 )
| ( in @ SY3875 @ SV26 ) )
| ~ ! [SY3876: $i,SY3877: $i] :
( ~ ( in @ ( ordered_pair @ SY3876 @ SY3877 ) @ SV254 )
| ( in @ ( ordered_pair @ SY3876 @ SY3877 ) @ SV88 ) ) ) ) )
= $true )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1381,plain,
! [SV108: $i,SV140: $i] :
( ( ( ~ ( in @ ( sK29_C @ SV140 @ SV108 ) @ SV108 ) )
= $false )
| ( ( subset @ SV108 @ SV140 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1249]) ).
thf(1382,plain,
! [SV108: $i,SV140: $i] :
( ( ( ~ ~ ( in @ ( sK29_C @ SV140 @ SV108 ) @ SV140 ) )
= $false )
| ( ( subset @ SV108 @ SV140 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1249]) ).
thf(1383,plain,
! [SV141: $i,SV109: $i,SV255: $i] :
( ( ( ~ ( in @ SV255 @ SV109 )
| ( in @ SV255 @ SV141 ) )
= $true )
| ( ( subset @ SV109 @ SV141 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1384,plain,
! [SV142: $i,SV27: $i,SV187: $i] :
( ( ( relation @ SV187 )
= $false )
| ( ( ~ ( in @ SV27 @ SV142 )
| ~ ( in @ SV27 @ ( relation_dom @ SV187 ) )
| ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SV187 @ SV142 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1251]) ).
thf(1385,plain,
! [SV256: $i,SV27: $i] :
( ( ! [SY3878: $i] :
( ~ ( relation @ SY3878 )
| ~ ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SY3878 @ SV256 ) ) )
| ( in @ SV27 @ SV256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1386,plain,
! [SV257: $i,SV27: $i] :
( ( ! [SY3879: $i] :
( ~ ( relation @ SY3879 )
| ~ ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SY3879 @ SV257 ) ) )
| ( in @ SV27 @ ( relation_dom @ SY3879 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1387,plain,
! [SV28: $i,SV218: $i] :
( ( ( ~ ( relation @ SV218 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV218 @ SV28 ) @ ( sK14_SY3290 @ SV218 @ SV28 ) ) @ SV218 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY3290 @ SV218 @ SV28 ) @ ( sK13_C @ SV218 @ SV28 ) ) @ SV28 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SV218 @ SV28 ) @ ( sK14_SY3290 @ SV218 @ SV28 ) ) @ SV218 )
| ( in @ ( ordered_pair @ ( sK14_SY3290 @ SV218 @ SV28 ) @ ( sK13_C @ SV218 @ SV28 ) ) @ SV28 ) ) )
| ( SV218
= ( relation_inverse @ SV28 ) ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1254]) ).
thf(1388,plain,
! [SV28: $i,SV219: $i] :
( ( ( ~ ( relation @ SV219 ) )
= $true )
| ( ( ( SV219
!= ( relation_inverse @ SV28 ) )
| ~ ( ~ ! [SY3815: $i,SY3816: $i] :
( ~ ( in @ ( ordered_pair @ SY3815 @ SY3816 ) @ SV219 )
| ( in @ ( ordered_pair @ SY3816 @ SY3815 ) @ SV28 ) )
| ~ ! [SY3817: $i,SY3818: $i] :
( ~ ( in @ ( ordered_pair @ SY3818 @ SY3817 ) @ SV28 )
| ( in @ ( ordered_pair @ SY3817 @ SY3818 ) @ SV219 ) ) ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1255]) ).
thf(1389,plain,
! [SV29: $i] :
( ( ( ! [SY3381: $i,SY3382: $i] :
( ~ ( ~ ( ! [SY3383: $i] :
( ~ ( in @ SY3383 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3383 @ SY3381 )
| ( ( sK61_D @ SY3382 @ SY3381 @ SV29 )
!= ( apply @ SV29 @ SY3383 ) ) )
| ~ ( in @ ( sK61_D @ SY3382 @ SY3381 @ SV29 ) @ SY3382 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY3318 @ SY3382 @ SY3381 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK62_SY3318 @ SY3382 @ SY3381 @ SV29 ) @ SY3381 ) )
| ( ( sK61_D @ SY3382 @ SY3381 @ SV29 )
!= ( apply @ SV29 @ ( sK62_SY3318 @ SY3382 @ SY3381 @ SV29 ) ) ) )
| ( in @ ( sK61_D @ SY3382 @ SY3381 @ SV29 ) @ SY3382 ) ) )
| ( SY3382
= ( relation_image @ SV29 @ SY3381 ) ) ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1256]) ).
thf(1390,plain,
! [SV29: $i] :
( ( ( ! [SY3384: $i,SY3385: $i] :
( ( SY3385
!= ( relation_image @ SV29 @ SY3384 ) )
| ~ ( ~ ! [SY3386: $i] :
( ! [SY3387: $i] :
( ~ ( in @ SY3387 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3387 @ SY3384 )
| ( SY3386
!= ( apply @ SV29 @ SY3387 ) ) )
| ( in @ SY3386 @ SY3385 ) )
| ~ ! [SY3388: $i] :
( ~ ( in @ SY3388 @ SY3385 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SY3388 @ SY3385 @ SY3384 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK60_E @ SY3388 @ SY3385 @ SY3384 @ SV29 ) @ SY3384 ) )
| ( SY3388
!= ( apply @ SV29 @ ( sK60_E @ SY3388 @ SY3385 @ SY3384 @ SV29 ) ) ) ) ) ) ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1257]) ).
thf(1391,plain,
! [SV30: $i,SV220: $i,SV258: $i] :
( ( ( ~ ( ~ ( ! [SY3880: $i] :
( ~ ( in @ ( ordered_pair @ SY3880 @ ( sK55_D @ SV258 @ SV220 @ SV30 ) ) @ SV30 )
| ~ ( in @ SY3880 @ SV220 ) )
| ~ ( in @ ( sK55_D @ SV258 @ SV220 @ SV30 ) @ SV258 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_SY3315 @ SV258 @ SV220 @ SV30 ) @ ( sK55_D @ SV258 @ SV220 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK56_SY3315 @ SV258 @ SV220 @ SV30 ) @ SV220 ) )
| ( in @ ( sK55_D @ SV258 @ SV220 @ SV30 ) @ SV258 ) ) )
| ( SV258
= ( relation_image @ SV30 @ SV220 ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1258]) ).
thf(1392,plain,
! [SV221: $i,SV30: $i,SV259: $i] :
( ( ( ( SV259
!= ( relation_image @ SV30 @ SV221 ) )
| ~ ( ~ ! [SY3881: $i] :
( ! [SY3823: $i] :
( ~ ( in @ ( ordered_pair @ SY3823 @ SY3881 ) @ SV30 )
| ~ ( in @ SY3823 @ SV221 ) )
| ( in @ SY3881 @ SV259 ) )
| ~ ! [SY3883: $i] :
( ~ ( in @ SY3883 @ SV259 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SY3883 @ SV259 @ SV221 @ SV30 ) @ SY3883 ) @ SV30 )
| ~ ( in @ ( sK54_E @ SY3883 @ SV259 @ SV221 @ SV30 ) @ SV221 ) ) ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1259]) ).
thf(1393,plain,
! [SV31: $i,SV222: $i,SV260: $i] :
( ( ( ~ ( ~ ( ! [SY3884: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SY3884 ) @ SV31 )
| ~ ( in @ SY3884 @ SV222 ) )
| ~ ( in @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SV260 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ ( sK53_SY3313 @ SV260 @ SV222 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( sK53_SY3313 @ SV260 @ SV222 @ SV31 ) @ SV222 ) )
| ( in @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SV260 ) ) )
| ( SV260
= ( relation_inverse_image @ SV31 @ SV222 ) ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1394,plain,
! [SV223: $i,SV31: $i,SV261: $i] :
( ( ( ( SV261
!= ( relation_inverse_image @ SV31 @ SV223 ) )
| ~ ( ~ ! [SY3885: $i] :
( ! [SY3829: $i] :
( ~ ( in @ ( ordered_pair @ SY3885 @ SY3829 ) @ SV31 )
| ~ ( in @ SY3829 @ SV223 ) )
| ( in @ SY3885 @ SV261 ) )
| ~ ! [SY3887: $i] :
( ~ ( in @ SY3887 @ SV261 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3887 @ ( sK51_E @ SY3887 @ SV261 @ SV223 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( sK51_E @ SY3887 @ SV261 @ SV223 @ SV31 ) @ SV223 ) ) ) ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1395,plain,
! [SV32: $i,SV224: $i,SV262: $i] :
( ( ( ~ ( relation @ SV262 )
| ~ ( ~ ( ~ ( in @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ SV224 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV32 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 ) )
| ~ ~ ( ~ ( ( in @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ SV224 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV32 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 ) ) ) )
| ( SV262
= ( relation_dom_restriction @ SV32 @ SV224 ) ) )
= $true )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1396,plain,
! [SV225: $i,SV32: $i,SV263: $i] :
( ( ( ~ ( relation @ SV263 )
| ( SV263
!= ( relation_dom_restriction @ SV32 @ SV225 ) )
| ~ ( ~ ! [SY3888: $i,SY3889: $i] :
( ~ ( in @ SY3888 @ SV225 )
| ~ ( in @ ( ordered_pair @ SY3888 @ SY3889 ) @ SV32 )
| ( in @ ( ordered_pair @ SY3888 @ SY3889 ) @ SV263 ) )
| ~ ~ ( ~ ! [SY3890: $i] :
( ! [SY3891: $i] :
~ ( in @ ( ordered_pair @ SY3890 @ SY3891 ) @ SV263 )
| ( in @ SY3890 @ SV225 ) )
| ~ ! [SY3892: $i,SY3893: $i] :
( ~ ( in @ ( ordered_pair @ SY3892 @ SY3893 ) @ SV263 )
| ( in @ ( ordered_pair @ SY3892 @ SY3893 ) @ SV32 ) ) ) ) )
= $true )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1397,plain,
! [SV143: $i,SV33: $i,SV188: $i] :
( ( ( relation @ SV188 )
= $false )
| ( ( ! [SY3786: $i] :
( ~ ( in @ SY3786 @ ( relation_rng @ SV188 ) )
| ~ ( in @ ( ordered_pair @ SV33 @ SY3786 ) @ SV188 )
| ~ ( in @ SY3786 @ SV143 ) )
| ( in @ SV33 @ ( relation_inverse_image @ SV188 @ SV143 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1264]) ).
thf(1398,plain,
! [SV144: $i,SV33: $i,SV189: $i] :
( ( ( relation @ SV189 )
= $false )
| ( ( ~ ( in @ SV33 @ ( relation_inverse_image @ SV189 @ SV144 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK75_D @ SV189 @ SV144 @ SV33 ) @ ( relation_rng @ SV189 ) )
| ~ ( in @ ( ordered_pair @ SV33 @ ( sK75_D @ SV189 @ SV144 @ SV33 ) ) @ SV189 ) )
| ~ ( in @ ( sK75_D @ SV189 @ SV144 @ SV33 ) @ SV144 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1265]) ).
thf(1399,plain,
! [SV110: $i,SV145: $i] :
( ( ( ~ ( ~ ( ( ( sK65_C @ SV145 @ SV110 )
!= ( sK66_SY3320 @ SV145 @ SV110 ) )
| ~ ( in @ ( sK65_C @ SV145 @ SV110 ) @ SV110 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 ) )
| ~ ~ ( ~ ( ( ( sK65_C @ SV145 @ SV110 )
= ( sK66_SY3320 @ SV145 @ SV110 ) )
| ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 ) )
| ~ ( ( in @ ( sK65_C @ SV145 @ SV110 ) @ SV110 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 ) ) ) ) )
= $true )
| ( ( SV145
= ( identity_relation @ SV110 ) )
= $true )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1266]) ).
thf(1400,plain,
! [SV111: $i,SV146: $i] :
( ( ( ( SV146
!= ( identity_relation @ SV111 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3732: $i,SY3733: $i] :
( ( SY3732 != SY3733 )
| ~ ( in @ SY3732 @ SV111 )
| ( in @ ( ordered_pair @ SY3732 @ SY3733 ) @ SV146 ) )
| ~ ~ ( ~ ! [SY3734: $i,SY3735: $i] :
( ~ ( in @ ( ordered_pair @ SY3734 @ SY3735 ) @ SV146 )
| ( SY3734 = SY3735 ) )
| ~ ! [SY3736: $i] :
( ! [SY3737: $i] :
~ ( in @ ( ordered_pair @ SY3736 @ SY3737 ) @ SV146 )
| ( in @ SY3736 @ SV111 ) ) ) ) )
= $true )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1267]) ).
thf(1401,plain,
! [SV34: $i,SV89: $i,SV190: $i,SV226: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV190 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV34 ) )
| ~ ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV89 ) ) ) )
| ~ ( ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
= SV190 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
= SV34 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
= SV89 ) ) ) )
= $true )
| ( ( SV226
= ( unordered_triple @ SV34 @ SV89 @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1268]) ).
thf(1402,plain,
! [SV191: $i,SV89: $i,SV34: $i,SV227: $i] :
( ( ( ( SV227
!= ( unordered_triple @ SV34 @ SV89 @ SV191 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3839: $i] :
( ~ ( in @ SY3839 @ SV227 )
| ( SY3839 = SV191 )
| ( SY3839 = SV34 )
| ( SY3839 = SV89 ) )
| ~ ~ ( ~ ! [SY3840: $i] :
( ( SY3840 != SV191 )
| ( in @ SY3840 @ SV227 ) )
| ~ ~ ( ~ ! [SY3841: $i] :
( ( SY3841 != SV34 )
| ( in @ SY3841 @ SV227 ) )
| ~ ! [SY3842: $i] :
( ( SY3842 != SV89 )
| ( in @ SY3842 @ SV227 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1269]) ).
thf(1403,plain,
! [SV147: $i,SV35: $i,SV192: $i] :
( ( ( relation @ SV192 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV35 @ SV147 ) @ SV192 )
| ( in @ SV35 @ ( relation_field @ SV192 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1270]) ).
thf(1404,plain,
! [SV148: $i,SV35: $i,SV193: $i] :
( ( ( relation @ SV193 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV35 @ SV148 ) @ SV193 )
| ( in @ SV148 @ ( relation_field @ SV193 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1271]) ).
thf(1405,plain,
! [SV36: $i,SV228: $i] :
( ( ( ~ ( ~ ( ! [SY3843: $i] :
~ ( in @ ( ordered_pair @ SY3843 @ ( sK16_C @ SV228 @ SV36 ) ) @ SV36 )
| ~ ( in @ ( sK16_C @ SV228 @ SV36 ) @ SV228 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_SY3292 @ SV228 @ SV36 ) @ ( sK16_C @ SV228 @ SV36 ) ) @ SV36 )
| ( in @ ( sK16_C @ SV228 @ SV36 ) @ SV228 ) ) ) )
= $true )
| ( ( SV228
= ( relation_rng @ SV36 ) )
= $true )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1272]) ).
thf(1406,plain,
! [SV36: $i,SV229: $i] :
( ( ( ( SV229
!= ( relation_rng @ SV36 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3844: $i] :
( ! [SY3437: $i] :
~ ( in @ ( ordered_pair @ SY3437 @ SY3844 ) @ SV36 )
| ( in @ SY3844 @ SV229 ) )
| ~ ! [SY3846: $i] :
( ~ ( in @ SY3846 @ SV229 )
| ( in @ ( ordered_pair @ ( sK15_D @ SY3846 @ SV229 @ SV36 ) @ SY3846 ) @ SV36 ) ) ) )
= $true )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1273]) ).
thf(1407,plain,
! [SV37: $i,SV149: $i] :
( ( ( subset @ SV149 @ ( sK77_B @ SV37 ) )
= $false )
| ( ( are_equipotent @ SV149 @ ( sK77_B @ SV37 ) )
= $true )
| ( ( in @ SV149 @ ( sK77_B @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1274]) ).
thf(1408,plain,
! [SV37: $i,SV264: $i] :
( ( ~ ( in @ SV264 @ ( sK77_B @ SV37 ) )
| ( in @ ( powerset @ SV264 ) @ ( sK77_B @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1275]) ).
thf(1409,plain,
! [SV37: $i] :
( ( ~ ! [SY3441: $i,SY3442: $i] :
( ~ ( in @ SY3441 @ ( sK77_B @ SV37 ) )
| ~ ( subset @ SY3442 @ SY3441 )
| ( in @ SY3442 @ ( sK77_B @ SV37 ) ) )
| ~ ( in @ SV37 @ ( sK77_B @ SV37 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1276]) ).
thf(1410,plain,
! [SV112: $i,SV150: $i] :
( ( ( ~ ( ~ ( in @ ( sK41_C @ SV150 @ SV112 ) @ SV150 )
| ~ ( subset @ ( sK41_C @ SV150 @ SV112 ) @ SV112 ) ) )
= $false )
| ( ( SV150
= ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1277]) ).
thf(1411,plain,
! [SV112: $i,SV150: $i] :
( ( ( ~ ( ( in @ ( sK41_C @ SV150 @ SV112 ) @ SV150 )
| ( subset @ ( sK41_C @ SV150 @ SV112 ) @ SV112 ) ) )
= $false )
| ( ( SV150
= ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1277]) ).
thf(1412,plain,
! [SV113: $i,SV151: $i] :
( ( ( ~ ! [SY3740: $i] :
( ~ ( in @ SY3740 @ SV151 )
| ( subset @ SY3740 @ SV113 ) )
| ~ ! [SY3741: $i] :
( ~ ( subset @ SY3741 @ SV113 )
| ( in @ SY3741 @ SV151 ) ) )
= $false )
| ( ( SV151
= ( powerset @ SV113 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1278]) ).
thf(1413,plain,
! [SV38: $i,SV90: $i] :
( ( ( in @ ( sK5_C @ SV90 @ SV38 ) @ SV38 )
= $false )
| ( ( ~ ( in @ ( sK5_C @ SV90 @ SV38 ) @ SV90 ) )
= $true )
| ( ( SV38 = SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1279]) ).
thf(1414,plain,
! [SV114: $i,SV152: $i] :
( ( ( function @ SV152 )
= $false )
| ( ( ~ ( relation @ SV152 ) )
= $true )
| ( ( ~ ( in @ SV114 @ ( relation_rng @ SV152 ) )
| ~ ( one_to_one @ SV152 )
| ( SV114
= ( apply @ SV152 @ ( apply @ ( function_inverse @ SV152 ) @ SV114 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1281]) ).
thf(1415,plain,
! [SV115: $i,SV153: $i] :
( ( ( function @ SV153 )
= $false )
| ( ( ~ ( relation @ SV153 ) )
= $true )
| ( ( ~ ( in @ SV115 @ ( relation_rng @ SV153 ) )
| ~ ( one_to_one @ SV153 )
| ( SV115
= ( apply @ ( relation_composition @ ( function_inverse @ SV153 ) @ SV153 ) @ SV115 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1282]) ).
thf(1416,plain,
! [SV91: $i,SV39: $i] :
( ( ( ~ ! [SY3641: $i] :
( ~ ( function @ SY3641 )
| ~ ( relation @ SY3641 )
| ~ ( in @ SV39 @ ( relation_dom @ SY3641 ) )
| ~ ( in @ ( apply @ SY3641 @ SV39 ) @ ( relation_dom @ SV91 ) )
| ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3641 @ SV91 ) ) ) ) )
= $false )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1283]) ).
thf(1417,plain,
! [SV91: $i,SV39: $i] :
( ( ( ~ ~ ( ~ ! [SY3642: $i] :
( ~ ( function @ SY3642 )
| ~ ( relation @ SY3642 )
| ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3642 @ SV91 ) ) )
| ( in @ SV39 @ ( relation_dom @ SY3642 ) ) )
| ~ ! [SY3643: $i] :
( ~ ( function @ SY3643 )
| ~ ( relation @ SY3643 )
| ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3643 @ SV91 ) ) )
| ( in @ ( apply @ SY3643 @ SV39 ) @ ( relation_dom @ SV91 ) ) ) ) )
= $false )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1283]) ).
thf(1418,plain,
! [SV92: $i,SV40: $i,SV265: $i] :
( ( ( ~ ( element @ SV265 @ ( powerset @ ( powerset @ SV40 ) ) )
| ~ ( ~ ( element @ ( sK6_D @ SV265 @ SV92 @ SV40 ) @ ( powerset @ SV40 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK6_D @ SV265 @ SV92 @ SV40 ) @ SV265 )
| ~ ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SV265 @ SV92 @ SV40 ) ) @ SV92 ) )
| ~ ( ( in @ ( sK6_D @ SV265 @ SV92 @ SV40 ) @ SV265 )
| ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SV265 @ SV92 @ SV40 ) ) @ SV92 ) ) ) )
| ( SV265
= ( complements_of_subsets @ SV40 @ SV92 ) ) )
= $true )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1419,plain,
! [SV92: $i,SV40: $i,SV266: $i] :
( ( ( ~ ( element @ SV266 @ ( powerset @ ( powerset @ SV40 ) ) )
| ( SV266
!= ( complements_of_subsets @ SV40 @ SV92 ) )
| ~ ( ~ ! [SY3894: $i] :
( ~ ( element @ SY3894 @ ( powerset @ SV40 ) )
| ~ ( in @ SY3894 @ SV266 )
| ( in @ ( subset_complement @ SV40 @ SY3894 ) @ SV92 ) )
| ~ ! [SY3895: $i] :
( ~ ( element @ SY3895 @ ( powerset @ SV40 ) )
| ~ ( in @ ( subset_complement @ SV40 @ SY3895 ) @ SV92 )
| ( in @ SY3895 @ SV266 ) ) ) )
= $true )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1285]) ).
thf(1420,plain,
! [SV41: $i,SV154: $i,SV194: $i] :
( ( ( ~ ( function @ SV194 ) )
= $true )
| ( ( ~ ( relation @ SV194 ) )
= $true )
| ( ( ( SV154
!= ( apply @ SV194 @ SV41 ) )
| ~ ( in @ SV41 @ ( relation_dom @ SV194 ) )
| ( in @ ( ordered_pair @ SV41 @ SV154 ) @ SV194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1286]) ).
thf(1421,plain,
! [SV267: $i,SV41: $i] :
( ( ! [SY3896: $i] :
( ~ ( function @ SY3896 )
| ~ ( relation @ SY3896 )
| ~ ( in @ ( ordered_pair @ SV41 @ SV267 ) @ SY3896 )
| ( SV267
= ( apply @ SY3896 @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1422,plain,
! [SV268: $i,SV41: $i] :
( ( ! [SY3897: $i] :
( ~ ( function @ SY3897 )
| ~ ( relation @ SY3897 )
| ~ ( in @ ( ordered_pair @ SV41 @ SV268 ) @ SY3897 )
| ( in @ SV41 @ ( relation_dom @ SY3897 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1423,plain,
! [SV155: $i,SV42: $i,SV195: $i] :
( ( ( relation @ SV195 )
= $false )
| ( ( ~ ( in @ SV42 @ SV155 )
| ~ ( in @ SV42 @ ( relation_rng @ SV195 ) )
| ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SV155 @ SV195 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1289]) ).
thf(1424,plain,
! [SV269: $i,SV42: $i] :
( ( ! [SY3898: $i] :
( ~ ( relation @ SY3898 )
| ~ ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SV269 @ SY3898 ) ) )
| ( in @ SV42 @ SV269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1290]) ).
thf(1425,plain,
! [SV270: $i,SV42: $i] :
( ( ! [SY3899: $i] :
( ~ ( relation @ SY3899 )
| ~ ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SV270 @ SY3899 ) ) )
| ( in @ SV42 @ ( relation_rng @ SY3899 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1291]) ).
thf(1426,plain,
! [SV43: $i,SV156: $i] :
( ( ( subset @ SV156 @ ( sK2_B @ SV43 ) )
= $false )
| ( ( are_equipotent @ SV156 @ ( sK2_B @ SV43 ) )
= $true )
| ( ( in @ SV156 @ ( sK2_B @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1292]) ).
thf(1427,plain,
! [SV43: $i,SV271: $i] :
( ( ~ ( ~ ! [SY3900: $i] :
( ~ ( subset @ SY3900 @ SV271 )
| ( in @ SY3900 @ ( sK3_SY3278 @ SV271 @ SV43 ) ) )
| ~ ( in @ ( sK3_SY3278 @ SV271 @ SV43 ) @ ( sK2_B @ SV43 ) ) )
| ~ ( in @ SV271 @ ( sK2_B @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1428,plain,
! [SV43: $i] :
( ( ~ ! [SY3468: $i,SY3469: $i] :
( ~ ( in @ SY3468 @ ( sK2_B @ SV43 ) )
| ~ ( subset @ SY3469 @ SY3468 )
| ( in @ SY3469 @ ( sK2_B @ SV43 ) ) )
| ~ ( in @ SV43 @ ( sK2_B @ SV43 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1294]) ).
thf(1429,plain,
! [SV116: $i] :
( ( ( ! [SY3692: $i,SY3693: $i] :
( ( sK49_B @ SV116 )
!= ( ordered_pair @ SY3692 @ SY3693 ) ) )
= $true )
| ( ( relation @ SV116 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1295]) ).
thf(1430,plain,
! [SV116: $i] :
( ( ( in @ ( sK49_B @ SV116 ) @ SV116 )
= $true )
| ( ( relation @ SV116 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1296]) ).
thf(1431,plain,
! [SV117: $i,SV230: $i] :
( ( ( SV230
= ( ordered_pair @ ( sK47_C @ SV230 @ SV117 ) @ ( sK48_SY3309 @ SV230 @ SV117 ) ) )
= $true )
| ( ( ~ ( in @ SV230 @ SV117 ) )
= $true )
| ( ( relation @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1297]) ).
thf(1432,plain,
! [SV231: $i,SV93: $i,SV196: $i,SV44: $i] :
( ( ( ~ ( in @ SV44 @ SV196 )
| ~ ( in @ SV93 @ SV231 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SV196 @ SV231 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1298]) ).
thf(1433,plain,
! [SV93: $i,SV44: $i] :
( ( ! [SY3650: $i] :
( ! [SY3651: $i] :
~ ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SY3650 @ SY3651 ) )
| ( in @ SV44 @ SY3650 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1299]) ).
thf(1434,plain,
! [SV93: $i,SV44: $i] :
( ( ! [SY3652: $i,SY3653: $i] :
( ~ ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SY3652 @ SY3653 ) )
| ( in @ SV93 @ SY3653 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1300]) ).
thf(1435,plain,
! [SV45: $i,SV232: $i] :
( ( ( ~ ( ~ ( ! [SY3847: $i] :
~ ( in @ ( ordered_pair @ ( sK26_C @ SV232 @ SV45 ) @ SY3847 ) @ SV45 )
| ~ ( in @ ( sK26_C @ SV232 @ SV45 ) @ SV232 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK26_C @ SV232 @ SV45 ) @ ( sK27_SY3298 @ SV232 @ SV45 ) ) @ SV45 )
| ( in @ ( sK26_C @ SV232 @ SV45 ) @ SV232 ) ) ) )
= $true )
| ( ( SV232
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1301]) ).
thf(1436,plain,
! [SV45: $i,SV233: $i] :
( ( ( ( SV233
!= ( relation_dom @ SV45 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3848: $i] :
( ! [SY3481: $i] :
~ ( in @ ( ordered_pair @ SY3848 @ SY3481 ) @ SV45 )
| ( in @ SY3848 @ SV233 ) )
| ~ ! [SY3850: $i] :
( ~ ( in @ SY3850 @ SV233 )
| ( in @ ( ordered_pair @ SY3850 @ ( sK25_D @ SY3850 @ SV233 @ SV45 ) ) @ SV45 ) ) ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1302]) ).
thf(1437,plain,
! [SV234: $i] :
( ( ( empty @ SV234 )
= $true )
| ( ( ! [SY3851: $i] :
( ~ ( element @ SY3851 @ SV234 )
| ( in @ SY3851 @ SV234 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1303]) ).
thf(1438,plain,
! [SV235: $i] :
( ( ( empty @ SV235 )
= $true )
| ( ( ! [SY3852: $i] :
( ~ ( in @ SY3852 @ SV235 )
| ( element @ SY3852 @ SV235 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1304]) ).
thf(1439,plain,
! [SV236: $i] :
( ( ( ~ ( empty @ SV236 ) )
= $true )
| ( ( ! [SY3853: $i] :
( ~ ( element @ SY3853 @ SV236 )
| ( empty @ SY3853 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1305]) ).
thf(1440,plain,
! [SV237: $i] :
( ( ( ~ ( empty @ SV237 ) )
= $true )
| ( ( ! [SY3854: $i] :
( ~ ( empty @ SY3854 )
| ( element @ SY3854 @ SV237 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1306]) ).
thf(1441,plain,
! [SV119: $i,SV238: $i] :
( ( ( in @ SV238 @ SV119 )
= $false )
| ( ( SV119 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1307]) ).
thf(1442,plain,
! [SV120: $i,SV157: $i] :
( ( ( ~ ( ( ( sK43_C @ SV157 @ SV120 )
!= SV120 )
| ~ ( in @ ( sK43_C @ SV157 @ SV120 ) @ SV157 ) ) )
= $false )
| ( ( SV157
= ( singleton @ SV120 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1308]) ).
thf(1443,plain,
! [SV120: $i,SV157: $i] :
( ( ( ~ ( ( ( sK43_C @ SV157 @ SV120 )
= SV120 )
| ( in @ ( sK43_C @ SV157 @ SV120 ) @ SV157 ) ) )
= $false )
| ( ( SV157
= ( singleton @ SV120 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1308]) ).
thf(1444,plain,
! [SV158: $i,SV121: $i] :
( ( ( ~ ! [SY3744: $i] :
( ( SY3744 != SV121 )
| ( in @ SY3744 @ SV158 ) )
| ~ ! [SY3745: $i] :
( ~ ( in @ SY3745 @ SV158 )
| ( SY3745 = SV121 ) ) )
= $false )
| ( ( SV158
= ( singleton @ SV121 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1309]) ).
thf(1445,plain,
! [SV122: $i,SV159: $i] :
( ( ( function @ SV159 )
= $false )
| ( ( ~ ( relation @ SV159 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK74_C @ SV159 @ SV122 ) @ SV122 )
| ~ ( ( ( apply @ SV159 @ ( sK74_C @ SV159 @ SV122 ) )
!= ( sK74_C @ SV159 @ SV122 ) ) ) )
| ( ( relation_dom @ SV159 )
!= SV122 )
| ( SV159
= ( identity_relation @ SV122 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1310]) ).
thf(1446,plain,
! [SV239: $i,SV272: $i] :
( ( ~ ( function @ SV272 )
| ~ ( relation @ SV272 )
| ( SV272
!= ( identity_relation @ SV239 ) )
| ! [SY3901: $i] :
( ~ ( in @ SY3901 @ SV239 )
| ( ( apply @ SV272 @ SY3901 )
= SY3901 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1447,plain,
! [SV240: $i,SV273: $i] :
( ( ~ ( function @ SV273 )
| ~ ( relation @ SV273 )
| ( SV273
!= ( identity_relation @ SV240 ) )
| ( ( relation_dom @ SV273 )
= SV240 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1312]) ).
thf(1448,plain,
! [SV46: $i] :
( ( ( ~ ! [SY3483: $i] :
( ~ ( function @ SY3483 )
| ~ ( relation @ SY3483 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY3322 @ SY3483 @ SV46 )
= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ( ( sK70_C @ SY3483 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SY3483 @ SV46 )
= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SY3483 @ SV46 )
= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ( ( sK71_SY3322 @ SY3483 @ SV46 )
!= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK70_C @ SY3483 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK71_SY3322 @ SY3483 @ SV46 )
!= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY3483 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK70_C @ SY3483 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SY3483 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SY3483 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK71_SY3322 @ SY3483 @ SV46 )
!= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ( ( relation_dom @ SY3483 )
!= ( relation_rng @ SV46 ) )
| ( SY3483
= ( function_inverse @ SV46 ) ) )
| ~ ~ ( ~ ! [SY3484: $i] :
( ~ ( function @ SY3484 )
| ~ ( relation @ SY3484 )
| ( SY3484
!= ( function_inverse @ SV46 ) )
| ~ ( ~ ~ ( ~ ! [SY3485: $i,SY3486: $i] :
( ( SY3486
!= ( apply @ SY3484 @ SY3485 ) )
| ~ ( in @ SY3485 @ ( relation_rng @ SV46 ) )
| ( SY3485
= ( apply @ SV46 @ SY3486 ) ) )
| ~ ! [SY3487: $i,SY3488: $i] :
( ( SY3488
!= ( apply @ SY3484 @ SY3487 ) )
| ~ ( in @ SY3487 @ ( relation_rng @ SV46 ) )
| ( in @ SY3488 @ ( relation_dom @ SV46 ) ) ) )
| ~ ~ ( ~ ! [SY3489: $i,SY3490: $i] :
( ( SY3489
!= ( apply @ SV46 @ SY3490 ) )
| ~ ( in @ SY3490 @ ( relation_dom @ SV46 ) )
| ( SY3490
= ( apply @ SY3484 @ SY3489 ) ) )
| ~ ! [SY3491: $i] :
( ! [SY3492: $i] :
( ( SY3491
!= ( apply @ SV46 @ SY3492 ) )
| ~ ( in @ SY3492 @ ( relation_dom @ SV46 ) ) )
| ( in @ SY3491 @ ( relation_rng @ SV46 ) ) ) ) ) )
| ~ ! [SY3493: $i] :
( ~ ( function @ SY3493 )
| ~ ( relation @ SY3493 )
| ( SY3493
!= ( function_inverse @ SV46 ) )
| ( ( relation_dom @ SY3493 )
= ( relation_rng @ SV46 ) ) ) ) )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1313]) ).
thf(1449,plain,
! [SV47: $i,SV123: $i] :
( ( ( ~ ! [SY3701: $i] :
( ~ ( relation @ SY3701 )
| ~ ( ~ ( ! [SY3702: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY3701 @ SV123 @ SV47 ) @ SY3702 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3702 @ ( sK9_SY3284 @ SY3701 @ SV123 @ SV47 ) ) @ SV123 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SY3701 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SY3701 @ SV123 @ SV47 ) ) @ SY3701 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY3701 @ SV123 @ SV47 ) @ ( sK10_SY3288 @ SY3701 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY3288 @ SY3701 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SY3701 @ SV123 @ SV47 ) ) @ SV123 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SY3701 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SY3701 @ SV123 @ SV47 ) ) @ SY3701 ) ) )
| ( SY3701
= ( relation_composition @ SV47 @ SV123 ) ) ) )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1314]) ).
thf(1450,plain,
! [SV123: $i,SV47: $i] :
( ( ( ~ ! [SY3703: $i] :
( ~ ( relation @ SY3703 )
| ( SY3703
!= ( relation_composition @ SV47 @ SV123 ) )
| ~ ( ~ ! [SY3704: $i,SY3705: $i] :
( ! [SY3706: $i] :
( ~ ( in @ ( ordered_pair @ SY3704 @ SY3706 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3706 @ SY3705 ) @ SV123 ) )
| ( in @ ( ordered_pair @ SY3704 @ SY3705 ) @ SY3703 ) )
| ~ ! [SY3707: $i,SY3708: $i] :
( ~ ( in @ ( ordered_pair @ SY3707 @ SY3708 ) @ SY3703 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3707 @ ( sK7_F @ SY3708 @ SY3707 @ SY3703 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY3708 @ SY3707 @ SY3703 @ SV123 @ SV47 ) @ SY3708 ) @ SV123 ) ) ) ) ) )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1314]) ).
thf(1451,plain,
! [SV160: $i,SV197: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ SV197 ) )
= $true )
| ( ( ~ ( in @ SV160 @ SV197 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV48 @ SV160 ) @ SV197 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1315]) ).
thf(1452,plain,
! [SV274: $i,SV48: $i] :
( ( ! [SY3902: $i] :
( ~ ( subset @ ( unordered_pair @ SV48 @ SV274 ) @ SY3902 )
| ( in @ SV48 @ SY3902 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1453,plain,
! [SV275: $i,SV48: $i] :
( ( ! [SY3903: $i] :
( ~ ( subset @ ( unordered_pair @ SV48 @ SV275 ) @ SY3903 )
| ( in @ SV275 @ SY3903 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1317]) ).
thf(1454,plain,
! [SV94: $i,SV198: $i,SV49: $i,SV241: $i] :
( ( ( ~ ( relation @ SV241 ) )
= $true )
| ( ( ~ ( in @ SV49 @ SV198 )
| ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ SV241 )
| ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SV198 ) @ SV241 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1318]) ).
thf(1455,plain,
! [SV94: $i,SV49: $i] :
( ( ! [SY3656: $i,SY3657: $i] :
( ~ ( relation @ SY3657 )
| ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SY3656 ) @ SY3657 ) )
| ( in @ SV49 @ SY3656 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1319]) ).
thf(1456,plain,
! [SV94: $i,SV49: $i] :
( ( ! [SY3658: $i,SY3659: $i] :
( ~ ( relation @ SY3659 )
| ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SY3658 ) @ SY3659 ) )
| ( in @ ( ordered_pair @ SV49 @ SV94 ) @ SY3659 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1320]) ).
thf(1457,plain,
! [SV50: $i,SV95: $i,SV242: $i] :
( ( ( ~ ( in @ SV242 @ SV95 ) )
= $true )
| ( ( ~ ( in @ SV242 @ ( sK4_C @ SV95 @ SV50 ) ) )
= $true )
| ( ( ~ ( in @ SV50 @ SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1321]) ).
thf(1458,plain,
! [SV124: $i] :
( ( ( relation @ SV124 )
= $false )
| ( ( function @ SV124 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_B @ SV124 ) @ ( relation_dom @ SV124 ) )
| ~ ( in @ ( sK12_SY3289 @ SV124 ) @ ( relation_dom @ SV124 ) ) )
| ( ( apply @ SV124 @ ( sK11_B @ SV124 ) )
!= ( apply @ SV124 @ ( sK12_SY3289 @ SV124 ) ) ) )
| ~ ( ( ( sK11_B @ SV124 )
!= ( sK12_SY3289 @ SV124 ) ) ) )
| ( one_to_one @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1323]) ).
thf(1459,plain,
! [SV125: $i] :
( ( ( relation @ SV125 )
= $false )
| ( ( function @ SV125 )
= $false )
| ( ( ~ ( one_to_one @ SV125 )
| ! [SY3709: $i,SY3710: $i] :
( ~ ( in @ SY3709 @ ( relation_dom @ SV125 ) )
| ~ ( in @ SY3710 @ ( relation_dom @ SV125 ) )
| ( ( apply @ SV125 @ SY3709 )
!= ( apply @ SV125 @ SY3710 ) )
| ( SY3709 = SY3710 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1324]) ).
thf(1460,plain,
! [SV51: $i,SV161: $i,SV199: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV199 )
| ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV51 ) )
| ~ ( ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV199 )
| ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV161 ) ) )
| ~ ( ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV199 )
| ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV51 )
| ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV161 ) ) )
= $false )
| ( ( SV199
= ( set_union2 @ SV51 @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1325]) ).
thf(1461,plain,
! [SV162: $i,SV51: $i,SV200: $i] :
( ( ( SV200
= ( set_union2 @ SV51 @ SV162 ) )
= $false )
| ( ( ~ ( ~ ! [SY3795: $i] :
( ~ ( in @ SY3795 @ SV200 )
| ( in @ SY3795 @ SV51 )
| ( in @ SY3795 @ SV162 ) )
| ~ ~ ( ~ ! [SY3796: $i] :
( ~ ( in @ SY3796 @ SV51 )
| ( in @ SY3796 @ SV200 ) )
| ~ ! [SY3797: $i] :
( ~ ( in @ SY3797 @ SV162 )
| ( in @ SY3797 @ SV200 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1326]) ).
thf(1462,plain,
! [SV126: $i,SV163: $i] :
( ( ( in @ SV163 @ SV126 )
= $false )
| ( ( ( set_difference @ SV126 @ ( singleton @ SV163 ) )
= SV126 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1327]) ).
thf(1463,plain,
! [SV52: $i,SV243: $i] :
( ( ( ~ ( relation @ SV243 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK30_C @ SV243 @ SV52 ) @ ( sK31_SY3299 @ SV243 @ SV52 ) ) @ SV52 )
| ~ ~ ( in @ ( ordered_pair @ ( sK30_C @ SV243 @ SV52 ) @ ( sK31_SY3299 @ SV243 @ SV52 ) ) @ SV243 ) )
| ( subset @ SV52 @ SV243 ) )
= $true )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1328]) ).
thf(1464,plain,
! [SV52: $i,SV244: $i] :
( ( ( ~ ( relation @ SV244 ) )
= $true )
| ( ( ~ ( subset @ SV52 @ SV244 )
| ! [SY3858: $i,SY3859: $i] :
( ~ ( in @ ( ordered_pair @ SY3858 @ SY3859 ) @ SV52 )
| ( in @ ( ordered_pair @ SY3858 @ SY3859 ) @ SV244 ) ) )
= $true )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1329]) ).
thf(1465,plain,
! [SV245: $i] :
( ( ( SV245 = empty_set )
= $true )
| ( ( ! [SY3860: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK46_SY3307 @ SY3860 @ SV245 ) @ SV245 )
| ~ ~ ( in @ ( sK45_C @ SY3860 @ SV245 ) @ ( sK46_SY3307 @ SY3860 @ SV245 ) ) )
| ~ ( in @ ( sK45_C @ SY3860 @ SV245 ) @ SY3860 ) )
| ~ ( ! [SY3861: $i] :
( ~ ( in @ SY3861 @ SV245 )
| ( in @ ( sK45_C @ SY3860 @ SV245 ) @ SY3861 ) )
| ( in @ ( sK45_C @ SY3860 @ SV245 ) @ SY3860 ) ) )
| ( SY3860
= ( set_meet @ SV245 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1330]) ).
thf(1466,plain,
! [SV246: $i] :
( ( ( SV246 = empty_set )
= $true )
| ( ( ! [SY3862: $i] :
( ( SY3862
!= ( set_meet @ SV246 ) )
| ~ ( ~ ! [SY3863: $i] :
( ~ ( ~ ( in @ ( sK44_D @ SY3863 @ SY3862 @ SV246 ) @ SV246 )
| ~ ~ ( in @ SY3863 @ ( sK44_D @ SY3863 @ SY3862 @ SV246 ) ) )
| ( in @ SY3863 @ SY3862 ) )
| ~ ! [SY3864: $i] :
( ~ ( in @ SY3864 @ SY3862 )
| ! [SY3865: $i] :
( ~ ( in @ SY3865 @ SV246 )
| ( in @ SY3864 @ SY3865 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1331]) ).
thf(1467,plain,
! [SV247: $i] :
( ( ( ( SV247 != empty_set ) )
= $true )
| ( ( ! [SY3866: $i] :
( ( SY3866
!= ( set_meet @ SV247 ) )
| ( SY3866 = empty_set ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1332]) ).
thf(1468,plain,
! [SV248: $i] :
( ( ( ( SV248 != empty_set ) )
= $true )
| ( ( ! [SY3867: $i] :
( ( SY3867 != empty_set )
| ( SY3867
= ( set_meet @ SV248 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1333]) ).
thf(1469,plain,
! [SV53: $i] :
( ( ( ! [SY3529: $i,SY3530: $i] :
( ~ ( ~ ( ~ ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) ) @ SY3529 )
| ~ ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ SY3530 ) )
| ~ ~ ( ~ ( ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ SY3530 ) )
| ~ ( ( in @ ( apply @ SV53 @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) ) @ SY3529 )
| ( in @ ( sK57_D @ SY3530 @ SY3529 @ SV53 ) @ SY3530 ) ) ) )
| ( SY3530
= ( relation_inverse_image @ SV53 @ SY3529 ) ) ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1334]) ).
thf(1470,plain,
! [SV53: $i] :
( ( ( ! [SY3531: $i,SY3532: $i] :
( ( SY3532
!= ( relation_inverse_image @ SV53 @ SY3531 ) )
| ~ ( ~ ! [SY3533: $i] :
( ~ ( in @ SY3533 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SY3533 ) @ SY3531 )
| ( in @ SY3533 @ SY3532 ) )
| ~ ~ ( ~ ! [SY3534: $i] :
( ~ ( in @ SY3534 @ SY3532 )
| ( in @ SY3534 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY3535: $i] :
( ~ ( in @ SY3535 @ SY3532 )
| ( in @ ( apply @ SV53 @ SY3535 ) @ SY3531 ) ) ) ) ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1335]) ).
thf(1471,plain,
! [SV54: $i,SV165: $i,SV201: $i] :
( ( ( ~ ( ~ ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV54 )
| ~ ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV165 )
| ~ ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV201 ) )
| ~ ~ ( ~ ( ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV54 )
| ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV201 ) )
| ~ ( ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV165 )
| ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV201 ) ) ) )
= $false )
| ( ( SV201
= ( set_intersection2 @ SV54 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1336]) ).
thf(1472,plain,
! [SV166: $i,SV54: $i,SV202: $i] :
( ( ( SV202
= ( set_intersection2 @ SV54 @ SV166 ) )
= $false )
| ( ( ~ ( ~ ! [SY3798: $i] :
( ~ ( in @ SY3798 @ SV54 )
| ~ ( in @ SY3798 @ SV166 )
| ( in @ SY3798 @ SV202 ) )
| ~ ~ ( ~ ! [SY3799: $i] :
( ~ ( in @ SY3799 @ SV202 )
| ( in @ SY3799 @ SV54 ) )
| ~ ! [SY3800: $i] :
( ~ ( in @ SY3800 @ SV202 )
| ( in @ SY3800 @ SV166 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1337]) ).
thf(1473,plain,
! [SV55: $i,SV169: $i,SV203: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV55 )
| ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV169 )
| ~ ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV203 ) )
| ~ ~ ( ~ ( ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV55 )
| ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV203 ) )
| ~ ( ~ ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV169 )
| ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV203 ) ) ) )
= $false )
| ( ( SV203
= ( set_difference @ SV55 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1340]) ).
thf(1474,plain,
! [SV170: $i,SV55: $i,SV204: $i] :
( ( ( SV204
= ( set_difference @ SV55 @ SV170 ) )
= $false )
| ( ( ~ ( ~ ! [SY3801: $i] :
( ~ ( in @ SY3801 @ SV55 )
| ( in @ SY3801 @ SV170 )
| ( in @ SY3801 @ SV204 ) )
| ~ ~ ( ~ ! [SY3802: $i] :
( ~ ( in @ SY3802 @ SV204 )
| ( in @ SY3802 @ SV55 ) )
| ~ ! [SY3803: $i] :
( ~ ( in @ SY3803 @ SV204 )
| ~ ( in @ SY3803 @ SV170 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1341]) ).
thf(1475,plain,
! [SV56: $i] :
( ( ( ! [SY3550: $i] :
( ~ ( ~ ( ! [SY3551: $i] :
( ( ( sK19_C @ SY3550 @ SV56 )
!= ( apply @ SV56 @ SY3551 ) )
| ~ ( in @ SY3551 @ ( relation_dom @ SV56 ) ) )
| ~ ( in @ ( sK19_C @ SY3550 @ SV56 ) @ SY3550 ) )
| ~ ( ~ ( ( ( sK19_C @ SY3550 @ SV56 )
!= ( apply @ SV56 @ ( sK20_SY3294 @ SY3550 @ SV56 ) ) )
| ~ ( in @ ( sK20_SY3294 @ SY3550 @ SV56 ) @ ( relation_dom @ SV56 ) ) )
| ( in @ ( sK19_C @ SY3550 @ SV56 ) @ SY3550 ) ) )
| ( SY3550
= ( relation_rng @ SV56 ) ) ) )
= $true )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1342]) ).
thf(1476,plain,
! [SV56: $i] :
( ( ( ! [SY3552: $i] :
( ( SY3552
!= ( relation_rng @ SV56 ) )
| ~ ( ~ ! [SY3553: $i] :
( ! [SY3554: $i] :
( ( SY3553
!= ( apply @ SV56 @ SY3554 ) )
| ~ ( in @ SY3554 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY3553 @ SY3552 ) )
| ~ ! [SY3555: $i] :
( ~ ( in @ SY3555 @ SY3552 )
| ~ ( ( SY3555
!= ( apply @ SV56 @ ( sK18_D @ SY3555 @ SY3552 @ SV56 ) ) )
| ~ ( in @ ( sK18_D @ SY3555 @ SY3552 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) ) ) ) )
= $true )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1343]) ).
thf(1477,plain,
! [SV57: $i,SV171: $i,SV205: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK38_D @ SV205 @ SV171 @ SV57 ) @ SV205 )
| ( ( sK38_D @ SV205 @ SV171 @ SV57 )
!= SV57 ) )
| ~ ( ~ ( in @ ( sK38_D @ SV205 @ SV171 @ SV57 ) @ SV205 )
| ( ( sK38_D @ SV205 @ SV171 @ SV57 )
!= SV171 ) ) )
| ~ ( ( in @ ( sK38_D @ SV205 @ SV171 @ SV57 ) @ SV205 )
| ( ( sK38_D @ SV205 @ SV171 @ SV57 )
= SV57 )
| ( ( sK38_D @ SV205 @ SV171 @ SV57 )
= SV171 ) ) )
= $false )
| ( ( SV205
= ( unordered_pair @ SV57 @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1344]) ).
thf(1478,plain,
! [SV172: $i,SV57: $i,SV206: $i] :
( ( ( SV206
= ( unordered_pair @ SV57 @ SV172 ) )
= $false )
| ( ( ~ ( ~ ! [SY3804: $i] :
( ~ ( in @ SY3804 @ SV206 )
| ( SY3804 = SV57 )
| ( SY3804 = SV172 ) )
| ~ ~ ( ~ ! [SY3805: $i] :
( ( SY3805 != SV57 )
| ( in @ SY3805 @ SV206 ) )
| ~ ! [SY3806: $i] :
( ( SY3806 != SV172 )
| ( in @ SY3806 @ SV206 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1345]) ).
thf(1479,plain,
! [SV58: $i,SV96: $i] :
( ( ( ~ ! [SY3661: $i] :
( ~ ( function @ SY3661 )
| ~ ( relation @ SY3661 )
| ~ ( ~ ( in @ ( sK67_D @ SY3661 @ SV96 @ SV58 ) @ ( relation_dom @ SV96 ) )
| ~ ( ( ( apply @ SV96 @ ( sK67_D @ SY3661 @ SV96 @ SV58 ) )
!= ( apply @ SY3661 @ ( sK67_D @ SY3661 @ SV96 @ SV58 ) ) ) ) )
| ( ( relation_dom @ SV96 )
!= ( set_intersection2 @ ( relation_dom @ SY3661 ) @ SV58 ) )
| ( SV96
= ( relation_dom_restriction @ SY3661 @ SV58 ) ) ) )
= $false )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1346]) ).
thf(1480,plain,
! [SV58: $i,SV96: $i] :
( ( ( ~ ~ ( ~ ! [SY3662: $i] :
( ~ ( function @ SY3662 )
| ~ ( relation @ SY3662 )
| ( SV96
!= ( relation_dom_restriction @ SY3662 @ SV58 ) )
| ! [SY3663: $i] :
( ~ ( in @ SY3663 @ ( relation_dom @ SV96 ) )
| ( ( apply @ SV96 @ SY3663 )
= ( apply @ SY3662 @ SY3663 ) ) ) )
| ~ ! [SY3664: $i] :
( ~ ( function @ SY3664 )
| ~ ( relation @ SY3664 )
| ( SV96
!= ( relation_dom_restriction @ SY3664 @ SV58 ) )
| ( ( relation_dom @ SV96 )
= ( set_intersection2 @ ( relation_dom @ SY3664 ) @ SV58 ) ) ) ) )
= $false )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1346]) ).
thf(1481,plain,
! [SV59: $i,SV249: $i] :
( ( ( ~ ( relation @ SV249 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV249 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV249 ) ) )
| ( SV59 = SV249 ) )
= $true )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1347]) ).
thf(1482,plain,
! [SV59: $i,SV250: $i] :
( ( ( ~ ( relation @ SV250 ) )
= $true )
| ( ( ( SV59 != SV250 )
| ~ ( ~ ! [SY3868: $i,SY3869: $i] :
( ~ ( in @ ( ordered_pair @ SY3868 @ SY3869 ) @ SV59 )
| ( in @ ( ordered_pair @ SY3868 @ SY3869 ) @ SV250 ) )
| ~ ! [SY3870: $i,SY3871: $i] :
( ~ ( in @ ( ordered_pair @ SY3870 @ SY3871 ) @ SV250 )
| ( in @ ( ordered_pair @ SY3870 @ SY3871 ) @ SV59 ) ) ) )
= $true )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1348]) ).
thf(1483,plain,
! [SV130: $i,SV173: $i] :
( ( ( ~ ( ! [SY3767: $i] :
( ~ ( in @ ( sK23_C @ SV173 @ SV130 ) @ SY3767 )
| ~ ( in @ SY3767 @ SV130 ) )
| ~ ( in @ ( sK23_C @ SV173 @ SV130 ) @ SV173 ) ) )
= $false )
| ( ( SV173
= ( union @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1350]) ).
thf(1484,plain,
! [SV130: $i,SV173: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK23_C @ SV173 @ SV130 ) @ ( sK24_SY3296 @ SV173 @ SV130 ) )
| ~ ( in @ ( sK24_SY3296 @ SV173 @ SV130 ) @ SV130 ) )
| ( in @ ( sK23_C @ SV173 @ SV130 ) @ SV173 ) ) )
= $false )
| ( ( SV173
= ( union @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1350]) ).
thf(1485,plain,
! [SV174: $i,SV131: $i] :
( ( ( ~ ! [SY3768: $i] :
( ! [SY3719: $i] :
( ~ ( in @ SY3768 @ SY3719 )
| ~ ( in @ SY3719 @ SV131 ) )
| ( in @ SY3768 @ SV174 ) )
| ~ ! [SY3770: $i] :
( ~ ( in @ SY3770 @ SV174 )
| ~ ( ~ ( in @ SY3770 @ ( sK22_D @ SY3770 @ SV174 @ SV131 ) )
| ~ ( in @ ( sK22_D @ SY3770 @ SV174 @ SV131 ) @ SV131 ) ) ) )
= $false )
| ( ( SV174
= ( union @ SV131 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1351]) ).
thf(1486,plain,
! [SV251: $i,SV98: $i,SV207: $i,SV61: $i] :
( ( ( ~ ( in @ SV61 @ SV207 )
| ~ ( in @ SV98 @ SV251 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SV207 @ SV251 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1352]) ).
thf(1487,plain,
! [SV98: $i,SV61: $i] :
( ( ! [SY3667: $i] :
( ! [SY3668: $i] :
~ ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SY3667 @ SY3668 ) )
| ( in @ SV61 @ SY3667 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1353]) ).
thf(1488,plain,
! [SV98: $i,SV61: $i] :
( ( ! [SY3669: $i,SY3670: $i] :
( ~ ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SY3669 @ SY3670 ) )
| ( in @ SV98 @ SY3670 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1354]) ).
thf(1489,plain,
! [SV62: $i,SV175: $i,SV208: $i] :
( ( ( ~ ( function @ SV208 ) )
= $true )
| ( ( ~ ( relation @ SV208 ) )
= $true )
| ( ( ~ ( in @ SV175 @ ( relation_dom @ SV208 ) )
| ~ ( in @ SV175 @ SV62 )
| ( in @ SV175 @ ( relation_dom @ ( relation_dom_restriction @ SV208 @ SV62 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1355]) ).
thf(1490,plain,
! [SV62: $i,SV276: $i] :
( ( ! [SY3904: $i] :
( ~ ( function @ SY3904 )
| ~ ( relation @ SY3904 )
| ~ ( in @ SV276 @ ( relation_dom @ ( relation_dom_restriction @ SY3904 @ SV62 ) ) )
| ( in @ SV276 @ ( relation_dom @ SY3904 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1356]) ).
thf(1491,plain,
! [SV62: $i,SV277: $i] :
( ( ! [SY3905: $i] :
( ~ ( function @ SY3905 )
| ~ ( relation @ SY3905 )
| ~ ( in @ SV277 @ ( relation_dom @ ( relation_dom_restriction @ SY3905 @ SV62 ) ) )
| ( in @ SV277 @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1357]) ).
thf(1492,plain,
! [SV209: $i,SV176: $i,SV63: $i] :
( ( ( ~ ( ! [SY3808: $i,SY3809: $i] :
( ~ ( in @ SY3808 @ SV63 )
| ~ ( in @ SY3809 @ SV176 )
| ( ( sK34_D @ SV209 @ SV176 @ SV63 )
!= ( ordered_pair @ SY3808 @ SY3809 ) ) )
| ~ ( in @ ( sK34_D @ SV209 @ SV176 @ SV63 ) @ SV209 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK35_SY3303 @ SV209 @ SV176 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK36_SY3305 @ SV209 @ SV176 @ SV63 ) @ SV176 ) )
| ( ( sK34_D @ SV209 @ SV176 @ SV63 )
!= ( ordered_pair @ ( sK35_SY3303 @ SV209 @ SV176 @ SV63 ) @ ( sK36_SY3305 @ SV209 @ SV176 @ SV63 ) ) ) )
| ( in @ ( sK34_D @ SV209 @ SV176 @ SV63 ) @ SV209 ) ) )
= $false )
| ( ( SV209
= ( cartesian_product2 @ SV63 @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1358]) ).
thf(1493,plain,
! [SV177: $i,SV63: $i,SV210: $i] :
( ( ( SV210
= ( cartesian_product2 @ SV63 @ SV177 ) )
= $false )
| ( ( ~ ( ~ ! [SY3810: $i] :
( ! [SY3777: $i,SY3778: $i] :
( ~ ( in @ SY3777 @ SV63 )
| ~ ( in @ SY3778 @ SV177 )
| ( SY3810
!= ( ordered_pair @ SY3777 @ SY3778 ) ) )
| ( in @ SY3810 @ SV210 ) )
| ~ ! [SY3813: $i] :
( ~ ( in @ SY3813 @ SV210 )
| ~ ( ~ ~ ( ~ ( in @ ( sK32_E @ SY3813 @ SV210 @ SV177 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK33_SY3300 @ SY3813 @ SV210 @ SV177 @ SV63 ) @ SV177 ) )
| ( SY3813
!= ( ordered_pair @ ( sK32_E @ SY3813 @ SV210 @ SV177 @ SV63 ) @ ( sK33_SY3300 @ SY3813 @ SV210 @ SV177 @ SV63 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1359]) ).
thf(1494,plain,
! [SV132: $i,SV178: $i] :
( ( ( ~ ( in @ ( sK73_C @ SV178 @ SV132 ) @ SV132 ) )
= $false )
| ( ( disjoint @ SV132 @ SV178 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1360]) ).
thf(1495,plain,
! [SV132: $i,SV178: $i] :
( ( ( ~ ( in @ ( sK73_C @ SV178 @ SV132 ) @ SV178 ) )
= $false )
| ( ( disjoint @ SV132 @ SV178 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1360]) ).
thf(1496,plain,
! [SV179: $i,SV133: $i,SV252: $i] :
( ( ( ~ ( in @ SV252 @ SV133 ) )
= $true )
| ( ( ~ ( in @ SV252 @ SV179 ) )
= $true )
| ( ( ~ ( disjoint @ SV133 @ SV179 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1361]) ).
thf(1497,plain,
! [SV180: $i,SV64: $i,SV211: $i] :
( ( ( relation @ SV211 )
= $false )
| ( ( ! [SY3814: $i] :
( ~ ( in @ SY3814 @ ( relation_dom @ SV211 ) )
| ~ ( in @ ( ordered_pair @ SY3814 @ SV64 ) @ SV211 )
| ~ ( in @ SY3814 @ SV180 ) )
| ( in @ SV64 @ ( relation_image @ SV211 @ SV180 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1362]) ).
thf(1498,plain,
! [SV181: $i,SV64: $i,SV212: $i] :
( ( ( relation @ SV212 )
= $false )
| ( ( ~ ( in @ SV64 @ ( relation_image @ SV212 @ SV181 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK76_D @ SV212 @ SV181 @ SV64 ) @ ( relation_dom @ SV212 ) )
| ~ ( in @ ( ordered_pair @ ( sK76_D @ SV212 @ SV181 @ SV64 ) @ SV64 ) @ SV212 ) )
| ~ ( in @ ( sK76_D @ SV212 @ SV181 @ SV64 ) @ SV181 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1363]) ).
thf(1499,plain,
! [SV182: $i,SV65: $i,SV213: $i] :
( ( ( relation @ SV213 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV65 @ SV182 ) @ SV213 )
| ( in @ SV65 @ ( relation_dom @ SV213 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1364]) ).
thf(1500,plain,
! [SV183: $i,SV65: $i,SV214: $i] :
( ( ( relation @ SV214 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV65 @ SV183 ) @ SV214 )
| ( in @ SV183 @ ( relation_rng @ SV214 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1365]) ).
thf(1501,plain,
! [SV66: $i] :
( ( ( ~ ( ~ ! [SY3607: $i] :
( ~ ( in @ SY3607 @ ( relation_dom @ SV66 ) )
| ! [SY3608: $i] :
( ( SY3608
!= ( apply @ SV66 @ SY3607 ) )
| ( in @ ( ordered_pair @ SY3607 @ SY3608 ) @ SV66 ) ) )
| ~ ! [SY3609: $i] :
( ~ ( in @ SY3609 @ ( relation_dom @ SV66 ) )
| ! [SY3610: $i] :
( ~ ( in @ ( ordered_pair @ SY3609 @ SY3610 ) @ SV66 )
| ( SY3610
= ( apply @ SV66 @ SY3609 ) ) ) ) ) )
= $true )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1366]) ).
thf(1502,plain,
! [SV66: $i] :
( ( ( ~ ( ~ ! [SY3611: $i] :
( ( in @ SY3611 @ ( relation_dom @ SV66 ) )
| ! [SY3612: $i] :
( ( SY3612
!= ( apply @ SV66 @ SY3611 ) )
| ( SY3612 = empty_set ) ) )
| ~ ! [SY3613: $i] :
( ( in @ SY3613 @ ( relation_dom @ SV66 ) )
| ! [SY3614: $i] :
( ( SY3614 != empty_set )
| ( SY3614
= ( apply @ SV66 @ SY3613 ) ) ) ) ) )
= $true )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1367]) ).
thf(1503,plain,
! [SV73: $i,SV7: $i,SV215: $i] :
( ( ( ~ ( function @ SV215 ) )
= $true )
| ( ( ~ ( relation @ SV215 ) )
= $true )
| ( ( ~ ( in @ SV7 @ ( relation_dom @ ( relation_composition @ SV215 @ SV73 ) ) )
| ( ( apply @ ( relation_composition @ SV215 @ SV73 ) @ SV7 )
= ( apply @ SV73 @ ( apply @ SV215 @ SV7 ) ) ) )
= $true )
| ( ( function @ SV73 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1370]) ).
thf(1504,plain,
! [SV74: $i,SV8: $i,SV216: $i] :
( ( ( ~ ( function @ SV216 ) )
= $true )
| ( ( ~ ( relation @ SV216 ) )
= $true )
| ( ( ~ ( in @ SV8 @ ( relation_dom @ SV74 ) )
| ( ( apply @ ( relation_composition @ SV74 @ SV216 ) @ SV8 )
= ( apply @ SV216 @ ( apply @ SV74 @ SV8 ) ) ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1371]) ).
thf(1505,plain,
! [SV12: $i,SV100: $i,SV186: $i] :
( ( ( in @ SV186 @ SV100 )
= $true )
| ( ( in @ SV186 @ ( subset_complement @ SV12 @ SV100 ) )
= $true )
| ( ( element @ SV186 @ SV12 )
= $false )
| ( ( element @ SV100 @ ( powerset @ SV12 ) )
= $false )
| ( ( SV12 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1373]) ).
thf(1506,plain,
! [SV15: $i,SV102: $i,SV79: $i] :
( ( ( in @ SV79 @ ( relation_dom @ ( relation_dom_restriction @ SV102 @ SV15 ) ) )
= $false )
| ( ( ( apply @ ( relation_dom_restriction @ SV102 @ SV15 ) @ SV79 )
= ( apply @ SV102 @ SV79 ) )
= $true )
| ( ( function @ SV102 )
= $false )
| ( ( relation @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1375]) ).
thf(1507,plain,
! [SV103: $i,SV16: $i,SV80: $i] :
( ( ( in @ SV80 @ SV16 )
= $false )
| ( ( ( apply @ ( relation_dom_restriction @ SV103 @ SV16 ) @ SV80 )
= ( apply @ SV103 @ SV80 ) )
= $true )
| ( ( function @ SV103 )
= $false )
| ( ( relation @ SV103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1376]) ).
thf(1508,plain,
! [SV217: $i,SV139: $i,SV107: $i] :
( ( ( disjoint @ SV107 @ SV139 )
= $false )
| ( ( in @ SV217 @ ( set_intersection2 @ SV107 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1378]) ).
thf(1509,plain,
! [SV26: $i,SV88: $i,SV253: $i] :
( ( ( ~ ( relation @ SV253 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) @ SV26 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV88 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 ) )
| ~ ~ ( ~ ( ( in @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) @ SV26 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV88 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 ) ) ) )
| ( SV253
= ( relation_rng_restriction @ SV26 @ SV88 ) ) )
= $true )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1379]) ).
thf(1510,plain,
! [SV88: $i,SV26: $i,SV254: $i] :
( ( ( ~ ( relation @ SV254 ) )
= $true )
| ( ( ( SV254
!= ( relation_rng_restriction @ SV26 @ SV88 ) )
| ~ ( ~ ! [SY3872: $i,SY3873: $i] :
( ~ ( in @ SY3873 @ SV26 )
| ~ ( in @ ( ordered_pair @ SY3872 @ SY3873 ) @ SV88 )
| ( in @ ( ordered_pair @ SY3872 @ SY3873 ) @ SV254 ) )
| ~ ~ ( ~ ! [SY3874: $i,SY3875: $i] :
( ~ ( in @ ( ordered_pair @ SY3874 @ SY3875 ) @ SV254 )
| ( in @ SY3875 @ SV26 ) )
| ~ ! [SY3876: $i,SY3877: $i] :
( ~ ( in @ ( ordered_pair @ SY3876 @ SY3877 ) @ SV254 )
| ( in @ ( ordered_pair @ SY3876 @ SY3877 ) @ SV88 ) ) ) ) )
= $true )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1380]) ).
thf(1511,plain,
! [SV108: $i,SV140: $i] :
( ( ( in @ ( sK29_C @ SV140 @ SV108 ) @ SV108 )
= $true )
| ( ( subset @ SV108 @ SV140 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1381]) ).
thf(1512,plain,
! [SV108: $i,SV140: $i] :
( ( ( ~ ( in @ ( sK29_C @ SV140 @ SV108 ) @ SV140 ) )
= $true )
| ( ( subset @ SV108 @ SV140 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1382]) ).
thf(1513,plain,
! [SV141: $i,SV109: $i,SV255: $i] :
( ( ( ~ ( in @ SV255 @ SV109 ) )
= $true )
| ( ( in @ SV255 @ SV141 )
= $true )
| ( ( subset @ SV109 @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1383]) ).
thf(1514,plain,
! [SV187: $i,SV142: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ SV142 )
| ~ ( in @ SV27 @ ( relation_dom @ SV187 ) ) )
= $true )
| ( ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SV187 @ SV142 ) ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1384]) ).
thf(1515,plain,
! [SV256: $i,SV27: $i,SV278: $i] :
( ( ~ ( relation @ SV278 )
| ~ ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SV278 @ SV256 ) ) )
| ( in @ SV27 @ SV256 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1385]) ).
thf(1516,plain,
! [SV257: $i,SV27: $i,SV279: $i] :
( ( ~ ( relation @ SV279 )
| ~ ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SV279 @ SV257 ) ) )
| ( in @ SV27 @ ( relation_dom @ SV279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1386]) ).
thf(1517,plain,
! [SV28: $i,SV218: $i] :
( ( ( relation @ SV218 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV218 @ SV28 ) @ ( sK14_SY3290 @ SV218 @ SV28 ) ) @ SV218 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY3290 @ SV218 @ SV28 ) @ ( sK13_C @ SV218 @ SV28 ) ) @ SV28 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SV218 @ SV28 ) @ ( sK14_SY3290 @ SV218 @ SV28 ) ) @ SV218 )
| ( in @ ( ordered_pair @ ( sK14_SY3290 @ SV218 @ SV28 ) @ ( sK13_C @ SV218 @ SV28 ) ) @ SV28 ) ) )
| ( SV218
= ( relation_inverse @ SV28 ) ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1387]) ).
thf(1518,plain,
! [SV28: $i,SV219: $i] :
( ( ( relation @ SV219 )
= $false )
| ( ( ( SV219
!= ( relation_inverse @ SV28 ) )
| ~ ( ~ ! [SY3815: $i,SY3816: $i] :
( ~ ( in @ ( ordered_pair @ SY3815 @ SY3816 ) @ SV219 )
| ( in @ ( ordered_pair @ SY3816 @ SY3815 ) @ SV28 ) )
| ~ ! [SY3817: $i,SY3818: $i] :
( ~ ( in @ ( ordered_pair @ SY3818 @ SY3817 ) @ SV28 )
| ( in @ ( ordered_pair @ SY3817 @ SY3818 ) @ SV219 ) ) ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1388]) ).
thf(1519,plain,
! [SV280: $i,SV29: $i] :
( ( ( ! [SY3906: $i] :
( ~ ( ~ ( ! [SY3907: $i] :
( ~ ( in @ SY3907 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3907 @ SV280 )
| ( ( sK61_D @ SY3906 @ SV280 @ SV29 )
!= ( apply @ SV29 @ SY3907 ) ) )
| ~ ( in @ ( sK61_D @ SY3906 @ SV280 @ SV29 ) @ SY3906 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY3318 @ SY3906 @ SV280 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK62_SY3318 @ SY3906 @ SV280 @ SV29 ) @ SV280 ) )
| ( ( sK61_D @ SY3906 @ SV280 @ SV29 )
!= ( apply @ SV29 @ ( sK62_SY3318 @ SY3906 @ SV280 @ SV29 ) ) ) )
| ( in @ ( sK61_D @ SY3906 @ SV280 @ SV29 ) @ SY3906 ) ) )
| ( SY3906
= ( relation_image @ SV29 @ SV280 ) ) ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1389]) ).
thf(1520,plain,
! [SV281: $i,SV29: $i] :
( ( ( ! [SY3908: $i] :
( ( SY3908
!= ( relation_image @ SV29 @ SV281 ) )
| ~ ( ~ ! [SY3909: $i] :
( ! [SY3910: $i] :
( ~ ( in @ SY3910 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3910 @ SV281 )
| ( SY3909
!= ( apply @ SV29 @ SY3910 ) ) )
| ( in @ SY3909 @ SY3908 ) )
| ~ ! [SY3911: $i] :
( ~ ( in @ SY3911 @ SY3908 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SY3911 @ SY3908 @ SV281 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK60_E @ SY3911 @ SY3908 @ SV281 @ SV29 ) @ SV281 ) )
| ( SY3911
!= ( apply @ SV29 @ ( sK60_E @ SY3911 @ SY3908 @ SV281 @ SV29 ) ) ) ) ) ) ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1390]) ).
thf(1521,plain,
! [SV30: $i,SV220: $i,SV258: $i] :
( ( ( ~ ( ~ ( ! [SY3880: $i] :
( ~ ( in @ ( ordered_pair @ SY3880 @ ( sK55_D @ SV258 @ SV220 @ SV30 ) ) @ SV30 )
| ~ ( in @ SY3880 @ SV220 ) )
| ~ ( in @ ( sK55_D @ SV258 @ SV220 @ SV30 ) @ SV258 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_SY3315 @ SV258 @ SV220 @ SV30 ) @ ( sK55_D @ SV258 @ SV220 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK56_SY3315 @ SV258 @ SV220 @ SV30 ) @ SV220 ) )
| ( in @ ( sK55_D @ SV258 @ SV220 @ SV30 ) @ SV258 ) ) ) )
= $true )
| ( ( SV258
= ( relation_image @ SV30 @ SV220 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1391]) ).
thf(1522,plain,
! [SV221: $i,SV30: $i,SV259: $i] :
( ( ( ( SV259
!= ( relation_image @ SV30 @ SV221 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3881: $i] :
( ! [SY3823: $i] :
( ~ ( in @ ( ordered_pair @ SY3823 @ SY3881 ) @ SV30 )
| ~ ( in @ SY3823 @ SV221 ) )
| ( in @ SY3881 @ SV259 ) )
| ~ ! [SY3883: $i] :
( ~ ( in @ SY3883 @ SV259 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SY3883 @ SV259 @ SV221 @ SV30 ) @ SY3883 ) @ SV30 )
| ~ ( in @ ( sK54_E @ SY3883 @ SV259 @ SV221 @ SV30 ) @ SV221 ) ) ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1392]) ).
thf(1523,plain,
! [SV31: $i,SV222: $i,SV260: $i] :
( ( ( ~ ( ~ ( ! [SY3884: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SY3884 ) @ SV31 )
| ~ ( in @ SY3884 @ SV222 ) )
| ~ ( in @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SV260 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ ( sK53_SY3313 @ SV260 @ SV222 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( sK53_SY3313 @ SV260 @ SV222 @ SV31 ) @ SV222 ) )
| ( in @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SV260 ) ) ) )
= $true )
| ( ( SV260
= ( relation_inverse_image @ SV31 @ SV222 ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1393]) ).
thf(1524,plain,
! [SV223: $i,SV31: $i,SV261: $i] :
( ( ( ( SV261
!= ( relation_inverse_image @ SV31 @ SV223 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3885: $i] :
( ! [SY3829: $i] :
( ~ ( in @ ( ordered_pair @ SY3885 @ SY3829 ) @ SV31 )
| ~ ( in @ SY3829 @ SV223 ) )
| ( in @ SY3885 @ SV261 ) )
| ~ ! [SY3887: $i] :
( ~ ( in @ SY3887 @ SV261 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3887 @ ( sK51_E @ SY3887 @ SV261 @ SV223 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( sK51_E @ SY3887 @ SV261 @ SV223 @ SV31 ) @ SV223 ) ) ) ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1394]) ).
thf(1525,plain,
! [SV32: $i,SV224: $i,SV262: $i] :
( ( ( ~ ( relation @ SV262 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ SV224 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV32 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 ) )
| ~ ~ ( ~ ( ( in @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ SV224 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV32 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 ) ) ) )
| ( SV262
= ( relation_dom_restriction @ SV32 @ SV224 ) ) )
= $true )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1395]) ).
thf(1526,plain,
! [SV225: $i,SV32: $i,SV263: $i] :
( ( ( ~ ( relation @ SV263 ) )
= $true )
| ( ( ( SV263
!= ( relation_dom_restriction @ SV32 @ SV225 ) )
| ~ ( ~ ! [SY3888: $i,SY3889: $i] :
( ~ ( in @ SY3888 @ SV225 )
| ~ ( in @ ( ordered_pair @ SY3888 @ SY3889 ) @ SV32 )
| ( in @ ( ordered_pair @ SY3888 @ SY3889 ) @ SV263 ) )
| ~ ~ ( ~ ! [SY3890: $i] :
( ! [SY3891: $i] :
~ ( in @ ( ordered_pair @ SY3890 @ SY3891 ) @ SV263 )
| ( in @ SY3890 @ SV225 ) )
| ~ ! [SY3892: $i,SY3893: $i] :
( ~ ( in @ ( ordered_pair @ SY3892 @ SY3893 ) @ SV263 )
| ( in @ ( ordered_pair @ SY3892 @ SY3893 ) @ SV32 ) ) ) ) )
= $true )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1396]) ).
thf(1527,plain,
! [SV143: $i,SV33: $i,SV188: $i] :
( ( ( ! [SY3786: $i] :
( ~ ( in @ SY3786 @ ( relation_rng @ SV188 ) )
| ~ ( in @ ( ordered_pair @ SV33 @ SY3786 ) @ SV188 )
| ~ ( in @ SY3786 @ SV143 ) ) )
= $true )
| ( ( in @ SV33 @ ( relation_inverse_image @ SV188 @ SV143 ) )
= $true )
| ( ( relation @ SV188 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1397]) ).
thf(1528,plain,
! [SV144: $i,SV189: $i,SV33: $i] :
( ( ( ~ ( in @ SV33 @ ( relation_inverse_image @ SV189 @ SV144 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK75_D @ SV189 @ SV144 @ SV33 ) @ ( relation_rng @ SV189 ) )
| ~ ( in @ ( ordered_pair @ SV33 @ ( sK75_D @ SV189 @ SV144 @ SV33 ) ) @ SV189 ) )
| ~ ( in @ ( sK75_D @ SV189 @ SV144 @ SV33 ) @ SV144 ) ) )
= $true )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1398]) ).
thf(1529,plain,
! [SV110: $i,SV145: $i] :
( ( ( ~ ( ( ( sK65_C @ SV145 @ SV110 )
!= ( sK66_SY3320 @ SV145 @ SV110 ) )
| ~ ( in @ ( sK65_C @ SV145 @ SV110 ) @ SV110 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 ) )
| ~ ~ ( ~ ( ( ( sK65_C @ SV145 @ SV110 )
= ( sK66_SY3320 @ SV145 @ SV110 ) )
| ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 ) )
| ~ ( ( in @ ( sK65_C @ SV145 @ SV110 ) @ SV110 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 ) ) ) )
= $false )
| ( ( SV145
= ( identity_relation @ SV110 ) )
= $true )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1399]) ).
thf(1530,plain,
! [SV111: $i,SV146: $i] :
( ( ( SV146
= ( identity_relation @ SV111 ) )
= $false )
| ( ( ~ ( ~ ! [SY3732: $i,SY3733: $i] :
( ( SY3732 != SY3733 )
| ~ ( in @ SY3732 @ SV111 )
| ( in @ ( ordered_pair @ SY3732 @ SY3733 ) @ SV146 ) )
| ~ ~ ( ~ ! [SY3734: $i,SY3735: $i] :
( ~ ( in @ ( ordered_pair @ SY3734 @ SY3735 ) @ SV146 )
| ( SY3734 = SY3735 ) )
| ~ ! [SY3736: $i] :
( ! [SY3737: $i] :
~ ( in @ ( ordered_pair @ SY3736 @ SY3737 ) @ SV146 )
| ( in @ SY3736 @ SV111 ) ) ) ) )
= $true )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1400]) ).
thf(1531,plain,
! [SV34: $i,SV89: $i,SV190: $i,SV226: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV190 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV34 ) )
| ~ ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV89 ) ) ) )
| ~ ( ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
= SV190 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
= SV34 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
= SV89 ) ) )
= $false )
| ( ( SV226
= ( unordered_triple @ SV34 @ SV89 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1401]) ).
thf(1532,plain,
! [SV191: $i,SV89: $i,SV34: $i,SV227: $i] :
( ( ( SV227
= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
= $false )
| ( ( ~ ( ~ ! [SY3839: $i] :
( ~ ( in @ SY3839 @ SV227 )
| ( SY3839 = SV191 )
| ( SY3839 = SV34 )
| ( SY3839 = SV89 ) )
| ~ ~ ( ~ ! [SY3840: $i] :
( ( SY3840 != SV191 )
| ( in @ SY3840 @ SV227 ) )
| ~ ~ ( ~ ! [SY3841: $i] :
( ( SY3841 != SV34 )
| ( in @ SY3841 @ SV227 ) )
| ~ ! [SY3842: $i] :
( ( SY3842 != SV89 )
| ( in @ SY3842 @ SV227 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1402]) ).
thf(1533,plain,
! [SV192: $i,SV147: $i,SV35: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV35 @ SV147 ) @ SV192 ) )
= $true )
| ( ( in @ SV35 @ ( relation_field @ SV192 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1403]) ).
thf(1534,plain,
! [SV193: $i,SV148: $i,SV35: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV35 @ SV148 ) @ SV193 ) )
= $true )
| ( ( in @ SV148 @ ( relation_field @ SV193 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1404]) ).
thf(1535,plain,
! [SV36: $i,SV228: $i] :
( ( ( ~ ( ! [SY3843: $i] :
~ ( in @ ( ordered_pair @ SY3843 @ ( sK16_C @ SV228 @ SV36 ) ) @ SV36 )
| ~ ( in @ ( sK16_C @ SV228 @ SV36 ) @ SV228 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK17_SY3292 @ SV228 @ SV36 ) @ ( sK16_C @ SV228 @ SV36 ) ) @ SV36 )
| ( in @ ( sK16_C @ SV228 @ SV36 ) @ SV228 ) ) )
= $false )
| ( ( SV228
= ( relation_rng @ SV36 ) )
= $true )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1405]) ).
thf(1536,plain,
! [SV36: $i,SV229: $i] :
( ( ( SV229
= ( relation_rng @ SV36 ) )
= $false )
| ( ( ~ ( ~ ! [SY3844: $i] :
( ! [SY3437: $i] :
~ ( in @ ( ordered_pair @ SY3437 @ SY3844 ) @ SV36 )
| ( in @ SY3844 @ SV229 ) )
| ~ ! [SY3846: $i] :
( ~ ( in @ SY3846 @ SV229 )
| ( in @ ( ordered_pair @ ( sK15_D @ SY3846 @ SV229 @ SV36 ) @ SY3846 ) @ SV36 ) ) ) )
= $true )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1406]) ).
thf(1537,plain,
! [SV37: $i,SV264: $i] :
( ( ( ~ ( in @ SV264 @ ( sK77_B @ SV37 ) ) )
= $true )
| ( ( in @ ( powerset @ SV264 ) @ ( sK77_B @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1408]) ).
thf(1538,plain,
! [SV37: $i] :
( ( ~ ! [SY3441: $i,SY3442: $i] :
( ~ ( in @ SY3441 @ ( sK77_B @ SV37 ) )
| ~ ( subset @ SY3442 @ SY3441 )
| ( in @ SY3442 @ ( sK77_B @ SV37 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1409]) ).
thf(1539,plain,
! [SV37: $i] :
( ( ~ ( in @ SV37 @ ( sK77_B @ SV37 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1409]) ).
thf(1540,plain,
! [SV112: $i,SV150: $i] :
( ( ( ~ ( in @ ( sK41_C @ SV150 @ SV112 ) @ SV150 )
| ~ ( subset @ ( sK41_C @ SV150 @ SV112 ) @ SV112 ) )
= $true )
| ( ( SV150
= ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1410]) ).
thf(1541,plain,
! [SV112: $i,SV150: $i] :
( ( ( ( in @ ( sK41_C @ SV150 @ SV112 ) @ SV150 )
| ( subset @ ( sK41_C @ SV150 @ SV112 ) @ SV112 ) )
= $true )
| ( ( SV150
= ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1411]) ).
thf(1542,plain,
! [SV113: $i,SV151: $i] :
( ( ( ~ ! [SY3740: $i] :
( ~ ( in @ SY3740 @ SV151 )
| ( subset @ SY3740 @ SV113 ) ) )
= $false )
| ( ( SV151
= ( powerset @ SV113 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1412]) ).
thf(1543,plain,
! [SV151: $i,SV113: $i] :
( ( ( ~ ! [SY3741: $i] :
( ~ ( subset @ SY3741 @ SV113 )
| ( in @ SY3741 @ SV151 ) ) )
= $false )
| ( ( SV151
= ( powerset @ SV113 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1412]) ).
thf(1544,plain,
! [SV38: $i,SV90: $i] :
( ( ( in @ ( sK5_C @ SV90 @ SV38 ) @ SV90 )
= $false )
| ( ( in @ ( sK5_C @ SV90 @ SV38 ) @ SV38 )
= $false )
| ( ( SV38 = SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1413]) ).
thf(1545,plain,
! [SV114: $i,SV152: $i] :
( ( ( relation @ SV152 )
= $false )
| ( ( function @ SV152 )
= $false )
| ( ( ~ ( in @ SV114 @ ( relation_rng @ SV152 ) )
| ~ ( one_to_one @ SV152 )
| ( SV114
= ( apply @ SV152 @ ( apply @ ( function_inverse @ SV152 ) @ SV114 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1414]) ).
thf(1546,plain,
! [SV115: $i,SV153: $i] :
( ( ( relation @ SV153 )
= $false )
| ( ( function @ SV153 )
= $false )
| ( ( ~ ( in @ SV115 @ ( relation_rng @ SV153 ) )
| ~ ( one_to_one @ SV153 )
| ( SV115
= ( apply @ ( relation_composition @ ( function_inverse @ SV153 ) @ SV153 ) @ SV115 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1415]) ).
thf(1547,plain,
! [SV91: $i,SV39: $i] :
( ( ( ! [SY3641: $i] :
( ~ ( function @ SY3641 )
| ~ ( relation @ SY3641 )
| ~ ( in @ SV39 @ ( relation_dom @ SY3641 ) )
| ~ ( in @ ( apply @ SY3641 @ SV39 ) @ ( relation_dom @ SV91 ) )
| ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3641 @ SV91 ) ) ) ) )
= $true )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1416]) ).
thf(1548,plain,
! [SV91: $i,SV39: $i] :
( ( ( ~ ( ~ ! [SY3642: $i] :
( ~ ( function @ SY3642 )
| ~ ( relation @ SY3642 )
| ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3642 @ SV91 ) ) )
| ( in @ SV39 @ ( relation_dom @ SY3642 ) ) )
| ~ ! [SY3643: $i] :
( ~ ( function @ SY3643 )
| ~ ( relation @ SY3643 )
| ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3643 @ SV91 ) ) )
| ( in @ ( apply @ SY3643 @ SV39 ) @ ( relation_dom @ SV91 ) ) ) ) )
= $true )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1417]) ).
thf(1549,plain,
! [SV92: $i,SV40: $i,SV265: $i] :
( ( ( ~ ( element @ SV265 @ ( powerset @ ( powerset @ SV40 ) ) ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK6_D @ SV265 @ SV92 @ SV40 ) @ ( powerset @ SV40 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK6_D @ SV265 @ SV92 @ SV40 ) @ SV265 )
| ~ ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SV265 @ SV92 @ SV40 ) ) @ SV92 ) )
| ~ ( ( in @ ( sK6_D @ SV265 @ SV92 @ SV40 ) @ SV265 )
| ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SV265 @ SV92 @ SV40 ) ) @ SV92 ) ) ) )
| ( SV265
= ( complements_of_subsets @ SV40 @ SV92 ) ) )
= $true )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1418]) ).
thf(1550,plain,
! [SV92: $i,SV40: $i,SV266: $i] :
( ( ( ~ ( element @ SV266 @ ( powerset @ ( powerset @ SV40 ) ) ) )
= $true )
| ( ( ( SV266
!= ( complements_of_subsets @ SV40 @ SV92 ) )
| ~ ( ~ ! [SY3894: $i] :
( ~ ( element @ SY3894 @ ( powerset @ SV40 ) )
| ~ ( in @ SY3894 @ SV266 )
| ( in @ ( subset_complement @ SV40 @ SY3894 ) @ SV92 ) )
| ~ ! [SY3895: $i] :
( ~ ( element @ SY3895 @ ( powerset @ SV40 ) )
| ~ ( in @ ( subset_complement @ SV40 @ SY3895 ) @ SV92 )
| ( in @ SY3895 @ SV266 ) ) ) )
= $true )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1419]) ).
thf(1551,plain,
! [SV41: $i,SV154: $i,SV194: $i] :
( ( ( function @ SV194 )
= $false )
| ( ( ~ ( relation @ SV194 ) )
= $true )
| ( ( ( SV154
!= ( apply @ SV194 @ SV41 ) )
| ~ ( in @ SV41 @ ( relation_dom @ SV194 ) )
| ( in @ ( ordered_pair @ SV41 @ SV154 ) @ SV194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1420]) ).
thf(1552,plain,
! [SV267: $i,SV41: $i,SV282: $i] :
( ( ~ ( function @ SV282 )
| ~ ( relation @ SV282 )
| ~ ( in @ ( ordered_pair @ SV41 @ SV267 ) @ SV282 )
| ( SV267
= ( apply @ SV282 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1421]) ).
thf(1553,plain,
! [SV268: $i,SV41: $i,SV283: $i] :
( ( ~ ( function @ SV283 )
| ~ ( relation @ SV283 )
| ~ ( in @ ( ordered_pair @ SV41 @ SV268 ) @ SV283 )
| ( in @ SV41 @ ( relation_dom @ SV283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1422]) ).
thf(1554,plain,
! [SV195: $i,SV155: $i,SV42: $i] :
( ( ( ~ ( in @ SV42 @ SV155 )
| ~ ( in @ SV42 @ ( relation_rng @ SV195 ) ) )
= $true )
| ( ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SV155 @ SV195 ) ) )
= $true )
| ( ( relation @ SV195 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1423]) ).
thf(1555,plain,
! [SV269: $i,SV42: $i,SV284: $i] :
( ( ~ ( relation @ SV284 )
| ~ ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SV269 @ SV284 ) ) )
| ( in @ SV42 @ SV269 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1424]) ).
thf(1556,plain,
! [SV270: $i,SV42: $i,SV285: $i] :
( ( ~ ( relation @ SV285 )
| ~ ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SV270 @ SV285 ) ) )
| ( in @ SV42 @ ( relation_rng @ SV285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1425]) ).
thf(1557,plain,
! [SV43: $i,SV271: $i] :
( ( ( ~ ( ~ ! [SY3900: $i] :
( ~ ( subset @ SY3900 @ SV271 )
| ( in @ SY3900 @ ( sK3_SY3278 @ SV271 @ SV43 ) ) )
| ~ ( in @ ( sK3_SY3278 @ SV271 @ SV43 ) @ ( sK2_B @ SV43 ) ) ) )
= $true )
| ( ( ~ ( in @ SV271 @ ( sK2_B @ SV43 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1427]) ).
thf(1558,plain,
! [SV43: $i] :
( ( ~ ! [SY3468: $i,SY3469: $i] :
( ~ ( in @ SY3468 @ ( sK2_B @ SV43 ) )
| ~ ( subset @ SY3469 @ SY3468 )
| ( in @ SY3469 @ ( sK2_B @ SV43 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1428]) ).
thf(1559,plain,
! [SV43: $i] :
( ( ~ ( in @ SV43 @ ( sK2_B @ SV43 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1428]) ).
thf(1560,plain,
! [SV286: $i,SV116: $i] :
( ( ( ! [SY3912: $i] :
( ( sK49_B @ SV116 )
!= ( ordered_pair @ SV286 @ SY3912 ) ) )
= $true )
| ( ( relation @ SV116 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1429]) ).
thf(1561,plain,
! [SV117: $i,SV230: $i] :
( ( ( in @ SV230 @ SV117 )
= $false )
| ( ( SV230
= ( ordered_pair @ ( sK47_C @ SV230 @ SV117 ) @ ( sK48_SY3309 @ SV230 @ SV117 ) ) )
= $true )
| ( ( relation @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1431]) ).
thf(1562,plain,
! [SV231: $i,SV93: $i,SV196: $i,SV44: $i] :
( ( ( ~ ( in @ SV44 @ SV196 ) )
= $true )
| ( ( ~ ( in @ SV93 @ SV231 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SV196 @ SV231 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1432]) ).
thf(1563,plain,
! [SV287: $i,SV93: $i,SV44: $i] :
( ( ! [SY3913: $i] :
~ ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SV287 @ SY3913 ) )
| ( in @ SV44 @ SV287 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1433]) ).
thf(1564,plain,
! [SV288: $i,SV93: $i,SV44: $i] :
( ( ! [SY3914: $i] :
( ~ ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SV288 @ SY3914 ) )
| ( in @ SV93 @ SY3914 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1434]) ).
thf(1565,plain,
! [SV45: $i,SV232: $i] :
( ( ( ~ ( ! [SY3847: $i] :
~ ( in @ ( ordered_pair @ ( sK26_C @ SV232 @ SV45 ) @ SY3847 ) @ SV45 )
| ~ ( in @ ( sK26_C @ SV232 @ SV45 ) @ SV232 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK26_C @ SV232 @ SV45 ) @ ( sK27_SY3298 @ SV232 @ SV45 ) ) @ SV45 )
| ( in @ ( sK26_C @ SV232 @ SV45 ) @ SV232 ) ) )
= $false )
| ( ( SV232
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1435]) ).
thf(1566,plain,
! [SV45: $i,SV233: $i] :
( ( ( SV233
= ( relation_dom @ SV45 ) )
= $false )
| ( ( ~ ( ~ ! [SY3848: $i] :
( ! [SY3481: $i] :
~ ( in @ ( ordered_pair @ SY3848 @ SY3481 ) @ SV45 )
| ( in @ SY3848 @ SV233 ) )
| ~ ! [SY3850: $i] :
( ~ ( in @ SY3850 @ SV233 )
| ( in @ ( ordered_pair @ SY3850 @ ( sK25_D @ SY3850 @ SV233 @ SV45 ) ) @ SV45 ) ) ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1436]) ).
thf(1567,plain,
! [SV234: $i,SV289: $i] :
( ( ( ~ ( element @ SV289 @ SV234 )
| ( in @ SV289 @ SV234 ) )
= $true )
| ( ( empty @ SV234 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1437]) ).
thf(1568,plain,
! [SV235: $i,SV290: $i] :
( ( ( ~ ( in @ SV290 @ SV235 )
| ( element @ SV290 @ SV235 ) )
= $true )
| ( ( empty @ SV235 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(1569,plain,
! [SV236: $i] :
( ( ( empty @ SV236 )
= $false )
| ( ( ! [SY3853: $i] :
( ~ ( element @ SY3853 @ SV236 )
| ( empty @ SY3853 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1439]) ).
thf(1570,plain,
! [SV237: $i] :
( ( ( empty @ SV237 )
= $false )
| ( ( ! [SY3854: $i] :
( ~ ( empty @ SY3854 )
| ( element @ SY3854 @ SV237 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1440]) ).
thf(1571,plain,
! [SV120: $i,SV157: $i] :
( ( ( ( ( sK43_C @ SV157 @ SV120 )
!= SV120 )
| ~ ( in @ ( sK43_C @ SV157 @ SV120 ) @ SV157 ) )
= $true )
| ( ( SV157
= ( singleton @ SV120 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1442]) ).
thf(1572,plain,
! [SV120: $i,SV157: $i] :
( ( ( ( ( sK43_C @ SV157 @ SV120 )
= SV120 )
| ( in @ ( sK43_C @ SV157 @ SV120 ) @ SV157 ) )
= $true )
| ( ( SV157
= ( singleton @ SV120 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1443]) ).
thf(1573,plain,
! [SV158: $i,SV121: $i] :
( ( ( ~ ! [SY3744: $i] :
( ( SY3744 != SV121 )
| ( in @ SY3744 @ SV158 ) ) )
= $false )
| ( ( SV158
= ( singleton @ SV121 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1444]) ).
thf(1574,plain,
! [SV121: $i,SV158: $i] :
( ( ( ~ ! [SY3745: $i] :
( ~ ( in @ SY3745 @ SV158 )
| ( SY3745 = SV121 ) ) )
= $false )
| ( ( SV158
= ( singleton @ SV121 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1444]) ).
thf(1575,plain,
! [SV122: $i,SV159: $i] :
( ( ( relation @ SV159 )
= $false )
| ( ( function @ SV159 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK74_C @ SV159 @ SV122 ) @ SV122 )
| ~ ( ( ( apply @ SV159 @ ( sK74_C @ SV159 @ SV122 ) )
!= ( sK74_C @ SV159 @ SV122 ) ) ) )
| ( ( relation_dom @ SV159 )
!= SV122 )
| ( SV159
= ( identity_relation @ SV122 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1445]) ).
thf(1576,plain,
! [SV239: $i,SV272: $i] :
( ( ( ~ ( function @ SV272 )
| ~ ( relation @ SV272 ) )
= $true )
| ( ( ( SV272
!= ( identity_relation @ SV239 ) )
| ! [SY3901: $i] :
( ~ ( in @ SY3901 @ SV239 )
| ( ( apply @ SV272 @ SY3901 )
= SY3901 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1446]) ).
thf(1577,plain,
! [SV240: $i,SV273: $i] :
( ( ( ~ ( function @ SV273 )
| ~ ( relation @ SV273 ) )
= $true )
| ( ( ( SV273
!= ( identity_relation @ SV240 ) )
| ( ( relation_dom @ SV273 )
= SV240 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1447]) ).
thf(1578,plain,
! [SV46: $i] :
( ( ( ~ ! [SY3483: $i] :
( ~ ( function @ SY3483 )
| ~ ( relation @ SY3483 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY3322 @ SY3483 @ SV46 )
= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ( ( sK70_C @ SY3483 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SY3483 @ SV46 )
= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SY3483 @ SV46 )
= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ( ( sK71_SY3322 @ SY3483 @ SV46 )
!= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK70_C @ SY3483 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK71_SY3322 @ SY3483 @ SV46 )
!= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY3483 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK70_C @ SY3483 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SY3483 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SY3483 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK71_SY3322 @ SY3483 @ SV46 )
!= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ( ( relation_dom @ SY3483 )
!= ( relation_rng @ SV46 ) )
| ( SY3483
= ( function_inverse @ SV46 ) ) ) )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1448]) ).
thf(1579,plain,
! [SV46: $i] :
( ( ( ~ ~ ( ~ ! [SY3484: $i] :
( ~ ( function @ SY3484 )
| ~ ( relation @ SY3484 )
| ( SY3484
!= ( function_inverse @ SV46 ) )
| ~ ( ~ ~ ( ~ ! [SY3485: $i,SY3486: $i] :
( ( SY3486
!= ( apply @ SY3484 @ SY3485 ) )
| ~ ( in @ SY3485 @ ( relation_rng @ SV46 ) )
| ( SY3485
= ( apply @ SV46 @ SY3486 ) ) )
| ~ ! [SY3487: $i,SY3488: $i] :
( ( SY3488
!= ( apply @ SY3484 @ SY3487 ) )
| ~ ( in @ SY3487 @ ( relation_rng @ SV46 ) )
| ( in @ SY3488 @ ( relation_dom @ SV46 ) ) ) )
| ~ ~ ( ~ ! [SY3489: $i,SY3490: $i] :
( ( SY3489
!= ( apply @ SV46 @ SY3490 ) )
| ~ ( in @ SY3490 @ ( relation_dom @ SV46 ) )
| ( SY3490
= ( apply @ SY3484 @ SY3489 ) ) )
| ~ ! [SY3491: $i] :
( ! [SY3492: $i] :
( ( SY3491
!= ( apply @ SV46 @ SY3492 ) )
| ~ ( in @ SY3492 @ ( relation_dom @ SV46 ) ) )
| ( in @ SY3491 @ ( relation_rng @ SV46 ) ) ) ) ) )
| ~ ! [SY3493: $i] :
( ~ ( function @ SY3493 )
| ~ ( relation @ SY3493 )
| ( SY3493
!= ( function_inverse @ SV46 ) )
| ( ( relation_dom @ SY3493 )
= ( relation_rng @ SV46 ) ) ) ) )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1448]) ).
thf(1580,plain,
! [SV47: $i,SV123: $i] :
( ( ( ! [SY3701: $i] :
( ~ ( relation @ SY3701 )
| ~ ( ~ ( ! [SY3702: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY3701 @ SV123 @ SV47 ) @ SY3702 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3702 @ ( sK9_SY3284 @ SY3701 @ SV123 @ SV47 ) ) @ SV123 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SY3701 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SY3701 @ SV123 @ SV47 ) ) @ SY3701 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SY3701 @ SV123 @ SV47 ) @ ( sK10_SY3288 @ SY3701 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY3288 @ SY3701 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SY3701 @ SV123 @ SV47 ) ) @ SV123 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SY3701 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SY3701 @ SV123 @ SV47 ) ) @ SY3701 ) ) )
| ( SY3701
= ( relation_composition @ SV47 @ SV123 ) ) ) )
= $true )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1449]) ).
thf(1581,plain,
! [SV123: $i,SV47: $i] :
( ( ( ! [SY3703: $i] :
( ~ ( relation @ SY3703 )
| ( SY3703
!= ( relation_composition @ SV47 @ SV123 ) )
| ~ ( ~ ! [SY3704: $i,SY3705: $i] :
( ! [SY3706: $i] :
( ~ ( in @ ( ordered_pair @ SY3704 @ SY3706 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3706 @ SY3705 ) @ SV123 ) )
| ( in @ ( ordered_pair @ SY3704 @ SY3705 ) @ SY3703 ) )
| ~ ! [SY3707: $i,SY3708: $i] :
( ~ ( in @ ( ordered_pair @ SY3707 @ SY3708 ) @ SY3703 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3707 @ ( sK7_F @ SY3708 @ SY3707 @ SY3703 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY3708 @ SY3707 @ SY3703 @ SV123 @ SV47 ) @ SY3708 ) @ SV123 ) ) ) ) ) )
= $true )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1450]) ).
thf(1582,plain,
! [SV160: $i,SV197: $i,SV48: $i] :
( ( ( in @ SV48 @ SV197 )
= $false )
| ( ( ~ ( in @ SV160 @ SV197 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV48 @ SV160 ) @ SV197 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1451]) ).
thf(1583,plain,
! [SV291: $i,SV274: $i,SV48: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV48 @ SV274 ) @ SV291 )
| ( in @ SV48 @ SV291 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(1584,plain,
! [SV292: $i,SV275: $i,SV48: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV48 @ SV275 ) @ SV292 )
| ( in @ SV275 @ SV292 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(1585,plain,
! [SV94: $i,SV198: $i,SV49: $i,SV241: $i] :
( ( ( relation @ SV241 )
= $false )
| ( ( ~ ( in @ SV49 @ SV198 )
| ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ SV241 )
| ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SV198 ) @ SV241 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1454]) ).
thf(1586,plain,
! [SV293: $i,SV94: $i,SV49: $i] :
( ( ! [SY3915: $i] :
( ~ ( relation @ SY3915 )
| ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SV293 ) @ SY3915 ) )
| ( in @ SV49 @ SV293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1455]) ).
thf(1587,plain,
! [SV294: $i,SV94: $i,SV49: $i] :
( ( ! [SY3916: $i] :
( ~ ( relation @ SY3916 )
| ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SV294 ) @ SY3916 ) )
| ( in @ ( ordered_pair @ SV49 @ SV94 ) @ SY3916 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1456]) ).
thf(1588,plain,
! [SV50: $i,SV95: $i,SV242: $i] :
( ( ( in @ SV242 @ SV95 )
= $false )
| ( ( ~ ( in @ SV242 @ ( sK4_C @ SV95 @ SV50 ) ) )
= $true )
| ( ( ~ ( in @ SV50 @ SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1457]) ).
thf(1589,plain,
! [SV124: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_B @ SV124 ) @ ( relation_dom @ SV124 ) )
| ~ ( in @ ( sK12_SY3289 @ SV124 ) @ ( relation_dom @ SV124 ) ) )
| ( ( apply @ SV124 @ ( sK11_B @ SV124 ) )
!= ( apply @ SV124 @ ( sK12_SY3289 @ SV124 ) ) ) )
| ~ ( ( ( sK11_B @ SV124 )
!= ( sK12_SY3289 @ SV124 ) ) ) ) )
= $true )
| ( ( one_to_one @ SV124 )
= $true )
| ( ( function @ SV124 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1458]) ).
thf(1590,plain,
! [SV125: $i] :
( ( ( ~ ( one_to_one @ SV125 ) )
= $true )
| ( ( ! [SY3709: $i,SY3710: $i] :
( ~ ( in @ SY3709 @ ( relation_dom @ SV125 ) )
| ~ ( in @ SY3710 @ ( relation_dom @ SV125 ) )
| ( ( apply @ SV125 @ SY3709 )
!= ( apply @ SV125 @ SY3710 ) )
| ( SY3709 = SY3710 ) ) )
= $true )
| ( ( function @ SV125 )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1459]) ).
thf(1591,plain,
! [SV51: $i,SV161: $i,SV199: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV199 )
| ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV51 ) )
| ~ ( ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV199 )
| ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV161 ) ) ) )
= $false )
| ( ( SV199
= ( set_union2 @ SV51 @ SV161 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1460]) ).
thf(1592,plain,
! [SV51: $i,SV161: $i,SV199: $i] :
( ( ( ~ ( ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV199 )
| ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV51 )
| ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV161 ) ) )
= $false )
| ( ( SV199
= ( set_union2 @ SV51 @ SV161 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1460]) ).
thf(1593,plain,
! [SV162: $i,SV51: $i,SV200: $i] :
( ( ( ~ ! [SY3795: $i] :
( ~ ( in @ SY3795 @ SV200 )
| ( in @ SY3795 @ SV51 )
| ( in @ SY3795 @ SV162 ) )
| ~ ~ ( ~ ! [SY3796: $i] :
( ~ ( in @ SY3796 @ SV51 )
| ( in @ SY3796 @ SV200 ) )
| ~ ! [SY3797: $i] :
( ~ ( in @ SY3797 @ SV162 )
| ( in @ SY3797 @ SV200 ) ) ) )
= $false )
| ( ( SV200
= ( set_union2 @ SV51 @ SV162 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1461]) ).
thf(1594,plain,
! [SV52: $i,SV243: $i] :
( ( ( relation @ SV243 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK30_C @ SV243 @ SV52 ) @ ( sK31_SY3299 @ SV243 @ SV52 ) ) @ SV52 )
| ~ ~ ( in @ ( ordered_pair @ ( sK30_C @ SV243 @ SV52 ) @ ( sK31_SY3299 @ SV243 @ SV52 ) ) @ SV243 ) )
| ( subset @ SV52 @ SV243 ) )
= $true )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1463]) ).
thf(1595,plain,
! [SV52: $i,SV244: $i] :
( ( ( relation @ SV244 )
= $false )
| ( ( ~ ( subset @ SV52 @ SV244 )
| ! [SY3858: $i,SY3859: $i] :
( ~ ( in @ ( ordered_pair @ SY3858 @ SY3859 ) @ SV52 )
| ( in @ ( ordered_pair @ SY3858 @ SY3859 ) @ SV244 ) ) )
= $true )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1464]) ).
thf(1596,plain,
! [SV245: $i,SV295: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( in @ ( sK46_SY3307 @ SV295 @ SV245 ) @ SV245 )
| ~ ~ ( in @ ( sK45_C @ SV295 @ SV245 ) @ ( sK46_SY3307 @ SV295 @ SV245 ) ) )
| ~ ( in @ ( sK45_C @ SV295 @ SV245 ) @ SV295 ) )
| ~ ( ! [SY3917: $i] :
( ~ ( in @ SY3917 @ SV245 )
| ( in @ ( sK45_C @ SV295 @ SV245 ) @ SY3917 ) )
| ( in @ ( sK45_C @ SV295 @ SV245 ) @ SV295 ) ) )
| ( SV295
= ( set_meet @ SV245 ) ) )
= $true )
| ( ( SV245 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1465]) ).
thf(1597,plain,
! [SV246: $i,SV296: $i] :
( ( ( ( SV296
!= ( set_meet @ SV246 ) )
| ~ ( ~ ! [SY3918: $i] :
( ~ ( ~ ( in @ ( sK44_D @ SY3918 @ SV296 @ SV246 ) @ SV246 )
| ~ ~ ( in @ SY3918 @ ( sK44_D @ SY3918 @ SV296 @ SV246 ) ) )
| ( in @ SY3918 @ SV296 ) )
| ~ ! [SY3919: $i] :
( ~ ( in @ SY3919 @ SV296 )
| ! [SY3865: $i] :
( ~ ( in @ SY3865 @ SV246 )
| ( in @ SY3919 @ SY3865 ) ) ) ) )
= $true )
| ( ( SV246 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1466]) ).
thf(1598,plain,
! [SV247: $i] :
( ( ( SV247 = empty_set )
= $false )
| ( ( ! [SY3866: $i] :
( ( SY3866
!= ( set_meet @ SV247 ) )
| ( SY3866 = empty_set ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1467]) ).
thf(1599,plain,
! [SV248: $i] :
( ( ( SV248 = empty_set )
= $false )
| ( ( ! [SY3867: $i] :
( ( SY3867 != empty_set )
| ( SY3867
= ( set_meet @ SV248 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1468]) ).
thf(1600,plain,
! [SV53: $i,SV297: $i] :
( ( ( ! [SY3921: $i] :
( ~ ( ~ ( ~ ( in @ ( sK57_D @ SY3921 @ SV297 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ ( sK57_D @ SY3921 @ SV297 @ SV53 ) ) @ SV297 )
| ~ ( in @ ( sK57_D @ SY3921 @ SV297 @ SV53 ) @ SY3921 ) )
| ~ ~ ( ~ ( ( in @ ( sK57_D @ SY3921 @ SV297 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK57_D @ SY3921 @ SV297 @ SV53 ) @ SY3921 ) )
| ~ ( ( in @ ( apply @ SV53 @ ( sK57_D @ SY3921 @ SV297 @ SV53 ) ) @ SV297 )
| ( in @ ( sK57_D @ SY3921 @ SV297 @ SV53 ) @ SY3921 ) ) ) )
| ( SY3921
= ( relation_inverse_image @ SV53 @ SV297 ) ) ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1469]) ).
thf(1601,plain,
! [SV298: $i,SV53: $i] :
( ( ( ! [SY3922: $i] :
( ( SY3922
!= ( relation_inverse_image @ SV53 @ SV298 ) )
| ~ ( ~ ! [SY3923: $i] :
( ~ ( in @ SY3923 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SY3923 ) @ SV298 )
| ( in @ SY3923 @ SY3922 ) )
| ~ ~ ( ~ ! [SY3534: $i] :
( ~ ( in @ SY3534 @ SY3922 )
| ( in @ SY3534 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY3925: $i] :
( ~ ( in @ SY3925 @ SY3922 )
| ( in @ ( apply @ SV53 @ SY3925 ) @ SV298 ) ) ) ) ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1470]) ).
thf(1602,plain,
! [SV54: $i,SV165: $i,SV201: $i] :
( ( ( ~ ( ~ ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV54 )
| ~ ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV165 )
| ~ ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV201 ) ) )
= $false )
| ( ( SV201
= ( set_intersection2 @ SV54 @ SV165 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1471]) ).
thf(1603,plain,
! [SV54: $i,SV165: $i,SV201: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV54 )
| ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV201 ) )
| ~ ( ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV165 )
| ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV201 ) ) ) )
= $false )
| ( ( SV201
= ( set_intersection2 @ SV54 @ SV165 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1471]) ).
thf(1604,plain,
! [SV202: $i,SV166: $i,SV54: $i] :
( ( ( ~ ! [SY3798: $i] :
( ~ ( in @ SY3798 @ SV54 )
| ~ ( in @ SY3798 @ SV166 )
| ( in @ SY3798 @ SV202 ) )
| ~ ~ ( ~ ! [SY3799: $i] :
( ~ ( in @ SY3799 @ SV202 )
| ( in @ SY3799 @ SV54 ) )
| ~ ! [SY3800: $i] :
( ~ ( in @ SY3800 @ SV202 )
| ( in @ SY3800 @ SV166 ) ) ) )
= $false )
| ( ( SV202
= ( set_intersection2 @ SV54 @ SV166 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1472]) ).
thf(1605,plain,
! [SV55: $i,SV169: $i,SV203: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV55 )
| ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV169 )
| ~ ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV203 ) ) )
= $false )
| ( ( SV203
= ( set_difference @ SV55 @ SV169 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1473]) ).
thf(1606,plain,
! [SV55: $i,SV169: $i,SV203: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV55 )
| ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV203 ) )
| ~ ( ~ ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV169 )
| ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV203 ) ) ) )
= $false )
| ( ( SV203
= ( set_difference @ SV55 @ SV169 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1473]) ).
thf(1607,plain,
! [SV204: $i,SV170: $i,SV55: $i] :
( ( ( ~ ! [SY3801: $i] :
( ~ ( in @ SY3801 @ SV55 )
| ( in @ SY3801 @ SV170 )
| ( in @ SY3801 @ SV204 ) )
| ~ ~ ( ~ ! [SY3802: $i] :
( ~ ( in @ SY3802 @ SV204 )
| ( in @ SY3802 @ SV55 ) )
| ~ ! [SY3803: $i] :
( ~ ( in @ SY3803 @ SV204 )
| ~ ( in @ SY3803 @ SV170 ) ) ) )
= $false )
| ( ( SV204
= ( set_difference @ SV55 @ SV170 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1474]) ).
thf(1608,plain,
! [SV56: $i,SV299: $i] :
( ( ( ~ ( ~ ( ! [SY3926: $i] :
( ( ( sK19_C @ SV299 @ SV56 )
!= ( apply @ SV56 @ SY3926 ) )
| ~ ( in @ SY3926 @ ( relation_dom @ SV56 ) ) )
| ~ ( in @ ( sK19_C @ SV299 @ SV56 ) @ SV299 ) )
| ~ ( ~ ( ( ( sK19_C @ SV299 @ SV56 )
!= ( apply @ SV56 @ ( sK20_SY3294 @ SV299 @ SV56 ) ) )
| ~ ( in @ ( sK20_SY3294 @ SV299 @ SV56 ) @ ( relation_dom @ SV56 ) ) )
| ( in @ ( sK19_C @ SV299 @ SV56 ) @ SV299 ) ) )
| ( SV299
= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1475]) ).
thf(1609,plain,
! [SV56: $i,SV300: $i] :
( ( ( ( SV300
!= ( relation_rng @ SV56 ) )
| ~ ( ~ ! [SY3927: $i] :
( ! [SY3554: $i] :
( ( SY3927
!= ( apply @ SV56 @ SY3554 ) )
| ~ ( in @ SY3554 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY3927 @ SV300 ) )
| ~ ! [SY3929: $i] :
( ~ ( in @ SY3929 @ SV300 )
| ~ ( ( SY3929
!= ( apply @ SV56 @ ( sK18_D @ SY3929 @ SV300 @ SV56 ) ) )
| ~ ( in @ ( sK18_D @ SY3929 @ SV300 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) ) ) )
= $true )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1476]) ).
thf(1610,plain,
! [SV57: $i,SV171: $i,SV205: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK38_D @ SV205 @ SV171 @ SV57 ) @ SV205 )
| ( ( sK38_D @ SV205 @ SV171 @ SV57 )
!= SV57 ) )
| ~ ( ~ ( in @ ( sK38_D @ SV205 @ SV171 @ SV57 ) @ SV205 )
| ( ( sK38_D @ SV205 @ SV171 @ SV57 )
!= SV171 ) ) ) )
= $false )
| ( ( SV205
= ( unordered_pair @ SV57 @ SV171 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1477]) ).
thf(1611,plain,
! [SV57: $i,SV171: $i,SV205: $i] :
( ( ( ~ ( ( in @ ( sK38_D @ SV205 @ SV171 @ SV57 ) @ SV205 )
| ( ( sK38_D @ SV205 @ SV171 @ SV57 )
= SV57 )
| ( ( sK38_D @ SV205 @ SV171 @ SV57 )
= SV171 ) ) )
= $false )
| ( ( SV205
= ( unordered_pair @ SV57 @ SV171 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1477]) ).
thf(1612,plain,
! [SV172: $i,SV57: $i,SV206: $i] :
( ( ( ~ ! [SY3804: $i] :
( ~ ( in @ SY3804 @ SV206 )
| ( SY3804 = SV57 )
| ( SY3804 = SV172 ) )
| ~ ~ ( ~ ! [SY3805: $i] :
( ( SY3805 != SV57 )
| ( in @ SY3805 @ SV206 ) )
| ~ ! [SY3806: $i] :
( ( SY3806 != SV172 )
| ( in @ SY3806 @ SV206 ) ) ) )
= $false )
| ( ( SV206
= ( unordered_pair @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1478]) ).
thf(1613,plain,
! [SV58: $i,SV96: $i] :
( ( ( ! [SY3661: $i] :
( ~ ( function @ SY3661 )
| ~ ( relation @ SY3661 )
| ~ ( ~ ( in @ ( sK67_D @ SY3661 @ SV96 @ SV58 ) @ ( relation_dom @ SV96 ) )
| ~ ( ( ( apply @ SV96 @ ( sK67_D @ SY3661 @ SV96 @ SV58 ) )
!= ( apply @ SY3661 @ ( sK67_D @ SY3661 @ SV96 @ SV58 ) ) ) ) )
| ( ( relation_dom @ SV96 )
!= ( set_intersection2 @ ( relation_dom @ SY3661 ) @ SV58 ) )
| ( SV96
= ( relation_dom_restriction @ SY3661 @ SV58 ) ) ) )
= $true )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1479]) ).
thf(1614,plain,
! [SV58: $i,SV96: $i] :
( ( ( ~ ( ~ ! [SY3662: $i] :
( ~ ( function @ SY3662 )
| ~ ( relation @ SY3662 )
| ( SV96
!= ( relation_dom_restriction @ SY3662 @ SV58 ) )
| ! [SY3663: $i] :
( ~ ( in @ SY3663 @ ( relation_dom @ SV96 ) )
| ( ( apply @ SV96 @ SY3663 )
= ( apply @ SY3662 @ SY3663 ) ) ) )
| ~ ! [SY3664: $i] :
( ~ ( function @ SY3664 )
| ~ ( relation @ SY3664 )
| ( SV96
!= ( relation_dom_restriction @ SY3664 @ SV58 ) )
| ( ( relation_dom @ SV96 )
= ( set_intersection2 @ ( relation_dom @ SY3664 ) @ SV58 ) ) ) ) )
= $true )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1480]) ).
thf(1615,plain,
! [SV59: $i,SV249: $i] :
( ( ( relation @ SV249 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV249 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV249 ) ) )
| ( SV59 = SV249 ) )
= $true )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1481]) ).
thf(1616,plain,
! [SV59: $i,SV250: $i] :
( ( ( relation @ SV250 )
= $false )
| ( ( ( SV59 != SV250 )
| ~ ( ~ ! [SY3868: $i,SY3869: $i] :
( ~ ( in @ ( ordered_pair @ SY3868 @ SY3869 ) @ SV59 )
| ( in @ ( ordered_pair @ SY3868 @ SY3869 ) @ SV250 ) )
| ~ ! [SY3870: $i,SY3871: $i] :
( ~ ( in @ ( ordered_pair @ SY3870 @ SY3871 ) @ SV250 )
| ( in @ ( ordered_pair @ SY3870 @ SY3871 ) @ SV59 ) ) ) )
= $true )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1482]) ).
thf(1617,plain,
! [SV130: $i,SV173: $i] :
( ( ( ! [SY3767: $i] :
( ~ ( in @ ( sK23_C @ SV173 @ SV130 ) @ SY3767 )
| ~ ( in @ SY3767 @ SV130 ) )
| ~ ( in @ ( sK23_C @ SV173 @ SV130 ) @ SV173 ) )
= $true )
| ( ( SV173
= ( union @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1483]) ).
thf(1618,plain,
! [SV130: $i,SV173: $i] :
( ( ( ~ ( ~ ( in @ ( sK23_C @ SV173 @ SV130 ) @ ( sK24_SY3296 @ SV173 @ SV130 ) )
| ~ ( in @ ( sK24_SY3296 @ SV173 @ SV130 ) @ SV130 ) )
| ( in @ ( sK23_C @ SV173 @ SV130 ) @ SV173 ) )
= $true )
| ( ( SV173
= ( union @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1484]) ).
thf(1619,plain,
! [SV174: $i,SV131: $i] :
( ( ( ~ ! [SY3768: $i] :
( ! [SY3719: $i] :
( ~ ( in @ SY3768 @ SY3719 )
| ~ ( in @ SY3719 @ SV131 ) )
| ( in @ SY3768 @ SV174 ) ) )
= $false )
| ( ( SV174
= ( union @ SV131 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1485]) ).
thf(1620,plain,
! [SV131: $i,SV174: $i] :
( ( ( ~ ! [SY3770: $i] :
( ~ ( in @ SY3770 @ SV174 )
| ~ ( ~ ( in @ SY3770 @ ( sK22_D @ SY3770 @ SV174 @ SV131 ) )
| ~ ( in @ ( sK22_D @ SY3770 @ SV174 @ SV131 ) @ SV131 ) ) ) )
= $false )
| ( ( SV174
= ( union @ SV131 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1485]) ).
thf(1621,plain,
! [SV251: $i,SV98: $i,SV207: $i,SV61: $i] :
( ( ( ~ ( in @ SV61 @ SV207 ) )
= $true )
| ( ( ~ ( in @ SV98 @ SV251 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SV207 @ SV251 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1486]) ).
thf(1622,plain,
! [SV301: $i,SV98: $i,SV61: $i] :
( ( ! [SY3930: $i] :
~ ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SV301 @ SY3930 ) )
| ( in @ SV61 @ SV301 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1487]) ).
thf(1623,plain,
! [SV302: $i,SV98: $i,SV61: $i] :
( ( ! [SY3931: $i] :
( ~ ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SV302 @ SY3931 ) )
| ( in @ SV98 @ SY3931 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1488]) ).
thf(1624,plain,
! [SV62: $i,SV175: $i,SV208: $i] :
( ( ( function @ SV208 )
= $false )
| ( ( ~ ( relation @ SV208 ) )
= $true )
| ( ( ~ ( in @ SV175 @ ( relation_dom @ SV208 ) )
| ~ ( in @ SV175 @ SV62 )
| ( in @ SV175 @ ( relation_dom @ ( relation_dom_restriction @ SV208 @ SV62 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1489]) ).
thf(1625,plain,
! [SV62: $i,SV276: $i,SV303: $i] :
( ( ~ ( function @ SV303 )
| ~ ( relation @ SV303 )
| ~ ( in @ SV276 @ ( relation_dom @ ( relation_dom_restriction @ SV303 @ SV62 ) ) )
| ( in @ SV276 @ ( relation_dom @ SV303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(1626,plain,
! [SV62: $i,SV277: $i,SV304: $i] :
( ( ~ ( function @ SV304 )
| ~ ( relation @ SV304 )
| ~ ( in @ SV277 @ ( relation_dom @ ( relation_dom_restriction @ SV304 @ SV62 ) ) )
| ( in @ SV277 @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1491]) ).
thf(1627,plain,
! [SV209: $i,SV176: $i,SV63: $i] :
( ( ( ~ ( ! [SY3808: $i,SY3809: $i] :
( ~ ( in @ SY3808 @ SV63 )
| ~ ( in @ SY3809 @ SV176 )
| ( ( sK34_D @ SV209 @ SV176 @ SV63 )
!= ( ordered_pair @ SY3808 @ SY3809 ) ) )
| ~ ( in @ ( sK34_D @ SV209 @ SV176 @ SV63 ) @ SV209 ) ) )
= $false )
| ( ( SV209
= ( cartesian_product2 @ SV63 @ SV176 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1492]) ).
thf(1628,plain,
! [SV63: $i,SV176: $i,SV209: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK35_SY3303 @ SV209 @ SV176 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK36_SY3305 @ SV209 @ SV176 @ SV63 ) @ SV176 ) )
| ( ( sK34_D @ SV209 @ SV176 @ SV63 )
!= ( ordered_pair @ ( sK35_SY3303 @ SV209 @ SV176 @ SV63 ) @ ( sK36_SY3305 @ SV209 @ SV176 @ SV63 ) ) ) )
| ( in @ ( sK34_D @ SV209 @ SV176 @ SV63 ) @ SV209 ) ) )
= $false )
| ( ( SV209
= ( cartesian_product2 @ SV63 @ SV176 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1492]) ).
thf(1629,plain,
! [SV210: $i,SV177: $i,SV63: $i] :
( ( ( ~ ! [SY3810: $i] :
( ! [SY3777: $i,SY3778: $i] :
( ~ ( in @ SY3777 @ SV63 )
| ~ ( in @ SY3778 @ SV177 )
| ( SY3810
!= ( ordered_pair @ SY3777 @ SY3778 ) ) )
| ( in @ SY3810 @ SV210 ) )
| ~ ! [SY3813: $i] :
( ~ ( in @ SY3813 @ SV210 )
| ~ ( ~ ~ ( ~ ( in @ ( sK32_E @ SY3813 @ SV210 @ SV177 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK33_SY3300 @ SY3813 @ SV210 @ SV177 @ SV63 ) @ SV177 ) )
| ( SY3813
!= ( ordered_pair @ ( sK32_E @ SY3813 @ SV210 @ SV177 @ SV63 ) @ ( sK33_SY3300 @ SY3813 @ SV210 @ SV177 @ SV63 ) ) ) ) ) )
= $false )
| ( ( SV210
= ( cartesian_product2 @ SV63 @ SV177 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1493]) ).
thf(1630,plain,
! [SV132: $i,SV178: $i] :
( ( ( in @ ( sK73_C @ SV178 @ SV132 ) @ SV132 )
= $true )
| ( ( disjoint @ SV132 @ SV178 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1494]) ).
thf(1631,plain,
! [SV132: $i,SV178: $i] :
( ( ( in @ ( sK73_C @ SV178 @ SV132 ) @ SV178 )
= $true )
| ( ( disjoint @ SV132 @ SV178 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1495]) ).
thf(1632,plain,
! [SV179: $i,SV133: $i,SV252: $i] :
( ( ( in @ SV252 @ SV133 )
= $false )
| ( ( ~ ( in @ SV252 @ SV179 ) )
= $true )
| ( ( ~ ( disjoint @ SV133 @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1496]) ).
thf(1633,plain,
! [SV180: $i,SV64: $i,SV211: $i] :
( ( ( ! [SY3814: $i] :
( ~ ( in @ SY3814 @ ( relation_dom @ SV211 ) )
| ~ ( in @ ( ordered_pair @ SY3814 @ SV64 ) @ SV211 )
| ~ ( in @ SY3814 @ SV180 ) ) )
= $true )
| ( ( in @ SV64 @ ( relation_image @ SV211 @ SV180 ) )
= $true )
| ( ( relation @ SV211 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1497]) ).
thf(1634,plain,
! [SV181: $i,SV212: $i,SV64: $i] :
( ( ( ~ ( in @ SV64 @ ( relation_image @ SV212 @ SV181 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK76_D @ SV212 @ SV181 @ SV64 ) @ ( relation_dom @ SV212 ) )
| ~ ( in @ ( ordered_pair @ ( sK76_D @ SV212 @ SV181 @ SV64 ) @ SV64 ) @ SV212 ) )
| ~ ( in @ ( sK76_D @ SV212 @ SV181 @ SV64 ) @ SV181 ) ) )
= $true )
| ( ( relation @ SV212 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1498]) ).
thf(1635,plain,
! [SV213: $i,SV182: $i,SV65: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV65 @ SV182 ) @ SV213 ) )
= $true )
| ( ( in @ SV65 @ ( relation_dom @ SV213 ) )
= $true )
| ( ( relation @ SV213 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1499]) ).
thf(1636,plain,
! [SV214: $i,SV183: $i,SV65: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV65 @ SV183 ) @ SV214 ) )
= $true )
| ( ( in @ SV183 @ ( relation_rng @ SV214 ) )
= $true )
| ( ( relation @ SV214 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1500]) ).
thf(1637,plain,
! [SV66: $i] :
( ( ( ~ ! [SY3607: $i] :
( ~ ( in @ SY3607 @ ( relation_dom @ SV66 ) )
| ! [SY3608: $i] :
( ( SY3608
!= ( apply @ SV66 @ SY3607 ) )
| ( in @ ( ordered_pair @ SY3607 @ SY3608 ) @ SV66 ) ) )
| ~ ! [SY3609: $i] :
( ~ ( in @ SY3609 @ ( relation_dom @ SV66 ) )
| ! [SY3610: $i] :
( ~ ( in @ ( ordered_pair @ SY3609 @ SY3610 ) @ SV66 )
| ( SY3610
= ( apply @ SV66 @ SY3609 ) ) ) ) )
= $false )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1501]) ).
thf(1638,plain,
! [SV66: $i] :
( ( ( ~ ! [SY3611: $i] :
( ( in @ SY3611 @ ( relation_dom @ SV66 ) )
| ! [SY3612: $i] :
( ( SY3612
!= ( apply @ SV66 @ SY3611 ) )
| ( SY3612 = empty_set ) ) )
| ~ ! [SY3613: $i] :
( ( in @ SY3613 @ ( relation_dom @ SV66 ) )
| ! [SY3614: $i] :
( ( SY3614 != empty_set )
| ( SY3614
= ( apply @ SV66 @ SY3613 ) ) ) ) )
= $false )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1502]) ).
thf(1639,plain,
! [SV73: $i,SV7: $i,SV215: $i] :
( ( ( function @ SV215 )
= $false )
| ( ( ~ ( relation @ SV215 ) )
= $true )
| ( ( ~ ( in @ SV7 @ ( relation_dom @ ( relation_composition @ SV215 @ SV73 ) ) )
| ( ( apply @ ( relation_composition @ SV215 @ SV73 ) @ SV7 )
= ( apply @ SV73 @ ( apply @ SV215 @ SV7 ) ) ) )
= $true )
| ( ( function @ SV73 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1503]) ).
thf(1640,plain,
! [SV74: $i,SV8: $i,SV216: $i] :
( ( ( function @ SV216 )
= $false )
| ( ( ~ ( relation @ SV216 ) )
= $true )
| ( ( ~ ( in @ SV8 @ ( relation_dom @ SV74 ) )
| ( ( apply @ ( relation_composition @ SV74 @ SV216 ) @ SV8 )
= ( apply @ SV216 @ ( apply @ SV74 @ SV8 ) ) ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1504]) ).
thf(1641,plain,
! [SV26: $i,SV88: $i,SV253: $i] :
( ( ( relation @ SV253 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) @ SV26 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV88 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 ) )
| ~ ~ ( ~ ( ( in @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) @ SV26 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV88 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 ) ) ) )
| ( SV253
= ( relation_rng_restriction @ SV26 @ SV88 ) ) )
= $true )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1509]) ).
thf(1642,plain,
! [SV88: $i,SV26: $i,SV254: $i] :
( ( ( relation @ SV254 )
= $false )
| ( ( ( SV254
!= ( relation_rng_restriction @ SV26 @ SV88 ) )
| ~ ( ~ ! [SY3872: $i,SY3873: $i] :
( ~ ( in @ SY3873 @ SV26 )
| ~ ( in @ ( ordered_pair @ SY3872 @ SY3873 ) @ SV88 )
| ( in @ ( ordered_pair @ SY3872 @ SY3873 ) @ SV254 ) )
| ~ ~ ( ~ ! [SY3874: $i,SY3875: $i] :
( ~ ( in @ ( ordered_pair @ SY3874 @ SY3875 ) @ SV254 )
| ( in @ SY3875 @ SV26 ) )
| ~ ! [SY3876: $i,SY3877: $i] :
( ~ ( in @ ( ordered_pair @ SY3876 @ SY3877 ) @ SV254 )
| ( in @ ( ordered_pair @ SY3876 @ SY3877 ) @ SV88 ) ) ) ) )
= $true )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1510]) ).
thf(1643,plain,
! [SV108: $i,SV140: $i] :
( ( ( in @ ( sK29_C @ SV140 @ SV108 ) @ SV140 )
= $false )
| ( ( subset @ SV108 @ SV140 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1512]) ).
thf(1644,plain,
! [SV141: $i,SV109: $i,SV255: $i] :
( ( ( in @ SV255 @ SV109 )
= $false )
| ( ( in @ SV255 @ SV141 )
= $true )
| ( ( subset @ SV109 @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1513]) ).
thf(1645,plain,
! [SV187: $i,SV142: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ SV142 ) )
= $true )
| ( ( ~ ( in @ SV27 @ ( relation_dom @ SV187 ) ) )
= $true )
| ( ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SV187 @ SV142 ) ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1514]) ).
thf(1646,plain,
! [SV256: $i,SV27: $i,SV278: $i] :
( ( ( ~ ( relation @ SV278 ) )
= $true )
| ( ( ~ ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SV278 @ SV256 ) ) )
| ( in @ SV27 @ SV256 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1515]) ).
thf(1647,plain,
! [SV257: $i,SV27: $i,SV279: $i] :
( ( ( ~ ( relation @ SV279 ) )
= $true )
| ( ( ~ ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SV279 @ SV257 ) ) )
| ( in @ SV27 @ ( relation_dom @ SV279 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1516]) ).
thf(1648,plain,
! [SV28: $i,SV218: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV218 @ SV28 ) @ ( sK14_SY3290 @ SV218 @ SV28 ) ) @ SV218 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY3290 @ SV218 @ SV28 ) @ ( sK13_C @ SV218 @ SV28 ) ) @ SV28 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SV218 @ SV28 ) @ ( sK14_SY3290 @ SV218 @ SV28 ) ) @ SV218 )
| ( in @ ( ordered_pair @ ( sK14_SY3290 @ SV218 @ SV28 ) @ ( sK13_C @ SV218 @ SV28 ) ) @ SV28 ) ) ) )
= $true )
| ( ( SV218
= ( relation_inverse @ SV28 ) )
= $true )
| ( ( relation @ SV218 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1517]) ).
thf(1649,plain,
! [SV28: $i,SV219: $i] :
( ( ( ( SV219
!= ( relation_inverse @ SV28 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3815: $i,SY3816: $i] :
( ~ ( in @ ( ordered_pair @ SY3815 @ SY3816 ) @ SV219 )
| ( in @ ( ordered_pair @ SY3816 @ SY3815 ) @ SV28 ) )
| ~ ! [SY3817: $i,SY3818: $i] :
( ~ ( in @ ( ordered_pair @ SY3818 @ SY3817 ) @ SV28 )
| ( in @ ( ordered_pair @ SY3817 @ SY3818 ) @ SV219 ) ) ) )
= $true )
| ( ( relation @ SV219 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1518]) ).
thf(1650,plain,
! [SV305: $i,SV280: $i,SV29: $i] :
( ( ( ~ ( ~ ( ! [SY3932: $i] :
( ~ ( in @ SY3932 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3932 @ SV280 )
| ( ( sK61_D @ SV305 @ SV280 @ SV29 )
!= ( apply @ SV29 @ SY3932 ) ) )
| ~ ( in @ ( sK61_D @ SV305 @ SV280 @ SV29 ) @ SV305 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) @ SV280 ) )
| ( ( sK61_D @ SV305 @ SV280 @ SV29 )
!= ( apply @ SV29 @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) ) ) )
| ( in @ ( sK61_D @ SV305 @ SV280 @ SV29 ) @ SV305 ) ) )
| ( SV305
= ( relation_image @ SV29 @ SV280 ) ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1519]) ).
thf(1651,plain,
! [SV281: $i,SV29: $i,SV306: $i] :
( ( ( ( SV306
!= ( relation_image @ SV29 @ SV281 ) )
| ~ ( ~ ! [SY3933: $i] :
( ! [SY3910: $i] :
( ~ ( in @ SY3910 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3910 @ SV281 )
| ( SY3933
!= ( apply @ SV29 @ SY3910 ) ) )
| ( in @ SY3933 @ SV306 ) )
| ~ ! [SY3935: $i] :
( ~ ( in @ SY3935 @ SV306 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SY3935 @ SV306 @ SV281 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK60_E @ SY3935 @ SV306 @ SV281 @ SV29 ) @ SV281 ) )
| ( SY3935
!= ( apply @ SV29 @ ( sK60_E @ SY3935 @ SV306 @ SV281 @ SV29 ) ) ) ) ) ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(1652,plain,
! [SV30: $i,SV220: $i,SV258: $i] :
( ( ( ~ ( ! [SY3880: $i] :
( ~ ( in @ ( ordered_pair @ SY3880 @ ( sK55_D @ SV258 @ SV220 @ SV30 ) ) @ SV30 )
| ~ ( in @ SY3880 @ SV220 ) )
| ~ ( in @ ( sK55_D @ SV258 @ SV220 @ SV30 ) @ SV258 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_SY3315 @ SV258 @ SV220 @ SV30 ) @ ( sK55_D @ SV258 @ SV220 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK56_SY3315 @ SV258 @ SV220 @ SV30 ) @ SV220 ) )
| ( in @ ( sK55_D @ SV258 @ SV220 @ SV30 ) @ SV258 ) ) )
= $false )
| ( ( SV258
= ( relation_image @ SV30 @ SV220 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1521]) ).
thf(1653,plain,
! [SV221: $i,SV30: $i,SV259: $i] :
( ( ( SV259
= ( relation_image @ SV30 @ SV221 ) )
= $false )
| ( ( ~ ( ~ ! [SY3881: $i] :
( ! [SY3823: $i] :
( ~ ( in @ ( ordered_pair @ SY3823 @ SY3881 ) @ SV30 )
| ~ ( in @ SY3823 @ SV221 ) )
| ( in @ SY3881 @ SV259 ) )
| ~ ! [SY3883: $i] :
( ~ ( in @ SY3883 @ SV259 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SY3883 @ SV259 @ SV221 @ SV30 ) @ SY3883 ) @ SV30 )
| ~ ( in @ ( sK54_E @ SY3883 @ SV259 @ SV221 @ SV30 ) @ SV221 ) ) ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1522]) ).
thf(1654,plain,
! [SV31: $i,SV222: $i,SV260: $i] :
( ( ( ~ ( ! [SY3884: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SY3884 ) @ SV31 )
| ~ ( in @ SY3884 @ SV222 ) )
| ~ ( in @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SV260 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ ( sK53_SY3313 @ SV260 @ SV222 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( sK53_SY3313 @ SV260 @ SV222 @ SV31 ) @ SV222 ) )
| ( in @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SV260 ) ) )
= $false )
| ( ( SV260
= ( relation_inverse_image @ SV31 @ SV222 ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1523]) ).
thf(1655,plain,
! [SV223: $i,SV31: $i,SV261: $i] :
( ( ( SV261
= ( relation_inverse_image @ SV31 @ SV223 ) )
= $false )
| ( ( ~ ( ~ ! [SY3885: $i] :
( ! [SY3829: $i] :
( ~ ( in @ ( ordered_pair @ SY3885 @ SY3829 ) @ SV31 )
| ~ ( in @ SY3829 @ SV223 ) )
| ( in @ SY3885 @ SV261 ) )
| ~ ! [SY3887: $i] :
( ~ ( in @ SY3887 @ SV261 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3887 @ ( sK51_E @ SY3887 @ SV261 @ SV223 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( sK51_E @ SY3887 @ SV261 @ SV223 @ SV31 ) @ SV223 ) ) ) ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1524]) ).
thf(1656,plain,
! [SV32: $i,SV224: $i,SV262: $i] :
( ( ( relation @ SV262 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ SV224 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV32 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 ) )
| ~ ~ ( ~ ( ( in @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ SV224 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV32 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 ) ) ) )
| ( SV262
= ( relation_dom_restriction @ SV32 @ SV224 ) ) )
= $true )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1525]) ).
thf(1657,plain,
! [SV225: $i,SV32: $i,SV263: $i] :
( ( ( relation @ SV263 )
= $false )
| ( ( ( SV263
!= ( relation_dom_restriction @ SV32 @ SV225 ) )
| ~ ( ~ ! [SY3888: $i,SY3889: $i] :
( ~ ( in @ SY3888 @ SV225 )
| ~ ( in @ ( ordered_pair @ SY3888 @ SY3889 ) @ SV32 )
| ( in @ ( ordered_pair @ SY3888 @ SY3889 ) @ SV263 ) )
| ~ ~ ( ~ ! [SY3890: $i] :
( ! [SY3891: $i] :
~ ( in @ ( ordered_pair @ SY3890 @ SY3891 ) @ SV263 )
| ( in @ SY3890 @ SV225 ) )
| ~ ! [SY3892: $i,SY3893: $i] :
( ~ ( in @ ( ordered_pair @ SY3892 @ SY3893 ) @ SV263 )
| ( in @ ( ordered_pair @ SY3892 @ SY3893 ) @ SV32 ) ) ) ) )
= $true )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1526]) ).
thf(1658,plain,
! [SV143: $i,SV33: $i,SV188: $i,SV307: $i] :
( ( ( ~ ( in @ SV307 @ ( relation_rng @ SV188 ) )
| ~ ( in @ ( ordered_pair @ SV33 @ SV307 ) @ SV188 )
| ~ ( in @ SV307 @ SV143 ) )
= $true )
| ( ( in @ SV33 @ ( relation_inverse_image @ SV188 @ SV143 ) )
= $true )
| ( ( relation @ SV188 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1527]) ).
thf(1659,plain,
! [SV144: $i,SV189: $i,SV33: $i] :
( ( ( in @ SV33 @ ( relation_inverse_image @ SV189 @ SV144 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK75_D @ SV189 @ SV144 @ SV33 ) @ ( relation_rng @ SV189 ) )
| ~ ( in @ ( ordered_pair @ SV33 @ ( sK75_D @ SV189 @ SV144 @ SV33 ) ) @ SV189 ) )
| ~ ( in @ ( sK75_D @ SV189 @ SV144 @ SV33 ) @ SV144 ) ) )
= $true )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1528]) ).
thf(1660,plain,
! [SV110: $i,SV145: $i] :
( ( ( ~ ( ( ( sK65_C @ SV145 @ SV110 )
!= ( sK66_SY3320 @ SV145 @ SV110 ) )
| ~ ( in @ ( sK65_C @ SV145 @ SV110 ) @ SV110 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 ) ) )
= $false )
| ( ( SV145
= ( identity_relation @ SV110 ) )
= $true )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1529]) ).
thf(1661,plain,
! [SV110: $i,SV145: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK65_C @ SV145 @ SV110 )
= ( sK66_SY3320 @ SV145 @ SV110 ) )
| ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 ) )
| ~ ( ( in @ ( sK65_C @ SV145 @ SV110 ) @ SV110 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 ) ) ) )
= $false )
| ( ( SV145
= ( identity_relation @ SV110 ) )
= $true )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1529]) ).
thf(1662,plain,
! [SV146: $i,SV111: $i] :
( ( ( ~ ! [SY3732: $i,SY3733: $i] :
( ( SY3732 != SY3733 )
| ~ ( in @ SY3732 @ SV111 )
| ( in @ ( ordered_pair @ SY3732 @ SY3733 ) @ SV146 ) )
| ~ ~ ( ~ ! [SY3734: $i,SY3735: $i] :
( ~ ( in @ ( ordered_pair @ SY3734 @ SY3735 ) @ SV146 )
| ( SY3734 = SY3735 ) )
| ~ ! [SY3736: $i] :
( ! [SY3737: $i] :
~ ( in @ ( ordered_pair @ SY3736 @ SY3737 ) @ SV146 )
| ( in @ SY3736 @ SV111 ) ) ) )
= $false )
| ( ( SV146
= ( identity_relation @ SV111 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1530]) ).
thf(1663,plain,
! [SV34: $i,SV89: $i,SV190: $i,SV226: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV190 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV34 ) )
| ~ ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV89 ) ) ) ) )
= $false )
| ( ( SV226
= ( unordered_triple @ SV34 @ SV89 @ SV190 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1531]) ).
thf(1664,plain,
! [SV34: $i,SV89: $i,SV190: $i,SV226: $i] :
( ( ( ~ ( ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
= SV190 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
= SV34 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
= SV89 ) ) )
= $false )
| ( ( SV226
= ( unordered_triple @ SV34 @ SV89 @ SV190 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1531]) ).
thf(1665,plain,
! [SV89: $i,SV34: $i,SV191: $i,SV227: $i] :
( ( ( ~ ! [SY3839: $i] :
( ~ ( in @ SY3839 @ SV227 )
| ( SY3839 = SV191 )
| ( SY3839 = SV34 )
| ( SY3839 = SV89 ) )
| ~ ~ ( ~ ! [SY3840: $i] :
( ( SY3840 != SV191 )
| ( in @ SY3840 @ SV227 ) )
| ~ ~ ( ~ ! [SY3841: $i] :
( ( SY3841 != SV34 )
| ( in @ SY3841 @ SV227 ) )
| ~ ! [SY3842: $i] :
( ( SY3842 != SV89 )
| ( in @ SY3842 @ SV227 ) ) ) ) )
= $false )
| ( ( SV227
= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1532]) ).
thf(1666,plain,
! [SV192: $i,SV147: $i,SV35: $i] :
( ( ( in @ ( ordered_pair @ SV35 @ SV147 ) @ SV192 )
= $false )
| ( ( in @ SV35 @ ( relation_field @ SV192 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1533]) ).
thf(1667,plain,
! [SV193: $i,SV148: $i,SV35: $i] :
( ( ( in @ ( ordered_pair @ SV35 @ SV148 ) @ SV193 )
= $false )
| ( ( in @ SV148 @ ( relation_field @ SV193 ) )
= $true )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1534]) ).
thf(1668,plain,
! [SV36: $i,SV228: $i] :
( ( ( ~ ( ! [SY3843: $i] :
~ ( in @ ( ordered_pair @ SY3843 @ ( sK16_C @ SV228 @ SV36 ) ) @ SV36 )
| ~ ( in @ ( sK16_C @ SV228 @ SV36 ) @ SV228 ) ) )
= $false )
| ( ( SV228
= ( relation_rng @ SV36 ) )
= $true )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1535]) ).
thf(1669,plain,
! [SV36: $i,SV228: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK17_SY3292 @ SV228 @ SV36 ) @ ( sK16_C @ SV228 @ SV36 ) ) @ SV36 )
| ( in @ ( sK16_C @ SV228 @ SV36 ) @ SV228 ) ) )
= $false )
| ( ( SV228
= ( relation_rng @ SV36 ) )
= $true )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1535]) ).
thf(1670,plain,
! [SV229: $i,SV36: $i] :
( ( ( ~ ! [SY3844: $i] :
( ! [SY3437: $i] :
~ ( in @ ( ordered_pair @ SY3437 @ SY3844 ) @ SV36 )
| ( in @ SY3844 @ SV229 ) )
| ~ ! [SY3846: $i] :
( ~ ( in @ SY3846 @ SV229 )
| ( in @ ( ordered_pair @ ( sK15_D @ SY3846 @ SV229 @ SV36 ) @ SY3846 ) @ SV36 ) ) )
= $false )
| ( ( SV229
= ( relation_rng @ SV36 ) )
= $false )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1536]) ).
thf(1671,plain,
! [SV37: $i,SV264: $i] :
( ( ( in @ SV264 @ ( sK77_B @ SV37 ) )
= $false )
| ( ( in @ ( powerset @ SV264 ) @ ( sK77_B @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1537]) ).
thf(1672,plain,
! [SV37: $i] :
( ( ! [SY3441: $i,SY3442: $i] :
( ~ ( in @ SY3441 @ ( sK77_B @ SV37 ) )
| ~ ( subset @ SY3442 @ SY3441 )
| ( in @ SY3442 @ ( sK77_B @ SV37 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1538]) ).
thf(1673,plain,
! [SV37: $i] :
( ( in @ SV37 @ ( sK77_B @ SV37 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1539]) ).
thf(1674,plain,
! [SV112: $i,SV150: $i] :
( ( ( ~ ( in @ ( sK41_C @ SV150 @ SV112 ) @ SV150 ) )
= $true )
| ( ( ~ ( subset @ ( sK41_C @ SV150 @ SV112 ) @ SV112 ) )
= $true )
| ( ( SV150
= ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1540]) ).
thf(1675,plain,
! [SV112: $i,SV150: $i] :
( ( ( in @ ( sK41_C @ SV150 @ SV112 ) @ SV150 )
= $true )
| ( ( subset @ ( sK41_C @ SV150 @ SV112 ) @ SV112 )
= $true )
| ( ( SV150
= ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1541]) ).
thf(1676,plain,
! [SV113: $i,SV151: $i] :
( ( ( ! [SY3740: $i] :
( ~ ( in @ SY3740 @ SV151 )
| ( subset @ SY3740 @ SV113 ) ) )
= $true )
| ( ( SV151
= ( powerset @ SV113 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1542]) ).
thf(1677,plain,
! [SV151: $i,SV113: $i] :
( ( ( ! [SY3741: $i] :
( ~ ( subset @ SY3741 @ SV113 )
| ( in @ SY3741 @ SV151 ) ) )
= $true )
| ( ( SV151
= ( powerset @ SV113 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1543]) ).
thf(1678,plain,
! [SV152: $i,SV114: $i] :
( ( ( ~ ( in @ SV114 @ ( relation_rng @ SV152 ) )
| ~ ( one_to_one @ SV152 ) )
= $true )
| ( ( SV114
= ( apply @ SV152 @ ( apply @ ( function_inverse @ SV152 ) @ SV114 ) ) )
= $true )
| ( ( function @ SV152 )
= $false )
| ( ( relation @ SV152 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1545]) ).
thf(1679,plain,
! [SV153: $i,SV115: $i] :
( ( ( ~ ( in @ SV115 @ ( relation_rng @ SV153 ) )
| ~ ( one_to_one @ SV153 ) )
= $true )
| ( ( SV115
= ( apply @ ( relation_composition @ ( function_inverse @ SV153 ) @ SV153 ) @ SV115 ) )
= $true )
| ( ( function @ SV153 )
= $false )
| ( ( relation @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1546]) ).
thf(1680,plain,
! [SV91: $i,SV39: $i,SV308: $i] :
( ( ( ~ ( function @ SV308 )
| ~ ( relation @ SV308 )
| ~ ( in @ SV39 @ ( relation_dom @ SV308 ) )
| ~ ( in @ ( apply @ SV308 @ SV39 ) @ ( relation_dom @ SV91 ) )
| ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SV308 @ SV91 ) ) ) )
= $true )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1547]) ).
thf(1681,plain,
! [SV91: $i,SV39: $i] :
( ( ( ~ ! [SY3642: $i] :
( ~ ( function @ SY3642 )
| ~ ( relation @ SY3642 )
| ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3642 @ SV91 ) ) )
| ( in @ SV39 @ ( relation_dom @ SY3642 ) ) )
| ~ ! [SY3643: $i] :
( ~ ( function @ SY3643 )
| ~ ( relation @ SY3643 )
| ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3643 @ SV91 ) ) )
| ( in @ ( apply @ SY3643 @ SV39 ) @ ( relation_dom @ SV91 ) ) ) )
= $false )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1548]) ).
thf(1682,plain,
! [SV92: $i,SV40: $i,SV265: $i] :
( ( ( element @ SV265 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK6_D @ SV265 @ SV92 @ SV40 ) @ ( powerset @ SV40 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK6_D @ SV265 @ SV92 @ SV40 ) @ SV265 )
| ~ ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SV265 @ SV92 @ SV40 ) ) @ SV92 ) )
| ~ ( ( in @ ( sK6_D @ SV265 @ SV92 @ SV40 ) @ SV265 )
| ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SV265 @ SV92 @ SV40 ) ) @ SV92 ) ) ) )
| ( SV265
= ( complements_of_subsets @ SV40 @ SV92 ) ) )
= $true )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1549]) ).
thf(1683,plain,
! [SV92: $i,SV40: $i,SV266: $i] :
( ( ( element @ SV266 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( ( SV266
!= ( complements_of_subsets @ SV40 @ SV92 ) )
| ~ ( ~ ! [SY3894: $i] :
( ~ ( element @ SY3894 @ ( powerset @ SV40 ) )
| ~ ( in @ SY3894 @ SV266 )
| ( in @ ( subset_complement @ SV40 @ SY3894 ) @ SV92 ) )
| ~ ! [SY3895: $i] :
( ~ ( element @ SY3895 @ ( powerset @ SV40 ) )
| ~ ( in @ ( subset_complement @ SV40 @ SY3895 ) @ SV92 )
| ( in @ SY3895 @ SV266 ) ) ) )
= $true )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1550]) ).
thf(1684,plain,
! [SV41: $i,SV154: $i,SV194: $i] :
( ( ( relation @ SV194 )
= $false )
| ( ( function @ SV194 )
= $false )
| ( ( ( SV154
!= ( apply @ SV194 @ SV41 ) )
| ~ ( in @ SV41 @ ( relation_dom @ SV194 ) )
| ( in @ ( ordered_pair @ SV41 @ SV154 ) @ SV194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1551]) ).
thf(1685,plain,
! [SV267: $i,SV41: $i,SV282: $i] :
( ( ( ~ ( function @ SV282 )
| ~ ( relation @ SV282 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV41 @ SV267 ) @ SV282 )
| ( SV267
= ( apply @ SV282 @ SV41 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1552]) ).
thf(1686,plain,
! [SV268: $i,SV41: $i,SV283: $i] :
( ( ( ~ ( function @ SV283 )
| ~ ( relation @ SV283 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV41 @ SV268 ) @ SV283 )
| ( in @ SV41 @ ( relation_dom @ SV283 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1553]) ).
thf(1687,plain,
! [SV195: $i,SV155: $i,SV42: $i] :
( ( ( ~ ( in @ SV42 @ SV155 ) )
= $true )
| ( ( ~ ( in @ SV42 @ ( relation_rng @ SV195 ) ) )
= $true )
| ( ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SV155 @ SV195 ) ) )
= $true )
| ( ( relation @ SV195 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1554]) ).
thf(1688,plain,
! [SV269: $i,SV42: $i,SV284: $i] :
( ( ( ~ ( relation @ SV284 ) )
= $true )
| ( ( ~ ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SV269 @ SV284 ) ) )
| ( in @ SV42 @ SV269 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1555]) ).
thf(1689,plain,
! [SV270: $i,SV42: $i,SV285: $i] :
( ( ( ~ ( relation @ SV285 ) )
= $true )
| ( ( ~ ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SV270 @ SV285 ) ) )
| ( in @ SV42 @ ( relation_rng @ SV285 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1556]) ).
thf(1690,plain,
! [SV43: $i,SV271: $i] :
( ( ( ~ ! [SY3900: $i] :
( ~ ( subset @ SY3900 @ SV271 )
| ( in @ SY3900 @ ( sK3_SY3278 @ SV271 @ SV43 ) ) )
| ~ ( in @ ( sK3_SY3278 @ SV271 @ SV43 ) @ ( sK2_B @ SV43 ) ) )
= $false )
| ( ( ~ ( in @ SV271 @ ( sK2_B @ SV43 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1557]) ).
thf(1691,plain,
! [SV43: $i] :
( ( ! [SY3468: $i,SY3469: $i] :
( ~ ( in @ SY3468 @ ( sK2_B @ SV43 ) )
| ~ ( subset @ SY3469 @ SY3468 )
| ( in @ SY3469 @ ( sK2_B @ SV43 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1558]) ).
thf(1692,plain,
! [SV43: $i] :
( ( in @ SV43 @ ( sK2_B @ SV43 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1559]) ).
thf(1693,plain,
! [SV309: $i,SV286: $i,SV116: $i] :
( ( ( ( ( sK49_B @ SV116 )
!= ( ordered_pair @ SV286 @ SV309 ) ) )
= $true )
| ( ( relation @ SV116 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1560]) ).
thf(1694,plain,
! [SV231: $i,SV93: $i,SV196: $i,SV44: $i] :
( ( ( in @ SV44 @ SV196 )
= $false )
| ( ( ~ ( in @ SV93 @ SV231 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SV196 @ SV231 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1562]) ).
thf(1695,plain,
! [SV287: $i,SV93: $i,SV44: $i] :
( ( ( ! [SY3913: $i] :
~ ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SV287 @ SY3913 ) ) )
= $true )
| ( ( in @ SV44 @ SV287 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1563]) ).
thf(1696,plain,
! [SV310: $i,SV288: $i,SV93: $i,SV44: $i] :
( ( ~ ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SV288 @ SV310 ) )
| ( in @ SV93 @ SV310 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1564]) ).
thf(1697,plain,
! [SV45: $i,SV232: $i] :
( ( ( ~ ( ! [SY3847: $i] :
~ ( in @ ( ordered_pair @ ( sK26_C @ SV232 @ SV45 ) @ SY3847 ) @ SV45 )
| ~ ( in @ ( sK26_C @ SV232 @ SV45 ) @ SV232 ) ) )
= $false )
| ( ( SV232
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1565]) ).
thf(1698,plain,
! [SV45: $i,SV232: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK26_C @ SV232 @ SV45 ) @ ( sK27_SY3298 @ SV232 @ SV45 ) ) @ SV45 )
| ( in @ ( sK26_C @ SV232 @ SV45 ) @ SV232 ) ) )
= $false )
| ( ( SV232
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1565]) ).
thf(1699,plain,
! [SV233: $i,SV45: $i] :
( ( ( ~ ! [SY3848: $i] :
( ! [SY3481: $i] :
~ ( in @ ( ordered_pair @ SY3848 @ SY3481 ) @ SV45 )
| ( in @ SY3848 @ SV233 ) )
| ~ ! [SY3850: $i] :
( ~ ( in @ SY3850 @ SV233 )
| ( in @ ( ordered_pair @ SY3850 @ ( sK25_D @ SY3850 @ SV233 @ SV45 ) ) @ SV45 ) ) )
= $false )
| ( ( SV233
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1566]) ).
thf(1700,plain,
! [SV234: $i,SV289: $i] :
( ( ( ~ ( element @ SV289 @ SV234 ) )
= $true )
| ( ( in @ SV289 @ SV234 )
= $true )
| ( ( empty @ SV234 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1567]) ).
thf(1701,plain,
! [SV235: $i,SV290: $i] :
( ( ( ~ ( in @ SV290 @ SV235 ) )
= $true )
| ( ( element @ SV290 @ SV235 )
= $true )
| ( ( empty @ SV235 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1568]) ).
thf(1702,plain,
! [SV236: $i,SV311: $i] :
( ( ( ~ ( element @ SV311 @ SV236 )
| ( empty @ SV311 ) )
= $true )
| ( ( empty @ SV236 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1569]) ).
thf(1703,plain,
! [SV237: $i,SV312: $i] :
( ( ( ~ ( empty @ SV312 )
| ( element @ SV312 @ SV237 ) )
= $true )
| ( ( empty @ SV237 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1570]) ).
thf(1704,plain,
! [SV120: $i,SV157: $i] :
( ( ( ( ( sK43_C @ SV157 @ SV120 )
!= SV120 ) )
= $true )
| ( ( ~ ( in @ ( sK43_C @ SV157 @ SV120 ) @ SV157 ) )
= $true )
| ( ( SV157
= ( singleton @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1571]) ).
thf(1705,plain,
! [SV120: $i,SV157: $i] :
( ( ( ( sK43_C @ SV157 @ SV120 )
= SV120 )
= $true )
| ( ( in @ ( sK43_C @ SV157 @ SV120 ) @ SV157 )
= $true )
| ( ( SV157
= ( singleton @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1572]) ).
thf(1706,plain,
! [SV158: $i,SV121: $i] :
( ( ( ! [SY3744: $i] :
( ( SY3744 != SV121 )
| ( in @ SY3744 @ SV158 ) ) )
= $true )
| ( ( SV158
= ( singleton @ SV121 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1573]) ).
thf(1707,plain,
! [SV121: $i,SV158: $i] :
( ( ( ! [SY3745: $i] :
( ~ ( in @ SY3745 @ SV158 )
| ( SY3745 = SV121 ) ) )
= $true )
| ( ( SV158
= ( singleton @ SV121 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1574]) ).
thf(1708,plain,
! [SV122: $i,SV159: $i] :
( ( ( ~ ( ~ ( in @ ( sK74_C @ SV159 @ SV122 ) @ SV122 )
| ~ ( ( ( apply @ SV159 @ ( sK74_C @ SV159 @ SV122 ) )
!= ( sK74_C @ SV159 @ SV122 ) ) ) )
| ( ( relation_dom @ SV159 )
!= SV122 ) )
= $true )
| ( ( SV159
= ( identity_relation @ SV122 ) )
= $true )
| ( ( function @ SV159 )
= $false )
| ( ( relation @ SV159 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1575]) ).
thf(1709,plain,
! [SV239: $i,SV272: $i] :
( ( ( ~ ( function @ SV272 ) )
= $true )
| ( ( ~ ( relation @ SV272 ) )
= $true )
| ( ( ( SV272
!= ( identity_relation @ SV239 ) )
| ! [SY3901: $i] :
( ~ ( in @ SY3901 @ SV239 )
| ( ( apply @ SV272 @ SY3901 )
= SY3901 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1576]) ).
thf(1710,plain,
! [SV240: $i,SV273: $i] :
( ( ( ~ ( function @ SV273 ) )
= $true )
| ( ( ~ ( relation @ SV273 ) )
= $true )
| ( ( ( SV273
!= ( identity_relation @ SV240 ) )
| ( ( relation_dom @ SV273 )
= SV240 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1577]) ).
thf(1711,plain,
! [SV46: $i] :
( ( ( ! [SY3483: $i] :
( ~ ( function @ SY3483 )
| ~ ( relation @ SY3483 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY3322 @ SY3483 @ SV46 )
= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ( ( sK70_C @ SY3483 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SY3483 @ SV46 )
= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SY3483 @ SV46 )
= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ( ( sK71_SY3322 @ SY3483 @ SV46 )
!= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK70_C @ SY3483 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK71_SY3322 @ SY3483 @ SV46 )
!= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY3483 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK70_C @ SY3483 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SY3483 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SY3483 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SY3483 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK71_SY3322 @ SY3483 @ SV46 )
!= ( apply @ SY3483 @ ( sK70_C @ SY3483 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SY3483 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ( ( relation_dom @ SY3483 )
!= ( relation_rng @ SV46 ) )
| ( SY3483
= ( function_inverse @ SV46 ) ) ) )
= $true )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1578]) ).
thf(1712,plain,
! [SV46: $i] :
( ( ( ~ ( ~ ! [SY3484: $i] :
( ~ ( function @ SY3484 )
| ~ ( relation @ SY3484 )
| ( SY3484
!= ( function_inverse @ SV46 ) )
| ~ ( ~ ~ ( ~ ! [SY3485: $i,SY3486: $i] :
( ( SY3486
!= ( apply @ SY3484 @ SY3485 ) )
| ~ ( in @ SY3485 @ ( relation_rng @ SV46 ) )
| ( SY3485
= ( apply @ SV46 @ SY3486 ) ) )
| ~ ! [SY3487: $i,SY3488: $i] :
( ( SY3488
!= ( apply @ SY3484 @ SY3487 ) )
| ~ ( in @ SY3487 @ ( relation_rng @ SV46 ) )
| ( in @ SY3488 @ ( relation_dom @ SV46 ) ) ) )
| ~ ~ ( ~ ! [SY3489: $i,SY3490: $i] :
( ( SY3489
!= ( apply @ SV46 @ SY3490 ) )
| ~ ( in @ SY3490 @ ( relation_dom @ SV46 ) )
| ( SY3490
= ( apply @ SY3484 @ SY3489 ) ) )
| ~ ! [SY3491: $i] :
( ! [SY3492: $i] :
( ( SY3491
!= ( apply @ SV46 @ SY3492 ) )
| ~ ( in @ SY3492 @ ( relation_dom @ SV46 ) ) )
| ( in @ SY3491 @ ( relation_rng @ SV46 ) ) ) ) ) )
| ~ ! [SY3493: $i] :
( ~ ( function @ SY3493 )
| ~ ( relation @ SY3493 )
| ( SY3493
!= ( function_inverse @ SV46 ) )
| ( ( relation_dom @ SY3493 )
= ( relation_rng @ SV46 ) ) ) ) )
= $true )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1579]) ).
thf(1713,plain,
! [SV47: $i,SV123: $i,SV313: $i] :
( ( ( ~ ( relation @ SV313 )
| ~ ( ~ ( ! [SY3936: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ SY3936 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3936 @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV123 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV313 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK10_SY3288 @ SV313 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY3288 @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV123 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV313 ) ) )
| ( SV313
= ( relation_composition @ SV47 @ SV123 ) ) )
= $true )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1580]) ).
thf(1714,plain,
! [SV123: $i,SV47: $i,SV314: $i] :
( ( ( ~ ( relation @ SV314 )
| ( SV314
!= ( relation_composition @ SV47 @ SV123 ) )
| ~ ( ~ ! [SY3937: $i,SY3938: $i] :
( ! [SY3706: $i] :
( ~ ( in @ ( ordered_pair @ SY3937 @ SY3706 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3706 @ SY3938 ) @ SV123 ) )
| ( in @ ( ordered_pair @ SY3937 @ SY3938 ) @ SV314 ) )
| ~ ! [SY3940: $i,SY3941: $i] :
( ~ ( in @ ( ordered_pair @ SY3940 @ SY3941 ) @ SV314 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3940 @ ( sK7_F @ SY3941 @ SY3940 @ SV314 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY3941 @ SY3940 @ SV314 @ SV123 @ SV47 ) @ SY3941 ) @ SV123 ) ) ) ) )
= $true )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1581]) ).
thf(1715,plain,
! [SV48: $i,SV197: $i,SV160: $i] :
( ( ( in @ SV160 @ SV197 )
= $false )
| ( ( in @ SV48 @ SV197 )
= $false )
| ( ( subset @ ( unordered_pair @ SV48 @ SV160 ) @ SV197 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1582]) ).
thf(1716,plain,
! [SV291: $i,SV274: $i,SV48: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV48 @ SV274 ) @ SV291 ) )
= $true )
| ( ( in @ SV48 @ SV291 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1583]) ).
thf(1717,plain,
! [SV292: $i,SV275: $i,SV48: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV48 @ SV275 ) @ SV292 ) )
= $true )
| ( ( in @ SV275 @ SV292 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1584]) ).
thf(1718,plain,
! [SV241: $i,SV94: $i,SV198: $i,SV49: $i] :
( ( ( ~ ( in @ SV49 @ SV198 )
| ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ SV241 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SV198 ) @ SV241 ) )
= $true )
| ( ( relation @ SV241 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1585]) ).
thf(1719,plain,
! [SV293: $i,SV94: $i,SV49: $i,SV315: $i] :
( ( ~ ( relation @ SV315 )
| ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SV293 ) @ SV315 ) )
| ( in @ SV49 @ SV293 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1586]) ).
thf(1720,plain,
! [SV294: $i,SV94: $i,SV49: $i,SV316: $i] :
( ( ~ ( relation @ SV316 )
| ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SV294 ) @ SV316 ) )
| ( in @ ( ordered_pair @ SV49 @ SV94 ) @ SV316 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1587]) ).
thf(1721,plain,
! [SV50: $i,SV95: $i,SV242: $i] :
( ( ( in @ SV242 @ ( sK4_C @ SV95 @ SV50 ) )
= $false )
| ( ( in @ SV242 @ SV95 )
= $false )
| ( ( ~ ( in @ SV50 @ SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1588]) ).
thf(1722,plain,
! [SV124: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_B @ SV124 ) @ ( relation_dom @ SV124 ) )
| ~ ( in @ ( sK12_SY3289 @ SV124 ) @ ( relation_dom @ SV124 ) ) )
| ( ( apply @ SV124 @ ( sK11_B @ SV124 ) )
!= ( apply @ SV124 @ ( sK12_SY3289 @ SV124 ) ) ) )
| ~ ( ( ( sK11_B @ SV124 )
!= ( sK12_SY3289 @ SV124 ) ) ) )
= $false )
| ( ( one_to_one @ SV124 )
= $true )
| ( ( function @ SV124 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1589]) ).
thf(1723,plain,
! [SV125: $i] :
( ( ( one_to_one @ SV125 )
= $false )
| ( ( ! [SY3709: $i,SY3710: $i] :
( ~ ( in @ SY3709 @ ( relation_dom @ SV125 ) )
| ~ ( in @ SY3710 @ ( relation_dom @ SV125 ) )
| ( ( apply @ SV125 @ SY3709 )
!= ( apply @ SV125 @ SY3710 ) )
| ( SY3709 = SY3710 ) ) )
= $true )
| ( ( function @ SV125 )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1590]) ).
thf(1724,plain,
! [SV51: $i,SV161: $i,SV199: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV199 )
| ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV51 ) )
| ~ ( ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV199 )
| ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV161 ) ) ) )
= $true )
| ( ( SV199
= ( set_union2 @ SV51 @ SV161 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1591]) ).
thf(1725,plain,
! [SV51: $i,SV161: $i,SV199: $i] :
( ( ( ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV199 )
| ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV51 )
| ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV161 ) )
= $true )
| ( ( SV199
= ( set_union2 @ SV51 @ SV161 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1592]) ).
thf(1726,plain,
! [SV162: $i,SV51: $i,SV200: $i] :
( ( ( ~ ! [SY3795: $i] :
( ~ ( in @ SY3795 @ SV200 )
| ( in @ SY3795 @ SV51 )
| ( in @ SY3795 @ SV162 ) ) )
= $false )
| ( ( SV200
= ( set_union2 @ SV51 @ SV162 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1593]) ).
thf(1727,plain,
! [SV162: $i,SV200: $i,SV51: $i] :
( ( ( ~ ~ ( ~ ! [SY3796: $i] :
( ~ ( in @ SY3796 @ SV51 )
| ( in @ SY3796 @ SV200 ) )
| ~ ! [SY3797: $i] :
( ~ ( in @ SY3797 @ SV162 )
| ( in @ SY3797 @ SV200 ) ) ) )
= $false )
| ( ( SV200
= ( set_union2 @ SV51 @ SV162 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1593]) ).
thf(1728,plain,
! [SV52: $i,SV243: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK30_C @ SV243 @ SV52 ) @ ( sK31_SY3299 @ SV243 @ SV52 ) ) @ SV52 )
| ~ ~ ( in @ ( ordered_pair @ ( sK30_C @ SV243 @ SV52 ) @ ( sK31_SY3299 @ SV243 @ SV52 ) ) @ SV243 ) ) )
= $true )
| ( ( subset @ SV52 @ SV243 )
= $true )
| ( ( relation @ SV243 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1594]) ).
thf(1729,plain,
! [SV244: $i,SV52: $i] :
( ( ( ~ ( subset @ SV52 @ SV244 ) )
= $true )
| ( ( ! [SY3858: $i,SY3859: $i] :
( ~ ( in @ ( ordered_pair @ SY3858 @ SY3859 ) @ SV52 )
| ( in @ ( ordered_pair @ SY3858 @ SY3859 ) @ SV244 ) ) )
= $true )
| ( ( relation @ SV244 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1595]) ).
thf(1730,plain,
! [SV245: $i,SV295: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( in @ ( sK46_SY3307 @ SV295 @ SV245 ) @ SV245 )
| ~ ~ ( in @ ( sK45_C @ SV295 @ SV245 ) @ ( sK46_SY3307 @ SV295 @ SV245 ) ) )
| ~ ( in @ ( sK45_C @ SV295 @ SV245 ) @ SV295 ) )
| ~ ( ! [SY3917: $i] :
( ~ ( in @ SY3917 @ SV245 )
| ( in @ ( sK45_C @ SV295 @ SV245 ) @ SY3917 ) )
| ( in @ ( sK45_C @ SV295 @ SV245 ) @ SV295 ) ) ) )
= $true )
| ( ( SV295
= ( set_meet @ SV245 ) )
= $true )
| ( ( SV245 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1596]) ).
thf(1731,plain,
! [SV246: $i,SV296: $i] :
( ( ( ( SV296
!= ( set_meet @ SV246 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3918: $i] :
( ~ ( ~ ( in @ ( sK44_D @ SY3918 @ SV296 @ SV246 ) @ SV246 )
| ~ ~ ( in @ SY3918 @ ( sK44_D @ SY3918 @ SV296 @ SV246 ) ) )
| ( in @ SY3918 @ SV296 ) )
| ~ ! [SY3919: $i] :
( ~ ( in @ SY3919 @ SV296 )
| ! [SY3865: $i] :
( ~ ( in @ SY3865 @ SV246 )
| ( in @ SY3919 @ SY3865 ) ) ) ) )
= $true )
| ( ( SV246 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1597]) ).
thf(1732,plain,
! [SV247: $i,SV317: $i] :
( ( ( ( SV317
!= ( set_meet @ SV247 ) )
| ( SV317 = empty_set ) )
= $true )
| ( ( SV247 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1598]) ).
thf(1733,plain,
! [SV248: $i,SV318: $i] :
( ( ( ( SV318 != empty_set )
| ( SV318
= ( set_meet @ SV248 ) ) )
= $true )
| ( ( SV248 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1599]) ).
thf(1734,plain,
! [SV53: $i,SV297: $i,SV319: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ ( sK57_D @ SV319 @ SV297 @ SV53 ) ) @ SV297 )
| ~ ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ SV319 ) )
| ~ ~ ( ~ ( ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ SV319 ) )
| ~ ( ( in @ ( apply @ SV53 @ ( sK57_D @ SV319 @ SV297 @ SV53 ) ) @ SV297 )
| ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ SV319 ) ) ) )
| ( SV319
= ( relation_inverse_image @ SV53 @ SV297 ) ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1600]) ).
thf(1735,plain,
! [SV298: $i,SV53: $i,SV320: $i] :
( ( ( ( SV320
!= ( relation_inverse_image @ SV53 @ SV298 ) )
| ~ ( ~ ! [SY3942: $i] :
( ~ ( in @ SY3942 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SY3942 ) @ SV298 )
| ( in @ SY3942 @ SV320 ) )
| ~ ~ ( ~ ! [SY3943: $i] :
( ~ ( in @ SY3943 @ SV320 )
| ( in @ SY3943 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY3944: $i] :
( ~ ( in @ SY3944 @ SV320 )
| ( in @ ( apply @ SV53 @ SY3944 ) @ SV298 ) ) ) ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1601]) ).
thf(1736,plain,
! [SV54: $i,SV165: $i,SV201: $i] :
( ( ( ~ ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV54 )
| ~ ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV165 )
| ~ ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV201 ) )
= $true )
| ( ( SV201
= ( set_intersection2 @ SV54 @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1602]) ).
thf(1737,plain,
! [SV54: $i,SV165: $i,SV201: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV54 )
| ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV201 ) )
| ~ ( ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV165 )
| ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV201 ) ) ) )
= $true )
| ( ( SV201
= ( set_intersection2 @ SV54 @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1603]) ).
thf(1738,plain,
! [SV202: $i,SV166: $i,SV54: $i] :
( ( ( ~ ! [SY3798: $i] :
( ~ ( in @ SY3798 @ SV54 )
| ~ ( in @ SY3798 @ SV166 )
| ( in @ SY3798 @ SV202 ) ) )
= $false )
| ( ( SV202
= ( set_intersection2 @ SV54 @ SV166 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1604]) ).
thf(1739,plain,
! [SV166: $i,SV54: $i,SV202: $i] :
( ( ( ~ ~ ( ~ ! [SY3799: $i] :
( ~ ( in @ SY3799 @ SV202 )
| ( in @ SY3799 @ SV54 ) )
| ~ ! [SY3800: $i] :
( ~ ( in @ SY3800 @ SV202 )
| ( in @ SY3800 @ SV166 ) ) ) )
= $false )
| ( ( SV202
= ( set_intersection2 @ SV54 @ SV166 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1604]) ).
thf(1740,plain,
! [SV55: $i,SV169: $i,SV203: $i] :
( ( ( ~ ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV55 )
| ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV169 )
| ~ ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV203 ) )
= $true )
| ( ( SV203
= ( set_difference @ SV55 @ SV169 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1605]) ).
thf(1741,plain,
! [SV55: $i,SV169: $i,SV203: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV55 )
| ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV203 ) )
| ~ ( ~ ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV169 )
| ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV203 ) ) ) )
= $true )
| ( ( SV203
= ( set_difference @ SV55 @ SV169 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1606]) ).
thf(1742,plain,
! [SV204: $i,SV170: $i,SV55: $i] :
( ( ( ~ ! [SY3801: $i] :
( ~ ( in @ SY3801 @ SV55 )
| ( in @ SY3801 @ SV170 )
| ( in @ SY3801 @ SV204 ) ) )
= $false )
| ( ( SV204
= ( set_difference @ SV55 @ SV170 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1607]) ).
thf(1743,plain,
! [SV170: $i,SV55: $i,SV204: $i] :
( ( ( ~ ~ ( ~ ! [SY3802: $i] :
( ~ ( in @ SY3802 @ SV204 )
| ( in @ SY3802 @ SV55 ) )
| ~ ! [SY3803: $i] :
( ~ ( in @ SY3803 @ SV204 )
| ~ ( in @ SY3803 @ SV170 ) ) ) )
= $false )
| ( ( SV204
= ( set_difference @ SV55 @ SV170 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1607]) ).
thf(1744,plain,
! [SV56: $i,SV299: $i] :
( ( ( ~ ( ~ ( ! [SY3926: $i] :
( ( ( sK19_C @ SV299 @ SV56 )
!= ( apply @ SV56 @ SY3926 ) )
| ~ ( in @ SY3926 @ ( relation_dom @ SV56 ) ) )
| ~ ( in @ ( sK19_C @ SV299 @ SV56 ) @ SV299 ) )
| ~ ( ~ ( ( ( sK19_C @ SV299 @ SV56 )
!= ( apply @ SV56 @ ( sK20_SY3294 @ SV299 @ SV56 ) ) )
| ~ ( in @ ( sK20_SY3294 @ SV299 @ SV56 ) @ ( relation_dom @ SV56 ) ) )
| ( in @ ( sK19_C @ SV299 @ SV56 ) @ SV299 ) ) ) )
= $true )
| ( ( SV299
= ( relation_rng @ SV56 ) )
= $true )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1608]) ).
thf(1745,plain,
! [SV56: $i,SV300: $i] :
( ( ( ( SV300
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3927: $i] :
( ! [SY3554: $i] :
( ( SY3927
!= ( apply @ SV56 @ SY3554 ) )
| ~ ( in @ SY3554 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY3927 @ SV300 ) )
| ~ ! [SY3929: $i] :
( ~ ( in @ SY3929 @ SV300 )
| ~ ( ( SY3929
!= ( apply @ SV56 @ ( sK18_D @ SY3929 @ SV300 @ SV56 ) ) )
| ~ ( in @ ( sK18_D @ SY3929 @ SV300 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) ) ) )
= $true )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1609]) ).
thf(1746,plain,
! [SV57: $i,SV171: $i,SV205: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK38_D @ SV205 @ SV171 @ SV57 ) @ SV205 )
| ( ( sK38_D @ SV205 @ SV171 @ SV57 )
!= SV57 ) )
| ~ ( ~ ( in @ ( sK38_D @ SV205 @ SV171 @ SV57 ) @ SV205 )
| ( ( sK38_D @ SV205 @ SV171 @ SV57 )
!= SV171 ) ) ) )
= $true )
| ( ( SV205
= ( unordered_pair @ SV57 @ SV171 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1610]) ).
thf(1747,plain,
! [SV57: $i,SV171: $i,SV205: $i] :
( ( ( ( in @ ( sK38_D @ SV205 @ SV171 @ SV57 ) @ SV205 )
| ( ( sK38_D @ SV205 @ SV171 @ SV57 )
= SV57 )
| ( ( sK38_D @ SV205 @ SV171 @ SV57 )
= SV171 ) )
= $true )
| ( ( SV205
= ( unordered_pair @ SV57 @ SV171 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1611]) ).
thf(1748,plain,
! [SV172: $i,SV57: $i,SV206: $i] :
( ( ( ~ ! [SY3804: $i] :
( ~ ( in @ SY3804 @ SV206 )
| ( SY3804 = SV57 )
| ( SY3804 = SV172 ) ) )
= $false )
| ( ( SV206
= ( unordered_pair @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1612]) ).
thf(1749,plain,
! [SV172: $i,SV206: $i,SV57: $i] :
( ( ( ~ ~ ( ~ ! [SY3805: $i] :
( ( SY3805 != SV57 )
| ( in @ SY3805 @ SV206 ) )
| ~ ! [SY3806: $i] :
( ( SY3806 != SV172 )
| ( in @ SY3806 @ SV206 ) ) ) )
= $false )
| ( ( SV206
= ( unordered_pair @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1612]) ).
thf(1750,plain,
! [SV58: $i,SV96: $i,SV321: $i] :
( ( ( ~ ( function @ SV321 )
| ~ ( relation @ SV321 )
| ~ ( ~ ( in @ ( sK67_D @ SV321 @ SV96 @ SV58 ) @ ( relation_dom @ SV96 ) )
| ~ ( ( ( apply @ SV96 @ ( sK67_D @ SV321 @ SV96 @ SV58 ) )
!= ( apply @ SV321 @ ( sK67_D @ SV321 @ SV96 @ SV58 ) ) ) ) )
| ( ( relation_dom @ SV96 )
!= ( set_intersection2 @ ( relation_dom @ SV321 ) @ SV58 ) )
| ( SV96
= ( relation_dom_restriction @ SV321 @ SV58 ) ) )
= $true )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(1751,plain,
! [SV58: $i,SV96: $i] :
( ( ( ~ ! [SY3662: $i] :
( ~ ( function @ SY3662 )
| ~ ( relation @ SY3662 )
| ( SV96
!= ( relation_dom_restriction @ SY3662 @ SV58 ) )
| ! [SY3663: $i] :
( ~ ( in @ SY3663 @ ( relation_dom @ SV96 ) )
| ( ( apply @ SV96 @ SY3663 )
= ( apply @ SY3662 @ SY3663 ) ) ) )
| ~ ! [SY3664: $i] :
( ~ ( function @ SY3664 )
| ~ ( relation @ SY3664 )
| ( SV96
!= ( relation_dom_restriction @ SY3664 @ SV58 ) )
| ( ( relation_dom @ SV96 )
= ( set_intersection2 @ ( relation_dom @ SY3664 ) @ SV58 ) ) ) )
= $false )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1614]) ).
thf(1752,plain,
! [SV59: $i,SV249: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV249 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV249 ) ) ) )
= $true )
| ( ( SV59 = SV249 )
= $true )
| ( ( relation @ SV249 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1615]) ).
thf(1753,plain,
! [SV250: $i,SV59: $i] :
( ( ( ( SV59 != SV250 ) )
= $true )
| ( ( ~ ( ~ ! [SY3868: $i,SY3869: $i] :
( ~ ( in @ ( ordered_pair @ SY3868 @ SY3869 ) @ SV59 )
| ( in @ ( ordered_pair @ SY3868 @ SY3869 ) @ SV250 ) )
| ~ ! [SY3870: $i,SY3871: $i] :
( ~ ( in @ ( ordered_pair @ SY3870 @ SY3871 ) @ SV250 )
| ( in @ ( ordered_pair @ SY3870 @ SY3871 ) @ SV59 ) ) ) )
= $true )
| ( ( relation @ SV250 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1616]) ).
thf(1754,plain,
! [SV130: $i,SV173: $i] :
( ( ( ! [SY3767: $i] :
( ~ ( in @ ( sK23_C @ SV173 @ SV130 ) @ SY3767 )
| ~ ( in @ SY3767 @ SV130 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_C @ SV173 @ SV130 ) @ SV173 ) )
= $true )
| ( ( SV173
= ( union @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1617]) ).
thf(1755,plain,
! [SV130: $i,SV173: $i] :
( ( ( ~ ( ~ ( in @ ( sK23_C @ SV173 @ SV130 ) @ ( sK24_SY3296 @ SV173 @ SV130 ) )
| ~ ( in @ ( sK24_SY3296 @ SV173 @ SV130 ) @ SV130 ) ) )
= $true )
| ( ( in @ ( sK23_C @ SV173 @ SV130 ) @ SV173 )
= $true )
| ( ( SV173
= ( union @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1618]) ).
thf(1756,plain,
! [SV174: $i,SV131: $i] :
( ( ( ! [SY3768: $i] :
( ! [SY3719: $i] :
( ~ ( in @ SY3768 @ SY3719 )
| ~ ( in @ SY3719 @ SV131 ) )
| ( in @ SY3768 @ SV174 ) ) )
= $true )
| ( ( SV174
= ( union @ SV131 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1619]) ).
thf(1757,plain,
! [SV131: $i,SV174: $i] :
( ( ( ! [SY3770: $i] :
( ~ ( in @ SY3770 @ SV174 )
| ~ ( ~ ( in @ SY3770 @ ( sK22_D @ SY3770 @ SV174 @ SV131 ) )
| ~ ( in @ ( sK22_D @ SY3770 @ SV174 @ SV131 ) @ SV131 ) ) ) )
= $true )
| ( ( SV174
= ( union @ SV131 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1620]) ).
thf(1758,plain,
! [SV251: $i,SV98: $i,SV207: $i,SV61: $i] :
( ( ( in @ SV61 @ SV207 )
= $false )
| ( ( ~ ( in @ SV98 @ SV251 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SV207 @ SV251 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1621]) ).
thf(1759,plain,
! [SV301: $i,SV98: $i,SV61: $i] :
( ( ( ! [SY3930: $i] :
~ ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SV301 @ SY3930 ) ) )
= $true )
| ( ( in @ SV61 @ SV301 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1622]) ).
thf(1760,plain,
! [SV322: $i,SV302: $i,SV98: $i,SV61: $i] :
( ( ~ ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SV302 @ SV322 ) )
| ( in @ SV98 @ SV322 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1623]) ).
thf(1761,plain,
! [SV62: $i,SV175: $i,SV208: $i] :
( ( ( relation @ SV208 )
= $false )
| ( ( function @ SV208 )
= $false )
| ( ( ~ ( in @ SV175 @ ( relation_dom @ SV208 ) )
| ~ ( in @ SV175 @ SV62 )
| ( in @ SV175 @ ( relation_dom @ ( relation_dom_restriction @ SV208 @ SV62 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1624]) ).
thf(1762,plain,
! [SV62: $i,SV276: $i,SV303: $i] :
( ( ( ~ ( function @ SV303 )
| ~ ( relation @ SV303 ) )
= $true )
| ( ( ~ ( in @ SV276 @ ( relation_dom @ ( relation_dom_restriction @ SV303 @ SV62 ) ) )
| ( in @ SV276 @ ( relation_dom @ SV303 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1625]) ).
thf(1763,plain,
! [SV62: $i,SV277: $i,SV304: $i] :
( ( ( ~ ( function @ SV304 )
| ~ ( relation @ SV304 ) )
= $true )
| ( ( ~ ( in @ SV277 @ ( relation_dom @ ( relation_dom_restriction @ SV304 @ SV62 ) ) )
| ( in @ SV277 @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1626]) ).
thf(1764,plain,
! [SV209: $i,SV176: $i,SV63: $i] :
( ( ( ! [SY3808: $i,SY3809: $i] :
( ~ ( in @ SY3808 @ SV63 )
| ~ ( in @ SY3809 @ SV176 )
| ( ( sK34_D @ SV209 @ SV176 @ SV63 )
!= ( ordered_pair @ SY3808 @ SY3809 ) ) )
| ~ ( in @ ( sK34_D @ SV209 @ SV176 @ SV63 ) @ SV209 ) )
= $true )
| ( ( SV209
= ( cartesian_product2 @ SV63 @ SV176 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1627]) ).
thf(1765,plain,
! [SV63: $i,SV176: $i,SV209: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK35_SY3303 @ SV209 @ SV176 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK36_SY3305 @ SV209 @ SV176 @ SV63 ) @ SV176 ) )
| ( ( sK34_D @ SV209 @ SV176 @ SV63 )
!= ( ordered_pair @ ( sK35_SY3303 @ SV209 @ SV176 @ SV63 ) @ ( sK36_SY3305 @ SV209 @ SV176 @ SV63 ) ) ) )
| ( in @ ( sK34_D @ SV209 @ SV176 @ SV63 ) @ SV209 ) )
= $true )
| ( ( SV209
= ( cartesian_product2 @ SV63 @ SV176 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1628]) ).
thf(1766,plain,
! [SV210: $i,SV177: $i,SV63: $i] :
( ( ( ~ ! [SY3810: $i] :
( ! [SY3777: $i,SY3778: $i] :
( ~ ( in @ SY3777 @ SV63 )
| ~ ( in @ SY3778 @ SV177 )
| ( SY3810
!= ( ordered_pair @ SY3777 @ SY3778 ) ) )
| ( in @ SY3810 @ SV210 ) ) )
= $false )
| ( ( SV210
= ( cartesian_product2 @ SV63 @ SV177 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1629]) ).
thf(1767,plain,
! [SV63: $i,SV177: $i,SV210: $i] :
( ( ( ~ ! [SY3813: $i] :
( ~ ( in @ SY3813 @ SV210 )
| ~ ( ~ ~ ( ~ ( in @ ( sK32_E @ SY3813 @ SV210 @ SV177 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK33_SY3300 @ SY3813 @ SV210 @ SV177 @ SV63 ) @ SV177 ) )
| ( SY3813
!= ( ordered_pair @ ( sK32_E @ SY3813 @ SV210 @ SV177 @ SV63 ) @ ( sK33_SY3300 @ SY3813 @ SV210 @ SV177 @ SV63 ) ) ) ) ) )
= $false )
| ( ( SV210
= ( cartesian_product2 @ SV63 @ SV177 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1629]) ).
thf(1768,plain,
! [SV133: $i,SV179: $i,SV252: $i] :
( ( ( in @ SV252 @ SV179 )
= $false )
| ( ( in @ SV252 @ SV133 )
= $false )
| ( ( ~ ( disjoint @ SV133 @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1632]) ).
thf(1769,plain,
! [SV180: $i,SV64: $i,SV211: $i,SV323: $i] :
( ( ( ~ ( in @ SV323 @ ( relation_dom @ SV211 ) )
| ~ ( in @ ( ordered_pair @ SV323 @ SV64 ) @ SV211 )
| ~ ( in @ SV323 @ SV180 ) )
= $true )
| ( ( in @ SV64 @ ( relation_image @ SV211 @ SV180 ) )
= $true )
| ( ( relation @ SV211 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1633]) ).
thf(1770,plain,
! [SV181: $i,SV212: $i,SV64: $i] :
( ( ( in @ SV64 @ ( relation_image @ SV212 @ SV181 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK76_D @ SV212 @ SV181 @ SV64 ) @ ( relation_dom @ SV212 ) )
| ~ ( in @ ( ordered_pair @ ( sK76_D @ SV212 @ SV181 @ SV64 ) @ SV64 ) @ SV212 ) )
| ~ ( in @ ( sK76_D @ SV212 @ SV181 @ SV64 ) @ SV181 ) ) )
= $true )
| ( ( relation @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1634]) ).
thf(1771,plain,
! [SV213: $i,SV182: $i,SV65: $i] :
( ( ( in @ ( ordered_pair @ SV65 @ SV182 ) @ SV213 )
= $false )
| ( ( in @ SV65 @ ( relation_dom @ SV213 ) )
= $true )
| ( ( relation @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1635]) ).
thf(1772,plain,
! [SV214: $i,SV183: $i,SV65: $i] :
( ( ( in @ ( ordered_pair @ SV65 @ SV183 ) @ SV214 )
= $false )
| ( ( in @ SV183 @ ( relation_rng @ SV214 ) )
= $true )
| ( ( relation @ SV214 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1636]) ).
thf(1773,plain,
! [SV66: $i] :
( ( ( ~ ! [SY3607: $i] :
( ~ ( in @ SY3607 @ ( relation_dom @ SV66 ) )
| ! [SY3608: $i] :
( ( SY3608
!= ( apply @ SV66 @ SY3607 ) )
| ( in @ ( ordered_pair @ SY3607 @ SY3608 ) @ SV66 ) ) ) )
= $false )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1637]) ).
thf(1774,plain,
! [SV66: $i] :
( ( ( ~ ! [SY3609: $i] :
( ~ ( in @ SY3609 @ ( relation_dom @ SV66 ) )
| ! [SY3610: $i] :
( ~ ( in @ ( ordered_pair @ SY3609 @ SY3610 ) @ SV66 )
| ( SY3610
= ( apply @ SV66 @ SY3609 ) ) ) ) )
= $false )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1637]) ).
thf(1775,plain,
! [SV66: $i] :
( ( ( ~ ! [SY3611: $i] :
( ( in @ SY3611 @ ( relation_dom @ SV66 ) )
| ! [SY3612: $i] :
( ( SY3612
!= ( apply @ SV66 @ SY3611 ) )
| ( SY3612 = empty_set ) ) ) )
= $false )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1638]) ).
thf(1776,plain,
! [SV66: $i] :
( ( ( ~ ! [SY3613: $i] :
( ( in @ SY3613 @ ( relation_dom @ SV66 ) )
| ! [SY3614: $i] :
( ( SY3614 != empty_set )
| ( SY3614
= ( apply @ SV66 @ SY3613 ) ) ) ) )
= $false )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1638]) ).
thf(1777,plain,
! [SV73: $i,SV7: $i,SV215: $i] :
( ( ( relation @ SV215 )
= $false )
| ( ( function @ SV215 )
= $false )
| ( ( ~ ( in @ SV7 @ ( relation_dom @ ( relation_composition @ SV215 @ SV73 ) ) )
| ( ( apply @ ( relation_composition @ SV215 @ SV73 ) @ SV7 )
= ( apply @ SV73 @ ( apply @ SV215 @ SV7 ) ) ) )
= $true )
| ( ( function @ SV73 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1639]) ).
thf(1778,plain,
! [SV74: $i,SV8: $i,SV216: $i] :
( ( ( relation @ SV216 )
= $false )
| ( ( function @ SV216 )
= $false )
| ( ( ~ ( in @ SV8 @ ( relation_dom @ SV74 ) )
| ( ( apply @ ( relation_composition @ SV74 @ SV216 ) @ SV8 )
= ( apply @ SV216 @ ( apply @ SV74 @ SV8 ) ) ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1640]) ).
thf(1779,plain,
! [SV26: $i,SV88: $i,SV253: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) @ SV26 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV88 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 ) )
| ~ ~ ( ~ ( ( in @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) @ SV26 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV88 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 ) ) ) ) )
= $true )
| ( ( SV253
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $true )
| ( ( relation @ SV253 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1641]) ).
thf(1780,plain,
! [SV88: $i,SV26: $i,SV254: $i] :
( ( ( ( SV254
!= ( relation_rng_restriction @ SV26 @ SV88 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3872: $i,SY3873: $i] :
( ~ ( in @ SY3873 @ SV26 )
| ~ ( in @ ( ordered_pair @ SY3872 @ SY3873 ) @ SV88 )
| ( in @ ( ordered_pair @ SY3872 @ SY3873 ) @ SV254 ) )
| ~ ~ ( ~ ! [SY3874: $i,SY3875: $i] :
( ~ ( in @ ( ordered_pair @ SY3874 @ SY3875 ) @ SV254 )
| ( in @ SY3875 @ SV26 ) )
| ~ ! [SY3876: $i,SY3877: $i] :
( ~ ( in @ ( ordered_pair @ SY3876 @ SY3877 ) @ SV254 )
| ( in @ ( ordered_pair @ SY3876 @ SY3877 ) @ SV88 ) ) ) ) )
= $true )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1642]) ).
thf(1781,plain,
! [SV187: $i,SV142: $i,SV27: $i] :
( ( ( in @ SV27 @ SV142 )
= $false )
| ( ( ~ ( in @ SV27 @ ( relation_dom @ SV187 ) ) )
= $true )
| ( ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SV187 @ SV142 ) ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1645]) ).
thf(1782,plain,
! [SV256: $i,SV27: $i,SV278: $i] :
( ( ( relation @ SV278 )
= $false )
| ( ( ~ ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SV278 @ SV256 ) ) )
| ( in @ SV27 @ SV256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1646]) ).
thf(1783,plain,
! [SV257: $i,SV27: $i,SV279: $i] :
( ( ( relation @ SV279 )
= $false )
| ( ( ~ ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SV279 @ SV257 ) ) )
| ( in @ SV27 @ ( relation_dom @ SV279 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1647]) ).
thf(1784,plain,
! [SV28: $i,SV218: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV218 @ SV28 ) @ ( sK14_SY3290 @ SV218 @ SV28 ) ) @ SV218 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY3290 @ SV218 @ SV28 ) @ ( sK13_C @ SV218 @ SV28 ) ) @ SV28 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SV218 @ SV28 ) @ ( sK14_SY3290 @ SV218 @ SV28 ) ) @ SV218 )
| ( in @ ( ordered_pair @ ( sK14_SY3290 @ SV218 @ SV28 ) @ ( sK13_C @ SV218 @ SV28 ) ) @ SV28 ) ) )
= $false )
| ( ( SV218
= ( relation_inverse @ SV28 ) )
= $true )
| ( ( relation @ SV218 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1648]) ).
thf(1785,plain,
! [SV28: $i,SV219: $i] :
( ( ( SV219
= ( relation_inverse @ SV28 ) )
= $false )
| ( ( ~ ( ~ ! [SY3815: $i,SY3816: $i] :
( ~ ( in @ ( ordered_pair @ SY3815 @ SY3816 ) @ SV219 )
| ( in @ ( ordered_pair @ SY3816 @ SY3815 ) @ SV28 ) )
| ~ ! [SY3817: $i,SY3818: $i] :
( ~ ( in @ ( ordered_pair @ SY3818 @ SY3817 ) @ SV28 )
| ( in @ ( ordered_pair @ SY3817 @ SY3818 ) @ SV219 ) ) ) )
= $true )
| ( ( relation @ SV219 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1649]) ).
thf(1786,plain,
! [SV305: $i,SV280: $i,SV29: $i] :
( ( ( ~ ( ~ ( ! [SY3932: $i] :
( ~ ( in @ SY3932 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3932 @ SV280 )
| ( ( sK61_D @ SV305 @ SV280 @ SV29 )
!= ( apply @ SV29 @ SY3932 ) ) )
| ~ ( in @ ( sK61_D @ SV305 @ SV280 @ SV29 ) @ SV305 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) @ SV280 ) )
| ( ( sK61_D @ SV305 @ SV280 @ SV29 )
!= ( apply @ SV29 @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) ) ) )
| ( in @ ( sK61_D @ SV305 @ SV280 @ SV29 ) @ SV305 ) ) ) )
= $true )
| ( ( SV305
= ( relation_image @ SV29 @ SV280 ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1650]) ).
thf(1787,plain,
! [SV281: $i,SV29: $i,SV306: $i] :
( ( ( ( SV306
!= ( relation_image @ SV29 @ SV281 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3933: $i] :
( ! [SY3910: $i] :
( ~ ( in @ SY3910 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3910 @ SV281 )
| ( SY3933
!= ( apply @ SV29 @ SY3910 ) ) )
| ( in @ SY3933 @ SV306 ) )
| ~ ! [SY3935: $i] :
( ~ ( in @ SY3935 @ SV306 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SY3935 @ SV306 @ SV281 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK60_E @ SY3935 @ SV306 @ SV281 @ SV29 ) @ SV281 ) )
| ( SY3935
!= ( apply @ SV29 @ ( sK60_E @ SY3935 @ SV306 @ SV281 @ SV29 ) ) ) ) ) ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1651]) ).
thf(1788,plain,
! [SV30: $i,SV220: $i,SV258: $i] :
( ( ( ~ ( ! [SY3880: $i] :
( ~ ( in @ ( ordered_pair @ SY3880 @ ( sK55_D @ SV258 @ SV220 @ SV30 ) ) @ SV30 )
| ~ ( in @ SY3880 @ SV220 ) )
| ~ ( in @ ( sK55_D @ SV258 @ SV220 @ SV30 ) @ SV258 ) ) )
= $false )
| ( ( SV258
= ( relation_image @ SV30 @ SV220 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1652]) ).
thf(1789,plain,
! [SV30: $i,SV220: $i,SV258: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_SY3315 @ SV258 @ SV220 @ SV30 ) @ ( sK55_D @ SV258 @ SV220 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK56_SY3315 @ SV258 @ SV220 @ SV30 ) @ SV220 ) )
| ( in @ ( sK55_D @ SV258 @ SV220 @ SV30 ) @ SV258 ) ) )
= $false )
| ( ( SV258
= ( relation_image @ SV30 @ SV220 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1652]) ).
thf(1790,plain,
! [SV259: $i,SV221: $i,SV30: $i] :
( ( ( ~ ! [SY3881: $i] :
( ! [SY3823: $i] :
( ~ ( in @ ( ordered_pair @ SY3823 @ SY3881 ) @ SV30 )
| ~ ( in @ SY3823 @ SV221 ) )
| ( in @ SY3881 @ SV259 ) )
| ~ ! [SY3883: $i] :
( ~ ( in @ SY3883 @ SV259 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SY3883 @ SV259 @ SV221 @ SV30 ) @ SY3883 ) @ SV30 )
| ~ ( in @ ( sK54_E @ SY3883 @ SV259 @ SV221 @ SV30 ) @ SV221 ) ) ) )
= $false )
| ( ( SV259
= ( relation_image @ SV30 @ SV221 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1653]) ).
thf(1791,plain,
! [SV31: $i,SV222: $i,SV260: $i] :
( ( ( ~ ( ! [SY3884: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SY3884 ) @ SV31 )
| ~ ( in @ SY3884 @ SV222 ) )
| ~ ( in @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SV260 ) ) )
= $false )
| ( ( SV260
= ( relation_inverse_image @ SV31 @ SV222 ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1654]) ).
thf(1792,plain,
! [SV31: $i,SV222: $i,SV260: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ ( sK53_SY3313 @ SV260 @ SV222 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( sK53_SY3313 @ SV260 @ SV222 @ SV31 ) @ SV222 ) )
| ( in @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SV260 ) ) )
= $false )
| ( ( SV260
= ( relation_inverse_image @ SV31 @ SV222 ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1654]) ).
thf(1793,plain,
! [SV261: $i,SV223: $i,SV31: $i] :
( ( ( ~ ! [SY3885: $i] :
( ! [SY3829: $i] :
( ~ ( in @ ( ordered_pair @ SY3885 @ SY3829 ) @ SV31 )
| ~ ( in @ SY3829 @ SV223 ) )
| ( in @ SY3885 @ SV261 ) )
| ~ ! [SY3887: $i] :
( ~ ( in @ SY3887 @ SV261 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3887 @ ( sK51_E @ SY3887 @ SV261 @ SV223 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( sK51_E @ SY3887 @ SV261 @ SV223 @ SV31 ) @ SV223 ) ) ) )
= $false )
| ( ( SV261
= ( relation_inverse_image @ SV31 @ SV223 ) )
= $false )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1655]) ).
thf(1794,plain,
! [SV32: $i,SV224: $i,SV262: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ SV224 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV32 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 ) )
| ~ ~ ( ~ ( ( in @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ SV224 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV32 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 ) ) ) ) )
= $true )
| ( ( SV262
= ( relation_dom_restriction @ SV32 @ SV224 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1656]) ).
thf(1795,plain,
! [SV225: $i,SV32: $i,SV263: $i] :
( ( ( ( SV263
!= ( relation_dom_restriction @ SV32 @ SV225 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3888: $i,SY3889: $i] :
( ~ ( in @ SY3888 @ SV225 )
| ~ ( in @ ( ordered_pair @ SY3888 @ SY3889 ) @ SV32 )
| ( in @ ( ordered_pair @ SY3888 @ SY3889 ) @ SV263 ) )
| ~ ~ ( ~ ! [SY3890: $i] :
( ! [SY3891: $i] :
~ ( in @ ( ordered_pair @ SY3890 @ SY3891 ) @ SV263 )
| ( in @ SY3890 @ SV225 ) )
| ~ ! [SY3892: $i,SY3893: $i] :
( ~ ( in @ ( ordered_pair @ SY3892 @ SY3893 ) @ SV263 )
| ( in @ ( ordered_pair @ SY3892 @ SY3893 ) @ SV32 ) ) ) ) )
= $true )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1657]) ).
thf(1796,plain,
! [SV143: $i,SV33: $i,SV188: $i,SV307: $i] :
( ( ( ~ ( in @ SV307 @ ( relation_rng @ SV188 ) )
| ~ ( in @ ( ordered_pair @ SV33 @ SV307 ) @ SV188 ) )
= $true )
| ( ( ~ ( in @ SV307 @ SV143 ) )
= $true )
| ( ( in @ SV33 @ ( relation_inverse_image @ SV188 @ SV143 ) )
= $true )
| ( ( relation @ SV188 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1658]) ).
thf(1797,plain,
! [SV33: $i,SV144: $i,SV189: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK75_D @ SV189 @ SV144 @ SV33 ) @ ( relation_rng @ SV189 ) )
| ~ ( in @ ( ordered_pair @ SV33 @ ( sK75_D @ SV189 @ SV144 @ SV33 ) ) @ SV189 ) )
| ~ ( in @ ( sK75_D @ SV189 @ SV144 @ SV33 ) @ SV144 ) )
= $false )
| ( ( in @ SV33 @ ( relation_inverse_image @ SV189 @ SV144 ) )
= $false )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1659]) ).
thf(1798,plain,
! [SV110: $i,SV145: $i] :
( ( ( ( ( sK65_C @ SV145 @ SV110 )
!= ( sK66_SY3320 @ SV145 @ SV110 ) )
| ~ ( in @ ( sK65_C @ SV145 @ SV110 ) @ SV110 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 ) )
= $true )
| ( ( SV145
= ( identity_relation @ SV110 ) )
= $true )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1660]) ).
thf(1799,plain,
! [SV110: $i,SV145: $i] :
( ( ( ~ ( ~ ( ( ( sK65_C @ SV145 @ SV110 )
= ( sK66_SY3320 @ SV145 @ SV110 ) )
| ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 ) )
| ~ ( ( in @ ( sK65_C @ SV145 @ SV110 ) @ SV110 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 ) ) ) )
= $true )
| ( ( SV145
= ( identity_relation @ SV110 ) )
= $true )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1661]) ).
thf(1800,plain,
! [SV146: $i,SV111: $i] :
( ( ( ~ ! [SY3732: $i,SY3733: $i] :
( ( SY3732 != SY3733 )
| ~ ( in @ SY3732 @ SV111 )
| ( in @ ( ordered_pair @ SY3732 @ SY3733 ) @ SV146 ) ) )
= $false )
| ( ( SV146
= ( identity_relation @ SV111 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1662]) ).
thf(1801,plain,
! [SV111: $i,SV146: $i] :
( ( ( ~ ~ ( ~ ! [SY3734: $i,SY3735: $i] :
( ~ ( in @ ( ordered_pair @ SY3734 @ SY3735 ) @ SV146 )
| ( SY3734 = SY3735 ) )
| ~ ! [SY3736: $i] :
( ! [SY3737: $i] :
~ ( in @ ( ordered_pair @ SY3736 @ SY3737 ) @ SV146 )
| ( in @ SY3736 @ SV111 ) ) ) )
= $false )
| ( ( SV146
= ( identity_relation @ SV111 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1662]) ).
thf(1802,plain,
! [SV34: $i,SV89: $i,SV190: $i,SV226: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV190 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV34 ) )
| ~ ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV89 ) ) ) ) )
= $true )
| ( ( SV226
= ( unordered_triple @ SV34 @ SV89 @ SV190 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1663]) ).
thf(1803,plain,
! [SV34: $i,SV89: $i,SV190: $i,SV226: $i] :
( ( ( ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
= SV190 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
= SV34 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
= SV89 ) )
= $true )
| ( ( SV226
= ( unordered_triple @ SV34 @ SV89 @ SV190 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1664]) ).
thf(1804,plain,
! [SV89: $i,SV34: $i,SV191: $i,SV227: $i] :
( ( ( ~ ! [SY3839: $i] :
( ~ ( in @ SY3839 @ SV227 )
| ( SY3839 = SV191 )
| ( SY3839 = SV34 )
| ( SY3839 = SV89 ) ) )
= $false )
| ( ( SV227
= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1665]) ).
thf(1805,plain,
! [SV89: $i,SV34: $i,SV227: $i,SV191: $i] :
( ( ( ~ ~ ( ~ ! [SY3840: $i] :
( ( SY3840 != SV191 )
| ( in @ SY3840 @ SV227 ) )
| ~ ~ ( ~ ! [SY3841: $i] :
( ( SY3841 != SV34 )
| ( in @ SY3841 @ SV227 ) )
| ~ ! [SY3842: $i] :
( ( SY3842 != SV89 )
| ( in @ SY3842 @ SV227 ) ) ) ) )
= $false )
| ( ( SV227
= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1665]) ).
thf(1806,plain,
! [SV36: $i,SV228: $i] :
( ( ( ! [SY3843: $i] :
~ ( in @ ( ordered_pair @ SY3843 @ ( sK16_C @ SV228 @ SV36 ) ) @ SV36 )
| ~ ( in @ ( sK16_C @ SV228 @ SV36 ) @ SV228 ) )
= $true )
| ( ( SV228
= ( relation_rng @ SV36 ) )
= $true )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1668]) ).
thf(1807,plain,
! [SV36: $i,SV228: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK17_SY3292 @ SV228 @ SV36 ) @ ( sK16_C @ SV228 @ SV36 ) ) @ SV36 )
| ( in @ ( sK16_C @ SV228 @ SV36 ) @ SV228 ) )
= $true )
| ( ( SV228
= ( relation_rng @ SV36 ) )
= $true )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1669]) ).
thf(1808,plain,
! [SV229: $i,SV36: $i] :
( ( ( ~ ! [SY3844: $i] :
( ! [SY3437: $i] :
~ ( in @ ( ordered_pair @ SY3437 @ SY3844 ) @ SV36 )
| ( in @ SY3844 @ SV229 ) ) )
= $false )
| ( ( SV229
= ( relation_rng @ SV36 ) )
= $false )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1670]) ).
thf(1809,plain,
! [SV36: $i,SV229: $i] :
( ( ( ~ ! [SY3846: $i] :
( ~ ( in @ SY3846 @ SV229 )
| ( in @ ( ordered_pair @ ( sK15_D @ SY3846 @ SV229 @ SV36 ) @ SY3846 ) @ SV36 ) ) )
= $false )
| ( ( SV229
= ( relation_rng @ SV36 ) )
= $false )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1670]) ).
thf(1810,plain,
! [SV37: $i,SV324: $i] :
( ( ! [SY3945: $i] :
( ~ ( in @ SV324 @ ( sK77_B @ SV37 ) )
| ~ ( subset @ SY3945 @ SV324 )
| ( in @ SY3945 @ ( sK77_B @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1672]) ).
thf(1811,plain,
! [SV112: $i,SV150: $i] :
( ( ( in @ ( sK41_C @ SV150 @ SV112 ) @ SV150 )
= $false )
| ( ( ~ ( subset @ ( sK41_C @ SV150 @ SV112 ) @ SV112 ) )
= $true )
| ( ( SV150
= ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1674]) ).
thf(1812,plain,
! [SV113: $i,SV151: $i,SV325: $i] :
( ( ( ~ ( in @ SV325 @ SV151 )
| ( subset @ SV325 @ SV113 ) )
= $true )
| ( ( SV151
= ( powerset @ SV113 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1676]) ).
thf(1813,plain,
! [SV151: $i,SV113: $i,SV326: $i] :
( ( ( ~ ( subset @ SV326 @ SV113 )
| ( in @ SV326 @ SV151 ) )
= $true )
| ( ( SV151
= ( powerset @ SV113 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1677]) ).
thf(1814,plain,
! [SV152: $i,SV114: $i] :
( ( ( ~ ( in @ SV114 @ ( relation_rng @ SV152 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV152 ) )
= $true )
| ( ( SV114
= ( apply @ SV152 @ ( apply @ ( function_inverse @ SV152 ) @ SV114 ) ) )
= $true )
| ( ( function @ SV152 )
= $false )
| ( ( relation @ SV152 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1678]) ).
thf(1815,plain,
! [SV153: $i,SV115: $i] :
( ( ( ~ ( in @ SV115 @ ( relation_rng @ SV153 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV153 ) )
= $true )
| ( ( SV115
= ( apply @ ( relation_composition @ ( function_inverse @ SV153 ) @ SV153 ) @ SV115 ) )
= $true )
| ( ( function @ SV153 )
= $false )
| ( ( relation @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1679]) ).
thf(1816,plain,
! [SV91: $i,SV39: $i,SV308: $i] :
( ( ( ~ ( function @ SV308 )
| ~ ( relation @ SV308 ) )
= $true )
| ( ( ~ ( in @ SV39 @ ( relation_dom @ SV308 ) )
| ~ ( in @ ( apply @ SV308 @ SV39 ) @ ( relation_dom @ SV91 ) )
| ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SV308 @ SV91 ) ) ) )
= $true )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1680]) ).
thf(1817,plain,
! [SV91: $i,SV39: $i] :
( ( ( ~ ! [SY3642: $i] :
( ~ ( function @ SY3642 )
| ~ ( relation @ SY3642 )
| ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3642 @ SV91 ) ) )
| ( in @ SV39 @ ( relation_dom @ SY3642 ) ) ) )
= $false )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1681]) ).
thf(1818,plain,
! [SV91: $i,SV39: $i] :
( ( ( ~ ! [SY3643: $i] :
( ~ ( function @ SY3643 )
| ~ ( relation @ SY3643 )
| ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3643 @ SV91 ) ) )
| ( in @ ( apply @ SY3643 @ SV39 ) @ ( relation_dom @ SV91 ) ) ) )
= $false )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1681]) ).
thf(1819,plain,
! [SV40: $i,SV92: $i,SV265: $i] :
( ( ( ~ ( ~ ( element @ ( sK6_D @ SV265 @ SV92 @ SV40 ) @ ( powerset @ SV40 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK6_D @ SV265 @ SV92 @ SV40 ) @ SV265 )
| ~ ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SV265 @ SV92 @ SV40 ) ) @ SV92 ) )
| ~ ( ( in @ ( sK6_D @ SV265 @ SV92 @ SV40 ) @ SV265 )
| ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SV265 @ SV92 @ SV40 ) ) @ SV92 ) ) ) ) )
= $true )
| ( ( SV265
= ( complements_of_subsets @ SV40 @ SV92 ) )
= $true )
| ( ( element @ SV265 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1682]) ).
thf(1820,plain,
! [SV92: $i,SV40: $i,SV266: $i] :
( ( ( ( SV266
!= ( complements_of_subsets @ SV40 @ SV92 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3894: $i] :
( ~ ( element @ SY3894 @ ( powerset @ SV40 ) )
| ~ ( in @ SY3894 @ SV266 )
| ( in @ ( subset_complement @ SV40 @ SY3894 ) @ SV92 ) )
| ~ ! [SY3895: $i] :
( ~ ( element @ SY3895 @ ( powerset @ SV40 ) )
| ~ ( in @ ( subset_complement @ SV40 @ SY3895 ) @ SV92 )
| ( in @ SY3895 @ SV266 ) ) ) )
= $true )
| ( ( element @ SV266 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1683]) ).
thf(1821,plain,
! [SV41: $i,SV194: $i,SV154: $i] :
( ( ( ( SV154
!= ( apply @ SV194 @ SV41 ) )
| ~ ( in @ SV41 @ ( relation_dom @ SV194 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV41 @ SV154 ) @ SV194 )
= $true )
| ( ( function @ SV194 )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1684]) ).
thf(1822,plain,
! [SV267: $i,SV41: $i,SV282: $i] :
( ( ( ~ ( function @ SV282 ) )
= $true )
| ( ( ~ ( relation @ SV282 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV41 @ SV267 ) @ SV282 )
| ( SV267
= ( apply @ SV282 @ SV41 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1685]) ).
thf(1823,plain,
! [SV268: $i,SV41: $i,SV283: $i] :
( ( ( ~ ( function @ SV283 ) )
= $true )
| ( ( ~ ( relation @ SV283 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV41 @ SV268 ) @ SV283 )
| ( in @ SV41 @ ( relation_dom @ SV283 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1686]) ).
thf(1824,plain,
! [SV195: $i,SV155: $i,SV42: $i] :
( ( ( in @ SV42 @ SV155 )
= $false )
| ( ( ~ ( in @ SV42 @ ( relation_rng @ SV195 ) ) )
= $true )
| ( ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SV155 @ SV195 ) ) )
= $true )
| ( ( relation @ SV195 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1687]) ).
thf(1825,plain,
! [SV269: $i,SV42: $i,SV284: $i] :
( ( ( relation @ SV284 )
= $false )
| ( ( ~ ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SV269 @ SV284 ) ) )
| ( in @ SV42 @ SV269 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1688]) ).
thf(1826,plain,
! [SV270: $i,SV42: $i,SV285: $i] :
( ( ( relation @ SV285 )
= $false )
| ( ( ~ ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SV270 @ SV285 ) ) )
| ( in @ SV42 @ ( relation_rng @ SV285 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1689]) ).
thf(1827,plain,
! [SV43: $i,SV271: $i] :
( ( ( ~ ! [SY3900: $i] :
( ~ ( subset @ SY3900 @ SV271 )
| ( in @ SY3900 @ ( sK3_SY3278 @ SV271 @ SV43 ) ) ) )
= $false )
| ( ( ~ ( in @ SV271 @ ( sK2_B @ SV43 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1690]) ).
thf(1828,plain,
! [SV43: $i,SV271: $i] :
( ( ( ~ ( in @ ( sK3_SY3278 @ SV271 @ SV43 ) @ ( sK2_B @ SV43 ) ) )
= $false )
| ( ( ~ ( in @ SV271 @ ( sK2_B @ SV43 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1690]) ).
thf(1829,plain,
! [SV43: $i,SV327: $i] :
( ( ! [SY3946: $i] :
( ~ ( in @ SV327 @ ( sK2_B @ SV43 ) )
| ~ ( subset @ SY3946 @ SV327 )
| ( in @ SY3946 @ ( sK2_B @ SV43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1691]) ).
thf(1830,plain,
! [SV309: $i,SV286: $i,SV116: $i] :
( ( ( ( sK49_B @ SV116 )
= ( ordered_pair @ SV286 @ SV309 ) )
= $false )
| ( ( relation @ SV116 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1693]) ).
thf(1831,plain,
! [SV196: $i,SV44: $i,SV231: $i,SV93: $i] :
( ( ( in @ SV93 @ SV231 )
= $false )
| ( ( in @ SV44 @ SV196 )
= $false )
| ( ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SV196 @ SV231 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1694]) ).
thf(1832,plain,
! [SV328: $i,SV287: $i,SV93: $i,SV44: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SV287 @ SV328 ) ) )
= $true )
| ( ( in @ SV44 @ SV287 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1695]) ).
thf(1833,plain,
! [SV310: $i,SV288: $i,SV93: $i,SV44: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SV288 @ SV310 ) ) )
= $true )
| ( ( in @ SV93 @ SV310 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1696]) ).
thf(1834,plain,
! [SV45: $i,SV232: $i] :
( ( ( ! [SY3847: $i] :
~ ( in @ ( ordered_pair @ ( sK26_C @ SV232 @ SV45 ) @ SY3847 ) @ SV45 )
| ~ ( in @ ( sK26_C @ SV232 @ SV45 ) @ SV232 ) )
= $true )
| ( ( SV232
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1697]) ).
thf(1835,plain,
! [SV45: $i,SV232: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK26_C @ SV232 @ SV45 ) @ ( sK27_SY3298 @ SV232 @ SV45 ) ) @ SV45 )
| ( in @ ( sK26_C @ SV232 @ SV45 ) @ SV232 ) )
= $true )
| ( ( SV232
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1698]) ).
thf(1836,plain,
! [SV233: $i,SV45: $i] :
( ( ( ~ ! [SY3848: $i] :
( ! [SY3481: $i] :
~ ( in @ ( ordered_pair @ SY3848 @ SY3481 ) @ SV45 )
| ( in @ SY3848 @ SV233 ) ) )
= $false )
| ( ( SV233
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1699]) ).
thf(1837,plain,
! [SV45: $i,SV233: $i] :
( ( ( ~ ! [SY3850: $i] :
( ~ ( in @ SY3850 @ SV233 )
| ( in @ ( ordered_pair @ SY3850 @ ( sK25_D @ SY3850 @ SV233 @ SV45 ) ) @ SV45 ) ) )
= $false )
| ( ( SV233
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1699]) ).
thf(1838,plain,
! [SV234: $i,SV289: $i] :
( ( ( element @ SV289 @ SV234 )
= $false )
| ( ( in @ SV289 @ SV234 )
= $true )
| ( ( empty @ SV234 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1700]) ).
thf(1839,plain,
! [SV235: $i,SV290: $i] :
( ( ( in @ SV290 @ SV235 )
= $false )
| ( ( element @ SV290 @ SV235 )
= $true )
| ( ( empty @ SV235 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1701]) ).
thf(1840,plain,
! [SV236: $i,SV311: $i] :
( ( ( ~ ( element @ SV311 @ SV236 ) )
= $true )
| ( ( empty @ SV311 )
= $true )
| ( ( empty @ SV236 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1702]) ).
thf(1841,plain,
! [SV237: $i,SV312: $i] :
( ( ( ~ ( empty @ SV312 ) )
= $true )
| ( ( element @ SV312 @ SV237 )
= $true )
| ( ( empty @ SV237 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1703]) ).
thf(1842,plain,
! [SV120: $i,SV157: $i] :
( ( ( ( sK43_C @ SV157 @ SV120 )
= SV120 )
= $false )
| ( ( ~ ( in @ ( sK43_C @ SV157 @ SV120 ) @ SV157 ) )
= $true )
| ( ( SV157
= ( singleton @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1704]) ).
thf(1843,plain,
! [SV158: $i,SV121: $i,SV329: $i] :
( ( ( ( SV329 != SV121 )
| ( in @ SV329 @ SV158 ) )
= $true )
| ( ( SV158
= ( singleton @ SV121 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1706]) ).
thf(1844,plain,
! [SV121: $i,SV158: $i,SV330: $i] :
( ( ( ~ ( in @ SV330 @ SV158 )
| ( SV330 = SV121 ) )
= $true )
| ( ( SV158
= ( singleton @ SV121 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1707]) ).
thf(1845,plain,
! [SV122: $i,SV159: $i] :
( ( ( ~ ( ~ ( in @ ( sK74_C @ SV159 @ SV122 ) @ SV122 )
| ~ ( ( ( apply @ SV159 @ ( sK74_C @ SV159 @ SV122 ) )
!= ( sK74_C @ SV159 @ SV122 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV159 )
!= SV122 ) )
= $true )
| ( ( SV159
= ( identity_relation @ SV122 ) )
= $true )
| ( ( function @ SV159 )
= $false )
| ( ( relation @ SV159 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1708]) ).
thf(1846,plain,
! [SV239: $i,SV272: $i] :
( ( ( function @ SV272 )
= $false )
| ( ( ~ ( relation @ SV272 ) )
= $true )
| ( ( ( SV272
!= ( identity_relation @ SV239 ) )
| ! [SY3901: $i] :
( ~ ( in @ SY3901 @ SV239 )
| ( ( apply @ SV272 @ SY3901 )
= SY3901 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1709]) ).
thf(1847,plain,
! [SV240: $i,SV273: $i] :
( ( ( function @ SV273 )
= $false )
| ( ( ~ ( relation @ SV273 ) )
= $true )
| ( ( ( SV273
!= ( identity_relation @ SV240 ) )
| ( ( relation_dom @ SV273 )
= SV240 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1710]) ).
thf(1848,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ( function @ SV331 )
| ~ ( relation @ SV331 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) )
| ( SV331
= ( function_inverse @ SV46 ) ) )
= $true )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1711]) ).
thf(1849,plain,
! [SV46: $i] :
( ( ( ~ ! [SY3484: $i] :
( ~ ( function @ SY3484 )
| ~ ( relation @ SY3484 )
| ( SY3484
!= ( function_inverse @ SV46 ) )
| ~ ( ~ ~ ( ~ ! [SY3485: $i,SY3486: $i] :
( ( SY3486
!= ( apply @ SY3484 @ SY3485 ) )
| ~ ( in @ SY3485 @ ( relation_rng @ SV46 ) )
| ( SY3485
= ( apply @ SV46 @ SY3486 ) ) )
| ~ ! [SY3487: $i,SY3488: $i] :
( ( SY3488
!= ( apply @ SY3484 @ SY3487 ) )
| ~ ( in @ SY3487 @ ( relation_rng @ SV46 ) )
| ( in @ SY3488 @ ( relation_dom @ SV46 ) ) ) )
| ~ ~ ( ~ ! [SY3489: $i,SY3490: $i] :
( ( SY3489
!= ( apply @ SV46 @ SY3490 ) )
| ~ ( in @ SY3490 @ ( relation_dom @ SV46 ) )
| ( SY3490
= ( apply @ SY3484 @ SY3489 ) ) )
| ~ ! [SY3491: $i] :
( ! [SY3492: $i] :
( ( SY3491
!= ( apply @ SV46 @ SY3492 ) )
| ~ ( in @ SY3492 @ ( relation_dom @ SV46 ) ) )
| ( in @ SY3491 @ ( relation_rng @ SV46 ) ) ) ) ) )
| ~ ! [SY3493: $i] :
( ~ ( function @ SY3493 )
| ~ ( relation @ SY3493 )
| ( SY3493
!= ( function_inverse @ SV46 ) )
| ( ( relation_dom @ SY3493 )
= ( relation_rng @ SV46 ) ) ) )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1712]) ).
thf(1850,plain,
! [SV47: $i,SV123: $i,SV313: $i] :
( ( ( ~ ( relation @ SV313 ) )
= $true )
| ( ( ~ ( ~ ( ! [SY3936: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ SY3936 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3936 @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV123 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV313 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK10_SY3288 @ SV313 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY3288 @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV123 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV313 ) ) )
| ( SV313
= ( relation_composition @ SV47 @ SV123 ) ) )
= $true )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1713]) ).
thf(1851,plain,
! [SV123: $i,SV47: $i,SV314: $i] :
( ( ( ~ ( relation @ SV314 ) )
= $true )
| ( ( ( SV314
!= ( relation_composition @ SV47 @ SV123 ) )
| ~ ( ~ ! [SY3937: $i,SY3938: $i] :
( ! [SY3706: $i] :
( ~ ( in @ ( ordered_pair @ SY3937 @ SY3706 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3706 @ SY3938 ) @ SV123 ) )
| ( in @ ( ordered_pair @ SY3937 @ SY3938 ) @ SV314 ) )
| ~ ! [SY3940: $i,SY3941: $i] :
( ~ ( in @ ( ordered_pair @ SY3940 @ SY3941 ) @ SV314 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3940 @ ( sK7_F @ SY3941 @ SY3940 @ SV314 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY3941 @ SY3940 @ SV314 @ SV123 @ SV47 ) @ SY3941 ) @ SV123 ) ) ) ) )
= $true )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1714]) ).
thf(1852,plain,
! [SV291: $i,SV274: $i,SV48: $i] :
( ( ( subset @ ( unordered_pair @ SV48 @ SV274 ) @ SV291 )
= $false )
| ( ( in @ SV48 @ SV291 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1716]) ).
thf(1853,plain,
! [SV292: $i,SV275: $i,SV48: $i] :
( ( ( subset @ ( unordered_pair @ SV48 @ SV275 ) @ SV292 )
= $false )
| ( ( in @ SV275 @ SV292 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1717]) ).
thf(1854,plain,
! [SV241: $i,SV94: $i,SV198: $i,SV49: $i] :
( ( ( ~ ( in @ SV49 @ SV198 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ SV241 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SV198 ) @ SV241 ) )
= $true )
| ( ( relation @ SV241 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1718]) ).
thf(1855,plain,
! [SV293: $i,SV94: $i,SV49: $i,SV315: $i] :
( ( ( ~ ( relation @ SV315 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SV293 ) @ SV315 ) )
| ( in @ SV49 @ SV293 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1719]) ).
thf(1856,plain,
! [SV294: $i,SV94: $i,SV49: $i,SV316: $i] :
( ( ( ~ ( relation @ SV316 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SV294 ) @ SV316 ) )
| ( in @ ( ordered_pair @ SV49 @ SV94 ) @ SV316 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1720]) ).
thf(1857,plain,
! [SV242: $i,SV95: $i,SV50: $i] :
( ( ( in @ SV50 @ SV95 )
= $false )
| ( ( in @ SV242 @ SV95 )
= $false )
| ( ( in @ SV242 @ ( sK4_C @ SV95 @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1721]) ).
thf(1858,plain,
! [SV124: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_B @ SV124 ) @ ( relation_dom @ SV124 ) )
| ~ ( in @ ( sK12_SY3289 @ SV124 ) @ ( relation_dom @ SV124 ) ) )
| ( ( apply @ SV124 @ ( sK11_B @ SV124 ) )
!= ( apply @ SV124 @ ( sK12_SY3289 @ SV124 ) ) ) ) )
= $false )
| ( ( one_to_one @ SV124 )
= $true )
| ( ( function @ SV124 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1722]) ).
thf(1859,plain,
! [SV124: $i] :
( ( ( ~ ( ( ( sK11_B @ SV124 )
!= ( sK12_SY3289 @ SV124 ) ) ) )
= $false )
| ( ( one_to_one @ SV124 )
= $true )
| ( ( function @ SV124 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1722]) ).
thf(1860,plain,
! [SV125: $i,SV332: $i] :
( ( ( ! [SY3947: $i] :
( ~ ( in @ SV332 @ ( relation_dom @ SV125 ) )
| ~ ( in @ SY3947 @ ( relation_dom @ SV125 ) )
| ( ( apply @ SV125 @ SV332 )
!= ( apply @ SV125 @ SY3947 ) )
| ( SV332 = SY3947 ) ) )
= $true )
| ( ( one_to_one @ SV125 )
= $false )
| ( ( function @ SV125 )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1723]) ).
thf(1861,plain,
! [SV51: $i,SV161: $i,SV199: $i] :
( ( ( ~ ( ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV199 )
| ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV51 ) )
| ~ ( ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV199 )
| ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV161 ) ) )
= $false )
| ( ( SV199
= ( set_union2 @ SV51 @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1724]) ).
thf(1862,plain,
! [SV51: $i,SV161: $i,SV199: $i] :
( ( ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV199 )
= $true )
| ( ( ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV51 )
| ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV161 ) )
= $true )
| ( ( SV199
= ( set_union2 @ SV51 @ SV161 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1725]) ).
thf(1863,plain,
! [SV162: $i,SV51: $i,SV200: $i] :
( ( ( ! [SY3795: $i] :
( ~ ( in @ SY3795 @ SV200 )
| ( in @ SY3795 @ SV51 )
| ( in @ SY3795 @ SV162 ) ) )
= $true )
| ( ( SV200
= ( set_union2 @ SV51 @ SV162 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1726]) ).
thf(1864,plain,
! [SV162: $i,SV200: $i,SV51: $i] :
( ( ( ~ ( ~ ! [SY3796: $i] :
( ~ ( in @ SY3796 @ SV51 )
| ( in @ SY3796 @ SV200 ) )
| ~ ! [SY3797: $i] :
( ~ ( in @ SY3797 @ SV162 )
| ( in @ SY3797 @ SV200 ) ) ) )
= $true )
| ( ( SV200
= ( set_union2 @ SV51 @ SV162 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1727]) ).
thf(1865,plain,
! [SV52: $i,SV243: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK30_C @ SV243 @ SV52 ) @ ( sK31_SY3299 @ SV243 @ SV52 ) ) @ SV52 )
| ~ ~ ( in @ ( ordered_pair @ ( sK30_C @ SV243 @ SV52 ) @ ( sK31_SY3299 @ SV243 @ SV52 ) ) @ SV243 ) )
= $false )
| ( ( subset @ SV52 @ SV243 )
= $true )
| ( ( relation @ SV243 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1728]) ).
thf(1866,plain,
! [SV244: $i,SV52: $i] :
( ( ( subset @ SV52 @ SV244 )
= $false )
| ( ( ! [SY3858: $i,SY3859: $i] :
( ~ ( in @ ( ordered_pair @ SY3858 @ SY3859 ) @ SV52 )
| ( in @ ( ordered_pair @ SY3858 @ SY3859 ) @ SV244 ) ) )
= $true )
| ( ( relation @ SV244 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1729]) ).
thf(1867,plain,
! [SV245: $i,SV295: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK46_SY3307 @ SV295 @ SV245 ) @ SV245 )
| ~ ~ ( in @ ( sK45_C @ SV295 @ SV245 ) @ ( sK46_SY3307 @ SV295 @ SV245 ) ) )
| ~ ( in @ ( sK45_C @ SV295 @ SV245 ) @ SV295 ) )
| ~ ( ! [SY3917: $i] :
( ~ ( in @ SY3917 @ SV245 )
| ( in @ ( sK45_C @ SV295 @ SV245 ) @ SY3917 ) )
| ( in @ ( sK45_C @ SV295 @ SV245 ) @ SV295 ) ) )
= $false )
| ( ( SV295
= ( set_meet @ SV245 ) )
= $true )
| ( ( SV245 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1730]) ).
thf(1868,plain,
! [SV246: $i,SV296: $i] :
( ( ( SV296
= ( set_meet @ SV246 ) )
= $false )
| ( ( ~ ( ~ ! [SY3918: $i] :
( ~ ( ~ ( in @ ( sK44_D @ SY3918 @ SV296 @ SV246 ) @ SV246 )
| ~ ~ ( in @ SY3918 @ ( sK44_D @ SY3918 @ SV296 @ SV246 ) ) )
| ( in @ SY3918 @ SV296 ) )
| ~ ! [SY3919: $i] :
( ~ ( in @ SY3919 @ SV296 )
| ! [SY3865: $i] :
( ~ ( in @ SY3865 @ SV246 )
| ( in @ SY3919 @ SY3865 ) ) ) ) )
= $true )
| ( ( SV246 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1731]) ).
thf(1869,plain,
! [SV247: $i,SV317: $i] :
( ( ( ( SV317
!= ( set_meet @ SV247 ) ) )
= $true )
| ( ( SV317 = empty_set )
= $true )
| ( ( SV247 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1732]) ).
thf(1870,plain,
! [SV248: $i,SV318: $i] :
( ( ( ( SV318 != empty_set ) )
= $true )
| ( ( SV318
= ( set_meet @ SV248 ) )
= $true )
| ( ( SV248 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1733]) ).
thf(1871,plain,
! [SV53: $i,SV297: $i,SV319: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ ( sK57_D @ SV319 @ SV297 @ SV53 ) ) @ SV297 )
| ~ ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ SV319 ) )
| ~ ~ ( ~ ( ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ SV319 ) )
| ~ ( ( in @ ( apply @ SV53 @ ( sK57_D @ SV319 @ SV297 @ SV53 ) ) @ SV297 )
| ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ SV319 ) ) ) ) )
= $true )
| ( ( SV319
= ( relation_inverse_image @ SV53 @ SV297 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1734]) ).
thf(1872,plain,
! [SV298: $i,SV53: $i,SV320: $i] :
( ( ( ( SV320
!= ( relation_inverse_image @ SV53 @ SV298 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3942: $i] :
( ~ ( in @ SY3942 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SY3942 ) @ SV298 )
| ( in @ SY3942 @ SV320 ) )
| ~ ~ ( ~ ! [SY3943: $i] :
( ~ ( in @ SY3943 @ SV320 )
| ( in @ SY3943 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY3944: $i] :
( ~ ( in @ SY3944 @ SV320 )
| ( in @ ( apply @ SV53 @ SY3944 ) @ SV298 ) ) ) ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1735]) ).
thf(1873,plain,
! [SV54: $i,SV165: $i,SV201: $i] :
( ( ( ~ ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV54 )
| ~ ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV165 ) )
= $true )
| ( ( ~ ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV201 ) )
= $true )
| ( ( SV201
= ( set_intersection2 @ SV54 @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1736]) ).
thf(1874,plain,
! [SV54: $i,SV165: $i,SV201: $i] :
( ( ( ~ ( ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV54 )
| ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV201 ) )
| ~ ( ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV165 )
| ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV201 ) ) )
= $false )
| ( ( SV201
= ( set_intersection2 @ SV54 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1737]) ).
thf(1875,plain,
! [SV202: $i,SV166: $i,SV54: $i] :
( ( ( ! [SY3798: $i] :
( ~ ( in @ SY3798 @ SV54 )
| ~ ( in @ SY3798 @ SV166 )
| ( in @ SY3798 @ SV202 ) ) )
= $true )
| ( ( SV202
= ( set_intersection2 @ SV54 @ SV166 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1738]) ).
thf(1876,plain,
! [SV166: $i,SV54: $i,SV202: $i] :
( ( ( ~ ( ~ ! [SY3799: $i] :
( ~ ( in @ SY3799 @ SV202 )
| ( in @ SY3799 @ SV54 ) )
| ~ ! [SY3800: $i] :
( ~ ( in @ SY3800 @ SV202 )
| ( in @ SY3800 @ SV166 ) ) ) )
= $true )
| ( ( SV202
= ( set_intersection2 @ SV54 @ SV166 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1739]) ).
thf(1877,plain,
! [SV55: $i,SV169: $i,SV203: $i] :
( ( ( ~ ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV55 )
| ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV169 ) )
= $true )
| ( ( ~ ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV203 ) )
= $true )
| ( ( SV203
= ( set_difference @ SV55 @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1740]) ).
thf(1878,plain,
! [SV55: $i,SV169: $i,SV203: $i] :
( ( ( ~ ( ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV55 )
| ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV203 ) )
| ~ ( ~ ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV169 )
| ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV203 ) ) )
= $false )
| ( ( SV203
= ( set_difference @ SV55 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1741]) ).
thf(1879,plain,
! [SV204: $i,SV170: $i,SV55: $i] :
( ( ( ! [SY3801: $i] :
( ~ ( in @ SY3801 @ SV55 )
| ( in @ SY3801 @ SV170 )
| ( in @ SY3801 @ SV204 ) ) )
= $true )
| ( ( SV204
= ( set_difference @ SV55 @ SV170 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1742]) ).
thf(1880,plain,
! [SV170: $i,SV55: $i,SV204: $i] :
( ( ( ~ ( ~ ! [SY3802: $i] :
( ~ ( in @ SY3802 @ SV204 )
| ( in @ SY3802 @ SV55 ) )
| ~ ! [SY3803: $i] :
( ~ ( in @ SY3803 @ SV204 )
| ~ ( in @ SY3803 @ SV170 ) ) ) )
= $true )
| ( ( SV204
= ( set_difference @ SV55 @ SV170 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1743]) ).
thf(1881,plain,
! [SV56: $i,SV299: $i] :
( ( ( ~ ( ! [SY3926: $i] :
( ( ( sK19_C @ SV299 @ SV56 )
!= ( apply @ SV56 @ SY3926 ) )
| ~ ( in @ SY3926 @ ( relation_dom @ SV56 ) ) )
| ~ ( in @ ( sK19_C @ SV299 @ SV56 ) @ SV299 ) )
| ~ ( ~ ( ( ( sK19_C @ SV299 @ SV56 )
!= ( apply @ SV56 @ ( sK20_SY3294 @ SV299 @ SV56 ) ) )
| ~ ( in @ ( sK20_SY3294 @ SV299 @ SV56 ) @ ( relation_dom @ SV56 ) ) )
| ( in @ ( sK19_C @ SV299 @ SV56 ) @ SV299 ) ) )
= $false )
| ( ( SV299
= ( relation_rng @ SV56 ) )
= $true )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1744]) ).
thf(1882,plain,
! [SV56: $i,SV300: $i] :
( ( ( SV300
= ( relation_rng @ SV56 ) )
= $false )
| ( ( ~ ( ~ ! [SY3927: $i] :
( ! [SY3554: $i] :
( ( SY3927
!= ( apply @ SV56 @ SY3554 ) )
| ~ ( in @ SY3554 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY3927 @ SV300 ) )
| ~ ! [SY3929: $i] :
( ~ ( in @ SY3929 @ SV300 )
| ~ ( ( SY3929
!= ( apply @ SV56 @ ( sK18_D @ SY3929 @ SV300 @ SV56 ) ) )
| ~ ( in @ ( sK18_D @ SY3929 @ SV300 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) ) ) )
= $true )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1745]) ).
thf(1883,plain,
! [SV57: $i,SV171: $i,SV205: $i] :
( ( ( ~ ( ~ ( in @ ( sK38_D @ SV205 @ SV171 @ SV57 ) @ SV205 )
| ( ( sK38_D @ SV205 @ SV171 @ SV57 )
!= SV57 ) )
| ~ ( ~ ( in @ ( sK38_D @ SV205 @ SV171 @ SV57 ) @ SV205 )
| ( ( sK38_D @ SV205 @ SV171 @ SV57 )
!= SV171 ) ) )
= $false )
| ( ( SV205
= ( unordered_pair @ SV57 @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1746]) ).
thf(1884,plain,
! [SV57: $i,SV171: $i,SV205: $i] :
( ( ( in @ ( sK38_D @ SV205 @ SV171 @ SV57 ) @ SV205 )
= $true )
| ( ( ( ( sK38_D @ SV205 @ SV171 @ SV57 )
= SV57 )
| ( ( sK38_D @ SV205 @ SV171 @ SV57 )
= SV171 ) )
= $true )
| ( ( SV205
= ( unordered_pair @ SV57 @ SV171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1747]) ).
thf(1885,plain,
! [SV172: $i,SV57: $i,SV206: $i] :
( ( ( ! [SY3804: $i] :
( ~ ( in @ SY3804 @ SV206 )
| ( SY3804 = SV57 )
| ( SY3804 = SV172 ) ) )
= $true )
| ( ( SV206
= ( unordered_pair @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1748]) ).
thf(1886,plain,
! [SV172: $i,SV206: $i,SV57: $i] :
( ( ( ~ ( ~ ! [SY3805: $i] :
( ( SY3805 != SV57 )
| ( in @ SY3805 @ SV206 ) )
| ~ ! [SY3806: $i] :
( ( SY3806 != SV172 )
| ( in @ SY3806 @ SV206 ) ) ) )
= $true )
| ( ( SV206
= ( unordered_pair @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1749]) ).
thf(1887,plain,
! [SV58: $i,SV96: $i,SV321: $i] :
( ( ( ~ ( function @ SV321 )
| ~ ( relation @ SV321 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK67_D @ SV321 @ SV96 @ SV58 ) @ ( relation_dom @ SV96 ) )
| ~ ( ( ( apply @ SV96 @ ( sK67_D @ SV321 @ SV96 @ SV58 ) )
!= ( apply @ SV321 @ ( sK67_D @ SV321 @ SV96 @ SV58 ) ) ) ) )
| ( ( relation_dom @ SV96 )
!= ( set_intersection2 @ ( relation_dom @ SV321 ) @ SV58 ) )
| ( SV96
= ( relation_dom_restriction @ SV321 @ SV58 ) ) )
= $true )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1750]) ).
thf(1888,plain,
! [SV58: $i,SV96: $i] :
( ( ( ~ ! [SY3662: $i] :
( ~ ( function @ SY3662 )
| ~ ( relation @ SY3662 )
| ( SV96
!= ( relation_dom_restriction @ SY3662 @ SV58 ) )
| ! [SY3663: $i] :
( ~ ( in @ SY3663 @ ( relation_dom @ SV96 ) )
| ( ( apply @ SV96 @ SY3663 )
= ( apply @ SY3662 @ SY3663 ) ) ) ) )
= $false )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1751]) ).
thf(1889,plain,
! [SV58: $i,SV96: $i] :
( ( ( ~ ! [SY3664: $i] :
( ~ ( function @ SY3664 )
| ~ ( relation @ SY3664 )
| ( SV96
!= ( relation_dom_restriction @ SY3664 @ SV58 ) )
| ( ( relation_dom @ SV96 )
= ( set_intersection2 @ ( relation_dom @ SY3664 ) @ SV58 ) ) ) )
= $false )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1751]) ).
thf(1890,plain,
! [SV59: $i,SV249: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV249 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV249 ) ) )
= $false )
| ( ( SV59 = SV249 )
= $true )
| ( ( relation @ SV249 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1752]) ).
thf(1891,plain,
! [SV250: $i,SV59: $i] :
( ( ( SV59 = SV250 )
= $false )
| ( ( ~ ( ~ ! [SY3868: $i,SY3869: $i] :
( ~ ( in @ ( ordered_pair @ SY3868 @ SY3869 ) @ SV59 )
| ( in @ ( ordered_pair @ SY3868 @ SY3869 ) @ SV250 ) )
| ~ ! [SY3870: $i,SY3871: $i] :
( ~ ( in @ ( ordered_pair @ SY3870 @ SY3871 ) @ SV250 )
| ( in @ ( ordered_pair @ SY3870 @ SY3871 ) @ SV59 ) ) ) )
= $true )
| ( ( relation @ SV250 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1753]) ).
thf(1892,plain,
! [SV333: $i,SV130: $i,SV173: $i] :
( ( ( ~ ( in @ ( sK23_C @ SV173 @ SV130 ) @ SV333 )
| ~ ( in @ SV333 @ SV130 ) )
= $true )
| ( ( ~ ( in @ ( sK23_C @ SV173 @ SV130 ) @ SV173 ) )
= $true )
| ( ( SV173
= ( union @ SV130 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1754]) ).
thf(1893,plain,
! [SV130: $i,SV173: $i] :
( ( ( ~ ( in @ ( sK23_C @ SV173 @ SV130 ) @ ( sK24_SY3296 @ SV173 @ SV130 ) )
| ~ ( in @ ( sK24_SY3296 @ SV173 @ SV130 ) @ SV130 ) )
= $false )
| ( ( in @ ( sK23_C @ SV173 @ SV130 ) @ SV173 )
= $true )
| ( ( SV173
= ( union @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1755]) ).
thf(1894,plain,
! [SV174: $i,SV131: $i,SV334: $i] :
( ( ( ! [SY3948: $i] :
( ~ ( in @ SV334 @ SY3948 )
| ~ ( in @ SY3948 @ SV131 ) )
| ( in @ SV334 @ SV174 ) )
= $true )
| ( ( SV174
= ( union @ SV131 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1756]) ).
thf(1895,plain,
! [SV131: $i,SV174: $i,SV335: $i] :
( ( ( ~ ( in @ SV335 @ SV174 )
| ~ ( ~ ( in @ SV335 @ ( sK22_D @ SV335 @ SV174 @ SV131 ) )
| ~ ( in @ ( sK22_D @ SV335 @ SV174 @ SV131 ) @ SV131 ) ) )
= $true )
| ( ( SV174
= ( union @ SV131 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1757]) ).
thf(1896,plain,
! [SV207: $i,SV61: $i,SV251: $i,SV98: $i] :
( ( ( in @ SV98 @ SV251 )
= $false )
| ( ( in @ SV61 @ SV207 )
= $false )
| ( ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SV207 @ SV251 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1758]) ).
thf(1897,plain,
! [SV336: $i,SV301: $i,SV98: $i,SV61: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SV301 @ SV336 ) ) )
= $true )
| ( ( in @ SV61 @ SV301 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1759]) ).
thf(1898,plain,
! [SV322: $i,SV302: $i,SV98: $i,SV61: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SV302 @ SV322 ) ) )
= $true )
| ( ( in @ SV98 @ SV322 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1760]) ).
thf(1899,plain,
! [SV62: $i,SV208: $i,SV175: $i] :
( ( ( ~ ( in @ SV175 @ ( relation_dom @ SV208 ) )
| ~ ( in @ SV175 @ SV62 ) )
= $true )
| ( ( in @ SV175 @ ( relation_dom @ ( relation_dom_restriction @ SV208 @ SV62 ) ) )
= $true )
| ( ( function @ SV208 )
= $false )
| ( ( relation @ SV208 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1761]) ).
thf(1900,plain,
! [SV62: $i,SV276: $i,SV303: $i] :
( ( ( ~ ( function @ SV303 ) )
= $true )
| ( ( ~ ( relation @ SV303 ) )
= $true )
| ( ( ~ ( in @ SV276 @ ( relation_dom @ ( relation_dom_restriction @ SV303 @ SV62 ) ) )
| ( in @ SV276 @ ( relation_dom @ SV303 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1762]) ).
thf(1901,plain,
! [SV62: $i,SV277: $i,SV304: $i] :
( ( ( ~ ( function @ SV304 ) )
= $true )
| ( ( ~ ( relation @ SV304 ) )
= $true )
| ( ( ~ ( in @ SV277 @ ( relation_dom @ ( relation_dom_restriction @ SV304 @ SV62 ) ) )
| ( in @ SV277 @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1763]) ).
thf(1902,plain,
! [SV209: $i,SV176: $i,SV63: $i] :
( ( ( ! [SY3808: $i,SY3809: $i] :
( ~ ( in @ SY3808 @ SV63 )
| ~ ( in @ SY3809 @ SV176 )
| ( ( sK34_D @ SV209 @ SV176 @ SV63 )
!= ( ordered_pair @ SY3808 @ SY3809 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK34_D @ SV209 @ SV176 @ SV63 ) @ SV209 ) )
= $true )
| ( ( SV209
= ( cartesian_product2 @ SV63 @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1764]) ).
thf(1903,plain,
! [SV63: $i,SV176: $i,SV209: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK35_SY3303 @ SV209 @ SV176 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK36_SY3305 @ SV209 @ SV176 @ SV63 ) @ SV176 ) )
| ( ( sK34_D @ SV209 @ SV176 @ SV63 )
!= ( ordered_pair @ ( sK35_SY3303 @ SV209 @ SV176 @ SV63 ) @ ( sK36_SY3305 @ SV209 @ SV176 @ SV63 ) ) ) ) )
= $true )
| ( ( in @ ( sK34_D @ SV209 @ SV176 @ SV63 ) @ SV209 )
= $true )
| ( ( SV209
= ( cartesian_product2 @ SV63 @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1765]) ).
thf(1904,plain,
! [SV210: $i,SV177: $i,SV63: $i] :
( ( ( ! [SY3810: $i] :
( ! [SY3777: $i,SY3778: $i] :
( ~ ( in @ SY3777 @ SV63 )
| ~ ( in @ SY3778 @ SV177 )
| ( SY3810
!= ( ordered_pair @ SY3777 @ SY3778 ) ) )
| ( in @ SY3810 @ SV210 ) ) )
= $true )
| ( ( SV210
= ( cartesian_product2 @ SV63 @ SV177 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1766]) ).
thf(1905,plain,
! [SV63: $i,SV177: $i,SV210: $i] :
( ( ( ! [SY3813: $i] :
( ~ ( in @ SY3813 @ SV210 )
| ~ ( ~ ~ ( ~ ( in @ ( sK32_E @ SY3813 @ SV210 @ SV177 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK33_SY3300 @ SY3813 @ SV210 @ SV177 @ SV63 ) @ SV177 ) )
| ( SY3813
!= ( ordered_pair @ ( sK32_E @ SY3813 @ SV210 @ SV177 @ SV63 ) @ ( sK33_SY3300 @ SY3813 @ SV210 @ SV177 @ SV63 ) ) ) ) ) )
= $true )
| ( ( SV210
= ( cartesian_product2 @ SV63 @ SV177 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1767]) ).
thf(1906,plain,
! [SV252: $i,SV179: $i,SV133: $i] :
( ( ( disjoint @ SV133 @ SV179 )
= $false )
| ( ( in @ SV252 @ SV133 )
= $false )
| ( ( in @ SV252 @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1768]) ).
thf(1907,plain,
! [SV180: $i,SV64: $i,SV211: $i,SV323: $i] :
( ( ( ~ ( in @ SV323 @ ( relation_dom @ SV211 ) )
| ~ ( in @ ( ordered_pair @ SV323 @ SV64 ) @ SV211 ) )
= $true )
| ( ( ~ ( in @ SV323 @ SV180 ) )
= $true )
| ( ( in @ SV64 @ ( relation_image @ SV211 @ SV180 ) )
= $true )
| ( ( relation @ SV211 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1769]) ).
thf(1908,plain,
! [SV64: $i,SV181: $i,SV212: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK76_D @ SV212 @ SV181 @ SV64 ) @ ( relation_dom @ SV212 ) )
| ~ ( in @ ( ordered_pair @ ( sK76_D @ SV212 @ SV181 @ SV64 ) @ SV64 ) @ SV212 ) )
| ~ ( in @ ( sK76_D @ SV212 @ SV181 @ SV64 ) @ SV181 ) )
= $false )
| ( ( in @ SV64 @ ( relation_image @ SV212 @ SV181 ) )
= $false )
| ( ( relation @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1770]) ).
thf(1909,plain,
! [SV66: $i] :
( ( ( ! [SY3607: $i] :
( ~ ( in @ SY3607 @ ( relation_dom @ SV66 ) )
| ! [SY3608: $i] :
( ( SY3608
!= ( apply @ SV66 @ SY3607 ) )
| ( in @ ( ordered_pair @ SY3607 @ SY3608 ) @ SV66 ) ) ) )
= $true )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1773]) ).
thf(1910,plain,
! [SV66: $i] :
( ( ( ! [SY3609: $i] :
( ~ ( in @ SY3609 @ ( relation_dom @ SV66 ) )
| ! [SY3610: $i] :
( ~ ( in @ ( ordered_pair @ SY3609 @ SY3610 ) @ SV66 )
| ( SY3610
= ( apply @ SV66 @ SY3609 ) ) ) ) )
= $true )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1774]) ).
thf(1911,plain,
! [SV66: $i] :
( ( ( ! [SY3611: $i] :
( ( in @ SY3611 @ ( relation_dom @ SV66 ) )
| ! [SY3612: $i] :
( ( SY3612
!= ( apply @ SV66 @ SY3611 ) )
| ( SY3612 = empty_set ) ) ) )
= $true )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1775]) ).
thf(1912,plain,
! [SV66: $i] :
( ( ( ! [SY3613: $i] :
( ( in @ SY3613 @ ( relation_dom @ SV66 ) )
| ! [SY3614: $i] :
( ( SY3614 != empty_set )
| ( SY3614
= ( apply @ SV66 @ SY3613 ) ) ) ) )
= $true )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1776]) ).
thf(1913,plain,
! [SV73: $i,SV215: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ ( relation_dom @ ( relation_composition @ SV215 @ SV73 ) ) ) )
= $true )
| ( ( ( apply @ ( relation_composition @ SV215 @ SV73 ) @ SV7 )
= ( apply @ SV73 @ ( apply @ SV215 @ SV7 ) ) )
= $true )
| ( ( function @ SV215 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( function @ SV73 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1777]) ).
thf(1914,plain,
! [SV216: $i,SV74: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ ( relation_dom @ SV74 ) ) )
= $true )
| ( ( ( apply @ ( relation_composition @ SV74 @ SV216 ) @ SV8 )
= ( apply @ SV216 @ ( apply @ SV74 @ SV8 ) ) )
= $true )
| ( ( function @ SV216 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1778]) ).
thf(1915,plain,
! [SV26: $i,SV88: $i,SV253: $i] :
( ( ( ~ ( ~ ( in @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) @ SV26 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV88 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 ) )
| ~ ~ ( ~ ( ( in @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) @ SV26 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV88 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 ) ) ) )
= $false )
| ( ( SV253
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $true )
| ( ( relation @ SV253 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1779]) ).
thf(1916,plain,
! [SV88: $i,SV26: $i,SV254: $i] :
( ( ( SV254
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $false )
| ( ( ~ ( ~ ! [SY3872: $i,SY3873: $i] :
( ~ ( in @ SY3873 @ SV26 )
| ~ ( in @ ( ordered_pair @ SY3872 @ SY3873 ) @ SV88 )
| ( in @ ( ordered_pair @ SY3872 @ SY3873 ) @ SV254 ) )
| ~ ~ ( ~ ! [SY3874: $i,SY3875: $i] :
( ~ ( in @ ( ordered_pair @ SY3874 @ SY3875 ) @ SV254 )
| ( in @ SY3875 @ SV26 ) )
| ~ ! [SY3876: $i,SY3877: $i] :
( ~ ( in @ ( ordered_pair @ SY3876 @ SY3877 ) @ SV254 )
| ( in @ ( ordered_pair @ SY3876 @ SY3877 ) @ SV88 ) ) ) ) )
= $true )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1780]) ).
thf(1917,plain,
! [SV142: $i,SV187: $i,SV27: $i] :
( ( ( in @ SV27 @ ( relation_dom @ SV187 ) )
= $false )
| ( ( in @ SV27 @ SV142 )
= $false )
| ( ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SV187 @ SV142 ) ) )
= $true )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1781]) ).
thf(1918,plain,
! [SV256: $i,SV278: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SV278 @ SV256 ) ) ) )
= $true )
| ( ( in @ SV27 @ SV256 )
= $true )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1782]) ).
thf(1919,plain,
! [SV257: $i,SV279: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SV279 @ SV257 ) ) ) )
= $true )
| ( ( in @ SV27 @ ( relation_dom @ SV279 ) )
= $true )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1783]) ).
thf(1920,plain,
! [SV28: $i,SV218: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV218 @ SV28 ) @ ( sK14_SY3290 @ SV218 @ SV28 ) ) @ SV218 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY3290 @ SV218 @ SV28 ) @ ( sK13_C @ SV218 @ SV28 ) ) @ SV28 ) ) )
= $false )
| ( ( SV218
= ( relation_inverse @ SV28 ) )
= $true )
| ( ( relation @ SV218 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1784]) ).
thf(1921,plain,
! [SV28: $i,SV218: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK13_C @ SV218 @ SV28 ) @ ( sK14_SY3290 @ SV218 @ SV28 ) ) @ SV218 )
| ( in @ ( ordered_pair @ ( sK14_SY3290 @ SV218 @ SV28 ) @ ( sK13_C @ SV218 @ SV28 ) ) @ SV28 ) ) )
= $false )
| ( ( SV218
= ( relation_inverse @ SV28 ) )
= $true )
| ( ( relation @ SV218 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1784]) ).
thf(1922,plain,
! [SV28: $i,SV219: $i] :
( ( ( ~ ! [SY3815: $i,SY3816: $i] :
( ~ ( in @ ( ordered_pair @ SY3815 @ SY3816 ) @ SV219 )
| ( in @ ( ordered_pair @ SY3816 @ SY3815 ) @ SV28 ) )
| ~ ! [SY3817: $i,SY3818: $i] :
( ~ ( in @ ( ordered_pair @ SY3818 @ SY3817 ) @ SV28 )
| ( in @ ( ordered_pair @ SY3817 @ SY3818 ) @ SV219 ) ) )
= $false )
| ( ( SV219
= ( relation_inverse @ SV28 ) )
= $false )
| ( ( relation @ SV219 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1785]) ).
thf(1923,plain,
! [SV305: $i,SV280: $i,SV29: $i] :
( ( ( ~ ( ! [SY3932: $i] :
( ~ ( in @ SY3932 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3932 @ SV280 )
| ( ( sK61_D @ SV305 @ SV280 @ SV29 )
!= ( apply @ SV29 @ SY3932 ) ) )
| ~ ( in @ ( sK61_D @ SV305 @ SV280 @ SV29 ) @ SV305 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) @ SV280 ) )
| ( ( sK61_D @ SV305 @ SV280 @ SV29 )
!= ( apply @ SV29 @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) ) ) )
| ( in @ ( sK61_D @ SV305 @ SV280 @ SV29 ) @ SV305 ) ) )
= $false )
| ( ( SV305
= ( relation_image @ SV29 @ SV280 ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1786]) ).
thf(1924,plain,
! [SV281: $i,SV29: $i,SV306: $i] :
( ( ( SV306
= ( relation_image @ SV29 @ SV281 ) )
= $false )
| ( ( ~ ( ~ ! [SY3933: $i] :
( ! [SY3910: $i] :
( ~ ( in @ SY3910 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3910 @ SV281 )
| ( SY3933
!= ( apply @ SV29 @ SY3910 ) ) )
| ( in @ SY3933 @ SV306 ) )
| ~ ! [SY3935: $i] :
( ~ ( in @ SY3935 @ SV306 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SY3935 @ SV306 @ SV281 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK60_E @ SY3935 @ SV306 @ SV281 @ SV29 ) @ SV281 ) )
| ( SY3935
!= ( apply @ SV29 @ ( sK60_E @ SY3935 @ SV306 @ SV281 @ SV29 ) ) ) ) ) ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1787]) ).
thf(1925,plain,
! [SV30: $i,SV220: $i,SV258: $i] :
( ( ( ! [SY3880: $i] :
( ~ ( in @ ( ordered_pair @ SY3880 @ ( sK55_D @ SV258 @ SV220 @ SV30 ) ) @ SV30 )
| ~ ( in @ SY3880 @ SV220 ) )
| ~ ( in @ ( sK55_D @ SV258 @ SV220 @ SV30 ) @ SV258 ) )
= $true )
| ( ( SV258
= ( relation_image @ SV30 @ SV220 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1788]) ).
thf(1926,plain,
! [SV30: $i,SV220: $i,SV258: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_SY3315 @ SV258 @ SV220 @ SV30 ) @ ( sK55_D @ SV258 @ SV220 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK56_SY3315 @ SV258 @ SV220 @ SV30 ) @ SV220 ) )
| ( in @ ( sK55_D @ SV258 @ SV220 @ SV30 ) @ SV258 ) )
= $true )
| ( ( SV258
= ( relation_image @ SV30 @ SV220 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1789]) ).
thf(1927,plain,
! [SV259: $i,SV221: $i,SV30: $i] :
( ( ( ~ ! [SY3881: $i] :
( ! [SY3823: $i] :
( ~ ( in @ ( ordered_pair @ SY3823 @ SY3881 ) @ SV30 )
| ~ ( in @ SY3823 @ SV221 ) )
| ( in @ SY3881 @ SV259 ) ) )
= $false )
| ( ( SV259
= ( relation_image @ SV30 @ SV221 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1790]) ).
thf(1928,plain,
! [SV30: $i,SV221: $i,SV259: $i] :
( ( ( ~ ! [SY3883: $i] :
( ~ ( in @ SY3883 @ SV259 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SY3883 @ SV259 @ SV221 @ SV30 ) @ SY3883 ) @ SV30 )
| ~ ( in @ ( sK54_E @ SY3883 @ SV259 @ SV221 @ SV30 ) @ SV221 ) ) ) )
= $false )
| ( ( SV259
= ( relation_image @ SV30 @ SV221 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1790]) ).
thf(1929,plain,
! [SV31: $i,SV222: $i,SV260: $i] :
( ( ( ! [SY3884: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SY3884 ) @ SV31 )
| ~ ( in @ SY3884 @ SV222 ) )
| ~ ( in @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SV260 ) )
= $true )
| ( ( SV260
= ( relation_inverse_image @ SV31 @ SV222 ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1791]) ).
thf(1930,plain,
! [SV31: $i,SV222: $i,SV260: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ ( sK53_SY3313 @ SV260 @ SV222 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( sK53_SY3313 @ SV260 @ SV222 @ SV31 ) @ SV222 ) )
| ( in @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SV260 ) )
= $true )
| ( ( SV260
= ( relation_inverse_image @ SV31 @ SV222 ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1792]) ).
thf(1931,plain,
! [SV261: $i,SV223: $i,SV31: $i] :
( ( ( ~ ! [SY3885: $i] :
( ! [SY3829: $i] :
( ~ ( in @ ( ordered_pair @ SY3885 @ SY3829 ) @ SV31 )
| ~ ( in @ SY3829 @ SV223 ) )
| ( in @ SY3885 @ SV261 ) ) )
= $false )
| ( ( SV261
= ( relation_inverse_image @ SV31 @ SV223 ) )
= $false )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1793]) ).
thf(1932,plain,
! [SV31: $i,SV223: $i,SV261: $i] :
( ( ( ~ ! [SY3887: $i] :
( ~ ( in @ SY3887 @ SV261 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3887 @ ( sK51_E @ SY3887 @ SV261 @ SV223 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( sK51_E @ SY3887 @ SV261 @ SV223 @ SV31 ) @ SV223 ) ) ) )
= $false )
| ( ( SV261
= ( relation_inverse_image @ SV31 @ SV223 ) )
= $false )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1793]) ).
thf(1933,plain,
! [SV32: $i,SV224: $i,SV262: $i] :
( ( ( ~ ( ~ ( in @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ SV224 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV32 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 ) )
| ~ ~ ( ~ ( ( in @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ SV224 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV32 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 ) ) ) )
= $false )
| ( ( SV262
= ( relation_dom_restriction @ SV32 @ SV224 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1794]) ).
thf(1934,plain,
! [SV225: $i,SV32: $i,SV263: $i] :
( ( ( SV263
= ( relation_dom_restriction @ SV32 @ SV225 ) )
= $false )
| ( ( ~ ( ~ ! [SY3888: $i,SY3889: $i] :
( ~ ( in @ SY3888 @ SV225 )
| ~ ( in @ ( ordered_pair @ SY3888 @ SY3889 ) @ SV32 )
| ( in @ ( ordered_pair @ SY3888 @ SY3889 ) @ SV263 ) )
| ~ ~ ( ~ ! [SY3890: $i] :
( ! [SY3891: $i] :
~ ( in @ ( ordered_pair @ SY3890 @ SY3891 ) @ SV263 )
| ( in @ SY3890 @ SV225 ) )
| ~ ! [SY3892: $i,SY3893: $i] :
( ~ ( in @ ( ordered_pair @ SY3892 @ SY3893 ) @ SV263 )
| ( in @ ( ordered_pair @ SY3892 @ SY3893 ) @ SV32 ) ) ) ) )
= $true )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1795]) ).
thf(1935,plain,
! [SV143: $i,SV33: $i,SV188: $i,SV307: $i] :
( ( ( ~ ( in @ SV307 @ ( relation_rng @ SV188 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV33 @ SV307 ) @ SV188 ) )
= $true )
| ( ( ~ ( in @ SV307 @ SV143 ) )
= $true )
| ( ( in @ SV33 @ ( relation_inverse_image @ SV188 @ SV143 ) )
= $true )
| ( ( relation @ SV188 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1796]) ).
thf(1936,plain,
! [SV33: $i,SV144: $i,SV189: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK75_D @ SV189 @ SV144 @ SV33 ) @ ( relation_rng @ SV189 ) )
| ~ ( in @ ( ordered_pair @ SV33 @ ( sK75_D @ SV189 @ SV144 @ SV33 ) ) @ SV189 ) ) )
= $false )
| ( ( in @ SV33 @ ( relation_inverse_image @ SV189 @ SV144 ) )
= $false )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1797]) ).
thf(1937,plain,
! [SV33: $i,SV144: $i,SV189: $i] :
( ( ( ~ ( in @ ( sK75_D @ SV189 @ SV144 @ SV33 ) @ SV144 ) )
= $false )
| ( ( in @ SV33 @ ( relation_inverse_image @ SV189 @ SV144 ) )
= $false )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1797]) ).
thf(1938,plain,
! [SV110: $i,SV145: $i] :
( ( ( ( ( sK65_C @ SV145 @ SV110 )
!= ( sK66_SY3320 @ SV145 @ SV110 ) )
| ~ ( in @ ( sK65_C @ SV145 @ SV110 ) @ SV110 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 ) )
= $true )
| ( ( SV145
= ( identity_relation @ SV110 ) )
= $true )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1798]) ).
thf(1939,plain,
! [SV110: $i,SV145: $i] :
( ( ( ~ ( ( ( sK65_C @ SV145 @ SV110 )
= ( sK66_SY3320 @ SV145 @ SV110 ) )
| ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 ) )
| ~ ( ( in @ ( sK65_C @ SV145 @ SV110 ) @ SV110 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 ) ) )
= $false )
| ( ( SV145
= ( identity_relation @ SV110 ) )
= $true )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1799]) ).
thf(1940,plain,
! [SV146: $i,SV111: $i] :
( ( ( ! [SY3732: $i,SY3733: $i] :
( ( SY3732 != SY3733 )
| ~ ( in @ SY3732 @ SV111 )
| ( in @ ( ordered_pair @ SY3732 @ SY3733 ) @ SV146 ) ) )
= $true )
| ( ( SV146
= ( identity_relation @ SV111 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1800]) ).
thf(1941,plain,
! [SV111: $i,SV146: $i] :
( ( ( ~ ( ~ ! [SY3734: $i,SY3735: $i] :
( ~ ( in @ ( ordered_pair @ SY3734 @ SY3735 ) @ SV146 )
| ( SY3734 = SY3735 ) )
| ~ ! [SY3736: $i] :
( ! [SY3737: $i] :
~ ( in @ ( ordered_pair @ SY3736 @ SY3737 ) @ SV146 )
| ( in @ SY3736 @ SV111 ) ) ) )
= $true )
| ( ( SV146
= ( identity_relation @ SV111 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1801]) ).
thf(1942,plain,
! [SV34: $i,SV89: $i,SV190: $i,SV226: $i] :
( ( ( ~ ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV190 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV34 ) )
| ~ ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV89 ) ) ) )
= $false )
| ( ( SV226
= ( unordered_triple @ SV34 @ SV89 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1802]) ).
thf(1943,plain,
! [SV34: $i,SV89: $i,SV190: $i,SV226: $i] :
( ( ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
= $true )
| ( ( ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
= SV190 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
= SV34 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
= SV89 ) )
= $true )
| ( ( SV226
= ( unordered_triple @ SV34 @ SV89 @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1803]) ).
thf(1944,plain,
! [SV89: $i,SV34: $i,SV191: $i,SV227: $i] :
( ( ( ! [SY3839: $i] :
( ~ ( in @ SY3839 @ SV227 )
| ( SY3839 = SV191 )
| ( SY3839 = SV34 )
| ( SY3839 = SV89 ) ) )
= $true )
| ( ( SV227
= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1804]) ).
thf(1945,plain,
! [SV89: $i,SV34: $i,SV227: $i,SV191: $i] :
( ( ( ~ ( ~ ! [SY3840: $i] :
( ( SY3840 != SV191 )
| ( in @ SY3840 @ SV227 ) )
| ~ ~ ( ~ ! [SY3841: $i] :
( ( SY3841 != SV34 )
| ( in @ SY3841 @ SV227 ) )
| ~ ! [SY3842: $i] :
( ( SY3842 != SV89 )
| ( in @ SY3842 @ SV227 ) ) ) ) )
= $true )
| ( ( SV227
= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1805]) ).
thf(1946,plain,
! [SV36: $i,SV228: $i] :
( ( ( ! [SY3843: $i] :
~ ( in @ ( ordered_pair @ SY3843 @ ( sK16_C @ SV228 @ SV36 ) ) @ SV36 ) )
= $true )
| ( ( ~ ( in @ ( sK16_C @ SV228 @ SV36 ) @ SV228 ) )
= $true )
| ( ( SV228
= ( relation_rng @ SV36 ) )
= $true )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1806]) ).
thf(1947,plain,
! [SV36: $i,SV228: $i] :
( ( ( in @ ( ordered_pair @ ( sK17_SY3292 @ SV228 @ SV36 ) @ ( sK16_C @ SV228 @ SV36 ) ) @ SV36 )
= $true )
| ( ( in @ ( sK16_C @ SV228 @ SV36 ) @ SV228 )
= $true )
| ( ( SV228
= ( relation_rng @ SV36 ) )
= $true )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1807]) ).
thf(1948,plain,
! [SV229: $i,SV36: $i] :
( ( ( ! [SY3844: $i] :
( ! [SY3437: $i] :
~ ( in @ ( ordered_pair @ SY3437 @ SY3844 ) @ SV36 )
| ( in @ SY3844 @ SV229 ) ) )
= $true )
| ( ( SV229
= ( relation_rng @ SV36 ) )
= $false )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1808]) ).
thf(1949,plain,
! [SV36: $i,SV229: $i] :
( ( ( ! [SY3846: $i] :
( ~ ( in @ SY3846 @ SV229 )
| ( in @ ( ordered_pair @ ( sK15_D @ SY3846 @ SV229 @ SV36 ) @ SY3846 ) @ SV36 ) ) )
= $true )
| ( ( SV229
= ( relation_rng @ SV36 ) )
= $false )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1809]) ).
thf(1950,plain,
! [SV337: $i,SV37: $i,SV324: $i] :
( ( ~ ( in @ SV324 @ ( sK77_B @ SV37 ) )
| ~ ( subset @ SV337 @ SV324 )
| ( in @ SV337 @ ( sK77_B @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(1951,plain,
! [SV112: $i,SV150: $i] :
( ( ( subset @ ( sK41_C @ SV150 @ SV112 ) @ SV112 )
= $false )
| ( ( in @ ( sK41_C @ SV150 @ SV112 ) @ SV150 )
= $false )
| ( ( SV150
= ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1811]) ).
thf(1952,plain,
! [SV113: $i,SV151: $i,SV325: $i] :
( ( ( ~ ( in @ SV325 @ SV151 ) )
= $true )
| ( ( subset @ SV325 @ SV113 )
= $true )
| ( ( SV151
= ( powerset @ SV113 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1812]) ).
thf(1953,plain,
! [SV151: $i,SV113: $i,SV326: $i] :
( ( ( ~ ( subset @ SV326 @ SV113 ) )
= $true )
| ( ( in @ SV326 @ SV151 )
= $true )
| ( ( SV151
= ( powerset @ SV113 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1813]) ).
thf(1954,plain,
! [SV152: $i,SV114: $i] :
( ( ( in @ SV114 @ ( relation_rng @ SV152 ) )
= $false )
| ( ( ~ ( one_to_one @ SV152 ) )
= $true )
| ( ( SV114
= ( apply @ SV152 @ ( apply @ ( function_inverse @ SV152 ) @ SV114 ) ) )
= $true )
| ( ( function @ SV152 )
= $false )
| ( ( relation @ SV152 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1814]) ).
thf(1955,plain,
! [SV153: $i,SV115: $i] :
( ( ( in @ SV115 @ ( relation_rng @ SV153 ) )
= $false )
| ( ( ~ ( one_to_one @ SV153 ) )
= $true )
| ( ( SV115
= ( apply @ ( relation_composition @ ( function_inverse @ SV153 ) @ SV153 ) @ SV115 ) )
= $true )
| ( ( function @ SV153 )
= $false )
| ( ( relation @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1815]) ).
thf(1956,plain,
! [SV91: $i,SV39: $i,SV308: $i] :
( ( ( ~ ( function @ SV308 ) )
= $true )
| ( ( ~ ( relation @ SV308 ) )
= $true )
| ( ( ~ ( in @ SV39 @ ( relation_dom @ SV308 ) )
| ~ ( in @ ( apply @ SV308 @ SV39 ) @ ( relation_dom @ SV91 ) )
| ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SV308 @ SV91 ) ) ) )
= $true )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1816]) ).
thf(1957,plain,
! [SV91: $i,SV39: $i] :
( ( ( ! [SY3642: $i] :
( ~ ( function @ SY3642 )
| ~ ( relation @ SY3642 )
| ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3642 @ SV91 ) ) )
| ( in @ SV39 @ ( relation_dom @ SY3642 ) ) ) )
= $true )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1817]) ).
thf(1958,plain,
! [SV91: $i,SV39: $i] :
( ( ( ! [SY3643: $i] :
( ~ ( function @ SY3643 )
| ~ ( relation @ SY3643 )
| ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SY3643 @ SV91 ) ) )
| ( in @ ( apply @ SY3643 @ SV39 ) @ ( relation_dom @ SV91 ) ) ) )
= $true )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1818]) ).
thf(1959,plain,
! [SV40: $i,SV92: $i,SV265: $i] :
( ( ( ~ ( element @ ( sK6_D @ SV265 @ SV92 @ SV40 ) @ ( powerset @ SV40 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK6_D @ SV265 @ SV92 @ SV40 ) @ SV265 )
| ~ ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SV265 @ SV92 @ SV40 ) ) @ SV92 ) )
| ~ ( ( in @ ( sK6_D @ SV265 @ SV92 @ SV40 ) @ SV265 )
| ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SV265 @ SV92 @ SV40 ) ) @ SV92 ) ) ) )
= $false )
| ( ( SV265
= ( complements_of_subsets @ SV40 @ SV92 ) )
= $true )
| ( ( element @ SV265 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1819]) ).
thf(1960,plain,
! [SV92: $i,SV40: $i,SV266: $i] :
( ( ( SV266
= ( complements_of_subsets @ SV40 @ SV92 ) )
= $false )
| ( ( ~ ( ~ ! [SY3894: $i] :
( ~ ( element @ SY3894 @ ( powerset @ SV40 ) )
| ~ ( in @ SY3894 @ SV266 )
| ( in @ ( subset_complement @ SV40 @ SY3894 ) @ SV92 ) )
| ~ ! [SY3895: $i] :
( ~ ( element @ SY3895 @ ( powerset @ SV40 ) )
| ~ ( in @ ( subset_complement @ SV40 @ SY3895 ) @ SV92 )
| ( in @ SY3895 @ SV266 ) ) ) )
= $true )
| ( ( element @ SV266 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1820]) ).
thf(1961,plain,
! [SV41: $i,SV194: $i,SV154: $i] :
( ( ( ( SV154
!= ( apply @ SV194 @ SV41 ) ) )
= $true )
| ( ( ~ ( in @ SV41 @ ( relation_dom @ SV194 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV41 @ SV154 ) @ SV194 )
= $true )
| ( ( function @ SV194 )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1821]) ).
thf(1962,plain,
! [SV267: $i,SV41: $i,SV282: $i] :
( ( ( function @ SV282 )
= $false )
| ( ( ~ ( relation @ SV282 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV41 @ SV267 ) @ SV282 )
| ( SV267
= ( apply @ SV282 @ SV41 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1822]) ).
thf(1963,plain,
! [SV268: $i,SV41: $i,SV283: $i] :
( ( ( function @ SV283 )
= $false )
| ( ( ~ ( relation @ SV283 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV41 @ SV268 ) @ SV283 )
| ( in @ SV41 @ ( relation_dom @ SV283 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1823]) ).
thf(1964,plain,
! [SV155: $i,SV195: $i,SV42: $i] :
( ( ( in @ SV42 @ ( relation_rng @ SV195 ) )
= $false )
| ( ( in @ SV42 @ SV155 )
= $false )
| ( ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SV155 @ SV195 ) ) )
= $true )
| ( ( relation @ SV195 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1824]) ).
thf(1965,plain,
! [SV284: $i,SV269: $i,SV42: $i] :
( ( ( ~ ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SV269 @ SV284 ) ) ) )
= $true )
| ( ( in @ SV42 @ SV269 )
= $true )
| ( ( relation @ SV284 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1825]) ).
thf(1966,plain,
! [SV285: $i,SV270: $i,SV42: $i] :
( ( ( ~ ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SV270 @ SV285 ) ) ) )
= $true )
| ( ( in @ SV42 @ ( relation_rng @ SV285 ) )
= $true )
| ( ( relation @ SV285 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1826]) ).
thf(1967,plain,
! [SV43: $i,SV271: $i] :
( ( ( ! [SY3900: $i] :
( ~ ( subset @ SY3900 @ SV271 )
| ( in @ SY3900 @ ( sK3_SY3278 @ SV271 @ SV43 ) ) ) )
= $true )
| ( ( ~ ( in @ SV271 @ ( sK2_B @ SV43 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1827]) ).
thf(1968,plain,
! [SV43: $i,SV271: $i] :
( ( ( in @ ( sK3_SY3278 @ SV271 @ SV43 ) @ ( sK2_B @ SV43 ) )
= $true )
| ( ( ~ ( in @ SV271 @ ( sK2_B @ SV43 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1828]) ).
thf(1969,plain,
! [SV338: $i,SV43: $i,SV327: $i] :
( ( ~ ( in @ SV327 @ ( sK2_B @ SV43 ) )
| ~ ( subset @ SV338 @ SV327 )
| ( in @ SV338 @ ( sK2_B @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(1970,plain,
! [SV328: $i,SV287: $i,SV93: $i,SV44: $i] :
( ( ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SV287 @ SV328 ) )
= $false )
| ( ( in @ SV44 @ SV287 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1832]) ).
thf(1971,plain,
! [SV310: $i,SV288: $i,SV93: $i,SV44: $i] :
( ( ( in @ ( ordered_pair @ SV44 @ SV93 ) @ ( cartesian_product2 @ SV288 @ SV310 ) )
= $false )
| ( ( in @ SV93 @ SV310 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1833]) ).
thf(1972,plain,
! [SV45: $i,SV232: $i] :
( ( ( ! [SY3847: $i] :
~ ( in @ ( ordered_pair @ ( sK26_C @ SV232 @ SV45 ) @ SY3847 ) @ SV45 ) )
= $true )
| ( ( ~ ( in @ ( sK26_C @ SV232 @ SV45 ) @ SV232 ) )
= $true )
| ( ( SV232
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1834]) ).
thf(1973,plain,
! [SV45: $i,SV232: $i] :
( ( ( in @ ( ordered_pair @ ( sK26_C @ SV232 @ SV45 ) @ ( sK27_SY3298 @ SV232 @ SV45 ) ) @ SV45 )
= $true )
| ( ( in @ ( sK26_C @ SV232 @ SV45 ) @ SV232 )
= $true )
| ( ( SV232
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1835]) ).
thf(1974,plain,
! [SV233: $i,SV45: $i] :
( ( ( ! [SY3848: $i] :
( ! [SY3481: $i] :
~ ( in @ ( ordered_pair @ SY3848 @ SY3481 ) @ SV45 )
| ( in @ SY3848 @ SV233 ) ) )
= $true )
| ( ( SV233
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1836]) ).
thf(1975,plain,
! [SV45: $i,SV233: $i] :
( ( ( ! [SY3850: $i] :
( ~ ( in @ SY3850 @ SV233 )
| ( in @ ( ordered_pair @ SY3850 @ ( sK25_D @ SY3850 @ SV233 @ SV45 ) ) @ SV45 ) ) )
= $true )
| ( ( SV233
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1837]) ).
thf(1976,plain,
! [SV236: $i,SV311: $i] :
( ( ( element @ SV311 @ SV236 )
= $false )
| ( ( empty @ SV311 )
= $true )
| ( ( empty @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1840]) ).
thf(1977,plain,
! [SV237: $i,SV312: $i] :
( ( ( empty @ SV312 )
= $false )
| ( ( element @ SV312 @ SV237 )
= $true )
| ( ( empty @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1841]) ).
thf(1978,plain,
! [SV120: $i,SV157: $i] :
( ( ( in @ ( sK43_C @ SV157 @ SV120 ) @ SV157 )
= $false )
| ( ( ( sK43_C @ SV157 @ SV120 )
= SV120 )
= $false )
| ( ( SV157
= ( singleton @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1842]) ).
thf(1979,plain,
! [SV158: $i,SV121: $i,SV329: $i] :
( ( ( ( SV329 != SV121 ) )
= $true )
| ( ( in @ SV329 @ SV158 )
= $true )
| ( ( SV158
= ( singleton @ SV121 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1843]) ).
thf(1980,plain,
! [SV121: $i,SV158: $i,SV330: $i] :
( ( ( ~ ( in @ SV330 @ SV158 ) )
= $true )
| ( ( SV330 = SV121 )
= $true )
| ( ( SV158
= ( singleton @ SV121 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1844]) ).
thf(1981,plain,
! [SV122: $i,SV159: $i] :
( ( ( ~ ( in @ ( sK74_C @ SV159 @ SV122 ) @ SV122 )
| ~ ( ( ( apply @ SV159 @ ( sK74_C @ SV159 @ SV122 ) )
!= ( sK74_C @ SV159 @ SV122 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV159 )
!= SV122 ) )
= $true )
| ( ( SV159
= ( identity_relation @ SV122 ) )
= $true )
| ( ( function @ SV159 )
= $false )
| ( ( relation @ SV159 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1845]) ).
thf(1982,plain,
! [SV239: $i,SV272: $i] :
( ( ( relation @ SV272 )
= $false )
| ( ( function @ SV272 )
= $false )
| ( ( ( SV272
!= ( identity_relation @ SV239 ) )
| ! [SY3901: $i] :
( ~ ( in @ SY3901 @ SV239 )
| ( ( apply @ SV272 @ SY3901 )
= SY3901 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1846]) ).
thf(1983,plain,
! [SV240: $i,SV273: $i] :
( ( ( relation @ SV273 )
= $false )
| ( ( function @ SV273 )
= $false )
| ( ( ( SV273
!= ( identity_relation @ SV240 ) )
| ( ( relation_dom @ SV273 )
= SV240 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1847]) ).
thf(1984,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ( function @ SV331 )
| ~ ( relation @ SV331 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) )
| ( SV331
= ( function_inverse @ SV46 ) ) )
= $true )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1848]) ).
thf(1985,plain,
! [SV46: $i] :
( ( ( ~ ! [SY3484: $i] :
( ~ ( function @ SY3484 )
| ~ ( relation @ SY3484 )
| ( SY3484
!= ( function_inverse @ SV46 ) )
| ~ ( ~ ~ ( ~ ! [SY3485: $i,SY3486: $i] :
( ( SY3486
!= ( apply @ SY3484 @ SY3485 ) )
| ~ ( in @ SY3485 @ ( relation_rng @ SV46 ) )
| ( SY3485
= ( apply @ SV46 @ SY3486 ) ) )
| ~ ! [SY3487: $i,SY3488: $i] :
( ( SY3488
!= ( apply @ SY3484 @ SY3487 ) )
| ~ ( in @ SY3487 @ ( relation_rng @ SV46 ) )
| ( in @ SY3488 @ ( relation_dom @ SV46 ) ) ) )
| ~ ~ ( ~ ! [SY3489: $i,SY3490: $i] :
( ( SY3489
!= ( apply @ SV46 @ SY3490 ) )
| ~ ( in @ SY3490 @ ( relation_dom @ SV46 ) )
| ( SY3490
= ( apply @ SY3484 @ SY3489 ) ) )
| ~ ! [SY3491: $i] :
( ! [SY3492: $i] :
( ( SY3491
!= ( apply @ SV46 @ SY3492 ) )
| ~ ( in @ SY3492 @ ( relation_dom @ SV46 ) ) )
| ( in @ SY3491 @ ( relation_rng @ SV46 ) ) ) ) ) ) )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1849]) ).
thf(1986,plain,
! [SV46: $i] :
( ( ( ~ ! [SY3493: $i] :
( ~ ( function @ SY3493 )
| ~ ( relation @ SY3493 )
| ( SY3493
!= ( function_inverse @ SV46 ) )
| ( ( relation_dom @ SY3493 )
= ( relation_rng @ SV46 ) ) ) )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1849]) ).
thf(1987,plain,
! [SV47: $i,SV123: $i,SV313: $i] :
( ( ( relation @ SV313 )
= $false )
| ( ( ~ ( ~ ( ! [SY3936: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ SY3936 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3936 @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV123 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV313 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK10_SY3288 @ SV313 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY3288 @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV123 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV313 ) ) )
| ( SV313
= ( relation_composition @ SV47 @ SV123 ) ) )
= $true )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1850]) ).
thf(1988,plain,
! [SV123: $i,SV47: $i,SV314: $i] :
( ( ( relation @ SV314 )
= $false )
| ( ( ( SV314
!= ( relation_composition @ SV47 @ SV123 ) )
| ~ ( ~ ! [SY3937: $i,SY3938: $i] :
( ! [SY3706: $i] :
( ~ ( in @ ( ordered_pair @ SY3937 @ SY3706 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3706 @ SY3938 ) @ SV123 ) )
| ( in @ ( ordered_pair @ SY3937 @ SY3938 ) @ SV314 ) )
| ~ ! [SY3940: $i,SY3941: $i] :
( ~ ( in @ ( ordered_pair @ SY3940 @ SY3941 ) @ SV314 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3940 @ ( sK7_F @ SY3941 @ SY3940 @ SV314 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY3941 @ SY3940 @ SV314 @ SV123 @ SV47 ) @ SY3941 ) @ SV123 ) ) ) ) )
= $true )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1851]) ).
thf(1989,plain,
! [SV241: $i,SV94: $i,SV198: $i,SV49: $i] :
( ( ( in @ SV49 @ SV198 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ SV241 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SV198 ) @ SV241 ) )
= $true )
| ( ( relation @ SV241 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1854]) ).
thf(1990,plain,
! [SV293: $i,SV94: $i,SV49: $i,SV315: $i] :
( ( ( relation @ SV315 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SV293 ) @ SV315 ) )
| ( in @ SV49 @ SV293 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1855]) ).
thf(1991,plain,
! [SV294: $i,SV94: $i,SV49: $i,SV316: $i] :
( ( ( relation @ SV316 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SV294 ) @ SV316 ) )
| ( in @ ( ordered_pair @ SV49 @ SV94 ) @ SV316 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1856]) ).
thf(1992,plain,
! [SV124: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK11_B @ SV124 ) @ ( relation_dom @ SV124 ) )
| ~ ( in @ ( sK12_SY3289 @ SV124 ) @ ( relation_dom @ SV124 ) ) )
| ( ( apply @ SV124 @ ( sK11_B @ SV124 ) )
!= ( apply @ SV124 @ ( sK12_SY3289 @ SV124 ) ) ) ) )
= $true )
| ( ( one_to_one @ SV124 )
= $true )
| ( ( function @ SV124 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1858]) ).
thf(1993,plain,
! [SV124: $i] :
( ( ( ( ( sK11_B @ SV124 )
!= ( sK12_SY3289 @ SV124 ) ) )
= $true )
| ( ( one_to_one @ SV124 )
= $true )
| ( ( function @ SV124 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1859]) ).
thf(1994,plain,
! [SV339: $i,SV125: $i,SV332: $i] :
( ( ( ~ ( in @ SV332 @ ( relation_dom @ SV125 ) )
| ~ ( in @ SV339 @ ( relation_dom @ SV125 ) )
| ( ( apply @ SV125 @ SV332 )
!= ( apply @ SV125 @ SV339 ) )
| ( SV332 = SV339 ) )
= $true )
| ( ( one_to_one @ SV125 )
= $false )
| ( ( function @ SV125 )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1860]) ).
thf(1995,plain,
! [SV51: $i,SV161: $i,SV199: $i] :
( ( ( ~ ( ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV199 )
| ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV51 ) ) )
= $false )
| ( ( SV199
= ( set_union2 @ SV51 @ SV161 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1861]) ).
thf(1996,plain,
! [SV51: $i,SV161: $i,SV199: $i] :
( ( ( ~ ( ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV199 )
| ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV161 ) ) )
= $false )
| ( ( SV199
= ( set_union2 @ SV51 @ SV161 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1861]) ).
thf(1997,plain,
! [SV51: $i,SV161: $i,SV199: $i] :
( ( ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV51 )
= $true )
| ( ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV161 )
= $true )
| ( ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV199 )
= $true )
| ( ( SV199
= ( set_union2 @ SV51 @ SV161 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1862]) ).
thf(1998,plain,
! [SV162: $i,SV51: $i,SV200: $i,SV340: $i] :
( ( ( ~ ( in @ SV340 @ SV200 )
| ( in @ SV340 @ SV51 )
| ( in @ SV340 @ SV162 ) )
= $true )
| ( ( SV200
= ( set_union2 @ SV51 @ SV162 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(1999,plain,
! [SV162: $i,SV200: $i,SV51: $i] :
( ( ( ~ ! [SY3796: $i] :
( ~ ( in @ SY3796 @ SV51 )
| ( in @ SY3796 @ SV200 ) )
| ~ ! [SY3797: $i] :
( ~ ( in @ SY3797 @ SV162 )
| ( in @ SY3797 @ SV200 ) ) )
= $false )
| ( ( SV200
= ( set_union2 @ SV51 @ SV162 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1864]) ).
thf(2000,plain,
! [SV52: $i,SV243: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK30_C @ SV243 @ SV52 ) @ ( sK31_SY3299 @ SV243 @ SV52 ) ) @ SV52 ) )
= $false )
| ( ( subset @ SV52 @ SV243 )
= $true )
| ( ( relation @ SV243 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1865]) ).
thf(2001,plain,
! [SV52: $i,SV243: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK30_C @ SV243 @ SV52 ) @ ( sK31_SY3299 @ SV243 @ SV52 ) ) @ SV243 ) )
= $false )
| ( ( subset @ SV52 @ SV243 )
= $true )
| ( ( relation @ SV243 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1865]) ).
thf(2002,plain,
! [SV244: $i,SV52: $i,SV341: $i] :
( ( ( ! [SY3949: $i] :
( ~ ( in @ ( ordered_pair @ SV341 @ SY3949 ) @ SV52 )
| ( in @ ( ordered_pair @ SV341 @ SY3949 ) @ SV244 ) ) )
= $true )
| ( ( subset @ SV52 @ SV244 )
= $false )
| ( ( relation @ SV244 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1866]) ).
thf(2003,plain,
! [SV245: $i,SV295: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK46_SY3307 @ SV295 @ SV245 ) @ SV245 )
| ~ ~ ( in @ ( sK45_C @ SV295 @ SV245 ) @ ( sK46_SY3307 @ SV295 @ SV245 ) ) )
| ~ ( in @ ( sK45_C @ SV295 @ SV245 ) @ SV295 ) ) )
= $false )
| ( ( SV295
= ( set_meet @ SV245 ) )
= $true )
| ( ( SV245 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1867]) ).
thf(2004,plain,
! [SV295: $i,SV245: $i] :
( ( ( ~ ( ! [SY3917: $i] :
( ~ ( in @ SY3917 @ SV245 )
| ( in @ ( sK45_C @ SV295 @ SV245 ) @ SY3917 ) )
| ( in @ ( sK45_C @ SV295 @ SV245 ) @ SV295 ) ) )
= $false )
| ( ( SV295
= ( set_meet @ SV245 ) )
= $true )
| ( ( SV245 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1867]) ).
thf(2005,plain,
! [SV246: $i,SV296: $i] :
( ( ( ~ ! [SY3918: $i] :
( ~ ( ~ ( in @ ( sK44_D @ SY3918 @ SV296 @ SV246 ) @ SV246 )
| ~ ~ ( in @ SY3918 @ ( sK44_D @ SY3918 @ SV296 @ SV246 ) ) )
| ( in @ SY3918 @ SV296 ) )
| ~ ! [SY3919: $i] :
( ~ ( in @ SY3919 @ SV296 )
| ! [SY3865: $i] :
( ~ ( in @ SY3865 @ SV246 )
| ( in @ SY3919 @ SY3865 ) ) ) )
= $false )
| ( ( SV296
= ( set_meet @ SV246 ) )
= $false )
| ( ( SV246 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1868]) ).
thf(2006,plain,
! [SV247: $i,SV317: $i] :
( ( ( SV317
= ( set_meet @ SV247 ) )
= $false )
| ( ( SV317 = empty_set )
= $true )
| ( ( SV247 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1869]) ).
thf(2007,plain,
! [SV248: $i,SV318: $i] :
( ( ( SV318 = empty_set )
= $false )
| ( ( SV318
= ( set_meet @ SV248 ) )
= $true )
| ( ( SV248 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1870]) ).
thf(2008,plain,
! [SV53: $i,SV297: $i,SV319: $i] :
( ( ( ~ ( ~ ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ ( sK57_D @ SV319 @ SV297 @ SV53 ) ) @ SV297 )
| ~ ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ SV319 ) )
| ~ ~ ( ~ ( ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ SV319 ) )
| ~ ( ( in @ ( apply @ SV53 @ ( sK57_D @ SV319 @ SV297 @ SV53 ) ) @ SV297 )
| ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ SV319 ) ) ) )
= $false )
| ( ( SV319
= ( relation_inverse_image @ SV53 @ SV297 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1871]) ).
thf(2009,plain,
! [SV298: $i,SV53: $i,SV320: $i] :
( ( ( SV320
= ( relation_inverse_image @ SV53 @ SV298 ) )
= $false )
| ( ( ~ ( ~ ! [SY3942: $i] :
( ~ ( in @ SY3942 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SY3942 ) @ SV298 )
| ( in @ SY3942 @ SV320 ) )
| ~ ~ ( ~ ! [SY3943: $i] :
( ~ ( in @ SY3943 @ SV320 )
| ( in @ SY3943 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY3944: $i] :
( ~ ( in @ SY3944 @ SV320 )
| ( in @ ( apply @ SV53 @ SY3944 ) @ SV298 ) ) ) ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1872]) ).
thf(2010,plain,
! [SV54: $i,SV165: $i,SV201: $i] :
( ( ( ~ ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV54 ) )
= $true )
| ( ( ~ ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV165 ) )
= $true )
| ( ( ~ ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV201 ) )
= $true )
| ( ( SV201
= ( set_intersection2 @ SV54 @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1873]) ).
thf(2011,plain,
! [SV54: $i,SV165: $i,SV201: $i] :
( ( ( ~ ( ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV54 )
| ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV201 ) ) )
= $false )
| ( ( SV201
= ( set_intersection2 @ SV54 @ SV165 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1874]) ).
thf(2012,plain,
! [SV54: $i,SV165: $i,SV201: $i] :
( ( ( ~ ( ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV165 )
| ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV201 ) ) )
= $false )
| ( ( SV201
= ( set_intersection2 @ SV54 @ SV165 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1874]) ).
thf(2013,plain,
! [SV202: $i,SV166: $i,SV54: $i,SV342: $i] :
( ( ( ~ ( in @ SV342 @ SV54 )
| ~ ( in @ SV342 @ SV166 )
| ( in @ SV342 @ SV202 ) )
= $true )
| ( ( SV202
= ( set_intersection2 @ SV54 @ SV166 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1875]) ).
thf(2014,plain,
! [SV166: $i,SV54: $i,SV202: $i] :
( ( ( ~ ! [SY3799: $i] :
( ~ ( in @ SY3799 @ SV202 )
| ( in @ SY3799 @ SV54 ) )
| ~ ! [SY3800: $i] :
( ~ ( in @ SY3800 @ SV202 )
| ( in @ SY3800 @ SV166 ) ) )
= $false )
| ( ( SV202
= ( set_intersection2 @ SV54 @ SV166 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1876]) ).
thf(2015,plain,
! [SV55: $i,SV169: $i,SV203: $i] :
( ( ( ~ ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV55 ) )
= $true )
| ( ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV169 )
= $true )
| ( ( ~ ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV203 ) )
= $true )
| ( ( SV203
= ( set_difference @ SV55 @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1877]) ).
thf(2016,plain,
! [SV55: $i,SV169: $i,SV203: $i] :
( ( ( ~ ( ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV55 )
| ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV203 ) ) )
= $false )
| ( ( SV203
= ( set_difference @ SV55 @ SV169 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1878]) ).
thf(2017,plain,
! [SV55: $i,SV169: $i,SV203: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV169 )
| ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV203 ) ) )
= $false )
| ( ( SV203
= ( set_difference @ SV55 @ SV169 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1878]) ).
thf(2018,plain,
! [SV204: $i,SV170: $i,SV55: $i,SV343: $i] :
( ( ( ~ ( in @ SV343 @ SV55 )
| ( in @ SV343 @ SV170 )
| ( in @ SV343 @ SV204 ) )
= $true )
| ( ( SV204
= ( set_difference @ SV55 @ SV170 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1879]) ).
thf(2019,plain,
! [SV170: $i,SV55: $i,SV204: $i] :
( ( ( ~ ! [SY3802: $i] :
( ~ ( in @ SY3802 @ SV204 )
| ( in @ SY3802 @ SV55 ) )
| ~ ! [SY3803: $i] :
( ~ ( in @ SY3803 @ SV204 )
| ~ ( in @ SY3803 @ SV170 ) ) )
= $false )
| ( ( SV204
= ( set_difference @ SV55 @ SV170 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1880]) ).
thf(2020,plain,
! [SV56: $i,SV299: $i] :
( ( ( ~ ( ! [SY3926: $i] :
( ( ( sK19_C @ SV299 @ SV56 )
!= ( apply @ SV56 @ SY3926 ) )
| ~ ( in @ SY3926 @ ( relation_dom @ SV56 ) ) )
| ~ ( in @ ( sK19_C @ SV299 @ SV56 ) @ SV299 ) ) )
= $false )
| ( ( SV299
= ( relation_rng @ SV56 ) )
= $true )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1881]) ).
thf(2021,plain,
! [SV56: $i,SV299: $i] :
( ( ( ~ ( ~ ( ( ( sK19_C @ SV299 @ SV56 )
!= ( apply @ SV56 @ ( sK20_SY3294 @ SV299 @ SV56 ) ) )
| ~ ( in @ ( sK20_SY3294 @ SV299 @ SV56 ) @ ( relation_dom @ SV56 ) ) )
| ( in @ ( sK19_C @ SV299 @ SV56 ) @ SV299 ) ) )
= $false )
| ( ( SV299
= ( relation_rng @ SV56 ) )
= $true )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1881]) ).
thf(2022,plain,
! [SV300: $i,SV56: $i] :
( ( ( ~ ! [SY3927: $i] :
( ! [SY3554: $i] :
( ( SY3927
!= ( apply @ SV56 @ SY3554 ) )
| ~ ( in @ SY3554 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY3927 @ SV300 ) )
| ~ ! [SY3929: $i] :
( ~ ( in @ SY3929 @ SV300 )
| ~ ( ( SY3929
!= ( apply @ SV56 @ ( sK18_D @ SY3929 @ SV300 @ SV56 ) ) )
| ~ ( in @ ( sK18_D @ SY3929 @ SV300 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) ) )
= $false )
| ( ( SV300
= ( relation_rng @ SV56 ) )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1882]) ).
thf(2023,plain,
! [SV57: $i,SV171: $i,SV205: $i] :
( ( ( ~ ( ~ ( in @ ( sK38_D @ SV205 @ SV171 @ SV57 ) @ SV205 )
| ( ( sK38_D @ SV205 @ SV171 @ SV57 )
!= SV57 ) ) )
= $false )
| ( ( SV205
= ( unordered_pair @ SV57 @ SV171 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1883]) ).
thf(2024,plain,
! [SV57: $i,SV171: $i,SV205: $i] :
( ( ( ~ ( ~ ( in @ ( sK38_D @ SV205 @ SV171 @ SV57 ) @ SV205 )
| ( ( sK38_D @ SV205 @ SV171 @ SV57 )
!= SV171 ) ) )
= $false )
| ( ( SV205
= ( unordered_pair @ SV57 @ SV171 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1883]) ).
thf(2025,plain,
! [SV57: $i,SV171: $i,SV205: $i] :
( ( ( ( sK38_D @ SV205 @ SV171 @ SV57 )
= SV57 )
= $true )
| ( ( ( sK38_D @ SV205 @ SV171 @ SV57 )
= SV171 )
= $true )
| ( ( in @ ( sK38_D @ SV205 @ SV171 @ SV57 ) @ SV205 )
= $true )
| ( ( SV205
= ( unordered_pair @ SV57 @ SV171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1884]) ).
thf(2026,plain,
! [SV172: $i,SV57: $i,SV206: $i,SV344: $i] :
( ( ( ~ ( in @ SV344 @ SV206 )
| ( SV344 = SV57 )
| ( SV344 = SV172 ) )
= $true )
| ( ( SV206
= ( unordered_pair @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(2027,plain,
! [SV172: $i,SV206: $i,SV57: $i] :
( ( ( ~ ! [SY3805: $i] :
( ( SY3805 != SV57 )
| ( in @ SY3805 @ SV206 ) )
| ~ ! [SY3806: $i] :
( ( SY3806 != SV172 )
| ( in @ SY3806 @ SV206 ) ) )
= $false )
| ( ( SV206
= ( unordered_pair @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1886]) ).
thf(2028,plain,
! [SV58: $i,SV96: $i,SV321: $i] :
( ( ( ~ ( function @ SV321 ) )
= $true )
| ( ( ~ ( relation @ SV321 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK67_D @ SV321 @ SV96 @ SV58 ) @ ( relation_dom @ SV96 ) )
| ~ ( ( ( apply @ SV96 @ ( sK67_D @ SV321 @ SV96 @ SV58 ) )
!= ( apply @ SV321 @ ( sK67_D @ SV321 @ SV96 @ SV58 ) ) ) ) )
| ( ( relation_dom @ SV96 )
!= ( set_intersection2 @ ( relation_dom @ SV321 ) @ SV58 ) )
| ( SV96
= ( relation_dom_restriction @ SV321 @ SV58 ) ) )
= $true )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1887]) ).
thf(2029,plain,
! [SV58: $i,SV96: $i] :
( ( ( ! [SY3662: $i] :
( ~ ( function @ SY3662 )
| ~ ( relation @ SY3662 )
| ( SV96
!= ( relation_dom_restriction @ SY3662 @ SV58 ) )
| ! [SY3663: $i] :
( ~ ( in @ SY3663 @ ( relation_dom @ SV96 ) )
| ( ( apply @ SV96 @ SY3663 )
= ( apply @ SY3662 @ SY3663 ) ) ) ) )
= $true )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1888]) ).
thf(2030,plain,
! [SV58: $i,SV96: $i] :
( ( ( ! [SY3664: $i] :
( ~ ( function @ SY3664 )
| ~ ( relation @ SY3664 )
| ( SV96
!= ( relation_dom_restriction @ SY3664 @ SV58 ) )
| ( ( relation_dom @ SV96 )
= ( set_intersection2 @ ( relation_dom @ SY3664 ) @ SV58 ) ) ) )
= $true )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1889]) ).
thf(2031,plain,
! [SV59: $i,SV249: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV249 ) ) )
= $false )
| ( ( SV59 = SV249 )
= $true )
| ( ( relation @ SV249 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1890]) ).
thf(2032,plain,
! [SV59: $i,SV249: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV249 ) ) )
= $false )
| ( ( SV59 = SV249 )
= $true )
| ( ( relation @ SV249 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1890]) ).
thf(2033,plain,
! [SV250: $i,SV59: $i] :
( ( ( ~ ! [SY3868: $i,SY3869: $i] :
( ~ ( in @ ( ordered_pair @ SY3868 @ SY3869 ) @ SV59 )
| ( in @ ( ordered_pair @ SY3868 @ SY3869 ) @ SV250 ) )
| ~ ! [SY3870: $i,SY3871: $i] :
( ~ ( in @ ( ordered_pair @ SY3870 @ SY3871 ) @ SV250 )
| ( in @ ( ordered_pair @ SY3870 @ SY3871 ) @ SV59 ) ) )
= $false )
| ( ( SV59 = SV250 )
= $false )
| ( ( relation @ SV250 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1891]) ).
thf(2034,plain,
! [SV333: $i,SV130: $i,SV173: $i] :
( ( ( ~ ( in @ ( sK23_C @ SV173 @ SV130 ) @ SV333 ) )
= $true )
| ( ( ~ ( in @ SV333 @ SV130 ) )
= $true )
| ( ( ~ ( in @ ( sK23_C @ SV173 @ SV130 ) @ SV173 ) )
= $true )
| ( ( SV173
= ( union @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1892]) ).
thf(2035,plain,
! [SV130: $i,SV173: $i] :
( ( ( ~ ( in @ ( sK23_C @ SV173 @ SV130 ) @ ( sK24_SY3296 @ SV173 @ SV130 ) ) )
= $false )
| ( ( in @ ( sK23_C @ SV173 @ SV130 ) @ SV173 )
= $true )
| ( ( SV173
= ( union @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1893]) ).
thf(2036,plain,
! [SV130: $i,SV173: $i] :
( ( ( ~ ( in @ ( sK24_SY3296 @ SV173 @ SV130 ) @ SV130 ) )
= $false )
| ( ( in @ ( sK23_C @ SV173 @ SV130 ) @ SV173 )
= $true )
| ( ( SV173
= ( union @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1893]) ).
thf(2037,plain,
! [SV174: $i,SV131: $i,SV334: $i] :
( ( ( ! [SY3948: $i] :
( ~ ( in @ SV334 @ SY3948 )
| ~ ( in @ SY3948 @ SV131 ) ) )
= $true )
| ( ( in @ SV334 @ SV174 )
= $true )
| ( ( SV174
= ( union @ SV131 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1894]) ).
thf(2038,plain,
! [SV131: $i,SV174: $i,SV335: $i] :
( ( ( ~ ( in @ SV335 @ SV174 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV335 @ ( sK22_D @ SV335 @ SV174 @ SV131 ) )
| ~ ( in @ ( sK22_D @ SV335 @ SV174 @ SV131 ) @ SV131 ) ) )
= $true )
| ( ( SV174
= ( union @ SV131 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1895]) ).
thf(2039,plain,
! [SV336: $i,SV301: $i,SV98: $i,SV61: $i] :
( ( ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SV301 @ SV336 ) )
= $false )
| ( ( in @ SV61 @ SV301 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1897]) ).
thf(2040,plain,
! [SV322: $i,SV302: $i,SV98: $i,SV61: $i] :
( ( ( in @ ( ordered_pair @ SV61 @ SV98 ) @ ( cartesian_product2 @ SV302 @ SV322 ) )
= $false )
| ( ( in @ SV98 @ SV322 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1898]) ).
thf(2041,plain,
! [SV62: $i,SV208: $i,SV175: $i] :
( ( ( ~ ( in @ SV175 @ ( relation_dom @ SV208 ) ) )
= $true )
| ( ( ~ ( in @ SV175 @ SV62 ) )
= $true )
| ( ( in @ SV175 @ ( relation_dom @ ( relation_dom_restriction @ SV208 @ SV62 ) ) )
= $true )
| ( ( function @ SV208 )
= $false )
| ( ( relation @ SV208 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1899]) ).
thf(2042,plain,
! [SV62: $i,SV276: $i,SV303: $i] :
( ( ( function @ SV303 )
= $false )
| ( ( ~ ( relation @ SV303 ) )
= $true )
| ( ( ~ ( in @ SV276 @ ( relation_dom @ ( relation_dom_restriction @ SV303 @ SV62 ) ) )
| ( in @ SV276 @ ( relation_dom @ SV303 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1900]) ).
thf(2043,plain,
! [SV62: $i,SV277: $i,SV304: $i] :
( ( ( function @ SV304 )
= $false )
| ( ( ~ ( relation @ SV304 ) )
= $true )
| ( ( ~ ( in @ SV277 @ ( relation_dom @ ( relation_dom_restriction @ SV304 @ SV62 ) ) )
| ( in @ SV277 @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1901]) ).
thf(2044,plain,
! [SV209: $i,SV176: $i,SV63: $i,SV345: $i] :
( ( ( ! [SY3950: $i] :
( ~ ( in @ SV345 @ SV63 )
| ~ ( in @ SY3950 @ SV176 )
| ( ( sK34_D @ SV209 @ SV176 @ SV63 )
!= ( ordered_pair @ SV345 @ SY3950 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK34_D @ SV209 @ SV176 @ SV63 ) @ SV209 ) )
= $true )
| ( ( SV209
= ( cartesian_product2 @ SV63 @ SV176 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1902]) ).
thf(2045,plain,
! [SV63: $i,SV176: $i,SV209: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK35_SY3303 @ SV209 @ SV176 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK36_SY3305 @ SV209 @ SV176 @ SV63 ) @ SV176 ) )
| ( ( sK34_D @ SV209 @ SV176 @ SV63 )
!= ( ordered_pair @ ( sK35_SY3303 @ SV209 @ SV176 @ SV63 ) @ ( sK36_SY3305 @ SV209 @ SV176 @ SV63 ) ) ) )
= $false )
| ( ( in @ ( sK34_D @ SV209 @ SV176 @ SV63 ) @ SV209 )
= $true )
| ( ( SV209
= ( cartesian_product2 @ SV63 @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1903]) ).
thf(2046,plain,
! [SV210: $i,SV346: $i,SV177: $i,SV63: $i] :
( ( ( ! [SY3951: $i,SY3952: $i] :
( ~ ( in @ SY3951 @ SV63 )
| ~ ( in @ SY3952 @ SV177 )
| ( SV346
!= ( ordered_pair @ SY3951 @ SY3952 ) ) )
| ( in @ SV346 @ SV210 ) )
= $true )
| ( ( SV210
= ( cartesian_product2 @ SV63 @ SV177 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1904]) ).
thf(2047,plain,
! [SV63: $i,SV177: $i,SV210: $i,SV347: $i] :
( ( ( ~ ( in @ SV347 @ SV210 )
| ~ ( ~ ~ ( ~ ( in @ ( sK32_E @ SV347 @ SV210 @ SV177 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK33_SY3300 @ SV347 @ SV210 @ SV177 @ SV63 ) @ SV177 ) )
| ( SV347
!= ( ordered_pair @ ( sK32_E @ SV347 @ SV210 @ SV177 @ SV63 ) @ ( sK33_SY3300 @ SV347 @ SV210 @ SV177 @ SV63 ) ) ) ) )
= $true )
| ( ( SV210
= ( cartesian_product2 @ SV63 @ SV177 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1905]) ).
thf(2048,plain,
! [SV180: $i,SV64: $i,SV211: $i,SV323: $i] :
( ( ( ~ ( in @ SV323 @ ( relation_dom @ SV211 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV323 @ SV64 ) @ SV211 ) )
= $true )
| ( ( ~ ( in @ SV323 @ SV180 ) )
= $true )
| ( ( in @ SV64 @ ( relation_image @ SV211 @ SV180 ) )
= $true )
| ( ( relation @ SV211 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1907]) ).
thf(2049,plain,
! [SV64: $i,SV181: $i,SV212: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK76_D @ SV212 @ SV181 @ SV64 ) @ ( relation_dom @ SV212 ) )
| ~ ( in @ ( ordered_pair @ ( sK76_D @ SV212 @ SV181 @ SV64 ) @ SV64 ) @ SV212 ) ) )
= $false )
| ( ( in @ SV64 @ ( relation_image @ SV212 @ SV181 ) )
= $false )
| ( ( relation @ SV212 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1908]) ).
thf(2050,plain,
! [SV64: $i,SV181: $i,SV212: $i] :
( ( ( ~ ( in @ ( sK76_D @ SV212 @ SV181 @ SV64 ) @ SV181 ) )
= $false )
| ( ( in @ SV64 @ ( relation_image @ SV212 @ SV181 ) )
= $false )
| ( ( relation @ SV212 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1908]) ).
thf(2051,plain,
! [SV66: $i,SV348: $i] :
( ( ( ~ ( in @ SV348 @ ( relation_dom @ SV66 ) )
| ! [SY3953: $i] :
( ( SY3953
!= ( apply @ SV66 @ SV348 ) )
| ( in @ ( ordered_pair @ SV348 @ SY3953 ) @ SV66 ) ) )
= $true )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1909]) ).
thf(2052,plain,
! [SV66: $i,SV349: $i] :
( ( ( ~ ( in @ SV349 @ ( relation_dom @ SV66 ) )
| ! [SY3954: $i] :
( ~ ( in @ ( ordered_pair @ SV349 @ SY3954 ) @ SV66 )
| ( SY3954
= ( apply @ SV66 @ SV349 ) ) ) )
= $true )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1910]) ).
thf(2053,plain,
! [SV66: $i,SV350: $i] :
( ( ( ( in @ SV350 @ ( relation_dom @ SV66 ) )
| ! [SY3955: $i] :
( ( SY3955
!= ( apply @ SV66 @ SV350 ) )
| ( SY3955 = empty_set ) ) )
= $true )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1911]) ).
thf(2054,plain,
! [SV66: $i,SV351: $i] :
( ( ( ( in @ SV351 @ ( relation_dom @ SV66 ) )
| ! [SY3956: $i] :
( ( SY3956 != empty_set )
| ( SY3956
= ( apply @ SV66 @ SV351 ) ) ) )
= $true )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1912]) ).
thf(2055,plain,
! [SV73: $i,SV215: $i,SV7: $i] :
( ( ( in @ SV7 @ ( relation_dom @ ( relation_composition @ SV215 @ SV73 ) ) )
= $false )
| ( ( ( apply @ ( relation_composition @ SV215 @ SV73 ) @ SV7 )
= ( apply @ SV73 @ ( apply @ SV215 @ SV7 ) ) )
= $true )
| ( ( function @ SV215 )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( function @ SV73 )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1913]) ).
thf(2056,plain,
! [SV216: $i,SV74: $i,SV8: $i] :
( ( ( in @ SV8 @ ( relation_dom @ SV74 ) )
= $false )
| ( ( ( apply @ ( relation_composition @ SV74 @ SV216 ) @ SV8 )
= ( apply @ SV216 @ ( apply @ SV74 @ SV8 ) ) )
= $true )
| ( ( function @ SV216 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1914]) ).
thf(2057,plain,
! [SV26: $i,SV88: $i,SV253: $i] :
( ( ( ~ ( ~ ( in @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) @ SV26 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV88 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 ) ) )
= $false )
| ( ( SV253
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $true )
| ( ( relation @ SV253 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1915]) ).
thf(2058,plain,
! [SV26: $i,SV88: $i,SV253: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) @ SV26 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV88 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 ) ) ) )
= $false )
| ( ( SV253
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $true )
| ( ( relation @ SV253 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1915]) ).
thf(2059,plain,
! [SV254: $i,SV88: $i,SV26: $i] :
( ( ( ~ ! [SY3872: $i,SY3873: $i] :
( ~ ( in @ SY3873 @ SV26 )
| ~ ( in @ ( ordered_pair @ SY3872 @ SY3873 ) @ SV88 )
| ( in @ ( ordered_pair @ SY3872 @ SY3873 ) @ SV254 ) )
| ~ ~ ( ~ ! [SY3874: $i,SY3875: $i] :
( ~ ( in @ ( ordered_pair @ SY3874 @ SY3875 ) @ SV254 )
| ( in @ SY3875 @ SV26 ) )
| ~ ! [SY3876: $i,SY3877: $i] :
( ~ ( in @ ( ordered_pair @ SY3876 @ SY3877 ) @ SV254 )
| ( in @ ( ordered_pair @ SY3876 @ SY3877 ) @ SV88 ) ) ) )
= $false )
| ( ( SV254
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1916]) ).
thf(2060,plain,
! [SV256: $i,SV278: $i,SV27: $i] :
( ( ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SV278 @ SV256 ) ) )
= $false )
| ( ( in @ SV27 @ SV256 )
= $true )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1918]) ).
thf(2061,plain,
! [SV257: $i,SV279: $i,SV27: $i] :
( ( ( in @ SV27 @ ( relation_dom @ ( relation_dom_restriction @ SV279 @ SV257 ) ) )
= $false )
| ( ( in @ SV27 @ ( relation_dom @ SV279 ) )
= $true )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1919]) ).
thf(2062,plain,
! [SV28: $i,SV218: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV218 @ SV28 ) @ ( sK14_SY3290 @ SV218 @ SV28 ) ) @ SV218 )
| ~ ( in @ ( ordered_pair @ ( sK14_SY3290 @ SV218 @ SV28 ) @ ( sK13_C @ SV218 @ SV28 ) ) @ SV28 ) )
= $true )
| ( ( SV218
= ( relation_inverse @ SV28 ) )
= $true )
| ( ( relation @ SV218 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1920]) ).
thf(2063,plain,
! [SV28: $i,SV218: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK13_C @ SV218 @ SV28 ) @ ( sK14_SY3290 @ SV218 @ SV28 ) ) @ SV218 )
| ( in @ ( ordered_pair @ ( sK14_SY3290 @ SV218 @ SV28 ) @ ( sK13_C @ SV218 @ SV28 ) ) @ SV28 ) )
= $true )
| ( ( SV218
= ( relation_inverse @ SV28 ) )
= $true )
| ( ( relation @ SV218 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1921]) ).
thf(2064,plain,
! [SV28: $i,SV219: $i] :
( ( ( ~ ! [SY3815: $i,SY3816: $i] :
( ~ ( in @ ( ordered_pair @ SY3815 @ SY3816 ) @ SV219 )
| ( in @ ( ordered_pair @ SY3816 @ SY3815 ) @ SV28 ) ) )
= $false )
| ( ( SV219
= ( relation_inverse @ SV28 ) )
= $false )
| ( ( relation @ SV219 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1922]) ).
thf(2065,plain,
! [SV219: $i,SV28: $i] :
( ( ( ~ ! [SY3817: $i,SY3818: $i] :
( ~ ( in @ ( ordered_pair @ SY3818 @ SY3817 ) @ SV28 )
| ( in @ ( ordered_pair @ SY3817 @ SY3818 ) @ SV219 ) ) )
= $false )
| ( ( SV219
= ( relation_inverse @ SV28 ) )
= $false )
| ( ( relation @ SV219 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1922]) ).
thf(2066,plain,
! [SV305: $i,SV280: $i,SV29: $i] :
( ( ( ~ ( ! [SY3932: $i] :
( ~ ( in @ SY3932 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3932 @ SV280 )
| ( ( sK61_D @ SV305 @ SV280 @ SV29 )
!= ( apply @ SV29 @ SY3932 ) ) )
| ~ ( in @ ( sK61_D @ SV305 @ SV280 @ SV29 ) @ SV305 ) ) )
= $false )
| ( ( SV305
= ( relation_image @ SV29 @ SV280 ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1923]) ).
thf(2067,plain,
! [SV29: $i,SV280: $i,SV305: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) @ SV280 ) )
| ( ( sK61_D @ SV305 @ SV280 @ SV29 )
!= ( apply @ SV29 @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) ) ) )
| ( in @ ( sK61_D @ SV305 @ SV280 @ SV29 ) @ SV305 ) ) )
= $false )
| ( ( SV305
= ( relation_image @ SV29 @ SV280 ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1923]) ).
thf(2068,plain,
! [SV306: $i,SV281: $i,SV29: $i] :
( ( ( ~ ! [SY3933: $i] :
( ! [SY3910: $i] :
( ~ ( in @ SY3910 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3910 @ SV281 )
| ( SY3933
!= ( apply @ SV29 @ SY3910 ) ) )
| ( in @ SY3933 @ SV306 ) )
| ~ ! [SY3935: $i] :
( ~ ( in @ SY3935 @ SV306 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SY3935 @ SV306 @ SV281 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK60_E @ SY3935 @ SV306 @ SV281 @ SV29 ) @ SV281 ) )
| ( SY3935
!= ( apply @ SV29 @ ( sK60_E @ SY3935 @ SV306 @ SV281 @ SV29 ) ) ) ) ) )
= $false )
| ( ( SV306
= ( relation_image @ SV29 @ SV281 ) )
= $false )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1924]) ).
thf(2069,plain,
! [SV30: $i,SV220: $i,SV258: $i] :
( ( ( ! [SY3880: $i] :
( ~ ( in @ ( ordered_pair @ SY3880 @ ( sK55_D @ SV258 @ SV220 @ SV30 ) ) @ SV30 )
| ~ ( in @ SY3880 @ SV220 ) ) )
= $true )
| ( ( ~ ( in @ ( sK55_D @ SV258 @ SV220 @ SV30 ) @ SV258 ) )
= $true )
| ( ( SV258
= ( relation_image @ SV30 @ SV220 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1925]) ).
thf(2070,plain,
! [SV30: $i,SV220: $i,SV258: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_SY3315 @ SV258 @ SV220 @ SV30 ) @ ( sK55_D @ SV258 @ SV220 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK56_SY3315 @ SV258 @ SV220 @ SV30 ) @ SV220 ) ) )
= $true )
| ( ( in @ ( sK55_D @ SV258 @ SV220 @ SV30 ) @ SV258 )
= $true )
| ( ( SV258
= ( relation_image @ SV30 @ SV220 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1926]) ).
thf(2071,plain,
! [SV259: $i,SV221: $i,SV30: $i] :
( ( ( ! [SY3881: $i] :
( ! [SY3823: $i] :
( ~ ( in @ ( ordered_pair @ SY3823 @ SY3881 ) @ SV30 )
| ~ ( in @ SY3823 @ SV221 ) )
| ( in @ SY3881 @ SV259 ) ) )
= $true )
| ( ( SV259
= ( relation_image @ SV30 @ SV221 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1927]) ).
thf(2072,plain,
! [SV30: $i,SV221: $i,SV259: $i] :
( ( ( ! [SY3883: $i] :
( ~ ( in @ SY3883 @ SV259 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SY3883 @ SV259 @ SV221 @ SV30 ) @ SY3883 ) @ SV30 )
| ~ ( in @ ( sK54_E @ SY3883 @ SV259 @ SV221 @ SV30 ) @ SV221 ) ) ) )
= $true )
| ( ( SV259
= ( relation_image @ SV30 @ SV221 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1928]) ).
thf(2073,plain,
! [SV31: $i,SV222: $i,SV260: $i] :
( ( ( ! [SY3884: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SY3884 ) @ SV31 )
| ~ ( in @ SY3884 @ SV222 ) ) )
= $true )
| ( ( ~ ( in @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SV260 ) )
= $true )
| ( ( SV260
= ( relation_inverse_image @ SV31 @ SV222 ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1929]) ).
thf(2074,plain,
! [SV31: $i,SV222: $i,SV260: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ ( sK53_SY3313 @ SV260 @ SV222 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( sK53_SY3313 @ SV260 @ SV222 @ SV31 ) @ SV222 ) ) )
= $true )
| ( ( in @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SV260 )
= $true )
| ( ( SV260
= ( relation_inverse_image @ SV31 @ SV222 ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1930]) ).
thf(2075,plain,
! [SV261: $i,SV223: $i,SV31: $i] :
( ( ( ! [SY3885: $i] :
( ! [SY3829: $i] :
( ~ ( in @ ( ordered_pair @ SY3885 @ SY3829 ) @ SV31 )
| ~ ( in @ SY3829 @ SV223 ) )
| ( in @ SY3885 @ SV261 ) ) )
= $true )
| ( ( SV261
= ( relation_inverse_image @ SV31 @ SV223 ) )
= $false )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1931]) ).
thf(2076,plain,
! [SV31: $i,SV223: $i,SV261: $i] :
( ( ( ! [SY3887: $i] :
( ~ ( in @ SY3887 @ SV261 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3887 @ ( sK51_E @ SY3887 @ SV261 @ SV223 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( sK51_E @ SY3887 @ SV261 @ SV223 @ SV31 ) @ SV223 ) ) ) )
= $true )
| ( ( SV261
= ( relation_inverse_image @ SV31 @ SV223 ) )
= $false )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1932]) ).
thf(2077,plain,
! [SV32: $i,SV224: $i,SV262: $i] :
( ( ( ~ ( ~ ( in @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ SV224 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV32 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 ) ) )
= $false )
| ( ( SV262
= ( relation_dom_restriction @ SV32 @ SV224 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1933]) ).
thf(2078,plain,
! [SV32: $i,SV224: $i,SV262: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ SV224 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV32 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 ) ) ) )
= $false )
| ( ( SV262
= ( relation_dom_restriction @ SV32 @ SV224 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1933]) ).
thf(2079,plain,
! [SV263: $i,SV32: $i,SV225: $i] :
( ( ( ~ ! [SY3888: $i,SY3889: $i] :
( ~ ( in @ SY3888 @ SV225 )
| ~ ( in @ ( ordered_pair @ SY3888 @ SY3889 ) @ SV32 )
| ( in @ ( ordered_pair @ SY3888 @ SY3889 ) @ SV263 ) )
| ~ ~ ( ~ ! [SY3890: $i] :
( ! [SY3891: $i] :
~ ( in @ ( ordered_pair @ SY3890 @ SY3891 ) @ SV263 )
| ( in @ SY3890 @ SV225 ) )
| ~ ! [SY3892: $i,SY3893: $i] :
( ~ ( in @ ( ordered_pair @ SY3892 @ SY3893 ) @ SV263 )
| ( in @ ( ordered_pair @ SY3892 @ SY3893 ) @ SV32 ) ) ) )
= $false )
| ( ( SV263
= ( relation_dom_restriction @ SV32 @ SV225 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1934]) ).
thf(2080,plain,
! [SV143: $i,SV33: $i,SV188: $i,SV307: $i] :
( ( ( in @ SV307 @ ( relation_rng @ SV188 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV33 @ SV307 ) @ SV188 ) )
= $true )
| ( ( ~ ( in @ SV307 @ SV143 ) )
= $true )
| ( ( in @ SV33 @ ( relation_inverse_image @ SV188 @ SV143 ) )
= $true )
| ( ( relation @ SV188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1935]) ).
thf(2081,plain,
! [SV33: $i,SV144: $i,SV189: $i] :
( ( ( ~ ( ~ ( in @ ( sK75_D @ SV189 @ SV144 @ SV33 ) @ ( relation_rng @ SV189 ) )
| ~ ( in @ ( ordered_pair @ SV33 @ ( sK75_D @ SV189 @ SV144 @ SV33 ) ) @ SV189 ) ) )
= $true )
| ( ( in @ SV33 @ ( relation_inverse_image @ SV189 @ SV144 ) )
= $false )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1936]) ).
thf(2082,plain,
! [SV33: $i,SV144: $i,SV189: $i] :
( ( ( in @ ( sK75_D @ SV189 @ SV144 @ SV33 ) @ SV144 )
= $true )
| ( ( in @ SV33 @ ( relation_inverse_image @ SV189 @ SV144 ) )
= $false )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1937]) ).
thf(2083,plain,
! [SV110: $i,SV145: $i] :
( ( ( ( ( sK65_C @ SV145 @ SV110 )
!= ( sK66_SY3320 @ SV145 @ SV110 ) ) )
= $true )
| ( ( ~ ( in @ ( sK65_C @ SV145 @ SV110 ) @ SV110 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 ) )
= $true )
| ( ( SV145
= ( identity_relation @ SV110 ) )
= $true )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1938]) ).
thf(2084,plain,
! [SV110: $i,SV145: $i] :
( ( ( ~ ( ( ( sK65_C @ SV145 @ SV110 )
= ( sK66_SY3320 @ SV145 @ SV110 ) )
| ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 ) ) )
= $false )
| ( ( SV145
= ( identity_relation @ SV110 ) )
= $true )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1939]) ).
thf(2085,plain,
! [SV110: $i,SV145: $i] :
( ( ( ~ ( ( in @ ( sK65_C @ SV145 @ SV110 ) @ SV110 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 ) ) )
= $false )
| ( ( SV145
= ( identity_relation @ SV110 ) )
= $true )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1939]) ).
thf(2086,plain,
! [SV146: $i,SV111: $i,SV352: $i] :
( ( ( ! [SY3957: $i] :
( ( SV352 != SY3957 )
| ~ ( in @ SV352 @ SV111 )
| ( in @ ( ordered_pair @ SV352 @ SY3957 ) @ SV146 ) ) )
= $true )
| ( ( SV146
= ( identity_relation @ SV111 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(2087,plain,
! [SV111: $i,SV146: $i] :
( ( ( ~ ! [SY3734: $i,SY3735: $i] :
( ~ ( in @ ( ordered_pair @ SY3734 @ SY3735 ) @ SV146 )
| ( SY3734 = SY3735 ) )
| ~ ! [SY3736: $i] :
( ! [SY3737: $i] :
~ ( in @ ( ordered_pair @ SY3736 @ SY3737 ) @ SV146 )
| ( in @ SY3736 @ SV111 ) ) )
= $false )
| ( ( SV146
= ( identity_relation @ SV111 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1941]) ).
thf(2088,plain,
! [SV34: $i,SV89: $i,SV190: $i,SV226: $i] :
( ( ( ~ ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV190 ) ) )
= $false )
| ( ( SV226
= ( unordered_triple @ SV34 @ SV89 @ SV190 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1942]) ).
thf(2089,plain,
! [SV34: $i,SV89: $i,SV190: $i,SV226: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV34 ) )
| ~ ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV89 ) ) ) )
= $false )
| ( ( SV226
= ( unordered_triple @ SV34 @ SV89 @ SV190 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1942]) ).
thf(2090,plain,
! [SV34: $i,SV89: $i,SV190: $i,SV226: $i] :
( ( ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
= SV190 )
= $true )
| ( ( ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
= SV34 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
= SV89 ) )
= $true )
| ( ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
= $true )
| ( ( SV226
= ( unordered_triple @ SV34 @ SV89 @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1943]) ).
thf(2091,plain,
! [SV89: $i,SV34: $i,SV191: $i,SV227: $i,SV353: $i] :
( ( ( ~ ( in @ SV353 @ SV227 )
| ( SV353 = SV191 )
| ( SV353 = SV34 )
| ( SV353 = SV89 ) )
= $true )
| ( ( SV227
= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(2092,plain,
! [SV89: $i,SV34: $i,SV227: $i,SV191: $i] :
( ( ( ~ ! [SY3840: $i] :
( ( SY3840 != SV191 )
| ( in @ SY3840 @ SV227 ) )
| ~ ~ ( ~ ! [SY3841: $i] :
( ( SY3841 != SV34 )
| ( in @ SY3841 @ SV227 ) )
| ~ ! [SY3842: $i] :
( ( SY3842 != SV89 )
| ( in @ SY3842 @ SV227 ) ) ) )
= $false )
| ( ( SV227
= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1945]) ).
thf(2093,plain,
! [SV36: $i,SV228: $i,SV354: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV354 @ ( sK16_C @ SV228 @ SV36 ) ) @ SV36 ) )
= $true )
| ( ( ~ ( in @ ( sK16_C @ SV228 @ SV36 ) @ SV228 ) )
= $true )
| ( ( SV228
= ( relation_rng @ SV36 ) )
= $true )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1946]) ).
thf(2094,plain,
! [SV229: $i,SV36: $i,SV355: $i] :
( ( ( ! [SY3958: $i] :
~ ( in @ ( ordered_pair @ SY3958 @ SV355 ) @ SV36 )
| ( in @ SV355 @ SV229 ) )
= $true )
| ( ( SV229
= ( relation_rng @ SV36 ) )
= $false )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1948]) ).
thf(2095,plain,
! [SV36: $i,SV229: $i,SV356: $i] :
( ( ( ~ ( in @ SV356 @ SV229 )
| ( in @ ( ordered_pair @ ( sK15_D @ SV356 @ SV229 @ SV36 ) @ SV356 ) @ SV36 ) )
= $true )
| ( ( SV229
= ( relation_rng @ SV36 ) )
= $false )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1949]) ).
thf(2096,plain,
! [SV337: $i,SV37: $i,SV324: $i] :
( ( ( ~ ( in @ SV324 @ ( sK77_B @ SV37 ) )
| ~ ( subset @ SV337 @ SV324 ) )
= $true )
| ( ( in @ SV337 @ ( sK77_B @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1950]) ).
thf(2097,plain,
! [SV113: $i,SV151: $i,SV325: $i] :
( ( ( in @ SV325 @ SV151 )
= $false )
| ( ( subset @ SV325 @ SV113 )
= $true )
| ( ( SV151
= ( powerset @ SV113 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1952]) ).
thf(2098,plain,
! [SV151: $i,SV113: $i,SV326: $i] :
( ( ( subset @ SV326 @ SV113 )
= $false )
| ( ( in @ SV326 @ SV151 )
= $true )
| ( ( SV151
= ( powerset @ SV113 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1953]) ).
thf(2099,plain,
! [SV114: $i,SV152: $i] :
( ( ( one_to_one @ SV152 )
= $false )
| ( ( in @ SV114 @ ( relation_rng @ SV152 ) )
= $false )
| ( ( SV114
= ( apply @ SV152 @ ( apply @ ( function_inverse @ SV152 ) @ SV114 ) ) )
= $true )
| ( ( function @ SV152 )
= $false )
| ( ( relation @ SV152 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1954]) ).
thf(2100,plain,
! [SV115: $i,SV153: $i] :
( ( ( one_to_one @ SV153 )
= $false )
| ( ( in @ SV115 @ ( relation_rng @ SV153 ) )
= $false )
| ( ( SV115
= ( apply @ ( relation_composition @ ( function_inverse @ SV153 ) @ SV153 ) @ SV115 ) )
= $true )
| ( ( function @ SV153 )
= $false )
| ( ( relation @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1955]) ).
thf(2101,plain,
! [SV91: $i,SV39: $i,SV308: $i] :
( ( ( function @ SV308 )
= $false )
| ( ( ~ ( relation @ SV308 ) )
= $true )
| ( ( ~ ( in @ SV39 @ ( relation_dom @ SV308 ) )
| ~ ( in @ ( apply @ SV308 @ SV39 ) @ ( relation_dom @ SV91 ) )
| ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SV308 @ SV91 ) ) ) )
= $true )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1956]) ).
thf(2102,plain,
! [SV91: $i,SV39: $i,SV357: $i] :
( ( ( ~ ( function @ SV357 )
| ~ ( relation @ SV357 )
| ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SV357 @ SV91 ) ) )
| ( in @ SV39 @ ( relation_dom @ SV357 ) ) )
= $true )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2103,plain,
! [SV91: $i,SV39: $i,SV358: $i] :
( ( ( ~ ( function @ SV358 )
| ~ ( relation @ SV358 )
| ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SV358 @ SV91 ) ) )
| ( in @ ( apply @ SV358 @ SV39 ) @ ( relation_dom @ SV91 ) ) )
= $true )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1958]) ).
thf(2104,plain,
! [SV40: $i,SV92: $i,SV265: $i] :
( ( ( ~ ( element @ ( sK6_D @ SV265 @ SV92 @ SV40 ) @ ( powerset @ SV40 ) ) )
= $false )
| ( ( SV265
= ( complements_of_subsets @ SV40 @ SV92 ) )
= $true )
| ( ( element @ SV265 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1959]) ).
thf(2105,plain,
! [SV40: $i,SV92: $i,SV265: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK6_D @ SV265 @ SV92 @ SV40 ) @ SV265 )
| ~ ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SV265 @ SV92 @ SV40 ) ) @ SV92 ) )
| ~ ( ( in @ ( sK6_D @ SV265 @ SV92 @ SV40 ) @ SV265 )
| ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SV265 @ SV92 @ SV40 ) ) @ SV92 ) ) ) )
= $false )
| ( ( SV265
= ( complements_of_subsets @ SV40 @ SV92 ) )
= $true )
| ( ( element @ SV265 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1959]) ).
thf(2106,plain,
! [SV92: $i,SV266: $i,SV40: $i] :
( ( ( ~ ! [SY3894: $i] :
( ~ ( element @ SY3894 @ ( powerset @ SV40 ) )
| ~ ( in @ SY3894 @ SV266 )
| ( in @ ( subset_complement @ SV40 @ SY3894 ) @ SV92 ) )
| ~ ! [SY3895: $i] :
( ~ ( element @ SY3895 @ ( powerset @ SV40 ) )
| ~ ( in @ ( subset_complement @ SV40 @ SY3895 ) @ SV92 )
| ( in @ SY3895 @ SV266 ) ) )
= $false )
| ( ( SV266
= ( complements_of_subsets @ SV40 @ SV92 ) )
= $false )
| ( ( element @ SV266 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1960]) ).
thf(2107,plain,
! [SV41: $i,SV194: $i,SV154: $i] :
( ( ( SV154
= ( apply @ SV194 @ SV41 ) )
= $false )
| ( ( ~ ( in @ SV41 @ ( relation_dom @ SV194 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV41 @ SV154 ) @ SV194 )
= $true )
| ( ( function @ SV194 )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1961]) ).
thf(2108,plain,
! [SV267: $i,SV41: $i,SV282: $i] :
( ( ( relation @ SV282 )
= $false )
| ( ( function @ SV282 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV41 @ SV267 ) @ SV282 )
| ( SV267
= ( apply @ SV282 @ SV41 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1962]) ).
thf(2109,plain,
! [SV268: $i,SV41: $i,SV283: $i] :
( ( ( relation @ SV283 )
= $false )
| ( ( function @ SV283 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV41 @ SV268 ) @ SV283 )
| ( in @ SV41 @ ( relation_dom @ SV283 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1963]) ).
thf(2110,plain,
! [SV284: $i,SV269: $i,SV42: $i] :
( ( ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SV269 @ SV284 ) ) )
= $false )
| ( ( in @ SV42 @ SV269 )
= $true )
| ( ( relation @ SV284 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1965]) ).
thf(2111,plain,
! [SV285: $i,SV270: $i,SV42: $i] :
( ( ( in @ SV42 @ ( relation_rng @ ( relation_rng_restriction @ SV270 @ SV285 ) ) )
= $false )
| ( ( in @ SV42 @ ( relation_rng @ SV285 ) )
= $true )
| ( ( relation @ SV285 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1966]) ).
thf(2112,plain,
! [SV43: $i,SV271: $i,SV359: $i] :
( ( ( ~ ( subset @ SV359 @ SV271 )
| ( in @ SV359 @ ( sK3_SY3278 @ SV271 @ SV43 ) ) )
= $true )
| ( ( ~ ( in @ SV271 @ ( sK2_B @ SV43 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2113,plain,
! [SV43: $i,SV271: $i] :
( ( ( in @ SV271 @ ( sK2_B @ SV43 ) )
= $false )
| ( ( in @ ( sK3_SY3278 @ SV271 @ SV43 ) @ ( sK2_B @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1968]) ).
thf(2114,plain,
! [SV338: $i,SV43: $i,SV327: $i] :
( ( ( ~ ( in @ SV327 @ ( sK2_B @ SV43 ) )
| ~ ( subset @ SV338 @ SV327 ) )
= $true )
| ( ( in @ SV338 @ ( sK2_B @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1969]) ).
thf(2115,plain,
! [SV360: $i,SV45: $i,SV232: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK26_C @ SV232 @ SV45 ) @ SV360 ) @ SV45 ) )
= $true )
| ( ( ~ ( in @ ( sK26_C @ SV232 @ SV45 ) @ SV232 ) )
= $true )
| ( ( SV232
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1972]) ).
thf(2116,plain,
! [SV233: $i,SV45: $i,SV361: $i] :
( ( ( ! [SY3959: $i] :
~ ( in @ ( ordered_pair @ SV361 @ SY3959 ) @ SV45 )
| ( in @ SV361 @ SV233 ) )
= $true )
| ( ( SV233
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1974]) ).
thf(2117,plain,
! [SV45: $i,SV233: $i,SV362: $i] :
( ( ( ~ ( in @ SV362 @ SV233 )
| ( in @ ( ordered_pair @ SV362 @ ( sK25_D @ SV362 @ SV233 @ SV45 ) ) @ SV45 ) )
= $true )
| ( ( SV233
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1975]) ).
thf(2118,plain,
! [SV158: $i,SV121: $i,SV329: $i] :
( ( ( SV329 = SV121 )
= $false )
| ( ( in @ SV329 @ SV158 )
= $true )
| ( ( SV158
= ( singleton @ SV121 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1979]) ).
thf(2119,plain,
! [SV121: $i,SV158: $i,SV330: $i] :
( ( ( in @ SV330 @ SV158 )
= $false )
| ( ( SV330 = SV121 )
= $true )
| ( ( SV158
= ( singleton @ SV121 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1980]) ).
thf(2120,plain,
! [SV122: $i,SV159: $i] :
( ( ( ~ ( in @ ( sK74_C @ SV159 @ SV122 ) @ SV122 ) )
= $false )
| ( ( ( ( relation_dom @ SV159 )
!= SV122 ) )
= $true )
| ( ( SV159
= ( identity_relation @ SV122 ) )
= $true )
| ( ( function @ SV159 )
= $false )
| ( ( relation @ SV159 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1981]) ).
thf(2121,plain,
! [SV122: $i,SV159: $i] :
( ( ( ~ ( ( ( apply @ SV159 @ ( sK74_C @ SV159 @ SV122 ) )
!= ( sK74_C @ SV159 @ SV122 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV159 )
!= SV122 ) )
= $true )
| ( ( SV159
= ( identity_relation @ SV122 ) )
= $true )
| ( ( function @ SV159 )
= $false )
| ( ( relation @ SV159 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1981]) ).
thf(2122,plain,
! [SV239: $i,SV272: $i] :
( ( ( ( SV272
!= ( identity_relation @ SV239 ) ) )
= $true )
| ( ( ! [SY3901: $i] :
( ~ ( in @ SY3901 @ SV239 )
| ( ( apply @ SV272 @ SY3901 )
= SY3901 ) ) )
= $true )
| ( ( function @ SV272 )
= $false )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1982]) ).
thf(2123,plain,
! [SV240: $i,SV273: $i] :
( ( ( ( SV273
!= ( identity_relation @ SV240 ) ) )
= $true )
| ( ( ( relation_dom @ SV273 )
= SV240 )
= $true )
| ( ( function @ SV273 )
= $false )
| ( ( relation @ SV273 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1983]) ).
thf(2124,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ( function @ SV331 ) )
= $true )
| ( ( ~ ( relation @ SV331 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) )
| ( SV331
= ( function_inverse @ SV46 ) ) )
= $true )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1984]) ).
thf(2125,plain,
! [SV46: $i] :
( ( ( ! [SY3484: $i] :
( ~ ( function @ SY3484 )
| ~ ( relation @ SY3484 )
| ( SY3484
!= ( function_inverse @ SV46 ) )
| ~ ( ~ ~ ( ~ ! [SY3485: $i,SY3486: $i] :
( ( SY3486
!= ( apply @ SY3484 @ SY3485 ) )
| ~ ( in @ SY3485 @ ( relation_rng @ SV46 ) )
| ( SY3485
= ( apply @ SV46 @ SY3486 ) ) )
| ~ ! [SY3487: $i,SY3488: $i] :
( ( SY3488
!= ( apply @ SY3484 @ SY3487 ) )
| ~ ( in @ SY3487 @ ( relation_rng @ SV46 ) )
| ( in @ SY3488 @ ( relation_dom @ SV46 ) ) ) )
| ~ ~ ( ~ ! [SY3489: $i,SY3490: $i] :
( ( SY3489
!= ( apply @ SV46 @ SY3490 ) )
| ~ ( in @ SY3490 @ ( relation_dom @ SV46 ) )
| ( SY3490
= ( apply @ SY3484 @ SY3489 ) ) )
| ~ ! [SY3491: $i] :
( ! [SY3492: $i] :
( ( SY3491
!= ( apply @ SV46 @ SY3492 ) )
| ~ ( in @ SY3492 @ ( relation_dom @ SV46 ) ) )
| ( in @ SY3491 @ ( relation_rng @ SV46 ) ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1985]) ).
thf(2126,plain,
! [SV46: $i] :
( ( ( ! [SY3493: $i] :
( ~ ( function @ SY3493 )
| ~ ( relation @ SY3493 )
| ( SY3493
!= ( function_inverse @ SV46 ) )
| ( ( relation_dom @ SY3493 )
= ( relation_rng @ SV46 ) ) ) )
= $true )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1986]) ).
thf(2127,plain,
! [SV47: $i,SV123: $i,SV313: $i] :
( ( ( ~ ( ~ ( ! [SY3936: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ SY3936 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3936 @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV123 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV313 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK10_SY3288 @ SV313 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY3288 @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV123 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV313 ) ) ) )
= $true )
| ( ( SV313
= ( relation_composition @ SV47 @ SV123 ) )
= $true )
| ( ( relation @ SV313 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1987]) ).
thf(2128,plain,
! [SV123: $i,SV47: $i,SV314: $i] :
( ( ( ( SV314
!= ( relation_composition @ SV47 @ SV123 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3937: $i,SY3938: $i] :
( ! [SY3706: $i] :
( ~ ( in @ ( ordered_pair @ SY3937 @ SY3706 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3706 @ SY3938 ) @ SV123 ) )
| ( in @ ( ordered_pair @ SY3937 @ SY3938 ) @ SV314 ) )
| ~ ! [SY3940: $i,SY3941: $i] :
( ~ ( in @ ( ordered_pair @ SY3940 @ SY3941 ) @ SV314 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3940 @ ( sK7_F @ SY3941 @ SY3940 @ SV314 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY3941 @ SY3940 @ SV314 @ SV123 @ SV47 ) @ SY3941 ) @ SV123 ) ) ) ) )
= $true )
| ( ( relation @ SV314 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1988]) ).
thf(2129,plain,
! [SV198: $i,SV241: $i,SV94: $i,SV49: $i] :
( ( ( in @ ( ordered_pair @ SV49 @ SV94 ) @ SV241 )
= $false )
| ( ( in @ SV49 @ SV198 )
= $false )
| ( ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SV198 ) @ SV241 ) )
= $true )
| ( ( relation @ SV241 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1989]) ).
thf(2130,plain,
! [SV315: $i,SV293: $i,SV94: $i,SV49: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SV293 ) @ SV315 ) ) )
= $true )
| ( ( in @ SV49 @ SV293 )
= $true )
| ( ( relation @ SV315 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1990]) ).
thf(2131,plain,
! [SV316: $i,SV294: $i,SV94: $i,SV49: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SV294 ) @ SV316 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV49 @ SV94 ) @ SV316 )
= $true )
| ( ( relation @ SV316 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1991]) ).
thf(2132,plain,
! [SV124: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK11_B @ SV124 ) @ ( relation_dom @ SV124 ) )
| ~ ( in @ ( sK12_SY3289 @ SV124 ) @ ( relation_dom @ SV124 ) ) )
| ( ( apply @ SV124 @ ( sK11_B @ SV124 ) )
!= ( apply @ SV124 @ ( sK12_SY3289 @ SV124 ) ) ) )
= $false )
| ( ( one_to_one @ SV124 )
= $true )
| ( ( function @ SV124 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1992]) ).
thf(2133,plain,
! [SV124: $i] :
( ( ( ( sK11_B @ SV124 )
= ( sK12_SY3289 @ SV124 ) )
= $false )
| ( ( one_to_one @ SV124 )
= $true )
| ( ( function @ SV124 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1993]) ).
thf(2134,plain,
! [SV339: $i,SV125: $i,SV332: $i] :
( ( ( ~ ( in @ SV332 @ ( relation_dom @ SV125 ) )
| ~ ( in @ SV339 @ ( relation_dom @ SV125 ) )
| ( ( apply @ SV125 @ SV332 )
!= ( apply @ SV125 @ SV339 ) ) )
= $true )
| ( ( SV332 = SV339 )
= $true )
| ( ( one_to_one @ SV125 )
= $false )
| ( ( function @ SV125 )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1994]) ).
thf(2135,plain,
! [SV51: $i,SV161: $i,SV199: $i] :
( ( ( ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV199 )
| ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV51 ) )
= $true )
| ( ( SV199
= ( set_union2 @ SV51 @ SV161 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1995]) ).
thf(2136,plain,
! [SV51: $i,SV161: $i,SV199: $i] :
( ( ( ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV199 )
| ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV161 ) )
= $true )
| ( ( SV199
= ( set_union2 @ SV51 @ SV161 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1996]) ).
thf(2137,plain,
! [SV162: $i,SV51: $i,SV200: $i,SV340: $i] :
( ( ( ~ ( in @ SV340 @ SV200 ) )
= $true )
| ( ( ( in @ SV340 @ SV51 )
| ( in @ SV340 @ SV162 ) )
= $true )
| ( ( SV200
= ( set_union2 @ SV51 @ SV162 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1998]) ).
thf(2138,plain,
! [SV162: $i,SV200: $i,SV51: $i] :
( ( ( ~ ! [SY3796: $i] :
( ~ ( in @ SY3796 @ SV51 )
| ( in @ SY3796 @ SV200 ) ) )
= $false )
| ( ( SV200
= ( set_union2 @ SV51 @ SV162 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1999]) ).
thf(2139,plain,
! [SV51: $i,SV200: $i,SV162: $i] :
( ( ( ~ ! [SY3797: $i] :
( ~ ( in @ SY3797 @ SV162 )
| ( in @ SY3797 @ SV200 ) ) )
= $false )
| ( ( SV200
= ( set_union2 @ SV51 @ SV162 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1999]) ).
thf(2140,plain,
! [SV52: $i,SV243: $i] :
( ( ( in @ ( ordered_pair @ ( sK30_C @ SV243 @ SV52 ) @ ( sK31_SY3299 @ SV243 @ SV52 ) ) @ SV52 )
= $true )
| ( ( subset @ SV52 @ SV243 )
= $true )
| ( ( relation @ SV243 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2000]) ).
thf(2141,plain,
! [SV52: $i,SV243: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK30_C @ SV243 @ SV52 ) @ ( sK31_SY3299 @ SV243 @ SV52 ) ) @ SV243 ) )
= $true )
| ( ( subset @ SV52 @ SV243 )
= $true )
| ( ( relation @ SV243 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2001]) ).
thf(2142,plain,
! [SV244: $i,SV52: $i,SV363: $i,SV341: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV341 @ SV363 ) @ SV52 )
| ( in @ ( ordered_pair @ SV341 @ SV363 ) @ SV244 ) )
= $true )
| ( ( subset @ SV52 @ SV244 )
= $false )
| ( ( relation @ SV244 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2002]) ).
thf(2143,plain,
! [SV245: $i,SV295: $i] :
( ( ( ~ ( ~ ( in @ ( sK46_SY3307 @ SV295 @ SV245 ) @ SV245 )
| ~ ~ ( in @ ( sK45_C @ SV295 @ SV245 ) @ ( sK46_SY3307 @ SV295 @ SV245 ) ) )
| ~ ( in @ ( sK45_C @ SV295 @ SV245 ) @ SV295 ) )
= $true )
| ( ( SV295
= ( set_meet @ SV245 ) )
= $true )
| ( ( SV245 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2003]) ).
thf(2144,plain,
! [SV295: $i,SV245: $i] :
( ( ( ! [SY3917: $i] :
( ~ ( in @ SY3917 @ SV245 )
| ( in @ ( sK45_C @ SV295 @ SV245 ) @ SY3917 ) )
| ( in @ ( sK45_C @ SV295 @ SV245 ) @ SV295 ) )
= $true )
| ( ( SV295
= ( set_meet @ SV245 ) )
= $true )
| ( ( SV245 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2004]) ).
thf(2145,plain,
! [SV246: $i,SV296: $i] :
( ( ( ~ ! [SY3918: $i] :
( ~ ( ~ ( in @ ( sK44_D @ SY3918 @ SV296 @ SV246 ) @ SV246 )
| ~ ~ ( in @ SY3918 @ ( sK44_D @ SY3918 @ SV296 @ SV246 ) ) )
| ( in @ SY3918 @ SV296 ) ) )
= $false )
| ( ( SV296
= ( set_meet @ SV246 ) )
= $false )
| ( ( SV246 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2005]) ).
thf(2146,plain,
! [SV246: $i,SV296: $i] :
( ( ( ~ ! [SY3919: $i] :
( ~ ( in @ SY3919 @ SV296 )
| ! [SY3865: $i] :
( ~ ( in @ SY3865 @ SV246 )
| ( in @ SY3919 @ SY3865 ) ) ) )
= $false )
| ( ( SV296
= ( set_meet @ SV246 ) )
= $false )
| ( ( SV246 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2005]) ).
thf(2147,plain,
! [SV53: $i,SV297: $i,SV319: $i] :
( ( ( ~ ( ~ ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ ( sK57_D @ SV319 @ SV297 @ SV53 ) ) @ SV297 )
| ~ ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ SV319 ) ) )
= $false )
| ( ( SV319
= ( relation_inverse_image @ SV53 @ SV297 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2008]) ).
thf(2148,plain,
! [SV53: $i,SV297: $i,SV319: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ SV319 ) )
| ~ ( ( in @ ( apply @ SV53 @ ( sK57_D @ SV319 @ SV297 @ SV53 ) ) @ SV297 )
| ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ SV319 ) ) ) )
= $false )
| ( ( SV319
= ( relation_inverse_image @ SV53 @ SV297 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2008]) ).
thf(2149,plain,
! [SV320: $i,SV298: $i,SV53: $i] :
( ( ( ~ ! [SY3942: $i] :
( ~ ( in @ SY3942 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SY3942 ) @ SV298 )
| ( in @ SY3942 @ SV320 ) )
| ~ ~ ( ~ ! [SY3943: $i] :
( ~ ( in @ SY3943 @ SV320 )
| ( in @ SY3943 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY3944: $i] :
( ~ ( in @ SY3944 @ SV320 )
| ( in @ ( apply @ SV53 @ SY3944 ) @ SV298 ) ) ) )
= $false )
| ( ( SV320
= ( relation_inverse_image @ SV53 @ SV298 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2009]) ).
thf(2150,plain,
! [SV54: $i,SV165: $i,SV201: $i] :
( ( ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV54 )
= $false )
| ( ( ~ ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV165 ) )
= $true )
| ( ( ~ ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV201 ) )
= $true )
| ( ( SV201
= ( set_intersection2 @ SV54 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2010]) ).
thf(2151,plain,
! [SV54: $i,SV165: $i,SV201: $i] :
( ( ( ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV54 )
| ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV201 ) )
= $true )
| ( ( SV201
= ( set_intersection2 @ SV54 @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2011]) ).
thf(2152,plain,
! [SV54: $i,SV165: $i,SV201: $i] :
( ( ( ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV165 )
| ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV201 ) )
= $true )
| ( ( SV201
= ( set_intersection2 @ SV54 @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2012]) ).
thf(2153,plain,
! [SV202: $i,SV166: $i,SV54: $i,SV342: $i] :
( ( ( ~ ( in @ SV342 @ SV54 )
| ~ ( in @ SV342 @ SV166 ) )
= $true )
| ( ( in @ SV342 @ SV202 )
= $true )
| ( ( SV202
= ( set_intersection2 @ SV54 @ SV166 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2013]) ).
thf(2154,plain,
! [SV166: $i,SV54: $i,SV202: $i] :
( ( ( ~ ! [SY3799: $i] :
( ~ ( in @ SY3799 @ SV202 )
| ( in @ SY3799 @ SV54 ) ) )
= $false )
| ( ( SV202
= ( set_intersection2 @ SV54 @ SV166 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2014]) ).
thf(2155,plain,
! [SV54: $i,SV166: $i,SV202: $i] :
( ( ( ~ ! [SY3800: $i] :
( ~ ( in @ SY3800 @ SV202 )
| ( in @ SY3800 @ SV166 ) ) )
= $false )
| ( ( SV202
= ( set_intersection2 @ SV54 @ SV166 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2014]) ).
thf(2156,plain,
! [SV55: $i,SV169: $i,SV203: $i] :
( ( ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV55 )
= $false )
| ( ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV169 )
= $true )
| ( ( ~ ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV203 ) )
= $true )
| ( ( SV203
= ( set_difference @ SV55 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2015]) ).
thf(2157,plain,
! [SV55: $i,SV169: $i,SV203: $i] :
( ( ( ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV55 )
| ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV203 ) )
= $true )
| ( ( SV203
= ( set_difference @ SV55 @ SV169 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2016]) ).
thf(2158,plain,
! [SV55: $i,SV169: $i,SV203: $i] :
( ( ( ~ ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV169 )
| ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV203 ) )
= $true )
| ( ( SV203
= ( set_difference @ SV55 @ SV169 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2017]) ).
thf(2159,plain,
! [SV204: $i,SV170: $i,SV55: $i,SV343: $i] :
( ( ( ~ ( in @ SV343 @ SV55 )
| ( in @ SV343 @ SV170 ) )
= $true )
| ( ( in @ SV343 @ SV204 )
= $true )
| ( ( SV204
= ( set_difference @ SV55 @ SV170 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2018]) ).
thf(2160,plain,
! [SV170: $i,SV55: $i,SV204: $i] :
( ( ( ~ ! [SY3802: $i] :
( ~ ( in @ SY3802 @ SV204 )
| ( in @ SY3802 @ SV55 ) ) )
= $false )
| ( ( SV204
= ( set_difference @ SV55 @ SV170 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2019]) ).
thf(2161,plain,
! [SV55: $i,SV170: $i,SV204: $i] :
( ( ( ~ ! [SY3803: $i] :
( ~ ( in @ SY3803 @ SV204 )
| ~ ( in @ SY3803 @ SV170 ) ) )
= $false )
| ( ( SV204
= ( set_difference @ SV55 @ SV170 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2019]) ).
thf(2162,plain,
! [SV56: $i,SV299: $i] :
( ( ( ! [SY3926: $i] :
( ( ( sK19_C @ SV299 @ SV56 )
!= ( apply @ SV56 @ SY3926 ) )
| ~ ( in @ SY3926 @ ( relation_dom @ SV56 ) ) )
| ~ ( in @ ( sK19_C @ SV299 @ SV56 ) @ SV299 ) )
= $true )
| ( ( SV299
= ( relation_rng @ SV56 ) )
= $true )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2020]) ).
thf(2163,plain,
! [SV56: $i,SV299: $i] :
( ( ( ~ ( ( ( sK19_C @ SV299 @ SV56 )
!= ( apply @ SV56 @ ( sK20_SY3294 @ SV299 @ SV56 ) ) )
| ~ ( in @ ( sK20_SY3294 @ SV299 @ SV56 ) @ ( relation_dom @ SV56 ) ) )
| ( in @ ( sK19_C @ SV299 @ SV56 ) @ SV299 ) )
= $true )
| ( ( SV299
= ( relation_rng @ SV56 ) )
= $true )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2021]) ).
thf(2164,plain,
! [SV300: $i,SV56: $i] :
( ( ( ~ ! [SY3927: $i] :
( ! [SY3554: $i] :
( ( SY3927
!= ( apply @ SV56 @ SY3554 ) )
| ~ ( in @ SY3554 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY3927 @ SV300 ) ) )
= $false )
| ( ( SV300
= ( relation_rng @ SV56 ) )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2022]) ).
thf(2165,plain,
! [SV56: $i,SV300: $i] :
( ( ( ~ ! [SY3929: $i] :
( ~ ( in @ SY3929 @ SV300 )
| ~ ( ( SY3929
!= ( apply @ SV56 @ ( sK18_D @ SY3929 @ SV300 @ SV56 ) ) )
| ~ ( in @ ( sK18_D @ SY3929 @ SV300 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) ) )
= $false )
| ( ( SV300
= ( relation_rng @ SV56 ) )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2022]) ).
thf(2166,plain,
! [SV57: $i,SV171: $i,SV205: $i] :
( ( ( ~ ( in @ ( sK38_D @ SV205 @ SV171 @ SV57 ) @ SV205 )
| ( ( sK38_D @ SV205 @ SV171 @ SV57 )
!= SV57 ) )
= $true )
| ( ( SV205
= ( unordered_pair @ SV57 @ SV171 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2023]) ).
thf(2167,plain,
! [SV57: $i,SV171: $i,SV205: $i] :
( ( ( ~ ( in @ ( sK38_D @ SV205 @ SV171 @ SV57 ) @ SV205 )
| ( ( sK38_D @ SV205 @ SV171 @ SV57 )
!= SV171 ) )
= $true )
| ( ( SV205
= ( unordered_pair @ SV57 @ SV171 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2024]) ).
thf(2168,plain,
! [SV172: $i,SV57: $i,SV206: $i,SV344: $i] :
( ( ( ~ ( in @ SV344 @ SV206 ) )
= $true )
| ( ( ( SV344 = SV57 )
| ( SV344 = SV172 ) )
= $true )
| ( ( SV206
= ( unordered_pair @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2026]) ).
thf(2169,plain,
! [SV172: $i,SV206: $i,SV57: $i] :
( ( ( ~ ! [SY3805: $i] :
( ( SY3805 != SV57 )
| ( in @ SY3805 @ SV206 ) ) )
= $false )
| ( ( SV206
= ( unordered_pair @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2027]) ).
thf(2170,plain,
! [SV57: $i,SV206: $i,SV172: $i] :
( ( ( ~ ! [SY3806: $i] :
( ( SY3806 != SV172 )
| ( in @ SY3806 @ SV206 ) ) )
= $false )
| ( ( SV206
= ( unordered_pair @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2027]) ).
thf(2171,plain,
! [SV58: $i,SV96: $i,SV321: $i] :
( ( ( function @ SV321 )
= $false )
| ( ( ~ ( relation @ SV321 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK67_D @ SV321 @ SV96 @ SV58 ) @ ( relation_dom @ SV96 ) )
| ~ ( ( ( apply @ SV96 @ ( sK67_D @ SV321 @ SV96 @ SV58 ) )
!= ( apply @ SV321 @ ( sK67_D @ SV321 @ SV96 @ SV58 ) ) ) ) )
| ( ( relation_dom @ SV96 )
!= ( set_intersection2 @ ( relation_dom @ SV321 ) @ SV58 ) )
| ( SV96
= ( relation_dom_restriction @ SV321 @ SV58 ) ) )
= $true )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2028]) ).
thf(2172,plain,
! [SV58: $i,SV96: $i,SV364: $i] :
( ( ( ~ ( function @ SV364 )
| ~ ( relation @ SV364 )
| ( SV96
!= ( relation_dom_restriction @ SV364 @ SV58 ) )
| ! [SY3960: $i] :
( ~ ( in @ SY3960 @ ( relation_dom @ SV96 ) )
| ( ( apply @ SV96 @ SY3960 )
= ( apply @ SV364 @ SY3960 ) ) ) )
= $true )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(2173,plain,
! [SV58: $i,SV96: $i,SV365: $i] :
( ( ( ~ ( function @ SV365 )
| ~ ( relation @ SV365 )
| ( SV96
!= ( relation_dom_restriction @ SV365 @ SV58 ) )
| ( ( relation_dom @ SV96 )
= ( set_intersection2 @ ( relation_dom @ SV365 ) @ SV58 ) ) )
= $true )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2030]) ).
thf(2174,plain,
! [SV59: $i,SV249: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV249 ) )
= $true )
| ( ( SV59 = SV249 )
= $true )
| ( ( relation @ SV249 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2031]) ).
thf(2175,plain,
! [SV59: $i,SV249: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV249 ) )
= $true )
| ( ( SV59 = SV249 )
= $true )
| ( ( relation @ SV249 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2032]) ).
thf(2176,plain,
! [SV250: $i,SV59: $i] :
( ( ( ~ ! [SY3868: $i,SY3869: $i] :
( ~ ( in @ ( ordered_pair @ SY3868 @ SY3869 ) @ SV59 )
| ( in @ ( ordered_pair @ SY3868 @ SY3869 ) @ SV250 ) ) )
= $false )
| ( ( SV59 = SV250 )
= $false )
| ( ( relation @ SV250 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2033]) ).
thf(2177,plain,
! [SV59: $i,SV250: $i] :
( ( ( ~ ! [SY3870: $i,SY3871: $i] :
( ~ ( in @ ( ordered_pair @ SY3870 @ SY3871 ) @ SV250 )
| ( in @ ( ordered_pair @ SY3870 @ SY3871 ) @ SV59 ) ) )
= $false )
| ( ( SV59 = SV250 )
= $false )
| ( ( relation @ SV250 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2033]) ).
thf(2178,plain,
! [SV333: $i,SV130: $i,SV173: $i] :
( ( ( in @ ( sK23_C @ SV173 @ SV130 ) @ SV333 )
= $false )
| ( ( ~ ( in @ SV333 @ SV130 ) )
= $true )
| ( ( ~ ( in @ ( sK23_C @ SV173 @ SV130 ) @ SV173 ) )
= $true )
| ( ( SV173
= ( union @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2034]) ).
thf(2179,plain,
! [SV130: $i,SV173: $i] :
( ( ( in @ ( sK23_C @ SV173 @ SV130 ) @ ( sK24_SY3296 @ SV173 @ SV130 ) )
= $true )
| ( ( in @ ( sK23_C @ SV173 @ SV130 ) @ SV173 )
= $true )
| ( ( SV173
= ( union @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2035]) ).
thf(2180,plain,
! [SV130: $i,SV173: $i] :
( ( ( in @ ( sK24_SY3296 @ SV173 @ SV130 ) @ SV130 )
= $true )
| ( ( in @ ( sK23_C @ SV173 @ SV130 ) @ SV173 )
= $true )
| ( ( SV173
= ( union @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2036]) ).
thf(2181,plain,
! [SV174: $i,SV131: $i,SV366: $i,SV334: $i] :
( ( ( ~ ( in @ SV334 @ SV366 )
| ~ ( in @ SV366 @ SV131 ) )
= $true )
| ( ( in @ SV334 @ SV174 )
= $true )
| ( ( SV174
= ( union @ SV131 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2037]) ).
thf(2182,plain,
! [SV131: $i,SV174: $i,SV335: $i] :
( ( ( in @ SV335 @ SV174 )
= $false )
| ( ( ~ ( ~ ( in @ SV335 @ ( sK22_D @ SV335 @ SV174 @ SV131 ) )
| ~ ( in @ ( sK22_D @ SV335 @ SV174 @ SV131 ) @ SV131 ) ) )
= $true )
| ( ( SV174
= ( union @ SV131 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2038]) ).
thf(2183,plain,
! [SV62: $i,SV208: $i,SV175: $i] :
( ( ( in @ SV175 @ ( relation_dom @ SV208 ) )
= $false )
| ( ( ~ ( in @ SV175 @ SV62 ) )
= $true )
| ( ( in @ SV175 @ ( relation_dom @ ( relation_dom_restriction @ SV208 @ SV62 ) ) )
= $true )
| ( ( function @ SV208 )
= $false )
| ( ( relation @ SV208 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2041]) ).
thf(2184,plain,
! [SV62: $i,SV276: $i,SV303: $i] :
( ( ( relation @ SV303 )
= $false )
| ( ( function @ SV303 )
= $false )
| ( ( ~ ( in @ SV276 @ ( relation_dom @ ( relation_dom_restriction @ SV303 @ SV62 ) ) )
| ( in @ SV276 @ ( relation_dom @ SV303 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2042]) ).
thf(2185,plain,
! [SV62: $i,SV277: $i,SV304: $i] :
( ( ( relation @ SV304 )
= $false )
| ( ( function @ SV304 )
= $false )
| ( ( ~ ( in @ SV277 @ ( relation_dom @ ( relation_dom_restriction @ SV304 @ SV62 ) ) )
| ( in @ SV277 @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2043]) ).
thf(2186,plain,
! [SV209: $i,SV176: $i,SV367: $i,SV63: $i,SV345: $i] :
( ( ( ~ ( in @ SV345 @ SV63 )
| ~ ( in @ SV367 @ SV176 )
| ( ( sK34_D @ SV209 @ SV176 @ SV63 )
!= ( ordered_pair @ SV345 @ SV367 ) ) )
= $true )
| ( ( ~ ( in @ ( sK34_D @ SV209 @ SV176 @ SV63 ) @ SV209 ) )
= $true )
| ( ( SV209
= ( cartesian_product2 @ SV63 @ SV176 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(2187,plain,
! [SV63: $i,SV176: $i,SV209: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK35_SY3303 @ SV209 @ SV176 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK36_SY3305 @ SV209 @ SV176 @ SV63 ) @ SV176 ) ) )
= $false )
| ( ( in @ ( sK34_D @ SV209 @ SV176 @ SV63 ) @ SV209 )
= $true )
| ( ( SV209
= ( cartesian_product2 @ SV63 @ SV176 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2045]) ).
thf(2188,plain,
! [SV63: $i,SV176: $i,SV209: $i] :
( ( ( ( ( sK34_D @ SV209 @ SV176 @ SV63 )
!= ( ordered_pair @ ( sK35_SY3303 @ SV209 @ SV176 @ SV63 ) @ ( sK36_SY3305 @ SV209 @ SV176 @ SV63 ) ) ) )
= $false )
| ( ( in @ ( sK34_D @ SV209 @ SV176 @ SV63 ) @ SV209 )
= $true )
| ( ( SV209
= ( cartesian_product2 @ SV63 @ SV176 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2045]) ).
thf(2189,plain,
! [SV210: $i,SV346: $i,SV177: $i,SV63: $i] :
( ( ( ! [SY3951: $i,SY3952: $i] :
( ~ ( in @ SY3951 @ SV63 )
| ~ ( in @ SY3952 @ SV177 )
| ( SV346
!= ( ordered_pair @ SY3951 @ SY3952 ) ) ) )
= $true )
| ( ( in @ SV346 @ SV210 )
= $true )
| ( ( SV210
= ( cartesian_product2 @ SV63 @ SV177 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2046]) ).
thf(2190,plain,
! [SV63: $i,SV177: $i,SV210: $i,SV347: $i] :
( ( ( ~ ( in @ SV347 @ SV210 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK32_E @ SV347 @ SV210 @ SV177 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK33_SY3300 @ SV347 @ SV210 @ SV177 @ SV63 ) @ SV177 ) )
| ( SV347
!= ( ordered_pair @ ( sK32_E @ SV347 @ SV210 @ SV177 @ SV63 ) @ ( sK33_SY3300 @ SV347 @ SV210 @ SV177 @ SV63 ) ) ) ) )
= $true )
| ( ( SV210
= ( cartesian_product2 @ SV63 @ SV177 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2047]) ).
thf(2191,plain,
! [SV180: $i,SV64: $i,SV211: $i,SV323: $i] :
( ( ( in @ SV323 @ ( relation_dom @ SV211 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV323 @ SV64 ) @ SV211 ) )
= $true )
| ( ( ~ ( in @ SV323 @ SV180 ) )
= $true )
| ( ( in @ SV64 @ ( relation_image @ SV211 @ SV180 ) )
= $true )
| ( ( relation @ SV211 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2048]) ).
thf(2192,plain,
! [SV64: $i,SV181: $i,SV212: $i] :
( ( ( ~ ( ~ ( in @ ( sK76_D @ SV212 @ SV181 @ SV64 ) @ ( relation_dom @ SV212 ) )
| ~ ( in @ ( ordered_pair @ ( sK76_D @ SV212 @ SV181 @ SV64 ) @ SV64 ) @ SV212 ) ) )
= $true )
| ( ( in @ SV64 @ ( relation_image @ SV212 @ SV181 ) )
= $false )
| ( ( relation @ SV212 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2049]) ).
thf(2193,plain,
! [SV64: $i,SV181: $i,SV212: $i] :
( ( ( in @ ( sK76_D @ SV212 @ SV181 @ SV64 ) @ SV181 )
= $true )
| ( ( in @ SV64 @ ( relation_image @ SV212 @ SV181 ) )
= $false )
| ( ( relation @ SV212 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2050]) ).
thf(2194,plain,
! [SV66: $i,SV348: $i] :
( ( ( ~ ( in @ SV348 @ ( relation_dom @ SV66 ) ) )
= $true )
| ( ( ! [SY3953: $i] :
( ( SY3953
!= ( apply @ SV66 @ SV348 ) )
| ( in @ ( ordered_pair @ SV348 @ SY3953 ) @ SV66 ) ) )
= $true )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2051]) ).
thf(2195,plain,
! [SV66: $i,SV349: $i] :
( ( ( ~ ( in @ SV349 @ ( relation_dom @ SV66 ) ) )
= $true )
| ( ( ! [SY3954: $i] :
( ~ ( in @ ( ordered_pair @ SV349 @ SY3954 ) @ SV66 )
| ( SY3954
= ( apply @ SV66 @ SV349 ) ) ) )
= $true )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2052]) ).
thf(2196,plain,
! [SV66: $i,SV350: $i] :
( ( ( in @ SV350 @ ( relation_dom @ SV66 ) )
= $true )
| ( ( ! [SY3955: $i] :
( ( SY3955
!= ( apply @ SV66 @ SV350 ) )
| ( SY3955 = empty_set ) ) )
= $true )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2053]) ).
thf(2197,plain,
! [SV66: $i,SV351: $i] :
( ( ( in @ SV351 @ ( relation_dom @ SV66 ) )
= $true )
| ( ( ! [SY3956: $i] :
( ( SY3956 != empty_set )
| ( SY3956
= ( apply @ SV66 @ SV351 ) ) ) )
= $true )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2054]) ).
thf(2198,plain,
! [SV26: $i,SV88: $i,SV253: $i] :
( ( ( ~ ( in @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) @ SV26 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV88 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 ) )
= $true )
| ( ( SV253
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $true )
| ( ( relation @ SV253 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2057]) ).
thf(2199,plain,
! [SV26: $i,SV88: $i,SV253: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) @ SV26 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV88 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 ) ) ) )
= $true )
| ( ( SV253
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $true )
| ( ( relation @ SV253 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2058]) ).
thf(2200,plain,
! [SV254: $i,SV88: $i,SV26: $i] :
( ( ( ~ ! [SY3872: $i,SY3873: $i] :
( ~ ( in @ SY3873 @ SV26 )
| ~ ( in @ ( ordered_pair @ SY3872 @ SY3873 ) @ SV88 )
| ( in @ ( ordered_pair @ SY3872 @ SY3873 ) @ SV254 ) ) )
= $false )
| ( ( SV254
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2059]) ).
thf(2201,plain,
! [SV88: $i,SV26: $i,SV254: $i] :
( ( ( ~ ~ ( ~ ! [SY3874: $i,SY3875: $i] :
( ~ ( in @ ( ordered_pair @ SY3874 @ SY3875 ) @ SV254 )
| ( in @ SY3875 @ SV26 ) )
| ~ ! [SY3876: $i,SY3877: $i] :
( ~ ( in @ ( ordered_pair @ SY3876 @ SY3877 ) @ SV254 )
| ( in @ ( ordered_pair @ SY3876 @ SY3877 ) @ SV88 ) ) ) )
= $false )
| ( ( SV254
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2059]) ).
thf(2202,plain,
! [SV28: $i,SV218: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV218 @ SV28 ) @ ( sK14_SY3290 @ SV218 @ SV28 ) ) @ SV218 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK14_SY3290 @ SV218 @ SV28 ) @ ( sK13_C @ SV218 @ SV28 ) ) @ SV28 ) )
= $true )
| ( ( SV218
= ( relation_inverse @ SV28 ) )
= $true )
| ( ( relation @ SV218 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2062]) ).
thf(2203,plain,
! [SV28: $i,SV218: $i] :
( ( ( in @ ( ordered_pair @ ( sK13_C @ SV218 @ SV28 ) @ ( sK14_SY3290 @ SV218 @ SV28 ) ) @ SV218 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK14_SY3290 @ SV218 @ SV28 ) @ ( sK13_C @ SV218 @ SV28 ) ) @ SV28 )
= $true )
| ( ( SV218
= ( relation_inverse @ SV28 ) )
= $true )
| ( ( relation @ SV218 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2063]) ).
thf(2204,plain,
! [SV28: $i,SV219: $i] :
( ( ( ! [SY3815: $i,SY3816: $i] :
( ~ ( in @ ( ordered_pair @ SY3815 @ SY3816 ) @ SV219 )
| ( in @ ( ordered_pair @ SY3816 @ SY3815 ) @ SV28 ) ) )
= $true )
| ( ( SV219
= ( relation_inverse @ SV28 ) )
= $false )
| ( ( relation @ SV219 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2064]) ).
thf(2205,plain,
! [SV219: $i,SV28: $i] :
( ( ( ! [SY3817: $i,SY3818: $i] :
( ~ ( in @ ( ordered_pair @ SY3818 @ SY3817 ) @ SV28 )
| ( in @ ( ordered_pair @ SY3817 @ SY3818 ) @ SV219 ) ) )
= $true )
| ( ( SV219
= ( relation_inverse @ SV28 ) )
= $false )
| ( ( relation @ SV219 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2065]) ).
thf(2206,plain,
! [SV305: $i,SV280: $i,SV29: $i] :
( ( ( ! [SY3932: $i] :
( ~ ( in @ SY3932 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3932 @ SV280 )
| ( ( sK61_D @ SV305 @ SV280 @ SV29 )
!= ( apply @ SV29 @ SY3932 ) ) )
| ~ ( in @ ( sK61_D @ SV305 @ SV280 @ SV29 ) @ SV305 ) )
= $true )
| ( ( SV305
= ( relation_image @ SV29 @ SV280 ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2066]) ).
thf(2207,plain,
! [SV29: $i,SV280: $i,SV305: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) @ SV280 ) )
| ( ( sK61_D @ SV305 @ SV280 @ SV29 )
!= ( apply @ SV29 @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) ) ) )
| ( in @ ( sK61_D @ SV305 @ SV280 @ SV29 ) @ SV305 ) )
= $true )
| ( ( SV305
= ( relation_image @ SV29 @ SV280 ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2067]) ).
thf(2208,plain,
! [SV306: $i,SV281: $i,SV29: $i] :
( ( ( ~ ! [SY3933: $i] :
( ! [SY3910: $i] :
( ~ ( in @ SY3910 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3910 @ SV281 )
| ( SY3933
!= ( apply @ SV29 @ SY3910 ) ) )
| ( in @ SY3933 @ SV306 ) ) )
= $false )
| ( ( SV306
= ( relation_image @ SV29 @ SV281 ) )
= $false )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2068]) ).
thf(2209,plain,
! [SV29: $i,SV281: $i,SV306: $i] :
( ( ( ~ ! [SY3935: $i] :
( ~ ( in @ SY3935 @ SV306 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SY3935 @ SV306 @ SV281 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK60_E @ SY3935 @ SV306 @ SV281 @ SV29 ) @ SV281 ) )
| ( SY3935
!= ( apply @ SV29 @ ( sK60_E @ SY3935 @ SV306 @ SV281 @ SV29 ) ) ) ) ) )
= $false )
| ( ( SV306
= ( relation_image @ SV29 @ SV281 ) )
= $false )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2068]) ).
thf(2210,plain,
! [SV30: $i,SV220: $i,SV258: $i,SV368: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV368 @ ( sK55_D @ SV258 @ SV220 @ SV30 ) ) @ SV30 )
| ~ ( in @ SV368 @ SV220 ) )
= $true )
| ( ( ~ ( in @ ( sK55_D @ SV258 @ SV220 @ SV30 ) @ SV258 ) )
= $true )
| ( ( SV258
= ( relation_image @ SV30 @ SV220 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2069]) ).
thf(2211,plain,
! [SV30: $i,SV220: $i,SV258: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK56_SY3315 @ SV258 @ SV220 @ SV30 ) @ ( sK55_D @ SV258 @ SV220 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK56_SY3315 @ SV258 @ SV220 @ SV30 ) @ SV220 ) )
= $false )
| ( ( in @ ( sK55_D @ SV258 @ SV220 @ SV30 ) @ SV258 )
= $true )
| ( ( SV258
= ( relation_image @ SV30 @ SV220 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2070]) ).
thf(2212,plain,
! [SV259: $i,SV221: $i,SV30: $i,SV369: $i] :
( ( ( ! [SY3961: $i] :
( ~ ( in @ ( ordered_pair @ SY3961 @ SV369 ) @ SV30 )
| ~ ( in @ SY3961 @ SV221 ) )
| ( in @ SV369 @ SV259 ) )
= $true )
| ( ( SV259
= ( relation_image @ SV30 @ SV221 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2071]) ).
thf(2213,plain,
! [SV30: $i,SV221: $i,SV259: $i,SV370: $i] :
( ( ( ~ ( in @ SV370 @ SV259 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SV370 @ SV259 @ SV221 @ SV30 ) @ SV370 ) @ SV30 )
| ~ ( in @ ( sK54_E @ SV370 @ SV259 @ SV221 @ SV30 ) @ SV221 ) ) )
= $true )
| ( ( SV259
= ( relation_image @ SV30 @ SV221 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2072]) ).
thf(2214,plain,
! [SV371: $i,SV31: $i,SV222: $i,SV260: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SV371 ) @ SV31 )
| ~ ( in @ SV371 @ SV222 ) )
= $true )
| ( ( ~ ( in @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SV260 ) )
= $true )
| ( ( SV260
= ( relation_inverse_image @ SV31 @ SV222 ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2073]) ).
thf(2215,plain,
! [SV31: $i,SV222: $i,SV260: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ ( sK53_SY3313 @ SV260 @ SV222 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( sK53_SY3313 @ SV260 @ SV222 @ SV31 ) @ SV222 ) )
= $false )
| ( ( in @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SV260 )
= $true )
| ( ( SV260
= ( relation_inverse_image @ SV31 @ SV222 ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2074]) ).
thf(2216,plain,
! [SV261: $i,SV223: $i,SV31: $i,SV372: $i] :
( ( ( ! [SY3962: $i] :
( ~ ( in @ ( ordered_pair @ SV372 @ SY3962 ) @ SV31 )
| ~ ( in @ SY3962 @ SV223 ) )
| ( in @ SV372 @ SV261 ) )
= $true )
| ( ( SV261
= ( relation_inverse_image @ SV31 @ SV223 ) )
= $false )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2217,plain,
! [SV31: $i,SV223: $i,SV261: $i,SV373: $i] :
( ( ( ~ ( in @ SV373 @ SV261 )
| ~ ( ~ ( in @ ( ordered_pair @ SV373 @ ( sK51_E @ SV373 @ SV261 @ SV223 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( sK51_E @ SV373 @ SV261 @ SV223 @ SV31 ) @ SV223 ) ) )
= $true )
| ( ( SV261
= ( relation_inverse_image @ SV31 @ SV223 ) )
= $false )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2076]) ).
thf(2218,plain,
! [SV32: $i,SV224: $i,SV262: $i] :
( ( ( ~ ( in @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ SV224 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV32 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 ) )
= $true )
| ( ( SV262
= ( relation_dom_restriction @ SV32 @ SV224 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2077]) ).
thf(2219,plain,
! [SV32: $i,SV224: $i,SV262: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ SV224 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV32 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 ) ) ) )
= $true )
| ( ( SV262
= ( relation_dom_restriction @ SV32 @ SV224 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2078]) ).
thf(2220,plain,
! [SV263: $i,SV32: $i,SV225: $i] :
( ( ( ~ ! [SY3888: $i,SY3889: $i] :
( ~ ( in @ SY3888 @ SV225 )
| ~ ( in @ ( ordered_pair @ SY3888 @ SY3889 ) @ SV32 )
| ( in @ ( ordered_pair @ SY3888 @ SY3889 ) @ SV263 ) ) )
= $false )
| ( ( SV263
= ( relation_dom_restriction @ SV32 @ SV225 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2079]) ).
thf(2221,plain,
! [SV32: $i,SV225: $i,SV263: $i] :
( ( ( ~ ~ ( ~ ! [SY3890: $i] :
( ! [SY3891: $i] :
~ ( in @ ( ordered_pair @ SY3890 @ SY3891 ) @ SV263 )
| ( in @ SY3890 @ SV225 ) )
| ~ ! [SY3892: $i,SY3893: $i] :
( ~ ( in @ ( ordered_pair @ SY3892 @ SY3893 ) @ SV263 )
| ( in @ ( ordered_pair @ SY3892 @ SY3893 ) @ SV32 ) ) ) )
= $false )
| ( ( SV263
= ( relation_dom_restriction @ SV32 @ SV225 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2079]) ).
thf(2222,plain,
! [SV143: $i,SV188: $i,SV307: $i,SV33: $i] :
( ( ( in @ ( ordered_pair @ SV33 @ SV307 ) @ SV188 )
= $false )
| ( ( in @ SV307 @ ( relation_rng @ SV188 ) )
= $false )
| ( ( ~ ( in @ SV307 @ SV143 ) )
= $true )
| ( ( in @ SV33 @ ( relation_inverse_image @ SV188 @ SV143 ) )
= $true )
| ( ( relation @ SV188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2080]) ).
thf(2223,plain,
! [SV33: $i,SV144: $i,SV189: $i] :
( ( ( ~ ( in @ ( sK75_D @ SV189 @ SV144 @ SV33 ) @ ( relation_rng @ SV189 ) )
| ~ ( in @ ( ordered_pair @ SV33 @ ( sK75_D @ SV189 @ SV144 @ SV33 ) ) @ SV189 ) )
= $false )
| ( ( in @ SV33 @ ( relation_inverse_image @ SV189 @ SV144 ) )
= $false )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2081]) ).
thf(2224,plain,
! [SV110: $i,SV145: $i] :
( ( ( ( sK65_C @ SV145 @ SV110 )
= ( sK66_SY3320 @ SV145 @ SV110 ) )
= $false )
| ( ( ~ ( in @ ( sK65_C @ SV145 @ SV110 ) @ SV110 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 ) )
= $true )
| ( ( SV145
= ( identity_relation @ SV110 ) )
= $true )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2083]) ).
thf(2225,plain,
! [SV110: $i,SV145: $i] :
( ( ( ( ( sK65_C @ SV145 @ SV110 )
= ( sK66_SY3320 @ SV145 @ SV110 ) )
| ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 ) )
= $true )
| ( ( SV145
= ( identity_relation @ SV110 ) )
= $true )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2084]) ).
thf(2226,plain,
! [SV110: $i,SV145: $i] :
( ( ( ( in @ ( sK65_C @ SV145 @ SV110 ) @ SV110 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 ) )
= $true )
| ( ( SV145
= ( identity_relation @ SV110 ) )
= $true )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2085]) ).
thf(2227,plain,
! [SV146: $i,SV111: $i,SV374: $i,SV352: $i] :
( ( ( ( SV352 != SV374 )
| ~ ( in @ SV352 @ SV111 )
| ( in @ ( ordered_pair @ SV352 @ SV374 ) @ SV146 ) )
= $true )
| ( ( SV146
= ( identity_relation @ SV111 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2086]) ).
thf(2228,plain,
! [SV111: $i,SV146: $i] :
( ( ( ~ ! [SY3734: $i,SY3735: $i] :
( ~ ( in @ ( ordered_pair @ SY3734 @ SY3735 ) @ SV146 )
| ( SY3734 = SY3735 ) ) )
= $false )
| ( ( SV146
= ( identity_relation @ SV111 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2087]) ).
thf(2229,plain,
! [SV111: $i,SV146: $i] :
( ( ( ~ ! [SY3736: $i] :
( ! [SY3737: $i] :
~ ( in @ ( ordered_pair @ SY3736 @ SY3737 ) @ SV146 )
| ( in @ SY3736 @ SV111 ) ) )
= $false )
| ( ( SV146
= ( identity_relation @ SV111 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2087]) ).
thf(2230,plain,
! [SV34: $i,SV89: $i,SV190: $i,SV226: $i] :
( ( ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV190 ) )
= $true )
| ( ( SV226
= ( unordered_triple @ SV34 @ SV89 @ SV190 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2088]) ).
thf(2231,plain,
! [SV34: $i,SV89: $i,SV190: $i,SV226: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV34 ) )
| ~ ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV89 ) ) ) )
= $true )
| ( ( SV226
= ( unordered_triple @ SV34 @ SV89 @ SV190 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2089]) ).
thf(2232,plain,
! [SV34: $i,SV89: $i,SV190: $i,SV226: $i] :
( ( ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
= SV34 )
= $true )
| ( ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
= SV89 )
= $true )
| ( ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
= SV190 )
= $true )
| ( ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
= $true )
| ( ( SV226
= ( unordered_triple @ SV34 @ SV89 @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2090]) ).
thf(2233,plain,
! [SV89: $i,SV34: $i,SV191: $i,SV227: $i,SV353: $i] :
( ( ( ~ ( in @ SV353 @ SV227 ) )
= $true )
| ( ( ( SV353 = SV191 )
| ( SV353 = SV34 )
| ( SV353 = SV89 ) )
= $true )
| ( ( SV227
= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2091]) ).
thf(2234,plain,
! [SV89: $i,SV34: $i,SV227: $i,SV191: $i] :
( ( ( ~ ! [SY3840: $i] :
( ( SY3840 != SV191 )
| ( in @ SY3840 @ SV227 ) ) )
= $false )
| ( ( SV227
= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2092]) ).
thf(2235,plain,
! [SV191: $i,SV89: $i,SV227: $i,SV34: $i] :
( ( ( ~ ~ ( ~ ! [SY3841: $i] :
( ( SY3841 != SV34 )
| ( in @ SY3841 @ SV227 ) )
| ~ ! [SY3842: $i] :
( ( SY3842 != SV89 )
| ( in @ SY3842 @ SV227 ) ) ) )
= $false )
| ( ( SV227
= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2092]) ).
thf(2236,plain,
! [SV36: $i,SV228: $i,SV354: $i] :
( ( ( in @ ( ordered_pair @ SV354 @ ( sK16_C @ SV228 @ SV36 ) ) @ SV36 )
= $false )
| ( ( ~ ( in @ ( sK16_C @ SV228 @ SV36 ) @ SV228 ) )
= $true )
| ( ( SV228
= ( relation_rng @ SV36 ) )
= $true )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2093]) ).
thf(2237,plain,
! [SV229: $i,SV36: $i,SV355: $i] :
( ( ( ! [SY3958: $i] :
~ ( in @ ( ordered_pair @ SY3958 @ SV355 ) @ SV36 ) )
= $true )
| ( ( in @ SV355 @ SV229 )
= $true )
| ( ( SV229
= ( relation_rng @ SV36 ) )
= $false )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2094]) ).
thf(2238,plain,
! [SV36: $i,SV229: $i,SV356: $i] :
( ( ( ~ ( in @ SV356 @ SV229 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK15_D @ SV356 @ SV229 @ SV36 ) @ SV356 ) @ SV36 )
= $true )
| ( ( SV229
= ( relation_rng @ SV36 ) )
= $false )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2095]) ).
thf(2239,plain,
! [SV337: $i,SV37: $i,SV324: $i] :
( ( ( ~ ( in @ SV324 @ ( sK77_B @ SV37 ) ) )
= $true )
| ( ( ~ ( subset @ SV337 @ SV324 ) )
= $true )
| ( ( in @ SV337 @ ( sK77_B @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2096]) ).
thf(2240,plain,
! [SV91: $i,SV39: $i,SV308: $i] :
( ( ( relation @ SV308 )
= $false )
| ( ( function @ SV308 )
= $false )
| ( ( ~ ( in @ SV39 @ ( relation_dom @ SV308 ) )
| ~ ( in @ ( apply @ SV308 @ SV39 ) @ ( relation_dom @ SV91 ) )
| ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SV308 @ SV91 ) ) ) )
= $true )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2101]) ).
thf(2241,plain,
! [SV91: $i,SV39: $i,SV357: $i] :
( ( ( ~ ( function @ SV357 )
| ~ ( relation @ SV357 ) )
= $true )
| ( ( ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SV357 @ SV91 ) ) )
| ( in @ SV39 @ ( relation_dom @ SV357 ) ) )
= $true )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2102]) ).
thf(2242,plain,
! [SV91: $i,SV39: $i,SV358: $i] :
( ( ( ~ ( function @ SV358 )
| ~ ( relation @ SV358 ) )
= $true )
| ( ( ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SV358 @ SV91 ) ) )
| ( in @ ( apply @ SV358 @ SV39 ) @ ( relation_dom @ SV91 ) ) )
= $true )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2103]) ).
thf(2243,plain,
! [SV40: $i,SV92: $i,SV265: $i] :
( ( ( element @ ( sK6_D @ SV265 @ SV92 @ SV40 ) @ ( powerset @ SV40 ) )
= $true )
| ( ( SV265
= ( complements_of_subsets @ SV40 @ SV92 ) )
= $true )
| ( ( element @ SV265 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2104]) ).
thf(2244,plain,
! [SV40: $i,SV92: $i,SV265: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK6_D @ SV265 @ SV92 @ SV40 ) @ SV265 )
| ~ ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SV265 @ SV92 @ SV40 ) ) @ SV92 ) )
| ~ ( ( in @ ( sK6_D @ SV265 @ SV92 @ SV40 ) @ SV265 )
| ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SV265 @ SV92 @ SV40 ) ) @ SV92 ) ) ) )
= $true )
| ( ( SV265
= ( complements_of_subsets @ SV40 @ SV92 ) )
= $true )
| ( ( element @ SV265 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2105]) ).
thf(2245,plain,
! [SV92: $i,SV266: $i,SV40: $i] :
( ( ( ~ ! [SY3894: $i] :
( ~ ( element @ SY3894 @ ( powerset @ SV40 ) )
| ~ ( in @ SY3894 @ SV266 )
| ( in @ ( subset_complement @ SV40 @ SY3894 ) @ SV92 ) ) )
= $false )
| ( ( SV266
= ( complements_of_subsets @ SV40 @ SV92 ) )
= $false )
| ( ( element @ SV266 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2106]) ).
thf(2246,plain,
! [SV266: $i,SV92: $i,SV40: $i] :
( ( ( ~ ! [SY3895: $i] :
( ~ ( element @ SY3895 @ ( powerset @ SV40 ) )
| ~ ( in @ ( subset_complement @ SV40 @ SY3895 ) @ SV92 )
| ( in @ SY3895 @ SV266 ) ) )
= $false )
| ( ( SV266
= ( complements_of_subsets @ SV40 @ SV92 ) )
= $false )
| ( ( element @ SV266 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2106]) ).
thf(2247,plain,
! [SV154: $i,SV194: $i,SV41: $i] :
( ( ( in @ SV41 @ ( relation_dom @ SV194 ) )
= $false )
| ( ( SV154
= ( apply @ SV194 @ SV41 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV41 @ SV154 ) @ SV194 )
= $true )
| ( ( function @ SV194 )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2107]) ).
thf(2248,plain,
! [SV282: $i,SV267: $i,SV41: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV41 @ SV267 ) @ SV282 ) )
= $true )
| ( ( SV267
= ( apply @ SV282 @ SV41 ) )
= $true )
| ( ( function @ SV282 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2108]) ).
thf(2249,plain,
! [SV283: $i,SV268: $i,SV41: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV41 @ SV268 ) @ SV283 ) )
= $true )
| ( ( in @ SV41 @ ( relation_dom @ SV283 ) )
= $true )
| ( ( function @ SV283 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2109]) ).
thf(2250,plain,
! [SV43: $i,SV271: $i,SV359: $i] :
( ( ( ~ ( subset @ SV359 @ SV271 ) )
= $true )
| ( ( in @ SV359 @ ( sK3_SY3278 @ SV271 @ SV43 ) )
= $true )
| ( ( ~ ( in @ SV271 @ ( sK2_B @ SV43 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2112]) ).
thf(2251,plain,
! [SV338: $i,SV43: $i,SV327: $i] :
( ( ( ~ ( in @ SV327 @ ( sK2_B @ SV43 ) ) )
= $true )
| ( ( ~ ( subset @ SV338 @ SV327 ) )
= $true )
| ( ( in @ SV338 @ ( sK2_B @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2114]) ).
thf(2252,plain,
! [SV360: $i,SV45: $i,SV232: $i] :
( ( ( in @ ( ordered_pair @ ( sK26_C @ SV232 @ SV45 ) @ SV360 ) @ SV45 )
= $false )
| ( ( ~ ( in @ ( sK26_C @ SV232 @ SV45 ) @ SV232 ) )
= $true )
| ( ( SV232
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2115]) ).
thf(2253,plain,
! [SV233: $i,SV45: $i,SV361: $i] :
( ( ( ! [SY3959: $i] :
~ ( in @ ( ordered_pair @ SV361 @ SY3959 ) @ SV45 ) )
= $true )
| ( ( in @ SV361 @ SV233 )
= $true )
| ( ( SV233
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2116]) ).
thf(2254,plain,
! [SV45: $i,SV233: $i,SV362: $i] :
( ( ( ~ ( in @ SV362 @ SV233 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV362 @ ( sK25_D @ SV362 @ SV233 @ SV45 ) ) @ SV45 )
= $true )
| ( ( SV233
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2117]) ).
thf(2255,plain,
! [SV122: $i,SV159: $i] :
( ( ( in @ ( sK74_C @ SV159 @ SV122 ) @ SV122 )
= $true )
| ( ( ( ( relation_dom @ SV159 )
!= SV122 ) )
= $true )
| ( ( SV159
= ( identity_relation @ SV122 ) )
= $true )
| ( ( function @ SV159 )
= $false )
| ( ( relation @ SV159 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2120]) ).
thf(2256,plain,
! [SV122: $i,SV159: $i] :
( ( ( ( ( apply @ SV159 @ ( sK74_C @ SV159 @ SV122 ) )
!= ( sK74_C @ SV159 @ SV122 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV159 )
!= SV122 ) )
= $true )
| ( ( SV159
= ( identity_relation @ SV122 ) )
= $true )
| ( ( function @ SV159 )
= $false )
| ( ( relation @ SV159 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2121]) ).
thf(2257,plain,
! [SV239: $i,SV272: $i] :
( ( ( SV272
= ( identity_relation @ SV239 ) )
= $false )
| ( ( ! [SY3901: $i] :
( ~ ( in @ SY3901 @ SV239 )
| ( ( apply @ SV272 @ SY3901 )
= SY3901 ) ) )
= $true )
| ( ( function @ SV272 )
= $false )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2122]) ).
thf(2258,plain,
! [SV240: $i,SV273: $i] :
( ( ( SV273
= ( identity_relation @ SV240 ) )
= $false )
| ( ( ( relation_dom @ SV273 )
= SV240 )
= $true )
| ( ( function @ SV273 )
= $false )
| ( ( relation @ SV273 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2123]) ).
thf(2259,plain,
! [SV46: $i,SV331: $i] :
( ( ( function @ SV331 )
= $false )
| ( ( ~ ( relation @ SV331 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) )
| ( SV331
= ( function_inverse @ SV46 ) ) )
= $true )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2124]) ).
thf(2260,plain,
! [SV46: $i,SV375: $i] :
( ( ( ~ ( function @ SV375 )
| ~ ( relation @ SV375 )
| ( SV375
!= ( function_inverse @ SV46 ) )
| ~ ( ~ ~ ( ~ ! [SY3963: $i,SY3964: $i] :
( ( SY3964
!= ( apply @ SV375 @ SY3963 ) )
| ~ ( in @ SY3963 @ ( relation_rng @ SV46 ) )
| ( SY3963
= ( apply @ SV46 @ SY3964 ) ) )
| ~ ! [SY3965: $i,SY3966: $i] :
( ( SY3966
!= ( apply @ SV375 @ SY3965 ) )
| ~ ( in @ SY3965 @ ( relation_rng @ SV46 ) )
| ( in @ SY3966 @ ( relation_dom @ SV46 ) ) ) )
| ~ ~ ( ~ ! [SY3967: $i,SY3968: $i] :
( ( SY3967
!= ( apply @ SV46 @ SY3968 ) )
| ~ ( in @ SY3968 @ ( relation_dom @ SV46 ) )
| ( SY3968
= ( apply @ SV375 @ SY3967 ) ) )
| ~ ! [SY3491: $i] :
( ! [SY3492: $i] :
( ( SY3491
!= ( apply @ SV46 @ SY3492 ) )
| ~ ( in @ SY3492 @ ( relation_dom @ SV46 ) ) )
| ( in @ SY3491 @ ( relation_rng @ SV46 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2125]) ).
thf(2261,plain,
! [SV46: $i,SV376: $i] :
( ( ( ~ ( function @ SV376 )
| ~ ( relation @ SV376 )
| ( SV376
!= ( function_inverse @ SV46 ) )
| ( ( relation_dom @ SV376 )
= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2126]) ).
thf(2262,plain,
! [SV47: $i,SV123: $i,SV313: $i] :
( ( ( ~ ( ! [SY3936: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ SY3936 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3936 @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV123 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV313 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK10_SY3288 @ SV313 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY3288 @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV123 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV313 ) ) )
= $false )
| ( ( SV313
= ( relation_composition @ SV47 @ SV123 ) )
= $true )
| ( ( relation @ SV313 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2127]) ).
thf(2263,plain,
! [SV123: $i,SV47: $i,SV314: $i] :
( ( ( SV314
= ( relation_composition @ SV47 @ SV123 ) )
= $false )
| ( ( ~ ( ~ ! [SY3937: $i,SY3938: $i] :
( ! [SY3706: $i] :
( ~ ( in @ ( ordered_pair @ SY3937 @ SY3706 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3706 @ SY3938 ) @ SV123 ) )
| ( in @ ( ordered_pair @ SY3937 @ SY3938 ) @ SV314 ) )
| ~ ! [SY3940: $i,SY3941: $i] :
( ~ ( in @ ( ordered_pair @ SY3940 @ SY3941 ) @ SV314 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3940 @ ( sK7_F @ SY3941 @ SY3940 @ SV314 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY3941 @ SY3940 @ SV314 @ SV123 @ SV47 ) @ SY3941 ) @ SV123 ) ) ) ) )
= $true )
| ( ( relation @ SV314 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2128]) ).
thf(2264,plain,
! [SV315: $i,SV293: $i,SV94: $i,SV49: $i] :
( ( ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SV293 ) @ SV315 ) )
= $false )
| ( ( in @ SV49 @ SV293 )
= $true )
| ( ( relation @ SV315 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2130]) ).
thf(2265,plain,
! [SV316: $i,SV294: $i,SV94: $i,SV49: $i] :
( ( ( in @ ( ordered_pair @ SV49 @ SV94 ) @ ( relation_composition @ ( identity_relation @ SV294 ) @ SV316 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV49 @ SV94 ) @ SV316 )
= $true )
| ( ( relation @ SV316 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2131]) ).
thf(2266,plain,
! [SV124: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK11_B @ SV124 ) @ ( relation_dom @ SV124 ) )
| ~ ( in @ ( sK12_SY3289 @ SV124 ) @ ( relation_dom @ SV124 ) ) ) )
= $false )
| ( ( one_to_one @ SV124 )
= $true )
| ( ( function @ SV124 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2132]) ).
thf(2267,plain,
! [SV124: $i] :
( ( ( ( ( apply @ SV124 @ ( sK11_B @ SV124 ) )
!= ( apply @ SV124 @ ( sK12_SY3289 @ SV124 ) ) ) )
= $false )
| ( ( one_to_one @ SV124 )
= $true )
| ( ( function @ SV124 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2132]) ).
thf(2268,plain,
! [SV339: $i,SV125: $i,SV332: $i] :
( ( ( ~ ( in @ SV332 @ ( relation_dom @ SV125 ) )
| ~ ( in @ SV339 @ ( relation_dom @ SV125 ) ) )
= $true )
| ( ( ( ( apply @ SV125 @ SV332 )
!= ( apply @ SV125 @ SV339 ) ) )
= $true )
| ( ( SV332 = SV339 )
= $true )
| ( ( one_to_one @ SV125 )
= $false )
| ( ( function @ SV125 )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2134]) ).
thf(2269,plain,
! [SV51: $i,SV161: $i,SV199: $i] :
( ( ( ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV199 ) )
= $true )
| ( ( ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV51 ) )
= $true )
| ( ( SV199
= ( set_union2 @ SV51 @ SV161 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2135]) ).
thf(2270,plain,
! [SV51: $i,SV161: $i,SV199: $i] :
( ( ( ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV199 ) )
= $true )
| ( ( ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV161 ) )
= $true )
| ( ( SV199
= ( set_union2 @ SV51 @ SV161 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2136]) ).
thf(2271,plain,
! [SV162: $i,SV51: $i,SV200: $i,SV340: $i] :
( ( ( in @ SV340 @ SV200 )
= $false )
| ( ( ( in @ SV340 @ SV51 )
| ( in @ SV340 @ SV162 ) )
= $true )
| ( ( SV200
= ( set_union2 @ SV51 @ SV162 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2137]) ).
thf(2272,plain,
! [SV162: $i,SV200: $i,SV51: $i] :
( ( ( ! [SY3796: $i] :
( ~ ( in @ SY3796 @ SV51 )
| ( in @ SY3796 @ SV200 ) ) )
= $true )
| ( ( SV200
= ( set_union2 @ SV51 @ SV162 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2138]) ).
thf(2273,plain,
! [SV51: $i,SV200: $i,SV162: $i] :
( ( ( ! [SY3797: $i] :
( ~ ( in @ SY3797 @ SV162 )
| ( in @ SY3797 @ SV200 ) ) )
= $true )
| ( ( SV200
= ( set_union2 @ SV51 @ SV162 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2139]) ).
thf(2274,plain,
! [SV52: $i,SV243: $i] :
( ( ( in @ ( ordered_pair @ ( sK30_C @ SV243 @ SV52 ) @ ( sK31_SY3299 @ SV243 @ SV52 ) ) @ SV243 )
= $false )
| ( ( subset @ SV52 @ SV243 )
= $true )
| ( ( relation @ SV243 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2141]) ).
thf(2275,plain,
! [SV244: $i,SV52: $i,SV363: $i,SV341: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV341 @ SV363 ) @ SV52 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV341 @ SV363 ) @ SV244 )
= $true )
| ( ( subset @ SV52 @ SV244 )
= $false )
| ( ( relation @ SV244 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2142]) ).
thf(2276,plain,
! [SV245: $i,SV295: $i] :
( ( ( ~ ( ~ ( in @ ( sK46_SY3307 @ SV295 @ SV245 ) @ SV245 )
| ~ ~ ( in @ ( sK45_C @ SV295 @ SV245 ) @ ( sK46_SY3307 @ SV295 @ SV245 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK45_C @ SV295 @ SV245 ) @ SV295 ) )
= $true )
| ( ( SV295
= ( set_meet @ SV245 ) )
= $true )
| ( ( SV245 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2143]) ).
thf(2277,plain,
! [SV295: $i,SV245: $i] :
( ( ( ! [SY3917: $i] :
( ~ ( in @ SY3917 @ SV245 )
| ( in @ ( sK45_C @ SV295 @ SV245 ) @ SY3917 ) ) )
= $true )
| ( ( in @ ( sK45_C @ SV295 @ SV245 ) @ SV295 )
= $true )
| ( ( SV295
= ( set_meet @ SV245 ) )
= $true )
| ( ( SV245 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2144]) ).
thf(2278,plain,
! [SV246: $i,SV296: $i] :
( ( ( ! [SY3918: $i] :
( ~ ( ~ ( in @ ( sK44_D @ SY3918 @ SV296 @ SV246 ) @ SV246 )
| ~ ~ ( in @ SY3918 @ ( sK44_D @ SY3918 @ SV296 @ SV246 ) ) )
| ( in @ SY3918 @ SV296 ) ) )
= $true )
| ( ( SV296
= ( set_meet @ SV246 ) )
= $false )
| ( ( SV246 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2145]) ).
thf(2279,plain,
! [SV246: $i,SV296: $i] :
( ( ( ! [SY3919: $i] :
( ~ ( in @ SY3919 @ SV296 )
| ! [SY3865: $i] :
( ~ ( in @ SY3865 @ SV246 )
| ( in @ SY3919 @ SY3865 ) ) ) )
= $true )
| ( ( SV296
= ( set_meet @ SV246 ) )
= $false )
| ( ( SV246 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2146]) ).
thf(2280,plain,
! [SV53: $i,SV297: $i,SV319: $i] :
( ( ( ~ ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ ( sK57_D @ SV319 @ SV297 @ SV53 ) ) @ SV297 )
| ~ ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ SV319 ) )
= $true )
| ( ( SV319
= ( relation_inverse_image @ SV53 @ SV297 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2147]) ).
thf(2281,plain,
! [SV53: $i,SV297: $i,SV319: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ SV319 ) )
| ~ ( ( in @ ( apply @ SV53 @ ( sK57_D @ SV319 @ SV297 @ SV53 ) ) @ SV297 )
| ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ SV319 ) ) ) )
= $true )
| ( ( SV319
= ( relation_inverse_image @ SV53 @ SV297 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2148]) ).
thf(2282,plain,
! [SV320: $i,SV298: $i,SV53: $i] :
( ( ( ~ ! [SY3942: $i] :
( ~ ( in @ SY3942 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SY3942 ) @ SV298 )
| ( in @ SY3942 @ SV320 ) ) )
= $false )
| ( ( SV320
= ( relation_inverse_image @ SV53 @ SV298 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2149]) ).
thf(2283,plain,
! [SV298: $i,SV53: $i,SV320: $i] :
( ( ( ~ ~ ( ~ ! [SY3943: $i] :
( ~ ( in @ SY3943 @ SV320 )
| ( in @ SY3943 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY3944: $i] :
( ~ ( in @ SY3944 @ SV320 )
| ( in @ ( apply @ SV53 @ SY3944 ) @ SV298 ) ) ) )
= $false )
| ( ( SV320
= ( relation_inverse_image @ SV53 @ SV298 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2149]) ).
thf(2284,plain,
! [SV54: $i,SV165: $i,SV201: $i] :
( ( ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV165 )
= $false )
| ( ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV54 )
= $false )
| ( ( ~ ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV201 ) )
= $true )
| ( ( SV201
= ( set_intersection2 @ SV54 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2150]) ).
thf(2285,plain,
! [SV54: $i,SV165: $i,SV201: $i] :
( ( ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV54 )
= $true )
| ( ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV201 )
= $true )
| ( ( SV201
= ( set_intersection2 @ SV54 @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2151]) ).
thf(2286,plain,
! [SV54: $i,SV165: $i,SV201: $i] :
( ( ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV165 )
= $true )
| ( ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV201 )
= $true )
| ( ( SV201
= ( set_intersection2 @ SV54 @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2152]) ).
thf(2287,plain,
! [SV202: $i,SV166: $i,SV54: $i,SV342: $i] :
( ( ( ~ ( in @ SV342 @ SV54 ) )
= $true )
| ( ( ~ ( in @ SV342 @ SV166 ) )
= $true )
| ( ( in @ SV342 @ SV202 )
= $true )
| ( ( SV202
= ( set_intersection2 @ SV54 @ SV166 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2153]) ).
thf(2288,plain,
! [SV166: $i,SV54: $i,SV202: $i] :
( ( ( ! [SY3799: $i] :
( ~ ( in @ SY3799 @ SV202 )
| ( in @ SY3799 @ SV54 ) ) )
= $true )
| ( ( SV202
= ( set_intersection2 @ SV54 @ SV166 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2154]) ).
thf(2289,plain,
! [SV54: $i,SV166: $i,SV202: $i] :
( ( ( ! [SY3800: $i] :
( ~ ( in @ SY3800 @ SV202 )
| ( in @ SY3800 @ SV166 ) ) )
= $true )
| ( ( SV202
= ( set_intersection2 @ SV54 @ SV166 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2155]) ).
thf(2290,plain,
! [SV55: $i,SV169: $i,SV203: $i] :
( ( ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV203 )
= $false )
| ( ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV169 )
= $true )
| ( ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV55 )
= $false )
| ( ( SV203
= ( set_difference @ SV55 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2156]) ).
thf(2291,plain,
! [SV55: $i,SV169: $i,SV203: $i] :
( ( ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV55 )
= $true )
| ( ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV203 )
= $true )
| ( ( SV203
= ( set_difference @ SV55 @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2157]) ).
thf(2292,plain,
! [SV55: $i,SV169: $i,SV203: $i] :
( ( ( ~ ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV169 ) )
= $true )
| ( ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV203 )
= $true )
| ( ( SV203
= ( set_difference @ SV55 @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2158]) ).
thf(2293,plain,
! [SV204: $i,SV170: $i,SV55: $i,SV343: $i] :
( ( ( ~ ( in @ SV343 @ SV55 ) )
= $true )
| ( ( in @ SV343 @ SV170 )
= $true )
| ( ( in @ SV343 @ SV204 )
= $true )
| ( ( SV204
= ( set_difference @ SV55 @ SV170 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2159]) ).
thf(2294,plain,
! [SV170: $i,SV55: $i,SV204: $i] :
( ( ( ! [SY3802: $i] :
( ~ ( in @ SY3802 @ SV204 )
| ( in @ SY3802 @ SV55 ) ) )
= $true )
| ( ( SV204
= ( set_difference @ SV55 @ SV170 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2160]) ).
thf(2295,plain,
! [SV55: $i,SV170: $i,SV204: $i] :
( ( ( ! [SY3803: $i] :
( ~ ( in @ SY3803 @ SV204 )
| ~ ( in @ SY3803 @ SV170 ) ) )
= $true )
| ( ( SV204
= ( set_difference @ SV55 @ SV170 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2161]) ).
thf(2296,plain,
! [SV56: $i,SV299: $i] :
( ( ( ! [SY3926: $i] :
( ( ( sK19_C @ SV299 @ SV56 )
!= ( apply @ SV56 @ SY3926 ) )
| ~ ( in @ SY3926 @ ( relation_dom @ SV56 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK19_C @ SV299 @ SV56 ) @ SV299 ) )
= $true )
| ( ( SV299
= ( relation_rng @ SV56 ) )
= $true )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2162]) ).
thf(2297,plain,
! [SV56: $i,SV299: $i] :
( ( ( ~ ( ( ( sK19_C @ SV299 @ SV56 )
!= ( apply @ SV56 @ ( sK20_SY3294 @ SV299 @ SV56 ) ) )
| ~ ( in @ ( sK20_SY3294 @ SV299 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
= $true )
| ( ( in @ ( sK19_C @ SV299 @ SV56 ) @ SV299 )
= $true )
| ( ( SV299
= ( relation_rng @ SV56 ) )
= $true )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2163]) ).
thf(2298,plain,
! [SV300: $i,SV56: $i] :
( ( ( ! [SY3927: $i] :
( ! [SY3554: $i] :
( ( SY3927
!= ( apply @ SV56 @ SY3554 ) )
| ~ ( in @ SY3554 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY3927 @ SV300 ) ) )
= $true )
| ( ( SV300
= ( relation_rng @ SV56 ) )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2164]) ).
thf(2299,plain,
! [SV56: $i,SV300: $i] :
( ( ( ! [SY3929: $i] :
( ~ ( in @ SY3929 @ SV300 )
| ~ ( ( SY3929
!= ( apply @ SV56 @ ( sK18_D @ SY3929 @ SV300 @ SV56 ) ) )
| ~ ( in @ ( sK18_D @ SY3929 @ SV300 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) ) )
= $true )
| ( ( SV300
= ( relation_rng @ SV56 ) )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2165]) ).
thf(2300,plain,
! [SV57: $i,SV171: $i,SV205: $i] :
( ( ( ~ ( in @ ( sK38_D @ SV205 @ SV171 @ SV57 ) @ SV205 ) )
= $true )
| ( ( ( ( sK38_D @ SV205 @ SV171 @ SV57 )
!= SV57 ) )
= $true )
| ( ( SV205
= ( unordered_pair @ SV57 @ SV171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2166]) ).
thf(2301,plain,
! [SV57: $i,SV171: $i,SV205: $i] :
( ( ( ~ ( in @ ( sK38_D @ SV205 @ SV171 @ SV57 ) @ SV205 ) )
= $true )
| ( ( ( ( sK38_D @ SV205 @ SV171 @ SV57 )
!= SV171 ) )
= $true )
| ( ( SV205
= ( unordered_pair @ SV57 @ SV171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2167]) ).
thf(2302,plain,
! [SV172: $i,SV57: $i,SV206: $i,SV344: $i] :
( ( ( in @ SV344 @ SV206 )
= $false )
| ( ( ( SV344 = SV57 )
| ( SV344 = SV172 ) )
= $true )
| ( ( SV206
= ( unordered_pair @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2168]) ).
thf(2303,plain,
! [SV172: $i,SV206: $i,SV57: $i] :
( ( ( ! [SY3805: $i] :
( ( SY3805 != SV57 )
| ( in @ SY3805 @ SV206 ) ) )
= $true )
| ( ( SV206
= ( unordered_pair @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2169]) ).
thf(2304,plain,
! [SV57: $i,SV206: $i,SV172: $i] :
( ( ( ! [SY3806: $i] :
( ( SY3806 != SV172 )
| ( in @ SY3806 @ SV206 ) ) )
= $true )
| ( ( SV206
= ( unordered_pair @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2170]) ).
thf(2305,plain,
! [SV58: $i,SV96: $i,SV321: $i] :
( ( ( relation @ SV321 )
= $false )
| ( ( function @ SV321 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK67_D @ SV321 @ SV96 @ SV58 ) @ ( relation_dom @ SV96 ) )
| ~ ( ( ( apply @ SV96 @ ( sK67_D @ SV321 @ SV96 @ SV58 ) )
!= ( apply @ SV321 @ ( sK67_D @ SV321 @ SV96 @ SV58 ) ) ) ) )
| ( ( relation_dom @ SV96 )
!= ( set_intersection2 @ ( relation_dom @ SV321 ) @ SV58 ) )
| ( SV96
= ( relation_dom_restriction @ SV321 @ SV58 ) ) )
= $true )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2171]) ).
thf(2306,plain,
! [SV58: $i,SV96: $i,SV364: $i] :
( ( ( ~ ( function @ SV364 )
| ~ ( relation @ SV364 ) )
= $true )
| ( ( ( SV96
!= ( relation_dom_restriction @ SV364 @ SV58 ) )
| ! [SY3960: $i] :
( ~ ( in @ SY3960 @ ( relation_dom @ SV96 ) )
| ( ( apply @ SV96 @ SY3960 )
= ( apply @ SV364 @ SY3960 ) ) ) )
= $true )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2172]) ).
thf(2307,plain,
! [SV58: $i,SV96: $i,SV365: $i] :
( ( ( ~ ( function @ SV365 )
| ~ ( relation @ SV365 ) )
= $true )
| ( ( ( SV96
!= ( relation_dom_restriction @ SV365 @ SV58 ) )
| ( ( relation_dom @ SV96 )
= ( set_intersection2 @ ( relation_dom @ SV365 ) @ SV58 ) ) )
= $true )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2173]) ).
thf(2308,plain,
! [SV59: $i,SV249: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV59 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV249 ) )
= $true )
| ( ( SV59 = SV249 )
= $true )
| ( ( relation @ SV249 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2174]) ).
thf(2309,plain,
! [SV59: $i,SV249: $i] :
( ( ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV59 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV249 )
= $true )
| ( ( SV59 = SV249 )
= $true )
| ( ( relation @ SV249 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2175]) ).
thf(2310,plain,
! [SV250: $i,SV59: $i] :
( ( ( ! [SY3868: $i,SY3869: $i] :
( ~ ( in @ ( ordered_pair @ SY3868 @ SY3869 ) @ SV59 )
| ( in @ ( ordered_pair @ SY3868 @ SY3869 ) @ SV250 ) ) )
= $true )
| ( ( SV59 = SV250 )
= $false )
| ( ( relation @ SV250 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2176]) ).
thf(2311,plain,
! [SV59: $i,SV250: $i] :
( ( ( ! [SY3870: $i,SY3871: $i] :
( ~ ( in @ ( ordered_pair @ SY3870 @ SY3871 ) @ SV250 )
| ( in @ ( ordered_pair @ SY3870 @ SY3871 ) @ SV59 ) ) )
= $true )
| ( ( SV59 = SV250 )
= $false )
| ( ( relation @ SV250 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2177]) ).
thf(2312,plain,
! [SV173: $i,SV130: $i,SV333: $i] :
( ( ( in @ SV333 @ SV130 )
= $false )
| ( ( in @ ( sK23_C @ SV173 @ SV130 ) @ SV333 )
= $false )
| ( ( ~ ( in @ ( sK23_C @ SV173 @ SV130 ) @ SV173 ) )
= $true )
| ( ( SV173
= ( union @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2178]) ).
thf(2313,plain,
! [SV174: $i,SV131: $i,SV366: $i,SV334: $i] :
( ( ( ~ ( in @ SV334 @ SV366 ) )
= $true )
| ( ( ~ ( in @ SV366 @ SV131 ) )
= $true )
| ( ( in @ SV334 @ SV174 )
= $true )
| ( ( SV174
= ( union @ SV131 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2181]) ).
thf(2314,plain,
! [SV131: $i,SV174: $i,SV335: $i] :
( ( ( ~ ( in @ SV335 @ ( sK22_D @ SV335 @ SV174 @ SV131 ) )
| ~ ( in @ ( sK22_D @ SV335 @ SV174 @ SV131 ) @ SV131 ) )
= $false )
| ( ( in @ SV335 @ SV174 )
= $false )
| ( ( SV174
= ( union @ SV131 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2182]) ).
thf(2315,plain,
! [SV208: $i,SV62: $i,SV175: $i] :
( ( ( in @ SV175 @ SV62 )
= $false )
| ( ( in @ SV175 @ ( relation_dom @ SV208 ) )
= $false )
| ( ( in @ SV175 @ ( relation_dom @ ( relation_dom_restriction @ SV208 @ SV62 ) ) )
= $true )
| ( ( function @ SV208 )
= $false )
| ( ( relation @ SV208 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2183]) ).
thf(2316,plain,
! [SV62: $i,SV303: $i,SV276: $i] :
( ( ( ~ ( in @ SV276 @ ( relation_dom @ ( relation_dom_restriction @ SV303 @ SV62 ) ) ) )
= $true )
| ( ( in @ SV276 @ ( relation_dom @ SV303 ) )
= $true )
| ( ( function @ SV303 )
= $false )
| ( ( relation @ SV303 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2184]) ).
thf(2317,plain,
! [SV62: $i,SV304: $i,SV277: $i] :
( ( ( ~ ( in @ SV277 @ ( relation_dom @ ( relation_dom_restriction @ SV304 @ SV62 ) ) ) )
= $true )
| ( ( in @ SV277 @ SV62 )
= $true )
| ( ( function @ SV304 )
= $false )
| ( ( relation @ SV304 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2185]) ).
thf(2318,plain,
! [SV209: $i,SV176: $i,SV367: $i,SV63: $i,SV345: $i] :
( ( ( ~ ( in @ SV345 @ SV63 )
| ~ ( in @ SV367 @ SV176 ) )
= $true )
| ( ( ( ( sK34_D @ SV209 @ SV176 @ SV63 )
!= ( ordered_pair @ SV345 @ SV367 ) ) )
= $true )
| ( ( ~ ( in @ ( sK34_D @ SV209 @ SV176 @ SV63 ) @ SV209 ) )
= $true )
| ( ( SV209
= ( cartesian_product2 @ SV63 @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2186]) ).
thf(2319,plain,
! [SV63: $i,SV176: $i,SV209: $i] :
( ( ( ~ ( ~ ( in @ ( sK35_SY3303 @ SV209 @ SV176 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK36_SY3305 @ SV209 @ SV176 @ SV63 ) @ SV176 ) ) )
= $true )
| ( ( in @ ( sK34_D @ SV209 @ SV176 @ SV63 ) @ SV209 )
= $true )
| ( ( SV209
= ( cartesian_product2 @ SV63 @ SV176 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2187]) ).
thf(2320,plain,
! [SV63: $i,SV176: $i,SV209: $i] :
( ( ( ( sK34_D @ SV209 @ SV176 @ SV63 )
= ( ordered_pair @ ( sK35_SY3303 @ SV209 @ SV176 @ SV63 ) @ ( sK36_SY3305 @ SV209 @ SV176 @ SV63 ) ) )
= $true )
| ( ( in @ ( sK34_D @ SV209 @ SV176 @ SV63 ) @ SV209 )
= $true )
| ( ( SV209
= ( cartesian_product2 @ SV63 @ SV176 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2188]) ).
thf(2321,plain,
! [SV210: $i,SV346: $i,SV177: $i,SV63: $i,SV377: $i] :
( ( ( ! [SY3971: $i] :
( ~ ( in @ SV377 @ SV63 )
| ~ ( in @ SY3971 @ SV177 )
| ( SV346
!= ( ordered_pair @ SV377 @ SY3971 ) ) ) )
= $true )
| ( ( in @ SV346 @ SV210 )
= $true )
| ( ( SV210
= ( cartesian_product2 @ SV63 @ SV177 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2189]) ).
thf(2322,plain,
! [SV63: $i,SV177: $i,SV210: $i,SV347: $i] :
( ( ( in @ SV347 @ SV210 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK32_E @ SV347 @ SV210 @ SV177 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK33_SY3300 @ SV347 @ SV210 @ SV177 @ SV63 ) @ SV177 ) )
| ( SV347
!= ( ordered_pair @ ( sK32_E @ SV347 @ SV210 @ SV177 @ SV63 ) @ ( sK33_SY3300 @ SV347 @ SV210 @ SV177 @ SV63 ) ) ) ) )
= $true )
| ( ( SV210
= ( cartesian_product2 @ SV63 @ SV177 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2190]) ).
thf(2323,plain,
! [SV180: $i,SV211: $i,SV64: $i,SV323: $i] :
( ( ( in @ ( ordered_pair @ SV323 @ SV64 ) @ SV211 )
= $false )
| ( ( in @ SV323 @ ( relation_dom @ SV211 ) )
= $false )
| ( ( ~ ( in @ SV323 @ SV180 ) )
= $true )
| ( ( in @ SV64 @ ( relation_image @ SV211 @ SV180 ) )
= $true )
| ( ( relation @ SV211 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2191]) ).
thf(2324,plain,
! [SV64: $i,SV181: $i,SV212: $i] :
( ( ( ~ ( in @ ( sK76_D @ SV212 @ SV181 @ SV64 ) @ ( relation_dom @ SV212 ) )
| ~ ( in @ ( ordered_pair @ ( sK76_D @ SV212 @ SV181 @ SV64 ) @ SV64 ) @ SV212 ) )
= $false )
| ( ( in @ SV64 @ ( relation_image @ SV212 @ SV181 ) )
= $false )
| ( ( relation @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2192]) ).
thf(2325,plain,
! [SV66: $i,SV348: $i] :
( ( ( in @ SV348 @ ( relation_dom @ SV66 ) )
= $false )
| ( ( ! [SY3953: $i] :
( ( SY3953
!= ( apply @ SV66 @ SV348 ) )
| ( in @ ( ordered_pair @ SV348 @ SY3953 ) @ SV66 ) ) )
= $true )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2194]) ).
thf(2326,plain,
! [SV66: $i,SV349: $i] :
( ( ( in @ SV349 @ ( relation_dom @ SV66 ) )
= $false )
| ( ( ! [SY3954: $i] :
( ~ ( in @ ( ordered_pair @ SV349 @ SY3954 ) @ SV66 )
| ( SY3954
= ( apply @ SV66 @ SV349 ) ) ) )
= $true )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2195]) ).
thf(2327,plain,
! [SV350: $i,SV66: $i,SV378: $i] :
( ( ( ( SV378
!= ( apply @ SV66 @ SV350 ) )
| ( SV378 = empty_set ) )
= $true )
| ( ( in @ SV350 @ ( relation_dom @ SV66 ) )
= $true )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2196]) ).
thf(2328,plain,
! [SV351: $i,SV66: $i,SV379: $i] :
( ( ( ( SV379 != empty_set )
| ( SV379
= ( apply @ SV66 @ SV351 ) ) )
= $true )
| ( ( in @ SV351 @ ( relation_dom @ SV66 ) )
= $true )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2197]) ).
thf(2329,plain,
! [SV26: $i,SV88: $i,SV253: $i] :
( ( ( ~ ( in @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) @ SV26 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV88 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 ) )
= $true )
| ( ( SV253
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $true )
| ( ( relation @ SV253 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2198]) ).
thf(2330,plain,
! [SV26: $i,SV88: $i,SV253: $i] :
( ( ( ~ ( ( in @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) @ SV26 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV88 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 ) ) )
= $false )
| ( ( SV253
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $true )
| ( ( relation @ SV253 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2199]) ).
thf(2331,plain,
! [SV254: $i,SV88: $i,SV26: $i] :
( ( ( ! [SY3872: $i,SY3873: $i] :
( ~ ( in @ SY3873 @ SV26 )
| ~ ( in @ ( ordered_pair @ SY3872 @ SY3873 ) @ SV88 )
| ( in @ ( ordered_pair @ SY3872 @ SY3873 ) @ SV254 ) ) )
= $true )
| ( ( SV254
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2200]) ).
thf(2332,plain,
! [SV88: $i,SV26: $i,SV254: $i] :
( ( ( ~ ( ~ ! [SY3874: $i,SY3875: $i] :
( ~ ( in @ ( ordered_pair @ SY3874 @ SY3875 ) @ SV254 )
| ( in @ SY3875 @ SV26 ) )
| ~ ! [SY3876: $i,SY3877: $i] :
( ~ ( in @ ( ordered_pair @ SY3876 @ SY3877 ) @ SV254 )
| ( in @ ( ordered_pair @ SY3876 @ SY3877 ) @ SV88 ) ) ) )
= $true )
| ( ( SV254
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2201]) ).
thf(2333,plain,
! [SV28: $i,SV218: $i] :
( ( ( in @ ( ordered_pair @ ( sK13_C @ SV218 @ SV28 ) @ ( sK14_SY3290 @ SV218 @ SV28 ) ) @ SV218 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK14_SY3290 @ SV218 @ SV28 ) @ ( sK13_C @ SV218 @ SV28 ) ) @ SV28 ) )
= $true )
| ( ( SV218
= ( relation_inverse @ SV28 ) )
= $true )
| ( ( relation @ SV218 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2202]) ).
thf(2334,plain,
! [SV28: $i,SV219: $i,SV380: $i] :
( ( ( ! [SY3972: $i] :
( ~ ( in @ ( ordered_pair @ SV380 @ SY3972 ) @ SV219 )
| ( in @ ( ordered_pair @ SY3972 @ SV380 ) @ SV28 ) ) )
= $true )
| ( ( SV219
= ( relation_inverse @ SV28 ) )
= $false )
| ( ( relation @ SV219 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2204]) ).
thf(2335,plain,
! [SV219: $i,SV28: $i,SV381: $i] :
( ( ( ! [SY3973: $i] :
( ~ ( in @ ( ordered_pair @ SY3973 @ SV381 ) @ SV28 )
| ( in @ ( ordered_pair @ SV381 @ SY3973 ) @ SV219 ) ) )
= $true )
| ( ( SV219
= ( relation_inverse @ SV28 ) )
= $false )
| ( ( relation @ SV219 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2205]) ).
thf(2336,plain,
! [SV305: $i,SV280: $i,SV29: $i] :
( ( ( ! [SY3932: $i] :
( ~ ( in @ SY3932 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3932 @ SV280 )
| ( ( sK61_D @ SV305 @ SV280 @ SV29 )
!= ( apply @ SV29 @ SY3932 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK61_D @ SV305 @ SV280 @ SV29 ) @ SV305 ) )
= $true )
| ( ( SV305
= ( relation_image @ SV29 @ SV280 ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2206]) ).
thf(2337,plain,
! [SV29: $i,SV280: $i,SV305: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) @ SV280 ) )
| ( ( sK61_D @ SV305 @ SV280 @ SV29 )
!= ( apply @ SV29 @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) ) ) ) )
= $true )
| ( ( in @ ( sK61_D @ SV305 @ SV280 @ SV29 ) @ SV305 )
= $true )
| ( ( SV305
= ( relation_image @ SV29 @ SV280 ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2207]) ).
thf(2338,plain,
! [SV306: $i,SV281: $i,SV29: $i] :
( ( ( ! [SY3933: $i] :
( ! [SY3910: $i] :
( ~ ( in @ SY3910 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3910 @ SV281 )
| ( SY3933
!= ( apply @ SV29 @ SY3910 ) ) )
| ( in @ SY3933 @ SV306 ) ) )
= $true )
| ( ( SV306
= ( relation_image @ SV29 @ SV281 ) )
= $false )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2208]) ).
thf(2339,plain,
! [SV29: $i,SV281: $i,SV306: $i] :
( ( ( ! [SY3935: $i] :
( ~ ( in @ SY3935 @ SV306 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SY3935 @ SV306 @ SV281 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK60_E @ SY3935 @ SV306 @ SV281 @ SV29 ) @ SV281 ) )
| ( SY3935
!= ( apply @ SV29 @ ( sK60_E @ SY3935 @ SV306 @ SV281 @ SV29 ) ) ) ) ) )
= $true )
| ( ( SV306
= ( relation_image @ SV29 @ SV281 ) )
= $false )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2209]) ).
thf(2340,plain,
! [SV30: $i,SV220: $i,SV258: $i,SV368: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV368 @ ( sK55_D @ SV258 @ SV220 @ SV30 ) ) @ SV30 ) )
= $true )
| ( ( ~ ( in @ SV368 @ SV220 ) )
= $true )
| ( ( ~ ( in @ ( sK55_D @ SV258 @ SV220 @ SV30 ) @ SV258 ) )
= $true )
| ( ( SV258
= ( relation_image @ SV30 @ SV220 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2210]) ).
thf(2341,plain,
! [SV30: $i,SV220: $i,SV258: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK56_SY3315 @ SV258 @ SV220 @ SV30 ) @ ( sK55_D @ SV258 @ SV220 @ SV30 ) ) @ SV30 ) )
= $false )
| ( ( in @ ( sK55_D @ SV258 @ SV220 @ SV30 ) @ SV258 )
= $true )
| ( ( SV258
= ( relation_image @ SV30 @ SV220 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2211]) ).
thf(2342,plain,
! [SV30: $i,SV220: $i,SV258: $i] :
( ( ( ~ ( in @ ( sK56_SY3315 @ SV258 @ SV220 @ SV30 ) @ SV220 ) )
= $false )
| ( ( in @ ( sK55_D @ SV258 @ SV220 @ SV30 ) @ SV258 )
= $true )
| ( ( SV258
= ( relation_image @ SV30 @ SV220 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2211]) ).
thf(2343,plain,
! [SV259: $i,SV221: $i,SV30: $i,SV369: $i] :
( ( ( ! [SY3961: $i] :
( ~ ( in @ ( ordered_pair @ SY3961 @ SV369 ) @ SV30 )
| ~ ( in @ SY3961 @ SV221 ) ) )
= $true )
| ( ( in @ SV369 @ SV259 )
= $true )
| ( ( SV259
= ( relation_image @ SV30 @ SV221 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2212]) ).
thf(2344,plain,
! [SV30: $i,SV221: $i,SV259: $i,SV370: $i] :
( ( ( ~ ( in @ SV370 @ SV259 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SV370 @ SV259 @ SV221 @ SV30 ) @ SV370 ) @ SV30 )
| ~ ( in @ ( sK54_E @ SV370 @ SV259 @ SV221 @ SV30 ) @ SV221 ) ) )
= $true )
| ( ( SV259
= ( relation_image @ SV30 @ SV221 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2213]) ).
thf(2345,plain,
! [SV371: $i,SV31: $i,SV222: $i,SV260: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SV371 ) @ SV31 ) )
= $true )
| ( ( ~ ( in @ SV371 @ SV222 ) )
= $true )
| ( ( ~ ( in @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SV260 ) )
= $true )
| ( ( SV260
= ( relation_inverse_image @ SV31 @ SV222 ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2214]) ).
thf(2346,plain,
! [SV31: $i,SV222: $i,SV260: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ ( sK53_SY3313 @ SV260 @ SV222 @ SV31 ) ) @ SV31 ) )
= $false )
| ( ( in @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SV260 )
= $true )
| ( ( SV260
= ( relation_inverse_image @ SV31 @ SV222 ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2215]) ).
thf(2347,plain,
! [SV31: $i,SV222: $i,SV260: $i] :
( ( ( ~ ( in @ ( sK53_SY3313 @ SV260 @ SV222 @ SV31 ) @ SV222 ) )
= $false )
| ( ( in @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SV260 )
= $true )
| ( ( SV260
= ( relation_inverse_image @ SV31 @ SV222 ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2215]) ).
thf(2348,plain,
! [SV261: $i,SV223: $i,SV31: $i,SV372: $i] :
( ( ( ! [SY3962: $i] :
( ~ ( in @ ( ordered_pair @ SV372 @ SY3962 ) @ SV31 )
| ~ ( in @ SY3962 @ SV223 ) ) )
= $true )
| ( ( in @ SV372 @ SV261 )
= $true )
| ( ( SV261
= ( relation_inverse_image @ SV31 @ SV223 ) )
= $false )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2216]) ).
thf(2349,plain,
! [SV31: $i,SV223: $i,SV261: $i,SV373: $i] :
( ( ( ~ ( in @ SV373 @ SV261 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV373 @ ( sK51_E @ SV373 @ SV261 @ SV223 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( sK51_E @ SV373 @ SV261 @ SV223 @ SV31 ) @ SV223 ) ) )
= $true )
| ( ( SV261
= ( relation_inverse_image @ SV31 @ SV223 ) )
= $false )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2217]) ).
thf(2350,plain,
! [SV32: $i,SV224: $i,SV262: $i] :
( ( ( ~ ( in @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ SV224 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV32 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 ) )
= $true )
| ( ( SV262
= ( relation_dom_restriction @ SV32 @ SV224 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2218]) ).
thf(2351,plain,
! [SV32: $i,SV224: $i,SV262: $i] :
( ( ( ~ ( ( in @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ SV224 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV32 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 ) ) )
= $false )
| ( ( SV262
= ( relation_dom_restriction @ SV32 @ SV224 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2219]) ).
thf(2352,plain,
! [SV263: $i,SV32: $i,SV225: $i] :
( ( ( ! [SY3888: $i,SY3889: $i] :
( ~ ( in @ SY3888 @ SV225 )
| ~ ( in @ ( ordered_pair @ SY3888 @ SY3889 ) @ SV32 )
| ( in @ ( ordered_pair @ SY3888 @ SY3889 ) @ SV263 ) ) )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV32 @ SV225 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2220]) ).
thf(2353,plain,
! [SV32: $i,SV225: $i,SV263: $i] :
( ( ( ~ ( ~ ! [SY3890: $i] :
( ! [SY3891: $i] :
~ ( in @ ( ordered_pair @ SY3890 @ SY3891 ) @ SV263 )
| ( in @ SY3890 @ SV225 ) )
| ~ ! [SY3892: $i,SY3893: $i] :
( ~ ( in @ ( ordered_pair @ SY3892 @ SY3893 ) @ SV263 )
| ( in @ ( ordered_pair @ SY3892 @ SY3893 ) @ SV32 ) ) ) )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV32 @ SV225 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2221]) ).
thf(2354,plain,
! [SV33: $i,SV188: $i,SV143: $i,SV307: $i] :
( ( ( in @ SV307 @ SV143 )
= $false )
| ( ( in @ SV307 @ ( relation_rng @ SV188 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV33 @ SV307 ) @ SV188 )
= $false )
| ( ( in @ SV33 @ ( relation_inverse_image @ SV188 @ SV143 ) )
= $true )
| ( ( relation @ SV188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2222]) ).
thf(2355,plain,
! [SV33: $i,SV144: $i,SV189: $i] :
( ( ( ~ ( in @ ( sK75_D @ SV189 @ SV144 @ SV33 ) @ ( relation_rng @ SV189 ) ) )
= $false )
| ( ( in @ SV33 @ ( relation_inverse_image @ SV189 @ SV144 ) )
= $false )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2223]) ).
thf(2356,plain,
! [SV144: $i,SV189: $i,SV33: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV33 @ ( sK75_D @ SV189 @ SV144 @ SV33 ) ) @ SV189 ) )
= $false )
| ( ( in @ SV33 @ ( relation_inverse_image @ SV189 @ SV144 ) )
= $false )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2223]) ).
thf(2357,plain,
! [SV110: $i,SV145: $i] :
( ( ( in @ ( sK65_C @ SV145 @ SV110 ) @ SV110 )
= $false )
| ( ( ( sK65_C @ SV145 @ SV110 )
= ( sK66_SY3320 @ SV145 @ SV110 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 ) )
= $true )
| ( ( SV145
= ( identity_relation @ SV110 ) )
= $true )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2224]) ).
thf(2358,plain,
! [SV110: $i,SV145: $i] :
( ( ( ( sK65_C @ SV145 @ SV110 )
= ( sK66_SY3320 @ SV145 @ SV110 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 )
= $true )
| ( ( SV145
= ( identity_relation @ SV110 ) )
= $true )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2225]) ).
thf(2359,plain,
! [SV110: $i,SV145: $i] :
( ( ( in @ ( sK65_C @ SV145 @ SV110 ) @ SV110 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 )
= $true )
| ( ( SV145
= ( identity_relation @ SV110 ) )
= $true )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2226]) ).
thf(2360,plain,
! [SV146: $i,SV111: $i,SV374: $i,SV352: $i] :
( ( ( ( SV352 != SV374 )
| ~ ( in @ SV352 @ SV111 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV352 @ SV374 ) @ SV146 )
= $true )
| ( ( SV146
= ( identity_relation @ SV111 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2227]) ).
thf(2361,plain,
! [SV111: $i,SV146: $i] :
( ( ( ! [SY3734: $i,SY3735: $i] :
( ~ ( in @ ( ordered_pair @ SY3734 @ SY3735 ) @ SV146 )
| ( SY3734 = SY3735 ) ) )
= $true )
| ( ( SV146
= ( identity_relation @ SV111 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2228]) ).
thf(2362,plain,
! [SV111: $i,SV146: $i] :
( ( ( ! [SY3736: $i] :
( ! [SY3737: $i] :
~ ( in @ ( ordered_pair @ SY3736 @ SY3737 ) @ SV146 )
| ( in @ SY3736 @ SV111 ) ) )
= $true )
| ( ( SV146
= ( identity_relation @ SV111 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2229]) ).
thf(2363,plain,
! [SV34: $i,SV89: $i,SV190: $i,SV226: $i] :
( ( ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 ) )
= $true )
| ( ( ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV190 ) )
= $true )
| ( ( SV226
= ( unordered_triple @ SV34 @ SV89 @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2230]) ).
thf(2364,plain,
! [SV34: $i,SV89: $i,SV190: $i,SV226: $i] :
( ( ( ~ ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV34 ) )
| ~ ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV89 ) ) )
= $false )
| ( ( SV226
= ( unordered_triple @ SV34 @ SV89 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2231]) ).
thf(2365,plain,
! [SV89: $i,SV34: $i,SV191: $i,SV227: $i,SV353: $i] :
( ( ( in @ SV353 @ SV227 )
= $false )
| ( ( ( SV353 = SV191 )
| ( SV353 = SV34 )
| ( SV353 = SV89 ) )
= $true )
| ( ( SV227
= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2233]) ).
thf(2366,plain,
! [SV89: $i,SV34: $i,SV227: $i,SV191: $i] :
( ( ( ! [SY3840: $i] :
( ( SY3840 != SV191 )
| ( in @ SY3840 @ SV227 ) ) )
= $true )
| ( ( SV227
= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2234]) ).
thf(2367,plain,
! [SV191: $i,SV89: $i,SV227: $i,SV34: $i] :
( ( ( ~ ( ~ ! [SY3841: $i] :
( ( SY3841 != SV34 )
| ( in @ SY3841 @ SV227 ) )
| ~ ! [SY3842: $i] :
( ( SY3842 != SV89 )
| ( in @ SY3842 @ SV227 ) ) ) )
= $true )
| ( ( SV227
= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2235]) ).
thf(2368,plain,
! [SV354: $i,SV36: $i,SV228: $i] :
( ( ( in @ ( sK16_C @ SV228 @ SV36 ) @ SV228 )
= $false )
| ( ( in @ ( ordered_pair @ SV354 @ ( sK16_C @ SV228 @ SV36 ) ) @ SV36 )
= $false )
| ( ( SV228
= ( relation_rng @ SV36 ) )
= $true )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2236]) ).
thf(2369,plain,
! [SV229: $i,SV36: $i,SV355: $i,SV382: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV382 @ SV355 ) @ SV36 ) )
= $true )
| ( ( in @ SV355 @ SV229 )
= $true )
| ( ( SV229
= ( relation_rng @ SV36 ) )
= $false )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2237]) ).
thf(2370,plain,
! [SV36: $i,SV229: $i,SV356: $i] :
( ( ( in @ SV356 @ SV229 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK15_D @ SV356 @ SV229 @ SV36 ) @ SV356 ) @ SV36 )
= $true )
| ( ( SV229
= ( relation_rng @ SV36 ) )
= $false )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2238]) ).
thf(2371,plain,
! [SV337: $i,SV37: $i,SV324: $i] :
( ( ( in @ SV324 @ ( sK77_B @ SV37 ) )
= $false )
| ( ( ~ ( subset @ SV337 @ SV324 ) )
= $true )
| ( ( in @ SV337 @ ( sK77_B @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2239]) ).
thf(2372,plain,
! [SV91: $i,SV308: $i,SV39: $i] :
( ( ( ~ ( in @ SV39 @ ( relation_dom @ SV308 ) )
| ~ ( in @ ( apply @ SV308 @ SV39 ) @ ( relation_dom @ SV91 ) ) )
= $true )
| ( ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SV308 @ SV91 ) ) )
= $true )
| ( ( function @ SV308 )
= $false )
| ( ( relation @ SV308 )
= $false )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2240]) ).
thf(2373,plain,
! [SV91: $i,SV39: $i,SV357: $i] :
( ( ( ~ ( function @ SV357 ) )
= $true )
| ( ( ~ ( relation @ SV357 ) )
= $true )
| ( ( ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SV357 @ SV91 ) ) )
| ( in @ SV39 @ ( relation_dom @ SV357 ) ) )
= $true )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2241]) ).
thf(2374,plain,
! [SV91: $i,SV39: $i,SV358: $i] :
( ( ( ~ ( function @ SV358 ) )
= $true )
| ( ( ~ ( relation @ SV358 ) )
= $true )
| ( ( ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SV358 @ SV91 ) ) )
| ( in @ ( apply @ SV358 @ SV39 ) @ ( relation_dom @ SV91 ) ) )
= $true )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2242]) ).
thf(2375,plain,
! [SV40: $i,SV92: $i,SV265: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_D @ SV265 @ SV92 @ SV40 ) @ SV265 )
| ~ ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SV265 @ SV92 @ SV40 ) ) @ SV92 ) )
| ~ ( ( in @ ( sK6_D @ SV265 @ SV92 @ SV40 ) @ SV265 )
| ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SV265 @ SV92 @ SV40 ) ) @ SV92 ) ) )
= $false )
| ( ( SV265
= ( complements_of_subsets @ SV40 @ SV92 ) )
= $true )
| ( ( element @ SV265 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2244]) ).
thf(2376,plain,
! [SV92: $i,SV266: $i,SV40: $i] :
( ( ( ! [SY3894: $i] :
( ~ ( element @ SY3894 @ ( powerset @ SV40 ) )
| ~ ( in @ SY3894 @ SV266 )
| ( in @ ( subset_complement @ SV40 @ SY3894 ) @ SV92 ) ) )
= $true )
| ( ( SV266
= ( complements_of_subsets @ SV40 @ SV92 ) )
= $false )
| ( ( element @ SV266 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2245]) ).
thf(2377,plain,
! [SV266: $i,SV92: $i,SV40: $i] :
( ( ( ! [SY3895: $i] :
( ~ ( element @ SY3895 @ ( powerset @ SV40 ) )
| ~ ( in @ ( subset_complement @ SV40 @ SY3895 ) @ SV92 )
| ( in @ SY3895 @ SV266 ) ) )
= $true )
| ( ( SV266
= ( complements_of_subsets @ SV40 @ SV92 ) )
= $false )
| ( ( element @ SV266 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2246]) ).
thf(2378,plain,
! [SV282: $i,SV267: $i,SV41: $i] :
( ( ( in @ ( ordered_pair @ SV41 @ SV267 ) @ SV282 )
= $false )
| ( ( SV267
= ( apply @ SV282 @ SV41 ) )
= $true )
| ( ( function @ SV282 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2248]) ).
thf(2379,plain,
! [SV283: $i,SV268: $i,SV41: $i] :
( ( ( in @ ( ordered_pair @ SV41 @ SV268 ) @ SV283 )
= $false )
| ( ( in @ SV41 @ ( relation_dom @ SV283 ) )
= $true )
| ( ( function @ SV283 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2249]) ).
thf(2380,plain,
! [SV43: $i,SV271: $i,SV359: $i] :
( ( ( subset @ SV359 @ SV271 )
= $false )
| ( ( in @ SV359 @ ( sK3_SY3278 @ SV271 @ SV43 ) )
= $true )
| ( ( ~ ( in @ SV271 @ ( sK2_B @ SV43 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2250]) ).
thf(2381,plain,
! [SV338: $i,SV43: $i,SV327: $i] :
( ( ( in @ SV327 @ ( sK2_B @ SV43 ) )
= $false )
| ( ( ~ ( subset @ SV338 @ SV327 ) )
= $true )
| ( ( in @ SV338 @ ( sK2_B @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2251]) ).
thf(2382,plain,
! [SV360: $i,SV45: $i,SV232: $i] :
( ( ( in @ ( sK26_C @ SV232 @ SV45 ) @ SV232 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK26_C @ SV232 @ SV45 ) @ SV360 ) @ SV45 )
= $false )
| ( ( SV232
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2252]) ).
thf(2383,plain,
! [SV233: $i,SV45: $i,SV383: $i,SV361: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV361 @ SV383 ) @ SV45 ) )
= $true )
| ( ( in @ SV361 @ SV233 )
= $true )
| ( ( SV233
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2253]) ).
thf(2384,plain,
! [SV45: $i,SV233: $i,SV362: $i] :
( ( ( in @ SV362 @ SV233 )
= $false )
| ( ( in @ ( ordered_pair @ SV362 @ ( sK25_D @ SV362 @ SV233 @ SV45 ) ) @ SV45 )
= $true )
| ( ( SV233
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2254]) ).
thf(2385,plain,
! [SV122: $i,SV159: $i] :
( ( ( ( relation_dom @ SV159 )
= SV122 )
= $false )
| ( ( in @ ( sK74_C @ SV159 @ SV122 ) @ SV122 )
= $true )
| ( ( SV159
= ( identity_relation @ SV122 ) )
= $true )
| ( ( function @ SV159 )
= $false )
| ( ( relation @ SV159 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2255]) ).
thf(2386,plain,
! [SV122: $i,SV159: $i] :
( ( ( ( apply @ SV159 @ ( sK74_C @ SV159 @ SV122 ) )
= ( sK74_C @ SV159 @ SV122 ) )
= $false )
| ( ( ( ( relation_dom @ SV159 )
!= SV122 ) )
= $true )
| ( ( SV159
= ( identity_relation @ SV122 ) )
= $true )
| ( ( function @ SV159 )
= $false )
| ( ( relation @ SV159 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2256]) ).
thf(2387,plain,
! [SV272: $i,SV239: $i,SV384: $i] :
( ( ( ~ ( in @ SV384 @ SV239 )
| ( ( apply @ SV272 @ SV384 )
= SV384 ) )
= $true )
| ( ( SV272
= ( identity_relation @ SV239 ) )
= $false )
| ( ( function @ SV272 )
= $false )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2257]) ).
thf(2388,plain,
! [SV46: $i,SV331: $i] :
( ( ( relation @ SV331 )
= $false )
| ( ( function @ SV331 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) )
| ( SV331
= ( function_inverse @ SV46 ) ) )
= $true )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2259]) ).
thf(2389,plain,
! [SV46: $i,SV375: $i] :
( ( ( ~ ( function @ SV375 )
| ~ ( relation @ SV375 ) )
= $true )
| ( ( ( SV375
!= ( function_inverse @ SV46 ) )
| ~ ( ~ ~ ( ~ ! [SY3963: $i,SY3964: $i] :
( ( SY3964
!= ( apply @ SV375 @ SY3963 ) )
| ~ ( in @ SY3963 @ ( relation_rng @ SV46 ) )
| ( SY3963
= ( apply @ SV46 @ SY3964 ) ) )
| ~ ! [SY3965: $i,SY3966: $i] :
( ( SY3966
!= ( apply @ SV375 @ SY3965 ) )
| ~ ( in @ SY3965 @ ( relation_rng @ SV46 ) )
| ( in @ SY3966 @ ( relation_dom @ SV46 ) ) ) )
| ~ ~ ( ~ ! [SY3967: $i,SY3968: $i] :
( ( SY3967
!= ( apply @ SV46 @ SY3968 ) )
| ~ ( in @ SY3968 @ ( relation_dom @ SV46 ) )
| ( SY3968
= ( apply @ SV375 @ SY3967 ) ) )
| ~ ! [SY3491: $i] :
( ! [SY3492: $i] :
( ( SY3491
!= ( apply @ SV46 @ SY3492 ) )
| ~ ( in @ SY3492 @ ( relation_dom @ SV46 ) ) )
| ( in @ SY3491 @ ( relation_rng @ SV46 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2260]) ).
thf(2390,plain,
! [SV46: $i,SV376: $i] :
( ( ( ~ ( function @ SV376 )
| ~ ( relation @ SV376 ) )
= $true )
| ( ( ( SV376
!= ( function_inverse @ SV46 ) )
| ( ( relation_dom @ SV376 )
= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2261]) ).
thf(2391,plain,
! [SV47: $i,SV123: $i,SV313: $i] :
( ( ( ~ ( ! [SY3936: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ SY3936 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3936 @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV123 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV313 ) ) )
= $false )
| ( ( SV313
= ( relation_composition @ SV47 @ SV123 ) )
= $true )
| ( ( relation @ SV313 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2262]) ).
thf(2392,plain,
! [SV47: $i,SV123: $i,SV313: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK10_SY3288 @ SV313 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY3288 @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV123 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV313 ) ) )
= $false )
| ( ( SV313
= ( relation_composition @ SV47 @ SV123 ) )
= $true )
| ( ( relation @ SV313 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2262]) ).
thf(2393,plain,
! [SV314: $i,SV123: $i,SV47: $i] :
( ( ( ~ ! [SY3937: $i,SY3938: $i] :
( ! [SY3706: $i] :
( ~ ( in @ ( ordered_pair @ SY3937 @ SY3706 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3706 @ SY3938 ) @ SV123 ) )
| ( in @ ( ordered_pair @ SY3937 @ SY3938 ) @ SV314 ) )
| ~ ! [SY3940: $i,SY3941: $i] :
( ~ ( in @ ( ordered_pair @ SY3940 @ SY3941 ) @ SV314 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3940 @ ( sK7_F @ SY3941 @ SY3940 @ SV314 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY3941 @ SY3940 @ SV314 @ SV123 @ SV47 ) @ SY3941 ) @ SV123 ) ) ) )
= $false )
| ( ( SV314
= ( relation_composition @ SV47 @ SV123 ) )
= $false )
| ( ( relation @ SV314 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2263]) ).
thf(2394,plain,
! [SV124: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_B @ SV124 ) @ ( relation_dom @ SV124 ) )
| ~ ( in @ ( sK12_SY3289 @ SV124 ) @ ( relation_dom @ SV124 ) ) ) )
= $true )
| ( ( one_to_one @ SV124 )
= $true )
| ( ( function @ SV124 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2266]) ).
thf(2395,plain,
! [SV124: $i] :
( ( ( ( apply @ SV124 @ ( sK11_B @ SV124 ) )
= ( apply @ SV124 @ ( sK12_SY3289 @ SV124 ) ) )
= $true )
| ( ( one_to_one @ SV124 )
= $true )
| ( ( function @ SV124 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2267]) ).
thf(2396,plain,
! [SV339: $i,SV125: $i,SV332: $i] :
( ( ( ~ ( in @ SV332 @ ( relation_dom @ SV125 ) ) )
= $true )
| ( ( ~ ( in @ SV339 @ ( relation_dom @ SV125 ) ) )
= $true )
| ( ( ( ( apply @ SV125 @ SV332 )
!= ( apply @ SV125 @ SV339 ) ) )
= $true )
| ( ( SV332 = SV339 )
= $true )
| ( ( one_to_one @ SV125 )
= $false )
| ( ( function @ SV125 )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2268]) ).
thf(2397,plain,
! [SV51: $i,SV161: $i,SV199: $i] :
( ( ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV199 )
= $false )
| ( ( ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV51 ) )
= $true )
| ( ( SV199
= ( set_union2 @ SV51 @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2269]) ).
thf(2398,plain,
! [SV51: $i,SV161: $i,SV199: $i] :
( ( ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV199 )
= $false )
| ( ( ~ ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV161 ) )
= $true )
| ( ( SV199
= ( set_union2 @ SV51 @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2270]) ).
thf(2399,plain,
! [SV200: $i,SV162: $i,SV51: $i,SV340: $i] :
( ( ( in @ SV340 @ SV51 )
= $true )
| ( ( in @ SV340 @ SV162 )
= $true )
| ( ( in @ SV340 @ SV200 )
= $false )
| ( ( SV200
= ( set_union2 @ SV51 @ SV162 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2271]) ).
thf(2400,plain,
! [SV162: $i,SV200: $i,SV51: $i,SV385: $i] :
( ( ( ~ ( in @ SV385 @ SV51 )
| ( in @ SV385 @ SV200 ) )
= $true )
| ( ( SV200
= ( set_union2 @ SV51 @ SV162 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2272]) ).
thf(2401,plain,
! [SV51: $i,SV200: $i,SV162: $i,SV386: $i] :
( ( ( ~ ( in @ SV386 @ SV162 )
| ( in @ SV386 @ SV200 ) )
= $true )
| ( ( SV200
= ( set_union2 @ SV51 @ SV162 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2273]) ).
thf(2402,plain,
! [SV244: $i,SV52: $i,SV363: $i,SV341: $i] :
( ( ( in @ ( ordered_pair @ SV341 @ SV363 ) @ SV52 )
= $false )
| ( ( in @ ( ordered_pair @ SV341 @ SV363 ) @ SV244 )
= $true )
| ( ( subset @ SV52 @ SV244 )
= $false )
| ( ( relation @ SV244 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2275]) ).
thf(2403,plain,
! [SV245: $i,SV295: $i] :
( ( ( ~ ( in @ ( sK46_SY3307 @ SV295 @ SV245 ) @ SV245 )
| ~ ~ ( in @ ( sK45_C @ SV295 @ SV245 ) @ ( sK46_SY3307 @ SV295 @ SV245 ) ) )
= $false )
| ( ( ~ ( in @ ( sK45_C @ SV295 @ SV245 ) @ SV295 ) )
= $true )
| ( ( SV295
= ( set_meet @ SV245 ) )
= $true )
| ( ( SV245 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2276]) ).
thf(2404,plain,
! [SV295: $i,SV245: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ SV245 )
| ( in @ ( sK45_C @ SV295 @ SV245 ) @ SV387 ) )
= $true )
| ( ( in @ ( sK45_C @ SV295 @ SV245 ) @ SV295 )
= $true )
| ( ( SV295
= ( set_meet @ SV245 ) )
= $true )
| ( ( SV245 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2277]) ).
thf(2405,plain,
! [SV246: $i,SV296: $i,SV388: $i] :
( ( ( ~ ( ~ ( in @ ( sK44_D @ SV388 @ SV296 @ SV246 ) @ SV246 )
| ~ ~ ( in @ SV388 @ ( sK44_D @ SV388 @ SV296 @ SV246 ) ) )
| ( in @ SV388 @ SV296 ) )
= $true )
| ( ( SV296
= ( set_meet @ SV246 ) )
= $false )
| ( ( SV246 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2278]) ).
thf(2406,plain,
! [SV246: $i,SV296: $i,SV389: $i] :
( ( ( ~ ( in @ SV389 @ SV296 )
| ! [SY3974: $i] :
( ~ ( in @ SY3974 @ SV246 )
| ( in @ SV389 @ SY3974 ) ) )
= $true )
| ( ( SV296
= ( set_meet @ SV246 ) )
= $false )
| ( ( SV246 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2279]) ).
thf(2407,plain,
! [SV53: $i,SV297: $i,SV319: $i] :
( ( ( ~ ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ ( sK57_D @ SV319 @ SV297 @ SV53 ) ) @ SV297 ) )
= $true )
| ( ( ~ ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ SV319 ) )
= $true )
| ( ( SV319
= ( relation_inverse_image @ SV53 @ SV297 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2280]) ).
thf(2408,plain,
! [SV53: $i,SV297: $i,SV319: $i] :
( ( ( ~ ( ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ SV319 ) )
| ~ ( ( in @ ( apply @ SV53 @ ( sK57_D @ SV319 @ SV297 @ SV53 ) ) @ SV297 )
| ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ SV319 ) ) )
= $false )
| ( ( SV319
= ( relation_inverse_image @ SV53 @ SV297 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2281]) ).
thf(2409,plain,
! [SV320: $i,SV298: $i,SV53: $i] :
( ( ( ! [SY3942: $i] :
( ~ ( in @ SY3942 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SY3942 ) @ SV298 )
| ( in @ SY3942 @ SV320 ) ) )
= $true )
| ( ( SV320
= ( relation_inverse_image @ SV53 @ SV298 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2282]) ).
thf(2410,plain,
! [SV298: $i,SV53: $i,SV320: $i] :
( ( ( ~ ( ~ ! [SY3943: $i] :
( ~ ( in @ SY3943 @ SV320 )
| ( in @ SY3943 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY3944: $i] :
( ~ ( in @ SY3944 @ SV320 )
| ( in @ ( apply @ SV53 @ SY3944 ) @ SV298 ) ) ) )
= $true )
| ( ( SV320
= ( relation_inverse_image @ SV53 @ SV298 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2283]) ).
thf(2411,plain,
! [SV54: $i,SV165: $i,SV201: $i] :
( ( ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV201 )
= $false )
| ( ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV54 )
= $false )
| ( ( in @ ( sK28_D @ SV201 @ SV165 @ SV54 ) @ SV165 )
= $false )
| ( ( SV201
= ( set_intersection2 @ SV54 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2284]) ).
thf(2412,plain,
! [SV202: $i,SV166: $i,SV54: $i,SV342: $i] :
( ( ( in @ SV342 @ SV54 )
= $false )
| ( ( ~ ( in @ SV342 @ SV166 ) )
= $true )
| ( ( in @ SV342 @ SV202 )
= $true )
| ( ( SV202
= ( set_intersection2 @ SV54 @ SV166 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2287]) ).
thf(2413,plain,
! [SV166: $i,SV54: $i,SV202: $i,SV390: $i] :
( ( ( ~ ( in @ SV390 @ SV202 )
| ( in @ SV390 @ SV54 ) )
= $true )
| ( ( SV202
= ( set_intersection2 @ SV54 @ SV166 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2288]) ).
thf(2414,plain,
! [SV54: $i,SV166: $i,SV202: $i,SV391: $i] :
( ( ( ~ ( in @ SV391 @ SV202 )
| ( in @ SV391 @ SV166 ) )
= $true )
| ( ( SV202
= ( set_intersection2 @ SV54 @ SV166 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2289]) ).
thf(2415,plain,
! [SV55: $i,SV169: $i,SV203: $i] :
( ( ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV169 )
= $false )
| ( ( in @ ( sK21_D @ SV203 @ SV169 @ SV55 ) @ SV203 )
= $true )
| ( ( SV203
= ( set_difference @ SV55 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2292]) ).
thf(2416,plain,
! [SV204: $i,SV170: $i,SV55: $i,SV343: $i] :
( ( ( in @ SV343 @ SV55 )
= $false )
| ( ( in @ SV343 @ SV170 )
= $true )
| ( ( in @ SV343 @ SV204 )
= $true )
| ( ( SV204
= ( set_difference @ SV55 @ SV170 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2293]) ).
thf(2417,plain,
! [SV170: $i,SV55: $i,SV204: $i,SV392: $i] :
( ( ( ~ ( in @ SV392 @ SV204 )
| ( in @ SV392 @ SV55 ) )
= $true )
| ( ( SV204
= ( set_difference @ SV55 @ SV170 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2294]) ).
thf(2418,plain,
! [SV55: $i,SV170: $i,SV204: $i,SV393: $i] :
( ( ( ~ ( in @ SV393 @ SV204 )
| ~ ( in @ SV393 @ SV170 ) )
= $true )
| ( ( SV204
= ( set_difference @ SV55 @ SV170 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2295]) ).
thf(2419,plain,
! [SV394: $i,SV56: $i,SV299: $i] :
( ( ( ( ( sK19_C @ SV299 @ SV56 )
!= ( apply @ SV56 @ SV394 ) )
| ~ ( in @ SV394 @ ( relation_dom @ SV56 ) ) )
= $true )
| ( ( ~ ( in @ ( sK19_C @ SV299 @ SV56 ) @ SV299 ) )
= $true )
| ( ( SV299
= ( relation_rng @ SV56 ) )
= $true )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2296]) ).
thf(2420,plain,
! [SV56: $i,SV299: $i] :
( ( ( ( ( sK19_C @ SV299 @ SV56 )
!= ( apply @ SV56 @ ( sK20_SY3294 @ SV299 @ SV56 ) ) )
| ~ ( in @ ( sK20_SY3294 @ SV299 @ SV56 ) @ ( relation_dom @ SV56 ) ) )
= $false )
| ( ( in @ ( sK19_C @ SV299 @ SV56 ) @ SV299 )
= $true )
| ( ( SV299
= ( relation_rng @ SV56 ) )
= $true )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2297]) ).
thf(2421,plain,
! [SV300: $i,SV56: $i,SV395: $i] :
( ( ( ! [SY3975: $i] :
( ( SV395
!= ( apply @ SV56 @ SY3975 ) )
| ~ ( in @ SY3975 @ ( relation_dom @ SV56 ) ) )
| ( in @ SV395 @ SV300 ) )
= $true )
| ( ( SV300
= ( relation_rng @ SV56 ) )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2298]) ).
thf(2422,plain,
! [SV56: $i,SV300: $i,SV396: $i] :
( ( ( ~ ( in @ SV396 @ SV300 )
| ~ ( ( SV396
!= ( apply @ SV56 @ ( sK18_D @ SV396 @ SV300 @ SV56 ) ) )
| ~ ( in @ ( sK18_D @ SV396 @ SV300 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
= $true )
| ( ( SV300
= ( relation_rng @ SV56 ) )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2299]) ).
thf(2423,plain,
! [SV57: $i,SV171: $i,SV205: $i] :
( ( ( in @ ( sK38_D @ SV205 @ SV171 @ SV57 ) @ SV205 )
= $false )
| ( ( ( ( sK38_D @ SV205 @ SV171 @ SV57 )
!= SV57 ) )
= $true )
| ( ( SV205
= ( unordered_pair @ SV57 @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2300]) ).
thf(2424,plain,
! [SV57: $i,SV171: $i,SV205: $i] :
( ( ( in @ ( sK38_D @ SV205 @ SV171 @ SV57 ) @ SV205 )
= $false )
| ( ( ( ( sK38_D @ SV205 @ SV171 @ SV57 )
!= SV171 ) )
= $true )
| ( ( SV205
= ( unordered_pair @ SV57 @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2301]) ).
thf(2425,plain,
! [SV206: $i,SV172: $i,SV57: $i,SV344: $i] :
( ( ( SV344 = SV57 )
= $true )
| ( ( SV344 = SV172 )
= $true )
| ( ( in @ SV344 @ SV206 )
= $false )
| ( ( SV206
= ( unordered_pair @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2302]) ).
thf(2426,plain,
! [SV172: $i,SV206: $i,SV57: $i,SV397: $i] :
( ( ( ( SV397 != SV57 )
| ( in @ SV397 @ SV206 ) )
= $true )
| ( ( SV206
= ( unordered_pair @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2303]) ).
thf(2427,plain,
! [SV57: $i,SV206: $i,SV172: $i,SV398: $i] :
( ( ( ( SV398 != SV172 )
| ( in @ SV398 @ SV206 ) )
= $true )
| ( ( SV206
= ( unordered_pair @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2304]) ).
thf(2428,plain,
! [SV58: $i,SV96: $i,SV321: $i] :
( ( ( ~ ( ~ ( in @ ( sK67_D @ SV321 @ SV96 @ SV58 ) @ ( relation_dom @ SV96 ) )
| ~ ( ( ( apply @ SV96 @ ( sK67_D @ SV321 @ SV96 @ SV58 ) )
!= ( apply @ SV321 @ ( sK67_D @ SV321 @ SV96 @ SV58 ) ) ) ) )
| ( ( relation_dom @ SV96 )
!= ( set_intersection2 @ ( relation_dom @ SV321 ) @ SV58 ) ) )
= $true )
| ( ( SV96
= ( relation_dom_restriction @ SV321 @ SV58 ) )
= $true )
| ( ( function @ SV321 )
= $false )
| ( ( relation @ SV321 )
= $false )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2305]) ).
thf(2429,plain,
! [SV58: $i,SV96: $i,SV364: $i] :
( ( ( ~ ( function @ SV364 ) )
= $true )
| ( ( ~ ( relation @ SV364 ) )
= $true )
| ( ( ( SV96
!= ( relation_dom_restriction @ SV364 @ SV58 ) )
| ! [SY3960: $i] :
( ~ ( in @ SY3960 @ ( relation_dom @ SV96 ) )
| ( ( apply @ SV96 @ SY3960 )
= ( apply @ SV364 @ SY3960 ) ) ) )
= $true )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2306]) ).
thf(2430,plain,
! [SV58: $i,SV96: $i,SV365: $i] :
( ( ( ~ ( function @ SV365 ) )
= $true )
| ( ( ~ ( relation @ SV365 ) )
= $true )
| ( ( ( SV96
!= ( relation_dom_restriction @ SV365 @ SV58 ) )
| ( ( relation_dom @ SV96 )
= ( set_intersection2 @ ( relation_dom @ SV365 ) @ SV58 ) ) )
= $true )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2307]) ).
thf(2431,plain,
! [SV59: $i,SV249: $i] :
( ( ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV59 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV249 ) )
= $true )
| ( ( SV59 = SV249 )
= $true )
| ( ( relation @ SV249 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2308]) ).
thf(2432,plain,
! [SV250: $i,SV59: $i,SV399: $i] :
( ( ( ! [SY3976: $i] :
( ~ ( in @ ( ordered_pair @ SV399 @ SY3976 ) @ SV59 )
| ( in @ ( ordered_pair @ SV399 @ SY3976 ) @ SV250 ) ) )
= $true )
| ( ( SV59 = SV250 )
= $false )
| ( ( relation @ SV250 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2310]) ).
thf(2433,plain,
! [SV59: $i,SV250: $i,SV400: $i] :
( ( ( ! [SY3977: $i] :
( ~ ( in @ ( ordered_pair @ SV400 @ SY3977 ) @ SV250 )
| ( in @ ( ordered_pair @ SV400 @ SY3977 ) @ SV59 ) ) )
= $true )
| ( ( SV59 = SV250 )
= $false )
| ( ( relation @ SV250 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2311]) ).
thf(2434,plain,
! [SV333: $i,SV130: $i,SV173: $i] :
( ( ( in @ ( sK23_C @ SV173 @ SV130 ) @ SV173 )
= $false )
| ( ( in @ ( sK23_C @ SV173 @ SV130 ) @ SV333 )
= $false )
| ( ( in @ SV333 @ SV130 )
= $false )
| ( ( SV173
= ( union @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2312]) ).
thf(2435,plain,
! [SV174: $i,SV131: $i,SV366: $i,SV334: $i] :
( ( ( in @ SV334 @ SV366 )
= $false )
| ( ( ~ ( in @ SV366 @ SV131 ) )
= $true )
| ( ( in @ SV334 @ SV174 )
= $true )
| ( ( SV174
= ( union @ SV131 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2313]) ).
thf(2436,plain,
! [SV131: $i,SV174: $i,SV335: $i] :
( ( ( ~ ( in @ SV335 @ ( sK22_D @ SV335 @ SV174 @ SV131 ) ) )
= $false )
| ( ( in @ SV335 @ SV174 )
= $false )
| ( ( SV174
= ( union @ SV131 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2314]) ).
thf(2437,plain,
! [SV131: $i,SV174: $i,SV335: $i] :
( ( ( ~ ( in @ ( sK22_D @ SV335 @ SV174 @ SV131 ) @ SV131 ) )
= $false )
| ( ( in @ SV335 @ SV174 )
= $false )
| ( ( SV174
= ( union @ SV131 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2314]) ).
thf(2438,plain,
! [SV62: $i,SV303: $i,SV276: $i] :
( ( ( in @ SV276 @ ( relation_dom @ ( relation_dom_restriction @ SV303 @ SV62 ) ) )
= $false )
| ( ( in @ SV276 @ ( relation_dom @ SV303 ) )
= $true )
| ( ( function @ SV303 )
= $false )
| ( ( relation @ SV303 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2316]) ).
thf(2439,plain,
! [SV62: $i,SV304: $i,SV277: $i] :
( ( ( in @ SV277 @ ( relation_dom @ ( relation_dom_restriction @ SV304 @ SV62 ) ) )
= $false )
| ( ( in @ SV277 @ SV62 )
= $true )
| ( ( function @ SV304 )
= $false )
| ( ( relation @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2317]) ).
thf(2440,plain,
! [SV209: $i,SV176: $i,SV367: $i,SV63: $i,SV345: $i] :
( ( ( ~ ( in @ SV345 @ SV63 ) )
= $true )
| ( ( ~ ( in @ SV367 @ SV176 ) )
= $true )
| ( ( ( ( sK34_D @ SV209 @ SV176 @ SV63 )
!= ( ordered_pair @ SV345 @ SV367 ) ) )
= $true )
| ( ( ~ ( in @ ( sK34_D @ SV209 @ SV176 @ SV63 ) @ SV209 ) )
= $true )
| ( ( SV209
= ( cartesian_product2 @ SV63 @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2318]) ).
thf(2441,plain,
! [SV63: $i,SV176: $i,SV209: $i] :
( ( ( ~ ( in @ ( sK35_SY3303 @ SV209 @ SV176 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK36_SY3305 @ SV209 @ SV176 @ SV63 ) @ SV176 ) )
= $false )
| ( ( in @ ( sK34_D @ SV209 @ SV176 @ SV63 ) @ SV209 )
= $true )
| ( ( SV209
= ( cartesian_product2 @ SV63 @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2319]) ).
thf(2442,plain,
! [SV210: $i,SV346: $i,SV177: $i,SV401: $i,SV63: $i,SV377: $i] :
( ( ( ~ ( in @ SV377 @ SV63 )
| ~ ( in @ SV401 @ SV177 )
| ( SV346
!= ( ordered_pair @ SV377 @ SV401 ) ) )
= $true )
| ( ( in @ SV346 @ SV210 )
= $true )
| ( ( SV210
= ( cartesian_product2 @ SV63 @ SV177 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2321]) ).
thf(2443,plain,
! [SV63: $i,SV177: $i,SV210: $i,SV347: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK32_E @ SV347 @ SV210 @ SV177 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK33_SY3300 @ SV347 @ SV210 @ SV177 @ SV63 ) @ SV177 ) )
| ( SV347
!= ( ordered_pair @ ( sK32_E @ SV347 @ SV210 @ SV177 @ SV63 ) @ ( sK33_SY3300 @ SV347 @ SV210 @ SV177 @ SV63 ) ) ) )
= $false )
| ( ( in @ SV347 @ SV210 )
= $false )
| ( ( SV210
= ( cartesian_product2 @ SV63 @ SV177 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2322]) ).
thf(2444,plain,
! [SV64: $i,SV211: $i,SV180: $i,SV323: $i] :
( ( ( in @ SV323 @ SV180 )
= $false )
| ( ( in @ SV323 @ ( relation_dom @ SV211 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV323 @ SV64 ) @ SV211 )
= $false )
| ( ( in @ SV64 @ ( relation_image @ SV211 @ SV180 ) )
= $true )
| ( ( relation @ SV211 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2323]) ).
thf(2445,plain,
! [SV64: $i,SV181: $i,SV212: $i] :
( ( ( ~ ( in @ ( sK76_D @ SV212 @ SV181 @ SV64 ) @ ( relation_dom @ SV212 ) ) )
= $false )
| ( ( in @ SV64 @ ( relation_image @ SV212 @ SV181 ) )
= $false )
| ( ( relation @ SV212 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2324]) ).
thf(2446,plain,
! [SV64: $i,SV181: $i,SV212: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK76_D @ SV212 @ SV181 @ SV64 ) @ SV64 ) @ SV212 ) )
= $false )
| ( ( in @ SV64 @ ( relation_image @ SV212 @ SV181 ) )
= $false )
| ( ( relation @ SV212 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2324]) ).
thf(2447,plain,
! [SV348: $i,SV66: $i,SV402: $i] :
( ( ( ( SV402
!= ( apply @ SV66 @ SV348 ) )
| ( in @ ( ordered_pair @ SV348 @ SV402 ) @ SV66 ) )
= $true )
| ( ( in @ SV348 @ ( relation_dom @ SV66 ) )
= $false )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2325]) ).
thf(2448,plain,
! [SV66: $i,SV403: $i,SV349: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV349 @ SV403 ) @ SV66 )
| ( SV403
= ( apply @ SV66 @ SV349 ) ) )
= $true )
| ( ( in @ SV349 @ ( relation_dom @ SV66 ) )
= $false )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2326]) ).
thf(2449,plain,
! [SV350: $i,SV66: $i,SV378: $i] :
( ( ( ( SV378
!= ( apply @ SV66 @ SV350 ) ) )
= $true )
| ( ( SV378 = empty_set )
= $true )
| ( ( in @ SV350 @ ( relation_dom @ SV66 ) )
= $true )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2327]) ).
thf(2450,plain,
! [SV351: $i,SV66: $i,SV379: $i] :
( ( ( ( SV379 != empty_set ) )
= $true )
| ( ( SV379
= ( apply @ SV66 @ SV351 ) )
= $true )
| ( ( in @ SV351 @ ( relation_dom @ SV66 ) )
= $true )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2328]) ).
thf(2451,plain,
! [SV26: $i,SV88: $i,SV253: $i] :
( ( ( ~ ( in @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) @ SV26 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV88 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 ) )
= $true )
| ( ( SV253
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $true )
| ( ( relation @ SV253 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2329]) ).
thf(2452,plain,
! [SV26: $i,SV88: $i,SV253: $i] :
( ( ( ~ ( ( in @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) @ SV26 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 ) ) )
= $false )
| ( ( SV253
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $true )
| ( ( relation @ SV253 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2330]) ).
thf(2453,plain,
! [SV26: $i,SV88: $i,SV253: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV88 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 ) ) )
= $false )
| ( ( SV253
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $true )
| ( ( relation @ SV253 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2330]) ).
thf(2454,plain,
! [SV254: $i,SV88: $i,SV404: $i,SV26: $i] :
( ( ( ! [SY3978: $i] :
( ~ ( in @ SY3978 @ SV26 )
| ~ ( in @ ( ordered_pair @ SV404 @ SY3978 ) @ SV88 )
| ( in @ ( ordered_pair @ SV404 @ SY3978 ) @ SV254 ) ) )
= $true )
| ( ( SV254
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2331]) ).
thf(2455,plain,
! [SV88: $i,SV26: $i,SV254: $i] :
( ( ( ~ ! [SY3874: $i,SY3875: $i] :
( ~ ( in @ ( ordered_pair @ SY3874 @ SY3875 ) @ SV254 )
| ( in @ SY3875 @ SV26 ) )
| ~ ! [SY3876: $i,SY3877: $i] :
( ~ ( in @ ( ordered_pair @ SY3876 @ SY3877 ) @ SV254 )
| ( in @ ( ordered_pair @ SY3876 @ SY3877 ) @ SV88 ) ) )
= $false )
| ( ( SV254
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2332]) ).
thf(2456,plain,
! [SV28: $i,SV218: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_SY3290 @ SV218 @ SV28 ) @ ( sK13_C @ SV218 @ SV28 ) ) @ SV28 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK13_C @ SV218 @ SV28 ) @ ( sK14_SY3290 @ SV218 @ SV28 ) ) @ SV218 )
= $false )
| ( ( SV218
= ( relation_inverse @ SV28 ) )
= $true )
| ( ( relation @ SV218 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2333]) ).
thf(2457,plain,
! [SV28: $i,SV219: $i,SV405: $i,SV380: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV380 @ SV405 ) @ SV219 )
| ( in @ ( ordered_pair @ SV405 @ SV380 ) @ SV28 ) )
= $true )
| ( ( SV219
= ( relation_inverse @ SV28 ) )
= $false )
| ( ( relation @ SV219 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2334]) ).
thf(2458,plain,
! [SV219: $i,SV28: $i,SV381: $i,SV406: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV406 @ SV381 ) @ SV28 )
| ( in @ ( ordered_pair @ SV381 @ SV406 ) @ SV219 ) )
= $true )
| ( ( SV219
= ( relation_inverse @ SV28 ) )
= $false )
| ( ( relation @ SV219 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2335]) ).
thf(2459,plain,
! [SV305: $i,SV280: $i,SV29: $i,SV407: $i] :
( ( ( ~ ( in @ SV407 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SV407 @ SV280 )
| ( ( sK61_D @ SV305 @ SV280 @ SV29 )
!= ( apply @ SV29 @ SV407 ) ) )
= $true )
| ( ( ~ ( in @ ( sK61_D @ SV305 @ SV280 @ SV29 ) @ SV305 ) )
= $true )
| ( ( SV305
= ( relation_image @ SV29 @ SV280 ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2336]) ).
thf(2460,plain,
! [SV29: $i,SV280: $i,SV305: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) @ SV280 ) )
| ( ( sK61_D @ SV305 @ SV280 @ SV29 )
!= ( apply @ SV29 @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) ) ) )
= $false )
| ( ( in @ ( sK61_D @ SV305 @ SV280 @ SV29 ) @ SV305 )
= $true )
| ( ( SV305
= ( relation_image @ SV29 @ SV280 ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2337]) ).
thf(2461,plain,
! [SV306: $i,SV408: $i,SV281: $i,SV29: $i] :
( ( ( ! [SY3979: $i] :
( ~ ( in @ SY3979 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3979 @ SV281 )
| ( SV408
!= ( apply @ SV29 @ SY3979 ) ) )
| ( in @ SV408 @ SV306 ) )
= $true )
| ( ( SV306
= ( relation_image @ SV29 @ SV281 ) )
= $false )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2338]) ).
thf(2462,plain,
! [SV29: $i,SV281: $i,SV306: $i,SV409: $i] :
( ( ( ~ ( in @ SV409 @ SV306 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SV409 @ SV306 @ SV281 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK60_E @ SV409 @ SV306 @ SV281 @ SV29 ) @ SV281 ) )
| ( SV409
!= ( apply @ SV29 @ ( sK60_E @ SV409 @ SV306 @ SV281 @ SV29 ) ) ) ) )
= $true )
| ( ( SV306
= ( relation_image @ SV29 @ SV281 ) )
= $false )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2339]) ).
thf(2463,plain,
! [SV30: $i,SV220: $i,SV258: $i,SV368: $i] :
( ( ( in @ ( ordered_pair @ SV368 @ ( sK55_D @ SV258 @ SV220 @ SV30 ) ) @ SV30 )
= $false )
| ( ( ~ ( in @ SV368 @ SV220 ) )
= $true )
| ( ( ~ ( in @ ( sK55_D @ SV258 @ SV220 @ SV30 ) @ SV258 ) )
= $true )
| ( ( SV258
= ( relation_image @ SV30 @ SV220 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2340]) ).
thf(2464,plain,
! [SV30: $i,SV220: $i,SV258: $i] :
( ( ( in @ ( ordered_pair @ ( sK56_SY3315 @ SV258 @ SV220 @ SV30 ) @ ( sK55_D @ SV258 @ SV220 @ SV30 ) ) @ SV30 )
= $true )
| ( ( in @ ( sK55_D @ SV258 @ SV220 @ SV30 ) @ SV258 )
= $true )
| ( ( SV258
= ( relation_image @ SV30 @ SV220 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2341]) ).
thf(2465,plain,
! [SV30: $i,SV220: $i,SV258: $i] :
( ( ( in @ ( sK56_SY3315 @ SV258 @ SV220 @ SV30 ) @ SV220 )
= $true )
| ( ( in @ ( sK55_D @ SV258 @ SV220 @ SV30 ) @ SV258 )
= $true )
| ( ( SV258
= ( relation_image @ SV30 @ SV220 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2342]) ).
thf(2466,plain,
! [SV259: $i,SV221: $i,SV30: $i,SV369: $i,SV410: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV410 @ SV369 ) @ SV30 )
| ~ ( in @ SV410 @ SV221 ) )
= $true )
| ( ( in @ SV369 @ SV259 )
= $true )
| ( ( SV259
= ( relation_image @ SV30 @ SV221 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2343]) ).
thf(2467,plain,
! [SV30: $i,SV221: $i,SV259: $i,SV370: $i] :
( ( ( in @ SV370 @ SV259 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SV370 @ SV259 @ SV221 @ SV30 ) @ SV370 ) @ SV30 )
| ~ ( in @ ( sK54_E @ SV370 @ SV259 @ SV221 @ SV30 ) @ SV221 ) ) )
= $true )
| ( ( SV259
= ( relation_image @ SV30 @ SV221 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2344]) ).
thf(2468,plain,
! [SV371: $i,SV31: $i,SV222: $i,SV260: $i] :
( ( ( in @ ( ordered_pair @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SV371 ) @ SV31 )
= $false )
| ( ( ~ ( in @ SV371 @ SV222 ) )
= $true )
| ( ( ~ ( in @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SV260 ) )
= $true )
| ( ( SV260
= ( relation_inverse_image @ SV31 @ SV222 ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2345]) ).
thf(2469,plain,
! [SV31: $i,SV222: $i,SV260: $i] :
( ( ( in @ ( ordered_pair @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ ( sK53_SY3313 @ SV260 @ SV222 @ SV31 ) ) @ SV31 )
= $true )
| ( ( in @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SV260 )
= $true )
| ( ( SV260
= ( relation_inverse_image @ SV31 @ SV222 ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2346]) ).
thf(2470,plain,
! [SV31: $i,SV222: $i,SV260: $i] :
( ( ( in @ ( sK53_SY3313 @ SV260 @ SV222 @ SV31 ) @ SV222 )
= $true )
| ( ( in @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SV260 )
= $true )
| ( ( SV260
= ( relation_inverse_image @ SV31 @ SV222 ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2347]) ).
thf(2471,plain,
! [SV261: $i,SV223: $i,SV31: $i,SV411: $i,SV372: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV372 @ SV411 ) @ SV31 )
| ~ ( in @ SV411 @ SV223 ) )
= $true )
| ( ( in @ SV372 @ SV261 )
= $true )
| ( ( SV261
= ( relation_inverse_image @ SV31 @ SV223 ) )
= $false )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2348]) ).
thf(2472,plain,
! [SV31: $i,SV223: $i,SV261: $i,SV373: $i] :
( ( ( in @ SV373 @ SV261 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV373 @ ( sK51_E @ SV373 @ SV261 @ SV223 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( sK51_E @ SV373 @ SV261 @ SV223 @ SV31 ) @ SV223 ) ) )
= $true )
| ( ( SV261
= ( relation_inverse_image @ SV31 @ SV223 ) )
= $false )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2349]) ).
thf(2473,plain,
! [SV32: $i,SV224: $i,SV262: $i] :
( ( ( ~ ( in @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ SV224 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV32 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 ) )
= $true )
| ( ( SV262
= ( relation_dom_restriction @ SV32 @ SV224 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2350]) ).
thf(2474,plain,
! [SV32: $i,SV224: $i,SV262: $i] :
( ( ( ~ ( ( in @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ SV224 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 ) ) )
= $false )
| ( ( SV262
= ( relation_dom_restriction @ SV32 @ SV224 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2351]) ).
thf(2475,plain,
! [SV32: $i,SV224: $i,SV262: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV32 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 ) ) )
= $false )
| ( ( SV262
= ( relation_dom_restriction @ SV32 @ SV224 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2351]) ).
thf(2476,plain,
! [SV263: $i,SV32: $i,SV225: $i,SV412: $i] :
( ( ( ! [SY3980: $i] :
( ~ ( in @ SV412 @ SV225 )
| ~ ( in @ ( ordered_pair @ SV412 @ SY3980 ) @ SV32 )
| ( in @ ( ordered_pair @ SV412 @ SY3980 ) @ SV263 ) ) )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV32 @ SV225 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2352]) ).
thf(2477,plain,
! [SV32: $i,SV225: $i,SV263: $i] :
( ( ( ~ ! [SY3890: $i] :
( ! [SY3891: $i] :
~ ( in @ ( ordered_pair @ SY3890 @ SY3891 ) @ SV263 )
| ( in @ SY3890 @ SV225 ) )
| ~ ! [SY3892: $i,SY3893: $i] :
( ~ ( in @ ( ordered_pair @ SY3892 @ SY3893 ) @ SV263 )
| ( in @ ( ordered_pair @ SY3892 @ SY3893 ) @ SV32 ) ) )
= $false )
| ( ( SV263
= ( relation_dom_restriction @ SV32 @ SV225 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2353]) ).
thf(2478,plain,
! [SV33: $i,SV144: $i,SV189: $i] :
( ( ( in @ ( sK75_D @ SV189 @ SV144 @ SV33 ) @ ( relation_rng @ SV189 ) )
= $true )
| ( ( in @ SV33 @ ( relation_inverse_image @ SV189 @ SV144 ) )
= $false )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2355]) ).
thf(2479,plain,
! [SV144: $i,SV189: $i,SV33: $i] :
( ( ( in @ ( ordered_pair @ SV33 @ ( sK75_D @ SV189 @ SV144 @ SV33 ) ) @ SV189 )
= $true )
| ( ( in @ SV33 @ ( relation_inverse_image @ SV189 @ SV144 ) )
= $false )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2356]) ).
thf(2480,plain,
! [SV110: $i,SV145: $i] :
( ( ( in @ ( ordered_pair @ ( sK65_C @ SV145 @ SV110 ) @ ( sK66_SY3320 @ SV145 @ SV110 ) ) @ SV145 )
= $false )
| ( ( ( sK65_C @ SV145 @ SV110 )
= ( sK66_SY3320 @ SV145 @ SV110 ) )
= $false )
| ( ( in @ ( sK65_C @ SV145 @ SV110 ) @ SV110 )
= $false )
| ( ( SV145
= ( identity_relation @ SV110 ) )
= $true )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2357]) ).
thf(2481,plain,
! [SV146: $i,SV111: $i,SV374: $i,SV352: $i] :
( ( ( ( SV352 != SV374 ) )
= $true )
| ( ( ~ ( in @ SV352 @ SV111 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV352 @ SV374 ) @ SV146 )
= $true )
| ( ( SV146
= ( identity_relation @ SV111 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2360]) ).
thf(2482,plain,
! [SV111: $i,SV146: $i,SV413: $i] :
( ( ( ! [SY3981: $i] :
( ~ ( in @ ( ordered_pair @ SV413 @ SY3981 ) @ SV146 )
| ( SV413 = SY3981 ) ) )
= $true )
| ( ( SV146
= ( identity_relation @ SV111 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2361]) ).
thf(2483,plain,
! [SV111: $i,SV146: $i,SV414: $i] :
( ( ( ! [SY3982: $i] :
~ ( in @ ( ordered_pair @ SV414 @ SY3982 ) @ SV146 )
| ( in @ SV414 @ SV111 ) )
= $true )
| ( ( SV146
= ( identity_relation @ SV111 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2362]) ).
thf(2484,plain,
! [SV34: $i,SV89: $i,SV190: $i,SV226: $i] :
( ( ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
= $false )
| ( ( ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV190 ) )
= $true )
| ( ( SV226
= ( unordered_triple @ SV34 @ SV89 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2363]) ).
thf(2485,plain,
! [SV34: $i,SV89: $i,SV190: $i,SV226: $i] :
( ( ( ~ ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV34 ) ) )
= $false )
| ( ( SV226
= ( unordered_triple @ SV34 @ SV89 @ SV190 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2364]) ).
thf(2486,plain,
! [SV34: $i,SV89: $i,SV190: $i,SV226: $i] :
( ( ( ~ ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV89 ) ) )
= $false )
| ( ( SV226
= ( unordered_triple @ SV34 @ SV89 @ SV190 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2364]) ).
thf(2487,plain,
! [SV227: $i,SV89: $i,SV34: $i,SV191: $i,SV353: $i] :
( ( ( SV353 = SV191 )
= $true )
| ( ( ( SV353 = SV34 )
| ( SV353 = SV89 ) )
= $true )
| ( ( in @ SV353 @ SV227 )
= $false )
| ( ( SV227
= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2365]) ).
thf(2488,plain,
! [SV89: $i,SV34: $i,SV227: $i,SV191: $i,SV415: $i] :
( ( ( ( SV415 != SV191 )
| ( in @ SV415 @ SV227 ) )
= $true )
| ( ( SV227
= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2366]) ).
thf(2489,plain,
! [SV191: $i,SV89: $i,SV227: $i,SV34: $i] :
( ( ( ~ ! [SY3841: $i] :
( ( SY3841 != SV34 )
| ( in @ SY3841 @ SV227 ) )
| ~ ! [SY3842: $i] :
( ( SY3842 != SV89 )
| ( in @ SY3842 @ SV227 ) ) )
= $false )
| ( ( SV227
= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2367]) ).
thf(2490,plain,
! [SV229: $i,SV36: $i,SV355: $i,SV382: $i] :
( ( ( in @ ( ordered_pair @ SV382 @ SV355 ) @ SV36 )
= $false )
| ( ( in @ SV355 @ SV229 )
= $true )
| ( ( SV229
= ( relation_rng @ SV36 ) )
= $false )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2369]) ).
thf(2491,plain,
! [SV37: $i,SV324: $i,SV337: $i] :
( ( ( subset @ SV337 @ SV324 )
= $false )
| ( ( in @ SV324 @ ( sK77_B @ SV37 ) )
= $false )
| ( ( in @ SV337 @ ( sK77_B @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2371]) ).
thf(2492,plain,
! [SV91: $i,SV308: $i,SV39: $i] :
( ( ( ~ ( in @ SV39 @ ( relation_dom @ SV308 ) ) )
= $true )
| ( ( ~ ( in @ ( apply @ SV308 @ SV39 ) @ ( relation_dom @ SV91 ) ) )
= $true )
| ( ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SV308 @ SV91 ) ) )
= $true )
| ( ( function @ SV308 )
= $false )
| ( ( relation @ SV308 )
= $false )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2372]) ).
thf(2493,plain,
! [SV91: $i,SV39: $i,SV357: $i] :
( ( ( function @ SV357 )
= $false )
| ( ( ~ ( relation @ SV357 ) )
= $true )
| ( ( ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SV357 @ SV91 ) ) )
| ( in @ SV39 @ ( relation_dom @ SV357 ) ) )
= $true )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2373]) ).
thf(2494,plain,
! [SV91: $i,SV39: $i,SV358: $i] :
( ( ( function @ SV358 )
= $false )
| ( ( ~ ( relation @ SV358 ) )
= $true )
| ( ( ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SV358 @ SV91 ) ) )
| ( in @ ( apply @ SV358 @ SV39 ) @ ( relation_dom @ SV91 ) ) )
= $true )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2374]) ).
thf(2495,plain,
! [SV40: $i,SV92: $i,SV265: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_D @ SV265 @ SV92 @ SV40 ) @ SV265 )
| ~ ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SV265 @ SV92 @ SV40 ) ) @ SV92 ) ) )
= $false )
| ( ( SV265
= ( complements_of_subsets @ SV40 @ SV92 ) )
= $true )
| ( ( element @ SV265 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2375]) ).
thf(2496,plain,
! [SV40: $i,SV92: $i,SV265: $i] :
( ( ( ~ ( ( in @ ( sK6_D @ SV265 @ SV92 @ SV40 ) @ SV265 )
| ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SV265 @ SV92 @ SV40 ) ) @ SV92 ) ) )
= $false )
| ( ( SV265
= ( complements_of_subsets @ SV40 @ SV92 ) )
= $true )
| ( ( element @ SV265 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2375]) ).
thf(2497,plain,
! [SV92: $i,SV266: $i,SV40: $i,SV416: $i] :
( ( ( ~ ( element @ SV416 @ ( powerset @ SV40 ) )
| ~ ( in @ SV416 @ SV266 )
| ( in @ ( subset_complement @ SV40 @ SV416 ) @ SV92 ) )
= $true )
| ( ( SV266
= ( complements_of_subsets @ SV40 @ SV92 ) )
= $false )
| ( ( element @ SV266 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2376]) ).
thf(2498,plain,
! [SV266: $i,SV92: $i,SV40: $i,SV417: $i] :
( ( ( ~ ( element @ SV417 @ ( powerset @ SV40 ) )
| ~ ( in @ ( subset_complement @ SV40 @ SV417 ) @ SV92 )
| ( in @ SV417 @ SV266 ) )
= $true )
| ( ( SV266
= ( complements_of_subsets @ SV40 @ SV92 ) )
= $false )
| ( ( element @ SV266 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2377]) ).
thf(2499,plain,
! [SV359: $i,SV43: $i,SV271: $i] :
( ( ( in @ SV271 @ ( sK2_B @ SV43 ) )
= $false )
| ( ( in @ SV359 @ ( sK3_SY3278 @ SV271 @ SV43 ) )
= $true )
| ( ( subset @ SV359 @ SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2380]) ).
thf(2500,plain,
! [SV43: $i,SV327: $i,SV338: $i] :
( ( ( subset @ SV338 @ SV327 )
= $false )
| ( ( in @ SV327 @ ( sK2_B @ SV43 ) )
= $false )
| ( ( in @ SV338 @ ( sK2_B @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2381]) ).
thf(2501,plain,
! [SV233: $i,SV45: $i,SV383: $i,SV361: $i] :
( ( ( in @ ( ordered_pair @ SV361 @ SV383 ) @ SV45 )
= $false )
| ( ( in @ SV361 @ SV233 )
= $true )
| ( ( SV233
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2383]) ).
thf(2502,plain,
! [SV122: $i,SV159: $i] :
( ( ( ( relation_dom @ SV159 )
= SV122 )
= $false )
| ( ( ( apply @ SV159 @ ( sK74_C @ SV159 @ SV122 ) )
= ( sK74_C @ SV159 @ SV122 ) )
= $false )
| ( ( SV159
= ( identity_relation @ SV122 ) )
= $true )
| ( ( function @ SV159 )
= $false )
| ( ( relation @ SV159 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2386]) ).
thf(2503,plain,
! [SV272: $i,SV239: $i,SV384: $i] :
( ( ( ~ ( in @ SV384 @ SV239 ) )
= $true )
| ( ( ( apply @ SV272 @ SV384 )
= SV384 )
= $true )
| ( ( SV272
= ( identity_relation @ SV239 ) )
= $false )
| ( ( function @ SV272 )
= $false )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2387]) ).
thf(2504,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2388]) ).
thf(2505,plain,
! [SV46: $i,SV375: $i] :
( ( ( ~ ( function @ SV375 ) )
= $true )
| ( ( ~ ( relation @ SV375 ) )
= $true )
| ( ( ( SV375
!= ( function_inverse @ SV46 ) )
| ~ ( ~ ~ ( ~ ! [SY3963: $i,SY3964: $i] :
( ( SY3964
!= ( apply @ SV375 @ SY3963 ) )
| ~ ( in @ SY3963 @ ( relation_rng @ SV46 ) )
| ( SY3963
= ( apply @ SV46 @ SY3964 ) ) )
| ~ ! [SY3965: $i,SY3966: $i] :
( ( SY3966
!= ( apply @ SV375 @ SY3965 ) )
| ~ ( in @ SY3965 @ ( relation_rng @ SV46 ) )
| ( in @ SY3966 @ ( relation_dom @ SV46 ) ) ) )
| ~ ~ ( ~ ! [SY3967: $i,SY3968: $i] :
( ( SY3967
!= ( apply @ SV46 @ SY3968 ) )
| ~ ( in @ SY3968 @ ( relation_dom @ SV46 ) )
| ( SY3968
= ( apply @ SV375 @ SY3967 ) ) )
| ~ ! [SY3491: $i] :
( ! [SY3492: $i] :
( ( SY3491
!= ( apply @ SV46 @ SY3492 ) )
| ~ ( in @ SY3492 @ ( relation_dom @ SV46 ) ) )
| ( in @ SY3491 @ ( relation_rng @ SV46 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2389]) ).
thf(2506,plain,
! [SV46: $i,SV376: $i] :
( ( ( ~ ( function @ SV376 ) )
= $true )
| ( ( ~ ( relation @ SV376 ) )
= $true )
| ( ( ( SV376
!= ( function_inverse @ SV46 ) )
| ( ( relation_dom @ SV376 )
= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2390]) ).
thf(2507,plain,
! [SV47: $i,SV123: $i,SV313: $i] :
( ( ( ! [SY3936: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ SY3936 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3936 @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV123 ) )
| ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV313 ) )
= $true )
| ( ( SV313
= ( relation_composition @ SV47 @ SV123 ) )
= $true )
| ( ( relation @ SV313 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2391]) ).
thf(2508,plain,
! [SV47: $i,SV123: $i,SV313: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK10_SY3288 @ SV313 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY3288 @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV123 ) )
| ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV313 ) )
= $true )
| ( ( SV313
= ( relation_composition @ SV47 @ SV123 ) )
= $true )
| ( ( relation @ SV313 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2392]) ).
thf(2509,plain,
! [SV314: $i,SV123: $i,SV47: $i] :
( ( ( ~ ! [SY3937: $i,SY3938: $i] :
( ! [SY3706: $i] :
( ~ ( in @ ( ordered_pair @ SY3937 @ SY3706 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3706 @ SY3938 ) @ SV123 ) )
| ( in @ ( ordered_pair @ SY3937 @ SY3938 ) @ SV314 ) ) )
= $false )
| ( ( SV314
= ( relation_composition @ SV47 @ SV123 ) )
= $false )
| ( ( relation @ SV314 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2393]) ).
thf(2510,plain,
! [SV47: $i,SV123: $i,SV314: $i] :
( ( ( ~ ! [SY3940: $i,SY3941: $i] :
( ~ ( in @ ( ordered_pair @ SY3940 @ SY3941 ) @ SV314 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3940 @ ( sK7_F @ SY3941 @ SY3940 @ SV314 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY3941 @ SY3940 @ SV314 @ SV123 @ SV47 ) @ SY3941 ) @ SV123 ) ) ) )
= $false )
| ( ( SV314
= ( relation_composition @ SV47 @ SV123 ) )
= $false )
| ( ( relation @ SV314 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2393]) ).
thf(2511,plain,
! [SV124: $i] :
( ( ( ~ ( in @ ( sK11_B @ SV124 ) @ ( relation_dom @ SV124 ) )
| ~ ( in @ ( sK12_SY3289 @ SV124 ) @ ( relation_dom @ SV124 ) ) )
= $false )
| ( ( one_to_one @ SV124 )
= $true )
| ( ( function @ SV124 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2394]) ).
thf(2512,plain,
! [SV339: $i,SV125: $i,SV332: $i] :
( ( ( in @ SV332 @ ( relation_dom @ SV125 ) )
= $false )
| ( ( ~ ( in @ SV339 @ ( relation_dom @ SV125 ) ) )
= $true )
| ( ( ( ( apply @ SV125 @ SV332 )
!= ( apply @ SV125 @ SV339 ) ) )
= $true )
| ( ( SV332 = SV339 )
= $true )
| ( ( one_to_one @ SV125 )
= $false )
| ( ( function @ SV125 )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2396]) ).
thf(2513,plain,
! [SV51: $i,SV161: $i,SV199: $i] :
( ( ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV51 )
= $false )
| ( ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV199 )
= $false )
| ( ( SV199
= ( set_union2 @ SV51 @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2397]) ).
thf(2514,plain,
! [SV51: $i,SV161: $i,SV199: $i] :
( ( ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV161 )
= $false )
| ( ( in @ ( sK37_D @ SV199 @ SV161 @ SV51 ) @ SV199 )
= $false )
| ( ( SV199
= ( set_union2 @ SV51 @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2398]) ).
thf(2515,plain,
! [SV162: $i,SV200: $i,SV51: $i,SV385: $i] :
( ( ( ~ ( in @ SV385 @ SV51 ) )
= $true )
| ( ( in @ SV385 @ SV200 )
= $true )
| ( ( SV200
= ( set_union2 @ SV51 @ SV162 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2400]) ).
thf(2516,plain,
! [SV51: $i,SV200: $i,SV162: $i,SV386: $i] :
( ( ( ~ ( in @ SV386 @ SV162 ) )
= $true )
| ( ( in @ SV386 @ SV200 )
= $true )
| ( ( SV200
= ( set_union2 @ SV51 @ SV162 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2401]) ).
thf(2517,plain,
! [SV245: $i,SV295: $i] :
( ( ( ~ ( in @ ( sK46_SY3307 @ SV295 @ SV245 ) @ SV245 ) )
= $false )
| ( ( ~ ( in @ ( sK45_C @ SV295 @ SV245 ) @ SV295 ) )
= $true )
| ( ( SV295
= ( set_meet @ SV245 ) )
= $true )
| ( ( SV245 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2403]) ).
thf(2518,plain,
! [SV245: $i,SV295: $i] :
( ( ( ~ ~ ( in @ ( sK45_C @ SV295 @ SV245 ) @ ( sK46_SY3307 @ SV295 @ SV245 ) ) )
= $false )
| ( ( ~ ( in @ ( sK45_C @ SV295 @ SV245 ) @ SV295 ) )
= $true )
| ( ( SV295
= ( set_meet @ SV245 ) )
= $true )
| ( ( SV245 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2403]) ).
thf(2519,plain,
! [SV295: $i,SV245: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ SV245 ) )
= $true )
| ( ( in @ ( sK45_C @ SV295 @ SV245 ) @ SV387 )
= $true )
| ( ( in @ ( sK45_C @ SV295 @ SV245 ) @ SV295 )
= $true )
| ( ( SV295
= ( set_meet @ SV245 ) )
= $true )
| ( ( SV245 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2404]) ).
thf(2520,plain,
! [SV246: $i,SV296: $i,SV388: $i] :
( ( ( ~ ( ~ ( in @ ( sK44_D @ SV388 @ SV296 @ SV246 ) @ SV246 )
| ~ ~ ( in @ SV388 @ ( sK44_D @ SV388 @ SV296 @ SV246 ) ) ) )
= $true )
| ( ( in @ SV388 @ SV296 )
= $true )
| ( ( SV296
= ( set_meet @ SV246 ) )
= $false )
| ( ( SV246 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2405]) ).
thf(2521,plain,
! [SV246: $i,SV296: $i,SV389: $i] :
( ( ( ~ ( in @ SV389 @ SV296 ) )
= $true )
| ( ( ! [SY3974: $i] :
( ~ ( in @ SY3974 @ SV246 )
| ( in @ SV389 @ SY3974 ) ) )
= $true )
| ( ( SV296
= ( set_meet @ SV246 ) )
= $false )
| ( ( SV246 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2406]) ).
thf(2522,plain,
! [SV53: $i,SV297: $i,SV319: $i] :
( ( ( ~ ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ ( relation_dom @ SV53 ) ) )
= $true )
| ( ( ~ ( in @ ( apply @ SV53 @ ( sK57_D @ SV319 @ SV297 @ SV53 ) ) @ SV297 ) )
= $true )
| ( ( ~ ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ SV319 ) )
= $true )
| ( ( SV319
= ( relation_inverse_image @ SV53 @ SV297 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2407]) ).
thf(2523,plain,
! [SV53: $i,SV297: $i,SV319: $i] :
( ( ( ~ ( ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ SV319 ) ) )
= $false )
| ( ( SV319
= ( relation_inverse_image @ SV53 @ SV297 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2408]) ).
thf(2524,plain,
! [SV297: $i,SV319: $i,SV53: $i] :
( ( ( ~ ( ( in @ ( apply @ SV53 @ ( sK57_D @ SV319 @ SV297 @ SV53 ) ) @ SV297 )
| ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ SV319 ) ) )
= $false )
| ( ( SV319
= ( relation_inverse_image @ SV53 @ SV297 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2408]) ).
thf(2525,plain,
! [SV320: $i,SV298: $i,SV53: $i,SV418: $i] :
( ( ( ~ ( in @ SV418 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SV418 ) @ SV298 )
| ( in @ SV418 @ SV320 ) )
= $true )
| ( ( SV320
= ( relation_inverse_image @ SV53 @ SV298 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2409]) ).
thf(2526,plain,
! [SV298: $i,SV53: $i,SV320: $i] :
( ( ( ~ ! [SY3943: $i] :
( ~ ( in @ SY3943 @ SV320 )
| ( in @ SY3943 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY3944: $i] :
( ~ ( in @ SY3944 @ SV320 )
| ( in @ ( apply @ SV53 @ SY3944 ) @ SV298 ) ) )
= $false )
| ( ( SV320
= ( relation_inverse_image @ SV53 @ SV298 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2410]) ).
thf(2527,plain,
! [SV202: $i,SV54: $i,SV166: $i,SV342: $i] :
( ( ( in @ SV342 @ SV166 )
= $false )
| ( ( in @ SV342 @ SV54 )
= $false )
| ( ( in @ SV342 @ SV202 )
= $true )
| ( ( SV202
= ( set_intersection2 @ SV54 @ SV166 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2412]) ).
thf(2528,plain,
! [SV166: $i,SV54: $i,SV202: $i,SV390: $i] :
( ( ( ~ ( in @ SV390 @ SV202 ) )
= $true )
| ( ( in @ SV390 @ SV54 )
= $true )
| ( ( SV202
= ( set_intersection2 @ SV54 @ SV166 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2413]) ).
thf(2529,plain,
! [SV54: $i,SV166: $i,SV202: $i,SV391: $i] :
( ( ( ~ ( in @ SV391 @ SV202 ) )
= $true )
| ( ( in @ SV391 @ SV166 )
= $true )
| ( ( SV202
= ( set_intersection2 @ SV54 @ SV166 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2414]) ).
thf(2530,plain,
! [SV170: $i,SV55: $i,SV204: $i,SV392: $i] :
( ( ( ~ ( in @ SV392 @ SV204 ) )
= $true )
| ( ( in @ SV392 @ SV55 )
= $true )
| ( ( SV204
= ( set_difference @ SV55 @ SV170 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2417]) ).
thf(2531,plain,
! [SV55: $i,SV170: $i,SV204: $i,SV393: $i] :
( ( ( ~ ( in @ SV393 @ SV204 ) )
= $true )
| ( ( ~ ( in @ SV393 @ SV170 ) )
= $true )
| ( ( SV204
= ( set_difference @ SV55 @ SV170 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2418]) ).
thf(2532,plain,
! [SV394: $i,SV56: $i,SV299: $i] :
( ( ( ( ( sK19_C @ SV299 @ SV56 )
!= ( apply @ SV56 @ SV394 ) ) )
= $true )
| ( ( ~ ( in @ SV394 @ ( relation_dom @ SV56 ) ) )
= $true )
| ( ( ~ ( in @ ( sK19_C @ SV299 @ SV56 ) @ SV299 ) )
= $true )
| ( ( SV299
= ( relation_rng @ SV56 ) )
= $true )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2419]) ).
thf(2533,plain,
! [SV56: $i,SV299: $i] :
( ( ( ( ( sK19_C @ SV299 @ SV56 )
!= ( apply @ SV56 @ ( sK20_SY3294 @ SV299 @ SV56 ) ) ) )
= $false )
| ( ( in @ ( sK19_C @ SV299 @ SV56 ) @ SV299 )
= $true )
| ( ( SV299
= ( relation_rng @ SV56 ) )
= $true )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2420]) ).
thf(2534,plain,
! [SV56: $i,SV299: $i] :
( ( ( ~ ( in @ ( sK20_SY3294 @ SV299 @ SV56 ) @ ( relation_dom @ SV56 ) ) )
= $false )
| ( ( in @ ( sK19_C @ SV299 @ SV56 ) @ SV299 )
= $true )
| ( ( SV299
= ( relation_rng @ SV56 ) )
= $true )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2420]) ).
thf(2535,plain,
! [SV300: $i,SV56: $i,SV395: $i] :
( ( ( ! [SY3975: $i] :
( ( SV395
!= ( apply @ SV56 @ SY3975 ) )
| ~ ( in @ SY3975 @ ( relation_dom @ SV56 ) ) ) )
= $true )
| ( ( in @ SV395 @ SV300 )
= $true )
| ( ( SV300
= ( relation_rng @ SV56 ) )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2421]) ).
thf(2536,plain,
! [SV56: $i,SV300: $i,SV396: $i] :
( ( ( ~ ( in @ SV396 @ SV300 ) )
= $true )
| ( ( ~ ( ( SV396
!= ( apply @ SV56 @ ( sK18_D @ SV396 @ SV300 @ SV56 ) ) )
| ~ ( in @ ( sK18_D @ SV396 @ SV300 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
= $true )
| ( ( SV300
= ( relation_rng @ SV56 ) )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2422]) ).
thf(2537,plain,
! [SV57: $i,SV171: $i,SV205: $i] :
( ( ( ( sK38_D @ SV205 @ SV171 @ SV57 )
= SV57 )
= $false )
| ( ( in @ ( sK38_D @ SV205 @ SV171 @ SV57 ) @ SV205 )
= $false )
| ( ( SV205
= ( unordered_pair @ SV57 @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2423]) ).
thf(2538,plain,
! [SV57: $i,SV171: $i,SV205: $i] :
( ( ( ( sK38_D @ SV205 @ SV171 @ SV57 )
= SV171 )
= $false )
| ( ( in @ ( sK38_D @ SV205 @ SV171 @ SV57 ) @ SV205 )
= $false )
| ( ( SV205
= ( unordered_pair @ SV57 @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2424]) ).
thf(2539,plain,
! [SV172: $i,SV206: $i,SV57: $i,SV397: $i] :
( ( ( ( SV397 != SV57 ) )
= $true )
| ( ( in @ SV397 @ SV206 )
= $true )
| ( ( SV206
= ( unordered_pair @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2426]) ).
thf(2540,plain,
! [SV57: $i,SV206: $i,SV172: $i,SV398: $i] :
( ( ( ( SV398 != SV172 ) )
= $true )
| ( ( in @ SV398 @ SV206 )
= $true )
| ( ( SV206
= ( unordered_pair @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2427]) ).
thf(2541,plain,
! [SV58: $i,SV96: $i,SV321: $i] :
( ( ( ~ ( ~ ( in @ ( sK67_D @ SV321 @ SV96 @ SV58 ) @ ( relation_dom @ SV96 ) )
| ~ ( ( ( apply @ SV96 @ ( sK67_D @ SV321 @ SV96 @ SV58 ) )
!= ( apply @ SV321 @ ( sK67_D @ SV321 @ SV96 @ SV58 ) ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV96 )
!= ( set_intersection2 @ ( relation_dom @ SV321 ) @ SV58 ) ) )
= $true )
| ( ( SV96
= ( relation_dom_restriction @ SV321 @ SV58 ) )
= $true )
| ( ( function @ SV321 )
= $false )
| ( ( relation @ SV321 )
= $false )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2428]) ).
thf(2542,plain,
! [SV58: $i,SV96: $i,SV364: $i] :
( ( ( function @ SV364 )
= $false )
| ( ( ~ ( relation @ SV364 ) )
= $true )
| ( ( ( SV96
!= ( relation_dom_restriction @ SV364 @ SV58 ) )
| ! [SY3960: $i] :
( ~ ( in @ SY3960 @ ( relation_dom @ SV96 ) )
| ( ( apply @ SV96 @ SY3960 )
= ( apply @ SV364 @ SY3960 ) ) ) )
= $true )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2429]) ).
thf(2543,plain,
! [SV58: $i,SV96: $i,SV365: $i] :
( ( ( function @ SV365 )
= $false )
| ( ( ~ ( relation @ SV365 ) )
= $true )
| ( ( ( SV96
!= ( relation_dom_restriction @ SV365 @ SV58 ) )
| ( ( relation_dom @ SV96 )
= ( set_intersection2 @ ( relation_dom @ SV365 ) @ SV58 ) ) )
= $true )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2430]) ).
thf(2544,plain,
! [SV59: $i,SV249: $i] :
( ( ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV249 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_C @ SV249 @ SV59 ) @ ( sK40_SY3306 @ SV249 @ SV59 ) ) @ SV59 )
= $false )
| ( ( SV59 = SV249 )
= $true )
| ( ( relation @ SV249 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2431]) ).
thf(2545,plain,
! [SV250: $i,SV59: $i,SV419: $i,SV399: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV399 @ SV419 ) @ SV59 )
| ( in @ ( ordered_pair @ SV399 @ SV419 ) @ SV250 ) )
= $true )
| ( ( SV59 = SV250 )
= $false )
| ( ( relation @ SV250 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2432]) ).
thf(2546,plain,
! [SV59: $i,SV250: $i,SV420: $i,SV400: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV400 @ SV420 ) @ SV250 )
| ( in @ ( ordered_pair @ SV400 @ SV420 ) @ SV59 ) )
= $true )
| ( ( SV59 = SV250 )
= $false )
| ( ( relation @ SV250 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2433]) ).
thf(2547,plain,
! [SV174: $i,SV334: $i,SV131: $i,SV366: $i] :
( ( ( in @ SV366 @ SV131 )
= $false )
| ( ( in @ SV334 @ SV366 )
= $false )
| ( ( in @ SV334 @ SV174 )
= $true )
| ( ( SV174
= ( union @ SV131 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2435]) ).
thf(2548,plain,
! [SV131: $i,SV174: $i,SV335: $i] :
( ( ( in @ SV335 @ ( sK22_D @ SV335 @ SV174 @ SV131 ) )
= $true )
| ( ( in @ SV335 @ SV174 )
= $false )
| ( ( SV174
= ( union @ SV131 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2436]) ).
thf(2549,plain,
! [SV131: $i,SV174: $i,SV335: $i] :
( ( ( in @ ( sK22_D @ SV335 @ SV174 @ SV131 ) @ SV131 )
= $true )
| ( ( in @ SV335 @ SV174 )
= $false )
| ( ( SV174
= ( union @ SV131 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2437]) ).
thf(2550,plain,
! [SV209: $i,SV176: $i,SV367: $i,SV63: $i,SV345: $i] :
( ( ( in @ SV345 @ SV63 )
= $false )
| ( ( ~ ( in @ SV367 @ SV176 ) )
= $true )
| ( ( ( ( sK34_D @ SV209 @ SV176 @ SV63 )
!= ( ordered_pair @ SV345 @ SV367 ) ) )
= $true )
| ( ( ~ ( in @ ( sK34_D @ SV209 @ SV176 @ SV63 ) @ SV209 ) )
= $true )
| ( ( SV209
= ( cartesian_product2 @ SV63 @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2440]) ).
thf(2551,plain,
! [SV63: $i,SV176: $i,SV209: $i] :
( ( ( ~ ( in @ ( sK35_SY3303 @ SV209 @ SV176 @ SV63 ) @ SV63 ) )
= $false )
| ( ( in @ ( sK34_D @ SV209 @ SV176 @ SV63 ) @ SV209 )
= $true )
| ( ( SV209
= ( cartesian_product2 @ SV63 @ SV176 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2441]) ).
thf(2552,plain,
! [SV63: $i,SV176: $i,SV209: $i] :
( ( ( ~ ( in @ ( sK36_SY3305 @ SV209 @ SV176 @ SV63 ) @ SV176 ) )
= $false )
| ( ( in @ ( sK34_D @ SV209 @ SV176 @ SV63 ) @ SV209 )
= $true )
| ( ( SV209
= ( cartesian_product2 @ SV63 @ SV176 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2441]) ).
thf(2553,plain,
! [SV210: $i,SV346: $i,SV177: $i,SV401: $i,SV63: $i,SV377: $i] :
( ( ( ~ ( in @ SV377 @ SV63 )
| ~ ( in @ SV401 @ SV177 ) )
= $true )
| ( ( ( SV346
!= ( ordered_pair @ SV377 @ SV401 ) ) )
= $true )
| ( ( in @ SV346 @ SV210 )
= $true )
| ( ( SV210
= ( cartesian_product2 @ SV63 @ SV177 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2442]) ).
thf(2554,plain,
! [SV63: $i,SV177: $i,SV210: $i,SV347: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK32_E @ SV347 @ SV210 @ SV177 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK33_SY3300 @ SV347 @ SV210 @ SV177 @ SV63 ) @ SV177 ) ) )
= $false )
| ( ( in @ SV347 @ SV210 )
= $false )
| ( ( SV210
= ( cartesian_product2 @ SV63 @ SV177 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2443]) ).
thf(2555,plain,
! [SV63: $i,SV177: $i,SV210: $i,SV347: $i] :
( ( ( ( SV347
!= ( ordered_pair @ ( sK32_E @ SV347 @ SV210 @ SV177 @ SV63 ) @ ( sK33_SY3300 @ SV347 @ SV210 @ SV177 @ SV63 ) ) ) )
= $false )
| ( ( in @ SV347 @ SV210 )
= $false )
| ( ( SV210
= ( cartesian_product2 @ SV63 @ SV177 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2443]) ).
thf(2556,plain,
! [SV64: $i,SV181: $i,SV212: $i] :
( ( ( in @ ( sK76_D @ SV212 @ SV181 @ SV64 ) @ ( relation_dom @ SV212 ) )
= $true )
| ( ( in @ SV64 @ ( relation_image @ SV212 @ SV181 ) )
= $false )
| ( ( relation @ SV212 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2445]) ).
thf(2557,plain,
! [SV64: $i,SV181: $i,SV212: $i] :
( ( ( in @ ( ordered_pair @ ( sK76_D @ SV212 @ SV181 @ SV64 ) @ SV64 ) @ SV212 )
= $true )
| ( ( in @ SV64 @ ( relation_image @ SV212 @ SV181 ) )
= $false )
| ( ( relation @ SV212 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2446]) ).
thf(2558,plain,
! [SV348: $i,SV66: $i,SV402: $i] :
( ( ( ( SV402
!= ( apply @ SV66 @ SV348 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV348 @ SV402 ) @ SV66 )
= $true )
| ( ( in @ SV348 @ ( relation_dom @ SV66 ) )
= $false )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2447]) ).
thf(2559,plain,
! [SV66: $i,SV403: $i,SV349: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV349 @ SV403 ) @ SV66 ) )
= $true )
| ( ( SV403
= ( apply @ SV66 @ SV349 ) )
= $true )
| ( ( in @ SV349 @ ( relation_dom @ SV66 ) )
= $false )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2448]) ).
thf(2560,plain,
! [SV350: $i,SV66: $i,SV378: $i] :
( ( ( SV378
= ( apply @ SV66 @ SV350 ) )
= $false )
| ( ( SV378 = empty_set )
= $true )
| ( ( in @ SV350 @ ( relation_dom @ SV66 ) )
= $true )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2449]) ).
thf(2561,plain,
! [SV351: $i,SV66: $i,SV379: $i] :
( ( ( SV379 = empty_set )
= $false )
| ( ( SV379
= ( apply @ SV66 @ SV351 ) )
= $true )
| ( ( in @ SV351 @ ( relation_dom @ SV66 ) )
= $true )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2450]) ).
thf(2562,plain,
! [SV26: $i,SV88: $i,SV253: $i] :
( ( ( in @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) @ SV26 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV88 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 ) )
= $true )
| ( ( SV253
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $true )
| ( ( relation @ SV253 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2451]) ).
thf(2563,plain,
! [SV26: $i,SV88: $i,SV253: $i] :
( ( ( ( in @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) @ SV26 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 ) )
= $true )
| ( ( SV253
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $true )
| ( ( relation @ SV253 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2452]) ).
thf(2564,plain,
! [SV26: $i,SV88: $i,SV253: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV88 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 ) )
= $true )
| ( ( SV253
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $true )
| ( ( relation @ SV253 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2453]) ).
thf(2565,plain,
! [SV254: $i,SV88: $i,SV404: $i,SV26: $i,SV421: $i] :
( ( ( ~ ( in @ SV421 @ SV26 )
| ~ ( in @ ( ordered_pair @ SV404 @ SV421 ) @ SV88 )
| ( in @ ( ordered_pair @ SV404 @ SV421 ) @ SV254 ) )
= $true )
| ( ( SV254
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2454]) ).
thf(2566,plain,
! [SV88: $i,SV26: $i,SV254: $i] :
( ( ( ~ ! [SY3874: $i,SY3875: $i] :
( ~ ( in @ ( ordered_pair @ SY3874 @ SY3875 ) @ SV254 )
| ( in @ SY3875 @ SV26 ) ) )
= $false )
| ( ( SV254
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2455]) ).
thf(2567,plain,
! [SV26: $i,SV88: $i,SV254: $i] :
( ( ( ~ ! [SY3876: $i,SY3877: $i] :
( ~ ( in @ ( ordered_pair @ SY3876 @ SY3877 ) @ SV254 )
| ( in @ ( ordered_pair @ SY3876 @ SY3877 ) @ SV88 ) ) )
= $false )
| ( ( SV254
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2455]) ).
thf(2568,plain,
! [SV28: $i,SV219: $i,SV405: $i,SV380: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV380 @ SV405 ) @ SV219 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV405 @ SV380 ) @ SV28 )
= $true )
| ( ( SV219
= ( relation_inverse @ SV28 ) )
= $false )
| ( ( relation @ SV219 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2457]) ).
thf(2569,plain,
! [SV219: $i,SV28: $i,SV381: $i,SV406: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV406 @ SV381 ) @ SV28 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV381 @ SV406 ) @ SV219 )
= $true )
| ( ( SV219
= ( relation_inverse @ SV28 ) )
= $false )
| ( ( relation @ SV219 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2458]) ).
thf(2570,plain,
! [SV305: $i,SV280: $i,SV29: $i,SV407: $i] :
( ( ( ~ ( in @ SV407 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SV407 @ SV280 ) )
= $true )
| ( ( ( ( sK61_D @ SV305 @ SV280 @ SV29 )
!= ( apply @ SV29 @ SV407 ) ) )
= $true )
| ( ( ~ ( in @ ( sK61_D @ SV305 @ SV280 @ SV29 ) @ SV305 ) )
= $true )
| ( ( SV305
= ( relation_image @ SV29 @ SV280 ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2459]) ).
thf(2571,plain,
! [SV29: $i,SV280: $i,SV305: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) @ SV280 ) ) )
= $false )
| ( ( in @ ( sK61_D @ SV305 @ SV280 @ SV29 ) @ SV305 )
= $true )
| ( ( SV305
= ( relation_image @ SV29 @ SV280 ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2460]) ).
thf(2572,plain,
! [SV29: $i,SV280: $i,SV305: $i] :
( ( ( ( ( sK61_D @ SV305 @ SV280 @ SV29 )
!= ( apply @ SV29 @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) ) ) )
= $false )
| ( ( in @ ( sK61_D @ SV305 @ SV280 @ SV29 ) @ SV305 )
= $true )
| ( ( SV305
= ( relation_image @ SV29 @ SV280 ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2460]) ).
thf(2573,plain,
! [SV306: $i,SV408: $i,SV281: $i,SV29: $i] :
( ( ( ! [SY3979: $i] :
( ~ ( in @ SY3979 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SY3979 @ SV281 )
| ( SV408
!= ( apply @ SV29 @ SY3979 ) ) ) )
= $true )
| ( ( in @ SV408 @ SV306 )
= $true )
| ( ( SV306
= ( relation_image @ SV29 @ SV281 ) )
= $false )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2461]) ).
thf(2574,plain,
! [SV29: $i,SV281: $i,SV306: $i,SV409: $i] :
( ( ( ~ ( in @ SV409 @ SV306 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SV409 @ SV306 @ SV281 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK60_E @ SV409 @ SV306 @ SV281 @ SV29 ) @ SV281 ) )
| ( SV409
!= ( apply @ SV29 @ ( sK60_E @ SV409 @ SV306 @ SV281 @ SV29 ) ) ) ) )
= $true )
| ( ( SV306
= ( relation_image @ SV29 @ SV281 ) )
= $false )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2462]) ).
thf(2575,plain,
! [SV30: $i,SV258: $i,SV220: $i,SV368: $i] :
( ( ( in @ SV368 @ SV220 )
= $false )
| ( ( in @ ( ordered_pair @ SV368 @ ( sK55_D @ SV258 @ SV220 @ SV30 ) ) @ SV30 )
= $false )
| ( ( ~ ( in @ ( sK55_D @ SV258 @ SV220 @ SV30 ) @ SV258 ) )
= $true )
| ( ( SV258
= ( relation_image @ SV30 @ SV220 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2463]) ).
thf(2576,plain,
! [SV259: $i,SV221: $i,SV30: $i,SV369: $i,SV410: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV410 @ SV369 ) @ SV30 ) )
= $true )
| ( ( ~ ( in @ SV410 @ SV221 ) )
= $true )
| ( ( in @ SV369 @ SV259 )
= $true )
| ( ( SV259
= ( relation_image @ SV30 @ SV221 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2466]) ).
thf(2577,plain,
! [SV30: $i,SV221: $i,SV259: $i,SV370: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SV370 @ SV259 @ SV221 @ SV30 ) @ SV370 ) @ SV30 )
| ~ ( in @ ( sK54_E @ SV370 @ SV259 @ SV221 @ SV30 ) @ SV221 ) )
= $false )
| ( ( in @ SV370 @ SV259 )
= $false )
| ( ( SV259
= ( relation_image @ SV30 @ SV221 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2467]) ).
thf(2578,plain,
! [SV31: $i,SV260: $i,SV222: $i,SV371: $i] :
( ( ( in @ SV371 @ SV222 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SV371 ) @ SV31 )
= $false )
| ( ( ~ ( in @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SV260 ) )
= $true )
| ( ( SV260
= ( relation_inverse_image @ SV31 @ SV222 ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2468]) ).
thf(2579,plain,
! [SV261: $i,SV223: $i,SV31: $i,SV411: $i,SV372: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV372 @ SV411 ) @ SV31 ) )
= $true )
| ( ( ~ ( in @ SV411 @ SV223 ) )
= $true )
| ( ( in @ SV372 @ SV261 )
= $true )
| ( ( SV261
= ( relation_inverse_image @ SV31 @ SV223 ) )
= $false )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2471]) ).
thf(2580,plain,
! [SV31: $i,SV223: $i,SV261: $i,SV373: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV373 @ ( sK51_E @ SV373 @ SV261 @ SV223 @ SV31 ) ) @ SV31 )
| ~ ( in @ ( sK51_E @ SV373 @ SV261 @ SV223 @ SV31 ) @ SV223 ) )
= $false )
| ( ( in @ SV373 @ SV261 )
= $false )
| ( ( SV261
= ( relation_inverse_image @ SV31 @ SV223 ) )
= $false )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2472]) ).
thf(2581,plain,
! [SV32: $i,SV224: $i,SV262: $i] :
( ( ( in @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ SV224 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV32 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 ) )
= $true )
| ( ( SV262
= ( relation_dom_restriction @ SV32 @ SV224 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2473]) ).
thf(2582,plain,
! [SV32: $i,SV224: $i,SV262: $i] :
( ( ( ( in @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ SV224 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 ) )
= $true )
| ( ( SV262
= ( relation_dom_restriction @ SV32 @ SV224 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2474]) ).
thf(2583,plain,
! [SV32: $i,SV224: $i,SV262: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV32 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 ) )
= $true )
| ( ( SV262
= ( relation_dom_restriction @ SV32 @ SV224 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2475]) ).
thf(2584,plain,
! [SV263: $i,SV32: $i,SV422: $i,SV225: $i,SV412: $i] :
( ( ( ~ ( in @ SV412 @ SV225 )
| ~ ( in @ ( ordered_pair @ SV412 @ SV422 ) @ SV32 )
| ( in @ ( ordered_pair @ SV412 @ SV422 ) @ SV263 ) )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV32 @ SV225 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2476]) ).
thf(2585,plain,
! [SV32: $i,SV225: $i,SV263: $i] :
( ( ( ~ ! [SY3890: $i] :
( ! [SY3891: $i] :
~ ( in @ ( ordered_pair @ SY3890 @ SY3891 ) @ SV263 )
| ( in @ SY3890 @ SV225 ) ) )
= $false )
| ( ( SV263
= ( relation_dom_restriction @ SV32 @ SV225 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2477]) ).
thf(2586,plain,
! [SV225: $i,SV32: $i,SV263: $i] :
( ( ( ~ ! [SY3892: $i,SY3893: $i] :
( ~ ( in @ ( ordered_pair @ SY3892 @ SY3893 ) @ SV263 )
| ( in @ ( ordered_pair @ SY3892 @ SY3893 ) @ SV32 ) ) )
= $false )
| ( ( SV263
= ( relation_dom_restriction @ SV32 @ SV225 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2477]) ).
thf(2587,plain,
! [SV146: $i,SV111: $i,SV374: $i,SV352: $i] :
( ( ( SV352 = SV374 )
= $false )
| ( ( ~ ( in @ SV352 @ SV111 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV352 @ SV374 ) @ SV146 )
= $true )
| ( ( SV146
= ( identity_relation @ SV111 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2481]) ).
thf(2588,plain,
! [SV111: $i,SV146: $i,SV423: $i,SV413: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV413 @ SV423 ) @ SV146 )
| ( SV413 = SV423 ) )
= $true )
| ( ( SV146
= ( identity_relation @ SV111 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2482]) ).
thf(2589,plain,
! [SV111: $i,SV146: $i,SV414: $i] :
( ( ( ! [SY3982: $i] :
~ ( in @ ( ordered_pair @ SV414 @ SY3982 ) @ SV146 ) )
= $true )
| ( ( in @ SV414 @ SV111 )
= $true )
| ( ( SV146
= ( identity_relation @ SV111 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2483]) ).
thf(2590,plain,
! [SV34: $i,SV89: $i,SV190: $i,SV226: $i] :
( ( ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
= SV190 )
= $false )
| ( ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
= $false )
| ( ( SV226
= ( unordered_triple @ SV34 @ SV89 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2484]) ).
thf(2591,plain,
! [SV34: $i,SV89: $i,SV190: $i,SV226: $i] :
( ( ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV34 ) )
= $true )
| ( ( SV226
= ( unordered_triple @ SV34 @ SV89 @ SV190 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2485]) ).
thf(2592,plain,
! [SV34: $i,SV89: $i,SV190: $i,SV226: $i] :
( ( ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
| ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV89 ) )
= $true )
| ( ( SV226
= ( unordered_triple @ SV34 @ SV89 @ SV190 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2486]) ).
thf(2593,plain,
! [SV227: $i,SV191: $i,SV89: $i,SV34: $i,SV353: $i] :
( ( ( SV353 = SV34 )
= $true )
| ( ( SV353 = SV89 )
= $true )
| ( ( SV353 = SV191 )
= $true )
| ( ( in @ SV353 @ SV227 )
= $false )
| ( ( SV227
= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2487]) ).
thf(2594,plain,
! [SV89: $i,SV34: $i,SV227: $i,SV191: $i,SV415: $i] :
( ( ( ( SV415 != SV191 ) )
= $true )
| ( ( in @ SV415 @ SV227 )
= $true )
| ( ( SV227
= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2488]) ).
thf(2595,plain,
! [SV191: $i,SV89: $i,SV227: $i,SV34: $i] :
( ( ( ~ ! [SY3841: $i] :
( ( SY3841 != SV34 )
| ( in @ SY3841 @ SV227 ) ) )
= $false )
| ( ( SV227
= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2489]) ).
thf(2596,plain,
! [SV191: $i,SV34: $i,SV227: $i,SV89: $i] :
( ( ( ~ ! [SY3842: $i] :
( ( SY3842 != SV89 )
| ( in @ SY3842 @ SV227 ) ) )
= $false )
| ( ( SV227
= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2489]) ).
thf(2597,plain,
! [SV91: $i,SV308: $i,SV39: $i] :
( ( ( in @ SV39 @ ( relation_dom @ SV308 ) )
= $false )
| ( ( ~ ( in @ ( apply @ SV308 @ SV39 ) @ ( relation_dom @ SV91 ) ) )
= $true )
| ( ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SV308 @ SV91 ) ) )
= $true )
| ( ( function @ SV308 )
= $false )
| ( ( relation @ SV308 )
= $false )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2492]) ).
thf(2598,plain,
! [SV91: $i,SV39: $i,SV357: $i] :
( ( ( relation @ SV357 )
= $false )
| ( ( function @ SV357 )
= $false )
| ( ( ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SV357 @ SV91 ) ) )
| ( in @ SV39 @ ( relation_dom @ SV357 ) ) )
= $true )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2493]) ).
thf(2599,plain,
! [SV91: $i,SV39: $i,SV358: $i] :
( ( ( relation @ SV358 )
= $false )
| ( ( function @ SV358 )
= $false )
| ( ( ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SV358 @ SV91 ) ) )
| ( in @ ( apply @ SV358 @ SV39 ) @ ( relation_dom @ SV91 ) ) )
= $true )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2494]) ).
thf(2600,plain,
! [SV40: $i,SV92: $i,SV265: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV265 @ SV92 @ SV40 ) @ SV265 )
| ~ ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SV265 @ SV92 @ SV40 ) ) @ SV92 ) )
= $true )
| ( ( SV265
= ( complements_of_subsets @ SV40 @ SV92 ) )
= $true )
| ( ( element @ SV265 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2495]) ).
thf(2601,plain,
! [SV40: $i,SV92: $i,SV265: $i] :
( ( ( ( in @ ( sK6_D @ SV265 @ SV92 @ SV40 ) @ SV265 )
| ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SV265 @ SV92 @ SV40 ) ) @ SV92 ) )
= $true )
| ( ( SV265
= ( complements_of_subsets @ SV40 @ SV92 ) )
= $true )
| ( ( element @ SV265 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2496]) ).
thf(2602,plain,
! [SV92: $i,SV266: $i,SV40: $i,SV416: $i] :
( ( ( ~ ( element @ SV416 @ ( powerset @ SV40 ) ) )
= $true )
| ( ( ~ ( in @ SV416 @ SV266 )
| ( in @ ( subset_complement @ SV40 @ SV416 ) @ SV92 ) )
= $true )
| ( ( SV266
= ( complements_of_subsets @ SV40 @ SV92 ) )
= $false )
| ( ( element @ SV266 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2497]) ).
thf(2603,plain,
! [SV266: $i,SV92: $i,SV40: $i,SV417: $i] :
( ( ( ~ ( element @ SV417 @ ( powerset @ SV40 ) ) )
= $true )
| ( ( ~ ( in @ ( subset_complement @ SV40 @ SV417 ) @ SV92 )
| ( in @ SV417 @ SV266 ) )
= $true )
| ( ( SV266
= ( complements_of_subsets @ SV40 @ SV92 ) )
= $false )
| ( ( element @ SV266 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2498]) ).
thf(2604,plain,
! [SV272: $i,SV239: $i,SV384: $i] :
( ( ( in @ SV384 @ SV239 )
= $false )
| ( ( ( apply @ SV272 @ SV384 )
= SV384 )
= $true )
| ( ( SV272
= ( identity_relation @ SV239 ) )
= $false )
| ( ( function @ SV272 )
= $false )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2503]) ).
thf(2605,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2504]) ).
thf(2606,plain,
! [SV46: $i,SV375: $i] :
( ( ( function @ SV375 )
= $false )
| ( ( ~ ( relation @ SV375 ) )
= $true )
| ( ( ( SV375
!= ( function_inverse @ SV46 ) )
| ~ ( ~ ~ ( ~ ! [SY3963: $i,SY3964: $i] :
( ( SY3964
!= ( apply @ SV375 @ SY3963 ) )
| ~ ( in @ SY3963 @ ( relation_rng @ SV46 ) )
| ( SY3963
= ( apply @ SV46 @ SY3964 ) ) )
| ~ ! [SY3965: $i,SY3966: $i] :
( ( SY3966
!= ( apply @ SV375 @ SY3965 ) )
| ~ ( in @ SY3965 @ ( relation_rng @ SV46 ) )
| ( in @ SY3966 @ ( relation_dom @ SV46 ) ) ) )
| ~ ~ ( ~ ! [SY3967: $i,SY3968: $i] :
( ( SY3967
!= ( apply @ SV46 @ SY3968 ) )
| ~ ( in @ SY3968 @ ( relation_dom @ SV46 ) )
| ( SY3968
= ( apply @ SV375 @ SY3967 ) ) )
| ~ ! [SY3491: $i] :
( ! [SY3492: $i] :
( ( SY3491
!= ( apply @ SV46 @ SY3492 ) )
| ~ ( in @ SY3492 @ ( relation_dom @ SV46 ) ) )
| ( in @ SY3491 @ ( relation_rng @ SV46 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2505]) ).
thf(2607,plain,
! [SV46: $i,SV376: $i] :
( ( ( function @ SV376 )
= $false )
| ( ( ~ ( relation @ SV376 ) )
= $true )
| ( ( ( SV376
!= ( function_inverse @ SV46 ) )
| ( ( relation_dom @ SV376 )
= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2506]) ).
thf(2608,plain,
! [SV47: $i,SV123: $i,SV313: $i] :
( ( ( ! [SY3936: $i] :
( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ SY3936 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3936 @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV123 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV313 ) )
= $true )
| ( ( SV313
= ( relation_composition @ SV47 @ SV123 ) )
= $true )
| ( ( relation @ SV313 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2507]) ).
thf(2609,plain,
! [SV47: $i,SV123: $i,SV313: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK10_SY3288 @ SV313 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY3288 @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV123 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV313 )
= $true )
| ( ( SV313
= ( relation_composition @ SV47 @ SV123 ) )
= $true )
| ( ( relation @ SV313 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2508]) ).
thf(2610,plain,
! [SV314: $i,SV123: $i,SV47: $i] :
( ( ( ! [SY3937: $i,SY3938: $i] :
( ! [SY3706: $i] :
( ~ ( in @ ( ordered_pair @ SY3937 @ SY3706 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3706 @ SY3938 ) @ SV123 ) )
| ( in @ ( ordered_pair @ SY3937 @ SY3938 ) @ SV314 ) ) )
= $true )
| ( ( SV314
= ( relation_composition @ SV47 @ SV123 ) )
= $false )
| ( ( relation @ SV314 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2509]) ).
thf(2611,plain,
! [SV47: $i,SV123: $i,SV314: $i] :
( ( ( ! [SY3940: $i,SY3941: $i] :
( ~ ( in @ ( ordered_pair @ SY3940 @ SY3941 ) @ SV314 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3940 @ ( sK7_F @ SY3941 @ SY3940 @ SV314 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY3941 @ SY3940 @ SV314 @ SV123 @ SV47 ) @ SY3941 ) @ SV123 ) ) ) )
= $true )
| ( ( SV314
= ( relation_composition @ SV47 @ SV123 ) )
= $false )
| ( ( relation @ SV314 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2510]) ).
thf(2612,plain,
! [SV124: $i] :
( ( ( ~ ( in @ ( sK11_B @ SV124 ) @ ( relation_dom @ SV124 ) ) )
= $false )
| ( ( one_to_one @ SV124 )
= $true )
| ( ( function @ SV124 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2511]) ).
thf(2613,plain,
! [SV124: $i] :
( ( ( ~ ( in @ ( sK12_SY3289 @ SV124 ) @ ( relation_dom @ SV124 ) ) )
= $false )
| ( ( one_to_one @ SV124 )
= $true )
| ( ( function @ SV124 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2511]) ).
thf(2614,plain,
! [SV332: $i,SV125: $i,SV339: $i] :
( ( ( in @ SV339 @ ( relation_dom @ SV125 ) )
= $false )
| ( ( in @ SV332 @ ( relation_dom @ SV125 ) )
= $false )
| ( ( ( ( apply @ SV125 @ SV332 )
!= ( apply @ SV125 @ SV339 ) ) )
= $true )
| ( ( SV332 = SV339 )
= $true )
| ( ( one_to_one @ SV125 )
= $false )
| ( ( function @ SV125 )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2512]) ).
thf(2615,plain,
! [SV162: $i,SV200: $i,SV51: $i,SV385: $i] :
( ( ( in @ SV385 @ SV51 )
= $false )
| ( ( in @ SV385 @ SV200 )
= $true )
| ( ( SV200
= ( set_union2 @ SV51 @ SV162 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2515]) ).
thf(2616,plain,
! [SV51: $i,SV200: $i,SV162: $i,SV386: $i] :
( ( ( in @ SV386 @ SV162 )
= $false )
| ( ( in @ SV386 @ SV200 )
= $true )
| ( ( SV200
= ( set_union2 @ SV51 @ SV162 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2516]) ).
thf(2617,plain,
! [SV245: $i,SV295: $i] :
( ( ( in @ ( sK46_SY3307 @ SV295 @ SV245 ) @ SV245 )
= $true )
| ( ( ~ ( in @ ( sK45_C @ SV295 @ SV245 ) @ SV295 ) )
= $true )
| ( ( SV295
= ( set_meet @ SV245 ) )
= $true )
| ( ( SV245 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2517]) ).
thf(2618,plain,
! [SV245: $i,SV295: $i] :
( ( ( ~ ( in @ ( sK45_C @ SV295 @ SV245 ) @ ( sK46_SY3307 @ SV295 @ SV245 ) ) )
= $true )
| ( ( ~ ( in @ ( sK45_C @ SV295 @ SV245 ) @ SV295 ) )
= $true )
| ( ( SV295
= ( set_meet @ SV245 ) )
= $true )
| ( ( SV245 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2518]) ).
thf(2619,plain,
! [SV295: $i,SV245: $i,SV387: $i] :
( ( ( in @ SV387 @ SV245 )
= $false )
| ( ( in @ ( sK45_C @ SV295 @ SV245 ) @ SV387 )
= $true )
| ( ( in @ ( sK45_C @ SV295 @ SV245 ) @ SV295 )
= $true )
| ( ( SV295
= ( set_meet @ SV245 ) )
= $true )
| ( ( SV245 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2519]) ).
thf(2620,plain,
! [SV246: $i,SV296: $i,SV388: $i] :
( ( ( ~ ( in @ ( sK44_D @ SV388 @ SV296 @ SV246 ) @ SV246 )
| ~ ~ ( in @ SV388 @ ( sK44_D @ SV388 @ SV296 @ SV246 ) ) )
= $false )
| ( ( in @ SV388 @ SV296 )
= $true )
| ( ( SV296
= ( set_meet @ SV246 ) )
= $false )
| ( ( SV246 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2520]) ).
thf(2621,plain,
! [SV246: $i,SV296: $i,SV389: $i] :
( ( ( in @ SV389 @ SV296 )
= $false )
| ( ( ! [SY3974: $i] :
( ~ ( in @ SY3974 @ SV246 )
| ( in @ SV389 @ SY3974 ) ) )
= $true )
| ( ( SV296
= ( set_meet @ SV246 ) )
= $false )
| ( ( SV246 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2521]) ).
thf(2622,plain,
! [SV53: $i,SV297: $i,SV319: $i] :
( ( ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ ( relation_dom @ SV53 ) )
= $false )
| ( ( ~ ( in @ ( apply @ SV53 @ ( sK57_D @ SV319 @ SV297 @ SV53 ) ) @ SV297 ) )
= $true )
| ( ( ~ ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ SV319 ) )
= $true )
| ( ( SV319
= ( relation_inverse_image @ SV53 @ SV297 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2522]) ).
thf(2623,plain,
! [SV53: $i,SV297: $i,SV319: $i] :
( ( ( ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ SV319 ) )
= $true )
| ( ( SV319
= ( relation_inverse_image @ SV53 @ SV297 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2523]) ).
thf(2624,plain,
! [SV297: $i,SV319: $i,SV53: $i] :
( ( ( ( in @ ( apply @ SV53 @ ( sK57_D @ SV319 @ SV297 @ SV53 ) ) @ SV297 )
| ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ SV319 ) )
= $true )
| ( ( SV319
= ( relation_inverse_image @ SV53 @ SV297 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2524]) ).
thf(2625,plain,
! [SV320: $i,SV298: $i,SV53: $i,SV418: $i] :
( ( ( ~ ( in @ SV418 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SV418 ) @ SV298 ) )
= $true )
| ( ( in @ SV418 @ SV320 )
= $true )
| ( ( SV320
= ( relation_inverse_image @ SV53 @ SV298 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2525]) ).
thf(2626,plain,
! [SV298: $i,SV53: $i,SV320: $i] :
( ( ( ~ ! [SY3943: $i] :
( ~ ( in @ SY3943 @ SV320 )
| ( in @ SY3943 @ ( relation_dom @ SV53 ) ) ) )
= $false )
| ( ( SV320
= ( relation_inverse_image @ SV53 @ SV298 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2526]) ).
thf(2627,plain,
! [SV298: $i,SV53: $i,SV320: $i] :
( ( ( ~ ! [SY3944: $i] :
( ~ ( in @ SY3944 @ SV320 )
| ( in @ ( apply @ SV53 @ SY3944 ) @ SV298 ) ) )
= $false )
| ( ( SV320
= ( relation_inverse_image @ SV53 @ SV298 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2526]) ).
thf(2628,plain,
! [SV166: $i,SV54: $i,SV202: $i,SV390: $i] :
( ( ( in @ SV390 @ SV202 )
= $false )
| ( ( in @ SV390 @ SV54 )
= $true )
| ( ( SV202
= ( set_intersection2 @ SV54 @ SV166 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2528]) ).
thf(2629,plain,
! [SV54: $i,SV166: $i,SV202: $i,SV391: $i] :
( ( ( in @ SV391 @ SV202 )
= $false )
| ( ( in @ SV391 @ SV166 )
= $true )
| ( ( SV202
= ( set_intersection2 @ SV54 @ SV166 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2529]) ).
thf(2630,plain,
! [SV170: $i,SV55: $i,SV204: $i,SV392: $i] :
( ( ( in @ SV392 @ SV204 )
= $false )
| ( ( in @ SV392 @ SV55 )
= $true )
| ( ( SV204
= ( set_difference @ SV55 @ SV170 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2530]) ).
thf(2631,plain,
! [SV55: $i,SV170: $i,SV204: $i,SV393: $i] :
( ( ( in @ SV393 @ SV204 )
= $false )
| ( ( ~ ( in @ SV393 @ SV170 ) )
= $true )
| ( ( SV204
= ( set_difference @ SV55 @ SV170 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2531]) ).
thf(2632,plain,
! [SV394: $i,SV56: $i,SV299: $i] :
( ( ( ( sK19_C @ SV299 @ SV56 )
= ( apply @ SV56 @ SV394 ) )
= $false )
| ( ( ~ ( in @ SV394 @ ( relation_dom @ SV56 ) ) )
= $true )
| ( ( ~ ( in @ ( sK19_C @ SV299 @ SV56 ) @ SV299 ) )
= $true )
| ( ( SV299
= ( relation_rng @ SV56 ) )
= $true )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2532]) ).
thf(2633,plain,
! [SV56: $i,SV299: $i] :
( ( ( ( sK19_C @ SV299 @ SV56 )
= ( apply @ SV56 @ ( sK20_SY3294 @ SV299 @ SV56 ) ) )
= $true )
| ( ( in @ ( sK19_C @ SV299 @ SV56 ) @ SV299 )
= $true )
| ( ( SV299
= ( relation_rng @ SV56 ) )
= $true )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2533]) ).
thf(2634,plain,
! [SV56: $i,SV299: $i] :
( ( ( in @ ( sK20_SY3294 @ SV299 @ SV56 ) @ ( relation_dom @ SV56 ) )
= $true )
| ( ( in @ ( sK19_C @ SV299 @ SV56 ) @ SV299 )
= $true )
| ( ( SV299
= ( relation_rng @ SV56 ) )
= $true )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2534]) ).
thf(2635,plain,
! [SV300: $i,SV424: $i,SV56: $i,SV395: $i] :
( ( ( ( SV395
!= ( apply @ SV56 @ SV424 ) )
| ~ ( in @ SV424 @ ( relation_dom @ SV56 ) ) )
= $true )
| ( ( in @ SV395 @ SV300 )
= $true )
| ( ( SV300
= ( relation_rng @ SV56 ) )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2535]) ).
thf(2636,plain,
! [SV56: $i,SV300: $i,SV396: $i] :
( ( ( in @ SV396 @ SV300 )
= $false )
| ( ( ~ ( ( SV396
!= ( apply @ SV56 @ ( sK18_D @ SV396 @ SV300 @ SV56 ) ) )
| ~ ( in @ ( sK18_D @ SV396 @ SV300 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
= $true )
| ( ( SV300
= ( relation_rng @ SV56 ) )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2536]) ).
thf(2637,plain,
! [SV172: $i,SV206: $i,SV57: $i,SV397: $i] :
( ( ( SV397 = SV57 )
= $false )
| ( ( in @ SV397 @ SV206 )
= $true )
| ( ( SV206
= ( unordered_pair @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2539]) ).
thf(2638,plain,
! [SV57: $i,SV206: $i,SV172: $i,SV398: $i] :
( ( ( SV398 = SV172 )
= $false )
| ( ( in @ SV398 @ SV206 )
= $true )
| ( ( SV206
= ( unordered_pair @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2540]) ).
thf(2639,plain,
! [SV58: $i,SV96: $i,SV321: $i] :
( ( ( ~ ( in @ ( sK67_D @ SV321 @ SV96 @ SV58 ) @ ( relation_dom @ SV96 ) )
| ~ ( ( ( apply @ SV96 @ ( sK67_D @ SV321 @ SV96 @ SV58 ) )
!= ( apply @ SV321 @ ( sK67_D @ SV321 @ SV96 @ SV58 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV96 )
!= ( set_intersection2 @ ( relation_dom @ SV321 ) @ SV58 ) ) )
= $true )
| ( ( SV96
= ( relation_dom_restriction @ SV321 @ SV58 ) )
= $true )
| ( ( function @ SV321 )
= $false )
| ( ( relation @ SV321 )
= $false )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2541]) ).
thf(2640,plain,
! [SV58: $i,SV96: $i,SV364: $i] :
( ( ( relation @ SV364 )
= $false )
| ( ( function @ SV364 )
= $false )
| ( ( ( SV96
!= ( relation_dom_restriction @ SV364 @ SV58 ) )
| ! [SY3960: $i] :
( ~ ( in @ SY3960 @ ( relation_dom @ SV96 ) )
| ( ( apply @ SV96 @ SY3960 )
= ( apply @ SV364 @ SY3960 ) ) ) )
= $true )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2542]) ).
thf(2641,plain,
! [SV58: $i,SV96: $i,SV365: $i] :
( ( ( relation @ SV365 )
= $false )
| ( ( function @ SV365 )
= $false )
| ( ( ( SV96
!= ( relation_dom_restriction @ SV365 @ SV58 ) )
| ( ( relation_dom @ SV96 )
= ( set_intersection2 @ ( relation_dom @ SV365 ) @ SV58 ) ) )
= $true )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2543]) ).
thf(2642,plain,
! [SV250: $i,SV59: $i,SV419: $i,SV399: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV399 @ SV419 ) @ SV59 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV399 @ SV419 ) @ SV250 )
= $true )
| ( ( SV59 = SV250 )
= $false )
| ( ( relation @ SV250 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2545]) ).
thf(2643,plain,
! [SV59: $i,SV250: $i,SV420: $i,SV400: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV400 @ SV420 ) @ SV250 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV400 @ SV420 ) @ SV59 )
= $true )
| ( ( SV59 = SV250 )
= $false )
| ( ( relation @ SV250 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2546]) ).
thf(2644,plain,
! [SV209: $i,SV63: $i,SV345: $i,SV176: $i,SV367: $i] :
( ( ( in @ SV367 @ SV176 )
= $false )
| ( ( in @ SV345 @ SV63 )
= $false )
| ( ( ( ( sK34_D @ SV209 @ SV176 @ SV63 )
!= ( ordered_pair @ SV345 @ SV367 ) ) )
= $true )
| ( ( ~ ( in @ ( sK34_D @ SV209 @ SV176 @ SV63 ) @ SV209 ) )
= $true )
| ( ( SV209
= ( cartesian_product2 @ SV63 @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2550]) ).
thf(2645,plain,
! [SV63: $i,SV176: $i,SV209: $i] :
( ( ( in @ ( sK35_SY3303 @ SV209 @ SV176 @ SV63 ) @ SV63 )
= $true )
| ( ( in @ ( sK34_D @ SV209 @ SV176 @ SV63 ) @ SV209 )
= $true )
| ( ( SV209
= ( cartesian_product2 @ SV63 @ SV176 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2551]) ).
thf(2646,plain,
! [SV63: $i,SV176: $i,SV209: $i] :
( ( ( in @ ( sK36_SY3305 @ SV209 @ SV176 @ SV63 ) @ SV176 )
= $true )
| ( ( in @ ( sK34_D @ SV209 @ SV176 @ SV63 ) @ SV209 )
= $true )
| ( ( SV209
= ( cartesian_product2 @ SV63 @ SV176 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2552]) ).
thf(2647,plain,
! [SV210: $i,SV346: $i,SV177: $i,SV401: $i,SV63: $i,SV377: $i] :
( ( ( ~ ( in @ SV377 @ SV63 ) )
= $true )
| ( ( ~ ( in @ SV401 @ SV177 ) )
= $true )
| ( ( ( SV346
!= ( ordered_pair @ SV377 @ SV401 ) ) )
= $true )
| ( ( in @ SV346 @ SV210 )
= $true )
| ( ( SV210
= ( cartesian_product2 @ SV63 @ SV177 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2553]) ).
thf(2648,plain,
! [SV63: $i,SV177: $i,SV210: $i,SV347: $i] :
( ( ( ~ ( ~ ( in @ ( sK32_E @ SV347 @ SV210 @ SV177 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK33_SY3300 @ SV347 @ SV210 @ SV177 @ SV63 ) @ SV177 ) ) )
= $true )
| ( ( in @ SV347 @ SV210 )
= $false )
| ( ( SV210
= ( cartesian_product2 @ SV63 @ SV177 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2554]) ).
thf(2649,plain,
! [SV63: $i,SV177: $i,SV210: $i,SV347: $i] :
( ( ( SV347
= ( ordered_pair @ ( sK32_E @ SV347 @ SV210 @ SV177 @ SV63 ) @ ( sK33_SY3300 @ SV347 @ SV210 @ SV177 @ SV63 ) ) )
= $true )
| ( ( in @ SV347 @ SV210 )
= $false )
| ( ( SV210
= ( cartesian_product2 @ SV63 @ SV177 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2555]) ).
thf(2650,plain,
! [SV348: $i,SV66: $i,SV402: $i] :
( ( ( SV402
= ( apply @ SV66 @ SV348 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV348 @ SV402 ) @ SV66 )
= $true )
| ( ( in @ SV348 @ ( relation_dom @ SV66 ) )
= $false )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2558]) ).
thf(2651,plain,
! [SV66: $i,SV403: $i,SV349: $i] :
( ( ( in @ ( ordered_pair @ SV349 @ SV403 ) @ SV66 )
= $false )
| ( ( SV403
= ( apply @ SV66 @ SV349 ) )
= $true )
| ( ( in @ SV349 @ ( relation_dom @ SV66 ) )
= $false )
| ( ( function @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2559]) ).
thf(2652,plain,
! [SV26: $i,SV88: $i,SV253: $i] :
( ( ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV88 )
= $false )
| ( ( in @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) @ SV26 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 ) )
= $true )
| ( ( SV253
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $true )
| ( ( relation @ SV253 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2562]) ).
thf(2653,plain,
! [SV26: $i,SV88: $i,SV253: $i] :
( ( ( in @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) @ SV26 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 )
= $true )
| ( ( SV253
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $true )
| ( ( relation @ SV253 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2563]) ).
thf(2654,plain,
! [SV26: $i,SV88: $i,SV253: $i] :
( ( ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV88 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 )
= $true )
| ( ( SV253
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $true )
| ( ( relation @ SV253 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2564]) ).
thf(2655,plain,
! [SV254: $i,SV88: $i,SV404: $i,SV26: $i,SV421: $i] :
( ( ( ~ ( in @ SV421 @ SV26 )
| ~ ( in @ ( ordered_pair @ SV404 @ SV421 ) @ SV88 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV404 @ SV421 ) @ SV254 )
= $true )
| ( ( SV254
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2565]) ).
thf(2656,plain,
! [SV88: $i,SV26: $i,SV254: $i] :
( ( ( ! [SY3874: $i,SY3875: $i] :
( ~ ( in @ ( ordered_pair @ SY3874 @ SY3875 ) @ SV254 )
| ( in @ SY3875 @ SV26 ) ) )
= $true )
| ( ( SV254
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2566]) ).
thf(2657,plain,
! [SV26: $i,SV88: $i,SV254: $i] :
( ( ( ! [SY3876: $i,SY3877: $i] :
( ~ ( in @ ( ordered_pair @ SY3876 @ SY3877 ) @ SV254 )
| ( in @ ( ordered_pair @ SY3876 @ SY3877 ) @ SV88 ) ) )
= $true )
| ( ( SV254
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2567]) ).
thf(2658,plain,
! [SV28: $i,SV219: $i,SV405: $i,SV380: $i] :
( ( ( in @ ( ordered_pair @ SV380 @ SV405 ) @ SV219 )
= $false )
| ( ( in @ ( ordered_pair @ SV405 @ SV380 ) @ SV28 )
= $true )
| ( ( SV219
= ( relation_inverse @ SV28 ) )
= $false )
| ( ( relation @ SV219 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2568]) ).
thf(2659,plain,
! [SV219: $i,SV28: $i,SV381: $i,SV406: $i] :
( ( ( in @ ( ordered_pair @ SV406 @ SV381 ) @ SV28 )
= $false )
| ( ( in @ ( ordered_pair @ SV381 @ SV406 ) @ SV219 )
= $true )
| ( ( SV219
= ( relation_inverse @ SV28 ) )
= $false )
| ( ( relation @ SV219 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2569]) ).
thf(2660,plain,
! [SV305: $i,SV280: $i,SV29: $i,SV407: $i] :
( ( ( ~ ( in @ SV407 @ ( relation_dom @ SV29 ) ) )
= $true )
| ( ( ~ ( in @ SV407 @ SV280 ) )
= $true )
| ( ( ( ( sK61_D @ SV305 @ SV280 @ SV29 )
!= ( apply @ SV29 @ SV407 ) ) )
= $true )
| ( ( ~ ( in @ ( sK61_D @ SV305 @ SV280 @ SV29 ) @ SV305 ) )
= $true )
| ( ( SV305
= ( relation_image @ SV29 @ SV280 ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2570]) ).
thf(2661,plain,
! [SV29: $i,SV280: $i,SV305: $i] :
( ( ( ~ ( ~ ( in @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) @ SV280 ) ) )
= $true )
| ( ( in @ ( sK61_D @ SV305 @ SV280 @ SV29 ) @ SV305 )
= $true )
| ( ( SV305
= ( relation_image @ SV29 @ SV280 ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2571]) ).
thf(2662,plain,
! [SV29: $i,SV280: $i,SV305: $i] :
( ( ( ( sK61_D @ SV305 @ SV280 @ SV29 )
= ( apply @ SV29 @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) ) )
= $true )
| ( ( in @ ( sK61_D @ SV305 @ SV280 @ SV29 ) @ SV305 )
= $true )
| ( ( SV305
= ( relation_image @ SV29 @ SV280 ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2572]) ).
thf(2663,plain,
! [SV306: $i,SV408: $i,SV281: $i,SV29: $i,SV425: $i] :
( ( ( ~ ( in @ SV425 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SV425 @ SV281 )
| ( SV408
!= ( apply @ SV29 @ SV425 ) ) )
= $true )
| ( ( in @ SV408 @ SV306 )
= $true )
| ( ( SV306
= ( relation_image @ SV29 @ SV281 ) )
= $false )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2573]) ).
thf(2664,plain,
! [SV29: $i,SV281: $i,SV306: $i,SV409: $i] :
( ( ( in @ SV409 @ SV306 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SV409 @ SV306 @ SV281 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK60_E @ SV409 @ SV306 @ SV281 @ SV29 ) @ SV281 ) )
| ( SV409
!= ( apply @ SV29 @ ( sK60_E @ SV409 @ SV306 @ SV281 @ SV29 ) ) ) ) )
= $true )
| ( ( SV306
= ( relation_image @ SV29 @ SV281 ) )
= $false )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2574]) ).
thf(2665,plain,
! [SV368: $i,SV30: $i,SV220: $i,SV258: $i] :
( ( ( in @ ( sK55_D @ SV258 @ SV220 @ SV30 ) @ SV258 )
= $false )
| ( ( in @ ( ordered_pair @ SV368 @ ( sK55_D @ SV258 @ SV220 @ SV30 ) ) @ SV30 )
= $false )
| ( ( in @ SV368 @ SV220 )
= $false )
| ( ( SV258
= ( relation_image @ SV30 @ SV220 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2575]) ).
thf(2666,plain,
! [SV259: $i,SV221: $i,SV30: $i,SV369: $i,SV410: $i] :
( ( ( in @ ( ordered_pair @ SV410 @ SV369 ) @ SV30 )
= $false )
| ( ( ~ ( in @ SV410 @ SV221 ) )
= $true )
| ( ( in @ SV369 @ SV259 )
= $true )
| ( ( SV259
= ( relation_image @ SV30 @ SV221 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2576]) ).
thf(2667,plain,
! [SV30: $i,SV221: $i,SV259: $i,SV370: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SV370 @ SV259 @ SV221 @ SV30 ) @ SV370 ) @ SV30 ) )
= $false )
| ( ( in @ SV370 @ SV259 )
= $false )
| ( ( SV259
= ( relation_image @ SV30 @ SV221 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2577]) ).
thf(2668,plain,
! [SV30: $i,SV221: $i,SV259: $i,SV370: $i] :
( ( ( ~ ( in @ ( sK54_E @ SV370 @ SV259 @ SV221 @ SV30 ) @ SV221 ) )
= $false )
| ( ( in @ SV370 @ SV259 )
= $false )
| ( ( SV259
= ( relation_image @ SV30 @ SV221 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2577]) ).
thf(2669,plain,
! [SV371: $i,SV31: $i,SV222: $i,SV260: $i] :
( ( ( in @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SV260 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK52_D @ SV260 @ SV222 @ SV31 ) @ SV371 ) @ SV31 )
= $false )
| ( ( in @ SV371 @ SV222 )
= $false )
| ( ( SV260
= ( relation_inverse_image @ SV31 @ SV222 ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2578]) ).
thf(2670,plain,
! [SV261: $i,SV223: $i,SV31: $i,SV411: $i,SV372: $i] :
( ( ( in @ ( ordered_pair @ SV372 @ SV411 ) @ SV31 )
= $false )
| ( ( ~ ( in @ SV411 @ SV223 ) )
= $true )
| ( ( in @ SV372 @ SV261 )
= $true )
| ( ( SV261
= ( relation_inverse_image @ SV31 @ SV223 ) )
= $false )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2579]) ).
thf(2671,plain,
! [SV31: $i,SV223: $i,SV261: $i,SV373: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV373 @ ( sK51_E @ SV373 @ SV261 @ SV223 @ SV31 ) ) @ SV31 ) )
= $false )
| ( ( in @ SV373 @ SV261 )
= $false )
| ( ( SV261
= ( relation_inverse_image @ SV31 @ SV223 ) )
= $false )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2580]) ).
thf(2672,plain,
! [SV31: $i,SV223: $i,SV261: $i,SV373: $i] :
( ( ( ~ ( in @ ( sK51_E @ SV373 @ SV261 @ SV223 @ SV31 ) @ SV223 ) )
= $false )
| ( ( in @ SV373 @ SV261 )
= $false )
| ( ( SV261
= ( relation_inverse_image @ SV31 @ SV223 ) )
= $false )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2580]) ).
thf(2673,plain,
! [SV32: $i,SV224: $i,SV262: $i] :
( ( ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV32 )
= $false )
| ( ( in @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ SV224 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 ) )
= $true )
| ( ( SV262
= ( relation_dom_restriction @ SV32 @ SV224 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2581]) ).
thf(2674,plain,
! [SV32: $i,SV224: $i,SV262: $i] :
( ( ( in @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ SV224 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_dom_restriction @ SV32 @ SV224 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2582]) ).
thf(2675,plain,
! [SV32: $i,SV224: $i,SV262: $i] :
( ( ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV32 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_dom_restriction @ SV32 @ SV224 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2583]) ).
thf(2676,plain,
! [SV263: $i,SV32: $i,SV422: $i,SV225: $i,SV412: $i] :
( ( ( ~ ( in @ SV412 @ SV225 )
| ~ ( in @ ( ordered_pair @ SV412 @ SV422 ) @ SV32 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV412 @ SV422 ) @ SV263 )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV32 @ SV225 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2584]) ).
thf(2677,plain,
! [SV32: $i,SV225: $i,SV263: $i] :
( ( ( ! [SY3890: $i] :
( ! [SY3891: $i] :
~ ( in @ ( ordered_pair @ SY3890 @ SY3891 ) @ SV263 )
| ( in @ SY3890 @ SV225 ) ) )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV32 @ SV225 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2585]) ).
thf(2678,plain,
! [SV225: $i,SV32: $i,SV263: $i] :
( ( ( ! [SY3892: $i,SY3893: $i] :
( ~ ( in @ ( ordered_pair @ SY3892 @ SY3893 ) @ SV263 )
| ( in @ ( ordered_pair @ SY3892 @ SY3893 ) @ SV32 ) ) )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV32 @ SV225 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2586]) ).
thf(2679,plain,
! [SV146: $i,SV374: $i,SV111: $i,SV352: $i] :
( ( ( in @ SV352 @ SV111 )
= $false )
| ( ( SV352 = SV374 )
= $false )
| ( ( in @ ( ordered_pair @ SV352 @ SV374 ) @ SV146 )
= $true )
| ( ( SV146
= ( identity_relation @ SV111 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2587]) ).
thf(2680,plain,
! [SV111: $i,SV146: $i,SV423: $i,SV413: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV413 @ SV423 ) @ SV146 ) )
= $true )
| ( ( SV413 = SV423 )
= $true )
| ( ( SV146
= ( identity_relation @ SV111 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2588]) ).
thf(2681,plain,
! [SV111: $i,SV146: $i,SV426: $i,SV414: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV414 @ SV426 ) @ SV146 ) )
= $true )
| ( ( in @ SV414 @ SV111 )
= $true )
| ( ( SV146
= ( identity_relation @ SV111 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2589]) ).
thf(2682,plain,
! [SV34: $i,SV89: $i,SV190: $i,SV226: $i] :
( ( ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 ) )
= $true )
| ( ( ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV34 ) )
= $true )
| ( ( SV226
= ( unordered_triple @ SV34 @ SV89 @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2591]) ).
thf(2683,plain,
! [SV34: $i,SV89: $i,SV190: $i,SV226: $i] :
( ( ( ~ ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 ) )
= $true )
| ( ( ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV89 ) )
= $true )
| ( ( SV226
= ( unordered_triple @ SV34 @ SV89 @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2592]) ).
thf(2684,plain,
! [SV89: $i,SV34: $i,SV227: $i,SV191: $i,SV415: $i] :
( ( ( SV415 = SV191 )
= $false )
| ( ( in @ SV415 @ SV227 )
= $true )
| ( ( SV227
= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2594]) ).
thf(2685,plain,
! [SV191: $i,SV89: $i,SV227: $i,SV34: $i] :
( ( ( ! [SY3841: $i] :
( ( SY3841 != SV34 )
| ( in @ SY3841 @ SV227 ) ) )
= $true )
| ( ( SV227
= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2595]) ).
thf(2686,plain,
! [SV191: $i,SV34: $i,SV227: $i,SV89: $i] :
( ( ( ! [SY3842: $i] :
( ( SY3842 != SV89 )
| ( in @ SY3842 @ SV227 ) ) )
= $true )
| ( ( SV227
= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2596]) ).
thf(2687,plain,
! [SV91: $i,SV39: $i,SV308: $i] :
( ( ( in @ ( apply @ SV308 @ SV39 ) @ ( relation_dom @ SV91 ) )
= $false )
| ( ( in @ SV39 @ ( relation_dom @ SV308 ) )
= $false )
| ( ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SV308 @ SV91 ) ) )
= $true )
| ( ( function @ SV308 )
= $false )
| ( ( relation @ SV308 )
= $false )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2597]) ).
thf(2688,plain,
! [SV91: $i,SV357: $i,SV39: $i] :
( ( ( ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SV357 @ SV91 ) ) ) )
= $true )
| ( ( in @ SV39 @ ( relation_dom @ SV357 ) )
= $true )
| ( ( function @ SV357 )
= $false )
| ( ( relation @ SV357 )
= $false )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2598]) ).
thf(2689,plain,
! [SV91: $i,SV358: $i,SV39: $i] :
( ( ( ~ ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SV358 @ SV91 ) ) ) )
= $true )
| ( ( in @ ( apply @ SV358 @ SV39 ) @ ( relation_dom @ SV91 ) )
= $true )
| ( ( function @ SV358 )
= $false )
| ( ( relation @ SV358 )
= $false )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2599]) ).
thf(2690,plain,
! [SV40: $i,SV92: $i,SV265: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV265 @ SV92 @ SV40 ) @ SV265 ) )
= $true )
| ( ( ~ ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SV265 @ SV92 @ SV40 ) ) @ SV92 ) )
= $true )
| ( ( SV265
= ( complements_of_subsets @ SV40 @ SV92 ) )
= $true )
| ( ( element @ SV265 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2600]) ).
thf(2691,plain,
! [SV40: $i,SV92: $i,SV265: $i] :
( ( ( in @ ( sK6_D @ SV265 @ SV92 @ SV40 ) @ SV265 )
= $true )
| ( ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SV265 @ SV92 @ SV40 ) ) @ SV92 )
= $true )
| ( ( SV265
= ( complements_of_subsets @ SV40 @ SV92 ) )
= $true )
| ( ( element @ SV265 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2601]) ).
thf(2692,plain,
! [SV92: $i,SV266: $i,SV40: $i,SV416: $i] :
( ( ( element @ SV416 @ ( powerset @ SV40 ) )
= $false )
| ( ( ~ ( in @ SV416 @ SV266 )
| ( in @ ( subset_complement @ SV40 @ SV416 ) @ SV92 ) )
= $true )
| ( ( SV266
= ( complements_of_subsets @ SV40 @ SV92 ) )
= $false )
| ( ( element @ SV266 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2602]) ).
thf(2693,plain,
! [SV266: $i,SV92: $i,SV40: $i,SV417: $i] :
( ( ( element @ SV417 @ ( powerset @ SV40 ) )
= $false )
| ( ( ~ ( in @ ( subset_complement @ SV40 @ SV417 ) @ SV92 )
| ( in @ SV417 @ SV266 ) )
= $true )
| ( ( SV266
= ( complements_of_subsets @ SV40 @ SV92 ) )
= $false )
| ( ( element @ SV266 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2603]) ).
thf(2694,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2605]) ).
thf(2695,plain,
! [SV46: $i,SV375: $i] :
( ( ( relation @ SV375 )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( ( SV375
!= ( function_inverse @ SV46 ) )
| ~ ( ~ ~ ( ~ ! [SY3963: $i,SY3964: $i] :
( ( SY3964
!= ( apply @ SV375 @ SY3963 ) )
| ~ ( in @ SY3963 @ ( relation_rng @ SV46 ) )
| ( SY3963
= ( apply @ SV46 @ SY3964 ) ) )
| ~ ! [SY3965: $i,SY3966: $i] :
( ( SY3966
!= ( apply @ SV375 @ SY3965 ) )
| ~ ( in @ SY3965 @ ( relation_rng @ SV46 ) )
| ( in @ SY3966 @ ( relation_dom @ SV46 ) ) ) )
| ~ ~ ( ~ ! [SY3967: $i,SY3968: $i] :
( ( SY3967
!= ( apply @ SV46 @ SY3968 ) )
| ~ ( in @ SY3968 @ ( relation_dom @ SV46 ) )
| ( SY3968
= ( apply @ SV375 @ SY3967 ) ) )
| ~ ! [SY3491: $i] :
( ! [SY3492: $i] :
( ( SY3491
!= ( apply @ SV46 @ SY3492 ) )
| ~ ( in @ SY3492 @ ( relation_dom @ SV46 ) ) )
| ( in @ SY3491 @ ( relation_rng @ SV46 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2606]) ).
thf(2696,plain,
! [SV46: $i,SV376: $i] :
( ( ( relation @ SV376 )
= $false )
| ( ( function @ SV376 )
= $false )
| ( ( ( SV376
!= ( function_inverse @ SV46 ) )
| ( ( relation_dom @ SV376 )
= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2607]) ).
thf(2697,plain,
! [SV427: $i,SV47: $i,SV123: $i,SV313: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ SV427 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SV427 @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV123 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV313 ) )
= $true )
| ( ( SV313
= ( relation_composition @ SV47 @ SV123 ) )
= $true )
| ( ( relation @ SV313 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2608]) ).
thf(2698,plain,
! [SV47: $i,SV123: $i,SV313: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK10_SY3288 @ SV313 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK10_SY3288 @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV123 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV313 )
= $true )
| ( ( SV313
= ( relation_composition @ SV47 @ SV123 ) )
= $true )
| ( ( relation @ SV313 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2609]) ).
thf(2699,plain,
! [SV314: $i,SV123: $i,SV47: $i,SV428: $i] :
( ( ( ! [SY3983: $i] :
( ! [SY3984: $i] :
( ~ ( in @ ( ordered_pair @ SV428 @ SY3984 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3984 @ SY3983 ) @ SV123 ) )
| ( in @ ( ordered_pair @ SV428 @ SY3983 ) @ SV314 ) ) )
= $true )
| ( ( SV314
= ( relation_composition @ SV47 @ SV123 ) )
= $false )
| ( ( relation @ SV314 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2610]) ).
thf(2700,plain,
! [SV47: $i,SV123: $i,SV314: $i,SV429: $i] :
( ( ( ! [SY3985: $i] :
( ~ ( in @ ( ordered_pair @ SV429 @ SY3985 ) @ SV314 )
| ~ ( ~ ( in @ ( ordered_pair @ SV429 @ ( sK7_F @ SY3985 @ SV429 @ SV314 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SY3985 @ SV429 @ SV314 @ SV123 @ SV47 ) @ SY3985 ) @ SV123 ) ) ) )
= $true )
| ( ( SV314
= ( relation_composition @ SV47 @ SV123 ) )
= $false )
| ( ( relation @ SV314 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2611]) ).
thf(2701,plain,
! [SV124: $i] :
( ( ( in @ ( sK11_B @ SV124 ) @ ( relation_dom @ SV124 ) )
= $true )
| ( ( one_to_one @ SV124 )
= $true )
| ( ( function @ SV124 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2612]) ).
thf(2702,plain,
! [SV124: $i] :
( ( ( in @ ( sK12_SY3289 @ SV124 ) @ ( relation_dom @ SV124 ) )
= $true )
| ( ( one_to_one @ SV124 )
= $true )
| ( ( function @ SV124 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2613]) ).
thf(2703,plain,
! [SV339: $i,SV332: $i,SV125: $i] :
( ( ( ( apply @ SV125 @ SV332 )
= ( apply @ SV125 @ SV339 ) )
= $false )
| ( ( in @ SV332 @ ( relation_dom @ SV125 ) )
= $false )
| ( ( in @ SV339 @ ( relation_dom @ SV125 ) )
= $false )
| ( ( SV332 = SV339 )
= $true )
| ( ( one_to_one @ SV125 )
= $false )
| ( ( function @ SV125 )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2614]) ).
thf(2704,plain,
! [SV245: $i,SV295: $i] :
( ( ( in @ ( sK45_C @ SV295 @ SV245 ) @ SV295 )
= $false )
| ( ( in @ ( sK46_SY3307 @ SV295 @ SV245 ) @ SV245 )
= $true )
| ( ( SV295
= ( set_meet @ SV245 ) )
= $true )
| ( ( SV245 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2617]) ).
thf(2705,plain,
! [SV245: $i,SV295: $i] :
( ( ( in @ ( sK45_C @ SV295 @ SV245 ) @ ( sK46_SY3307 @ SV295 @ SV245 ) )
= $false )
| ( ( ~ ( in @ ( sK45_C @ SV295 @ SV245 ) @ SV295 ) )
= $true )
| ( ( SV295
= ( set_meet @ SV245 ) )
= $true )
| ( ( SV245 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2618]) ).
thf(2706,plain,
! [SV246: $i,SV296: $i,SV388: $i] :
( ( ( ~ ( in @ ( sK44_D @ SV388 @ SV296 @ SV246 ) @ SV246 ) )
= $false )
| ( ( in @ SV388 @ SV296 )
= $true )
| ( ( SV296
= ( set_meet @ SV246 ) )
= $false )
| ( ( SV246 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2620]) ).
thf(2707,plain,
! [SV246: $i,SV296: $i,SV388: $i] :
( ( ( ~ ~ ( in @ SV388 @ ( sK44_D @ SV388 @ SV296 @ SV246 ) ) )
= $false )
| ( ( in @ SV388 @ SV296 )
= $true )
| ( ( SV296
= ( set_meet @ SV246 ) )
= $false )
| ( ( SV246 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2620]) ).
thf(2708,plain,
! [SV296: $i,SV389: $i,SV246: $i,SV430: $i] :
( ( ( ~ ( in @ SV430 @ SV246 )
| ( in @ SV389 @ SV430 ) )
= $true )
| ( ( in @ SV389 @ SV296 )
= $false )
| ( ( SV296
= ( set_meet @ SV246 ) )
= $false )
| ( ( SV246 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2621]) ).
thf(2709,plain,
! [SV297: $i,SV319: $i,SV53: $i] :
( ( ( in @ ( apply @ SV53 @ ( sK57_D @ SV319 @ SV297 @ SV53 ) ) @ SV297 )
= $false )
| ( ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ ( relation_dom @ SV53 ) )
= $false )
| ( ( ~ ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ SV319 ) )
= $true )
| ( ( SV319
= ( relation_inverse_image @ SV53 @ SV297 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2622]) ).
thf(2710,plain,
! [SV53: $i,SV297: $i,SV319: $i] :
( ( ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ ( relation_dom @ SV53 ) )
= $true )
| ( ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ SV319 )
= $true )
| ( ( SV319
= ( relation_inverse_image @ SV53 @ SV297 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2623]) ).
thf(2711,plain,
! [SV297: $i,SV319: $i,SV53: $i] :
( ( ( in @ ( apply @ SV53 @ ( sK57_D @ SV319 @ SV297 @ SV53 ) ) @ SV297 )
= $true )
| ( ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ SV319 )
= $true )
| ( ( SV319
= ( relation_inverse_image @ SV53 @ SV297 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2624]) ).
thf(2712,plain,
! [SV320: $i,SV298: $i,SV53: $i,SV418: $i] :
( ( ( ~ ( in @ SV418 @ ( relation_dom @ SV53 ) ) )
= $true )
| ( ( ~ ( in @ ( apply @ SV53 @ SV418 ) @ SV298 ) )
= $true )
| ( ( in @ SV418 @ SV320 )
= $true )
| ( ( SV320
= ( relation_inverse_image @ SV53 @ SV298 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2625]) ).
thf(2713,plain,
! [SV298: $i,SV53: $i,SV320: $i] :
( ( ( ! [SY3943: $i] :
( ~ ( in @ SY3943 @ SV320 )
| ( in @ SY3943 @ ( relation_dom @ SV53 ) ) ) )
= $true )
| ( ( SV320
= ( relation_inverse_image @ SV53 @ SV298 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2626]) ).
thf(2714,plain,
! [SV298: $i,SV53: $i,SV320: $i] :
( ( ( ! [SY3944: $i] :
( ~ ( in @ SY3944 @ SV320 )
| ( in @ ( apply @ SV53 @ SY3944 ) @ SV298 ) ) )
= $true )
| ( ( SV320
= ( relation_inverse_image @ SV53 @ SV298 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2627]) ).
thf(2715,plain,
! [SV55: $i,SV204: $i,SV170: $i,SV393: $i] :
( ( ( in @ SV393 @ SV170 )
= $false )
| ( ( in @ SV393 @ SV204 )
= $false )
| ( ( SV204
= ( set_difference @ SV55 @ SV170 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2631]) ).
thf(2716,plain,
! [SV299: $i,SV56: $i,SV394: $i] :
( ( ( in @ SV394 @ ( relation_dom @ SV56 ) )
= $false )
| ( ( ( sK19_C @ SV299 @ SV56 )
= ( apply @ SV56 @ SV394 ) )
= $false )
| ( ( ~ ( in @ ( sK19_C @ SV299 @ SV56 ) @ SV299 ) )
= $true )
| ( ( SV299
= ( relation_rng @ SV56 ) )
= $true )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2632]) ).
thf(2717,plain,
! [SV300: $i,SV424: $i,SV56: $i,SV395: $i] :
( ( ( ( SV395
!= ( apply @ SV56 @ SV424 ) ) )
= $true )
| ( ( ~ ( in @ SV424 @ ( relation_dom @ SV56 ) ) )
= $true )
| ( ( in @ SV395 @ SV300 )
= $true )
| ( ( SV300
= ( relation_rng @ SV56 ) )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2635]) ).
thf(2718,plain,
! [SV300: $i,SV56: $i,SV396: $i] :
( ( ( ( SV396
!= ( apply @ SV56 @ ( sK18_D @ SV396 @ SV300 @ SV56 ) ) )
| ~ ( in @ ( sK18_D @ SV396 @ SV300 @ SV56 ) @ ( relation_dom @ SV56 ) ) )
= $false )
| ( ( in @ SV396 @ SV300 )
= $false )
| ( ( SV300
= ( relation_rng @ SV56 ) )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2636]) ).
thf(2719,plain,
! [SV58: $i,SV96: $i,SV321: $i] :
( ( ( ~ ( in @ ( sK67_D @ SV321 @ SV96 @ SV58 ) @ ( relation_dom @ SV96 ) ) )
= $false )
| ( ( ( ( relation_dom @ SV96 )
!= ( set_intersection2 @ ( relation_dom @ SV321 ) @ SV58 ) ) )
= $true )
| ( ( SV96
= ( relation_dom_restriction @ SV321 @ SV58 ) )
= $true )
| ( ( function @ SV321 )
= $false )
| ( ( relation @ SV321 )
= $false )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2639]) ).
thf(2720,plain,
! [SV58: $i,SV321: $i,SV96: $i] :
( ( ( ~ ( ( ( apply @ SV96 @ ( sK67_D @ SV321 @ SV96 @ SV58 ) )
!= ( apply @ SV321 @ ( sK67_D @ SV321 @ SV96 @ SV58 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV96 )
!= ( set_intersection2 @ ( relation_dom @ SV321 ) @ SV58 ) ) )
= $true )
| ( ( SV96
= ( relation_dom_restriction @ SV321 @ SV58 ) )
= $true )
| ( ( function @ SV321 )
= $false )
| ( ( relation @ SV321 )
= $false )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2639]) ).
thf(2721,plain,
! [SV58: $i,SV364: $i,SV96: $i] :
( ( ( ( SV96
!= ( relation_dom_restriction @ SV364 @ SV58 ) ) )
= $true )
| ( ( ! [SY3960: $i] :
( ~ ( in @ SY3960 @ ( relation_dom @ SV96 ) )
| ( ( apply @ SV96 @ SY3960 )
= ( apply @ SV364 @ SY3960 ) ) ) )
= $true )
| ( ( function @ SV364 )
= $false )
| ( ( relation @ SV364 )
= $false )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2640]) ).
thf(2722,plain,
! [SV58: $i,SV365: $i,SV96: $i] :
( ( ( ( SV96
!= ( relation_dom_restriction @ SV365 @ SV58 ) ) )
= $true )
| ( ( ( relation_dom @ SV96 )
= ( set_intersection2 @ ( relation_dom @ SV365 ) @ SV58 ) )
= $true )
| ( ( function @ SV365 )
= $false )
| ( ( relation @ SV365 )
= $false )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2641]) ).
thf(2723,plain,
! [SV250: $i,SV59: $i,SV419: $i,SV399: $i] :
( ( ( in @ ( ordered_pair @ SV399 @ SV419 ) @ SV59 )
= $false )
| ( ( in @ ( ordered_pair @ SV399 @ SV419 ) @ SV250 )
= $true )
| ( ( SV59 = SV250 )
= $false )
| ( ( relation @ SV250 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2642]) ).
thf(2724,plain,
! [SV59: $i,SV250: $i,SV420: $i,SV400: $i] :
( ( ( in @ ( ordered_pair @ SV400 @ SV420 ) @ SV250 )
= $false )
| ( ( in @ ( ordered_pair @ SV400 @ SV420 ) @ SV59 )
= $true )
| ( ( SV59 = SV250 )
= $false )
| ( ( relation @ SV250 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2643]) ).
thf(2725,plain,
! [SV367: $i,SV345: $i,SV63: $i,SV176: $i,SV209: $i] :
( ( ( ( sK34_D @ SV209 @ SV176 @ SV63 )
= ( ordered_pair @ SV345 @ SV367 ) )
= $false )
| ( ( in @ SV345 @ SV63 )
= $false )
| ( ( in @ SV367 @ SV176 )
= $false )
| ( ( ~ ( in @ ( sK34_D @ SV209 @ SV176 @ SV63 ) @ SV209 ) )
= $true )
| ( ( SV209
= ( cartesian_product2 @ SV63 @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2644]) ).
thf(2726,plain,
! [SV210: $i,SV346: $i,SV177: $i,SV401: $i,SV63: $i,SV377: $i] :
( ( ( in @ SV377 @ SV63 )
= $false )
| ( ( ~ ( in @ SV401 @ SV177 ) )
= $true )
| ( ( ( SV346
!= ( ordered_pair @ SV377 @ SV401 ) ) )
= $true )
| ( ( in @ SV346 @ SV210 )
= $true )
| ( ( SV210
= ( cartesian_product2 @ SV63 @ SV177 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2647]) ).
thf(2727,plain,
! [SV63: $i,SV177: $i,SV210: $i,SV347: $i] :
( ( ( ~ ( in @ ( sK32_E @ SV347 @ SV210 @ SV177 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK33_SY3300 @ SV347 @ SV210 @ SV177 @ SV63 ) @ SV177 ) )
= $false )
| ( ( in @ SV347 @ SV210 )
= $false )
| ( ( SV210
= ( cartesian_product2 @ SV63 @ SV177 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2648]) ).
thf(2728,plain,
! [SV26: $i,SV88: $i,SV253: $i] :
( ( ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV253 )
= $false )
| ( ( in @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) @ SV26 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK58_D @ SV253 @ SV88 @ SV26 ) @ ( sK59_SY3316 @ SV253 @ SV88 @ SV26 ) ) @ SV88 )
= $false )
| ( ( SV253
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $true )
| ( ( relation @ SV253 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2652]) ).
thf(2729,plain,
! [SV254: $i,SV88: $i,SV404: $i,SV26: $i,SV421: $i] :
( ( ( ~ ( in @ SV421 @ SV26 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV404 @ SV421 ) @ SV88 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV404 @ SV421 ) @ SV254 )
= $true )
| ( ( SV254
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2655]) ).
thf(2730,plain,
! [SV88: $i,SV26: $i,SV254: $i,SV431: $i] :
( ( ( ! [SY3986: $i] :
( ~ ( in @ ( ordered_pair @ SV431 @ SY3986 ) @ SV254 )
| ( in @ SY3986 @ SV26 ) ) )
= $true )
| ( ( SV254
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2656]) ).
thf(2731,plain,
! [SV26: $i,SV88: $i,SV254: $i,SV432: $i] :
( ( ( ! [SY3987: $i] :
( ~ ( in @ ( ordered_pair @ SV432 @ SY3987 ) @ SV254 )
| ( in @ ( ordered_pair @ SV432 @ SY3987 ) @ SV88 ) ) )
= $true )
| ( ( SV254
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2657]) ).
thf(2732,plain,
! [SV305: $i,SV280: $i,SV29: $i,SV407: $i] :
( ( ( in @ SV407 @ ( relation_dom @ SV29 ) )
= $false )
| ( ( ~ ( in @ SV407 @ SV280 ) )
= $true )
| ( ( ( ( sK61_D @ SV305 @ SV280 @ SV29 )
!= ( apply @ SV29 @ SV407 ) ) )
= $true )
| ( ( ~ ( in @ ( sK61_D @ SV305 @ SV280 @ SV29 ) @ SV305 ) )
= $true )
| ( ( SV305
= ( relation_image @ SV29 @ SV280 ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2660]) ).
thf(2733,plain,
! [SV29: $i,SV280: $i,SV305: $i] :
( ( ( ~ ( in @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) @ SV280 ) )
= $false )
| ( ( in @ ( sK61_D @ SV305 @ SV280 @ SV29 ) @ SV305 )
= $true )
| ( ( SV305
= ( relation_image @ SV29 @ SV280 ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2661]) ).
thf(2734,plain,
! [SV306: $i,SV408: $i,SV281: $i,SV29: $i,SV425: $i] :
( ( ( ~ ( in @ SV425 @ ( relation_dom @ SV29 ) )
| ~ ( in @ SV425 @ SV281 ) )
= $true )
| ( ( ( SV408
!= ( apply @ SV29 @ SV425 ) ) )
= $true )
| ( ( in @ SV408 @ SV306 )
= $true )
| ( ( SV306
= ( relation_image @ SV29 @ SV281 ) )
= $false )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2663]) ).
thf(2735,plain,
! [SV29: $i,SV281: $i,SV306: $i,SV409: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK60_E @ SV409 @ SV306 @ SV281 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK60_E @ SV409 @ SV306 @ SV281 @ SV29 ) @ SV281 ) )
| ( SV409
!= ( apply @ SV29 @ ( sK60_E @ SV409 @ SV306 @ SV281 @ SV29 ) ) ) )
= $false )
| ( ( in @ SV409 @ SV306 )
= $false )
| ( ( SV306
= ( relation_image @ SV29 @ SV281 ) )
= $false )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2664]) ).
thf(2736,plain,
! [SV259: $i,SV30: $i,SV369: $i,SV221: $i,SV410: $i] :
( ( ( in @ SV410 @ SV221 )
= $false )
| ( ( in @ ( ordered_pair @ SV410 @ SV369 ) @ SV30 )
= $false )
| ( ( in @ SV369 @ SV259 )
= $true )
| ( ( SV259
= ( relation_image @ SV30 @ SV221 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2666]) ).
thf(2737,plain,
! [SV30: $i,SV221: $i,SV259: $i,SV370: $i] :
( ( ( in @ ( ordered_pair @ ( sK54_E @ SV370 @ SV259 @ SV221 @ SV30 ) @ SV370 ) @ SV30 )
= $true )
| ( ( in @ SV370 @ SV259 )
= $false )
| ( ( SV259
= ( relation_image @ SV30 @ SV221 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2667]) ).
thf(2738,plain,
! [SV30: $i,SV221: $i,SV259: $i,SV370: $i] :
( ( ( in @ ( sK54_E @ SV370 @ SV259 @ SV221 @ SV30 ) @ SV221 )
= $true )
| ( ( in @ SV370 @ SV259 )
= $false )
| ( ( SV259
= ( relation_image @ SV30 @ SV221 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2668]) ).
thf(2739,plain,
! [SV261: $i,SV31: $i,SV372: $i,SV223: $i,SV411: $i] :
( ( ( in @ SV411 @ SV223 )
= $false )
| ( ( in @ ( ordered_pair @ SV372 @ SV411 ) @ SV31 )
= $false )
| ( ( in @ SV372 @ SV261 )
= $true )
| ( ( SV261
= ( relation_inverse_image @ SV31 @ SV223 ) )
= $false )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2670]) ).
thf(2740,plain,
! [SV31: $i,SV223: $i,SV261: $i,SV373: $i] :
( ( ( in @ ( ordered_pair @ SV373 @ ( sK51_E @ SV373 @ SV261 @ SV223 @ SV31 ) ) @ SV31 )
= $true )
| ( ( in @ SV373 @ SV261 )
= $false )
| ( ( SV261
= ( relation_inverse_image @ SV31 @ SV223 ) )
= $false )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2671]) ).
thf(2741,plain,
! [SV31: $i,SV223: $i,SV261: $i,SV373: $i] :
( ( ( in @ ( sK51_E @ SV373 @ SV261 @ SV223 @ SV31 ) @ SV223 )
= $true )
| ( ( in @ SV373 @ SV261 )
= $false )
| ( ( SV261
= ( relation_inverse_image @ SV31 @ SV223 ) )
= $false )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2672]) ).
thf(2742,plain,
! [SV32: $i,SV224: $i,SV262: $i] :
( ( ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV262 )
= $false )
| ( ( in @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ SV224 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK63_D @ SV262 @ SV224 @ SV32 ) @ ( sK64_SY3319 @ SV262 @ SV224 @ SV32 ) ) @ SV32 )
= $false )
| ( ( SV262
= ( relation_dom_restriction @ SV32 @ SV224 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2673]) ).
thf(2743,plain,
! [SV263: $i,SV32: $i,SV422: $i,SV225: $i,SV412: $i] :
( ( ( ~ ( in @ SV412 @ SV225 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV412 @ SV422 ) @ SV32 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV412 @ SV422 ) @ SV263 )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV32 @ SV225 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2676]) ).
thf(2744,plain,
! [SV32: $i,SV225: $i,SV263: $i,SV433: $i] :
( ( ( ! [SY3988: $i] :
~ ( in @ ( ordered_pair @ SV433 @ SY3988 ) @ SV263 )
| ( in @ SV433 @ SV225 ) )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV32 @ SV225 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2677]) ).
thf(2745,plain,
! [SV225: $i,SV32: $i,SV263: $i,SV434: $i] :
( ( ( ! [SY3989: $i] :
( ~ ( in @ ( ordered_pair @ SV434 @ SY3989 ) @ SV263 )
| ( in @ ( ordered_pair @ SV434 @ SY3989 ) @ SV32 ) ) )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV32 @ SV225 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2678]) ).
thf(2746,plain,
! [SV111: $i,SV146: $i,SV423: $i,SV413: $i] :
( ( ( in @ ( ordered_pair @ SV413 @ SV423 ) @ SV146 )
= $false )
| ( ( SV413 = SV423 )
= $true )
| ( ( SV146
= ( identity_relation @ SV111 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2680]) ).
thf(2747,plain,
! [SV111: $i,SV146: $i,SV426: $i,SV414: $i] :
( ( ( in @ ( ordered_pair @ SV414 @ SV426 ) @ SV146 )
= $false )
| ( ( in @ SV414 @ SV111 )
= $true )
| ( ( SV146
= ( identity_relation @ SV111 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2681]) ).
thf(2748,plain,
! [SV34: $i,SV89: $i,SV190: $i,SV226: $i] :
( ( ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
= $false )
| ( ( ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV34 ) )
= $true )
| ( ( SV226
= ( unordered_triple @ SV34 @ SV89 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2682]) ).
thf(2749,plain,
! [SV34: $i,SV89: $i,SV190: $i,SV226: $i] :
( ( ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
= $false )
| ( ( ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
!= SV89 ) )
= $true )
| ( ( SV226
= ( unordered_triple @ SV34 @ SV89 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2683]) ).
thf(2750,plain,
! [SV191: $i,SV89: $i,SV227: $i,SV34: $i,SV435: $i] :
( ( ( ( SV435 != SV34 )
| ( in @ SV435 @ SV227 ) )
= $true )
| ( ( SV227
= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2685]) ).
thf(2751,plain,
! [SV191: $i,SV34: $i,SV227: $i,SV89: $i,SV436: $i] :
( ( ( ( SV436 != SV89 )
| ( in @ SV436 @ SV227 ) )
= $true )
| ( ( SV227
= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2686]) ).
thf(2752,plain,
! [SV91: $i,SV357: $i,SV39: $i] :
( ( ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SV357 @ SV91 ) ) )
= $false )
| ( ( in @ SV39 @ ( relation_dom @ SV357 ) )
= $true )
| ( ( function @ SV357 )
= $false )
| ( ( relation @ SV357 )
= $false )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2688]) ).
thf(2753,plain,
! [SV91: $i,SV358: $i,SV39: $i] :
( ( ( in @ SV39 @ ( relation_dom @ ( relation_composition @ SV358 @ SV91 ) ) )
= $false )
| ( ( in @ ( apply @ SV358 @ SV39 ) @ ( relation_dom @ SV91 ) )
= $true )
| ( ( function @ SV358 )
= $false )
| ( ( relation @ SV358 )
= $false )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2689]) ).
thf(2754,plain,
! [SV40: $i,SV92: $i,SV265: $i] :
( ( ( in @ ( sK6_D @ SV265 @ SV92 @ SV40 ) @ SV265 )
= $false )
| ( ( ~ ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SV265 @ SV92 @ SV40 ) ) @ SV92 ) )
= $true )
| ( ( SV265
= ( complements_of_subsets @ SV40 @ SV92 ) )
= $true )
| ( ( element @ SV265 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2690]) ).
thf(2755,plain,
! [SV92: $i,SV40: $i,SV266: $i,SV416: $i] :
( ( ( ~ ( in @ SV416 @ SV266 ) )
= $true )
| ( ( in @ ( subset_complement @ SV40 @ SV416 ) @ SV92 )
= $true )
| ( ( element @ SV416 @ ( powerset @ SV40 ) )
= $false )
| ( ( SV266
= ( complements_of_subsets @ SV40 @ SV92 ) )
= $false )
| ( ( element @ SV266 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2692]) ).
thf(2756,plain,
! [SV266: $i,SV92: $i,SV417: $i,SV40: $i] :
( ( ( ~ ( in @ ( subset_complement @ SV40 @ SV417 ) @ SV92 ) )
= $true )
| ( ( in @ SV417 @ SV266 )
= $true )
| ( ( element @ SV417 @ ( powerset @ SV40 ) )
= $false )
| ( ( SV266
= ( complements_of_subsets @ SV40 @ SV92 ) )
= $false )
| ( ( element @ SV266 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2693]) ).
thf(2757,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2694]) ).
thf(2758,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2694]) ).
thf(2759,plain,
! [SV46: $i,SV375: $i] :
( ( ( ( SV375
!= ( function_inverse @ SV46 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY3963: $i,SY3964: $i] :
( ( SY3964
!= ( apply @ SV375 @ SY3963 ) )
| ~ ( in @ SY3963 @ ( relation_rng @ SV46 ) )
| ( SY3963
= ( apply @ SV46 @ SY3964 ) ) )
| ~ ! [SY3965: $i,SY3966: $i] :
( ( SY3966
!= ( apply @ SV375 @ SY3965 ) )
| ~ ( in @ SY3965 @ ( relation_rng @ SV46 ) )
| ( in @ SY3966 @ ( relation_dom @ SV46 ) ) ) )
| ~ ~ ( ~ ! [SY3967: $i,SY3968: $i] :
( ( SY3967
!= ( apply @ SV46 @ SY3968 ) )
| ~ ( in @ SY3968 @ ( relation_dom @ SV46 ) )
| ( SY3968
= ( apply @ SV375 @ SY3967 ) ) )
| ~ ! [SY3491: $i] :
( ! [SY3492: $i] :
( ( SY3491
!= ( apply @ SV46 @ SY3492 ) )
| ~ ( in @ SY3492 @ ( relation_dom @ SV46 ) ) )
| ( in @ SY3491 @ ( relation_rng @ SV46 ) ) ) ) ) )
= $true )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2695]) ).
thf(2760,plain,
! [SV46: $i,SV376: $i] :
( ( ( ( SV376
!= ( function_inverse @ SV46 ) ) )
= $true )
| ( ( ( relation_dom @ SV376 )
= ( relation_rng @ SV46 ) )
= $true )
| ( ( function @ SV376 )
= $false )
| ( ( relation @ SV376 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2696]) ).
thf(2761,plain,
! [SV427: $i,SV47: $i,SV123: $i,SV313: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ SV427 ) @ SV47 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV427 @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV123 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV313 ) )
= $true )
| ( ( SV313
= ( relation_composition @ SV47 @ SV123 ) )
= $true )
| ( ( relation @ SV313 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2697]) ).
thf(2762,plain,
! [SV47: $i,SV123: $i,SV313: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK10_SY3288 @ SV313 @ SV123 @ SV47 ) ) @ SV47 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV313 )
= $true )
| ( ( SV313
= ( relation_composition @ SV47 @ SV123 ) )
= $true )
| ( ( relation @ SV313 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2698]) ).
thf(2763,plain,
! [SV47: $i,SV123: $i,SV313: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK10_SY3288 @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV123 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV313 )
= $true )
| ( ( SV313
= ( relation_composition @ SV47 @ SV123 ) )
= $true )
| ( ( relation @ SV313 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2698]) ).
thf(2764,plain,
! [SV314: $i,SV123: $i,SV437: $i,SV47: $i,SV428: $i] :
( ( ( ! [SY3990: $i] :
( ~ ( in @ ( ordered_pair @ SV428 @ SY3990 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3990 @ SV437 ) @ SV123 ) )
| ( in @ ( ordered_pair @ SV428 @ SV437 ) @ SV314 ) )
= $true )
| ( ( SV314
= ( relation_composition @ SV47 @ SV123 ) )
= $false )
| ( ( relation @ SV314 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2699]) ).
thf(2765,plain,
! [SV47: $i,SV123: $i,SV314: $i,SV438: $i,SV429: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV429 @ SV438 ) @ SV314 )
| ~ ( ~ ( in @ ( ordered_pair @ SV429 @ ( sK7_F @ SV438 @ SV429 @ SV314 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SV438 @ SV429 @ SV314 @ SV123 @ SV47 ) @ SV438 ) @ SV123 ) ) )
= $true )
| ( ( SV314
= ( relation_composition @ SV47 @ SV123 ) )
= $false )
| ( ( relation @ SV314 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2700]) ).
thf(2766,plain,
! [SV245: $i,SV295: $i] :
( ( ( in @ ( sK45_C @ SV295 @ SV245 ) @ SV295 )
= $false )
| ( ( in @ ( sK45_C @ SV295 @ SV245 ) @ ( sK46_SY3307 @ SV295 @ SV245 ) )
= $false )
| ( ( SV295
= ( set_meet @ SV245 ) )
= $true )
| ( ( SV245 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2705]) ).
thf(2767,plain,
! [SV246: $i,SV296: $i,SV388: $i] :
( ( ( in @ ( sK44_D @ SV388 @ SV296 @ SV246 ) @ SV246 )
= $true )
| ( ( in @ SV388 @ SV296 )
= $true )
| ( ( SV296
= ( set_meet @ SV246 ) )
= $false )
| ( ( SV246 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2706]) ).
thf(2768,plain,
! [SV246: $i,SV296: $i,SV388: $i] :
( ( ( ~ ( in @ SV388 @ ( sK44_D @ SV388 @ SV296 @ SV246 ) ) )
= $true )
| ( ( in @ SV388 @ SV296 )
= $true )
| ( ( SV296
= ( set_meet @ SV246 ) )
= $false )
| ( ( SV246 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2707]) ).
thf(2769,plain,
! [SV296: $i,SV389: $i,SV246: $i,SV430: $i] :
( ( ( ~ ( in @ SV430 @ SV246 ) )
= $true )
| ( ( in @ SV389 @ SV430 )
= $true )
| ( ( in @ SV389 @ SV296 )
= $false )
| ( ( SV296
= ( set_meet @ SV246 ) )
= $false )
| ( ( SV246 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2708]) ).
thf(2770,plain,
! [SV53: $i,SV297: $i,SV319: $i] :
( ( ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ SV319 )
= $false )
| ( ( in @ ( sK57_D @ SV319 @ SV297 @ SV53 ) @ ( relation_dom @ SV53 ) )
= $false )
| ( ( in @ ( apply @ SV53 @ ( sK57_D @ SV319 @ SV297 @ SV53 ) ) @ SV297 )
= $false )
| ( ( SV319
= ( relation_inverse_image @ SV53 @ SV297 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2709]) ).
thf(2771,plain,
! [SV320: $i,SV298: $i,SV53: $i,SV418: $i] :
( ( ( in @ SV418 @ ( relation_dom @ SV53 ) )
= $false )
| ( ( ~ ( in @ ( apply @ SV53 @ SV418 ) @ SV298 ) )
= $true )
| ( ( in @ SV418 @ SV320 )
= $true )
| ( ( SV320
= ( relation_inverse_image @ SV53 @ SV298 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2712]) ).
thf(2772,plain,
! [SV298: $i,SV53: $i,SV320: $i,SV439: $i] :
( ( ( ~ ( in @ SV439 @ SV320 )
| ( in @ SV439 @ ( relation_dom @ SV53 ) ) )
= $true )
| ( ( SV320
= ( relation_inverse_image @ SV53 @ SV298 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2713]) ).
thf(2773,plain,
! [SV298: $i,SV53: $i,SV320: $i,SV440: $i] :
( ( ( ~ ( in @ SV440 @ SV320 )
| ( in @ ( apply @ SV53 @ SV440 ) @ SV298 ) )
= $true )
| ( ( SV320
= ( relation_inverse_image @ SV53 @ SV298 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2714]) ).
thf(2774,plain,
! [SV394: $i,SV56: $i,SV299: $i] :
( ( ( in @ ( sK19_C @ SV299 @ SV56 ) @ SV299 )
= $false )
| ( ( ( sK19_C @ SV299 @ SV56 )
= ( apply @ SV56 @ SV394 ) )
= $false )
| ( ( in @ SV394 @ ( relation_dom @ SV56 ) )
= $false )
| ( ( SV299
= ( relation_rng @ SV56 ) )
= $true )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2716]) ).
thf(2775,plain,
! [SV300: $i,SV424: $i,SV56: $i,SV395: $i] :
( ( ( SV395
= ( apply @ SV56 @ SV424 ) )
= $false )
| ( ( ~ ( in @ SV424 @ ( relation_dom @ SV56 ) ) )
= $true )
| ( ( in @ SV395 @ SV300 )
= $true )
| ( ( SV300
= ( relation_rng @ SV56 ) )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2717]) ).
thf(2776,plain,
! [SV300: $i,SV56: $i,SV396: $i] :
( ( ( ( SV396
!= ( apply @ SV56 @ ( sK18_D @ SV396 @ SV300 @ SV56 ) ) ) )
= $false )
| ( ( in @ SV396 @ SV300 )
= $false )
| ( ( SV300
= ( relation_rng @ SV56 ) )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2718]) ).
thf(2777,plain,
! [SV56: $i,SV300: $i,SV396: $i] :
( ( ( ~ ( in @ ( sK18_D @ SV396 @ SV300 @ SV56 ) @ ( relation_dom @ SV56 ) ) )
= $false )
| ( ( in @ SV396 @ SV300 )
= $false )
| ( ( SV300
= ( relation_rng @ SV56 ) )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2718]) ).
thf(2778,plain,
! [SV58: $i,SV96: $i,SV321: $i] :
( ( ( in @ ( sK67_D @ SV321 @ SV96 @ SV58 ) @ ( relation_dom @ SV96 ) )
= $true )
| ( ( ( ( relation_dom @ SV96 )
!= ( set_intersection2 @ ( relation_dom @ SV321 ) @ SV58 ) ) )
= $true )
| ( ( SV96
= ( relation_dom_restriction @ SV321 @ SV58 ) )
= $true )
| ( ( function @ SV321 )
= $false )
| ( ( relation @ SV321 )
= $false )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2719]) ).
thf(2779,plain,
! [SV58: $i,SV321: $i,SV96: $i] :
( ( ( ( ( apply @ SV96 @ ( sK67_D @ SV321 @ SV96 @ SV58 ) )
!= ( apply @ SV321 @ ( sK67_D @ SV321 @ SV96 @ SV58 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV96 )
!= ( set_intersection2 @ ( relation_dom @ SV321 ) @ SV58 ) ) )
= $true )
| ( ( SV96
= ( relation_dom_restriction @ SV321 @ SV58 ) )
= $true )
| ( ( function @ SV321 )
= $false )
| ( ( relation @ SV321 )
= $false )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2720]) ).
thf(2780,plain,
! [SV58: $i,SV364: $i,SV96: $i] :
( ( ( SV96
= ( relation_dom_restriction @ SV364 @ SV58 ) )
= $false )
| ( ( ! [SY3960: $i] :
( ~ ( in @ SY3960 @ ( relation_dom @ SV96 ) )
| ( ( apply @ SV96 @ SY3960 )
= ( apply @ SV364 @ SY3960 ) ) ) )
= $true )
| ( ( function @ SV364 )
= $false )
| ( ( relation @ SV364 )
= $false )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2721]) ).
thf(2781,plain,
! [SV58: $i,SV365: $i,SV96: $i] :
( ( ( SV96
= ( relation_dom_restriction @ SV365 @ SV58 ) )
= $false )
| ( ( ( relation_dom @ SV96 )
= ( set_intersection2 @ ( relation_dom @ SV365 ) @ SV58 ) )
= $true )
| ( ( function @ SV365 )
= $false )
| ( ( relation @ SV365 )
= $false )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2722]) ).
thf(2782,plain,
! [SV345: $i,SV367: $i,SV63: $i,SV176: $i,SV209: $i] :
( ( ( in @ ( sK34_D @ SV209 @ SV176 @ SV63 ) @ SV209 )
= $false )
| ( ( in @ SV367 @ SV176 )
= $false )
| ( ( in @ SV345 @ SV63 )
= $false )
| ( ( ( sK34_D @ SV209 @ SV176 @ SV63 )
= ( ordered_pair @ SV345 @ SV367 ) )
= $false )
| ( ( SV209
= ( cartesian_product2 @ SV63 @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2725]) ).
thf(2783,plain,
! [SV210: $i,SV346: $i,SV63: $i,SV377: $i,SV177: $i,SV401: $i] :
( ( ( in @ SV401 @ SV177 )
= $false )
| ( ( in @ SV377 @ SV63 )
= $false )
| ( ( ( SV346
!= ( ordered_pair @ SV377 @ SV401 ) ) )
= $true )
| ( ( in @ SV346 @ SV210 )
= $true )
| ( ( SV210
= ( cartesian_product2 @ SV63 @ SV177 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2726]) ).
thf(2784,plain,
! [SV63: $i,SV177: $i,SV210: $i,SV347: $i] :
( ( ( ~ ( in @ ( sK32_E @ SV347 @ SV210 @ SV177 @ SV63 ) @ SV63 ) )
= $false )
| ( ( in @ SV347 @ SV210 )
= $false )
| ( ( SV210
= ( cartesian_product2 @ SV63 @ SV177 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2727]) ).
thf(2785,plain,
! [SV63: $i,SV177: $i,SV210: $i,SV347: $i] :
( ( ( ~ ( in @ ( sK33_SY3300 @ SV347 @ SV210 @ SV177 @ SV63 ) @ SV177 ) )
= $false )
| ( ( in @ SV347 @ SV210 )
= $false )
| ( ( SV210
= ( cartesian_product2 @ SV63 @ SV177 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2727]) ).
thf(2786,plain,
! [SV254: $i,SV88: $i,SV404: $i,SV26: $i,SV421: $i] :
( ( ( in @ SV421 @ SV26 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV404 @ SV421 ) @ SV88 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV404 @ SV421 ) @ SV254 )
= $true )
| ( ( SV254
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2729]) ).
thf(2787,plain,
! [SV88: $i,SV26: $i,SV254: $i,SV441: $i,SV431: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV431 @ SV441 ) @ SV254 )
| ( in @ SV441 @ SV26 ) )
= $true )
| ( ( SV254
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2730]) ).
thf(2788,plain,
! [SV26: $i,SV88: $i,SV254: $i,SV442: $i,SV432: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV432 @ SV442 ) @ SV254 )
| ( in @ ( ordered_pair @ SV432 @ SV442 ) @ SV88 ) )
= $true )
| ( ( SV254
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2731]) ).
thf(2789,plain,
! [SV305: $i,SV29: $i,SV280: $i,SV407: $i] :
( ( ( in @ SV407 @ SV280 )
= $false )
| ( ( in @ SV407 @ ( relation_dom @ SV29 ) )
= $false )
| ( ( ( ( sK61_D @ SV305 @ SV280 @ SV29 )
!= ( apply @ SV29 @ SV407 ) ) )
= $true )
| ( ( ~ ( in @ ( sK61_D @ SV305 @ SV280 @ SV29 ) @ SV305 ) )
= $true )
| ( ( SV305
= ( relation_image @ SV29 @ SV280 ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2732]) ).
thf(2790,plain,
! [SV29: $i,SV280: $i,SV305: $i] :
( ( ( ~ ( in @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) @ ( relation_dom @ SV29 ) ) )
= $false )
| ( ( in @ ( sK61_D @ SV305 @ SV280 @ SV29 ) @ SV305 )
= $true )
| ( ( SV305
= ( relation_image @ SV29 @ SV280 ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2733]) ).
thf(2791,plain,
! [SV29: $i,SV280: $i,SV305: $i] :
( ( ( ~ ( in @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) @ SV280 ) )
= $false )
| ( ( in @ ( sK61_D @ SV305 @ SV280 @ SV29 ) @ SV305 )
= $true )
| ( ( SV305
= ( relation_image @ SV29 @ SV280 ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2733]) ).
thf(2792,plain,
! [SV306: $i,SV408: $i,SV281: $i,SV29: $i,SV425: $i] :
( ( ( ~ ( in @ SV425 @ ( relation_dom @ SV29 ) ) )
= $true )
| ( ( ~ ( in @ SV425 @ SV281 ) )
= $true )
| ( ( ( SV408
!= ( apply @ SV29 @ SV425 ) ) )
= $true )
| ( ( in @ SV408 @ SV306 )
= $true )
| ( ( SV306
= ( relation_image @ SV29 @ SV281 ) )
= $false )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2734]) ).
thf(2793,plain,
! [SV29: $i,SV281: $i,SV306: $i,SV409: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK60_E @ SV409 @ SV306 @ SV281 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK60_E @ SV409 @ SV306 @ SV281 @ SV29 ) @ SV281 ) ) )
= $false )
| ( ( in @ SV409 @ SV306 )
= $false )
| ( ( SV306
= ( relation_image @ SV29 @ SV281 ) )
= $false )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2735]) ).
thf(2794,plain,
! [SV281: $i,SV306: $i,SV29: $i,SV409: $i] :
( ( ( ( SV409
!= ( apply @ SV29 @ ( sK60_E @ SV409 @ SV306 @ SV281 @ SV29 ) ) ) )
= $false )
| ( ( in @ SV409 @ SV306 )
= $false )
| ( ( SV306
= ( relation_image @ SV29 @ SV281 ) )
= $false )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2735]) ).
thf(2795,plain,
! [SV263: $i,SV32: $i,SV422: $i,SV225: $i,SV412: $i] :
( ( ( in @ SV412 @ SV225 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV412 @ SV422 ) @ SV32 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV412 @ SV422 ) @ SV263 )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV32 @ SV225 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2743]) ).
thf(2796,plain,
! [SV32: $i,SV225: $i,SV263: $i,SV433: $i] :
( ( ( ! [SY3988: $i] :
~ ( in @ ( ordered_pair @ SV433 @ SY3988 ) @ SV263 ) )
= $true )
| ( ( in @ SV433 @ SV225 )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV32 @ SV225 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2744]) ).
thf(2797,plain,
! [SV225: $i,SV32: $i,SV263: $i,SV443: $i,SV434: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV434 @ SV443 ) @ SV263 )
| ( in @ ( ordered_pair @ SV434 @ SV443 ) @ SV32 ) )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV32 @ SV225 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2745]) ).
thf(2798,plain,
! [SV34: $i,SV89: $i,SV190: $i,SV226: $i] :
( ( ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
= SV34 )
= $false )
| ( ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
= $false )
| ( ( SV226
= ( unordered_triple @ SV34 @ SV89 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2748]) ).
thf(2799,plain,
! [SV34: $i,SV89: $i,SV190: $i,SV226: $i] :
( ( ( ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 )
= SV89 )
= $false )
| ( ( in @ ( sK50_E @ SV226 @ SV190 @ SV89 @ SV34 ) @ SV226 )
= $false )
| ( ( SV226
= ( unordered_triple @ SV34 @ SV89 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2749]) ).
thf(2800,plain,
! [SV191: $i,SV89: $i,SV227: $i,SV34: $i,SV435: $i] :
( ( ( ( SV435 != SV34 ) )
= $true )
| ( ( in @ SV435 @ SV227 )
= $true )
| ( ( SV227
= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2750]) ).
thf(2801,plain,
! [SV191: $i,SV34: $i,SV227: $i,SV89: $i,SV436: $i] :
( ( ( ( SV436 != SV89 ) )
= $true )
| ( ( in @ SV436 @ SV227 )
= $true )
| ( ( SV227
= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2751]) ).
thf(2802,plain,
! [SV92: $i,SV265: $i,SV40: $i] :
( ( ( in @ ( subset_complement @ SV40 @ ( sK6_D @ SV265 @ SV92 @ SV40 ) ) @ SV92 )
= $false )
| ( ( in @ ( sK6_D @ SV265 @ SV92 @ SV40 ) @ SV265 )
= $false )
| ( ( SV265
= ( complements_of_subsets @ SV40 @ SV92 ) )
= $true )
| ( ( element @ SV265 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2754]) ).
thf(2803,plain,
! [SV92: $i,SV40: $i,SV266: $i,SV416: $i] :
( ( ( in @ SV416 @ SV266 )
= $false )
| ( ( in @ ( subset_complement @ SV40 @ SV416 ) @ SV92 )
= $true )
| ( ( element @ SV416 @ ( powerset @ SV40 ) )
= $false )
| ( ( SV266
= ( complements_of_subsets @ SV40 @ SV92 ) )
= $false )
| ( ( element @ SV266 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2755]) ).
thf(2804,plain,
! [SV266: $i,SV92: $i,SV417: $i,SV40: $i] :
( ( ( in @ ( subset_complement @ SV40 @ SV417 ) @ SV92 )
= $false )
| ( ( in @ SV417 @ SV266 )
= $true )
| ( ( element @ SV417 @ ( powerset @ SV40 ) )
= $false )
| ( ( SV266
= ( complements_of_subsets @ SV40 @ SV92 ) )
= $false )
| ( ( element @ SV266 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false )
| ( ( element @ SV92 @ ( powerset @ ( powerset @ SV40 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2756]) ).
thf(2805,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2757]) ).
thf(2806,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2758]) ).
thf(2807,plain,
! [SV46: $i,SV375: $i] :
( ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY3963: $i,SY3964: $i] :
( ( SY3964
!= ( apply @ SV375 @ SY3963 ) )
| ~ ( in @ SY3963 @ ( relation_rng @ SV46 ) )
| ( SY3963
= ( apply @ SV46 @ SY3964 ) ) )
| ~ ! [SY3965: $i,SY3966: $i] :
( ( SY3966
!= ( apply @ SV375 @ SY3965 ) )
| ~ ( in @ SY3965 @ ( relation_rng @ SV46 ) )
| ( in @ SY3966 @ ( relation_dom @ SV46 ) ) ) )
| ~ ~ ( ~ ! [SY3967: $i,SY3968: $i] :
( ( SY3967
!= ( apply @ SV46 @ SY3968 ) )
| ~ ( in @ SY3968 @ ( relation_dom @ SV46 ) )
| ( SY3968
= ( apply @ SV375 @ SY3967 ) ) )
| ~ ! [SY3491: $i] :
( ! [SY3492: $i] :
( ( SY3491
!= ( apply @ SV46 @ SY3492 ) )
| ~ ( in @ SY3492 @ ( relation_dom @ SV46 ) ) )
| ( in @ SY3491 @ ( relation_rng @ SV46 ) ) ) ) ) )
= $true )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2759]) ).
thf(2808,plain,
! [SV46: $i,SV376: $i] :
( ( ( SV376
= ( function_inverse @ SV46 ) )
= $false )
| ( ( ( relation_dom @ SV376 )
= ( relation_rng @ SV46 ) )
= $true )
| ( ( function @ SV376 )
= $false )
| ( ( relation @ SV376 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2760]) ).
thf(2809,plain,
! [SV427: $i,SV47: $i,SV123: $i,SV313: $i] :
( ( ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ SV427 ) @ SV47 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV427 @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV123 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV313 ) )
= $true )
| ( ( SV313
= ( relation_composition @ SV47 @ SV123 ) )
= $true )
| ( ( relation @ SV313 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2761]) ).
thf(2810,plain,
! [SV47: $i,SV123: $i,SV313: $i] :
( ( ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK10_SY3288 @ SV313 @ SV123 @ SV47 ) ) @ SV47 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV313 )
= $true )
| ( ( SV313
= ( relation_composition @ SV47 @ SV123 ) )
= $true )
| ( ( relation @ SV313 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2762]) ).
thf(2811,plain,
! [SV47: $i,SV123: $i,SV313: $i] :
( ( ( in @ ( ordered_pair @ ( sK10_SY3288 @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV123 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV313 )
= $true )
| ( ( SV313
= ( relation_composition @ SV47 @ SV123 ) )
= $true )
| ( ( relation @ SV313 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2763]) ).
thf(2812,plain,
! [SV314: $i,SV123: $i,SV437: $i,SV47: $i,SV428: $i] :
( ( ( ! [SY3990: $i] :
( ~ ( in @ ( ordered_pair @ SV428 @ SY3990 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SY3990 @ SV437 ) @ SV123 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV428 @ SV437 ) @ SV314 )
= $true )
| ( ( SV314
= ( relation_composition @ SV47 @ SV123 ) )
= $false )
| ( ( relation @ SV314 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2764]) ).
thf(2813,plain,
! [SV47: $i,SV123: $i,SV314: $i,SV438: $i,SV429: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV429 @ SV438 ) @ SV314 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV429 @ ( sK7_F @ SV438 @ SV429 @ SV314 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SV438 @ SV429 @ SV314 @ SV123 @ SV47 ) @ SV438 ) @ SV123 ) ) )
= $true )
| ( ( SV314
= ( relation_composition @ SV47 @ SV123 ) )
= $false )
| ( ( relation @ SV314 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2765]) ).
thf(2814,plain,
! [SV246: $i,SV296: $i,SV388: $i] :
( ( ( in @ SV388 @ ( sK44_D @ SV388 @ SV296 @ SV246 ) )
= $false )
| ( ( in @ SV388 @ SV296 )
= $true )
| ( ( SV296
= ( set_meet @ SV246 ) )
= $false )
| ( ( SV246 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2768]) ).
thf(2815,plain,
! [SV296: $i,SV389: $i,SV246: $i,SV430: $i] :
( ( ( in @ SV430 @ SV246 )
= $false )
| ( ( in @ SV389 @ SV430 )
= $true )
| ( ( in @ SV389 @ SV296 )
= $false )
| ( ( SV296
= ( set_meet @ SV246 ) )
= $false )
| ( ( SV246 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2769]) ).
thf(2816,plain,
! [SV320: $i,SV298: $i,SV418: $i,SV53: $i] :
( ( ( in @ ( apply @ SV53 @ SV418 ) @ SV298 )
= $false )
| ( ( in @ SV418 @ ( relation_dom @ SV53 ) )
= $false )
| ( ( in @ SV418 @ SV320 )
= $true )
| ( ( SV320
= ( relation_inverse_image @ SV53 @ SV298 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2771]) ).
thf(2817,plain,
! [SV298: $i,SV53: $i,SV320: $i,SV439: $i] :
( ( ( ~ ( in @ SV439 @ SV320 ) )
= $true )
| ( ( in @ SV439 @ ( relation_dom @ SV53 ) )
= $true )
| ( ( SV320
= ( relation_inverse_image @ SV53 @ SV298 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2772]) ).
thf(2818,plain,
! [SV298: $i,SV53: $i,SV320: $i,SV440: $i] :
( ( ( ~ ( in @ SV440 @ SV320 ) )
= $true )
| ( ( in @ ( apply @ SV53 @ SV440 ) @ SV298 )
= $true )
| ( ( SV320
= ( relation_inverse_image @ SV53 @ SV298 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2773]) ).
thf(2819,plain,
! [SV300: $i,SV395: $i,SV56: $i,SV424: $i] :
( ( ( in @ SV424 @ ( relation_dom @ SV56 ) )
= $false )
| ( ( SV395
= ( apply @ SV56 @ SV424 ) )
= $false )
| ( ( in @ SV395 @ SV300 )
= $true )
| ( ( SV300
= ( relation_rng @ SV56 ) )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2775]) ).
thf(2820,plain,
! [SV300: $i,SV56: $i,SV396: $i] :
( ( ( SV396
= ( apply @ SV56 @ ( sK18_D @ SV396 @ SV300 @ SV56 ) ) )
= $true )
| ( ( in @ SV396 @ SV300 )
= $false )
| ( ( SV300
= ( relation_rng @ SV56 ) )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2776]) ).
thf(2821,plain,
! [SV56: $i,SV300: $i,SV396: $i] :
( ( ( in @ ( sK18_D @ SV396 @ SV300 @ SV56 ) @ ( relation_dom @ SV56 ) )
= $true )
| ( ( in @ SV396 @ SV300 )
= $false )
| ( ( SV300
= ( relation_rng @ SV56 ) )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2777]) ).
thf(2822,plain,
! [SV58: $i,SV321: $i,SV96: $i] :
( ( ( ( relation_dom @ SV96 )
= ( set_intersection2 @ ( relation_dom @ SV321 ) @ SV58 ) )
= $false )
| ( ( in @ ( sK67_D @ SV321 @ SV96 @ SV58 ) @ ( relation_dom @ SV96 ) )
= $true )
| ( ( SV96
= ( relation_dom_restriction @ SV321 @ SV58 ) )
= $true )
| ( ( function @ SV321 )
= $false )
| ( ( relation @ SV321 )
= $false )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2778]) ).
thf(2823,plain,
! [SV58: $i,SV321: $i,SV96: $i] :
( ( ( ( apply @ SV96 @ ( sK67_D @ SV321 @ SV96 @ SV58 ) )
= ( apply @ SV321 @ ( sK67_D @ SV321 @ SV96 @ SV58 ) ) )
= $false )
| ( ( ( ( relation_dom @ SV96 )
!= ( set_intersection2 @ ( relation_dom @ SV321 ) @ SV58 ) ) )
= $true )
| ( ( SV96
= ( relation_dom_restriction @ SV321 @ SV58 ) )
= $true )
| ( ( function @ SV321 )
= $false )
| ( ( relation @ SV321 )
= $false )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2779]) ).
thf(2824,plain,
! [SV58: $i,SV364: $i,SV96: $i,SV444: $i] :
( ( ( ~ ( in @ SV444 @ ( relation_dom @ SV96 ) )
| ( ( apply @ SV96 @ SV444 )
= ( apply @ SV364 @ SV444 ) ) )
= $true )
| ( ( SV96
= ( relation_dom_restriction @ SV364 @ SV58 ) )
= $false )
| ( ( function @ SV364 )
= $false )
| ( ( relation @ SV364 )
= $false )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2780]) ).
thf(2825,plain,
! [SV210: $i,SV177: $i,SV63: $i,SV401: $i,SV377: $i,SV346: $i] :
( ( ( SV346
= ( ordered_pair @ SV377 @ SV401 ) )
= $false )
| ( ( in @ SV377 @ SV63 )
= $false )
| ( ( in @ SV401 @ SV177 )
= $false )
| ( ( in @ SV346 @ SV210 )
= $true )
| ( ( SV210
= ( cartesian_product2 @ SV63 @ SV177 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2783]) ).
thf(2826,plain,
! [SV63: $i,SV177: $i,SV210: $i,SV347: $i] :
( ( ( in @ ( sK32_E @ SV347 @ SV210 @ SV177 @ SV63 ) @ SV63 )
= $true )
| ( ( in @ SV347 @ SV210 )
= $false )
| ( ( SV210
= ( cartesian_product2 @ SV63 @ SV177 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2784]) ).
thf(2827,plain,
! [SV63: $i,SV177: $i,SV210: $i,SV347: $i] :
( ( ( in @ ( sK33_SY3300 @ SV347 @ SV210 @ SV177 @ SV63 ) @ SV177 )
= $true )
| ( ( in @ SV347 @ SV210 )
= $false )
| ( ( SV210
= ( cartesian_product2 @ SV63 @ SV177 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2785]) ).
thf(2828,plain,
! [SV254: $i,SV26: $i,SV88: $i,SV421: $i,SV404: $i] :
( ( ( in @ ( ordered_pair @ SV404 @ SV421 ) @ SV88 )
= $false )
| ( ( in @ SV421 @ SV26 )
= $false )
| ( ( in @ ( ordered_pair @ SV404 @ SV421 ) @ SV254 )
= $true )
| ( ( SV254
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2786]) ).
thf(2829,plain,
! [SV88: $i,SV26: $i,SV254: $i,SV441: $i,SV431: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV431 @ SV441 ) @ SV254 ) )
= $true )
| ( ( in @ SV441 @ SV26 )
= $true )
| ( ( SV254
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2787]) ).
thf(2830,plain,
! [SV26: $i,SV88: $i,SV254: $i,SV442: $i,SV432: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV432 @ SV442 ) @ SV254 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV432 @ SV442 ) @ SV88 )
= $true )
| ( ( SV254
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2788]) ).
thf(2831,plain,
! [SV407: $i,SV29: $i,SV280: $i,SV305: $i] :
( ( ( ( sK61_D @ SV305 @ SV280 @ SV29 )
= ( apply @ SV29 @ SV407 ) )
= $false )
| ( ( in @ SV407 @ ( relation_dom @ SV29 ) )
= $false )
| ( ( in @ SV407 @ SV280 )
= $false )
| ( ( ~ ( in @ ( sK61_D @ SV305 @ SV280 @ SV29 ) @ SV305 ) )
= $true )
| ( ( SV305
= ( relation_image @ SV29 @ SV280 ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2789]) ).
thf(2832,plain,
! [SV29: $i,SV280: $i,SV305: $i] :
( ( ( in @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) @ ( relation_dom @ SV29 ) )
= $true )
| ( ( in @ ( sK61_D @ SV305 @ SV280 @ SV29 ) @ SV305 )
= $true )
| ( ( SV305
= ( relation_image @ SV29 @ SV280 ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2790]) ).
thf(2833,plain,
! [SV29: $i,SV280: $i,SV305: $i] :
( ( ( in @ ( sK62_SY3318 @ SV305 @ SV280 @ SV29 ) @ SV280 )
= $true )
| ( ( in @ ( sK61_D @ SV305 @ SV280 @ SV29 ) @ SV305 )
= $true )
| ( ( SV305
= ( relation_image @ SV29 @ SV280 ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2791]) ).
thf(2834,plain,
! [SV306: $i,SV408: $i,SV281: $i,SV29: $i,SV425: $i] :
( ( ( in @ SV425 @ ( relation_dom @ SV29 ) )
= $false )
| ( ( ~ ( in @ SV425 @ SV281 ) )
= $true )
| ( ( ( SV408
!= ( apply @ SV29 @ SV425 ) ) )
= $true )
| ( ( in @ SV408 @ SV306 )
= $true )
| ( ( SV306
= ( relation_image @ SV29 @ SV281 ) )
= $false )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2792]) ).
thf(2835,plain,
! [SV29: $i,SV281: $i,SV306: $i,SV409: $i] :
( ( ( ~ ( ~ ( in @ ( sK60_E @ SV409 @ SV306 @ SV281 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK60_E @ SV409 @ SV306 @ SV281 @ SV29 ) @ SV281 ) ) )
= $true )
| ( ( in @ SV409 @ SV306 )
= $false )
| ( ( SV306
= ( relation_image @ SV29 @ SV281 ) )
= $false )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2793]) ).
thf(2836,plain,
! [SV281: $i,SV306: $i,SV29: $i,SV409: $i] :
( ( ( SV409
= ( apply @ SV29 @ ( sK60_E @ SV409 @ SV306 @ SV281 @ SV29 ) ) )
= $true )
| ( ( in @ SV409 @ SV306 )
= $false )
| ( ( SV306
= ( relation_image @ SV29 @ SV281 ) )
= $false )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2794]) ).
thf(2837,plain,
! [SV263: $i,SV225: $i,SV32: $i,SV422: $i,SV412: $i] :
( ( ( in @ ( ordered_pair @ SV412 @ SV422 ) @ SV32 )
= $false )
| ( ( in @ SV412 @ SV225 )
= $false )
| ( ( in @ ( ordered_pair @ SV412 @ SV422 ) @ SV263 )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV32 @ SV225 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2795]) ).
thf(2838,plain,
! [SV32: $i,SV225: $i,SV263: $i,SV445: $i,SV433: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV433 @ SV445 ) @ SV263 ) )
= $true )
| ( ( in @ SV433 @ SV225 )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV32 @ SV225 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2796]) ).
thf(2839,plain,
! [SV225: $i,SV32: $i,SV263: $i,SV443: $i,SV434: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV434 @ SV443 ) @ SV263 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV434 @ SV443 ) @ SV32 )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV32 @ SV225 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2797]) ).
thf(2840,plain,
! [SV191: $i,SV89: $i,SV227: $i,SV34: $i,SV435: $i] :
( ( ( SV435 = SV34 )
= $false )
| ( ( in @ SV435 @ SV227 )
= $true )
| ( ( SV227
= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2800]) ).
thf(2841,plain,
! [SV191: $i,SV34: $i,SV227: $i,SV89: $i,SV436: $i] :
( ( ( SV436 = SV89 )
= $false )
| ( ( in @ SV436 @ SV227 )
= $true )
| ( ( SV227
= ( unordered_triple @ SV34 @ SV89 @ SV191 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2801]) ).
thf(2842,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2805]) ).
thf(2843,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2806]) ).
thf(2844,plain,
! [SV46: $i,SV375: $i] :
( ( ( ~ ~ ( ~ ! [SY3963: $i,SY3964: $i] :
( ( SY3964
!= ( apply @ SV375 @ SY3963 ) )
| ~ ( in @ SY3963 @ ( relation_rng @ SV46 ) )
| ( SY3963
= ( apply @ SV46 @ SY3964 ) ) )
| ~ ! [SY3965: $i,SY3966: $i] :
( ( SY3966
!= ( apply @ SV375 @ SY3965 ) )
| ~ ( in @ SY3965 @ ( relation_rng @ SV46 ) )
| ( in @ SY3966 @ ( relation_dom @ SV46 ) ) ) )
| ~ ~ ( ~ ! [SY3967: $i,SY3968: $i] :
( ( SY3967
!= ( apply @ SV46 @ SY3968 ) )
| ~ ( in @ SY3968 @ ( relation_dom @ SV46 ) )
| ( SY3968
= ( apply @ SV375 @ SY3967 ) ) )
| ~ ! [SY3491: $i] :
( ! [SY3492: $i] :
( ( SY3491
!= ( apply @ SV46 @ SY3492 ) )
| ~ ( in @ SY3492 @ ( relation_dom @ SV46 ) ) )
| ( in @ SY3491 @ ( relation_rng @ SV46 ) ) ) ) )
= $false )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2807]) ).
thf(2845,plain,
! [SV47: $i,SV123: $i,SV313: $i,SV427: $i] :
( ( ( in @ ( ordered_pair @ SV427 @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV123 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ SV427 ) @ SV47 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV313 ) )
= $true )
| ( ( SV313
= ( relation_composition @ SV47 @ SV123 ) )
= $true )
| ( ( relation @ SV313 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2809]) ).
thf(2846,plain,
! [SV314: $i,SV123: $i,SV437: $i,SV47: $i,SV446: $i,SV428: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV428 @ SV446 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ SV446 @ SV437 ) @ SV123 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV428 @ SV437 ) @ SV314 )
= $true )
| ( ( SV314
= ( relation_composition @ SV47 @ SV123 ) )
= $false )
| ( ( relation @ SV314 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2812]) ).
thf(2847,plain,
! [SV47: $i,SV123: $i,SV314: $i,SV438: $i,SV429: $i] :
( ( ( in @ ( ordered_pair @ SV429 @ SV438 ) @ SV314 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV429 @ ( sK7_F @ SV438 @ SV429 @ SV314 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SV438 @ SV429 @ SV314 @ SV123 @ SV47 ) @ SV438 ) @ SV123 ) ) )
= $true )
| ( ( SV314
= ( relation_composition @ SV47 @ SV123 ) )
= $false )
| ( ( relation @ SV314 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2813]) ).
thf(2848,plain,
! [SV298: $i,SV53: $i,SV320: $i,SV439: $i] :
( ( ( in @ SV439 @ SV320 )
= $false )
| ( ( in @ SV439 @ ( relation_dom @ SV53 ) )
= $true )
| ( ( SV320
= ( relation_inverse_image @ SV53 @ SV298 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2817]) ).
thf(2849,plain,
! [SV298: $i,SV53: $i,SV320: $i,SV440: $i] :
( ( ( in @ SV440 @ SV320 )
= $false )
| ( ( in @ ( apply @ SV53 @ SV440 ) @ SV298 )
= $true )
| ( ( SV320
= ( relation_inverse_image @ SV53 @ SV298 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2818]) ).
thf(2850,plain,
! [SV58: $i,SV321: $i,SV96: $i] :
( ( ( ( relation_dom @ SV96 )
= ( set_intersection2 @ ( relation_dom @ SV321 ) @ SV58 ) )
= $false )
| ( ( ( apply @ SV96 @ ( sK67_D @ SV321 @ SV96 @ SV58 ) )
= ( apply @ SV321 @ ( sK67_D @ SV321 @ SV96 @ SV58 ) ) )
= $false )
| ( ( SV96
= ( relation_dom_restriction @ SV321 @ SV58 ) )
= $true )
| ( ( function @ SV321 )
= $false )
| ( ( relation @ SV321 )
= $false )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2823]) ).
thf(2851,plain,
! [SV58: $i,SV364: $i,SV96: $i,SV444: $i] :
( ( ( ~ ( in @ SV444 @ ( relation_dom @ SV96 ) ) )
= $true )
| ( ( ( apply @ SV96 @ SV444 )
= ( apply @ SV364 @ SV444 ) )
= $true )
| ( ( SV96
= ( relation_dom_restriction @ SV364 @ SV58 ) )
= $false )
| ( ( function @ SV364 )
= $false )
| ( ( relation @ SV364 )
= $false )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2824]) ).
thf(2852,plain,
! [SV88: $i,SV26: $i,SV254: $i,SV441: $i,SV431: $i] :
( ( ( in @ ( ordered_pair @ SV431 @ SV441 ) @ SV254 )
= $false )
| ( ( in @ SV441 @ SV26 )
= $true )
| ( ( SV254
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2829]) ).
thf(2853,plain,
! [SV26: $i,SV88: $i,SV254: $i,SV442: $i,SV432: $i] :
( ( ( in @ ( ordered_pair @ SV432 @ SV442 ) @ SV254 )
= $false )
| ( ( in @ ( ordered_pair @ SV432 @ SV442 ) @ SV88 )
= $true )
| ( ( SV254
= ( relation_rng_restriction @ SV26 @ SV88 ) )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2830]) ).
thf(2854,plain,
! [SV407: $i,SV29: $i,SV280: $i,SV305: $i] :
( ( ( in @ ( sK61_D @ SV305 @ SV280 @ SV29 ) @ SV305 )
= $false )
| ( ( in @ SV407 @ SV280 )
= $false )
| ( ( in @ SV407 @ ( relation_dom @ SV29 ) )
= $false )
| ( ( ( sK61_D @ SV305 @ SV280 @ SV29 )
= ( apply @ SV29 @ SV407 ) )
= $false )
| ( ( SV305
= ( relation_image @ SV29 @ SV280 ) )
= $true )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2831]) ).
thf(2855,plain,
! [SV306: $i,SV408: $i,SV29: $i,SV281: $i,SV425: $i] :
( ( ( in @ SV425 @ SV281 )
= $false )
| ( ( in @ SV425 @ ( relation_dom @ SV29 ) )
= $false )
| ( ( ( SV408
!= ( apply @ SV29 @ SV425 ) ) )
= $true )
| ( ( in @ SV408 @ SV306 )
= $true )
| ( ( SV306
= ( relation_image @ SV29 @ SV281 ) )
= $false )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2834]) ).
thf(2856,plain,
! [SV29: $i,SV281: $i,SV306: $i,SV409: $i] :
( ( ( ~ ( in @ ( sK60_E @ SV409 @ SV306 @ SV281 @ SV29 ) @ ( relation_dom @ SV29 ) )
| ~ ( in @ ( sK60_E @ SV409 @ SV306 @ SV281 @ SV29 ) @ SV281 ) )
= $false )
| ( ( in @ SV409 @ SV306 )
= $false )
| ( ( SV306
= ( relation_image @ SV29 @ SV281 ) )
= $false )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2835]) ).
thf(2857,plain,
! [SV32: $i,SV225: $i,SV263: $i,SV445: $i,SV433: $i] :
( ( ( in @ ( ordered_pair @ SV433 @ SV445 ) @ SV263 )
= $false )
| ( ( in @ SV433 @ SV225 )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV32 @ SV225 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2838]) ).
thf(2858,plain,
! [SV225: $i,SV32: $i,SV263: $i,SV443: $i,SV434: $i] :
( ( ( in @ ( ordered_pair @ SV434 @ SV443 ) @ SV263 )
= $false )
| ( ( in @ ( ordered_pair @ SV434 @ SV443 ) @ SV32 )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV32 @ SV225 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2839]) ).
thf(2859,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2842]) ).
thf(2860,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2842]) ).
thf(2861,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2843]) ).
thf(2862,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2843]) ).
thf(2863,plain,
! [SV46: $i,SV375: $i] :
( ( ( ~ ~ ( ~ ! [SY3963: $i,SY3964: $i] :
( ( SY3964
!= ( apply @ SV375 @ SY3963 ) )
| ~ ( in @ SY3963 @ ( relation_rng @ SV46 ) )
| ( SY3963
= ( apply @ SV46 @ SY3964 ) ) )
| ~ ! [SY3965: $i,SY3966: $i] :
( ( SY3966
!= ( apply @ SV375 @ SY3965 ) )
| ~ ( in @ SY3965 @ ( relation_rng @ SV46 ) )
| ( in @ SY3966 @ ( relation_dom @ SV46 ) ) ) ) )
= $false )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2844]) ).
thf(2864,plain,
! [SV375: $i,SV46: $i] :
( ( ( ~ ~ ( ~ ! [SY3967: $i,SY3968: $i] :
( ( SY3967
!= ( apply @ SV46 @ SY3968 ) )
| ~ ( in @ SY3968 @ ( relation_dom @ SV46 ) )
| ( SY3968
= ( apply @ SV375 @ SY3967 ) ) )
| ~ ! [SY3491: $i] :
( ! [SY3492: $i] :
( ( SY3491
!= ( apply @ SV46 @ SY3492 ) )
| ~ ( in @ SY3492 @ ( relation_dom @ SV46 ) ) )
| ( in @ SY3491 @ ( relation_rng @ SV46 ) ) ) ) )
= $false )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2844]) ).
thf(2865,plain,
! [SV427: $i,SV47: $i,SV123: $i,SV313: $i] :
( ( ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV313 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_D @ SV313 @ SV123 @ SV47 ) @ SV427 ) @ SV47 )
= $false )
| ( ( in @ ( ordered_pair @ SV427 @ ( sK9_SY3284 @ SV313 @ SV123 @ SV47 ) ) @ SV123 )
= $false )
| ( ( SV313
= ( relation_composition @ SV47 @ SV123 ) )
= $true )
| ( ( relation @ SV313 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2845]) ).
thf(2866,plain,
! [SV314: $i,SV123: $i,SV437: $i,SV47: $i,SV446: $i,SV428: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV428 @ SV446 ) @ SV47 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV446 @ SV437 ) @ SV123 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV428 @ SV437 ) @ SV314 )
= $true )
| ( ( SV314
= ( relation_composition @ SV47 @ SV123 ) )
= $false )
| ( ( relation @ SV314 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2846]) ).
thf(2867,plain,
! [SV47: $i,SV123: $i,SV314: $i,SV438: $i,SV429: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV429 @ ( sK7_F @ SV438 @ SV429 @ SV314 @ SV123 @ SV47 ) ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK7_F @ SV438 @ SV429 @ SV314 @ SV123 @ SV47 ) @ SV438 ) @ SV123 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV429 @ SV438 ) @ SV314 )
= $false )
| ( ( SV314
= ( relation_composition @ SV47 @ SV123 ) )
= $false )
| ( ( relation @ SV314 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2847]) ).
thf(2868,plain,
! [SV58: $i,SV364: $i,SV96: $i,SV444: $i] :
( ( ( in @ SV444 @ ( relation_dom @ SV96 ) )
= $false )
| ( ( ( apply @ SV96 @ SV444 )
= ( apply @ SV364 @ SV444 ) )
= $true )
| ( ( SV96
= ( relation_dom_restriction @ SV364 @ SV58 ) )
= $false )
| ( ( function @ SV364 )
= $false )
| ( ( relation @ SV364 )
= $false )
| ( ( function @ SV96 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2851]) ).
thf(2869,plain,
! [SV306: $i,SV281: $i,SV425: $i,SV29: $i,SV408: $i] :
( ( ( SV408
= ( apply @ SV29 @ SV425 ) )
= $false )
| ( ( in @ SV425 @ ( relation_dom @ SV29 ) )
= $false )
| ( ( in @ SV425 @ SV281 )
= $false )
| ( ( in @ SV408 @ SV306 )
= $true )
| ( ( SV306
= ( relation_image @ SV29 @ SV281 ) )
= $false )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2855]) ).
thf(2870,plain,
! [SV29: $i,SV281: $i,SV306: $i,SV409: $i] :
( ( ( ~ ( in @ ( sK60_E @ SV409 @ SV306 @ SV281 @ SV29 ) @ ( relation_dom @ SV29 ) ) )
= $false )
| ( ( in @ SV409 @ SV306 )
= $false )
| ( ( SV306
= ( relation_image @ SV29 @ SV281 ) )
= $false )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2856]) ).
thf(2871,plain,
! [SV29: $i,SV281: $i,SV306: $i,SV409: $i] :
( ( ( ~ ( in @ ( sK60_E @ SV409 @ SV306 @ SV281 @ SV29 ) @ SV281 ) )
= $false )
| ( ( in @ SV409 @ SV306 )
= $false )
| ( ( SV306
= ( relation_image @ SV29 @ SV281 ) )
= $false )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2856]) ).
thf(2872,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2859]) ).
thf(2873,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2860]) ).
thf(2874,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ( ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2861]) ).
thf(2875,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2862]) ).
thf(2876,plain,
! [SV46: $i,SV375: $i] :
( ( ( ~ ( ~ ! [SY3963: $i,SY3964: $i] :
( ( SY3964
!= ( apply @ SV375 @ SY3963 ) )
| ~ ( in @ SY3963 @ ( relation_rng @ SV46 ) )
| ( SY3963
= ( apply @ SV46 @ SY3964 ) ) )
| ~ ! [SY3965: $i,SY3966: $i] :
( ( SY3966
!= ( apply @ SV375 @ SY3965 ) )
| ~ ( in @ SY3965 @ ( relation_rng @ SV46 ) )
| ( in @ SY3966 @ ( relation_dom @ SV46 ) ) ) ) )
= $true )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2863]) ).
thf(2877,plain,
! [SV375: $i,SV46: $i] :
( ( ( ~ ( ~ ! [SY3967: $i,SY3968: $i] :
( ( SY3967
!= ( apply @ SV46 @ SY3968 ) )
| ~ ( in @ SY3968 @ ( relation_dom @ SV46 ) )
| ( SY3968
= ( apply @ SV375 @ SY3967 ) ) )
| ~ ! [SY3491: $i] :
( ! [SY3492: $i] :
( ( SY3491
!= ( apply @ SV46 @ SY3492 ) )
| ~ ( in @ SY3492 @ ( relation_dom @ SV46 ) ) )
| ( in @ SY3491 @ ( relation_rng @ SV46 ) ) ) ) )
= $true )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2864]) ).
thf(2878,plain,
! [SV314: $i,SV123: $i,SV437: $i,SV47: $i,SV446: $i,SV428: $i] :
( ( ( in @ ( ordered_pair @ SV428 @ SV446 ) @ SV47 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV446 @ SV437 ) @ SV123 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV428 @ SV437 ) @ SV314 )
= $true )
| ( ( SV314
= ( relation_composition @ SV47 @ SV123 ) )
= $false )
| ( ( relation @ SV314 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2866]) ).
thf(2879,plain,
! [SV47: $i,SV123: $i,SV314: $i,SV438: $i,SV429: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV429 @ ( sK7_F @ SV438 @ SV429 @ SV314 @ SV123 @ SV47 ) ) @ SV47 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV429 @ SV438 ) @ SV314 )
= $false )
| ( ( SV314
= ( relation_composition @ SV47 @ SV123 ) )
= $false )
| ( ( relation @ SV314 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2867]) ).
thf(2880,plain,
! [SV47: $i,SV123: $i,SV314: $i,SV429: $i,SV438: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK7_F @ SV438 @ SV429 @ SV314 @ SV123 @ SV47 ) @ SV438 ) @ SV123 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV429 @ SV438 ) @ SV314 )
= $false )
| ( ( SV314
= ( relation_composition @ SV47 @ SV123 ) )
= $false )
| ( ( relation @ SV314 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2867]) ).
thf(2881,plain,
! [SV29: $i,SV281: $i,SV306: $i,SV409: $i] :
( ( ( in @ ( sK60_E @ SV409 @ SV306 @ SV281 @ SV29 ) @ ( relation_dom @ SV29 ) )
= $true )
| ( ( in @ SV409 @ SV306 )
= $false )
| ( ( SV306
= ( relation_image @ SV29 @ SV281 ) )
= $false )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2870]) ).
thf(2882,plain,
! [SV29: $i,SV281: $i,SV306: $i,SV409: $i] :
( ( ( in @ ( sK60_E @ SV409 @ SV306 @ SV281 @ SV29 ) @ SV281 )
= $true )
| ( ( in @ SV409 @ SV306 )
= $false )
| ( ( SV306
= ( relation_image @ SV29 @ SV281 ) )
= $false )
| ( ( function @ SV29 )
= $false )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2871]) ).
thf(2883,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2872]) ).
thf(2884,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2873]) ).
thf(2885,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2874]) ).
thf(2886,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) )
= $true )
| ( ( ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2875]) ).
thf(2887,plain,
! [SV46: $i,SV375: $i] :
( ( ( ~ ! [SY3963: $i,SY3964: $i] :
( ( SY3964
!= ( apply @ SV375 @ SY3963 ) )
| ~ ( in @ SY3963 @ ( relation_rng @ SV46 ) )
| ( SY3963
= ( apply @ SV46 @ SY3964 ) ) )
| ~ ! [SY3965: $i,SY3966: $i] :
( ( SY3966
!= ( apply @ SV375 @ SY3965 ) )
| ~ ( in @ SY3965 @ ( relation_rng @ SV46 ) )
| ( in @ SY3966 @ ( relation_dom @ SV46 ) ) ) )
= $false )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2876]) ).
thf(2888,plain,
! [SV375: $i,SV46: $i] :
( ( ( ~ ! [SY3967: $i,SY3968: $i] :
( ( SY3967
!= ( apply @ SV46 @ SY3968 ) )
| ~ ( in @ SY3968 @ ( relation_dom @ SV46 ) )
| ( SY3968
= ( apply @ SV375 @ SY3967 ) ) )
| ~ ! [SY3491: $i] :
( ! [SY3492: $i] :
( ( SY3491
!= ( apply @ SV46 @ SY3492 ) )
| ~ ( in @ SY3492 @ ( relation_dom @ SV46 ) ) )
| ( in @ SY3491 @ ( relation_rng @ SV46 ) ) ) )
= $false )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2877]) ).
thf(2889,plain,
! [SV314: $i,SV47: $i,SV428: $i,SV123: $i,SV437: $i,SV446: $i] :
( ( ( in @ ( ordered_pair @ SV446 @ SV437 ) @ SV123 )
= $false )
| ( ( in @ ( ordered_pair @ SV428 @ SV446 ) @ SV47 )
= $false )
| ( ( in @ ( ordered_pair @ SV428 @ SV437 ) @ SV314 )
= $true )
| ( ( SV314
= ( relation_composition @ SV47 @ SV123 ) )
= $false )
| ( ( relation @ SV314 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2878]) ).
thf(2890,plain,
! [SV47: $i,SV123: $i,SV314: $i,SV438: $i,SV429: $i] :
( ( ( in @ ( ordered_pair @ SV429 @ ( sK7_F @ SV438 @ SV429 @ SV314 @ SV123 @ SV47 ) ) @ SV47 )
= $true )
| ( ( in @ ( ordered_pair @ SV429 @ SV438 ) @ SV314 )
= $false )
| ( ( SV314
= ( relation_composition @ SV47 @ SV123 ) )
= $false )
| ( ( relation @ SV314 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2879]) ).
thf(2891,plain,
! [SV47: $i,SV123: $i,SV314: $i,SV429: $i,SV438: $i] :
( ( ( in @ ( ordered_pair @ ( sK7_F @ SV438 @ SV429 @ SV314 @ SV123 @ SV47 ) @ SV438 ) @ SV123 )
= $true )
| ( ( in @ ( ordered_pair @ SV429 @ SV438 ) @ SV314 )
= $false )
| ( ( SV314
= ( relation_composition @ SV47 @ SV123 ) )
= $false )
| ( ( relation @ SV314 )
= $false )
| ( ( relation @ SV123 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2880]) ).
thf(2892,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2883]) ).
thf(2893,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2883]) ).
thf(2894,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2884]) ).
thf(2895,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2884]) ).
thf(2896,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2885]) ).
thf(2897,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2885]) ).
thf(2898,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) )
= $true )
| ( ( ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2886]) ).
thf(2899,plain,
! [SV46: $i,SV375: $i] :
( ( ( ~ ! [SY3963: $i,SY3964: $i] :
( ( SY3964
!= ( apply @ SV375 @ SY3963 ) )
| ~ ( in @ SY3963 @ ( relation_rng @ SV46 ) )
| ( SY3963
= ( apply @ SV46 @ SY3964 ) ) ) )
= $false )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2887]) ).
thf(2900,plain,
! [SV46: $i,SV375: $i] :
( ( ( ~ ! [SY3965: $i,SY3966: $i] :
( ( SY3966
!= ( apply @ SV375 @ SY3965 ) )
| ~ ( in @ SY3965 @ ( relation_rng @ SV46 ) )
| ( in @ SY3966 @ ( relation_dom @ SV46 ) ) ) )
= $false )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2887]) ).
thf(2901,plain,
! [SV375: $i,SV46: $i] :
( ( ( ~ ! [SY3967: $i,SY3968: $i] :
( ( SY3967
!= ( apply @ SV46 @ SY3968 ) )
| ~ ( in @ SY3968 @ ( relation_dom @ SV46 ) )
| ( SY3968
= ( apply @ SV375 @ SY3967 ) ) ) )
= $false )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2888]) ).
thf(2902,plain,
! [SV375: $i,SV46: $i] :
( ( ( ~ ! [SY3491: $i] :
( ! [SY3492: $i] :
( ( SY3491
!= ( apply @ SV46 @ SY3492 ) )
| ~ ( in @ SY3492 @ ( relation_dom @ SV46 ) ) )
| ( in @ SY3491 @ ( relation_rng @ SV46 ) ) ) )
= $false )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2888]) ).
thf(2903,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ( ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2892]) ).
thf(2904,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2893]) ).
thf(2905,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2894]) ).
thf(2906,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2895]) ).
thf(2907,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2896]) ).
thf(2908,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2897]) ).
thf(2909,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
= $false )
| ( ( ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) )
= $true )
| ( ( ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2898]) ).
thf(2910,plain,
! [SV46: $i,SV375: $i] :
( ( ( ! [SY3963: $i,SY3964: $i] :
( ( SY3964
!= ( apply @ SV375 @ SY3963 ) )
| ~ ( in @ SY3963 @ ( relation_rng @ SV46 ) )
| ( SY3963
= ( apply @ SV46 @ SY3964 ) ) ) )
= $true )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2899]) ).
thf(2911,plain,
! [SV46: $i,SV375: $i] :
( ( ( ! [SY3965: $i,SY3966: $i] :
( ( SY3966
!= ( apply @ SV375 @ SY3965 ) )
| ~ ( in @ SY3965 @ ( relation_rng @ SV46 ) )
| ( in @ SY3966 @ ( relation_dom @ SV46 ) ) ) )
= $true )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2900]) ).
thf(2912,plain,
! [SV375: $i,SV46: $i] :
( ( ( ! [SY3967: $i,SY3968: $i] :
( ( SY3967
!= ( apply @ SV46 @ SY3968 ) )
| ~ ( in @ SY3968 @ ( relation_dom @ SV46 ) )
| ( SY3968
= ( apply @ SV375 @ SY3967 ) ) ) )
= $true )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2901]) ).
thf(2913,plain,
! [SV375: $i,SV46: $i] :
( ( ( ! [SY3491: $i] :
( ! [SY3492: $i] :
( ( SY3491
!= ( apply @ SV46 @ SY3492 ) )
| ~ ( in @ SY3492 @ ( relation_dom @ SV46 ) ) )
| ( in @ SY3491 @ ( relation_rng @ SV46 ) ) ) )
= $true )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2902]) ).
thf(2914,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2903]) ).
thf(2915,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
= $true )
| ( ( ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2904]) ).
thf(2916,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2905]) ).
thf(2917,plain,
! [SV46: $i,SV331: $i] :
( ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
= $true )
| ( ( ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2906]) ).
thf(2918,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) )
= $true )
| ( ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2907]) ).
thf(2919,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) )
= $true )
| ( ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2908]) ).
thf(2920,plain,
! [SV46: $i,SV331: $i] :
( ( ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
= $false )
| ( ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
= $false )
| ( ( ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2909]) ).
thf(2921,plain,
! [SV46: $i,SV447: $i,SV375: $i] :
( ( ( ! [SY3991: $i] :
( ( SY3991
!= ( apply @ SV375 @ SV447 ) )
| ~ ( in @ SV447 @ ( relation_rng @ SV46 ) )
| ( SV447
= ( apply @ SV46 @ SY3991 ) ) ) )
= $true )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2910]) ).
thf(2922,plain,
! [SV46: $i,SV448: $i,SV375: $i] :
( ( ( ! [SY3992: $i] :
( ( SY3992
!= ( apply @ SV375 @ SV448 ) )
| ~ ( in @ SV448 @ ( relation_rng @ SV46 ) )
| ( in @ SY3992 @ ( relation_dom @ SV46 ) ) ) )
= $true )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2911]) ).
thf(2923,plain,
! [SV375: $i,SV46: $i,SV449: $i] :
( ( ( ! [SY3993: $i] :
( ( SV449
!= ( apply @ SV46 @ SY3993 ) )
| ~ ( in @ SY3993 @ ( relation_dom @ SV46 ) )
| ( SY3993
= ( apply @ SV375 @ SV449 ) ) ) )
= $true )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2912]) ).
thf(2924,plain,
! [SV375: $i,SV46: $i,SV450: $i] :
( ( ( ! [SY3994: $i] :
( ( SV450
!= ( apply @ SV46 @ SY3994 ) )
| ~ ( in @ SY3994 @ ( relation_dom @ SV46 ) ) )
| ( in @ SV450 @ ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2913]) ).
thf(2925,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2914]) ).
thf(2926,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2914]) ).
thf(2927,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) )
= $true )
| ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2915]) ).
thf(2928,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2916]) ).
thf(2929,plain,
! [SV46: $i,SV331: $i] :
( ( ( ~ ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2916]) ).
thf(2930,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) )
= $true )
| ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2917]) ).
thf(2931,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) )
= $true )
| ( ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2918]) ).
thf(2932,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( ( sK70_C @ SV331 @ SV46 )
!= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) )
= $true )
| ( ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2919]) ).
thf(2933,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( ( sK71_SY3322 @ SV331 @ SV46 )
!= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) )
= $true )
| ( ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
= $false )
| ( ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
= $false )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2920]) ).
thf(2934,plain,
! [SV46: $i,SV447: $i,SV375: $i,SV451: $i] :
( ( ( ( SV451
!= ( apply @ SV375 @ SV447 ) )
| ~ ( in @ SV447 @ ( relation_rng @ SV46 ) )
| ( SV447
= ( apply @ SV46 @ SV451 ) ) )
= $true )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2921]) ).
thf(2935,plain,
! [SV46: $i,SV448: $i,SV375: $i,SV452: $i] :
( ( ( ( SV452
!= ( apply @ SV375 @ SV448 ) )
| ~ ( in @ SV448 @ ( relation_rng @ SV46 ) )
| ( in @ SV452 @ ( relation_dom @ SV46 ) ) )
= $true )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2922]) ).
thf(2936,plain,
! [SV375: $i,SV453: $i,SV46: $i,SV449: $i] :
( ( ( ( SV449
!= ( apply @ SV46 @ SV453 ) )
| ~ ( in @ SV453 @ ( relation_dom @ SV46 ) )
| ( SV453
= ( apply @ SV375 @ SV449 ) ) )
= $true )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2923]) ).
thf(2937,plain,
! [SV375: $i,SV46: $i,SV450: $i] :
( ( ( ! [SY3994: $i] :
( ( SV450
!= ( apply @ SV46 @ SY3994 ) )
| ~ ( in @ SY3994 @ ( relation_dom @ SV46 ) ) ) )
= $true )
| ( ( in @ SV450 @ ( relation_rng @ SV46 ) )
= $true )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2924]) ).
thf(2938,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2925]) ).
thf(2939,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2926]) ).
thf(2940,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
= $false )
| ( ( ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) )
= $true )
| ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2927]) ).
thf(2941,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2928]) ).
thf(2942,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
| ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2929]) ).
thf(2943,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
= $false )
| ( ( ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) )
= $true )
| ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2930]) ).
thf(2944,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
= $false )
| ( ( ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) )
= $true )
| ( ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2931]) ).
thf(2945,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
= $false )
| ( ( ~ ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) ) )
= $true )
| ( ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2932]) ).
thf(2946,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
= $false )
| ( ( ~ ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) ) )
= $true )
| ( ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
= $false )
| ( ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
= $false )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2933]) ).
thf(2947,plain,
! [SV46: $i,SV447: $i,SV375: $i,SV451: $i] :
( ( ( ( SV451
!= ( apply @ SV375 @ SV447 ) )
| ~ ( in @ SV447 @ ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV447
= ( apply @ SV46 @ SV451 ) )
= $true )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2934]) ).
thf(2948,plain,
! [SV46: $i,SV448: $i,SV375: $i,SV452: $i] :
( ( ( ( SV452
!= ( apply @ SV375 @ SV448 ) )
| ~ ( in @ SV448 @ ( relation_rng @ SV46 ) ) )
= $true )
| ( ( in @ SV452 @ ( relation_dom @ SV46 ) )
= $true )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2935]) ).
thf(2949,plain,
! [SV375: $i,SV453: $i,SV46: $i,SV449: $i] :
( ( ( ( SV449
!= ( apply @ SV46 @ SV453 ) )
| ~ ( in @ SV453 @ ( relation_dom @ SV46 ) ) )
= $true )
| ( ( SV453
= ( apply @ SV375 @ SV449 ) )
= $true )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2936]) ).
thf(2950,plain,
! [SV375: $i,SV454: $i,SV46: $i,SV450: $i] :
( ( ( ( SV450
!= ( apply @ SV46 @ SV454 ) )
| ~ ( in @ SV454 @ ( relation_dom @ SV46 ) ) )
= $true )
| ( ( in @ SV450 @ ( relation_rng @ SV46 ) )
= $true )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2937]) ).
thf(2951,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
= $true )
| ( ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2938]) ).
thf(2952,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
= $true )
| ( ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2939]) ).
thf(2953,plain,
! [SV46: $i,SV331: $i] :
( ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
= $false )
| ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
= $false )
| ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2940]) ).
thf(2954,plain,
! [SV46: $i,SV331: $i] :
( ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
= $true )
| ( ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2941]) ).
thf(2955,plain,
! [SV46: $i,SV331: $i] :
( ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
= $true )
| ( ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2942]) ).
thf(2956,plain,
! [SV46: $i,SV331: $i] :
( ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
= $false )
| ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
= $false )
| ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2943]) ).
thf(2957,plain,
! [SV46: $i,SV331: $i] :
( ( ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
= $false )
| ( ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
= $false )
| ( ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2944]) ).
thf(2958,plain,
! [SV46: $i,SV331: $i] :
( ( ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
= $false )
| ( ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
= $false )
| ( ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
= $true )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2945]) ).
thf(2959,plain,
! [SV46: $i,SV331: $i] :
( ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
= $false )
| ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
= $false )
| ( ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
= $false )
| ( ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
= $false )
| ( ( ( ( relation_dom @ SV331 )
!= ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2946]) ).
thf(2960,plain,
! [SV46: $i,SV447: $i,SV375: $i,SV451: $i] :
( ( ( ( SV451
!= ( apply @ SV375 @ SV447 ) ) )
= $true )
| ( ( ~ ( in @ SV447 @ ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV447
= ( apply @ SV46 @ SV451 ) )
= $true )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2947]) ).
thf(2961,plain,
! [SV46: $i,SV448: $i,SV375: $i,SV452: $i] :
( ( ( ( SV452
!= ( apply @ SV375 @ SV448 ) ) )
= $true )
| ( ( ~ ( in @ SV448 @ ( relation_rng @ SV46 ) ) )
= $true )
| ( ( in @ SV452 @ ( relation_dom @ SV46 ) )
= $true )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2948]) ).
thf(2962,plain,
! [SV375: $i,SV453: $i,SV46: $i,SV449: $i] :
( ( ( ( SV449
!= ( apply @ SV46 @ SV453 ) ) )
= $true )
| ( ( ~ ( in @ SV453 @ ( relation_dom @ SV46 ) ) )
= $true )
| ( ( SV453
= ( apply @ SV375 @ SV449 ) )
= $true )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2949]) ).
thf(2963,plain,
! [SV375: $i,SV454: $i,SV46: $i,SV450: $i] :
( ( ( ( SV450
!= ( apply @ SV46 @ SV454 ) ) )
= $true )
| ( ( ~ ( in @ SV454 @ ( relation_dom @ SV46 ) ) )
= $true )
| ( ( in @ SV450 @ ( relation_rng @ SV46 ) )
= $true )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2950]) ).
thf(2964,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( relation_dom @ SV331 )
= ( relation_rng @ SV46 ) )
= $false )
| ( ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
= $true )
| ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2951]) ).
thf(2965,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( relation_dom @ SV331 )
= ( relation_rng @ SV46 ) )
= $false )
| ( ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
= $true )
| ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2952]) ).
thf(2966,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( relation_dom @ SV331 )
= ( relation_rng @ SV46 ) )
= $false )
| ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
= $true )
| ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
= $false )
| ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
= $false )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2953]) ).
thf(2967,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( relation_dom @ SV331 )
= ( relation_rng @ SV46 ) )
= $false )
| ( ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
= $true )
| ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2954]) ).
thf(2968,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( relation_dom @ SV331 )
= ( relation_rng @ SV46 ) )
= $false )
| ( ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
= $true )
| ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
= $true )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2955]) ).
thf(2969,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( relation_dom @ SV331 )
= ( relation_rng @ SV46 ) )
= $false )
| ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
= $true )
| ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
= $false )
| ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
= $false )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2956]) ).
thf(2970,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( relation_dom @ SV331 )
= ( relation_rng @ SV46 ) )
= $false )
| ( ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
= $true )
| ( ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
= $false )
| ( ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
= $false )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2957]) ).
thf(2971,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( relation_dom @ SV331 )
= ( relation_rng @ SV46 ) )
= $false )
| ( ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
= $true )
| ( ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
= $false )
| ( ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
= $false )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2958]) ).
thf(2972,plain,
! [SV46: $i,SV331: $i] :
( ( ( ( relation_dom @ SV331 )
= ( relation_rng @ SV46 ) )
= $false )
| ( ( in @ ( sK71_SY3322 @ SV331 @ SV46 ) @ ( relation_dom @ SV46 ) )
= $false )
| ( ( ( sK70_C @ SV331 @ SV46 )
= ( apply @ SV46 @ ( sK71_SY3322 @ SV331 @ SV46 ) ) )
= $false )
| ( ( ( sK71_SY3322 @ SV331 @ SV46 )
= ( apply @ SV331 @ ( sK70_C @ SV331 @ SV46 ) ) )
= $false )
| ( ( in @ ( sK70_C @ SV331 @ SV46 ) @ ( relation_rng @ SV46 ) )
= $false )
| ( ( SV331
= ( function_inverse @ SV46 ) )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2959]) ).
thf(2973,plain,
! [SV46: $i,SV447: $i,SV375: $i,SV451: $i] :
( ( ( SV451
= ( apply @ SV375 @ SV447 ) )
= $false )
| ( ( ~ ( in @ SV447 @ ( relation_rng @ SV46 ) ) )
= $true )
| ( ( SV447
= ( apply @ SV46 @ SV451 ) )
= $true )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2960]) ).
thf(2974,plain,
! [SV46: $i,SV448: $i,SV375: $i,SV452: $i] :
( ( ( SV452
= ( apply @ SV375 @ SV448 ) )
= $false )
| ( ( ~ ( in @ SV448 @ ( relation_rng @ SV46 ) ) )
= $true )
| ( ( in @ SV452 @ ( relation_dom @ SV46 ) )
= $true )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2961]) ).
thf(2975,plain,
! [SV375: $i,SV453: $i,SV46: $i,SV449: $i] :
( ( ( SV449
= ( apply @ SV46 @ SV453 ) )
= $false )
| ( ( ~ ( in @ SV453 @ ( relation_dom @ SV46 ) ) )
= $true )
| ( ( SV453
= ( apply @ SV375 @ SV449 ) )
= $true )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2962]) ).
thf(2976,plain,
! [SV375: $i,SV454: $i,SV46: $i,SV450: $i] :
( ( ( SV450
= ( apply @ SV46 @ SV454 ) )
= $false )
| ( ( ~ ( in @ SV454 @ ( relation_dom @ SV46 ) ) )
= $true )
| ( ( in @ SV450 @ ( relation_rng @ SV46 ) )
= $true )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2963]) ).
thf(2977,plain,
! [SV375: $i,SV451: $i,SV46: $i,SV447: $i] :
( ( ( in @ SV447 @ ( relation_rng @ SV46 ) )
= $false )
| ( ( SV451
= ( apply @ SV375 @ SV447 ) )
= $false )
| ( ( SV447
= ( apply @ SV46 @ SV451 ) )
= $true )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2973]) ).
thf(2978,plain,
! [SV375: $i,SV452: $i,SV46: $i,SV448: $i] :
( ( ( in @ SV448 @ ( relation_rng @ SV46 ) )
= $false )
| ( ( SV452
= ( apply @ SV375 @ SV448 ) )
= $false )
| ( ( in @ SV452 @ ( relation_dom @ SV46 ) )
= $true )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2974]) ).
thf(2979,plain,
! [SV375: $i,SV449: $i,SV46: $i,SV453: $i] :
( ( ( in @ SV453 @ ( relation_dom @ SV46 ) )
= $false )
| ( ( SV449
= ( apply @ SV46 @ SV453 ) )
= $false )
| ( ( SV453
= ( apply @ SV375 @ SV449 ) )
= $true )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2975]) ).
thf(2980,plain,
! [SV375: $i,SV450: $i,SV46: $i,SV454: $i] :
( ( ( in @ SV454 @ ( relation_dom @ SV46 ) )
= $false )
| ( ( SV450
= ( apply @ SV46 @ SV454 ) )
= $false )
| ( ( in @ SV450 @ ( relation_rng @ SV46 ) )
= $true )
| ( ( SV375
= ( function_inverse @ SV46 ) )
= $false )
| ( ( function @ SV375 )
= $false )
| ( ( relation @ SV375 )
= $false )
| ( ( one_to_one @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2976]) ).
thf(2981,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[584,2980,2979,2978,2977,2972,2971,2970,2969,2968,2967,2966,2965,2964,2891,2890,2889,2882,2881,2869,2868,2865,2858,2857,2854,2853,2852,2850,2849,2848,2841,2840,2837,2836,2833,2832,2828,2827,2826,2825,2822,2821,2820,2819,2816,2815,2814,2811,2810,2808,2804,2803,2802,2799,2798,2782,2781,2774,2770,2767,2766,2753,2752,2747,2746,2742,2741,2740,2739,2738,2737,2736,2728,2724,2723,2715,2711,2710,2704,2703,2702,2701,2691,2687,2684,2679,2675,2674,2669,2665,2662,2659,2658,2654,2653,2651,2650,2649,2646,2645,2638,2637,2634,2633,2630,2629,2628,2619,2616,2615,2604,2593,2590,2561,2560,2557,2556,2549,2548,2547,2544,2538,2537,2527,2514,2513,2502,2501,2500,2499,2491,2490,2480,2479,2478,2470,2469,2465,2464,2456,2444,2439,2438,2434,2425,2416,2415,2411,2402,2399,2395,2385,2384,2382,2379,2378,2370,2368,2359,2358,2354,2320,2315,2309,2291,2290,2286,2285,2274,2265,2264,2258,2247,2243,2232,2203,2193,2180,2179,2140,2133,2129,2119,2118,2113,2111,2110,2100,2099,2098,2097,2082,2061,2060,2056,2055,2040,2039,2025,2007,2006,1997,1978,1977,1976,1973,1971,1970,1964,1951,1947,1917,1906,1896,1857,1853,1852,1839,1838,1831,1830,1772,1771,1715,1705,1692,1675,1673,1671,1667,1666,1644,1643,1631,1630,1561,1544,1511,1508,1507,1506,1505,1462,1441,1430,1426,1407,1377,1374,1372,1369,1368,1349,1339,1338,1322,1280,1244,1236,1216,1196,1117,1107,1047,994,991,990,980,880,878,875,872,870,867,863,751,668,591]) ).
thf(2982,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2981]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU230+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n005.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 Jun 20 11:55:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.21/0.44 .......
% 0.42/0.56
% 0.42/0.56 No.of.Axioms: 254
% 0.42/0.56
% 0.42/0.56 Length.of.Defs: 0
% 0.42/0.56
% 0.42/0.56 Contains.Choice.Funs: false
% 0.42/0.62 ...............
% 0.53/0.68 (rf:2,axioms:168,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:256,loop_count:0,foatp_calls:0,translation:fof_full)..................................................................................................................................................................................................................................eprover: CPU time limit exceeded, terminating
% 74.53/74.78 ..................ignored arguments false
% 75.64/75.86 .......
% 75.69/75.91 (rf:0,axioms:254,ps:0,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:256,loop_count:0,foatp_calls:0,translation:fof_full)...............................................................................................................................................................................................................................................................................................................................................eprover: CPU time limit exceeded, terminating
% 150.46/150.81 ............................
% 150.66/150.98 (rf:2,axioms:168,ps:0,u:1,ude:true,rLeibEQ:false,rAndEQ:false,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:256,loop_count:0,foatp_calls:0,translation:fof_full)...................................................................................................................................................................................................................................eprover: CPU time limit exceeded, terminating
% 225.21/225.60 ...................
% 225.37/225.76 (rf:-1,axioms:83,ps:0,u:1,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:256,loop_count:0,foatp_calls:0,translation:fof_full)..................................................................................................................................................................................................................................................................
% 235.02/235.46
% 235.02/235.46 ********************************
% 235.02/235.46 * All subproblems solved! *
% 235.02/235.46 ********************************
% 235.02/235.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:-1,axioms:83,ps:0,u:1,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:72,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2981,loop_count:0,foatp_calls:1,translation:fof_full)
% 239.86/240.28
% 239.86/240.28 %**** Beginning of derivation protocol ****
% 239.86/240.28 % SZS output start CNFRefutation
% See solution above
% 239.86/240.29
% 239.86/240.29 %**** End of derivation protocol ****
% 239.86/240.29 %**** no. of clauses in derivation: 2811 ****
% 239.86/240.29 %**** clause counter: 2981 ****
% 239.86/240.29
% 239.86/240.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:-1,axioms:83,ps:0,u:1,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:72,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2981,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------