TSTP Solution File: SEU221+2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU221+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 : n015.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 12:08:30 EDT 2022
% Result : Theorem 226.71s 227.02s
% Output : CNFRefutation 228.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 175
% Syntax : Number of formulae : 2099 ( 722 unt; 87 typ; 0 def)
% Number of atoms : 22833 (7860 equ; 0 cnn)
% Maximal formula atoms : 15 ( 11 avg)
% Number of connectives : 51930 (8294 ~;9162 |; 405 &;33763 @)
% ( 70 <=>; 236 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 160 ( 160 >; 0 *; 0 +; 0 <<)
% Number of symbols : 90 ( 87 usr; 10 con; 0-5 aty)
% Number of variables : 6288 ( 0 ^6262 !; 26 ?;6288 :)
% 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_SY3107,type,
sK10_SY3107: $i > $i > $i > $i ).
thf(tp_sK11_SY3111,type,
sK11_SY3111: $i > $i > $i > $i ).
thf(tp_sK12_B,type,
sK12_B: $i > $i ).
thf(tp_sK13_SY3112,type,
sK13_SY3112: $i > $i ).
thf(tp_sK14_C,type,
sK14_C: $i > $i > $i ).
thf(tp_sK15_SY3113,type,
sK15_SY3113: $i > $i > $i ).
thf(tp_sK16_D,type,
sK16_D: $i > $i > $i > $i ).
thf(tp_sK17_C,type,
sK17_C: $i > $i > $i ).
thf(tp_sK18_SY3115,type,
sK18_SY3115: $i > $i > $i ).
thf(tp_sK19_D,type,
sK19_D: $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_C,type,
sK20_C: $i > $i > $i ).
thf(tp_sK21_SY3117,type,
sK21_SY3117: $i > $i > $i ).
thf(tp_sK22_C,type,
sK22_C: $i > $i > $i ).
thf(tp_sK23_SY3118,type,
sK23_SY3118: $i > $i > $i ).
thf(tp_sK24_C,type,
sK24_C: $i > $i > $i ).
thf(tp_sK25_SY3119,type,
sK25_SY3119: $i > $i > $i ).
thf(tp_sK26_C,type,
sK26_C: $i > $i > $i ).
thf(tp_sK27_SY3120,type,
sK27_SY3120: $i > $i > $i ).
thf(tp_sK28_B,type,
sK28_B: $i > $i ).
thf(tp_sK29_E,type,
sK29_E: $i > $i > $i > $i > $i ).
thf(tp_sK2_A,type,
sK2_A: $i ).
thf(tp_sK30_D,type,
sK30_D: $i > $i > $i > $i ).
thf(tp_sK31_SY3124,type,
sK31_SY3124: $i > $i > $i > $i ).
thf(tp_sK32_E,type,
sK32_E: $i > $i > $i > $i > $i ).
thf(tp_sK33_D,type,
sK33_D: $i > $i > $i > $i ).
thf(tp_sK34_SY3126,type,
sK34_SY3126: $i > $i > $i > $i ).
thf(tp_sK35_D,type,
sK35_D: $i > $i > $i > $i ).
thf(tp_sK36_SY3127,type,
sK36_SY3127: $i > $i > $i > $i ).
thf(tp_sK37_D,type,
sK37_D: $i > $i > $i > $i ).
thf(tp_sK38_SY3128,type,
sK38_SY3128: $i > $i > $i > $i ).
thf(tp_sK39_C,type,
sK39_C: $i > $i > $i ).
thf(tp_sK3_A,type,
sK3_A: $i ).
thf(tp_sK40_SY3129,type,
sK40_SY3129: $i > $i > $i ).
thf(tp_sK41_B,type,
sK41_B: $i > $i ).
thf(tp_sK42_SY3130,type,
sK42_SY3130: $i > $i ).
thf(tp_sK43_C,type,
sK43_C: $i > $i > $i ).
thf(tp_sK44_SY3131,type,
sK44_SY3131: $i > $i > $i ).
thf(tp_sK45_C,type,
sK45_C: $i > $i > $i ).
thf(tp_sK46_D,type,
sK46_D: $i > $i > $i > $i ).
thf(tp_sK47_D,type,
sK47_D: $i > $i > $i > $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_sK6_A,type,
sK6_A: $i ).
thf(tp_sK7_A,type,
sK7_A: $i ).
thf(tp_sK8_F,type,
sK8_F: $i > $i > $i > $i > $i > $i ).
thf(tp_sK9_D,type,
sK9_D: $i > $i > $i > $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(tp_set_meet,type,
set_meet: $i > $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subset_complement,type,
subset_complement: $i > $i > $i ).
thf(tp_subset_difference,type,
subset_difference: $i > $i > $i > $i ).
thf(tp_union,type,
union: $i > $i ).
thf(tp_union_of_subsets,type,
union_of_subsets: $i > $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(20,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(21,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(24,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(25,axiom,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(28,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(29,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(32,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ A @ B ) )
& ( relation @ ( relation_composition @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_relat_1) ).
thf(37,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(38,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(39,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(40,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(42,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(45,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) )
=> ( ( relation @ ( relation_inverse @ A ) )
& ( function @ ( relation_inverse @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_funct_1) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_relat_1) ).
thf(49,axiom,
! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_relat_1) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_composition @ A @ B ) )
& ( function @ ( relation_composition @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
thf(55,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(56,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_inverse @ A ) )
& ( relation @ ( relation_inverse @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_relat_1) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ B @ A ) )
& ( relation @ ( relation_composition @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_relat_1) ).
thf(61,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
thf(66,axiom,
! [A: $i] : ( relation @ ( identity_relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(71,axiom,
! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(81,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( function_inverse @ A ) )
& ( function @ ( function_inverse @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
thf(89,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( ( function_inverse @ A )
= ( relation_inverse @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_funct_1) ).
thf(92,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_composition @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_1) ).
thf(93,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/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
thf(95,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/sandbox2/benchmark/theBenchmark.p',d7_relat_1) ).
thf(96,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_1) ).
thf(99,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/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
thf(103,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/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
thf(104,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/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
thf(107,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/sandbox2/benchmark/theBenchmark.p',d3_relat_1) ).
thf(112,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/sandbox2/benchmark/theBenchmark.p',d2_relat_1) ).
thf(117,axiom,
! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
thf(118,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/sandbox2/benchmark/theBenchmark.p',d14_relat_1) ).
thf(119,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/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
thf(120,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/sandbox2/benchmark/theBenchmark.p',d12_relat_1) ).
thf(121,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/sandbox2/benchmark/theBenchmark.p',d11_relat_1) ).
thf(123,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/sandbox2/benchmark/theBenchmark.p',d10_relat_1) ).
thf(127,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(128,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(129,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(134,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_relat_1) ).
thf(135,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_dom_restriction @ B @ A )
= ( relation_composition @ ( identity_relation @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_relat_1) ).
thf(137,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_dom @ ( relation_dom_restriction @ B @ A ) )
= ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_relat_1) ).
thf(140,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/sandbox2/benchmark/theBenchmark.p',t8_funct_1) ).
thf(141,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_relat_1) ).
thf(142,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/sandbox2/benchmark/theBenchmark.p',t86_relat_1) ).
thf(145,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/sandbox2/benchmark/theBenchmark.p',t74_relat_1) ).
thf(150,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_dom @ A )
= empty_set )
<=> ( ( relation_rng @ A )
= empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_relat_1) ).
thf(151,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_relat_1) ).
thf(155,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/sandbox2/benchmark/theBenchmark.p',t57_funct_1) ).
thf(156,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_relat_1) ).
thf(157,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( function_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( function_inverse @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).
thf(159,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/sandbox2/benchmark/theBenchmark.p',t54_funct_1) ).
thf(165,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_rng @ B ) )
=> ( ( relation_rng @ ( relation_composition @ B @ A ) )
= ( relation_rng @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_relat_1) ).
thf(168,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_rng @ A ) @ ( relation_dom @ B ) )
=> ( ( relation_dom @ ( relation_composition @ A @ B ) )
= ( relation_dom @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_relat_1) ).
thf(170,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_relat_1) ).
thf(171,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_relat_1) ).
thf(181,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_relat_1) ).
thf(184,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/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).
thf(187,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/sandbox2/benchmark/theBenchmark.p',t30_relat_1) ).
thf(191,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) )
& ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relat_1) ).
thf(192,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/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).
thf(193,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/sandbox2/benchmark/theBenchmark.p',t22_funct_1) ).
thf(194,axiom,
! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relat_1) ).
thf(195,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/sandbox2/benchmark/theBenchmark.p',t21_funct_1) ).
thf(196,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/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).
thf(201,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( subset @ A @ B )
=> ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t178_relat_1) ).
thf(202,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ~ ( ( A != empty_set )
& ( subset @ A @ ( relation_rng @ B ) )
& ( ( relation_inverse_image @ B @ A )
= empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t174_relat_1) ).
thf(203,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t167_relat_1) ).
thf(204,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/sandbox2/benchmark/theBenchmark.p',t166_relat_1) ).
thf(205,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( relation_rng @ ( relation_composition @ A @ B ) )
= ( relation_image @ B @ ( relation_rng @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t160_relat_1) ).
thf(206,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_relat_1) ).
thf(207,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_image @ B @ A )
= ( relation_image @ B @ ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_relat_1) ).
thf(208,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_relat_1) ).
thf(209,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/sandbox2/benchmark/theBenchmark.p',t143_relat_1) ).
thf(210,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( relation_dom_restriction @ ( relation_rng_restriction @ A @ C ) @ B )
= ( relation_rng_restriction @ A @ ( relation_dom_restriction @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t140_relat_1) ).
thf(214,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_rng @ ( relation_rng_restriction @ A @ B ) )
= ( set_intersection2 @ ( relation_rng @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_relat_1) ).
thf(216,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_relat_1) ).
thf(217,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_relat_1) ).
thf(218,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_relat_1) ).
thf(219,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/sandbox2/benchmark/theBenchmark.p',t115_relat_1) ).
thf(234,conjecture,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( one_to_one @ ( function_inverse @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_funct_1) ).
thf(235,negated_conjecture,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( one_to_one @ ( function_inverse @ A ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[234]) ).
thf(236,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( one_to_one @ ( function_inverse @ A ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[235]) ).
thf(237,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(238,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(239,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(240,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(241,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(242,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(243,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(244,plain,
( ( ! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ A @ B ) )
& ( relation @ ( relation_composition @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(245,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(246,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(247,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(248,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(249,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(250,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) )
=> ( ( relation @ ( relation_inverse @ A ) )
& ( function @ ( relation_inverse @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(251,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(252,plain,
( ( ! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(253,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(254,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_composition @ A @ B ) )
& ( function @ ( relation_composition @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(255,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(256,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_inverse @ A ) )
& ( relation @ ( relation_inverse @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(257,plain,
( ( ! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ B @ A ) )
& ( relation @ ( relation_composition @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(258,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(259,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(260,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(261,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(262,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(263,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( function_inverse @ A ) )
& ( function @ ( function_inverse @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(264,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( ( function_inverse @ A )
= ( relation_inverse @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(265,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_composition @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(266,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)],[93]) ).
thf(267,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)],[95]) ).
thf(268,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(269,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)],[99]) ).
thf(270,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)],[103]) ).
thf(271,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)],[104]) ).
thf(272,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)],[107]) ).
thf(273,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)],[112]) ).
thf(274,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)],[117]) ).
thf(275,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)],[118]) ).
thf(276,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)],[119]) ).
thf(277,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)],[120]) ).
thf(278,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)],[121]) ).
thf(279,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)],[123]) ).
thf(280,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(281,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(282,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(283,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(284,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_dom_restriction @ B @ A )
= ( relation_composition @ ( identity_relation @ A ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(285,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_dom @ ( relation_dom_restriction @ B @ A ) )
= ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(286,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)],[140]) ).
thf(287,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(288,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)],[142]) ).
thf(289,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)],[145]) ).
thf(290,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_dom @ A )
= empty_set )
<=> ( ( relation_rng @ A )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(291,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
=> ( A = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(292,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)],[155]) ).
thf(293,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(294,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( function_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( function_inverse @ A ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(295,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)],[159]) ).
thf(296,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_rng @ B ) )
=> ( ( relation_rng @ ( relation_composition @ B @ A ) )
= ( relation_rng @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(297,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_rng @ A ) @ ( relation_dom @ B ) )
=> ( ( relation_dom @ ( relation_composition @ A @ B ) )
= ( relation_dom @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(298,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(299,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(300,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(301,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)],[184]) ).
thf(302,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)],[187]) ).
thf(303,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) )
& ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(304,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)],[192]) ).
thf(305,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)],[193]) ).
thf(306,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(307,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)],[195]) ).
thf(308,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)],[196]) ).
thf(309,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( subset @ A @ B )
=> ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(310,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ~ ( ( A != empty_set )
& ( subset @ A @ ( relation_rng @ B ) )
& ( ( relation_inverse_image @ B @ A )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(311,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(312,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)],[204]) ).
thf(313,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( relation_rng @ ( relation_composition @ A @ B ) )
= ( relation_image @ B @ ( relation_rng @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(314,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(315,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_image @ B @ A )
= ( relation_image @ B @ ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(316,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(317,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)],[209]) ).
thf(318,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( relation_dom_restriction @ ( relation_rng_restriction @ A @ C ) @ B )
= ( relation_rng_restriction @ A @ ( relation_dom_restriction @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(319,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_rng @ ( relation_rng_restriction @ A @ B ) )
= ( set_intersection2 @ ( relation_rng @ B ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(320,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(321,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(322,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(323,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)],[219]) ).
thf(324,plain,
( ( ( ( relation @ sK1_A )
& ( function @ sK1_A ) )
=> ( ( one_to_one @ sK1_A )
=> ( one_to_one @ ( function_inverse @ sK1_A ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[236]) ).
thf(325,plain,
( ( relation @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[324]) ).
thf(326,plain,
( ( function @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[324]) ).
thf(327,plain,
( ( one_to_one @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[324]) ).
thf(328,plain,
( ( one_to_one @ ( function_inverse @ sK1_A ) )
= $false ),
inference(standard_cnf,[status(thm)],[324]) ).
thf(329,plain,
( ( ~ ( one_to_one @ ( function_inverse @ sK1_A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[328]) ).
thf(330,plain,
( ( ( relation @ sK2_A )
& ( relation_empty_yielding @ sK2_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[237]) ).
thf(331,plain,
( ( ( function @ sK3_A )
& ( relation @ sK3_A )
& ( one_to_one @ sK3_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[238]) ).
thf(332,plain,
( ( ~ ( empty @ sK4_A )
& ( relation @ sK4_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[239]) ).
thf(333,plain,
( ( ( empty @ sK5_A )
& ( relation @ sK5_A )
& ( function @ sK5_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[240]) ).
thf(334,plain,
( ( ( empty @ sK6_A )
& ( relation @ sK6_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[241]) ).
thf(335,plain,
( ( ( function @ sK7_A )
& ( relation @ sK7_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[242]) ).
thf(336,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[243]) ).
thf(337,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( empty @ ( relation_composition @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[244]) ).
thf(338,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[245]) ).
thf(339,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[246]) ).
thf(340,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[247]) ).
thf(341,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[248]) ).
thf(342,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( function @ ( relation_inverse @ A ) ) )
& ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[250]) ).
thf(343,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[251]) ).
thf(344,plain,
( ( ! [A: $i] : ( function @ ( identity_relation @ A ) )
& ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[252]) ).
thf(345,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[253]) ).
thf(346,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( function @ B )
| ( function @ ( relation_composition @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( function @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[254]) ).
thf(347,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_inverse @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[256]) ).
thf(348,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( empty @ ( relation_composition @ B @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[257]) ).
thf(349,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[258]) ).
thf(350,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[259]) ).
thf(351,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[261]) ).
thf(352,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[262]) ).
thf(353,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( function @ ( function_inverse @ A ) ) )
& ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( relation @ ( function_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[263]) ).
thf(354,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ( function_inverse @ A )
= ( relation_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[264]) ).
thf(355,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ! [SY3110: $i] :
( ~ ( in @ ( ordered_pair @ ( sK9_D @ C @ B @ A ) @ SY3110 ) @ A )
| ~ ( in @ ( ordered_pair @ SY3110 @ ( sK10_SY3107 @ C @ B @ A ) ) @ B ) )
| ~ ( in @ ( ordered_pair @ ( sK9_D @ C @ B @ A ) @ ( sK10_SY3107 @ C @ B @ A ) ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK9_D @ C @ B @ A ) @ ( sK11_SY3111 @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK11_SY3111 @ C @ B @ A ) @ ( sK10_SY3107 @ C @ B @ A ) ) @ B ) )
| ( in @ ( ordered_pair @ ( sK9_D @ C @ B @ A ) @ ( sK10_SY3107 @ 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 @ ( sK8_F @ E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK8_F @ E @ D @ C @ B @ A ) @ E ) @ B ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[265]) ).
thf(356,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ( in @ ( sK12_B @ A ) @ ( relation_dom @ A ) )
& ( in @ ( sK13_SY3112 @ A ) @ ( relation_dom @ A ) )
& ( ( apply @ A @ ( sK12_B @ A ) )
= ( apply @ A @ ( sK13_SY3112 @ A ) ) )
& ( ( sK12_B @ A )
!= ( sK13_SY3112 @ 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)],[266]) ).
thf(357,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK14_C @ B @ A ) @ ( sK15_SY3113 @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK15_SY3113 @ B @ A ) @ ( sK14_C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( sK14_C @ B @ A ) @ ( sK15_SY3113 @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK15_SY3113 @ B @ A ) @ ( sK14_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)],[267]) ).
thf(358,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[268]) ).
thf(359,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY3114: $i] :
~ ( in @ ( ordered_pair @ SY3114 @ ( sK17_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK17_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK18_SY3115 @ B @ A ) @ ( sK17_C @ B @ A ) ) @ A )
| ( in @ ( sK17_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 @ ( sK16_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[269]) ).
thf(360,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY3116: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ B @ A ) @ SY3116 ) @ A )
| ~ ( in @ ( sK20_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK20_C @ B @ A ) @ ( sK21_SY3117 @ B @ A ) ) @ A )
| ( in @ ( sK20_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 @ ( sK19_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[270]) ).
thf(361,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)],[271]) ).
thf(362,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( in @ ( ordered_pair @ ( sK22_C @ B @ A ) @ ( sK23_SY3118 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK22_C @ B @ A ) @ ( sK23_SY3118 @ 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)],[272]) ).
thf(363,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK24_C @ B @ A ) @ ( sK25_SY3119 @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK24_C @ B @ A ) @ ( sK25_SY3119 @ B @ A ) ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK24_C @ B @ A ) @ ( sK25_SY3119 @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK24_C @ B @ A ) @ ( sK25_SY3119 @ 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)],[273]) ).
thf(364,plain,
( ( ! [A: $i] :
( ( ! [SY3121: $i,SY3122: $i] :
( ( sK28_B @ A )
!= ( ordered_pair @ SY3121 @ SY3122 ) )
& ( in @ ( sK28_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK26_C @ B @ A ) @ ( sK27_SY3120 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[274]) ).
thf(365,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY3123: $i] :
( ~ ( in @ ( ordered_pair @ ( sK30_D @ C @ B @ A ) @ SY3123 ) @ A )
| ~ ( in @ SY3123 @ B ) )
| ~ ( in @ ( sK30_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK30_D @ C @ B @ A ) @ ( sK31_SY3124 @ C @ B @ A ) ) @ A )
& ( in @ ( sK31_SY3124 @ C @ B @ A ) @ B ) )
| ( in @ ( sK30_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 @ ( sK29_E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( sK29_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[275]) ).
thf(366,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY3125: $i] :
( ~ ( in @ ( ordered_pair @ SY3125 @ ( sK33_D @ C @ B @ A ) ) @ A )
| ~ ( in @ SY3125 @ B ) )
| ~ ( in @ ( sK33_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK34_SY3126 @ C @ B @ A ) @ ( sK33_D @ C @ B @ A ) ) @ A )
& ( in @ ( sK34_SY3126 @ C @ B @ A ) @ B ) )
| ( in @ ( sK33_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 @ ( sK32_E @ D @ C @ B @ A ) @ D ) @ A )
& ( in @ ( sK32_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[276]) ).
thf(367,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK36_SY3127 @ C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ C @ B @ A ) @ ( sK36_SY3127 @ C @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ C @ B @ A ) @ ( sK36_SY3127 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK36_SY3127 @ C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK35_D @ C @ B @ A ) @ ( sK36_SY3127 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK35_D @ C @ B @ A ) @ ( sK36_SY3127 @ C @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK35_D @ C @ B @ A ) @ ( sK36_SY3127 @ 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)],[277]) ).
thf(368,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK37_D @ C @ B @ A ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ C @ B @ A ) @ ( sK38_SY3128 @ C @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ C @ B @ A ) @ ( sK38_SY3128 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK37_D @ C @ B @ A ) @ B )
| ( in @ ( ordered_pair @ ( sK37_D @ C @ B @ A ) @ ( sK38_SY3128 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK37_D @ C @ B @ A ) @ ( sK38_SY3128 @ C @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK37_D @ C @ B @ A ) @ ( sK38_SY3128 @ 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)],[278]) ).
thf(369,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( ( ( sK39_C @ B @ A )
!= ( sK40_SY3129 @ B @ A ) )
| ~ ( in @ ( sK39_C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK39_C @ B @ A ) @ ( sK40_SY3129 @ B @ A ) ) @ B ) )
& ( ( ( sK39_C @ B @ A )
= ( sK40_SY3129 @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK39_C @ B @ A ) @ ( sK40_SY3129 @ B @ A ) ) @ B ) )
& ( ( in @ ( sK39_C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK39_C @ B @ A ) @ ( sK40_SY3129 @ 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)],[279]) ).
thf(370,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( function @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( one_to_one @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[280]) ).
thf(371,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[281]) ).
thf(372,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[282]) ).
thf(373,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[283]) ).
thf(374,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( relation_dom_restriction @ B @ A )
= ( relation_composition @ ( identity_relation @ A ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[284]) ).
thf(375,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( relation_dom @ ( relation_dom_restriction @ B @ A ) )
= ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[285]) ).
thf(376,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)],[286]) ).
thf(377,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[287]) ).
thf(378,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)],[288]) ).
thf(379,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)],[289]) ).
thf(380,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_dom @ A )
!= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_rng @ A )
!= empty_set )
| ( ( relation_dom @ A )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[290]) ).
thf(381,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_dom @ A )
!= empty_set )
| ( A = empty_set ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_rng @ A )
!= empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[291]) ).
thf(382,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)],[292]) ).
thf(383,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK41_B @ A ) @ ( sK42_SY3130 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[293]) ).
thf(384,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ( relation_rng @ A )
= ( relation_dom @ ( function_inverse @ A ) ) ) )
& ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ( relation_dom @ A )
= ( relation_rng @ ( function_inverse @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[294]) ).
thf(385,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ! [B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ( ( ( sK44_SY3131 @ B @ A )
= ( apply @ B @ ( sK43_C @ B @ A ) ) )
| ( ( sK43_C @ B @ A )
= ( apply @ A @ ( sK44_SY3131 @ B @ A ) ) ) )
& ( ( ( sK44_SY3131 @ B @ A )
= ( apply @ B @ ( sK43_C @ B @ A ) ) )
| ( in @ ( sK44_SY3131 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( ( sK44_SY3131 @ B @ A )
= ( apply @ B @ ( sK43_C @ B @ A ) ) )
| ( ( sK44_SY3131 @ B @ A )
!= ( apply @ B @ ( sK43_C @ B @ A ) ) )
| ~ ( in @ ( sK43_C @ B @ A ) @ ( relation_rng @ A ) ) )
& ( ( in @ ( sK43_C @ B @ A ) @ ( relation_rng @ A ) )
| ( ( sK43_C @ B @ A )
= ( apply @ A @ ( sK44_SY3131 @ B @ A ) ) ) )
& ( ( in @ ( sK43_C @ B @ A ) @ ( relation_rng @ A ) )
| ( in @ ( sK44_SY3131 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( in @ ( sK43_C @ B @ A ) @ ( relation_rng @ A ) )
| ( ( sK44_SY3131 @ B @ A )
!= ( apply @ B @ ( sK43_C @ B @ A ) ) )
| ~ ( in @ ( sK43_C @ B @ A ) @ ( relation_rng @ A ) ) )
& ( ( ( sK43_C @ B @ A )
!= ( apply @ A @ ( sK44_SY3131 @ B @ A ) ) )
| ~ ( in @ ( sK44_SY3131 @ B @ A ) @ ( relation_dom @ A ) )
| ( ( sK43_C @ B @ A )
= ( apply @ A @ ( sK44_SY3131 @ B @ A ) ) ) )
& ( ( ( sK43_C @ B @ A )
!= ( apply @ A @ ( sK44_SY3131 @ B @ A ) ) )
| ~ ( in @ ( sK44_SY3131 @ B @ A ) @ ( relation_dom @ A ) )
| ( in @ ( sK44_SY3131 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( ( sK43_C @ B @ A )
!= ( apply @ A @ ( sK44_SY3131 @ B @ A ) ) )
| ~ ( in @ ( sK44_SY3131 @ B @ A ) @ ( relation_dom @ A ) )
| ( ( sK44_SY3131 @ B @ A )
!= ( apply @ B @ ( sK43_C @ B @ A ) ) )
| ~ ( in @ ( sK43_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)],[295]) ).
thf(386,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ ( relation_dom @ A ) @ ( relation_rng @ B ) )
| ( ( relation_rng @ ( relation_composition @ B @ A ) )
= ( relation_rng @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[296]) ).
thf(387,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ ( relation_rng @ A ) @ ( relation_dom @ B ) )
| ( ( relation_dom @ ( relation_composition @ A @ B ) )
= ( relation_dom @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[297]) ).
thf(388,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[298]) ).
thf(389,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[299]) ).
thf(390,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[300]) ).
thf(391,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ( in @ ( sK45_C @ B @ A ) @ A )
& ( ( apply @ B @ ( sK45_C @ B @ A ) )
!= ( sK45_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)],[301]) ).
thf(392,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)],[302]) ).
thf(393,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[303]) ).
thf(394,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)],[304]) ).
thf(395,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)],[305]) ).
thf(396,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[306]) ).
thf(397,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)],[307]) ).
thf(398,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)],[308]) ).
thf(399,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[309]) ).
thf(400,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( A = empty_set )
| ~ ( subset @ A @ ( relation_rng @ B ) )
| ( ( relation_inverse_image @ B @ A )
!= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[310]) ).
thf(401,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[311]) ).
thf(402,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 @ ( sK46_D @ C @ B @ A ) @ ( relation_rng @ C ) )
& ( in @ ( ordered_pair @ A @ ( sK46_D @ C @ B @ A ) ) @ C )
& ( in @ ( sK46_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[312]) ).
thf(403,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ( relation_rng @ ( relation_composition @ A @ B ) )
= ( relation_image @ B @ ( relation_rng @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[313]) ).
thf(404,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[314]) ).
thf(405,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( relation_image @ B @ A )
= ( relation_image @ B @ ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[315]) ).
thf(406,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[316]) ).
thf(407,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 @ ( sK47_D @ C @ B @ A ) @ ( relation_dom @ C ) )
& ( in @ ( ordered_pair @ ( sK47_D @ C @ B @ A ) @ A ) @ C )
& ( in @ ( sK47_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[317]) ).
thf(408,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation @ C )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ A @ C ) @ B )
= ( relation_rng_restriction @ A @ ( relation_dom_restriction @ C @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[318]) ).
thf(409,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( relation_rng @ ( relation_rng_restriction @ A @ B ) )
= ( set_intersection2 @ ( relation_rng @ B ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[319]) ).
thf(410,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[320]) ).
thf(411,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[321]) ).
thf(412,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[322]) ).
thf(413,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)],[323]) ).
thf(414,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)],[413]) ).
thf(415,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(416,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(417,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(418,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( relation_rng @ ( relation_rng_restriction @ A @ B ) )
= ( set_intersection2 @ ( relation_rng @ B ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(419,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation @ C )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ A @ C ) @ B )
= ( relation_rng_restriction @ A @ ( relation_dom_restriction @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(420,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 @ ( sK47_D @ C @ B @ A ) @ ( relation_dom @ C ) )
& ( in @ ( ordered_pair @ ( sK47_D @ C @ B @ A ) @ A ) @ C )
& ( in @ ( sK47_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(421,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[406]) ).
thf(422,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( relation_image @ B @ A )
= ( relation_image @ B @ ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(423,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(424,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ( relation_rng @ ( relation_composition @ A @ B ) )
= ( relation_image @ B @ ( relation_rng @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(425,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 @ ( sK46_D @ C @ B @ A ) @ ( relation_rng @ C ) )
& ( in @ ( ordered_pair @ A @ ( sK46_D @ C @ B @ A ) ) @ C )
& ( in @ ( sK46_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(426,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[401]) ).
thf(427,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( A = empty_set )
| ~ ( subset @ A @ ( relation_rng @ B ) )
| ( ( relation_inverse_image @ B @ A )
!= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[400]) ).
thf(428,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[399]) ).
thf(429,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)],[398]) ).
thf(430,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)],[397]) ).
thf(431,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(432,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)],[395]) ).
thf(433,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)],[394]) ).
thf(434,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[393]) ).
thf(435,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)],[392]) ).
thf(436,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ( in @ ( sK45_C @ B @ A ) @ A )
& ( ( apply @ B @ ( sK45_C @ B @ A ) )
!= ( sK45_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)],[391]) ).
thf(437,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[390]) ).
thf(438,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(439,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[388]) ).
thf(440,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ ( relation_rng @ A ) @ ( relation_dom @ B ) )
| ( ( relation_dom @ ( relation_composition @ A @ B ) )
= ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[387]) ).
thf(441,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ ( relation_dom @ A ) @ ( relation_rng @ B ) )
| ( ( relation_rng @ ( relation_composition @ B @ A ) )
= ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[386]) ).
thf(442,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ! [B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ( ( ( sK44_SY3131 @ B @ A )
= ( apply @ B @ ( sK43_C @ B @ A ) ) )
| ( ( sK43_C @ B @ A )
= ( apply @ A @ ( sK44_SY3131 @ B @ A ) ) ) )
& ( ( ( sK44_SY3131 @ B @ A )
= ( apply @ B @ ( sK43_C @ B @ A ) ) )
| ( in @ ( sK44_SY3131 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( ( sK44_SY3131 @ B @ A )
= ( apply @ B @ ( sK43_C @ B @ A ) ) )
| ( ( sK44_SY3131 @ B @ A )
!= ( apply @ B @ ( sK43_C @ B @ A ) ) )
| ~ ( in @ ( sK43_C @ B @ A ) @ ( relation_rng @ A ) ) )
& ( ( in @ ( sK43_C @ B @ A ) @ ( relation_rng @ A ) )
| ( ( sK43_C @ B @ A )
= ( apply @ A @ ( sK44_SY3131 @ B @ A ) ) ) )
& ( ( in @ ( sK43_C @ B @ A ) @ ( relation_rng @ A ) )
| ( in @ ( sK44_SY3131 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( in @ ( sK43_C @ B @ A ) @ ( relation_rng @ A ) )
| ( ( sK44_SY3131 @ B @ A )
!= ( apply @ B @ ( sK43_C @ B @ A ) ) )
| ~ ( in @ ( sK43_C @ B @ A ) @ ( relation_rng @ A ) ) )
& ( ( ( sK43_C @ B @ A )
!= ( apply @ A @ ( sK44_SY3131 @ B @ A ) ) )
| ~ ( in @ ( sK44_SY3131 @ B @ A ) @ ( relation_dom @ A ) )
| ( ( sK43_C @ B @ A )
= ( apply @ A @ ( sK44_SY3131 @ B @ A ) ) ) )
& ( ( ( sK43_C @ B @ A )
!= ( apply @ A @ ( sK44_SY3131 @ B @ A ) ) )
| ~ ( in @ ( sK44_SY3131 @ B @ A ) @ ( relation_dom @ A ) )
| ( in @ ( sK44_SY3131 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( ( sK43_C @ B @ A )
!= ( apply @ A @ ( sK44_SY3131 @ B @ A ) ) )
| ~ ( in @ ( sK44_SY3131 @ B @ A ) @ ( relation_dom @ A ) )
| ( ( sK44_SY3131 @ B @ A )
!= ( apply @ B @ ( sK43_C @ B @ A ) ) )
| ~ ( in @ ( sK43_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)],[385]) ).
thf(443,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ( relation_rng @ A )
= ( relation_dom @ ( function_inverse @ A ) ) ) )
& ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ( relation_dom @ A )
= ( relation_rng @ ( function_inverse @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[384]) ).
thf(444,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK41_B @ A ) @ ( sK42_SY3130 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(445,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)],[382]) ).
thf(446,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_dom @ A )
!= empty_set )
| ( A = empty_set ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_rng @ A )
!= empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[381]) ).
thf(447,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_dom @ A )
!= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_rng @ A )
!= empty_set )
| ( ( relation_dom @ A )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[380]) ).
thf(448,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)],[379]) ).
thf(449,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)],[378]) ).
thf(450,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(451,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)],[376]) ).
thf(452,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( relation_dom @ ( relation_dom_restriction @ B @ A ) )
= ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(453,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( relation_dom_restriction @ B @ A )
= ( relation_composition @ ( identity_relation @ A ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(454,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(455,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(456,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(457,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( function @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( one_to_one @ A ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(458,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( ( ( sK39_C @ B @ A )
!= ( sK40_SY3129 @ B @ A ) )
| ~ ( in @ ( sK39_C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK39_C @ B @ A ) @ ( sK40_SY3129 @ B @ A ) ) @ B ) )
& ( ( ( sK39_C @ B @ A )
= ( sK40_SY3129 @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK39_C @ B @ A ) @ ( sK40_SY3129 @ B @ A ) ) @ B ) )
& ( ( in @ ( sK39_C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK39_C @ B @ A ) @ ( sK40_SY3129 @ 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)],[369]) ).
thf(459,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK37_D @ C @ B @ A ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ C @ B @ A ) @ ( sK38_SY3128 @ C @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ C @ B @ A ) @ ( sK38_SY3128 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK37_D @ C @ B @ A ) @ B )
| ( in @ ( ordered_pair @ ( sK37_D @ C @ B @ A ) @ ( sK38_SY3128 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK37_D @ C @ B @ A ) @ ( sK38_SY3128 @ C @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK37_D @ C @ B @ A ) @ ( sK38_SY3128 @ 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)],[368]) ).
thf(460,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK36_SY3127 @ C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ C @ B @ A ) @ ( sK36_SY3127 @ C @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ C @ B @ A ) @ ( sK36_SY3127 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK36_SY3127 @ C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK35_D @ C @ B @ A ) @ ( sK36_SY3127 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK35_D @ C @ B @ A ) @ ( sK36_SY3127 @ C @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK35_D @ C @ B @ A ) @ ( sK36_SY3127 @ 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)],[367]) ).
thf(461,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY3125: $i] :
( ~ ( in @ ( ordered_pair @ SY3125 @ ( sK33_D @ C @ B @ A ) ) @ A )
| ~ ( in @ SY3125 @ B ) )
| ~ ( in @ ( sK33_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK34_SY3126 @ C @ B @ A ) @ ( sK33_D @ C @ B @ A ) ) @ A )
& ( in @ ( sK34_SY3126 @ C @ B @ A ) @ B ) )
| ( in @ ( sK33_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 @ ( sK32_E @ D @ C @ B @ A ) @ D ) @ A )
& ( in @ ( sK32_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(462,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY3123: $i] :
( ~ ( in @ ( ordered_pair @ ( sK30_D @ C @ B @ A ) @ SY3123 ) @ A )
| ~ ( in @ SY3123 @ B ) )
| ~ ( in @ ( sK30_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK30_D @ C @ B @ A ) @ ( sK31_SY3124 @ C @ B @ A ) ) @ A )
& ( in @ ( sK31_SY3124 @ C @ B @ A ) @ B ) )
| ( in @ ( sK30_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 @ ( sK29_E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( sK29_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(463,plain,
( ( ! [A: $i] :
( ( ! [SY3121: $i,SY3122: $i] :
( ( sK28_B @ A )
!= ( ordered_pair @ SY3121 @ SY3122 ) )
& ( in @ ( sK28_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK26_C @ B @ A ) @ ( sK27_SY3120 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(464,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK24_C @ B @ A ) @ ( sK25_SY3119 @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK24_C @ B @ A ) @ ( sK25_SY3119 @ B @ A ) ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK24_C @ B @ A ) @ ( sK25_SY3119 @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK24_C @ B @ A ) @ ( sK25_SY3119 @ 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)],[363]) ).
thf(465,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( in @ ( ordered_pair @ ( sK22_C @ B @ A ) @ ( sK23_SY3118 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK22_C @ B @ A ) @ ( sK23_SY3118 @ 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)],[362]) ).
thf(466,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)],[361]) ).
thf(467,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY3116: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ B @ A ) @ SY3116 ) @ A )
| ~ ( in @ ( sK20_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK20_C @ B @ A ) @ ( sK21_SY3117 @ B @ A ) ) @ A )
| ( in @ ( sK20_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 @ ( sK19_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(468,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY3114: $i] :
~ ( in @ ( ordered_pair @ SY3114 @ ( sK17_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK17_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK18_SY3115 @ B @ A ) @ ( sK17_C @ B @ A ) ) @ A )
| ( in @ ( sK17_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 @ ( sK16_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(469,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(470,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK14_C @ B @ A ) @ ( sK15_SY3113 @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK15_SY3113 @ B @ A ) @ ( sK14_C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( sK14_C @ B @ A ) @ ( sK15_SY3113 @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK15_SY3113 @ B @ A ) @ ( sK14_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)],[357]) ).
thf(471,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ( in @ ( sK12_B @ A ) @ ( relation_dom @ A ) )
& ( in @ ( sK13_SY3112 @ A ) @ ( relation_dom @ A ) )
& ( ( apply @ A @ ( sK12_B @ A ) )
= ( apply @ A @ ( sK13_SY3112 @ A ) ) )
& ( ( sK12_B @ A )
!= ( sK13_SY3112 @ 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)],[356]) ).
thf(472,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ! [SY3110: $i] :
( ~ ( in @ ( ordered_pair @ ( sK9_D @ C @ B @ A ) @ SY3110 ) @ A )
| ~ ( in @ ( ordered_pair @ SY3110 @ ( sK10_SY3107 @ C @ B @ A ) ) @ B ) )
| ~ ( in @ ( ordered_pair @ ( sK9_D @ C @ B @ A ) @ ( sK10_SY3107 @ C @ B @ A ) ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK9_D @ C @ B @ A ) @ ( sK11_SY3111 @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK11_SY3111 @ C @ B @ A ) @ ( sK10_SY3107 @ C @ B @ A ) ) @ B ) )
| ( in @ ( ordered_pair @ ( sK9_D @ C @ B @ A ) @ ( sK10_SY3107 @ 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 @ ( sK8_F @ E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK8_F @ E @ D @ C @ B @ A ) @ E ) @ B ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[355]) ).
thf(473,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ( function_inverse @ A )
= ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[354]) ).
thf(474,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( function @ ( function_inverse @ A ) ) )
& ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( relation @ ( function_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[353]) ).
thf(475,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[352]) ).
thf(476,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[351]) ).
thf(477,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[260]) ).
thf(478,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[350]) ).
thf(479,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[349]) ).
thf(480,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( empty @ ( relation_composition @ B @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[348]) ).
thf(481,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_inverse @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[347]) ).
thf(482,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[255]) ).
thf(483,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( function @ B )
| ( function @ ( relation_composition @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( function @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[346]) ).
thf(484,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[345]) ).
thf(485,plain,
( ( ! [A: $i] : ( function @ ( identity_relation @ A ) )
& ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[344]) ).
thf(486,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[343]) ).
thf(487,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( function @ ( relation_inverse @ A ) ) )
& ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[342]) ).
thf(488,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[249]) ).
thf(489,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[341]) ).
thf(490,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[340]) ).
thf(491,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[339]) ).
thf(492,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[338]) ).
thf(493,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( empty @ ( relation_composition @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[337]) ).
thf(494,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[336]) ).
thf(495,plain,
( ( ( function @ sK7_A )
& ( relation @ sK7_A ) )
= $true ),
inference(copy,[status(thm)],[335]) ).
thf(496,plain,
( ( ( empty @ sK6_A )
& ( relation @ sK6_A ) )
= $true ),
inference(copy,[status(thm)],[334]) ).
thf(497,plain,
( ( ( empty @ sK5_A )
& ( relation @ sK5_A )
& ( function @ sK5_A ) )
= $true ),
inference(copy,[status(thm)],[333]) ).
thf(498,plain,
( ( ~ ( empty @ sK4_A )
& ( relation @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[332]) ).
thf(499,plain,
( ( ( function @ sK3_A )
& ( relation @ sK3_A )
& ( one_to_one @ sK3_A ) )
= $true ),
inference(copy,[status(thm)],[331]) ).
thf(500,plain,
( ( ( relation @ sK2_A )
& ( relation_empty_yielding @ sK2_A ) )
= $true ),
inference(copy,[status(thm)],[330]) ).
thf(501,plain,
( ( one_to_one @ sK1_A )
= $true ),
inference(copy,[status(thm)],[327]) ).
thf(502,plain,
( ( function @ sK1_A )
= $true ),
inference(copy,[status(thm)],[326]) ).
thf(503,plain,
( ( relation @ sK1_A )
= $true ),
inference(copy,[status(thm)],[325]) ).
thf(504,plain,
( ( ~ ( one_to_one @ ( function_inverse @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[329]) ).
thf(505,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)],[451]) ).
thf(506,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK44_SY3131 @ SX1 @ SX0 )
= ( apply @ SX1 @ ( sK43_C @ SX1 @ SX0 ) ) )
| ( ( sK43_C @ SX1 @ SX0 )
= ( apply @ SX0 @ ( sK44_SY3131 @ SX1 @ SX0 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SX1 @ SX0 )
= ( apply @ SX1 @ ( sK43_C @ SX1 @ SX0 ) ) )
| ( in @ ( sK44_SY3131 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SX1 @ SX0 )
= ( apply @ SX1 @ ( sK43_C @ SX1 @ SX0 ) ) )
| ( ( sK44_SY3131 @ SX1 @ SX0 )
!= ( apply @ SX1 @ ( sK43_C @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK43_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK43_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) )
| ( ( sK43_C @ SX1 @ SX0 )
= ( apply @ SX0 @ ( sK44_SY3131 @ SX1 @ SX0 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) )
| ( in @ ( sK44_SY3131 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) )
| ( ( sK44_SY3131 @ SX1 @ SX0 )
!= ( apply @ SX1 @ ( sK43_C @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK43_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK43_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK44_SY3131 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ( ( sK43_C @ SX1 @ SX0 )
= ( apply @ SX0 @ ( sK44_SY3131 @ SX1 @ SX0 ) ) ) )
| ~ ( ( ( sK43_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK44_SY3131 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ( in @ ( sK44_SY3131 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) ) )
| ~ ( ( ( sK43_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK44_SY3131 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ( ( sK44_SY3131 @ SX1 @ SX0 )
!= ( apply @ SX1 @ ( sK43_C @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK43_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)],[442]) ).
thf(507,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ ( sK30_D @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ~ ( in @ ( sK30_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK30_D @ SX2 @ SX1 @ SX0 ) @ ( sK31_SY3124 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK31_SY3124 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( in @ ( sK30_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 @ ( sK29_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK29_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[462]) ).
thf(508,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ SX2 @ ( sK17_C @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK18_SY3115 @ SX1 @ SX0 ) @ ( sK17_C @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK17_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 @ ( sK16_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[468]) ).
thf(509,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK12_B @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK13_SY3112 @ SX0 ) @ ( relation_dom @ SX0 ) ) )
| ( ( apply @ SX0 @ ( sK12_B @ SX0 ) )
!= ( apply @ SX0 @ ( sK13_SY3112 @ SX0 ) ) ) )
| ~ ( ( ( sK12_B @ SX0 )
!= ( sK13_SY3112 @ 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)],[471]) ).
thf(510,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ ( sK10_SY3107 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( in @ ( ordered_pair @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ ( sK10_SY3107 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ ( sK11_SY3111 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY3111 @ SX2 @ SX1 @ SX0 ) @ ( sK10_SY3107 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( in @ ( ordered_pair @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ ( sK10_SY3107 @ 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 @ ( sK8_F @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK8_F @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX4 ) @ SX1 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[472]) ).
thf(511,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SX1 @ SX0 ) @ SX2 ) @ SX0 )
| ~ ( in @ ( sK20_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SX1 @ SX0 ) @ ( sK21_SY3117 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK20_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 @ ( sK19_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[467]) ).
thf(512,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)],[466]) ).
thf(513,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)],[445]) ).
thf(514,plain,
( ( ~ ( ~ ( relation @ sK2_A )
| ~ ( relation_empty_yielding @ sK2_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[500]) ).
thf(515,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( function_inverse @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( function_inverse @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443]) ).
thf(516,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[493]) ).
thf(517,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK45_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK45_C @ SX1 @ SX0 ) )
!= ( sK45_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)],[436]) ).
thf(518,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ sK5_A )
| ~ ( relation @ sK5_A ) )
| ~ ( function @ sK5_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[497]) ).
thf(519,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK28_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK28_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK26_C @ SX1 @ SX0 ) @ ( sK27_SY3120 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
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)],[435]) ).
thf(521,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)],[448]) ).
thf(522,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( function @ ( function_inverse @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( relation @ ( function_inverse @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[474]) ).
thf(523,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)],[414]) ).
thf(524,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[481]) ).
thf(525,plain,
( ( ~ ( ~ ( empty @ sK6_A )
| ~ ( relation @ sK6_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[496]) ).
thf(526,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SX1 @ SX0 ) @ ( sK25_SY3119 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK24_C @ SX1 @ SX0 ) @ ( sK25_SY3119 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK24_C @ SX1 @ SX0 ) @ ( sK25_SY3119 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK24_C @ SX1 @ SX0 ) @ ( sK25_SY3119 @ 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)],[464]) ).
thf(527,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( ( relation_rng @ SX0 )
= empty_set ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( ( relation_dom @ SX0 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[447]) ).
thf(528,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ ( sK33_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ~ ( in @ ( sK33_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK34_SY3126 @ SX2 @ SX1 @ SX0 ) @ ( sK33_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK34_SY3126 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( in @ ( sK33_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 @ ( sK32_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ ( sK32_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[461]) ).
thf(529,plain,
( ( ~ ( ~ ( function @ sK7_A )
| ~ ( relation @ sK7_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[495]) ).
thf(530,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( relation @ SX1 )
| ~ ( function @ SX1 )
| ( function @ ( relation_composition @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( relation @ SX1 )
| ~ ( function @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[483]) ).
thf(531,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457]) ).
thf(532,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 @ ( sK47_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX2 ) )
| ~ ( in @ ( ordered_pair @ ( sK47_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) @ SX2 ) )
| ~ ( in @ ( sK47_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[420]) ).
thf(533,plain,
( ( ~ ( ~ ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) )
| ~ ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[485]) ).
thf(534,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_C @ SX1 @ SX0 ) @ ( sK15_SY3113 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY3113 @ SX1 @ SX0 ) @ ( sK14_C @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SX1 @ SX0 ) @ ( sK15_SY3113 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK15_SY3113 @ SX1 @ SX0 ) @ ( sK14_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)],[470]) ).
thf(535,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( function @ ( relation_inverse @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[487]) ).
thf(536,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[446]) ).
thf(537,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[491]) ).
thf(538,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[492]) ).
thf(539,plain,
( ( ~ ( ~ ~ ( empty @ sK4_A )
| ~ ( relation @ sK4_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[498]) ).
thf(540,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[482]) ).
thf(541,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK39_C @ SX1 @ SX0 )
!= ( sK40_SY3129 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK39_C @ SX1 @ SX0 ) @ ( sK40_SY3129 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK39_C @ SX1 @ SX0 )
= ( sK40_SY3129 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK39_C @ SX1 @ SX0 ) @ ( sK40_SY3129 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK39_C @ SX1 @ SX0 ) @ ( sK40_SY3129 @ 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)],[458]) ).
thf(542,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[480]) ).
thf(543,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ ( sK36_SY3127 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SX2 @ SX1 @ SX0 ) @ ( sK36_SY3127 @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SX2 @ SX1 @ SX0 ) @ ( sK36_SY3127 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK36_SY3127 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK35_D @ SX2 @ SX1 @ SX0 ) @ ( sK36_SY3127 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SX2 @ SX1 @ SX0 ) @ ( sK36_SY3127 @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK35_D @ SX2 @ SX1 @ SX0 ) @ ( sK36_SY3127 @ 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)],[460]) ).
thf(544,plain,
( ( ~ ( ~ ~ ( ~ ( function @ sK3_A )
| ~ ( relation @ sK3_A ) )
| ~ ( one_to_one @ sK3_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[499]) ).
thf(545,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( relation_dom @ SX0 ) @ ( relation_dom @ SX1 ) ) )
| ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( relation_rng @ SX0 ) @ ( relation_rng @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[434]) ).
thf(546,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)],[430]) ).
thf(547,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)],[449]) ).
thf(548,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[437]) ).
thf(549,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)],[429]) ).
thf(550,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 @ ( sK46_D @ SX2 @ SX1 @ SX0 ) @ ( relation_rng @ SX2 ) )
| ~ ( in @ ( ordered_pair @ SX0 @ ( sK46_D @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( in @ ( sK46_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[425]) ).
thf(551,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SX1 @ SX0 ) @ ( sK23_SY3118 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_C @ SX1 @ SX0 ) @ ( sK23_SY3118 @ 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)],[465]) ).
thf(552,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[488]) ).
thf(553,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ ( sK37_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ SX2 @ SX1 @ SX0 ) @ ( sK38_SY3128 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ SX2 @ SX1 @ SX0 ) @ ( sK38_SY3128 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK37_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK37_D @ SX2 @ SX1 @ SX0 ) @ ( sK38_SY3128 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK37_D @ SX2 @ SX1 @ SX0 ) @ ( sK38_SY3128 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK37_D @ SX2 @ SX1 @ SX0 ) @ ( sK38_SY3128 @ 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)],[459]) ).
thf(554,plain,
! [SV1: $i] :
( ( ! [SY3132: $i] :
( ~ ( relation @ SY3132 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV1 @ SY3132 ) ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(555,plain,
! [SV2: $i] :
( ( ! [SY3133: $i] :
( ~ ( relation @ SY3133 )
| ( subset @ ( relation_rng_restriction @ SV2 @ SY3133 ) @ SY3133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(556,plain,
! [SV3: $i] :
( ( ! [SY3134: $i] :
( ~ ( relation @ SY3134 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV3 @ SY3134 ) ) @ ( relation_rng @ SY3134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(557,plain,
! [SV4: $i] :
( ( ! [SY3135: $i] :
( ~ ( relation @ SY3135 )
| ( ( relation_rng @ ( relation_rng_restriction @ SV4 @ SY3135 ) )
= ( set_intersection2 @ ( relation_rng @ SY3135 ) @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(558,plain,
! [SV5: $i] :
( ( ! [SY3136: $i,SY3137: $i] :
( ~ ( relation @ SY3137 )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV5 @ SY3137 ) @ SY3136 )
= ( relation_rng_restriction @ SV5 @ ( relation_dom_restriction @ SY3137 @ SY3136 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(559,plain,
! [SV6: $i] :
( ( ! [SY3138: $i] :
( ~ ( relation @ SY3138 )
| ( subset @ ( relation_image @ SY3138 @ SV6 ) @ ( relation_rng @ SY3138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(560,plain,
! [SV7: $i] :
( ( ! [SY3139: $i] :
( ~ ( relation @ SY3139 )
| ( ( relation_image @ SY3139 @ SV7 )
= ( relation_image @ SY3139 @ ( set_intersection2 @ ( relation_dom @ SY3139 ) @ SV7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(561,plain,
! [SV8: $i] :
( ( ~ ( relation @ SV8 )
| ( ( relation_image @ SV8 @ ( relation_dom @ SV8 ) )
= ( relation_rng @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(562,plain,
! [SV9: $i] :
( ( ~ ( relation @ SV9 )
| ! [SY3140: $i] :
( ~ ( relation @ SY3140 )
| ( ( relation_rng @ ( relation_composition @ SV9 @ SY3140 ) )
= ( relation_image @ SY3140 @ ( relation_rng @ SV9 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(563,plain,
! [SV10: $i] :
( ( ! [SY3141: $i] :
( ~ ( relation @ SY3141 )
| ( subset @ ( relation_inverse_image @ SY3141 @ SV10 ) @ ( relation_dom @ SY3141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(564,plain,
! [SV11: $i] :
( ( ! [SY3142: $i] :
( ~ ( relation @ SY3142 )
| ( SV11 = empty_set )
| ~ ( subset @ SV11 @ ( relation_rng @ SY3142 ) )
| ( ( relation_inverse_image @ SY3142 @ SV11 )
!= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(565,plain,
! [SV12: $i] :
( ( ! [SY3143: $i,SY3144: $i] :
( ~ ( relation @ SY3144 )
| ~ ( subset @ SV12 @ SY3143 )
| ( subset @ ( relation_inverse_image @ SY3144 @ SV12 ) @ ( relation_inverse_image @ SY3144 @ SY3143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(566,plain,
! [SV13: $i] :
( ( ~ ( relation @ SV13 )
| ( subset @ SV13 @ ( cartesian_product2 @ ( relation_dom @ SV13 ) @ ( relation_rng @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(567,plain,
! [SV14: $i] :
( ( ! [SY3145: $i] :
( ~ ( function @ SY3145 )
| ~ ( relation @ SY3145 )
| ! [SY3146: $i] :
( ~ ( function @ SY3146 )
| ~ ( relation @ SY3146 )
| ~ ( in @ SV14 @ ( relation_dom @ ( relation_composition @ SY3146 @ SY3145 ) ) )
| ( ( apply @ ( relation_composition @ SY3146 @ SY3145 ) @ SV14 )
= ( apply @ SY3145 @ ( apply @ SY3146 @ SV14 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(568,plain,
! [SV15: $i] :
( ( ! [SY3147: $i] :
( ~ ( function @ SY3147 )
| ~ ( relation @ SY3147 )
| ! [SY3148: $i] :
( ~ ( function @ SY3148 )
| ~ ( relation @ SY3148 )
| ~ ( in @ SV15 @ ( relation_dom @ SY3147 ) )
| ( ( apply @ ( relation_composition @ SY3147 @ SY3148 ) @ SV15 )
= ( apply @ SY3148 @ ( apply @ SY3147 @ SV15 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(569,plain,
! [SV16: $i] :
( ( ~ ( relation @ SV16 )
| ! [SY3149: $i] :
( ~ ( relation @ SY3149 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV16 @ SY3149 ) ) @ ( relation_dom @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(570,plain,
! [SV17: $i] :
( ( ~ ( relation @ SV17 )
| ! [SY3150: $i] :
( ~ ( relation @ SY3150 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV17 @ SY3150 ) ) @ ( relation_rng @ SY3150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(571,plain,
! [SV18: $i] :
( ( ~ ( relation @ SV18 )
| ! [SY3151: $i] :
( ~ ( relation @ SY3151 )
| ~ ( subset @ ( relation_rng @ SV18 ) @ ( relation_dom @ SY3151 ) )
| ( ( relation_dom @ ( relation_composition @ SV18 @ SY3151 ) )
= ( relation_dom @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(572,plain,
! [SV19: $i] :
( ( ~ ( relation @ SV19 )
| ! [SY3152: $i] :
( ~ ( relation @ SY3152 )
| ~ ( subset @ ( relation_dom @ SV19 ) @ ( relation_rng @ SY3152 ) )
| ( ( relation_rng @ ( relation_composition @ SY3152 @ SV19 ) )
= ( relation_rng @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(573,plain,
! [SV20: $i] :
( ( ~ ( relation @ SV20 )
| ( in @ ( ordered_pair @ ( sK41_B @ SV20 ) @ ( sK42_SY3130 @ SV20 ) ) @ SV20 )
| ( SV20 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(574,plain,
! [SV21: $i] :
( ( ! [SY3153: $i] :
( ~ ( relation @ SY3153 )
| ( subset @ ( relation_dom_restriction @ SY3153 @ SV21 ) @ SY3153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(575,plain,
! [SV22: $i] :
( ( ! [SY3154: $i] :
( ~ ( relation @ SY3154 )
| ( ( relation_dom @ ( relation_dom_restriction @ SY3154 @ SV22 ) )
= ( set_intersection2 @ ( relation_dom @ SY3154 ) @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(576,plain,
! [SV23: $i] :
( ( ! [SY3155: $i] :
( ~ ( relation @ SY3155 )
| ( ( relation_dom_restriction @ SY3155 @ SV23 )
= ( relation_composition @ ( identity_relation @ SV23 ) @ SY3155 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(577,plain,
! [SV24: $i] :
( ( ! [SY3156: $i] :
( ~ ( relation @ SY3156 )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ SY3156 @ SV24 ) ) @ ( relation_rng @ SY3156 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(578,plain,
! [SV25: $i] :
( ( ~ ( empty @ SV25 )
| ( function @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(579,plain,
! [SV26: $i] :
( ( ~ ( empty @ SV26 )
| ( relation @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(580,plain,
! [SV27: $i] :
( ( ~ ( relation @ SV27 )
| ( ( relation_field @ SV27 )
= ( set_union2 @ ( relation_dom @ SV27 ) @ ( relation_rng @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(581,plain,
! [SV28: $i] :
( ( ~ ( function @ SV28 )
| ~ ( relation @ SV28 )
| ~ ( one_to_one @ SV28 )
| ( ( function_inverse @ SV28 )
= ( relation_inverse @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(582,plain,
! [SV29: $i] :
( ( ~ ( relation @ SV29 )
| ( relation @ ( relation_inverse @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(583,plain,
! [SV30: $i] :
( ( ! [SY3157: $i] :
( ~ ( relation @ SV30 )
| ~ ( relation @ SY3157 )
| ( relation @ ( relation_composition @ SV30 @ SY3157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(584,plain,
! [SV31: $i] :
( ( relation @ ( identity_relation @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(585,plain,
! [SV32: $i] :
( ( ~ ( relation @ SV32 )
| ! [SY3158: $i] : ( relation @ ( relation_dom_restriction @ SV32 @ SY3158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(586,plain,
! [SV33: $i] :
( ( ! [SY3159: $i] :
( ~ ( relation @ SY3159 )
| ( relation @ ( relation_rng_restriction @ SV33 @ SY3159 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(587,plain,
! [SV34: $i] :
( ( ! [SY3160: $i] :
( ~ ( relation @ SV34 )
| ~ ( relation @ SY3160 )
| ( relation @ ( set_intersection2 @ SV34 @ SY3160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(588,plain,
! [SV35: $i] :
( ( ! [SY3161: $i] :
( ~ ( relation @ SV35 )
| ~ ( relation @ SY3161 )
| ( relation @ ( set_union2 @ SV35 @ SY3161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(589,plain,
! [SV36: $i] :
( ( ( empty @ SV36 )
| ~ ( relation @ SV36 )
| ~ ( empty @ ( relation_dom @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(590,plain,
! [SV37: $i] :
( ( ( empty @ SV37 )
| ~ ( relation @ SV37 )
| ~ ( empty @ ( relation_rng @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(591,plain,
! [SV38: $i] :
( ( ~ ( relation @ SV38 )
| ( ( relation_inverse @ ( relation_inverse @ SV38 ) )
= SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(592,plain,
( ( one_to_one @ ( function_inverse @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(593,plain,
! [SV39: $i] :
( ( ~ ( ~ ! [SY3162: $i,SY3163: $i] :
( ~ ( function @ SY3163 )
| ~ ( relation @ SY3163 )
| ( SY3162
!= ( apply @ SY3163 @ SV39 ) )
| ~ ( in @ SV39 @ ( relation_dom @ SY3163 ) )
| ( in @ ( ordered_pair @ SV39 @ SY3162 ) @ SY3163 ) )
| ~ ~ ( ~ ! [SY3164: $i,SY3165: $i] :
( ~ ( function @ SY3165 )
| ~ ( relation @ SY3165 )
| ~ ( in @ ( ordered_pair @ SV39 @ SY3164 ) @ SY3165 )
| ( SY3164
= ( apply @ SY3165 @ SV39 ) ) )
| ~ ! [SY3166: $i,SY3167: $i] :
( ~ ( function @ SY3167 )
| ~ ( relation @ SY3167 )
| ~ ( in @ ( ordered_pair @ SV39 @ SY3166 ) @ SY3167 )
| ( in @ SV39 @ ( relation_dom @ SY3167 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(594,plain,
! [SV40: $i] :
( ( ~ ( function @ SV40 )
| ~ ( relation @ SV40 )
| ~ ( one_to_one @ SV40 )
| ~ ( ~ ! [SY3168: $i] :
( ~ ( function @ SY3168 )
| ~ ( relation @ SY3168 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK44_SY3131 @ SY3168 @ SV40 )
= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ( ( sK43_C @ SY3168 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SY3168 @ SV40 )
= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SY3168 @ SV40 )
= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ( ( sK44_SY3131 @ SY3168 @ SV40 )
!= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK43_C @ SY3168 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK44_SY3131 @ SY3168 @ SV40 )
!= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK43_C @ SY3168 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK43_C @ SY3168 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SY3168 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SY3168 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK44_SY3131 @ SY3168 @ SV40 )
!= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ( ( relation_dom @ SY3168 )
!= ( relation_rng @ SV40 ) )
| ( SY3168
= ( function_inverse @ SV40 ) ) )
| ~ ~ ( ~ ! [SY3169: $i] :
( ~ ( function @ SY3169 )
| ~ ( relation @ SY3169 )
| ( SY3169
!= ( function_inverse @ SV40 ) )
| ~ ( ~ ~ ( ~ ! [SY3170: $i,SY3171: $i] :
( ( SY3171
!= ( apply @ SY3169 @ SY3170 ) )
| ~ ( in @ SY3170 @ ( relation_rng @ SV40 ) )
| ( SY3170
= ( apply @ SV40 @ SY3171 ) ) )
| ~ ! [SY3172: $i,SY3173: $i] :
( ( SY3173
!= ( apply @ SY3169 @ SY3172 ) )
| ~ ( in @ SY3172 @ ( relation_rng @ SV40 ) )
| ( in @ SY3173 @ ( relation_dom @ SV40 ) ) ) )
| ~ ~ ( ~ ! [SY3174: $i,SY3175: $i] :
( ( SY3174
!= ( apply @ SV40 @ SY3175 ) )
| ~ ( in @ SY3175 @ ( relation_dom @ SV40 ) )
| ( SY3175
= ( apply @ SY3169 @ SY3174 ) ) )
| ~ ! [SY3176: $i] :
( ! [SY3177: $i] :
( ( SY3176
!= ( apply @ SV40 @ SY3177 ) )
| ~ ( in @ SY3177 @ ( relation_dom @ SV40 ) ) )
| ( in @ SY3176 @ ( relation_rng @ SV40 ) ) ) ) ) )
| ~ ! [SY3178: $i] :
( ~ ( function @ SY3178 )
| ~ ( relation @ SY3178 )
| ( SY3178
!= ( function_inverse @ SV40 ) )
| ( ( relation_dom @ SY3178 )
= ( relation_rng @ SV40 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(595,plain,
! [SV41: $i] :
( ( ~ ( relation @ SV41 )
| ~ ( ~ ! [SY3179: $i,SY3180: $i] :
( ~ ( ~ ( ! [SY3181: $i] :
( ~ ( in @ ( ordered_pair @ ( sK30_D @ SY3180 @ SY3179 @ SV41 ) @ SY3181 ) @ SV41 )
| ~ ( in @ SY3181 @ SY3179 ) )
| ~ ( in @ ( sK30_D @ SY3180 @ SY3179 @ SV41 ) @ SY3180 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK30_D @ SY3180 @ SY3179 @ SV41 ) @ ( sK31_SY3124 @ SY3180 @ SY3179 @ SV41 ) ) @ SV41 )
| ~ ( in @ ( sK31_SY3124 @ SY3180 @ SY3179 @ SV41 ) @ SY3179 ) )
| ( in @ ( sK30_D @ SY3180 @ SY3179 @ SV41 ) @ SY3180 ) ) )
| ( SY3180
= ( relation_inverse_image @ SV41 @ SY3179 ) ) )
| ~ ! [SY3182: $i,SY3183: $i] :
( ( SY3183
!= ( relation_inverse_image @ SV41 @ SY3182 ) )
| ~ ( ~ ! [SY3184: $i] :
( ! [SY3185: $i] :
( ~ ( in @ ( ordered_pair @ SY3184 @ SY3185 ) @ SV41 )
| ~ ( in @ SY3185 @ SY3182 ) )
| ( in @ SY3184 @ SY3183 ) )
| ~ ! [SY3186: $i] :
( ~ ( in @ SY3186 @ SY3183 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3186 @ ( sK29_E @ SY3186 @ SY3183 @ SY3182 @ SV41 ) ) @ SV41 )
| ~ ( in @ ( sK29_E @ SY3186 @ SY3183 @ SY3182 @ SV41 ) @ SY3182 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(596,plain,
! [SV42: $i] :
( ( ~ ( relation @ SV42 )
| ~ ( ~ ! [SY3187: $i] :
( ~ ( ~ ( ! [SY3188: $i] :
~ ( in @ ( ordered_pair @ SY3188 @ ( sK17_C @ SY3187 @ SV42 ) ) @ SV42 )
| ~ ( in @ ( sK17_C @ SY3187 @ SV42 ) @ SY3187 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK18_SY3115 @ SY3187 @ SV42 ) @ ( sK17_C @ SY3187 @ SV42 ) ) @ SV42 )
| ( in @ ( sK17_C @ SY3187 @ SV42 ) @ SY3187 ) ) )
| ( SY3187
= ( relation_rng @ SV42 ) ) )
| ~ ! [SY3189: $i] :
( ( SY3189
!= ( relation_rng @ SV42 ) )
| ~ ( ~ ! [SY3190: $i] :
( ! [SY3191: $i] :
~ ( in @ ( ordered_pair @ SY3191 @ SY3190 ) @ SV42 )
| ( in @ SY3190 @ SY3189 ) )
| ~ ! [SY3192: $i] :
( ~ ( in @ SY3192 @ SY3189 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3192 @ SY3189 @ SV42 ) @ SY3192 ) @ SV42 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(597,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK12_B @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK13_SY3112 @ SX0 ) @ ( relation_dom @ SX0 ) ) )
| ( ( apply @ SX0 @ ( sK12_B @ SX0 ) )
!= ( apply @ SX0 @ ( sK13_SY3112 @ SX0 ) ) ) )
| ~ ( ( ( sK12_B @ SX0 )
!= ( sK13_SY3112 @ 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)],[509]) ).
thf(598,plain,
! [SV43: $i] :
( ( ~ ( relation @ SV43 )
| ! [SY3193: $i] :
( ~ ( relation @ SY3193 )
| ~ ( ~ ! [SY3194: $i] :
( ~ ( relation @ SY3194 )
| ~ ( ~ ( ! [SY3195: $i] :
( ~ ( in @ ( ordered_pair @ ( sK9_D @ SY3194 @ SY3193 @ SV43 ) @ SY3195 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3195 @ ( sK10_SY3107 @ SY3194 @ SY3193 @ SV43 ) ) @ SY3193 ) )
| ~ ( in @ ( ordered_pair @ ( sK9_D @ SY3194 @ SY3193 @ SV43 ) @ ( sK10_SY3107 @ SY3194 @ SY3193 @ SV43 ) ) @ SY3194 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK9_D @ SY3194 @ SY3193 @ SV43 ) @ ( sK11_SY3111 @ SY3194 @ SY3193 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY3111 @ SY3194 @ SY3193 @ SV43 ) @ ( sK10_SY3107 @ SY3194 @ SY3193 @ SV43 ) ) @ SY3193 ) )
| ( in @ ( ordered_pair @ ( sK9_D @ SY3194 @ SY3193 @ SV43 ) @ ( sK10_SY3107 @ SY3194 @ SY3193 @ SV43 ) ) @ SY3194 ) ) )
| ( SY3194
= ( relation_composition @ SV43 @ SY3193 ) ) )
| ~ ! [SY3196: $i] :
( ~ ( relation @ SY3196 )
| ( SY3196
!= ( relation_composition @ SV43 @ SY3193 ) )
| ~ ( ~ ! [SY3197: $i,SY3198: $i] :
( ! [SY3199: $i] :
( ~ ( in @ ( ordered_pair @ SY3197 @ SY3199 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3199 @ SY3198 ) @ SY3193 ) )
| ( in @ ( ordered_pair @ SY3197 @ SY3198 ) @ SY3196 ) )
| ~ ! [SY3200: $i,SY3201: $i] :
( ~ ( in @ ( ordered_pair @ SY3200 @ SY3201 ) @ SY3196 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3200 @ ( sK8_F @ SY3201 @ SY3200 @ SY3196 @ SY3193 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK8_F @ SY3201 @ SY3200 @ SY3196 @ SY3193 @ SV43 ) @ SY3201 ) @ SY3193 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(599,plain,
! [SV44: $i] :
( ( ~ ( relation @ SV44 )
| ~ ( ~ ! [SY3202: $i] :
( ~ ( ~ ( ! [SY3203: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SY3202 @ SV44 ) @ SY3203 ) @ SV44 )
| ~ ( in @ ( sK20_C @ SY3202 @ SV44 ) @ SY3202 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SY3202 @ SV44 ) @ ( sK21_SY3117 @ SY3202 @ SV44 ) ) @ SV44 )
| ( in @ ( sK20_C @ SY3202 @ SV44 ) @ SY3202 ) ) )
| ( SY3202
= ( relation_dom @ SV44 ) ) )
| ~ ! [SY3204: $i] :
( ( SY3204
!= ( relation_dom @ SV44 ) )
| ~ ( ~ ! [SY3205: $i] :
( ! [SY3206: $i] :
~ ( in @ ( ordered_pair @ SY3205 @ SY3206 ) @ SV44 )
| ( in @ SY3205 @ SY3204 ) )
| ~ ! [SY3207: $i] :
( ~ ( in @ SY3207 @ SY3204 )
| ( in @ ( ordered_pair @ SY3207 @ ( sK19_D @ SY3207 @ SY3204 @ SV44 ) ) @ SV44 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(600,plain,
! [SV45: $i] :
( ( ~ ( function @ SV45 )
| ~ ( relation @ SV45 )
| ~ ( ~ ~ ( ~ ! [SY3208: $i] :
( ~ ( in @ SY3208 @ ( relation_dom @ SV45 ) )
| ! [SY3209: $i] :
( ( SY3209
!= ( apply @ SV45 @ SY3208 ) )
| ( in @ ( ordered_pair @ SY3208 @ SY3209 ) @ SV45 ) ) )
| ~ ! [SY3210: $i] :
( ~ ( in @ SY3210 @ ( relation_dom @ SV45 ) )
| ! [SY3211: $i] :
( ~ ( in @ ( ordered_pair @ SY3210 @ SY3211 ) @ SV45 )
| ( SY3211
= ( apply @ SV45 @ SY3210 ) ) ) ) )
| ~ ~ ( ~ ! [SY3212: $i] :
( ( in @ SY3212 @ ( relation_dom @ SV45 ) )
| ! [SY3213: $i] :
( ( SY3213
!= ( apply @ SV45 @ SY3212 ) )
| ( SY3213 = empty_set ) ) )
| ~ ! [SY3214: $i] :
( ( in @ SY3214 @ ( relation_dom @ SV45 ) )
| ! [SY3215: $i] :
( ( SY3215 != empty_set )
| ( SY3215
= ( apply @ SV45 @ SY3214 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(601,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)],[513]) ).
thf(602,plain,
( ( ~ ( relation @ sK2_A )
| ~ ( relation_empty_yielding @ sK2_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[514]) ).
thf(603,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( function_inverse @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( function_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[515]) ).
thf(604,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(605,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK45_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK45_C @ SX1 @ SX0 ) )
!= ( sK45_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)],[517]) ).
thf(606,plain,
( ( ~ ~ ( ~ ( empty @ sK5_A )
| ~ ( relation @ sK5_A ) )
| ~ ( function @ sK5_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(607,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK28_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK28_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK26_C @ SX1 @ SX0 ) @ ( sK27_SY3120 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(608,plain,
! [SV46: $i] :
( ( ~ ( ~ ! [SY3216: $i,SY3217: $i] :
( ~ ( relation @ SY3217 )
| ~ ( in @ ( ordered_pair @ SV46 @ SY3216 ) @ SY3217 )
| ( in @ SV46 @ ( relation_field @ SY3217 ) ) )
| ~ ! [SY3218: $i,SY3219: $i] :
( ~ ( relation @ SY3219 )
| ~ ( in @ ( ordered_pair @ SV46 @ SY3218 ) @ SY3219 )
| ( in @ SY3218 @ ( relation_field @ SY3219 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(609,plain,
! [SV47: $i] :
( ( ! [SY3220: $i] :
~ ( ~ ! [SY3221: $i,SY3222: $i] :
( ~ ( relation @ SY3222 )
| ~ ( in @ SV47 @ SY3221 )
| ~ ( in @ ( ordered_pair @ SV47 @ SY3220 ) @ SY3222 )
| ( in @ ( ordered_pair @ SV47 @ SY3220 ) @ ( relation_composition @ ( identity_relation @ SY3221 ) @ SY3222 ) ) )
| ~ ~ ( ~ ! [SY3223: $i,SY3224: $i] :
( ~ ( relation @ SY3224 )
| ~ ( in @ ( ordered_pair @ SV47 @ SY3220 ) @ ( relation_composition @ ( identity_relation @ SY3223 ) @ SY3224 ) )
| ( in @ SV47 @ SY3223 ) )
| ~ ! [SY3225: $i,SY3226: $i] :
( ~ ( relation @ SY3226 )
| ~ ( in @ ( ordered_pair @ SV47 @ SY3220 ) @ ( relation_composition @ ( identity_relation @ SY3225 ) @ SY3226 ) )
| ( in @ ( ordered_pair @ SV47 @ SY3220 ) @ SY3226 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(610,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( function @ ( function_inverse @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( relation @ ( function_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(611,plain,
! [SV48: $i] :
( ( ~ ( ~ ! [SY3227: $i,SY3228: $i] :
( ~ ( relation @ SY3228 )
| ~ ( in @ SV48 @ SY3227 )
| ~ ( in @ SV48 @ ( relation_rng @ SY3228 ) )
| ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SY3227 @ SY3228 ) ) ) )
| ~ ~ ( ~ ! [SY3229: $i,SY3230: $i] :
( ~ ( relation @ SY3230 )
| ~ ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SY3229 @ SY3230 ) ) )
| ( in @ SV48 @ SY3229 ) )
| ~ ! [SY3231: $i,SY3232: $i] :
( ~ ( relation @ SY3232 )
| ~ ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SY3231 @ SY3232 ) ) )
| ( in @ SV48 @ ( relation_rng @ SY3232 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(612,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(613,plain,
( ( ~ ( empty @ sK6_A )
| ~ ( relation @ sK6_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[525]) ).
thf(614,plain,
! [SV49: $i] :
( ( ~ ( relation @ SV49 )
| ~ ( ~ ! [SY3233: $i] :
( ~ ( relation @ SY3233 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3233 @ SV49 ) @ ( sK25_SY3119 @ SY3233 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3233 @ SV49 ) @ ( sK25_SY3119 @ SY3233 @ SV49 ) ) @ SY3233 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK24_C @ SY3233 @ SV49 ) @ ( sK25_SY3119 @ SY3233 @ SV49 ) ) @ SV49 )
| ( in @ ( ordered_pair @ ( sK24_C @ SY3233 @ SV49 ) @ ( sK25_SY3119 @ SY3233 @ SV49 ) ) @ SY3233 ) ) )
| ( SV49 = SY3233 ) )
| ~ ! [SY3234: $i] :
( ~ ( relation @ SY3234 )
| ( SV49 != SY3234 )
| ~ ( ~ ! [SY3235: $i,SY3236: $i] :
( ~ ( in @ ( ordered_pair @ SY3235 @ SY3236 ) @ SV49 )
| ( in @ ( ordered_pair @ SY3235 @ SY3236 ) @ SY3234 ) )
| ~ ! [SY3237: $i,SY3238: $i] :
( ~ ( in @ ( ordered_pair @ SY3237 @ SY3238 ) @ SY3234 )
| ( in @ ( ordered_pair @ SY3237 @ SY3238 ) @ SV49 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(615,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( ( relation_rng @ SX0 )
= empty_set ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( ( relation_dom @ SX0 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(616,plain,
! [SV50: $i] :
( ( ~ ( relation @ SV50 )
| ~ ( ~ ! [SY3239: $i,SY3240: $i] :
( ~ ( ~ ( ! [SY3241: $i] :
( ~ ( in @ ( ordered_pair @ SY3241 @ ( sK33_D @ SY3240 @ SY3239 @ SV50 ) ) @ SV50 )
| ~ ( in @ SY3241 @ SY3239 ) )
| ~ ( in @ ( sK33_D @ SY3240 @ SY3239 @ SV50 ) @ SY3240 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK34_SY3126 @ SY3240 @ SY3239 @ SV50 ) @ ( sK33_D @ SY3240 @ SY3239 @ SV50 ) ) @ SV50 )
| ~ ( in @ ( sK34_SY3126 @ SY3240 @ SY3239 @ SV50 ) @ SY3239 ) )
| ( in @ ( sK33_D @ SY3240 @ SY3239 @ SV50 ) @ SY3240 ) ) )
| ( SY3240
= ( relation_image @ SV50 @ SY3239 ) ) )
| ~ ! [SY3242: $i,SY3243: $i] :
( ( SY3243
!= ( relation_image @ SV50 @ SY3242 ) )
| ~ ( ~ ! [SY3244: $i] :
( ! [SY3245: $i] :
( ~ ( in @ ( ordered_pair @ SY3245 @ SY3244 ) @ SV50 )
| ~ ( in @ SY3245 @ SY3242 ) )
| ( in @ SY3244 @ SY3243 ) )
| ~ ! [SY3246: $i] :
( ~ ( in @ SY3246 @ SY3243 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK32_E @ SY3246 @ SY3243 @ SY3242 @ SV50 ) @ SY3246 ) @ SV50 )
| ~ ( in @ ( sK32_E @ SY3246 @ SY3243 @ SY3242 @ SV50 ) @ SY3242 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(617,plain,
( ( ~ ( function @ sK7_A )
| ~ ( relation @ sK7_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(618,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( relation @ SX1 )
| ~ ( function @ SX1 )
| ( function @ ( relation_composition @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( relation @ SX1 )
| ~ ( function @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[530]) ).
thf(619,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(620,plain,
! [SV51: $i] :
( ( ~ ( ~ ! [SY3247: $i,SY3248: $i] :
( ~ ( relation @ SY3248 )
| ! [SY3249: $i] :
( ~ ( in @ SY3249 @ ( relation_dom @ SY3248 ) )
| ~ ( in @ ( ordered_pair @ SY3249 @ SV51 ) @ SY3248 )
| ~ ( in @ SY3249 @ SY3247 ) )
| ( in @ SV51 @ ( relation_image @ SY3248 @ SY3247 ) ) )
| ~ ! [SY3250: $i,SY3251: $i] :
( ~ ( relation @ SY3251 )
| ~ ( in @ SV51 @ ( relation_image @ SY3251 @ SY3250 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK47_D @ SY3251 @ SY3250 @ SV51 ) @ ( relation_dom @ SY3251 ) )
| ~ ( in @ ( ordered_pair @ ( sK47_D @ SY3251 @ SY3250 @ SV51 ) @ SV51 ) @ SY3251 ) )
| ~ ( in @ ( sK47_D @ SY3251 @ SY3250 @ SV51 ) @ SY3250 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(621,plain,
( ( ~ ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) )
| ~ ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[533]) ).
thf(622,plain,
! [SV52: $i] :
( ( ~ ( relation @ SV52 )
| ~ ( ~ ! [SY3252: $i] :
( ~ ( relation @ SY3252 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_C @ SY3252 @ SV52 ) @ ( sK15_SY3113 @ SY3252 @ SV52 ) ) @ SY3252 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY3113 @ SY3252 @ SV52 ) @ ( sK14_C @ SY3252 @ SV52 ) ) @ SV52 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SY3252 @ SV52 ) @ ( sK15_SY3113 @ SY3252 @ SV52 ) ) @ SY3252 )
| ( in @ ( ordered_pair @ ( sK15_SY3113 @ SY3252 @ SV52 ) @ ( sK14_C @ SY3252 @ SV52 ) ) @ SV52 ) ) )
| ( SY3252
= ( relation_inverse @ SV52 ) ) )
| ~ ! [SY3253: $i] :
( ~ ( relation @ SY3253 )
| ( SY3253
!= ( relation_inverse @ SV52 ) )
| ~ ( ~ ! [SY3254: $i,SY3255: $i] :
( ~ ( in @ ( ordered_pair @ SY3254 @ SY3255 ) @ SY3253 )
| ( in @ ( ordered_pair @ SY3255 @ SY3254 ) @ SV52 ) )
| ~ ! [SY3256: $i,SY3257: $i] :
( ~ ( in @ ( ordered_pair @ SY3257 @ SY3256 ) @ SV52 )
| ( in @ ( ordered_pair @ SY3256 @ SY3257 ) @ SY3253 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(623,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( function @ ( relation_inverse @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[535]) ).
thf(624,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[536]) ).
thf(625,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(626,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(627,plain,
( ( ~ ~ ( empty @ sK4_A )
| ~ ( relation @ sK4_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(628,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(629,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK39_C @ SX1 @ SX0 )
!= ( sK40_SY3129 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK39_C @ SX1 @ SX0 ) @ ( sK40_SY3129 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK39_C @ SX1 @ SX0 )
= ( sK40_SY3129 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK39_C @ SX1 @ SX0 ) @ ( sK40_SY3129 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK39_C @ SX1 @ SX0 ) @ ( sK40_SY3129 @ 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)],[541]) ).
thf(630,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(631,plain,
! [SV53: $i] :
( ( ! [SY3258: $i] :
( ~ ( relation @ SY3258 )
| ~ ( ~ ! [SY3259: $i] :
( ~ ( relation @ SY3259 )
| ~ ( ~ ( ~ ( in @ ( sK36_SY3127 @ SY3259 @ SY3258 @ SV53 ) @ SV53 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SY3259 @ SY3258 @ SV53 ) @ ( sK36_SY3127 @ SY3259 @ SY3258 @ SV53 ) ) @ SY3258 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SY3259 @ SY3258 @ SV53 ) @ ( sK36_SY3127 @ SY3259 @ SY3258 @ SV53 ) ) @ SY3259 ) )
| ~ ~ ( ~ ( ( in @ ( sK36_SY3127 @ SY3259 @ SY3258 @ SV53 ) @ SV53 )
| ( in @ ( ordered_pair @ ( sK35_D @ SY3259 @ SY3258 @ SV53 ) @ ( sK36_SY3127 @ SY3259 @ SY3258 @ SV53 ) ) @ SY3259 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SY3259 @ SY3258 @ SV53 ) @ ( sK36_SY3127 @ SY3259 @ SY3258 @ SV53 ) ) @ SY3258 )
| ( in @ ( ordered_pair @ ( sK35_D @ SY3259 @ SY3258 @ SV53 ) @ ( sK36_SY3127 @ SY3259 @ SY3258 @ SV53 ) ) @ SY3259 ) ) ) )
| ( SY3259
= ( relation_rng_restriction @ SV53 @ SY3258 ) ) )
| ~ ! [SY3260: $i] :
( ~ ( relation @ SY3260 )
| ( SY3260
!= ( relation_rng_restriction @ SV53 @ SY3258 ) )
| ~ ( ~ ! [SY3261: $i,SY3262: $i] :
( ~ ( in @ SY3262 @ SV53 )
| ~ ( in @ ( ordered_pair @ SY3261 @ SY3262 ) @ SY3258 )
| ( in @ ( ordered_pair @ SY3261 @ SY3262 ) @ SY3260 ) )
| ~ ~ ( ~ ! [SY3263: $i,SY3264: $i] :
( ~ ( in @ ( ordered_pair @ SY3263 @ SY3264 ) @ SY3260 )
| ( in @ SY3264 @ SV53 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3260 )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3258 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(632,plain,
( ( ~ ~ ( ~ ( function @ sK3_A )
| ~ ( relation @ sK3_A ) )
| ~ ( one_to_one @ sK3_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(633,plain,
! [SV54: $i] :
( ( ~ ( relation @ SV54 )
| ~ ( ~ ! [SY3267: $i] :
( ~ ( relation @ SY3267 )
| ~ ( subset @ SV54 @ SY3267 )
| ( subset @ ( relation_dom @ SV54 ) @ ( relation_dom @ SY3267 ) ) )
| ~ ! [SY3268: $i] :
( ~ ( relation @ SY3268 )
| ~ ( subset @ SV54 @ SY3268 )
| ( subset @ ( relation_rng @ SV54 ) @ ( relation_rng @ SY3268 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(634,plain,
! [SV55: $i] :
( ( ! [SY3269: $i] :
( ~ ( function @ SY3269 )
| ~ ( relation @ SY3269 )
| ~ ( ~ ! [SY3270: $i] :
( ~ ( function @ SY3270 )
| ~ ( relation @ SY3270 )
| ~ ( in @ SV55 @ ( relation_dom @ SY3270 ) )
| ~ ( in @ ( apply @ SY3270 @ SV55 ) @ ( relation_dom @ SY3269 ) )
| ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3270 @ SY3269 ) ) ) )
| ~ ~ ( ~ ! [SY3271: $i] :
( ~ ( function @ SY3271 )
| ~ ( relation @ SY3271 )
| ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3271 @ SY3269 ) ) )
| ( in @ SV55 @ ( relation_dom @ SY3271 ) ) )
| ~ ! [SY3272: $i] :
( ~ ( function @ SY3272 )
| ~ ( relation @ SY3272 )
| ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3272 @ SY3269 ) ) )
| ( in @ ( apply @ SY3272 @ SV55 ) @ ( relation_dom @ SY3269 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(635,plain,
! [SV56: $i] :
( ( ~ ( ~ ! [SY3273: $i,SY3274: $i] :
( ~ ( relation @ SY3274 )
| ~ ( in @ SV56 @ SY3273 )
| ~ ( in @ SV56 @ ( relation_dom @ SY3274 ) )
| ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SY3274 @ SY3273 ) ) ) )
| ~ ~ ( ~ ! [SY3275: $i,SY3276: $i] :
( ~ ( relation @ SY3276 )
| ~ ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SY3276 @ SY3275 ) ) )
| ( in @ SV56 @ SY3275 ) )
| ~ ! [SY3277: $i,SY3278: $i] :
( ~ ( relation @ SY3278 )
| ~ ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SY3278 @ SY3277 ) ) )
| ( in @ SV56 @ ( relation_dom @ SY3278 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(636,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(637,plain,
! [SV57: $i] :
( ( ~ ( ~ ! [SY3279: $i,SY3280: $i] :
( ~ ( relation @ SY3280 )
| ~ ( in @ ( ordered_pair @ SV57 @ SY3279 ) @ SY3280 )
| ( in @ SV57 @ ( relation_dom @ SY3280 ) ) )
| ~ ! [SY3281: $i,SY3282: $i] :
( ~ ( relation @ SY3282 )
| ~ ( in @ ( ordered_pair @ SV57 @ SY3281 ) @ SY3282 )
| ( in @ SY3281 @ ( relation_rng @ SY3282 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(638,plain,
! [SV58: $i] :
( ( ~ ( ~ ! [SY3283: $i,SY3284: $i] :
( ~ ( relation @ SY3284 )
| ! [SY3285: $i] :
( ~ ( in @ SY3285 @ ( relation_rng @ SY3284 ) )
| ~ ( in @ ( ordered_pair @ SV58 @ SY3285 ) @ SY3284 )
| ~ ( in @ SY3285 @ SY3283 ) )
| ( in @ SV58 @ ( relation_inverse_image @ SY3284 @ SY3283 ) ) )
| ~ ! [SY3286: $i,SY3287: $i] :
( ~ ( relation @ SY3287 )
| ~ ( in @ SV58 @ ( relation_inverse_image @ SY3287 @ SY3286 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK46_D @ SY3287 @ SY3286 @ SV58 ) @ ( relation_rng @ SY3287 ) )
| ~ ( in @ ( ordered_pair @ SV58 @ ( sK46_D @ SY3287 @ SY3286 @ SV58 ) ) @ SY3287 ) )
| ~ ( in @ ( sK46_D @ SY3287 @ SY3286 @ SV58 ) @ SY3286 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(639,plain,
! [SV59: $i] :
( ( ~ ( relation @ SV59 )
| ~ ( ~ ! [SY3288: $i] :
( ~ ( relation @ SY3288 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SY3288 @ SV59 ) @ ( sK23_SY3118 @ SY3288 @ SV59 ) ) @ SV59 )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_C @ SY3288 @ SV59 ) @ ( sK23_SY3118 @ SY3288 @ SV59 ) ) @ SY3288 ) )
| ( subset @ SV59 @ SY3288 ) )
| ~ ! [SY3289: $i] :
( ~ ( relation @ SY3289 )
| ~ ( subset @ SV59 @ SY3289 )
| ! [SY3290: $i,SY3291: $i] :
( ~ ( in @ ( ordered_pair @ SY3290 @ SY3291 ) @ SV59 )
| ( in @ ( ordered_pair @ SY3290 @ SY3291 ) @ SY3289 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(640,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(641,plain,
! [SV60: $i] :
( ( ~ ( relation @ SV60 )
| ~ ( ~ ! [SY3292: $i,SY3293: $i] :
( ~ ( relation @ SY3293 )
| ~ ( ~ ( ~ ( in @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ SY3292 )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ ( sK38_SY3128 @ SY3293 @ SY3292 @ SV60 ) ) @ SV60 )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ ( sK38_SY3128 @ SY3293 @ SY3292 @ SV60 ) ) @ SY3293 ) )
| ~ ~ ( ~ ( ( in @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ SY3292 )
| ( in @ ( ordered_pair @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ ( sK38_SY3128 @ SY3293 @ SY3292 @ SV60 ) ) @ SY3293 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ ( sK38_SY3128 @ SY3293 @ SY3292 @ SV60 ) ) @ SV60 )
| ( in @ ( ordered_pair @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ ( sK38_SY3128 @ SY3293 @ SY3292 @ SV60 ) ) @ SY3293 ) ) ) )
| ( SY3293
= ( relation_dom_restriction @ SV60 @ SY3292 ) ) )
| ~ ! [SY3294: $i,SY3295: $i] :
( ~ ( relation @ SY3295 )
| ( SY3295
!= ( relation_dom_restriction @ SV60 @ SY3294 ) )
| ~ ( ~ ! [SY3296: $i,SY3297: $i] :
( ~ ( in @ SY3296 @ SY3294 )
| ~ ( in @ ( ordered_pair @ SY3296 @ SY3297 ) @ SV60 )
| ( in @ ( ordered_pair @ SY3296 @ SY3297 ) @ SY3295 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3295 )
| ( in @ SX3 @ SY3294 ) )
| ~ ! [SY3300: $i,SY3301: $i] :
( ~ ( in @ ( ordered_pair @ SY3300 @ SY3301 ) @ SY3295 )
| ( in @ ( ordered_pair @ SY3300 @ SY3301 ) @ SV60 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(642,plain,
! [SV1: $i,SV61: $i] :
( ( ~ ( relation @ SV61 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV1 @ SV61 ) ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(643,plain,
! [SV2: $i,SV62: $i] :
( ( ~ ( relation @ SV62 )
| ( subset @ ( relation_rng_restriction @ SV2 @ SV62 ) @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(644,plain,
! [SV3: $i,SV63: $i] :
( ( ~ ( relation @ SV63 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV3 @ SV63 ) ) @ ( relation_rng @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(645,plain,
! [SV4: $i,SV64: $i] :
( ( ~ ( relation @ SV64 )
| ( ( relation_rng @ ( relation_rng_restriction @ SV4 @ SV64 ) )
= ( set_intersection2 @ ( relation_rng @ SV64 ) @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(646,plain,
! [SV65: $i,SV5: $i] :
( ( ! [SY3302: $i] :
( ~ ( relation @ SY3302 )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV5 @ SY3302 ) @ SV65 )
= ( relation_rng_restriction @ SV5 @ ( relation_dom_restriction @ SY3302 @ SV65 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(647,plain,
! [SV6: $i,SV66: $i] :
( ( ~ ( relation @ SV66 )
| ( subset @ ( relation_image @ SV66 @ SV6 ) @ ( relation_rng @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(648,plain,
! [SV7: $i,SV67: $i] :
( ( ~ ( relation @ SV67 )
| ( ( relation_image @ SV67 @ SV7 )
= ( relation_image @ SV67 @ ( set_intersection2 @ ( relation_dom @ SV67 ) @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(649,plain,
! [SV8: $i] :
( ( ( ~ ( relation @ SV8 ) )
= $true )
| ( ( ( relation_image @ SV8 @ ( relation_dom @ SV8 ) )
= ( relation_rng @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[561]) ).
thf(650,plain,
! [SV9: $i] :
( ( ( ~ ( relation @ SV9 ) )
= $true )
| ( ( ! [SY3140: $i] :
( ~ ( relation @ SY3140 )
| ( ( relation_rng @ ( relation_composition @ SV9 @ SY3140 ) )
= ( relation_image @ SY3140 @ ( relation_rng @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[562]) ).
thf(651,plain,
! [SV10: $i,SV68: $i] :
( ( ~ ( relation @ SV68 )
| ( subset @ ( relation_inverse_image @ SV68 @ SV10 ) @ ( relation_dom @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(652,plain,
! [SV11: $i,SV69: $i] :
( ( ~ ( relation @ SV69 )
| ( SV11 = empty_set )
| ~ ( subset @ SV11 @ ( relation_rng @ SV69 ) )
| ( ( relation_inverse_image @ SV69 @ SV11 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(653,plain,
! [SV70: $i,SV12: $i] :
( ( ! [SY3303: $i] :
( ~ ( relation @ SY3303 )
| ~ ( subset @ SV12 @ SV70 )
| ( subset @ ( relation_inverse_image @ SY3303 @ SV12 ) @ ( relation_inverse_image @ SY3303 @ SV70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(654,plain,
! [SV13: $i] :
( ( ( ~ ( relation @ SV13 ) )
= $true )
| ( ( subset @ SV13 @ ( cartesian_product2 @ ( relation_dom @ SV13 ) @ ( relation_rng @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[566]) ).
thf(655,plain,
! [SV14: $i,SV71: $i] :
( ( ~ ( function @ SV71 )
| ~ ( relation @ SV71 )
| ! [SY3304: $i] :
( ~ ( function @ SY3304 )
| ~ ( relation @ SY3304 )
| ~ ( in @ SV14 @ ( relation_dom @ ( relation_composition @ SY3304 @ SV71 ) ) )
| ( ( apply @ ( relation_composition @ SY3304 @ SV71 ) @ SV14 )
= ( apply @ SV71 @ ( apply @ SY3304 @ SV14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(656,plain,
! [SV15: $i,SV72: $i] :
( ( ~ ( function @ SV72 )
| ~ ( relation @ SV72 )
| ! [SY3305: $i] :
( ~ ( function @ SY3305 )
| ~ ( relation @ SY3305 )
| ~ ( in @ SV15 @ ( relation_dom @ SV72 ) )
| ( ( apply @ ( relation_composition @ SV72 @ SY3305 ) @ SV15 )
= ( apply @ SY3305 @ ( apply @ SV72 @ SV15 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(657,plain,
! [SV16: $i] :
( ( ( ~ ( relation @ SV16 ) )
= $true )
| ( ( ! [SY3149: $i] :
( ~ ( relation @ SY3149 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV16 @ SY3149 ) ) @ ( relation_dom @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[569]) ).
thf(658,plain,
! [SV17: $i] :
( ( ( ~ ( relation @ SV17 ) )
= $true )
| ( ( ! [SY3150: $i] :
( ~ ( relation @ SY3150 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV17 @ SY3150 ) ) @ ( relation_rng @ SY3150 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[570]) ).
thf(659,plain,
! [SV18: $i] :
( ( ( ~ ( relation @ SV18 ) )
= $true )
| ( ( ! [SY3151: $i] :
( ~ ( relation @ SY3151 )
| ~ ( subset @ ( relation_rng @ SV18 ) @ ( relation_dom @ SY3151 ) )
| ( ( relation_dom @ ( relation_composition @ SV18 @ SY3151 ) )
= ( relation_dom @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[571]) ).
thf(660,plain,
! [SV19: $i] :
( ( ( ~ ( relation @ SV19 ) )
= $true )
| ( ( ! [SY3152: $i] :
( ~ ( relation @ SY3152 )
| ~ ( subset @ ( relation_dom @ SV19 ) @ ( relation_rng @ SY3152 ) )
| ( ( relation_rng @ ( relation_composition @ SY3152 @ SV19 ) )
= ( relation_rng @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[572]) ).
thf(661,plain,
! [SV20: $i] :
( ( ( ~ ( relation @ SV20 ) )
= $true )
| ( ( ( in @ ( ordered_pair @ ( sK41_B @ SV20 ) @ ( sK42_SY3130 @ SV20 ) ) @ SV20 )
| ( SV20 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[573]) ).
thf(662,plain,
! [SV21: $i,SV73: $i] :
( ( ~ ( relation @ SV73 )
| ( subset @ ( relation_dom_restriction @ SV73 @ SV21 ) @ SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(663,plain,
! [SV22: $i,SV74: $i] :
( ( ~ ( relation @ SV74 )
| ( ( relation_dom @ ( relation_dom_restriction @ SV74 @ SV22 ) )
= ( set_intersection2 @ ( relation_dom @ SV74 ) @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(664,plain,
! [SV23: $i,SV75: $i] :
( ( ~ ( relation @ SV75 )
| ( ( relation_dom_restriction @ SV75 @ SV23 )
= ( relation_composition @ ( identity_relation @ SV23 ) @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(665,plain,
! [SV24: $i,SV76: $i] :
( ( ~ ( relation @ SV76 )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV76 @ SV24 ) ) @ ( relation_rng @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(666,plain,
! [SV25: $i] :
( ( ( ~ ( empty @ SV25 ) )
= $true )
| ( ( function @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[578]) ).
thf(667,plain,
! [SV26: $i] :
( ( ( ~ ( empty @ SV26 ) )
= $true )
| ( ( relation @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[579]) ).
thf(668,plain,
! [SV27: $i] :
( ( ( ~ ( relation @ SV27 ) )
= $true )
| ( ( ( relation_field @ SV27 )
= ( set_union2 @ ( relation_dom @ SV27 ) @ ( relation_rng @ SV27 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[580]) ).
thf(669,plain,
! [SV28: $i] :
( ( ( ~ ( function @ SV28 )
| ~ ( relation @ SV28 ) )
= $true )
| ( ( ~ ( one_to_one @ SV28 )
| ( ( function_inverse @ SV28 )
= ( relation_inverse @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[581]) ).
thf(670,plain,
! [SV29: $i] :
( ( ( ~ ( relation @ SV29 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[582]) ).
thf(671,plain,
! [SV77: $i,SV30: $i] :
( ( ~ ( relation @ SV30 )
| ~ ( relation @ SV77 )
| ( relation @ ( relation_composition @ SV30 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(672,plain,
! [SV32: $i] :
( ( ( ~ ( relation @ SV32 ) )
= $true )
| ( ( ! [SY3158: $i] : ( relation @ ( relation_dom_restriction @ SV32 @ SY3158 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[585]) ).
thf(673,plain,
! [SV33: $i,SV78: $i] :
( ( ~ ( relation @ SV78 )
| ( relation @ ( relation_rng_restriction @ SV33 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(674,plain,
! [SV79: $i,SV34: $i] :
( ( ~ ( relation @ SV34 )
| ~ ( relation @ SV79 )
| ( relation @ ( set_intersection2 @ SV34 @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(675,plain,
! [SV80: $i,SV35: $i] :
( ( ~ ( relation @ SV35 )
| ~ ( relation @ SV80 )
| ( relation @ ( set_union2 @ SV35 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(676,plain,
! [SV36: $i] :
( ( ( ( empty @ SV36 )
| ~ ( relation @ SV36 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV36 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[589]) ).
thf(677,plain,
! [SV37: $i] :
( ( ( ( empty @ SV37 )
| ~ ( relation @ SV37 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[590]) ).
thf(678,plain,
! [SV38: $i] :
( ( ( ~ ( relation @ SV38 ) )
= $true )
| ( ( ( relation_inverse @ ( relation_inverse @ SV38 ) )
= SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[591]) ).
thf(679,plain,
! [SV39: $i] :
( ( ~ ! [SY3162: $i,SY3163: $i] :
( ~ ( function @ SY3163 )
| ~ ( relation @ SY3163 )
| ( SY3162
!= ( apply @ SY3163 @ SV39 ) )
| ~ ( in @ SV39 @ ( relation_dom @ SY3163 ) )
| ( in @ ( ordered_pair @ SV39 @ SY3162 ) @ SY3163 ) )
| ~ ~ ( ~ ! [SY3164: $i,SY3165: $i] :
( ~ ( function @ SY3165 )
| ~ ( relation @ SY3165 )
| ~ ( in @ ( ordered_pair @ SV39 @ SY3164 ) @ SY3165 )
| ( SY3164
= ( apply @ SY3165 @ SV39 ) ) )
| ~ ! [SY3166: $i,SY3167: $i] :
( ~ ( function @ SY3167 )
| ~ ( relation @ SY3167 )
| ~ ( in @ ( ordered_pair @ SV39 @ SY3166 ) @ SY3167 )
| ( in @ SV39 @ ( relation_dom @ SY3167 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[593]) ).
thf(680,plain,
! [SV40: $i] :
( ( ( ~ ( function @ SV40 )
| ~ ( relation @ SV40 ) )
= $true )
| ( ( ~ ( one_to_one @ SV40 )
| ~ ( ~ ! [SY3168: $i] :
( ~ ( function @ SY3168 )
| ~ ( relation @ SY3168 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK44_SY3131 @ SY3168 @ SV40 )
= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ( ( sK43_C @ SY3168 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SY3168 @ SV40 )
= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SY3168 @ SV40 )
= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ( ( sK44_SY3131 @ SY3168 @ SV40 )
!= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK43_C @ SY3168 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK44_SY3131 @ SY3168 @ SV40 )
!= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK43_C @ SY3168 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK43_C @ SY3168 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SY3168 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SY3168 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK44_SY3131 @ SY3168 @ SV40 )
!= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ( ( relation_dom @ SY3168 )
!= ( relation_rng @ SV40 ) )
| ( SY3168
= ( function_inverse @ SV40 ) ) )
| ~ ~ ( ~ ! [SY3169: $i] :
( ~ ( function @ SY3169 )
| ~ ( relation @ SY3169 )
| ( SY3169
!= ( function_inverse @ SV40 ) )
| ~ ( ~ ~ ( ~ ! [SY3170: $i,SY3171: $i] :
( ( SY3171
!= ( apply @ SY3169 @ SY3170 ) )
| ~ ( in @ SY3170 @ ( relation_rng @ SV40 ) )
| ( SY3170
= ( apply @ SV40 @ SY3171 ) ) )
| ~ ! [SY3172: $i,SY3173: $i] :
( ( SY3173
!= ( apply @ SY3169 @ SY3172 ) )
| ~ ( in @ SY3172 @ ( relation_rng @ SV40 ) )
| ( in @ SY3173 @ ( relation_dom @ SV40 ) ) ) )
| ~ ~ ( ~ ! [SY3174: $i,SY3175: $i] :
( ( SY3174
!= ( apply @ SV40 @ SY3175 ) )
| ~ ( in @ SY3175 @ ( relation_dom @ SV40 ) )
| ( SY3175
= ( apply @ SY3169 @ SY3174 ) ) )
| ~ ! [SY3176: $i] :
( ! [SY3177: $i] :
( ( SY3176
!= ( apply @ SV40 @ SY3177 ) )
| ~ ( in @ SY3177 @ ( relation_dom @ SV40 ) ) )
| ( in @ SY3176 @ ( relation_rng @ SV40 ) ) ) ) ) )
| ~ ! [SY3178: $i] :
( ~ ( function @ SY3178 )
| ~ ( relation @ SY3178 )
| ( SY3178
!= ( function_inverse @ SV40 ) )
| ( ( relation_dom @ SY3178 )
= ( relation_rng @ SV40 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[594]) ).
thf(681,plain,
! [SV41: $i] :
( ( ( ~ ( relation @ SV41 ) )
= $true )
| ( ( ~ ( ~ ! [SY3179: $i,SY3180: $i] :
( ~ ( ~ ( ! [SY3181: $i] :
( ~ ( in @ ( ordered_pair @ ( sK30_D @ SY3180 @ SY3179 @ SV41 ) @ SY3181 ) @ SV41 )
| ~ ( in @ SY3181 @ SY3179 ) )
| ~ ( in @ ( sK30_D @ SY3180 @ SY3179 @ SV41 ) @ SY3180 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK30_D @ SY3180 @ SY3179 @ SV41 ) @ ( sK31_SY3124 @ SY3180 @ SY3179 @ SV41 ) ) @ SV41 )
| ~ ( in @ ( sK31_SY3124 @ SY3180 @ SY3179 @ SV41 ) @ SY3179 ) )
| ( in @ ( sK30_D @ SY3180 @ SY3179 @ SV41 ) @ SY3180 ) ) )
| ( SY3180
= ( relation_inverse_image @ SV41 @ SY3179 ) ) )
| ~ ! [SY3182: $i,SY3183: $i] :
( ( SY3183
!= ( relation_inverse_image @ SV41 @ SY3182 ) )
| ~ ( ~ ! [SY3184: $i] :
( ! [SY3185: $i] :
( ~ ( in @ ( ordered_pair @ SY3184 @ SY3185 ) @ SV41 )
| ~ ( in @ SY3185 @ SY3182 ) )
| ( in @ SY3184 @ SY3183 ) )
| ~ ! [SY3186: $i] :
( ~ ( in @ SY3186 @ SY3183 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3186 @ ( sK29_E @ SY3186 @ SY3183 @ SY3182 @ SV41 ) ) @ SV41 )
| ~ ( in @ ( sK29_E @ SY3186 @ SY3183 @ SY3182 @ SV41 ) @ SY3182 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[595]) ).
thf(682,plain,
! [SV42: $i] :
( ( ( ~ ( relation @ SV42 ) )
= $true )
| ( ( ~ ( ~ ! [SY3187: $i] :
( ~ ( ~ ( ! [SY3188: $i] :
~ ( in @ ( ordered_pair @ SY3188 @ ( sK17_C @ SY3187 @ SV42 ) ) @ SV42 )
| ~ ( in @ ( sK17_C @ SY3187 @ SV42 ) @ SY3187 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK18_SY3115 @ SY3187 @ SV42 ) @ ( sK17_C @ SY3187 @ SV42 ) ) @ SV42 )
| ( in @ ( sK17_C @ SY3187 @ SV42 ) @ SY3187 ) ) )
| ( SY3187
= ( relation_rng @ SV42 ) ) )
| ~ ! [SY3189: $i] :
( ( SY3189
!= ( relation_rng @ SV42 ) )
| ~ ( ~ ! [SY3190: $i] :
( ! [SY3191: $i] :
~ ( in @ ( ordered_pair @ SY3191 @ SY3190 ) @ SV42 )
| ( in @ SY3190 @ SY3189 ) )
| ~ ! [SY3192: $i] :
( ~ ( in @ SY3192 @ SY3189 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3192 @ SY3189 @ SV42 ) @ SY3192 ) @ SV42 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[596]) ).
thf(683,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK12_B @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK13_SY3112 @ SX0 ) @ ( relation_dom @ SX0 ) ) )
| ( ( apply @ SX0 @ ( sK12_B @ SX0 ) )
!= ( apply @ SX0 @ ( sK13_SY3112 @ SX0 ) ) ) )
| ~ ( ( ( sK12_B @ SX0 )
!= ( sK13_SY3112 @ SX0 ) ) ) )
| ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[597]) ).
thf(684,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)],[597]) ).
thf(685,plain,
! [SV43: $i] :
( ( ( ~ ( relation @ SV43 ) )
= $true )
| ( ( ! [SY3193: $i] :
( ~ ( relation @ SY3193 )
| ~ ( ~ ! [SY3194: $i] :
( ~ ( relation @ SY3194 )
| ~ ( ~ ( ! [SY3195: $i] :
( ~ ( in @ ( ordered_pair @ ( sK9_D @ SY3194 @ SY3193 @ SV43 ) @ SY3195 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3195 @ ( sK10_SY3107 @ SY3194 @ SY3193 @ SV43 ) ) @ SY3193 ) )
| ~ ( in @ ( ordered_pair @ ( sK9_D @ SY3194 @ SY3193 @ SV43 ) @ ( sK10_SY3107 @ SY3194 @ SY3193 @ SV43 ) ) @ SY3194 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK9_D @ SY3194 @ SY3193 @ SV43 ) @ ( sK11_SY3111 @ SY3194 @ SY3193 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY3111 @ SY3194 @ SY3193 @ SV43 ) @ ( sK10_SY3107 @ SY3194 @ SY3193 @ SV43 ) ) @ SY3193 ) )
| ( in @ ( ordered_pair @ ( sK9_D @ SY3194 @ SY3193 @ SV43 ) @ ( sK10_SY3107 @ SY3194 @ SY3193 @ SV43 ) ) @ SY3194 ) ) )
| ( SY3194
= ( relation_composition @ SV43 @ SY3193 ) ) )
| ~ ! [SY3196: $i] :
( ~ ( relation @ SY3196 )
| ( SY3196
!= ( relation_composition @ SV43 @ SY3193 ) )
| ~ ( ~ ! [SY3197: $i,SY3198: $i] :
( ! [SY3199: $i] :
( ~ ( in @ ( ordered_pair @ SY3197 @ SY3199 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3199 @ SY3198 ) @ SY3193 ) )
| ( in @ ( ordered_pair @ SY3197 @ SY3198 ) @ SY3196 ) )
| ~ ! [SY3200: $i,SY3201: $i] :
( ~ ( in @ ( ordered_pair @ SY3200 @ SY3201 ) @ SY3196 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3200 @ ( sK8_F @ SY3201 @ SY3200 @ SY3196 @ SY3193 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK8_F @ SY3201 @ SY3200 @ SY3196 @ SY3193 @ SV43 ) @ SY3201 ) @ SY3193 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[598]) ).
thf(686,plain,
! [SV44: $i] :
( ( ( ~ ( relation @ SV44 ) )
= $true )
| ( ( ~ ( ~ ! [SY3202: $i] :
( ~ ( ~ ( ! [SY3203: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SY3202 @ SV44 ) @ SY3203 ) @ SV44 )
| ~ ( in @ ( sK20_C @ SY3202 @ SV44 ) @ SY3202 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SY3202 @ SV44 ) @ ( sK21_SY3117 @ SY3202 @ SV44 ) ) @ SV44 )
| ( in @ ( sK20_C @ SY3202 @ SV44 ) @ SY3202 ) ) )
| ( SY3202
= ( relation_dom @ SV44 ) ) )
| ~ ! [SY3204: $i] :
( ( SY3204
!= ( relation_dom @ SV44 ) )
| ~ ( ~ ! [SY3205: $i] :
( ! [SY3206: $i] :
~ ( in @ ( ordered_pair @ SY3205 @ SY3206 ) @ SV44 )
| ( in @ SY3205 @ SY3204 ) )
| ~ ! [SY3207: $i] :
( ~ ( in @ SY3207 @ SY3204 )
| ( in @ ( ordered_pair @ SY3207 @ ( sK19_D @ SY3207 @ SY3204 @ SV44 ) ) @ SV44 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[599]) ).
thf(687,plain,
! [SV45: $i] :
( ( ( ~ ( function @ SV45 )
| ~ ( relation @ SV45 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY3208: $i] :
( ~ ( in @ SY3208 @ ( relation_dom @ SV45 ) )
| ! [SY3209: $i] :
( ( SY3209
!= ( apply @ SV45 @ SY3208 ) )
| ( in @ ( ordered_pair @ SY3208 @ SY3209 ) @ SV45 ) ) )
| ~ ! [SY3210: $i] :
( ~ ( in @ SY3210 @ ( relation_dom @ SV45 ) )
| ! [SY3211: $i] :
( ~ ( in @ ( ordered_pair @ SY3210 @ SY3211 ) @ SV45 )
| ( SY3211
= ( apply @ SV45 @ SY3210 ) ) ) ) )
| ~ ~ ( ~ ! [SY3212: $i] :
( ( in @ SY3212 @ ( relation_dom @ SV45 ) )
| ! [SY3213: $i] :
( ( SY3213
!= ( apply @ SV45 @ SY3212 ) )
| ( SY3213 = empty_set ) ) )
| ~ ! [SY3214: $i] :
( ( in @ SY3214 @ ( relation_dom @ SV45 ) )
| ! [SY3215: $i] :
( ( SY3215 != empty_set )
| ( SY3215
= ( apply @ SV45 @ SY3214 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[600]) ).
thf(688,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)],[601]) ).
thf(689,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)],[601]) ).
thf(690,plain,
( ( ~ ( relation @ sK2_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[602]) ).
thf(691,plain,
( ( ~ ( relation_empty_yielding @ sK2_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[602]) ).
thf(692,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( function_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[603]) ).
thf(693,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( function_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[603]) ).
thf(694,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[604]) ).
thf(695,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[604]) ).
thf(696,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK45_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK45_C @ SX1 @ SX0 ) )
!= ( sK45_C @ SX1 @ SX0 ) ) ) )
| ( ( relation_dom @ SX1 )
!= SX0 )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[605]) ).
thf(697,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)],[605]) ).
thf(698,plain,
( ( ~ ~ ( ~ ( empty @ sK5_A )
| ~ ( relation @ sK5_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[606]) ).
thf(699,plain,
( ( ~ ( function @ sK5_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[606]) ).
thf(700,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK28_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK28_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[607]) ).
thf(701,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK26_C @ SX1 @ SX0 ) @ ( sK27_SY3120 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[607]) ).
thf(702,plain,
! [SV46: $i] :
( ( ~ ! [SY3216: $i,SY3217: $i] :
( ~ ( relation @ SY3217 )
| ~ ( in @ ( ordered_pair @ SV46 @ SY3216 ) @ SY3217 )
| ( in @ SV46 @ ( relation_field @ SY3217 ) ) )
| ~ ! [SY3218: $i,SY3219: $i] :
( ~ ( relation @ SY3219 )
| ~ ( in @ ( ordered_pair @ SV46 @ SY3218 ) @ SY3219 )
| ( in @ SY3218 @ ( relation_field @ SY3219 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[608]) ).
thf(703,plain,
! [SV81: $i,SV47: $i] :
( ( ~ ( ~ ! [SY3306: $i,SY3307: $i] :
( ~ ( relation @ SY3307 )
| ~ ( in @ SV47 @ SY3306 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ SY3307 )
| ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SY3306 ) @ SY3307 ) ) )
| ~ ~ ( ~ ! [SY3308: $i,SY3309: $i] :
( ~ ( relation @ SY3309 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SY3308 ) @ SY3309 ) )
| ( in @ SV47 @ SY3308 ) )
| ~ ! [SY3310: $i,SY3311: $i] :
( ~ ( relation @ SY3311 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SY3310 ) @ SY3311 ) )
| ( in @ ( ordered_pair @ SV47 @ SV81 ) @ SY3311 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(704,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( function @ ( function_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[610]) ).
thf(705,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( relation @ ( function_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[610]) ).
thf(706,plain,
! [SV48: $i] :
( ( ~ ! [SY3227: $i,SY3228: $i] :
( ~ ( relation @ SY3228 )
| ~ ( in @ SV48 @ SY3227 )
| ~ ( in @ SV48 @ ( relation_rng @ SY3228 ) )
| ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SY3227 @ SY3228 ) ) ) )
| ~ ~ ( ~ ! [SY3229: $i,SY3230: $i] :
( ~ ( relation @ SY3230 )
| ~ ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SY3229 @ SY3230 ) ) )
| ( in @ SV48 @ SY3229 ) )
| ~ ! [SY3231: $i,SY3232: $i] :
( ~ ( relation @ SY3232 )
| ~ ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SY3231 @ SY3232 ) ) )
| ( in @ SV48 @ ( relation_rng @ SY3232 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[611]) ).
thf(707,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[612]) ).
thf(708,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[612]) ).
thf(709,plain,
( ( ~ ( empty @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[613]) ).
thf(710,plain,
( ( ~ ( relation @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[613]) ).
thf(711,plain,
! [SV49: $i] :
( ( ( ~ ( relation @ SV49 ) )
= $true )
| ( ( ~ ( ~ ! [SY3233: $i] :
( ~ ( relation @ SY3233 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3233 @ SV49 ) @ ( sK25_SY3119 @ SY3233 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3233 @ SV49 ) @ ( sK25_SY3119 @ SY3233 @ SV49 ) ) @ SY3233 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK24_C @ SY3233 @ SV49 ) @ ( sK25_SY3119 @ SY3233 @ SV49 ) ) @ SV49 )
| ( in @ ( ordered_pair @ ( sK24_C @ SY3233 @ SV49 ) @ ( sK25_SY3119 @ SY3233 @ SV49 ) ) @ SY3233 ) ) )
| ( SV49 = SY3233 ) )
| ~ ! [SY3234: $i] :
( ~ ( relation @ SY3234 )
| ( SV49 != SY3234 )
| ~ ( ~ ! [SY3235: $i,SY3236: $i] :
( ~ ( in @ ( ordered_pair @ SY3235 @ SY3236 ) @ SV49 )
| ( in @ ( ordered_pair @ SY3235 @ SY3236 ) @ SY3234 ) )
| ~ ! [SY3237: $i,SY3238: $i] :
( ~ ( in @ ( ordered_pair @ SY3237 @ SY3238 ) @ SY3234 )
| ( in @ ( ordered_pair @ SY3237 @ SY3238 ) @ SV49 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[614]) ).
thf(712,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( ( relation_rng @ SX0 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[615]) ).
thf(713,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( ( relation_dom @ SX0 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[615]) ).
thf(714,plain,
! [SV50: $i] :
( ( ( ~ ( relation @ SV50 ) )
= $true )
| ( ( ~ ( ~ ! [SY3239: $i,SY3240: $i] :
( ~ ( ~ ( ! [SY3241: $i] :
( ~ ( in @ ( ordered_pair @ SY3241 @ ( sK33_D @ SY3240 @ SY3239 @ SV50 ) ) @ SV50 )
| ~ ( in @ SY3241 @ SY3239 ) )
| ~ ( in @ ( sK33_D @ SY3240 @ SY3239 @ SV50 ) @ SY3240 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK34_SY3126 @ SY3240 @ SY3239 @ SV50 ) @ ( sK33_D @ SY3240 @ SY3239 @ SV50 ) ) @ SV50 )
| ~ ( in @ ( sK34_SY3126 @ SY3240 @ SY3239 @ SV50 ) @ SY3239 ) )
| ( in @ ( sK33_D @ SY3240 @ SY3239 @ SV50 ) @ SY3240 ) ) )
| ( SY3240
= ( relation_image @ SV50 @ SY3239 ) ) )
| ~ ! [SY3242: $i,SY3243: $i] :
( ( SY3243
!= ( relation_image @ SV50 @ SY3242 ) )
| ~ ( ~ ! [SY3244: $i] :
( ! [SY3245: $i] :
( ~ ( in @ ( ordered_pair @ SY3245 @ SY3244 ) @ SV50 )
| ~ ( in @ SY3245 @ SY3242 ) )
| ( in @ SY3244 @ SY3243 ) )
| ~ ! [SY3246: $i] :
( ~ ( in @ SY3246 @ SY3243 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK32_E @ SY3246 @ SY3243 @ SY3242 @ SV50 ) @ SY3246 ) @ SV50 )
| ~ ( in @ ( sK32_E @ SY3246 @ SY3243 @ SY3242 @ SV50 ) @ SY3242 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[616]) ).
thf(715,plain,
( ( ~ ( function @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[617]) ).
thf(716,plain,
( ( ~ ( relation @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[617]) ).
thf(717,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( relation @ SX1 )
| ~ ( function @ SX1 )
| ( function @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[618]) ).
thf(718,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( relation @ SX1 )
| ~ ( function @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[618]) ).
thf(719,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[619]) ).
thf(720,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[619]) ).
thf(721,plain,
! [SV51: $i] :
( ( ~ ! [SY3247: $i,SY3248: $i] :
( ~ ( relation @ SY3248 )
| ! [SY3249: $i] :
( ~ ( in @ SY3249 @ ( relation_dom @ SY3248 ) )
| ~ ( in @ ( ordered_pair @ SY3249 @ SV51 ) @ SY3248 )
| ~ ( in @ SY3249 @ SY3247 ) )
| ( in @ SV51 @ ( relation_image @ SY3248 @ SY3247 ) ) )
| ~ ! [SY3250: $i,SY3251: $i] :
( ~ ( relation @ SY3251 )
| ~ ( in @ SV51 @ ( relation_image @ SY3251 @ SY3250 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK47_D @ SY3251 @ SY3250 @ SV51 ) @ ( relation_dom @ SY3251 ) )
| ~ ( in @ ( ordered_pair @ ( sK47_D @ SY3251 @ SY3250 @ SV51 ) @ SV51 ) @ SY3251 ) )
| ~ ( in @ ( sK47_D @ SY3251 @ SY3250 @ SV51 ) @ SY3250 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[620]) ).
thf(722,plain,
( ( ~ ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[621]) ).
thf(723,plain,
( ( ~ ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[621]) ).
thf(724,plain,
! [SV52: $i] :
( ( ( ~ ( relation @ SV52 ) )
= $true )
| ( ( ~ ( ~ ! [SY3252: $i] :
( ~ ( relation @ SY3252 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_C @ SY3252 @ SV52 ) @ ( sK15_SY3113 @ SY3252 @ SV52 ) ) @ SY3252 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY3113 @ SY3252 @ SV52 ) @ ( sK14_C @ SY3252 @ SV52 ) ) @ SV52 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SY3252 @ SV52 ) @ ( sK15_SY3113 @ SY3252 @ SV52 ) ) @ SY3252 )
| ( in @ ( ordered_pair @ ( sK15_SY3113 @ SY3252 @ SV52 ) @ ( sK14_C @ SY3252 @ SV52 ) ) @ SV52 ) ) )
| ( SY3252
= ( relation_inverse @ SV52 ) ) )
| ~ ! [SY3253: $i] :
( ~ ( relation @ SY3253 )
| ( SY3253
!= ( relation_inverse @ SV52 ) )
| ~ ( ~ ! [SY3254: $i,SY3255: $i] :
( ~ ( in @ ( ordered_pair @ SY3254 @ SY3255 ) @ SY3253 )
| ( in @ ( ordered_pair @ SY3255 @ SY3254 ) @ SV52 ) )
| ~ ! [SY3256: $i,SY3257: $i] :
( ~ ( in @ ( ordered_pair @ SY3257 @ SY3256 ) @ SV52 )
| ( in @ ( ordered_pair @ SY3256 @ SY3257 ) @ SY3253 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[622]) ).
thf(725,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( function @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[623]) ).
thf(726,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[623]) ).
thf(727,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[624]) ).
thf(728,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[624]) ).
thf(729,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[625]) ).
thf(730,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[625]) ).
thf(731,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[626]) ).
thf(732,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[626]) ).
thf(733,plain,
( ( ~ ~ ( empty @ sK4_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[627]) ).
thf(734,plain,
( ( ~ ( relation @ sK4_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[627]) ).
thf(735,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[628]) ).
thf(736,plain,
( ( ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[628]) ).
thf(737,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK39_C @ SX1 @ SX0 )
!= ( sK40_SY3129 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK39_C @ SX1 @ SX0 ) @ ( sK40_SY3129 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK39_C @ SX1 @ SX0 )
= ( sK40_SY3129 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK39_C @ SX1 @ SX0 ) @ ( sK40_SY3129 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK39_C @ SX1 @ SX0 ) @ ( sK40_SY3129 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[629]) ).
thf(738,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)],[629]) ).
thf(739,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[630]) ).
thf(740,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[630]) ).
thf(741,plain,
! [SV53: $i,SV82: $i] :
( ( ~ ( relation @ SV82 )
| ~ ( ~ ! [SY3312: $i] :
( ~ ( relation @ SY3312 )
| ~ ( ~ ( ~ ( in @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) @ SV53 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SY3312 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) ) @ SV82 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SY3312 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) ) @ SY3312 ) )
| ~ ~ ( ~ ( ( in @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) @ SV53 )
| ( in @ ( ordered_pair @ ( sK35_D @ SY3312 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) ) @ SY3312 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SY3312 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) ) @ SV82 )
| ( in @ ( ordered_pair @ ( sK35_D @ SY3312 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) ) @ SY3312 ) ) ) )
| ( SY3312
= ( relation_rng_restriction @ SV53 @ SV82 ) ) )
| ~ ! [SY3313: $i] :
( ~ ( relation @ SY3313 )
| ( SY3313
!= ( relation_rng_restriction @ SV53 @ SV82 ) )
| ~ ( ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ SY3315 @ SV53 )
| ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV82 )
| ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SY3313 ) )
| ~ ~ ( ~ ! [SY3263: $i,SY3264: $i] :
( ~ ( in @ ( ordered_pair @ SY3263 @ SY3264 ) @ SY3313 )
| ( in @ SY3264 @ SV53 ) )
| ~ ! [SY3318: $i,SY3319: $i] :
( ~ ( in @ ( ordered_pair @ SY3318 @ SY3319 ) @ SY3313 )
| ( in @ ( ordered_pair @ SY3318 @ SY3319 ) @ SV82 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(742,plain,
( ( ~ ~ ( ~ ( function @ sK3_A )
| ~ ( relation @ sK3_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[632]) ).
thf(743,plain,
( ( ~ ( one_to_one @ sK3_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[632]) ).
thf(744,plain,
! [SV54: $i] :
( ( ( ~ ( relation @ SV54 ) )
= $true )
| ( ( ~ ( ~ ! [SY3267: $i] :
( ~ ( relation @ SY3267 )
| ~ ( subset @ SV54 @ SY3267 )
| ( subset @ ( relation_dom @ SV54 ) @ ( relation_dom @ SY3267 ) ) )
| ~ ! [SY3268: $i] :
( ~ ( relation @ SY3268 )
| ~ ( subset @ SV54 @ SY3268 )
| ( subset @ ( relation_rng @ SV54 ) @ ( relation_rng @ SY3268 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[633]) ).
thf(745,plain,
! [SV55: $i,SV83: $i] :
( ( ~ ( function @ SV83 )
| ~ ( relation @ SV83 )
| ~ ( ~ ! [SY3320: $i] :
( ~ ( function @ SY3320 )
| ~ ( relation @ SY3320 )
| ~ ( in @ SV55 @ ( relation_dom @ SY3320 ) )
| ~ ( in @ ( apply @ SY3320 @ SV55 ) @ ( relation_dom @ SV83 ) )
| ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3320 @ SV83 ) ) ) )
| ~ ~ ( ~ ! [SY3321: $i] :
( ~ ( function @ SY3321 )
| ~ ( relation @ SY3321 )
| ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3321 @ SV83 ) ) )
| ( in @ SV55 @ ( relation_dom @ SY3321 ) ) )
| ~ ! [SY3322: $i] :
( ~ ( function @ SY3322 )
| ~ ( relation @ SY3322 )
| ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3322 @ SV83 ) ) )
| ( in @ ( apply @ SY3322 @ SV55 ) @ ( relation_dom @ SV83 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(746,plain,
! [SV56: $i] :
( ( ~ ! [SY3273: $i,SY3274: $i] :
( ~ ( relation @ SY3274 )
| ~ ( in @ SV56 @ SY3273 )
| ~ ( in @ SV56 @ ( relation_dom @ SY3274 ) )
| ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SY3274 @ SY3273 ) ) ) )
| ~ ~ ( ~ ! [SY3275: $i,SY3276: $i] :
( ~ ( relation @ SY3276 )
| ~ ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SY3276 @ SY3275 ) ) )
| ( in @ SV56 @ SY3275 ) )
| ~ ! [SY3277: $i,SY3278: $i] :
( ~ ( relation @ SY3278 )
| ~ ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SY3278 @ SY3277 ) ) )
| ( in @ SV56 @ ( relation_dom @ SY3278 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[635]) ).
thf(747,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[636]) ).
thf(748,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[636]) ).
thf(749,plain,
! [SV57: $i] :
( ( ~ ! [SY3279: $i,SY3280: $i] :
( ~ ( relation @ SY3280 )
| ~ ( in @ ( ordered_pair @ SV57 @ SY3279 ) @ SY3280 )
| ( in @ SV57 @ ( relation_dom @ SY3280 ) ) )
| ~ ! [SY3281: $i,SY3282: $i] :
( ~ ( relation @ SY3282 )
| ~ ( in @ ( ordered_pair @ SV57 @ SY3281 ) @ SY3282 )
| ( in @ SY3281 @ ( relation_rng @ SY3282 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[637]) ).
thf(750,plain,
! [SV58: $i] :
( ( ~ ! [SY3283: $i,SY3284: $i] :
( ~ ( relation @ SY3284 )
| ! [SY3285: $i] :
( ~ ( in @ SY3285 @ ( relation_rng @ SY3284 ) )
| ~ ( in @ ( ordered_pair @ SV58 @ SY3285 ) @ SY3284 )
| ~ ( in @ SY3285 @ SY3283 ) )
| ( in @ SV58 @ ( relation_inverse_image @ SY3284 @ SY3283 ) ) )
| ~ ! [SY3286: $i,SY3287: $i] :
( ~ ( relation @ SY3287 )
| ~ ( in @ SV58 @ ( relation_inverse_image @ SY3287 @ SY3286 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK46_D @ SY3287 @ SY3286 @ SV58 ) @ ( relation_rng @ SY3287 ) )
| ~ ( in @ ( ordered_pair @ SV58 @ ( sK46_D @ SY3287 @ SY3286 @ SV58 ) ) @ SY3287 ) )
| ~ ( in @ ( sK46_D @ SY3287 @ SY3286 @ SV58 ) @ SY3286 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[638]) ).
thf(751,plain,
! [SV59: $i] :
( ( ( ~ ( relation @ SV59 ) )
= $true )
| ( ( ~ ( ~ ! [SY3288: $i] :
( ~ ( relation @ SY3288 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SY3288 @ SV59 ) @ ( sK23_SY3118 @ SY3288 @ SV59 ) ) @ SV59 )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_C @ SY3288 @ SV59 ) @ ( sK23_SY3118 @ SY3288 @ SV59 ) ) @ SY3288 ) )
| ( subset @ SV59 @ SY3288 ) )
| ~ ! [SY3289: $i] :
( ~ ( relation @ SY3289 )
| ~ ( subset @ SV59 @ SY3289 )
| ! [SY3290: $i,SY3291: $i] :
( ~ ( in @ ( ordered_pair @ SY3290 @ SY3291 ) @ SV59 )
| ( in @ ( ordered_pair @ SY3290 @ SY3291 ) @ SY3289 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[639]) ).
thf(752,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[640]) ).
thf(753,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[640]) ).
thf(754,plain,
! [SV60: $i] :
( ( ( ~ ( relation @ SV60 ) )
= $true )
| ( ( ~ ( ~ ! [SY3292: $i,SY3293: $i] :
( ~ ( relation @ SY3293 )
| ~ ( ~ ( ~ ( in @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ SY3292 )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ ( sK38_SY3128 @ SY3293 @ SY3292 @ SV60 ) ) @ SV60 )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ ( sK38_SY3128 @ SY3293 @ SY3292 @ SV60 ) ) @ SY3293 ) )
| ~ ~ ( ~ ( ( in @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ SY3292 )
| ( in @ ( ordered_pair @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ ( sK38_SY3128 @ SY3293 @ SY3292 @ SV60 ) ) @ SY3293 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ ( sK38_SY3128 @ SY3293 @ SY3292 @ SV60 ) ) @ SV60 )
| ( in @ ( ordered_pair @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ ( sK38_SY3128 @ SY3293 @ SY3292 @ SV60 ) ) @ SY3293 ) ) ) )
| ( SY3293
= ( relation_dom_restriction @ SV60 @ SY3292 ) ) )
| ~ ! [SY3294: $i,SY3295: $i] :
( ~ ( relation @ SY3295 )
| ( SY3295
!= ( relation_dom_restriction @ SV60 @ SY3294 ) )
| ~ ( ~ ! [SY3296: $i,SY3297: $i] :
( ~ ( in @ SY3296 @ SY3294 )
| ~ ( in @ ( ordered_pair @ SY3296 @ SY3297 ) @ SV60 )
| ( in @ ( ordered_pair @ SY3296 @ SY3297 ) @ SY3295 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3295 )
| ( in @ SX3 @ SY3294 ) )
| ~ ! [SY3300: $i,SY3301: $i] :
( ~ ( in @ ( ordered_pair @ SY3300 @ SY3301 ) @ SY3295 )
| ( in @ ( ordered_pair @ SY3300 @ SY3301 ) @ SV60 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[641]) ).
thf(755,plain,
! [SV1: $i,SV61: $i] :
( ( ( ~ ( relation @ SV61 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV1 @ SV61 ) ) @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[642]) ).
thf(756,plain,
! [SV2: $i,SV62: $i] :
( ( ( ~ ( relation @ SV62 ) )
= $true )
| ( ( subset @ ( relation_rng_restriction @ SV2 @ SV62 ) @ SV62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[643]) ).
thf(757,plain,
! [SV3: $i,SV63: $i] :
( ( ( ~ ( relation @ SV63 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV3 @ SV63 ) ) @ ( relation_rng @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[644]) ).
thf(758,plain,
! [SV4: $i,SV64: $i] :
( ( ( ~ ( relation @ SV64 ) )
= $true )
| ( ( ( relation_rng @ ( relation_rng_restriction @ SV4 @ SV64 ) )
= ( set_intersection2 @ ( relation_rng @ SV64 ) @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[645]) ).
thf(759,plain,
! [SV65: $i,SV5: $i,SV84: $i] :
( ( ~ ( relation @ SV84 )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV5 @ SV84 ) @ SV65 )
= ( relation_rng_restriction @ SV5 @ ( relation_dom_restriction @ SV84 @ SV65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(760,plain,
! [SV6: $i,SV66: $i] :
( ( ( ~ ( relation @ SV66 ) )
= $true )
| ( ( subset @ ( relation_image @ SV66 @ SV6 ) @ ( relation_rng @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[647]) ).
thf(761,plain,
! [SV7: $i,SV67: $i] :
( ( ( ~ ( relation @ SV67 ) )
= $true )
| ( ( ( relation_image @ SV67 @ SV7 )
= ( relation_image @ SV67 @ ( set_intersection2 @ ( relation_dom @ SV67 ) @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[648]) ).
thf(762,plain,
! [SV8: $i] :
( ( ( relation @ SV8 )
= $false )
| ( ( ( relation_image @ SV8 @ ( relation_dom @ SV8 ) )
= ( relation_rng @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[649]) ).
thf(763,plain,
! [SV9: $i] :
( ( ( relation @ SV9 )
= $false )
| ( ( ! [SY3140: $i] :
( ~ ( relation @ SY3140 )
| ( ( relation_rng @ ( relation_composition @ SV9 @ SY3140 ) )
= ( relation_image @ SY3140 @ ( relation_rng @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[650]) ).
thf(764,plain,
! [SV10: $i,SV68: $i] :
( ( ( ~ ( relation @ SV68 ) )
= $true )
| ( ( subset @ ( relation_inverse_image @ SV68 @ SV10 ) @ ( relation_dom @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[651]) ).
thf(765,plain,
! [SV11: $i,SV69: $i] :
( ( ( ~ ( relation @ SV69 ) )
= $true )
| ( ( ( SV11 = empty_set )
| ~ ( subset @ SV11 @ ( relation_rng @ SV69 ) )
| ( ( relation_inverse_image @ SV69 @ SV11 )
!= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[652]) ).
thf(766,plain,
! [SV70: $i,SV12: $i,SV85: $i] :
( ( ~ ( relation @ SV85 )
| ~ ( subset @ SV12 @ SV70 )
| ( subset @ ( relation_inverse_image @ SV85 @ SV12 ) @ ( relation_inverse_image @ SV85 @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(767,plain,
! [SV13: $i] :
( ( ( relation @ SV13 )
= $false )
| ( ( subset @ SV13 @ ( cartesian_product2 @ ( relation_dom @ SV13 ) @ ( relation_rng @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[654]) ).
thf(768,plain,
! [SV14: $i,SV71: $i] :
( ( ( ~ ( function @ SV71 )
| ~ ( relation @ SV71 ) )
= $true )
| ( ( ! [SY3304: $i] :
( ~ ( function @ SY3304 )
| ~ ( relation @ SY3304 )
| ~ ( in @ SV14 @ ( relation_dom @ ( relation_composition @ SY3304 @ SV71 ) ) )
| ( ( apply @ ( relation_composition @ SY3304 @ SV71 ) @ SV14 )
= ( apply @ SV71 @ ( apply @ SY3304 @ SV14 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[655]) ).
thf(769,plain,
! [SV15: $i,SV72: $i] :
( ( ( ~ ( function @ SV72 )
| ~ ( relation @ SV72 ) )
= $true )
| ( ( ! [SY3305: $i] :
( ~ ( function @ SY3305 )
| ~ ( relation @ SY3305 )
| ~ ( in @ SV15 @ ( relation_dom @ SV72 ) )
| ( ( apply @ ( relation_composition @ SV72 @ SY3305 ) @ SV15 )
= ( apply @ SY3305 @ ( apply @ SV72 @ SV15 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[656]) ).
thf(770,plain,
! [SV16: $i] :
( ( ( relation @ SV16 )
= $false )
| ( ( ! [SY3149: $i] :
( ~ ( relation @ SY3149 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV16 @ SY3149 ) ) @ ( relation_dom @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[657]) ).
thf(771,plain,
! [SV17: $i] :
( ( ( relation @ SV17 )
= $false )
| ( ( ! [SY3150: $i] :
( ~ ( relation @ SY3150 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV17 @ SY3150 ) ) @ ( relation_rng @ SY3150 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(772,plain,
! [SV18: $i] :
( ( ( relation @ SV18 )
= $false )
| ( ( ! [SY3151: $i] :
( ~ ( relation @ SY3151 )
| ~ ( subset @ ( relation_rng @ SV18 ) @ ( relation_dom @ SY3151 ) )
| ( ( relation_dom @ ( relation_composition @ SV18 @ SY3151 ) )
= ( relation_dom @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[659]) ).
thf(773,plain,
! [SV19: $i] :
( ( ( relation @ SV19 )
= $false )
| ( ( ! [SY3152: $i] :
( ~ ( relation @ SY3152 )
| ~ ( subset @ ( relation_dom @ SV19 ) @ ( relation_rng @ SY3152 ) )
| ( ( relation_rng @ ( relation_composition @ SY3152 @ SV19 ) )
= ( relation_rng @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[660]) ).
thf(774,plain,
! [SV20: $i] :
( ( ( relation @ SV20 )
= $false )
| ( ( ( in @ ( ordered_pair @ ( sK41_B @ SV20 ) @ ( sK42_SY3130 @ SV20 ) ) @ SV20 )
| ( SV20 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[661]) ).
thf(775,plain,
! [SV21: $i,SV73: $i] :
( ( ( ~ ( relation @ SV73 ) )
= $true )
| ( ( subset @ ( relation_dom_restriction @ SV73 @ SV21 ) @ SV73 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[662]) ).
thf(776,plain,
! [SV22: $i,SV74: $i] :
( ( ( ~ ( relation @ SV74 ) )
= $true )
| ( ( ( relation_dom @ ( relation_dom_restriction @ SV74 @ SV22 ) )
= ( set_intersection2 @ ( relation_dom @ SV74 ) @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[663]) ).
thf(777,plain,
! [SV23: $i,SV75: $i] :
( ( ( ~ ( relation @ SV75 ) )
= $true )
| ( ( ( relation_dom_restriction @ SV75 @ SV23 )
= ( relation_composition @ ( identity_relation @ SV23 ) @ SV75 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[664]) ).
thf(778,plain,
! [SV24: $i,SV76: $i] :
( ( ( ~ ( relation @ SV76 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV76 @ SV24 ) ) @ ( relation_rng @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[665]) ).
thf(779,plain,
! [SV25: $i] :
( ( ( empty @ SV25 )
= $false )
| ( ( function @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[666]) ).
thf(780,plain,
! [SV26: $i] :
( ( ( empty @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[667]) ).
thf(781,plain,
! [SV27: $i] :
( ( ( relation @ SV27 )
= $false )
| ( ( ( relation_field @ SV27 )
= ( set_union2 @ ( relation_dom @ SV27 ) @ ( relation_rng @ SV27 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[668]) ).
thf(782,plain,
! [SV28: $i] :
( ( ( ~ ( function @ SV28 ) )
= $true )
| ( ( ~ ( relation @ SV28 ) )
= $true )
| ( ( ~ ( one_to_one @ SV28 )
| ( ( function_inverse @ SV28 )
= ( relation_inverse @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[669]) ).
thf(783,plain,
! [SV29: $i] :
( ( ( relation @ SV29 )
= $false )
| ( ( relation @ ( relation_inverse @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[670]) ).
thf(784,plain,
! [SV77: $i,SV30: $i] :
( ( ( ~ ( relation @ SV30 )
| ~ ( relation @ SV77 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV30 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[671]) ).
thf(785,plain,
! [SV32: $i] :
( ( ( relation @ SV32 )
= $false )
| ( ( ! [SY3158: $i] : ( relation @ ( relation_dom_restriction @ SV32 @ SY3158 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[672]) ).
thf(786,plain,
! [SV33: $i,SV78: $i] :
( ( ( ~ ( relation @ SV78 ) )
= $true )
| ( ( relation @ ( relation_rng_restriction @ SV33 @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[673]) ).
thf(787,plain,
! [SV79: $i,SV34: $i] :
( ( ( ~ ( relation @ SV34 )
| ~ ( relation @ SV79 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV34 @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[674]) ).
thf(788,plain,
! [SV80: $i,SV35: $i] :
( ( ( ~ ( relation @ SV35 )
| ~ ( relation @ SV80 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV35 @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[675]) ).
thf(789,plain,
! [SV36: $i] :
( ( ( empty @ SV36 )
= $true )
| ( ( ~ ( relation @ SV36 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV36 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[676]) ).
thf(790,plain,
! [SV37: $i] :
( ( ( empty @ SV37 )
= $true )
| ( ( ~ ( relation @ SV37 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[677]) ).
thf(791,plain,
! [SV38: $i] :
( ( ( relation @ SV38 )
= $false )
| ( ( ( relation_inverse @ ( relation_inverse @ SV38 ) )
= SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[678]) ).
thf(792,plain,
! [SV39: $i] :
( ( ~ ! [SY3162: $i,SY3163: $i] :
( ~ ( function @ SY3163 )
| ~ ( relation @ SY3163 )
| ( SY3162
!= ( apply @ SY3163 @ SV39 ) )
| ~ ( in @ SV39 @ ( relation_dom @ SY3163 ) )
| ( in @ ( ordered_pair @ SV39 @ SY3162 ) @ SY3163 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[679]) ).
thf(793,plain,
! [SV39: $i] :
( ( ~ ~ ( ~ ! [SY3164: $i,SY3165: $i] :
( ~ ( function @ SY3165 )
| ~ ( relation @ SY3165 )
| ~ ( in @ ( ordered_pair @ SV39 @ SY3164 ) @ SY3165 )
| ( SY3164
= ( apply @ SY3165 @ SV39 ) ) )
| ~ ! [SY3166: $i,SY3167: $i] :
( ~ ( function @ SY3167 )
| ~ ( relation @ SY3167 )
| ~ ( in @ ( ordered_pair @ SV39 @ SY3166 ) @ SY3167 )
| ( in @ SV39 @ ( relation_dom @ SY3167 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[679]) ).
thf(794,plain,
! [SV40: $i] :
( ( ( ~ ( function @ SV40 ) )
= $true )
| ( ( ~ ( relation @ SV40 ) )
= $true )
| ( ( ~ ( one_to_one @ SV40 )
| ~ ( ~ ! [SY3168: $i] :
( ~ ( function @ SY3168 )
| ~ ( relation @ SY3168 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK44_SY3131 @ SY3168 @ SV40 )
= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ( ( sK43_C @ SY3168 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SY3168 @ SV40 )
= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SY3168 @ SV40 )
= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ( ( sK44_SY3131 @ SY3168 @ SV40 )
!= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK43_C @ SY3168 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK44_SY3131 @ SY3168 @ SV40 )
!= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK43_C @ SY3168 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK43_C @ SY3168 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SY3168 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SY3168 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK44_SY3131 @ SY3168 @ SV40 )
!= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ( ( relation_dom @ SY3168 )
!= ( relation_rng @ SV40 ) )
| ( SY3168
= ( function_inverse @ SV40 ) ) )
| ~ ~ ( ~ ! [SY3169: $i] :
( ~ ( function @ SY3169 )
| ~ ( relation @ SY3169 )
| ( SY3169
!= ( function_inverse @ SV40 ) )
| ~ ( ~ ~ ( ~ ! [SY3170: $i,SY3171: $i] :
( ( SY3171
!= ( apply @ SY3169 @ SY3170 ) )
| ~ ( in @ SY3170 @ ( relation_rng @ SV40 ) )
| ( SY3170
= ( apply @ SV40 @ SY3171 ) ) )
| ~ ! [SY3172: $i,SY3173: $i] :
( ( SY3173
!= ( apply @ SY3169 @ SY3172 ) )
| ~ ( in @ SY3172 @ ( relation_rng @ SV40 ) )
| ( in @ SY3173 @ ( relation_dom @ SV40 ) ) ) )
| ~ ~ ( ~ ! [SY3174: $i,SY3175: $i] :
( ( SY3174
!= ( apply @ SV40 @ SY3175 ) )
| ~ ( in @ SY3175 @ ( relation_dom @ SV40 ) )
| ( SY3175
= ( apply @ SY3169 @ SY3174 ) ) )
| ~ ! [SY3176: $i] :
( ! [SY3177: $i] :
( ( SY3176
!= ( apply @ SV40 @ SY3177 ) )
| ~ ( in @ SY3177 @ ( relation_dom @ SV40 ) ) )
| ( in @ SY3176 @ ( relation_rng @ SV40 ) ) ) ) ) )
| ~ ! [SY3178: $i] :
( ~ ( function @ SY3178 )
| ~ ( relation @ SY3178 )
| ( SY3178
!= ( function_inverse @ SV40 ) )
| ( ( relation_dom @ SY3178 )
= ( relation_rng @ SV40 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[680]) ).
thf(795,plain,
! [SV41: $i] :
( ( ( relation @ SV41 )
= $false )
| ( ( ~ ( ~ ! [SY3179: $i,SY3180: $i] :
( ~ ( ~ ( ! [SY3181: $i] :
( ~ ( in @ ( ordered_pair @ ( sK30_D @ SY3180 @ SY3179 @ SV41 ) @ SY3181 ) @ SV41 )
| ~ ( in @ SY3181 @ SY3179 ) )
| ~ ( in @ ( sK30_D @ SY3180 @ SY3179 @ SV41 ) @ SY3180 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK30_D @ SY3180 @ SY3179 @ SV41 ) @ ( sK31_SY3124 @ SY3180 @ SY3179 @ SV41 ) ) @ SV41 )
| ~ ( in @ ( sK31_SY3124 @ SY3180 @ SY3179 @ SV41 ) @ SY3179 ) )
| ( in @ ( sK30_D @ SY3180 @ SY3179 @ SV41 ) @ SY3180 ) ) )
| ( SY3180
= ( relation_inverse_image @ SV41 @ SY3179 ) ) )
| ~ ! [SY3182: $i,SY3183: $i] :
( ( SY3183
!= ( relation_inverse_image @ SV41 @ SY3182 ) )
| ~ ( ~ ! [SY3184: $i] :
( ! [SY3185: $i] :
( ~ ( in @ ( ordered_pair @ SY3184 @ SY3185 ) @ SV41 )
| ~ ( in @ SY3185 @ SY3182 ) )
| ( in @ SY3184 @ SY3183 ) )
| ~ ! [SY3186: $i] :
( ~ ( in @ SY3186 @ SY3183 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3186 @ ( sK29_E @ SY3186 @ SY3183 @ SY3182 @ SV41 ) ) @ SV41 )
| ~ ( in @ ( sK29_E @ SY3186 @ SY3183 @ SY3182 @ SV41 ) @ SY3182 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[681]) ).
thf(796,plain,
! [SV42: $i] :
( ( ( relation @ SV42 )
= $false )
| ( ( ~ ( ~ ! [SY3187: $i] :
( ~ ( ~ ( ! [SY3188: $i] :
~ ( in @ ( ordered_pair @ SY3188 @ ( sK17_C @ SY3187 @ SV42 ) ) @ SV42 )
| ~ ( in @ ( sK17_C @ SY3187 @ SV42 ) @ SY3187 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK18_SY3115 @ SY3187 @ SV42 ) @ ( sK17_C @ SY3187 @ SV42 ) ) @ SV42 )
| ( in @ ( sK17_C @ SY3187 @ SV42 ) @ SY3187 ) ) )
| ( SY3187
= ( relation_rng @ SV42 ) ) )
| ~ ! [SY3189: $i] :
( ( SY3189
!= ( relation_rng @ SV42 ) )
| ~ ( ~ ! [SY3190: $i] :
( ! [SY3191: $i] :
~ ( in @ ( ordered_pair @ SY3191 @ SY3190 ) @ SV42 )
| ( in @ SY3190 @ SY3189 ) )
| ~ ! [SY3192: $i] :
( ~ ( in @ SY3192 @ SY3189 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3192 @ SY3189 @ SV42 ) @ SY3192 ) @ SV42 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[682]) ).
thf(797,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK12_B @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK13_SY3112 @ SX0 ) @ ( relation_dom @ SX0 ) ) )
| ( ( apply @ SX0 @ ( sK12_B @ SX0 ) )
!= ( apply @ SX0 @ ( sK13_SY3112 @ SX0 ) ) ) )
| ~ ( ( ( sK12_B @ SX0 )
!= ( sK13_SY3112 @ SX0 ) ) ) )
| ( one_to_one @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[683]) ).
thf(798,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)],[684]) ).
thf(799,plain,
! [SV43: $i] :
( ( ( relation @ SV43 )
= $false )
| ( ( ! [SY3193: $i] :
( ~ ( relation @ SY3193 )
| ~ ( ~ ! [SY3194: $i] :
( ~ ( relation @ SY3194 )
| ~ ( ~ ( ! [SY3195: $i] :
( ~ ( in @ ( ordered_pair @ ( sK9_D @ SY3194 @ SY3193 @ SV43 ) @ SY3195 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3195 @ ( sK10_SY3107 @ SY3194 @ SY3193 @ SV43 ) ) @ SY3193 ) )
| ~ ( in @ ( ordered_pair @ ( sK9_D @ SY3194 @ SY3193 @ SV43 ) @ ( sK10_SY3107 @ SY3194 @ SY3193 @ SV43 ) ) @ SY3194 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK9_D @ SY3194 @ SY3193 @ SV43 ) @ ( sK11_SY3111 @ SY3194 @ SY3193 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY3111 @ SY3194 @ SY3193 @ SV43 ) @ ( sK10_SY3107 @ SY3194 @ SY3193 @ SV43 ) ) @ SY3193 ) )
| ( in @ ( ordered_pair @ ( sK9_D @ SY3194 @ SY3193 @ SV43 ) @ ( sK10_SY3107 @ SY3194 @ SY3193 @ SV43 ) ) @ SY3194 ) ) )
| ( SY3194
= ( relation_composition @ SV43 @ SY3193 ) ) )
| ~ ! [SY3196: $i] :
( ~ ( relation @ SY3196 )
| ( SY3196
!= ( relation_composition @ SV43 @ SY3193 ) )
| ~ ( ~ ! [SY3197: $i,SY3198: $i] :
( ! [SY3199: $i] :
( ~ ( in @ ( ordered_pair @ SY3197 @ SY3199 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3199 @ SY3198 ) @ SY3193 ) )
| ( in @ ( ordered_pair @ SY3197 @ SY3198 ) @ SY3196 ) )
| ~ ! [SY3200: $i,SY3201: $i] :
( ~ ( in @ ( ordered_pair @ SY3200 @ SY3201 ) @ SY3196 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3200 @ ( sK8_F @ SY3201 @ SY3200 @ SY3196 @ SY3193 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK8_F @ SY3201 @ SY3200 @ SY3196 @ SY3193 @ SV43 ) @ SY3201 ) @ SY3193 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[685]) ).
thf(800,plain,
! [SV44: $i] :
( ( ( relation @ SV44 )
= $false )
| ( ( ~ ( ~ ! [SY3202: $i] :
( ~ ( ~ ( ! [SY3203: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SY3202 @ SV44 ) @ SY3203 ) @ SV44 )
| ~ ( in @ ( sK20_C @ SY3202 @ SV44 ) @ SY3202 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SY3202 @ SV44 ) @ ( sK21_SY3117 @ SY3202 @ SV44 ) ) @ SV44 )
| ( in @ ( sK20_C @ SY3202 @ SV44 ) @ SY3202 ) ) )
| ( SY3202
= ( relation_dom @ SV44 ) ) )
| ~ ! [SY3204: $i] :
( ( SY3204
!= ( relation_dom @ SV44 ) )
| ~ ( ~ ! [SY3205: $i] :
( ! [SY3206: $i] :
~ ( in @ ( ordered_pair @ SY3205 @ SY3206 ) @ SV44 )
| ( in @ SY3205 @ SY3204 ) )
| ~ ! [SY3207: $i] :
( ~ ( in @ SY3207 @ SY3204 )
| ( in @ ( ordered_pair @ SY3207 @ ( sK19_D @ SY3207 @ SY3204 @ SV44 ) ) @ SV44 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[686]) ).
thf(801,plain,
! [SV45: $i] :
( ( ( ~ ( function @ SV45 ) )
= $true )
| ( ( ~ ( relation @ SV45 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY3208: $i] :
( ~ ( in @ SY3208 @ ( relation_dom @ SV45 ) )
| ! [SY3209: $i] :
( ( SY3209
!= ( apply @ SV45 @ SY3208 ) )
| ( in @ ( ordered_pair @ SY3208 @ SY3209 ) @ SV45 ) ) )
| ~ ! [SY3210: $i] :
( ~ ( in @ SY3210 @ ( relation_dom @ SV45 ) )
| ! [SY3211: $i] :
( ~ ( in @ ( ordered_pair @ SY3210 @ SY3211 ) @ SV45 )
| ( SY3211
= ( apply @ SV45 @ SY3210 ) ) ) ) )
| ~ ~ ( ~ ! [SY3212: $i] :
( ( in @ SY3212 @ ( relation_dom @ SV45 ) )
| ! [SY3213: $i] :
( ( SY3213
!= ( apply @ SV45 @ SY3212 ) )
| ( SY3213 = empty_set ) ) )
| ~ ! [SY3214: $i] :
( ( in @ SY3214 @ ( relation_dom @ SV45 ) )
| ! [SY3215: $i] :
( ( SY3215 != empty_set )
| ( SY3215
= ( apply @ SV45 @ SY3214 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[687]) ).
thf(802,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)],[688]) ).
thf(803,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)],[689]) ).
thf(804,plain,
( ( relation @ sK2_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[690]) ).
thf(805,plain,
( ( relation_empty_yielding @ sK2_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[691]) ).
thf(806,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( function_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[692]) ).
thf(807,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( function_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[693]) ).
thf(808,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[694]) ).
thf(809,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[695]) ).
thf(810,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK45_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK45_C @ SX1 @ SX0 ) )
!= ( sK45_C @ SX1 @ SX0 ) ) ) )
| ( ( relation_dom @ SX1 )
!= SX0 )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[696]) ).
thf(811,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)],[697]) ).
thf(812,plain,
( ( ~ ( ~ ( empty @ sK5_A )
| ~ ( relation @ sK5_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[698]) ).
thf(813,plain,
( ( function @ sK5_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[699]) ).
thf(814,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK28_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK28_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[700]) ).
thf(815,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK26_C @ SX1 @ SX0 ) @ ( sK27_SY3120 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[701]) ).
thf(816,plain,
! [SV46: $i] :
( ( ~ ! [SY3216: $i,SY3217: $i] :
( ~ ( relation @ SY3217 )
| ~ ( in @ ( ordered_pair @ SV46 @ SY3216 ) @ SY3217 )
| ( in @ SV46 @ ( relation_field @ SY3217 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[702]) ).
thf(817,plain,
! [SV46: $i] :
( ( ~ ! [SY3218: $i,SY3219: $i] :
( ~ ( relation @ SY3219 )
| ~ ( in @ ( ordered_pair @ SV46 @ SY3218 ) @ SY3219 )
| ( in @ SY3218 @ ( relation_field @ SY3219 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[702]) ).
thf(818,plain,
! [SV81: $i,SV47: $i] :
( ( ~ ! [SY3306: $i,SY3307: $i] :
( ~ ( relation @ SY3307 )
| ~ ( in @ SV47 @ SY3306 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ SY3307 )
| ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SY3306 ) @ SY3307 ) ) )
| ~ ~ ( ~ ! [SY3308: $i,SY3309: $i] :
( ~ ( relation @ SY3309 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SY3308 ) @ SY3309 ) )
| ( in @ SV47 @ SY3308 ) )
| ~ ! [SY3310: $i,SY3311: $i] :
( ~ ( relation @ SY3311 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SY3310 ) @ SY3311 ) )
| ( in @ ( ordered_pair @ SV47 @ SV81 ) @ SY3311 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[703]) ).
thf(819,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( function @ ( function_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[704]) ).
thf(820,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( relation @ ( function_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[705]) ).
thf(821,plain,
! [SV48: $i] :
( ( ~ ! [SY3227: $i,SY3228: $i] :
( ~ ( relation @ SY3228 )
| ~ ( in @ SV48 @ SY3227 )
| ~ ( in @ SV48 @ ( relation_rng @ SY3228 ) )
| ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SY3227 @ SY3228 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[706]) ).
thf(822,plain,
! [SV48: $i] :
( ( ~ ~ ( ~ ! [SY3229: $i,SY3230: $i] :
( ~ ( relation @ SY3230 )
| ~ ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SY3229 @ SY3230 ) ) )
| ( in @ SV48 @ SY3229 ) )
| ~ ! [SY3231: $i,SY3232: $i] :
( ~ ( relation @ SY3232 )
| ~ ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SY3231 @ SY3232 ) ) )
| ( in @ SV48 @ ( relation_rng @ SY3232 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[706]) ).
thf(823,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[707]) ).
thf(824,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[708]) ).
thf(825,plain,
( ( empty @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[709]) ).
thf(826,plain,
( ( relation @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[710]) ).
thf(827,plain,
! [SV49: $i] :
( ( ( relation @ SV49 )
= $false )
| ( ( ~ ( ~ ! [SY3233: $i] :
( ~ ( relation @ SY3233 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3233 @ SV49 ) @ ( sK25_SY3119 @ SY3233 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3233 @ SV49 ) @ ( sK25_SY3119 @ SY3233 @ SV49 ) ) @ SY3233 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK24_C @ SY3233 @ SV49 ) @ ( sK25_SY3119 @ SY3233 @ SV49 ) ) @ SV49 )
| ( in @ ( ordered_pair @ ( sK24_C @ SY3233 @ SV49 ) @ ( sK25_SY3119 @ SY3233 @ SV49 ) ) @ SY3233 ) ) )
| ( SV49 = SY3233 ) )
| ~ ! [SY3234: $i] :
( ~ ( relation @ SY3234 )
| ( SV49 != SY3234 )
| ~ ( ~ ! [SY3235: $i,SY3236: $i] :
( ~ ( in @ ( ordered_pair @ SY3235 @ SY3236 ) @ SV49 )
| ( in @ ( ordered_pair @ SY3235 @ SY3236 ) @ SY3234 ) )
| ~ ! [SY3237: $i,SY3238: $i] :
( ~ ( in @ ( ordered_pair @ SY3237 @ SY3238 ) @ SY3234 )
| ( in @ ( ordered_pair @ SY3237 @ SY3238 ) @ SV49 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[711]) ).
thf(828,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( ( relation_rng @ SX0 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[712]) ).
thf(829,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( ( relation_dom @ SX0 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[713]) ).
thf(830,plain,
! [SV50: $i] :
( ( ( relation @ SV50 )
= $false )
| ( ( ~ ( ~ ! [SY3239: $i,SY3240: $i] :
( ~ ( ~ ( ! [SY3241: $i] :
( ~ ( in @ ( ordered_pair @ SY3241 @ ( sK33_D @ SY3240 @ SY3239 @ SV50 ) ) @ SV50 )
| ~ ( in @ SY3241 @ SY3239 ) )
| ~ ( in @ ( sK33_D @ SY3240 @ SY3239 @ SV50 ) @ SY3240 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK34_SY3126 @ SY3240 @ SY3239 @ SV50 ) @ ( sK33_D @ SY3240 @ SY3239 @ SV50 ) ) @ SV50 )
| ~ ( in @ ( sK34_SY3126 @ SY3240 @ SY3239 @ SV50 ) @ SY3239 ) )
| ( in @ ( sK33_D @ SY3240 @ SY3239 @ SV50 ) @ SY3240 ) ) )
| ( SY3240
= ( relation_image @ SV50 @ SY3239 ) ) )
| ~ ! [SY3242: $i,SY3243: $i] :
( ( SY3243
!= ( relation_image @ SV50 @ SY3242 ) )
| ~ ( ~ ! [SY3244: $i] :
( ! [SY3245: $i] :
( ~ ( in @ ( ordered_pair @ SY3245 @ SY3244 ) @ SV50 )
| ~ ( in @ SY3245 @ SY3242 ) )
| ( in @ SY3244 @ SY3243 ) )
| ~ ! [SY3246: $i] :
( ~ ( in @ SY3246 @ SY3243 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK32_E @ SY3246 @ SY3243 @ SY3242 @ SV50 ) @ SY3246 ) @ SV50 )
| ~ ( in @ ( sK32_E @ SY3246 @ SY3243 @ SY3242 @ SV50 ) @ SY3242 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[714]) ).
thf(831,plain,
( ( function @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[715]) ).
thf(832,plain,
( ( relation @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[716]) ).
thf(833,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( relation @ SX1 )
| ~ ( function @ SX1 )
| ( function @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[717]) ).
thf(834,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( relation @ SX1 )
| ~ ( function @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[718]) ).
thf(835,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[719]) ).
thf(836,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[720]) ).
thf(837,plain,
! [SV51: $i] :
( ( ~ ! [SY3247: $i,SY3248: $i] :
( ~ ( relation @ SY3248 )
| ! [SY3249: $i] :
( ~ ( in @ SY3249 @ ( relation_dom @ SY3248 ) )
| ~ ( in @ ( ordered_pair @ SY3249 @ SV51 ) @ SY3248 )
| ~ ( in @ SY3249 @ SY3247 ) )
| ( in @ SV51 @ ( relation_image @ SY3248 @ SY3247 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[721]) ).
thf(838,plain,
! [SV51: $i] :
( ( ~ ! [SY3250: $i,SY3251: $i] :
( ~ ( relation @ SY3251 )
| ~ ( in @ SV51 @ ( relation_image @ SY3251 @ SY3250 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK47_D @ SY3251 @ SY3250 @ SV51 ) @ ( relation_dom @ SY3251 ) )
| ~ ( in @ ( ordered_pair @ ( sK47_D @ SY3251 @ SY3250 @ SV51 ) @ SV51 ) @ SY3251 ) )
| ~ ( in @ ( sK47_D @ SY3251 @ SY3250 @ SV51 ) @ SY3250 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[721]) ).
thf(839,plain,
( ( ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[722]) ).
thf(840,plain,
( ( ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[723]) ).
thf(841,plain,
! [SV52: $i] :
( ( ( relation @ SV52 )
= $false )
| ( ( ~ ( ~ ! [SY3252: $i] :
( ~ ( relation @ SY3252 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_C @ SY3252 @ SV52 ) @ ( sK15_SY3113 @ SY3252 @ SV52 ) ) @ SY3252 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY3113 @ SY3252 @ SV52 ) @ ( sK14_C @ SY3252 @ SV52 ) ) @ SV52 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SY3252 @ SV52 ) @ ( sK15_SY3113 @ SY3252 @ SV52 ) ) @ SY3252 )
| ( in @ ( ordered_pair @ ( sK15_SY3113 @ SY3252 @ SV52 ) @ ( sK14_C @ SY3252 @ SV52 ) ) @ SV52 ) ) )
| ( SY3252
= ( relation_inverse @ SV52 ) ) )
| ~ ! [SY3253: $i] :
( ~ ( relation @ SY3253 )
| ( SY3253
!= ( relation_inverse @ SV52 ) )
| ~ ( ~ ! [SY3254: $i,SY3255: $i] :
( ~ ( in @ ( ordered_pair @ SY3254 @ SY3255 ) @ SY3253 )
| ( in @ ( ordered_pair @ SY3255 @ SY3254 ) @ SV52 ) )
| ~ ! [SY3256: $i,SY3257: $i] :
( ~ ( in @ ( ordered_pair @ SY3257 @ SY3256 ) @ SV52 )
| ( in @ ( ordered_pair @ SY3256 @ SY3257 ) @ SY3253 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[724]) ).
thf(842,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( function @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[725]) ).
thf(843,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[726]) ).
thf(844,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[727]) ).
thf(845,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[728]) ).
thf(846,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[729]) ).
thf(847,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[730]) ).
thf(848,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[731]) ).
thf(849,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[732]) ).
thf(850,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[733]) ).
thf(851,plain,
( ( relation @ sK4_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[734]) ).
thf(852,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[735]) ).
thf(853,plain,
( ( relation_empty_yielding @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[736]) ).
thf(854,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK39_C @ SX1 @ SX0 )
!= ( sK40_SY3129 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK39_C @ SX1 @ SX0 ) @ ( sK40_SY3129 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK39_C @ SX1 @ SX0 )
= ( sK40_SY3129 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK39_C @ SX1 @ SX0 ) @ ( sK40_SY3129 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK39_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK39_C @ SX1 @ SX0 ) @ ( sK40_SY3129 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[737]) ).
thf(855,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)],[738]) ).
thf(856,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[739]) ).
thf(857,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[740]) ).
thf(858,plain,
! [SV53: $i,SV82: $i] :
( ( ( ~ ( relation @ SV82 ) )
= $true )
| ( ( ~ ( ~ ! [SY3312: $i] :
( ~ ( relation @ SY3312 )
| ~ ( ~ ( ~ ( in @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) @ SV53 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SY3312 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) ) @ SV82 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SY3312 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) ) @ SY3312 ) )
| ~ ~ ( ~ ( ( in @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) @ SV53 )
| ( in @ ( ordered_pair @ ( sK35_D @ SY3312 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) ) @ SY3312 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SY3312 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) ) @ SV82 )
| ( in @ ( ordered_pair @ ( sK35_D @ SY3312 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) ) @ SY3312 ) ) ) )
| ( SY3312
= ( relation_rng_restriction @ SV53 @ SV82 ) ) )
| ~ ! [SY3313: $i] :
( ~ ( relation @ SY3313 )
| ( SY3313
!= ( relation_rng_restriction @ SV53 @ SV82 ) )
| ~ ( ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ SY3315 @ SV53 )
| ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV82 )
| ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SY3313 ) )
| ~ ~ ( ~ ! [SY3263: $i,SY3264: $i] :
( ~ ( in @ ( ordered_pair @ SY3263 @ SY3264 ) @ SY3313 )
| ( in @ SY3264 @ SV53 ) )
| ~ ! [SY3318: $i,SY3319: $i] :
( ~ ( in @ ( ordered_pair @ SY3318 @ SY3319 ) @ SY3313 )
| ( in @ ( ordered_pair @ SY3318 @ SY3319 ) @ SV82 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[741]) ).
thf(859,plain,
( ( ~ ( ~ ( function @ sK3_A )
| ~ ( relation @ sK3_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[742]) ).
thf(860,plain,
( ( one_to_one @ sK3_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[743]) ).
thf(861,plain,
! [SV54: $i] :
( ( ( relation @ SV54 )
= $false )
| ( ( ~ ( ~ ! [SY3267: $i] :
( ~ ( relation @ SY3267 )
| ~ ( subset @ SV54 @ SY3267 )
| ( subset @ ( relation_dom @ SV54 ) @ ( relation_dom @ SY3267 ) ) )
| ~ ! [SY3268: $i] :
( ~ ( relation @ SY3268 )
| ~ ( subset @ SV54 @ SY3268 )
| ( subset @ ( relation_rng @ SV54 ) @ ( relation_rng @ SY3268 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[744]) ).
thf(862,plain,
! [SV55: $i,SV83: $i] :
( ( ( ~ ( function @ SV83 )
| ~ ( relation @ SV83 ) )
= $true )
| ( ( ~ ( ~ ! [SY3320: $i] :
( ~ ( function @ SY3320 )
| ~ ( relation @ SY3320 )
| ~ ( in @ SV55 @ ( relation_dom @ SY3320 ) )
| ~ ( in @ ( apply @ SY3320 @ SV55 ) @ ( relation_dom @ SV83 ) )
| ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3320 @ SV83 ) ) ) )
| ~ ~ ( ~ ! [SY3321: $i] :
( ~ ( function @ SY3321 )
| ~ ( relation @ SY3321 )
| ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3321 @ SV83 ) ) )
| ( in @ SV55 @ ( relation_dom @ SY3321 ) ) )
| ~ ! [SY3322: $i] :
( ~ ( function @ SY3322 )
| ~ ( relation @ SY3322 )
| ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3322 @ SV83 ) ) )
| ( in @ ( apply @ SY3322 @ SV55 ) @ ( relation_dom @ SV83 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[745]) ).
thf(863,plain,
! [SV56: $i] :
( ( ~ ! [SY3273: $i,SY3274: $i] :
( ~ ( relation @ SY3274 )
| ~ ( in @ SV56 @ SY3273 )
| ~ ( in @ SV56 @ ( relation_dom @ SY3274 ) )
| ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SY3274 @ SY3273 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[746]) ).
thf(864,plain,
! [SV56: $i] :
( ( ~ ~ ( ~ ! [SY3275: $i,SY3276: $i] :
( ~ ( relation @ SY3276 )
| ~ ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SY3276 @ SY3275 ) ) )
| ( in @ SV56 @ SY3275 ) )
| ~ ! [SY3277: $i,SY3278: $i] :
( ~ ( relation @ SY3278 )
| ~ ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SY3278 @ SY3277 ) ) )
| ( in @ SV56 @ ( relation_dom @ SY3278 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[746]) ).
thf(865,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[747]) ).
thf(866,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[748]) ).
thf(867,plain,
! [SV57: $i] :
( ( ~ ! [SY3279: $i,SY3280: $i] :
( ~ ( relation @ SY3280 )
| ~ ( in @ ( ordered_pair @ SV57 @ SY3279 ) @ SY3280 )
| ( in @ SV57 @ ( relation_dom @ SY3280 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[749]) ).
thf(868,plain,
! [SV57: $i] :
( ( ~ ! [SY3281: $i,SY3282: $i] :
( ~ ( relation @ SY3282 )
| ~ ( in @ ( ordered_pair @ SV57 @ SY3281 ) @ SY3282 )
| ( in @ SY3281 @ ( relation_rng @ SY3282 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[749]) ).
thf(869,plain,
! [SV58: $i] :
( ( ~ ! [SY3283: $i,SY3284: $i] :
( ~ ( relation @ SY3284 )
| ! [SY3285: $i] :
( ~ ( in @ SY3285 @ ( relation_rng @ SY3284 ) )
| ~ ( in @ ( ordered_pair @ SV58 @ SY3285 ) @ SY3284 )
| ~ ( in @ SY3285 @ SY3283 ) )
| ( in @ SV58 @ ( relation_inverse_image @ SY3284 @ SY3283 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[750]) ).
thf(870,plain,
! [SV58: $i] :
( ( ~ ! [SY3286: $i,SY3287: $i] :
( ~ ( relation @ SY3287 )
| ~ ( in @ SV58 @ ( relation_inverse_image @ SY3287 @ SY3286 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK46_D @ SY3287 @ SY3286 @ SV58 ) @ ( relation_rng @ SY3287 ) )
| ~ ( in @ ( ordered_pair @ SV58 @ ( sK46_D @ SY3287 @ SY3286 @ SV58 ) ) @ SY3287 ) )
| ~ ( in @ ( sK46_D @ SY3287 @ SY3286 @ SV58 ) @ SY3286 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[750]) ).
thf(871,plain,
! [SV59: $i] :
( ( ( relation @ SV59 )
= $false )
| ( ( ~ ( ~ ! [SY3288: $i] :
( ~ ( relation @ SY3288 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SY3288 @ SV59 ) @ ( sK23_SY3118 @ SY3288 @ SV59 ) ) @ SV59 )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_C @ SY3288 @ SV59 ) @ ( sK23_SY3118 @ SY3288 @ SV59 ) ) @ SY3288 ) )
| ( subset @ SV59 @ SY3288 ) )
| ~ ! [SY3289: $i] :
( ~ ( relation @ SY3289 )
| ~ ( subset @ SV59 @ SY3289 )
| ! [SY3290: $i,SY3291: $i] :
( ~ ( in @ ( ordered_pair @ SY3290 @ SY3291 ) @ SV59 )
| ( in @ ( ordered_pair @ SY3290 @ SY3291 ) @ SY3289 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[751]) ).
thf(872,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[752]) ).
thf(873,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[753]) ).
thf(874,plain,
! [SV60: $i] :
( ( ( relation @ SV60 )
= $false )
| ( ( ~ ( ~ ! [SY3292: $i,SY3293: $i] :
( ~ ( relation @ SY3293 )
| ~ ( ~ ( ~ ( in @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ SY3292 )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ ( sK38_SY3128 @ SY3293 @ SY3292 @ SV60 ) ) @ SV60 )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ ( sK38_SY3128 @ SY3293 @ SY3292 @ SV60 ) ) @ SY3293 ) )
| ~ ~ ( ~ ( ( in @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ SY3292 )
| ( in @ ( ordered_pair @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ ( sK38_SY3128 @ SY3293 @ SY3292 @ SV60 ) ) @ SY3293 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ ( sK38_SY3128 @ SY3293 @ SY3292 @ SV60 ) ) @ SV60 )
| ( in @ ( ordered_pair @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ ( sK38_SY3128 @ SY3293 @ SY3292 @ SV60 ) ) @ SY3293 ) ) ) )
| ( SY3293
= ( relation_dom_restriction @ SV60 @ SY3292 ) ) )
| ~ ! [SY3294: $i,SY3295: $i] :
( ~ ( relation @ SY3295 )
| ( SY3295
!= ( relation_dom_restriction @ SV60 @ SY3294 ) )
| ~ ( ~ ! [SY3296: $i,SY3297: $i] :
( ~ ( in @ SY3296 @ SY3294 )
| ~ ( in @ ( ordered_pair @ SY3296 @ SY3297 ) @ SV60 )
| ( in @ ( ordered_pair @ SY3296 @ SY3297 ) @ SY3295 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3295 )
| ( in @ SX3 @ SY3294 ) )
| ~ ! [SY3300: $i,SY3301: $i] :
( ~ ( in @ ( ordered_pair @ SY3300 @ SY3301 ) @ SY3295 )
| ( in @ ( ordered_pair @ SY3300 @ SY3301 ) @ SV60 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[754]) ).
thf(875,plain,
! [SV1: $i,SV61: $i] :
( ( ( relation @ SV61 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV1 @ SV61 ) ) @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[755]) ).
thf(876,plain,
! [SV2: $i,SV62: $i] :
( ( ( relation @ SV62 )
= $false )
| ( ( subset @ ( relation_rng_restriction @ SV2 @ SV62 ) @ SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[756]) ).
thf(877,plain,
! [SV3: $i,SV63: $i] :
( ( ( relation @ SV63 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV3 @ SV63 ) ) @ ( relation_rng @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[757]) ).
thf(878,plain,
! [SV4: $i,SV64: $i] :
( ( ( relation @ SV64 )
= $false )
| ( ( ( relation_rng @ ( relation_rng_restriction @ SV4 @ SV64 ) )
= ( set_intersection2 @ ( relation_rng @ SV64 ) @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[758]) ).
thf(879,plain,
! [SV65: $i,SV5: $i,SV84: $i] :
( ( ( ~ ( relation @ SV84 ) )
= $true )
| ( ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV5 @ SV84 ) @ SV65 )
= ( relation_rng_restriction @ SV5 @ ( relation_dom_restriction @ SV84 @ SV65 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[759]) ).
thf(880,plain,
! [SV6: $i,SV66: $i] :
( ( ( relation @ SV66 )
= $false )
| ( ( subset @ ( relation_image @ SV66 @ SV6 ) @ ( relation_rng @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[760]) ).
thf(881,plain,
! [SV7: $i,SV67: $i] :
( ( ( relation @ SV67 )
= $false )
| ( ( ( relation_image @ SV67 @ SV7 )
= ( relation_image @ SV67 @ ( set_intersection2 @ ( relation_dom @ SV67 ) @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[761]) ).
thf(882,plain,
! [SV9: $i,SV86: $i] :
( ( ( ~ ( relation @ SV86 )
| ( ( relation_rng @ ( relation_composition @ SV9 @ SV86 ) )
= ( relation_image @ SV86 @ ( relation_rng @ SV9 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(883,plain,
! [SV10: $i,SV68: $i] :
( ( ( relation @ SV68 )
= $false )
| ( ( subset @ ( relation_inverse_image @ SV68 @ SV10 ) @ ( relation_dom @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[764]) ).
thf(884,plain,
! [SV11: $i,SV69: $i] :
( ( ( relation @ SV69 )
= $false )
| ( ( ( SV11 = empty_set )
| ~ ( subset @ SV11 @ ( relation_rng @ SV69 ) )
| ( ( relation_inverse_image @ SV69 @ SV11 )
!= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[765]) ).
thf(885,plain,
! [SV70: $i,SV12: $i,SV85: $i] :
( ( ( ~ ( relation @ SV85 ) )
= $true )
| ( ( ~ ( subset @ SV12 @ SV70 )
| ( subset @ ( relation_inverse_image @ SV85 @ SV12 ) @ ( relation_inverse_image @ SV85 @ SV70 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[766]) ).
thf(886,plain,
! [SV14: $i,SV71: $i] :
( ( ( ~ ( function @ SV71 ) )
= $true )
| ( ( ~ ( relation @ SV71 ) )
= $true )
| ( ( ! [SY3304: $i] :
( ~ ( function @ SY3304 )
| ~ ( relation @ SY3304 )
| ~ ( in @ SV14 @ ( relation_dom @ ( relation_composition @ SY3304 @ SV71 ) ) )
| ( ( apply @ ( relation_composition @ SY3304 @ SV71 ) @ SV14 )
= ( apply @ SV71 @ ( apply @ SY3304 @ SV14 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[768]) ).
thf(887,plain,
! [SV15: $i,SV72: $i] :
( ( ( ~ ( function @ SV72 ) )
= $true )
| ( ( ~ ( relation @ SV72 ) )
= $true )
| ( ( ! [SY3305: $i] :
( ~ ( function @ SY3305 )
| ~ ( relation @ SY3305 )
| ~ ( in @ SV15 @ ( relation_dom @ SV72 ) )
| ( ( apply @ ( relation_composition @ SV72 @ SY3305 ) @ SV15 )
= ( apply @ SY3305 @ ( apply @ SV72 @ SV15 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[769]) ).
thf(888,plain,
! [SV16: $i,SV87: $i] :
( ( ( ~ ( relation @ SV87 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV16 @ SV87 ) ) @ ( relation_dom @ SV16 ) ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(889,plain,
! [SV17: $i,SV88: $i] :
( ( ( ~ ( relation @ SV88 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV17 @ SV88 ) ) @ ( relation_rng @ SV88 ) ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(890,plain,
! [SV18: $i,SV89: $i] :
( ( ( ~ ( relation @ SV89 )
| ~ ( subset @ ( relation_rng @ SV18 ) @ ( relation_dom @ SV89 ) )
| ( ( relation_dom @ ( relation_composition @ SV18 @ SV89 ) )
= ( relation_dom @ SV18 ) ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(891,plain,
! [SV19: $i,SV90: $i] :
( ( ( ~ ( relation @ SV90 )
| ~ ( subset @ ( relation_dom @ SV19 ) @ ( relation_rng @ SV90 ) )
| ( ( relation_rng @ ( relation_composition @ SV90 @ SV19 ) )
= ( relation_rng @ SV19 ) ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(892,plain,
! [SV20: $i] :
( ( ( in @ ( ordered_pair @ ( sK41_B @ SV20 ) @ ( sK42_SY3130 @ SV20 ) ) @ SV20 )
= $true )
| ( ( SV20 = empty_set )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[774]) ).
thf(893,plain,
! [SV21: $i,SV73: $i] :
( ( ( relation @ SV73 )
= $false )
| ( ( subset @ ( relation_dom_restriction @ SV73 @ SV21 ) @ SV73 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[775]) ).
thf(894,plain,
! [SV22: $i,SV74: $i] :
( ( ( relation @ SV74 )
= $false )
| ( ( ( relation_dom @ ( relation_dom_restriction @ SV74 @ SV22 ) )
= ( set_intersection2 @ ( relation_dom @ SV74 ) @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[776]) ).
thf(895,plain,
! [SV23: $i,SV75: $i] :
( ( ( relation @ SV75 )
= $false )
| ( ( ( relation_dom_restriction @ SV75 @ SV23 )
= ( relation_composition @ ( identity_relation @ SV23 ) @ SV75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[777]) ).
thf(896,plain,
! [SV24: $i,SV76: $i] :
( ( ( relation @ SV76 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV76 @ SV24 ) ) @ ( relation_rng @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[778]) ).
thf(897,plain,
! [SV28: $i] :
( ( ( function @ SV28 )
= $false )
| ( ( ~ ( relation @ SV28 ) )
= $true )
| ( ( ~ ( one_to_one @ SV28 )
| ( ( function_inverse @ SV28 )
= ( relation_inverse @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[782]) ).
thf(898,plain,
! [SV77: $i,SV30: $i] :
( ( ( ~ ( relation @ SV30 ) )
= $true )
| ( ( ~ ( relation @ SV77 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV30 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[784]) ).
thf(899,plain,
! [SV91: $i,SV32: $i] :
( ( ( relation @ ( relation_dom_restriction @ SV32 @ SV91 ) )
= $true )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(900,plain,
! [SV33: $i,SV78: $i] :
( ( ( relation @ SV78 )
= $false )
| ( ( relation @ ( relation_rng_restriction @ SV33 @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[786]) ).
thf(901,plain,
! [SV79: $i,SV34: $i] :
( ( ( ~ ( relation @ SV34 ) )
= $true )
| ( ( ~ ( relation @ SV79 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV34 @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[787]) ).
thf(902,plain,
! [SV80: $i,SV35: $i] :
( ( ( ~ ( relation @ SV35 ) )
= $true )
| ( ( ~ ( relation @ SV80 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV35 @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[788]) ).
thf(903,plain,
! [SV36: $i] :
( ( ( relation @ SV36 )
= $false )
| ( ( empty @ SV36 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV36 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[789]) ).
thf(904,plain,
! [SV37: $i] :
( ( ( relation @ SV37 )
= $false )
| ( ( empty @ SV37 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[790]) ).
thf(905,plain,
! [SV39: $i] :
( ( ! [SY3162: $i,SY3163: $i] :
( ~ ( function @ SY3163 )
| ~ ( relation @ SY3163 )
| ( SY3162
!= ( apply @ SY3163 @ SV39 ) )
| ~ ( in @ SV39 @ ( relation_dom @ SY3163 ) )
| ( in @ ( ordered_pair @ SV39 @ SY3162 ) @ SY3163 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[792]) ).
thf(906,plain,
! [SV39: $i] :
( ( ~ ( ~ ! [SY3164: $i,SY3165: $i] :
( ~ ( function @ SY3165 )
| ~ ( relation @ SY3165 )
| ~ ( in @ ( ordered_pair @ SV39 @ SY3164 ) @ SY3165 )
| ( SY3164
= ( apply @ SY3165 @ SV39 ) ) )
| ~ ! [SY3166: $i,SY3167: $i] :
( ~ ( function @ SY3167 )
| ~ ( relation @ SY3167 )
| ~ ( in @ ( ordered_pair @ SV39 @ SY3166 ) @ SY3167 )
| ( in @ SV39 @ ( relation_dom @ SY3167 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[793]) ).
thf(907,plain,
! [SV40: $i] :
( ( ( function @ SV40 )
= $false )
| ( ( ~ ( relation @ SV40 ) )
= $true )
| ( ( ~ ( one_to_one @ SV40 )
| ~ ( ~ ! [SY3168: $i] :
( ~ ( function @ SY3168 )
| ~ ( relation @ SY3168 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK44_SY3131 @ SY3168 @ SV40 )
= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ( ( sK43_C @ SY3168 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SY3168 @ SV40 )
= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SY3168 @ SV40 )
= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ( ( sK44_SY3131 @ SY3168 @ SV40 )
!= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK43_C @ SY3168 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK44_SY3131 @ SY3168 @ SV40 )
!= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK43_C @ SY3168 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK43_C @ SY3168 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SY3168 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SY3168 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK44_SY3131 @ SY3168 @ SV40 )
!= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ( ( relation_dom @ SY3168 )
!= ( relation_rng @ SV40 ) )
| ( SY3168
= ( function_inverse @ SV40 ) ) )
| ~ ~ ( ~ ! [SY3169: $i] :
( ~ ( function @ SY3169 )
| ~ ( relation @ SY3169 )
| ( SY3169
!= ( function_inverse @ SV40 ) )
| ~ ( ~ ~ ( ~ ! [SY3170: $i,SY3171: $i] :
( ( SY3171
!= ( apply @ SY3169 @ SY3170 ) )
| ~ ( in @ SY3170 @ ( relation_rng @ SV40 ) )
| ( SY3170
= ( apply @ SV40 @ SY3171 ) ) )
| ~ ! [SY3172: $i,SY3173: $i] :
( ( SY3173
!= ( apply @ SY3169 @ SY3172 ) )
| ~ ( in @ SY3172 @ ( relation_rng @ SV40 ) )
| ( in @ SY3173 @ ( relation_dom @ SV40 ) ) ) )
| ~ ~ ( ~ ! [SY3174: $i,SY3175: $i] :
( ( SY3174
!= ( apply @ SV40 @ SY3175 ) )
| ~ ( in @ SY3175 @ ( relation_dom @ SV40 ) )
| ( SY3175
= ( apply @ SY3169 @ SY3174 ) ) )
| ~ ! [SY3176: $i] :
( ! [SY3177: $i] :
( ( SY3176
!= ( apply @ SV40 @ SY3177 ) )
| ~ ( in @ SY3177 @ ( relation_dom @ SV40 ) ) )
| ( in @ SY3176 @ ( relation_rng @ SV40 ) ) ) ) ) )
| ~ ! [SY3178: $i] :
( ~ ( function @ SY3178 )
| ~ ( relation @ SY3178 )
| ( SY3178
!= ( function_inverse @ SV40 ) )
| ( ( relation_dom @ SY3178 )
= ( relation_rng @ SV40 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[794]) ).
thf(908,plain,
! [SV41: $i] :
( ( ( ~ ! [SY3179: $i,SY3180: $i] :
( ~ ( ~ ( ! [SY3181: $i] :
( ~ ( in @ ( ordered_pair @ ( sK30_D @ SY3180 @ SY3179 @ SV41 ) @ SY3181 ) @ SV41 )
| ~ ( in @ SY3181 @ SY3179 ) )
| ~ ( in @ ( sK30_D @ SY3180 @ SY3179 @ SV41 ) @ SY3180 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK30_D @ SY3180 @ SY3179 @ SV41 ) @ ( sK31_SY3124 @ SY3180 @ SY3179 @ SV41 ) ) @ SV41 )
| ~ ( in @ ( sK31_SY3124 @ SY3180 @ SY3179 @ SV41 ) @ SY3179 ) )
| ( in @ ( sK30_D @ SY3180 @ SY3179 @ SV41 ) @ SY3180 ) ) )
| ( SY3180
= ( relation_inverse_image @ SV41 @ SY3179 ) ) )
| ~ ! [SY3182: $i,SY3183: $i] :
( ( SY3183
!= ( relation_inverse_image @ SV41 @ SY3182 ) )
| ~ ( ~ ! [SY3184: $i] :
( ! [SY3185: $i] :
( ~ ( in @ ( ordered_pair @ SY3184 @ SY3185 ) @ SV41 )
| ~ ( in @ SY3185 @ SY3182 ) )
| ( in @ SY3184 @ SY3183 ) )
| ~ ! [SY3186: $i] :
( ~ ( in @ SY3186 @ SY3183 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3186 @ ( sK29_E @ SY3186 @ SY3183 @ SY3182 @ SV41 ) ) @ SV41 )
| ~ ( in @ ( sK29_E @ SY3186 @ SY3183 @ SY3182 @ SV41 ) @ SY3182 ) ) ) ) ) )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[795]) ).
thf(909,plain,
! [SV42: $i] :
( ( ( ~ ! [SY3187: $i] :
( ~ ( ~ ( ! [SY3188: $i] :
~ ( in @ ( ordered_pair @ SY3188 @ ( sK17_C @ SY3187 @ SV42 ) ) @ SV42 )
| ~ ( in @ ( sK17_C @ SY3187 @ SV42 ) @ SY3187 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK18_SY3115 @ SY3187 @ SV42 ) @ ( sK17_C @ SY3187 @ SV42 ) ) @ SV42 )
| ( in @ ( sK17_C @ SY3187 @ SV42 ) @ SY3187 ) ) )
| ( SY3187
= ( relation_rng @ SV42 ) ) )
| ~ ! [SY3189: $i] :
( ( SY3189
!= ( relation_rng @ SV42 ) )
| ~ ( ~ ! [SY3190: $i] :
( ! [SY3191: $i] :
~ ( in @ ( ordered_pair @ SY3191 @ SY3190 ) @ SV42 )
| ( in @ SY3190 @ SY3189 ) )
| ~ ! [SY3192: $i] :
( ~ ( in @ SY3192 @ SY3189 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3192 @ SY3189 @ SV42 ) @ SY3192 ) @ SV42 ) ) ) ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[796]) ).
thf(910,plain,
! [SV92: $i] :
( ( ~ ( function @ SV92 )
| ~ ( relation @ SV92 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK12_B @ SV92 ) @ ( relation_dom @ SV92 ) )
| ~ ( in @ ( sK13_SY3112 @ SV92 ) @ ( relation_dom @ SV92 ) ) )
| ( ( apply @ SV92 @ ( sK12_B @ SV92 ) )
!= ( apply @ SV92 @ ( sK13_SY3112 @ SV92 ) ) ) )
| ~ ( ( ( sK12_B @ SV92 )
!= ( sK13_SY3112 @ SV92 ) ) ) )
| ( one_to_one @ SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(911,plain,
! [SV93: $i] :
( ( ~ ( function @ SV93 )
| ~ ( relation @ SV93 )
| ~ ( one_to_one @ SV93 )
| ! [SY3323: $i,SY3324: $i] :
( ~ ( in @ SY3323 @ ( relation_dom @ SV93 ) )
| ~ ( in @ SY3324 @ ( relation_dom @ SV93 ) )
| ( ( apply @ SV93 @ SY3323 )
!= ( apply @ SV93 @ SY3324 ) )
| ( SY3323 = SY3324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(912,plain,
! [SV43: $i,SV94: $i] :
( ( ( ~ ( relation @ SV94 )
| ~ ( ~ ! [SY3325: $i] :
( ~ ( relation @ SY3325 )
| ~ ( ~ ( ! [SY3326: $i] :
( ~ ( in @ ( ordered_pair @ ( sK9_D @ SY3325 @ SV94 @ SV43 ) @ SY3326 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3326 @ ( sK10_SY3107 @ SY3325 @ SV94 @ SV43 ) ) @ SV94 ) )
| ~ ( in @ ( ordered_pair @ ( sK9_D @ SY3325 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SY3325 @ SV94 @ SV43 ) ) @ SY3325 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK9_D @ SY3325 @ SV94 @ SV43 ) @ ( sK11_SY3111 @ SY3325 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY3111 @ SY3325 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SY3325 @ SV94 @ SV43 ) ) @ SV94 ) )
| ( in @ ( ordered_pair @ ( sK9_D @ SY3325 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SY3325 @ SV94 @ SV43 ) ) @ SY3325 ) ) )
| ( SY3325
= ( relation_composition @ SV43 @ SV94 ) ) )
| ~ ! [SY3327: $i] :
( ~ ( relation @ SY3327 )
| ( SY3327
!= ( relation_composition @ SV43 @ SV94 ) )
| ~ ( ~ ! [SY3328: $i,SY3329: $i] :
( ! [SY3330: $i] :
( ~ ( in @ ( ordered_pair @ SY3328 @ SY3330 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3330 @ SY3329 ) @ SV94 ) )
| ( in @ ( ordered_pair @ SY3328 @ SY3329 ) @ SY3327 ) )
| ~ ! [SY3331: $i,SY3332: $i] :
( ~ ( in @ ( ordered_pair @ SY3331 @ SY3332 ) @ SY3327 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3331 @ ( sK8_F @ SY3332 @ SY3331 @ SY3327 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK8_F @ SY3332 @ SY3331 @ SY3327 @ SV94 @ SV43 ) @ SY3332 ) @ SV94 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(913,plain,
! [SV44: $i] :
( ( ( ~ ! [SY3202: $i] :
( ~ ( ~ ( ! [SY3203: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SY3202 @ SV44 ) @ SY3203 ) @ SV44 )
| ~ ( in @ ( sK20_C @ SY3202 @ SV44 ) @ SY3202 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SY3202 @ SV44 ) @ ( sK21_SY3117 @ SY3202 @ SV44 ) ) @ SV44 )
| ( in @ ( sK20_C @ SY3202 @ SV44 ) @ SY3202 ) ) )
| ( SY3202
= ( relation_dom @ SV44 ) ) )
| ~ ! [SY3204: $i] :
( ( SY3204
!= ( relation_dom @ SV44 ) )
| ~ ( ~ ! [SY3205: $i] :
( ! [SY3206: $i] :
~ ( in @ ( ordered_pair @ SY3205 @ SY3206 ) @ SV44 )
| ( in @ SY3205 @ SY3204 ) )
| ~ ! [SY3207: $i] :
( ~ ( in @ SY3207 @ SY3204 )
| ( in @ ( ordered_pair @ SY3207 @ ( sK19_D @ SY3207 @ SY3204 @ SV44 ) ) @ SV44 ) ) ) ) )
= $false )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[800]) ).
thf(914,plain,
! [SV45: $i] :
( ( ( function @ SV45 )
= $false )
| ( ( ~ ( relation @ SV45 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY3208: $i] :
( ~ ( in @ SY3208 @ ( relation_dom @ SV45 ) )
| ! [SY3209: $i] :
( ( SY3209
!= ( apply @ SV45 @ SY3208 ) )
| ( in @ ( ordered_pair @ SY3208 @ SY3209 ) @ SV45 ) ) )
| ~ ! [SY3210: $i] :
( ~ ( in @ SY3210 @ ( relation_dom @ SV45 ) )
| ! [SY3211: $i] :
( ~ ( in @ ( ordered_pair @ SY3210 @ SY3211 ) @ SV45 )
| ( SY3211
= ( apply @ SV45 @ SY3210 ) ) ) ) )
| ~ ~ ( ~ ! [SY3212: $i] :
( ( in @ SY3212 @ ( relation_dom @ SV45 ) )
| ! [SY3213: $i] :
( ( SY3213
!= ( apply @ SV45 @ SY3212 ) )
| ( SY3213 = empty_set ) ) )
| ~ ! [SY3214: $i] :
( ( in @ SY3214 @ ( relation_dom @ SV45 ) )
| ! [SY3215: $i] :
( ( SY3215 != empty_set )
| ( SY3215
= ( apply @ SV45 @ SY3214 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[801]) ).
thf(915,plain,
! [SV95: $i] :
( ( ! [SY3333: $i] :
( ~ ( function @ SY3333 )
| ~ ( relation @ SY3333 )
| ~ ( in @ SV95 @ ( relation_rng @ SY3333 ) )
| ~ ( one_to_one @ SY3333 )
| ( SV95
= ( apply @ SY3333 @ ( apply @ ( function_inverse @ SY3333 ) @ SV95 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(916,plain,
! [SV96: $i] :
( ( ! [SY3334: $i] :
( ~ ( function @ SY3334 )
| ~ ( relation @ SY3334 )
| ~ ( in @ SV96 @ ( relation_rng @ SY3334 ) )
| ~ ( one_to_one @ SY3334 )
| ( SV96
= ( apply @ ( relation_composition @ ( function_inverse @ SY3334 ) @ SY3334 ) @ SV96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(917,plain,
! [SV97: $i] :
( ( ~ ( function @ SV97 )
| ~ ( relation @ SV97 )
| ~ ( one_to_one @ SV97 )
| ( ( relation_rng @ SV97 )
= ( relation_dom @ ( function_inverse @ SV97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(918,plain,
! [SV98: $i] :
( ( ~ ( function @ SV98 )
| ~ ( relation @ SV98 )
| ~ ( one_to_one @ SV98 )
| ( ( relation_dom @ SV98 )
= ( relation_rng @ ( function_inverse @ SV98 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(919,plain,
! [SV99: $i] :
( ( ! [SY3335: $i] :
( ~ ( empty @ SV99 )
| ~ ( relation @ SY3335 )
| ( empty @ ( relation_composition @ SV99 @ SY3335 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(920,plain,
! [SV100: $i] :
( ( ! [SY3336: $i] :
( ~ ( empty @ SV100 )
| ~ ( relation @ SY3336 )
| ( relation @ ( relation_composition @ SV100 @ SY3336 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(921,plain,
! [SV101: $i] :
( ( ! [SY3337: $i] :
( ~ ( function @ SY3337 )
| ~ ( relation @ SY3337 )
| ~ ( ~ ( in @ ( sK45_C @ SY3337 @ SV101 ) @ SV101 )
| ~ ( ( ( apply @ SY3337 @ ( sK45_C @ SY3337 @ SV101 ) )
!= ( sK45_C @ SY3337 @ SV101 ) ) ) )
| ( ( relation_dom @ SY3337 )
!= SV101 )
| ( SY3337
= ( identity_relation @ SV101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(922,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)],[811]) ).
thf(923,plain,
( ( ~ ( empty @ sK5_A )
| ~ ( relation @ sK5_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[812]) ).
thf(924,plain,
! [SV102: $i] :
( ( ~ ( ~ ! [SY3338: $i,SY3339: $i] :
( ( sK28_B @ SV102 )
!= ( ordered_pair @ SY3338 @ SY3339 ) )
| ~ ( in @ ( sK28_B @ SV102 ) @ SV102 ) )
| ( relation @ SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(925,plain,
! [SV103: $i] :
( ( ~ ( relation @ SV103 )
| ! [SY3340: $i] :
( ( SY3340
= ( ordered_pair @ ( sK26_C @ SY3340 @ SV103 ) @ ( sK27_SY3120 @ SY3340 @ SV103 ) ) )
| ~ ( in @ SY3340 @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(926,plain,
! [SV46: $i] :
( ( ! [SY3216: $i,SY3217: $i] :
( ~ ( relation @ SY3217 )
| ~ ( in @ ( ordered_pair @ SV46 @ SY3216 ) @ SY3217 )
| ( in @ SV46 @ ( relation_field @ SY3217 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[816]) ).
thf(927,plain,
! [SV46: $i] :
( ( ! [SY3218: $i,SY3219: $i] :
( ~ ( relation @ SY3219 )
| ~ ( in @ ( ordered_pair @ SV46 @ SY3218 ) @ SY3219 )
| ( in @ SY3218 @ ( relation_field @ SY3219 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[817]) ).
thf(928,plain,
! [SV81: $i,SV47: $i] :
( ( ~ ! [SY3306: $i,SY3307: $i] :
( ~ ( relation @ SY3307 )
| ~ ( in @ SV47 @ SY3306 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ SY3307 )
| ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SY3306 ) @ SY3307 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[818]) ).
thf(929,plain,
! [SV81: $i,SV47: $i] :
( ( ~ ~ ( ~ ! [SY3308: $i,SY3309: $i] :
( ~ ( relation @ SY3309 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SY3308 ) @ SY3309 ) )
| ( in @ SV47 @ SY3308 ) )
| ~ ! [SY3310: $i,SY3311: $i] :
( ~ ( relation @ SY3311 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SY3310 ) @ SY3311 ) )
| ( in @ ( ordered_pair @ SV47 @ SV81 ) @ SY3311 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[818]) ).
thf(930,plain,
! [SV104: $i] :
( ( ~ ( function @ SV104 )
| ~ ( relation @ SV104 )
| ( function @ ( function_inverse @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(931,plain,
! [SV105: $i] :
( ( ~ ( function @ SV105 )
| ~ ( relation @ SV105 )
| ( relation @ ( function_inverse @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(932,plain,
! [SV48: $i] :
( ( ! [SY3227: $i,SY3228: $i] :
( ~ ( relation @ SY3228 )
| ~ ( in @ SV48 @ SY3227 )
| ~ ( in @ SV48 @ ( relation_rng @ SY3228 ) )
| ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SY3227 @ SY3228 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[821]) ).
thf(933,plain,
! [SV48: $i] :
( ( ~ ( ~ ! [SY3229: $i,SY3230: $i] :
( ~ ( relation @ SY3230 )
| ~ ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SY3229 @ SY3230 ) ) )
| ( in @ SV48 @ SY3229 ) )
| ~ ! [SY3231: $i,SY3232: $i] :
( ~ ( relation @ SY3232 )
| ~ ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SY3231 @ SY3232 ) ) )
| ( in @ SV48 @ ( relation_rng @ SY3232 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[822]) ).
thf(934,plain,
! [SV106: $i] :
( ( ~ ( empty @ SV106 )
| ( empty @ ( relation_inverse @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(935,plain,
! [SV107: $i] :
( ( ~ ( empty @ SV107 )
| ( relation @ ( relation_inverse @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(936,plain,
! [SV49: $i] :
( ( ( ~ ! [SY3233: $i] :
( ~ ( relation @ SY3233 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3233 @ SV49 ) @ ( sK25_SY3119 @ SY3233 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3233 @ SV49 ) @ ( sK25_SY3119 @ SY3233 @ SV49 ) ) @ SY3233 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK24_C @ SY3233 @ SV49 ) @ ( sK25_SY3119 @ SY3233 @ SV49 ) ) @ SV49 )
| ( in @ ( ordered_pair @ ( sK24_C @ SY3233 @ SV49 ) @ ( sK25_SY3119 @ SY3233 @ SV49 ) ) @ SY3233 ) ) )
| ( SV49 = SY3233 ) )
| ~ ! [SY3234: $i] :
( ~ ( relation @ SY3234 )
| ( SV49 != SY3234 )
| ~ ( ~ ! [SY3235: $i,SY3236: $i] :
( ~ ( in @ ( ordered_pair @ SY3235 @ SY3236 ) @ SV49 )
| ( in @ ( ordered_pair @ SY3235 @ SY3236 ) @ SY3234 ) )
| ~ ! [SY3237: $i,SY3238: $i] :
( ~ ( in @ ( ordered_pair @ SY3237 @ SY3238 ) @ SY3234 )
| ( in @ ( ordered_pair @ SY3237 @ SY3238 ) @ SV49 ) ) ) ) )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[827]) ).
thf(937,plain,
! [SV108: $i] :
( ( ~ ( relation @ SV108 )
| ( ( relation_dom @ SV108 )
!= empty_set )
| ( ( relation_rng @ SV108 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(938,plain,
! [SV109: $i] :
( ( ~ ( relation @ SV109 )
| ( ( relation_rng @ SV109 )
!= empty_set )
| ( ( relation_dom @ SV109 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(939,plain,
! [SV50: $i] :
( ( ( ~ ! [SY3239: $i,SY3240: $i] :
( ~ ( ~ ( ! [SY3241: $i] :
( ~ ( in @ ( ordered_pair @ SY3241 @ ( sK33_D @ SY3240 @ SY3239 @ SV50 ) ) @ SV50 )
| ~ ( in @ SY3241 @ SY3239 ) )
| ~ ( in @ ( sK33_D @ SY3240 @ SY3239 @ SV50 ) @ SY3240 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK34_SY3126 @ SY3240 @ SY3239 @ SV50 ) @ ( sK33_D @ SY3240 @ SY3239 @ SV50 ) ) @ SV50 )
| ~ ( in @ ( sK34_SY3126 @ SY3240 @ SY3239 @ SV50 ) @ SY3239 ) )
| ( in @ ( sK33_D @ SY3240 @ SY3239 @ SV50 ) @ SY3240 ) ) )
| ( SY3240
= ( relation_image @ SV50 @ SY3239 ) ) )
| ~ ! [SY3242: $i,SY3243: $i] :
( ( SY3243
!= ( relation_image @ SV50 @ SY3242 ) )
| ~ ( ~ ! [SY3244: $i] :
( ! [SY3245: $i] :
( ~ ( in @ ( ordered_pair @ SY3245 @ SY3244 ) @ SV50 )
| ~ ( in @ SY3245 @ SY3242 ) )
| ( in @ SY3244 @ SY3243 ) )
| ~ ! [SY3246: $i] :
( ~ ( in @ SY3246 @ SY3243 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK32_E @ SY3246 @ SY3243 @ SY3242 @ SV50 ) @ SY3246 ) @ SV50 )
| ~ ( in @ ( sK32_E @ SY3246 @ SY3243 @ SY3242 @ SV50 ) @ SY3242 ) ) ) ) ) )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[830]) ).
thf(940,plain,
! [SV110: $i] :
( ( ! [SY3341: $i] :
( ~ ( function @ SV110 )
| ~ ( relation @ SV110 )
| ~ ( relation @ SY3341 )
| ~ ( function @ SY3341 )
| ( function @ ( relation_composition @ SV110 @ SY3341 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(941,plain,
! [SV111: $i] :
( ( ! [SY3342: $i] :
( ~ ( function @ SV111 )
| ~ ( relation @ SV111 )
| ~ ( relation @ SY3342 )
| ~ ( function @ SY3342 )
| ( relation @ ( relation_composition @ SV111 @ SY3342 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(942,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[835]) ).
thf(943,plain,
! [SV112: $i] :
( ( ~ ( empty @ SV112 )
| ~ ( relation @ SV112 )
| ~ ( function @ SV112 )
| ( one_to_one @ SV112 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(944,plain,
! [SV51: $i] :
( ( ! [SY3247: $i,SY3248: $i] :
( ~ ( relation @ SY3248 )
| ! [SY3249: $i] :
( ~ ( in @ SY3249 @ ( relation_dom @ SY3248 ) )
| ~ ( in @ ( ordered_pair @ SY3249 @ SV51 ) @ SY3248 )
| ~ ( in @ SY3249 @ SY3247 ) )
| ( in @ SV51 @ ( relation_image @ SY3248 @ SY3247 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[837]) ).
thf(945,plain,
! [SV51: $i] :
( ( ! [SY3250: $i,SY3251: $i] :
( ~ ( relation @ SY3251 )
| ~ ( in @ SV51 @ ( relation_image @ SY3251 @ SY3250 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK47_D @ SY3251 @ SY3250 @ SV51 ) @ ( relation_dom @ SY3251 ) )
| ~ ( in @ ( ordered_pair @ ( sK47_D @ SY3251 @ SY3250 @ SV51 ) @ SV51 ) @ SY3251 ) )
| ~ ( in @ ( sK47_D @ SY3251 @ SY3250 @ SV51 ) @ SY3250 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[838]) ).
thf(946,plain,
! [SV113: $i] :
( ( function @ ( identity_relation @ SV113 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(947,plain,
! [SV114: $i] :
( ( relation @ ( identity_relation @ SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(948,plain,
! [SV52: $i] :
( ( ( ~ ! [SY3252: $i] :
( ~ ( relation @ SY3252 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_C @ SY3252 @ SV52 ) @ ( sK15_SY3113 @ SY3252 @ SV52 ) ) @ SY3252 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY3113 @ SY3252 @ SV52 ) @ ( sK14_C @ SY3252 @ SV52 ) ) @ SV52 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SY3252 @ SV52 ) @ ( sK15_SY3113 @ SY3252 @ SV52 ) ) @ SY3252 )
| ( in @ ( ordered_pair @ ( sK15_SY3113 @ SY3252 @ SV52 ) @ ( sK14_C @ SY3252 @ SV52 ) ) @ SV52 ) ) )
| ( SY3252
= ( relation_inverse @ SV52 ) ) )
| ~ ! [SY3253: $i] :
( ~ ( relation @ SY3253 )
| ( SY3253
!= ( relation_inverse @ SV52 ) )
| ~ ( ~ ! [SY3254: $i,SY3255: $i] :
( ~ ( in @ ( ordered_pair @ SY3254 @ SY3255 ) @ SY3253 )
| ( in @ ( ordered_pair @ SY3255 @ SY3254 ) @ SV52 ) )
| ~ ! [SY3256: $i,SY3257: $i] :
( ~ ( in @ ( ordered_pair @ SY3257 @ SY3256 ) @ SV52 )
| ( in @ ( ordered_pair @ SY3256 @ SY3257 ) @ SY3253 ) ) ) ) )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[841]) ).
thf(949,plain,
! [SV115: $i] :
( ( ~ ( function @ SV115 )
| ~ ( relation @ SV115 )
| ~ ( one_to_one @ SV115 )
| ( function @ ( relation_inverse @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(950,plain,
! [SV116: $i] :
( ( ~ ( function @ SV116 )
| ~ ( relation @ SV116 )
| ~ ( one_to_one @ SV116 )
| ( relation @ ( relation_inverse @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(951,plain,
! [SV117: $i] :
( ( ~ ( relation @ SV117 )
| ( ( relation_dom @ SV117 )
!= empty_set )
| ( SV117 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(952,plain,
! [SV118: $i] :
( ( ~ ( relation @ SV118 )
| ( ( relation_rng @ SV118 )
!= empty_set )
| ( SV118 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(953,plain,
! [SV119: $i] :
( ( ~ ( empty @ SV119 )
| ( empty @ ( relation_dom @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(954,plain,
! [SV120: $i] :
( ( ~ ( empty @ SV120 )
| ( relation @ ( relation_dom @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(955,plain,
! [SV121: $i] :
( ( ~ ( empty @ SV121 )
| ( empty @ ( relation_rng @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(956,plain,
! [SV122: $i] :
( ( ~ ( empty @ SV122 )
| ( relation @ ( relation_rng @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(957,plain,
( ( empty @ sK4_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[850]) ).
thf(958,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[852]) ).
thf(959,plain,
! [SV123: $i] :
( ( ! [SY3343: $i] :
( ~ ( relation @ SY3343 )
| ~ ( ~ ( ( ( sK39_C @ SY3343 @ SV123 )
!= ( sK40_SY3129 @ SY3343 @ SV123 ) )
| ~ ( in @ ( sK39_C @ SY3343 @ SV123 ) @ SV123 )
| ~ ( in @ ( ordered_pair @ ( sK39_C @ SY3343 @ SV123 ) @ ( sK40_SY3129 @ SY3343 @ SV123 ) ) @ SY3343 ) )
| ~ ~ ( ~ ( ( ( sK39_C @ SY3343 @ SV123 )
= ( sK40_SY3129 @ SY3343 @ SV123 ) )
| ( in @ ( ordered_pair @ ( sK39_C @ SY3343 @ SV123 ) @ ( sK40_SY3129 @ SY3343 @ SV123 ) ) @ SY3343 ) )
| ~ ( ( in @ ( sK39_C @ SY3343 @ SV123 ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK39_C @ SY3343 @ SV123 ) @ ( sK40_SY3129 @ SY3343 @ SV123 ) ) @ SY3343 ) ) ) )
| ( SY3343
= ( identity_relation @ SV123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(960,plain,
! [SV124: $i] :
( ( ! [SY3344: $i] :
( ~ ( relation @ SY3344 )
| ( SY3344
!= ( identity_relation @ SV124 ) )
| ~ ( ~ ! [SY3345: $i,SY3346: $i] :
( ( SY3345 != SY3346 )
| ~ ( in @ SY3345 @ SV124 )
| ( in @ ( ordered_pair @ SY3345 @ SY3346 ) @ SY3344 ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SY3344 )
| ( SX2 = SX3 ) )
| ~ ! [SY3349: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SY3349 @ SX3 ) @ SY3344 )
| ( in @ SY3349 @ SV124 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(961,plain,
! [SV125: $i] :
( ( ! [SY3351: $i] :
( ~ ( empty @ SV125 )
| ~ ( relation @ SY3351 )
| ( empty @ ( relation_composition @ SY3351 @ SV125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(962,plain,
! [SV126: $i] :
( ( ! [SY3352: $i] :
( ~ ( empty @ SV126 )
| ~ ( relation @ SY3352 )
| ( relation @ ( relation_composition @ SY3352 @ SV126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(963,plain,
! [SV53: $i,SV82: $i] :
( ( ( relation @ SV82 )
= $false )
| ( ( ~ ( ~ ! [SY3312: $i] :
( ~ ( relation @ SY3312 )
| ~ ( ~ ( ~ ( in @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) @ SV53 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SY3312 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) ) @ SV82 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SY3312 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) ) @ SY3312 ) )
| ~ ~ ( ~ ( ( in @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) @ SV53 )
| ( in @ ( ordered_pair @ ( sK35_D @ SY3312 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) ) @ SY3312 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SY3312 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) ) @ SV82 )
| ( in @ ( ordered_pair @ ( sK35_D @ SY3312 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) ) @ SY3312 ) ) ) )
| ( SY3312
= ( relation_rng_restriction @ SV53 @ SV82 ) ) )
| ~ ! [SY3313: $i] :
( ~ ( relation @ SY3313 )
| ( SY3313
!= ( relation_rng_restriction @ SV53 @ SV82 ) )
| ~ ( ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ SY3315 @ SV53 )
| ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV82 )
| ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SY3313 ) )
| ~ ~ ( ~ ! [SY3263: $i,SY3264: $i] :
( ~ ( in @ ( ordered_pair @ SY3263 @ SY3264 ) @ SY3313 )
| ( in @ SY3264 @ SV53 ) )
| ~ ! [SY3318: $i,SY3319: $i] :
( ~ ( in @ ( ordered_pair @ SY3318 @ SY3319 ) @ SY3313 )
| ( in @ ( ordered_pair @ SY3318 @ SY3319 ) @ SV82 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[858]) ).
thf(964,plain,
( ( ~ ( function @ sK3_A )
| ~ ( relation @ sK3_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[859]) ).
thf(965,plain,
! [SV54: $i] :
( ( ( ~ ! [SY3267: $i] :
( ~ ( relation @ SY3267 )
| ~ ( subset @ SV54 @ SY3267 )
| ( subset @ ( relation_dom @ SV54 ) @ ( relation_dom @ SY3267 ) ) )
| ~ ! [SY3268: $i] :
( ~ ( relation @ SY3268 )
| ~ ( subset @ SV54 @ SY3268 )
| ( subset @ ( relation_rng @ SV54 ) @ ( relation_rng @ SY3268 ) ) ) )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[861]) ).
thf(966,plain,
! [SV55: $i,SV83: $i] :
( ( ( ~ ( function @ SV83 ) )
= $true )
| ( ( ~ ( relation @ SV83 ) )
= $true )
| ( ( ~ ( ~ ! [SY3320: $i] :
( ~ ( function @ SY3320 )
| ~ ( relation @ SY3320 )
| ~ ( in @ SV55 @ ( relation_dom @ SY3320 ) )
| ~ ( in @ ( apply @ SY3320 @ SV55 ) @ ( relation_dom @ SV83 ) )
| ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3320 @ SV83 ) ) ) )
| ~ ~ ( ~ ! [SY3321: $i] :
( ~ ( function @ SY3321 )
| ~ ( relation @ SY3321 )
| ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3321 @ SV83 ) ) )
| ( in @ SV55 @ ( relation_dom @ SY3321 ) ) )
| ~ ! [SY3322: $i] :
( ~ ( function @ SY3322 )
| ~ ( relation @ SY3322 )
| ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3322 @ SV83 ) ) )
| ( in @ ( apply @ SY3322 @ SV55 ) @ ( relation_dom @ SV83 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[862]) ).
thf(967,plain,
! [SV56: $i] :
( ( ! [SY3273: $i,SY3274: $i] :
( ~ ( relation @ SY3274 )
| ~ ( in @ SV56 @ SY3273 )
| ~ ( in @ SV56 @ ( relation_dom @ SY3274 ) )
| ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SY3274 @ SY3273 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[863]) ).
thf(968,plain,
! [SV56: $i] :
( ( ~ ( ~ ! [SY3275: $i,SY3276: $i] :
( ~ ( relation @ SY3276 )
| ~ ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SY3276 @ SY3275 ) ) )
| ( in @ SV56 @ SY3275 ) )
| ~ ! [SY3277: $i,SY3278: $i] :
( ~ ( relation @ SY3278 )
| ~ ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SY3278 @ SY3277 ) ) )
| ( in @ SV56 @ ( relation_dom @ SY3278 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[864]) ).
thf(969,plain,
! [SV127: $i] :
( ( ~ ( relation @ SV127 )
| ( ( relation_rng @ SV127 )
= ( relation_dom @ ( relation_inverse @ SV127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(970,plain,
! [SV128: $i] :
( ( ~ ( relation @ SV128 )
| ( ( relation_dom @ SV128 )
= ( relation_rng @ ( relation_inverse @ SV128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(971,plain,
! [SV57: $i] :
( ( ! [SY3279: $i,SY3280: $i] :
( ~ ( relation @ SY3280 )
| ~ ( in @ ( ordered_pair @ SV57 @ SY3279 ) @ SY3280 )
| ( in @ SV57 @ ( relation_dom @ SY3280 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[867]) ).
thf(972,plain,
! [SV57: $i] :
( ( ! [SY3281: $i,SY3282: $i] :
( ~ ( relation @ SY3282 )
| ~ ( in @ ( ordered_pair @ SV57 @ SY3281 ) @ SY3282 )
| ( in @ SY3281 @ ( relation_rng @ SY3282 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[868]) ).
thf(973,plain,
! [SV58: $i] :
( ( ! [SY3283: $i,SY3284: $i] :
( ~ ( relation @ SY3284 )
| ! [SY3285: $i] :
( ~ ( in @ SY3285 @ ( relation_rng @ SY3284 ) )
| ~ ( in @ ( ordered_pair @ SV58 @ SY3285 ) @ SY3284 )
| ~ ( in @ SY3285 @ SY3283 ) )
| ( in @ SV58 @ ( relation_inverse_image @ SY3284 @ SY3283 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[869]) ).
thf(974,plain,
! [SV58: $i] :
( ( ! [SY3286: $i,SY3287: $i] :
( ~ ( relation @ SY3287 )
| ~ ( in @ SV58 @ ( relation_inverse_image @ SY3287 @ SY3286 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK46_D @ SY3287 @ SY3286 @ SV58 ) @ ( relation_rng @ SY3287 ) )
| ~ ( in @ ( ordered_pair @ SV58 @ ( sK46_D @ SY3287 @ SY3286 @ SV58 ) ) @ SY3287 ) )
| ~ ( in @ ( sK46_D @ SY3287 @ SY3286 @ SV58 ) @ SY3286 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[870]) ).
thf(975,plain,
! [SV59: $i] :
( ( ( ~ ! [SY3288: $i] :
( ~ ( relation @ SY3288 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SY3288 @ SV59 ) @ ( sK23_SY3118 @ SY3288 @ SV59 ) ) @ SV59 )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_C @ SY3288 @ SV59 ) @ ( sK23_SY3118 @ SY3288 @ SV59 ) ) @ SY3288 ) )
| ( subset @ SV59 @ SY3288 ) )
| ~ ! [SY3289: $i] :
( ~ ( relation @ SY3289 )
| ~ ( subset @ SV59 @ SY3289 )
| ! [SY3290: $i,SY3291: $i] :
( ~ ( in @ ( ordered_pair @ SY3290 @ SY3291 ) @ SV59 )
| ( in @ ( ordered_pair @ SY3290 @ SY3291 ) @ SY3289 ) ) ) )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[871]) ).
thf(976,plain,
! [SV60: $i] :
( ( ( ~ ! [SY3292: $i,SY3293: $i] :
( ~ ( relation @ SY3293 )
| ~ ( ~ ( ~ ( in @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ SY3292 )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ ( sK38_SY3128 @ SY3293 @ SY3292 @ SV60 ) ) @ SV60 )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ ( sK38_SY3128 @ SY3293 @ SY3292 @ SV60 ) ) @ SY3293 ) )
| ~ ~ ( ~ ( ( in @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ SY3292 )
| ( in @ ( ordered_pair @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ ( sK38_SY3128 @ SY3293 @ SY3292 @ SV60 ) ) @ SY3293 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ ( sK38_SY3128 @ SY3293 @ SY3292 @ SV60 ) ) @ SV60 )
| ( in @ ( ordered_pair @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ ( sK38_SY3128 @ SY3293 @ SY3292 @ SV60 ) ) @ SY3293 ) ) ) )
| ( SY3293
= ( relation_dom_restriction @ SV60 @ SY3292 ) ) )
| ~ ! [SY3294: $i,SY3295: $i] :
( ~ ( relation @ SY3295 )
| ( SY3295
!= ( relation_dom_restriction @ SV60 @ SY3294 ) )
| ~ ( ~ ! [SY3296: $i,SY3297: $i] :
( ~ ( in @ SY3296 @ SY3294 )
| ~ ( in @ ( ordered_pair @ SY3296 @ SY3297 ) @ SV60 )
| ( in @ ( ordered_pair @ SY3296 @ SY3297 ) @ SY3295 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3295 )
| ( in @ SX3 @ SY3294 ) )
| ~ ! [SY3300: $i,SY3301: $i] :
( ~ ( in @ ( ordered_pair @ SY3300 @ SY3301 ) @ SY3295 )
| ( in @ ( ordered_pair @ SY3300 @ SY3301 ) @ SV60 ) ) ) ) ) )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[874]) ).
thf(977,plain,
! [SV65: $i,SV5: $i,SV84: $i] :
( ( ( relation @ SV84 )
= $false )
| ( ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV5 @ SV84 ) @ SV65 )
= ( relation_rng_restriction @ SV5 @ ( relation_dom_restriction @ SV84 @ SV65 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[879]) ).
thf(978,plain,
! [SV9: $i,SV86: $i] :
( ( ( ~ ( relation @ SV86 ) )
= $true )
| ( ( ( relation_rng @ ( relation_composition @ SV9 @ SV86 ) )
= ( relation_image @ SV86 @ ( relation_rng @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[882]) ).
thf(979,plain,
! [SV69: $i,SV11: $i] :
( ( ( ( SV11 = empty_set )
| ~ ( subset @ SV11 @ ( relation_rng @ SV69 ) ) )
= $true )
| ( ( ( ( relation_inverse_image @ SV69 @ SV11 )
!= empty_set ) )
= $true )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[884]) ).
thf(980,plain,
! [SV70: $i,SV12: $i,SV85: $i] :
( ( ( relation @ SV85 )
= $false )
| ( ( ~ ( subset @ SV12 @ SV70 )
| ( subset @ ( relation_inverse_image @ SV85 @ SV12 ) @ ( relation_inverse_image @ SV85 @ SV70 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[885]) ).
thf(981,plain,
! [SV14: $i,SV71: $i] :
( ( ( function @ SV71 )
= $false )
| ( ( ~ ( relation @ SV71 ) )
= $true )
| ( ( ! [SY3304: $i] :
( ~ ( function @ SY3304 )
| ~ ( relation @ SY3304 )
| ~ ( in @ SV14 @ ( relation_dom @ ( relation_composition @ SY3304 @ SV71 ) ) )
| ( ( apply @ ( relation_composition @ SY3304 @ SV71 ) @ SV14 )
= ( apply @ SV71 @ ( apply @ SY3304 @ SV14 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[886]) ).
thf(982,plain,
! [SV15: $i,SV72: $i] :
( ( ( function @ SV72 )
= $false )
| ( ( ~ ( relation @ SV72 ) )
= $true )
| ( ( ! [SY3305: $i] :
( ~ ( function @ SY3305 )
| ~ ( relation @ SY3305 )
| ~ ( in @ SV15 @ ( relation_dom @ SV72 ) )
| ( ( apply @ ( relation_composition @ SV72 @ SY3305 ) @ SV15 )
= ( apply @ SY3305 @ ( apply @ SV72 @ SV15 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[887]) ).
thf(983,plain,
! [SV16: $i,SV87: $i] :
( ( ( ~ ( relation @ SV87 ) )
= $true )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV16 @ SV87 ) ) @ ( relation_dom @ SV16 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[888]) ).
thf(984,plain,
! [SV17: $i,SV88: $i] :
( ( ( ~ ( relation @ SV88 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV17 @ SV88 ) ) @ ( relation_rng @ SV88 ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[889]) ).
thf(985,plain,
! [SV18: $i,SV89: $i] :
( ( ( ~ ( relation @ SV89 ) )
= $true )
| ( ( ~ ( subset @ ( relation_rng @ SV18 ) @ ( relation_dom @ SV89 ) )
| ( ( relation_dom @ ( relation_composition @ SV18 @ SV89 ) )
= ( relation_dom @ SV18 ) ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[890]) ).
thf(986,plain,
! [SV19: $i,SV90: $i] :
( ( ( ~ ( relation @ SV90 ) )
= $true )
| ( ( ~ ( subset @ ( relation_dom @ SV19 ) @ ( relation_rng @ SV90 ) )
| ( ( relation_rng @ ( relation_composition @ SV90 @ SV19 ) )
= ( relation_rng @ SV19 ) ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[891]) ).
thf(987,plain,
! [SV28: $i] :
( ( ( relation @ SV28 )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( ~ ( one_to_one @ SV28 )
| ( ( function_inverse @ SV28 )
= ( relation_inverse @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[897]) ).
thf(988,plain,
! [SV77: $i,SV30: $i] :
( ( ( relation @ SV30 )
= $false )
| ( ( ~ ( relation @ SV77 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV30 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[898]) ).
thf(989,plain,
! [SV79: $i,SV34: $i] :
( ( ( relation @ SV34 )
= $false )
| ( ( ~ ( relation @ SV79 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV34 @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[901]) ).
thf(990,plain,
! [SV80: $i,SV35: $i] :
( ( ( relation @ SV35 )
= $false )
| ( ( ~ ( relation @ SV80 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV35 @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(991,plain,
! [SV36: $i] :
( ( ( empty @ ( relation_dom @ SV36 ) )
= $false )
| ( ( empty @ SV36 )
= $true )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[903]) ).
thf(992,plain,
! [SV37: $i] :
( ( ( empty @ ( relation_rng @ SV37 ) )
= $false )
| ( ( empty @ SV37 )
= $true )
| ( ( relation @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[904]) ).
thf(993,plain,
! [SV39: $i,SV129: $i] :
( ( ! [SY3353: $i] :
( ~ ( function @ SY3353 )
| ~ ( relation @ SY3353 )
| ( SV129
!= ( apply @ SY3353 @ SV39 ) )
| ~ ( in @ SV39 @ ( relation_dom @ SY3353 ) )
| ( in @ ( ordered_pair @ SV39 @ SV129 ) @ SY3353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(994,plain,
! [SV39: $i] :
( ( ~ ! [SY3164: $i,SY3165: $i] :
( ~ ( function @ SY3165 )
| ~ ( relation @ SY3165 )
| ~ ( in @ ( ordered_pair @ SV39 @ SY3164 ) @ SY3165 )
| ( SY3164
= ( apply @ SY3165 @ SV39 ) ) )
| ~ ! [SY3166: $i,SY3167: $i] :
( ~ ( function @ SY3167 )
| ~ ( relation @ SY3167 )
| ~ ( in @ ( ordered_pair @ SV39 @ SY3166 ) @ SY3167 )
| ( in @ SV39 @ ( relation_dom @ SY3167 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[906]) ).
thf(995,plain,
! [SV40: $i] :
( ( ( relation @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( ~ ( one_to_one @ SV40 )
| ~ ( ~ ! [SY3168: $i] :
( ~ ( function @ SY3168 )
| ~ ( relation @ SY3168 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK44_SY3131 @ SY3168 @ SV40 )
= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ( ( sK43_C @ SY3168 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SY3168 @ SV40 )
= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SY3168 @ SV40 )
= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ( ( sK44_SY3131 @ SY3168 @ SV40 )
!= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK43_C @ SY3168 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK44_SY3131 @ SY3168 @ SV40 )
!= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK43_C @ SY3168 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK43_C @ SY3168 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SY3168 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SY3168 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK44_SY3131 @ SY3168 @ SV40 )
!= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ( ( relation_dom @ SY3168 )
!= ( relation_rng @ SV40 ) )
| ( SY3168
= ( function_inverse @ SV40 ) ) )
| ~ ~ ( ~ ! [SY3169: $i] :
( ~ ( function @ SY3169 )
| ~ ( relation @ SY3169 )
| ( SY3169
!= ( function_inverse @ SV40 ) )
| ~ ( ~ ~ ( ~ ! [SY3170: $i,SY3171: $i] :
( ( SY3171
!= ( apply @ SY3169 @ SY3170 ) )
| ~ ( in @ SY3170 @ ( relation_rng @ SV40 ) )
| ( SY3170
= ( apply @ SV40 @ SY3171 ) ) )
| ~ ! [SY3172: $i,SY3173: $i] :
( ( SY3173
!= ( apply @ SY3169 @ SY3172 ) )
| ~ ( in @ SY3172 @ ( relation_rng @ SV40 ) )
| ( in @ SY3173 @ ( relation_dom @ SV40 ) ) ) )
| ~ ~ ( ~ ! [SY3174: $i,SY3175: $i] :
( ( SY3174
!= ( apply @ SV40 @ SY3175 ) )
| ~ ( in @ SY3175 @ ( relation_dom @ SV40 ) )
| ( SY3175
= ( apply @ SY3169 @ SY3174 ) ) )
| ~ ! [SY3176: $i] :
( ! [SY3177: $i] :
( ( SY3176
!= ( apply @ SV40 @ SY3177 ) )
| ~ ( in @ SY3177 @ ( relation_dom @ SV40 ) ) )
| ( in @ SY3176 @ ( relation_rng @ SV40 ) ) ) ) ) )
| ~ ! [SY3178: $i] :
( ~ ( function @ SY3178 )
| ~ ( relation @ SY3178 )
| ( SY3178
!= ( function_inverse @ SV40 ) )
| ( ( relation_dom @ SY3178 )
= ( relation_rng @ SV40 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[907]) ).
thf(996,plain,
! [SV41: $i] :
( ( ( ~ ! [SY3179: $i,SY3180: $i] :
( ~ ( ~ ( ! [SY3181: $i] :
( ~ ( in @ ( ordered_pair @ ( sK30_D @ SY3180 @ SY3179 @ SV41 ) @ SY3181 ) @ SV41 )
| ~ ( in @ SY3181 @ SY3179 ) )
| ~ ( in @ ( sK30_D @ SY3180 @ SY3179 @ SV41 ) @ SY3180 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK30_D @ SY3180 @ SY3179 @ SV41 ) @ ( sK31_SY3124 @ SY3180 @ SY3179 @ SV41 ) ) @ SV41 )
| ~ ( in @ ( sK31_SY3124 @ SY3180 @ SY3179 @ SV41 ) @ SY3179 ) )
| ( in @ ( sK30_D @ SY3180 @ SY3179 @ SV41 ) @ SY3180 ) ) )
| ( SY3180
= ( relation_inverse_image @ SV41 @ SY3179 ) ) ) )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[908]) ).
thf(997,plain,
! [SV41: $i] :
( ( ( ~ ! [SY3182: $i,SY3183: $i] :
( ( SY3183
!= ( relation_inverse_image @ SV41 @ SY3182 ) )
| ~ ( ~ ! [SY3184: $i] :
( ! [SY3185: $i] :
( ~ ( in @ ( ordered_pair @ SY3184 @ SY3185 ) @ SV41 )
| ~ ( in @ SY3185 @ SY3182 ) )
| ( in @ SY3184 @ SY3183 ) )
| ~ ! [SY3186: $i] :
( ~ ( in @ SY3186 @ SY3183 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3186 @ ( sK29_E @ SY3186 @ SY3183 @ SY3182 @ SV41 ) ) @ SV41 )
| ~ ( in @ ( sK29_E @ SY3186 @ SY3183 @ SY3182 @ SV41 ) @ SY3182 ) ) ) ) ) )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[908]) ).
thf(998,plain,
! [SV42: $i] :
( ( ( ~ ! [SY3187: $i] :
( ~ ( ~ ( ! [SY3188: $i] :
~ ( in @ ( ordered_pair @ SY3188 @ ( sK17_C @ SY3187 @ SV42 ) ) @ SV42 )
| ~ ( in @ ( sK17_C @ SY3187 @ SV42 ) @ SY3187 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK18_SY3115 @ SY3187 @ SV42 ) @ ( sK17_C @ SY3187 @ SV42 ) ) @ SV42 )
| ( in @ ( sK17_C @ SY3187 @ SV42 ) @ SY3187 ) ) )
| ( SY3187
= ( relation_rng @ SV42 ) ) ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[909]) ).
thf(999,plain,
! [SV42: $i] :
( ( ( ~ ! [SY3189: $i] :
( ( SY3189
!= ( relation_rng @ SV42 ) )
| ~ ( ~ ! [SY3190: $i] :
( ! [SY3191: $i] :
~ ( in @ ( ordered_pair @ SY3191 @ SY3190 ) @ SV42 )
| ( in @ SY3190 @ SY3189 ) )
| ~ ! [SY3192: $i] :
( ~ ( in @ SY3192 @ SY3189 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3192 @ SY3189 @ SV42 ) @ SY3192 ) @ SV42 ) ) ) ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[909]) ).
thf(1000,plain,
! [SV92: $i] :
( ( ( ~ ( function @ SV92 )
| ~ ( relation @ SV92 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK12_B @ SV92 ) @ ( relation_dom @ SV92 ) )
| ~ ( in @ ( sK13_SY3112 @ SV92 ) @ ( relation_dom @ SV92 ) ) )
| ( ( apply @ SV92 @ ( sK12_B @ SV92 ) )
!= ( apply @ SV92 @ ( sK13_SY3112 @ SV92 ) ) ) )
| ~ ( ( ( sK12_B @ SV92 )
!= ( sK13_SY3112 @ SV92 ) ) ) )
| ( one_to_one @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[910]) ).
thf(1001,plain,
! [SV93: $i] :
( ( ( ~ ( function @ SV93 )
| ~ ( relation @ SV93 ) )
= $true )
| ( ( ~ ( one_to_one @ SV93 )
| ! [SY3323: $i,SY3324: $i] :
( ~ ( in @ SY3323 @ ( relation_dom @ SV93 ) )
| ~ ( in @ SY3324 @ ( relation_dom @ SV93 ) )
| ( ( apply @ SV93 @ SY3323 )
!= ( apply @ SV93 @ SY3324 ) )
| ( SY3323 = SY3324 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[911]) ).
thf(1002,plain,
! [SV43: $i,SV94: $i] :
( ( ( ~ ( relation @ SV94 ) )
= $true )
| ( ( ~ ( ~ ! [SY3325: $i] :
( ~ ( relation @ SY3325 )
| ~ ( ~ ( ! [SY3326: $i] :
( ~ ( in @ ( ordered_pair @ ( sK9_D @ SY3325 @ SV94 @ SV43 ) @ SY3326 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3326 @ ( sK10_SY3107 @ SY3325 @ SV94 @ SV43 ) ) @ SV94 ) )
| ~ ( in @ ( ordered_pair @ ( sK9_D @ SY3325 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SY3325 @ SV94 @ SV43 ) ) @ SY3325 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK9_D @ SY3325 @ SV94 @ SV43 ) @ ( sK11_SY3111 @ SY3325 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY3111 @ SY3325 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SY3325 @ SV94 @ SV43 ) ) @ SV94 ) )
| ( in @ ( ordered_pair @ ( sK9_D @ SY3325 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SY3325 @ SV94 @ SV43 ) ) @ SY3325 ) ) )
| ( SY3325
= ( relation_composition @ SV43 @ SV94 ) ) )
| ~ ! [SY3327: $i] :
( ~ ( relation @ SY3327 )
| ( SY3327
!= ( relation_composition @ SV43 @ SV94 ) )
| ~ ( ~ ! [SY3328: $i,SY3329: $i] :
( ! [SY3330: $i] :
( ~ ( in @ ( ordered_pair @ SY3328 @ SY3330 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3330 @ SY3329 ) @ SV94 ) )
| ( in @ ( ordered_pair @ SY3328 @ SY3329 ) @ SY3327 ) )
| ~ ! [SY3331: $i,SY3332: $i] :
( ~ ( in @ ( ordered_pair @ SY3331 @ SY3332 ) @ SY3327 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3331 @ ( sK8_F @ SY3332 @ SY3331 @ SY3327 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK8_F @ SY3332 @ SY3331 @ SY3327 @ SV94 @ SV43 ) @ SY3332 ) @ SV94 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[912]) ).
thf(1003,plain,
! [SV44: $i] :
( ( ( ~ ! [SY3202: $i] :
( ~ ( ~ ( ! [SY3203: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SY3202 @ SV44 ) @ SY3203 ) @ SV44 )
| ~ ( in @ ( sK20_C @ SY3202 @ SV44 ) @ SY3202 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SY3202 @ SV44 ) @ ( sK21_SY3117 @ SY3202 @ SV44 ) ) @ SV44 )
| ( in @ ( sK20_C @ SY3202 @ SV44 ) @ SY3202 ) ) )
| ( SY3202
= ( relation_dom @ SV44 ) ) ) )
= $false )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[913]) ).
thf(1004,plain,
! [SV44: $i] :
( ( ( ~ ! [SY3204: $i] :
( ( SY3204
!= ( relation_dom @ SV44 ) )
| ~ ( ~ ! [SY3205: $i] :
( ! [SY3206: $i] :
~ ( in @ ( ordered_pair @ SY3205 @ SY3206 ) @ SV44 )
| ( in @ SY3205 @ SY3204 ) )
| ~ ! [SY3207: $i] :
( ~ ( in @ SY3207 @ SY3204 )
| ( in @ ( ordered_pair @ SY3207 @ ( sK19_D @ SY3207 @ SY3204 @ SV44 ) ) @ SV44 ) ) ) ) )
= $false )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[913]) ).
thf(1005,plain,
! [SV45: $i] :
( ( ( relation @ SV45 )
= $false )
| ( ( function @ SV45 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY3208: $i] :
( ~ ( in @ SY3208 @ ( relation_dom @ SV45 ) )
| ! [SY3209: $i] :
( ( SY3209
!= ( apply @ SV45 @ SY3208 ) )
| ( in @ ( ordered_pair @ SY3208 @ SY3209 ) @ SV45 ) ) )
| ~ ! [SY3210: $i] :
( ~ ( in @ SY3210 @ ( relation_dom @ SV45 ) )
| ! [SY3211: $i] :
( ~ ( in @ ( ordered_pair @ SY3210 @ SY3211 ) @ SV45 )
| ( SY3211
= ( apply @ SV45 @ SY3210 ) ) ) ) )
| ~ ~ ( ~ ! [SY3212: $i] :
( ( in @ SY3212 @ ( relation_dom @ SV45 ) )
| ! [SY3213: $i] :
( ( SY3213
!= ( apply @ SV45 @ SY3212 ) )
| ( SY3213 = empty_set ) ) )
| ~ ! [SY3214: $i] :
( ( in @ SY3214 @ ( relation_dom @ SV45 ) )
| ! [SY3215: $i] :
( ( SY3215 != empty_set )
| ( SY3215
= ( apply @ SV45 @ SY3214 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[914]) ).
thf(1006,plain,
! [SV95: $i,SV130: $i] :
( ( ~ ( function @ SV130 )
| ~ ( relation @ SV130 )
| ~ ( in @ SV95 @ ( relation_rng @ SV130 ) )
| ~ ( one_to_one @ SV130 )
| ( SV95
= ( apply @ SV130 @ ( apply @ ( function_inverse @ SV130 ) @ SV95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1007,plain,
! [SV96: $i,SV131: $i] :
( ( ~ ( function @ SV131 )
| ~ ( relation @ SV131 )
| ~ ( in @ SV96 @ ( relation_rng @ SV131 ) )
| ~ ( one_to_one @ SV131 )
| ( SV96
= ( apply @ ( relation_composition @ ( function_inverse @ SV131 ) @ SV131 ) @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(1008,plain,
! [SV97: $i] :
( ( ( ~ ( function @ SV97 )
| ~ ( relation @ SV97 ) )
= $true )
| ( ( ~ ( one_to_one @ SV97 )
| ( ( relation_rng @ SV97 )
= ( relation_dom @ ( function_inverse @ SV97 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[917]) ).
thf(1009,plain,
! [SV98: $i] :
( ( ( ~ ( function @ SV98 )
| ~ ( relation @ SV98 ) )
= $true )
| ( ( ~ ( one_to_one @ SV98 )
| ( ( relation_dom @ SV98 )
= ( relation_rng @ ( function_inverse @ SV98 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[918]) ).
thf(1010,plain,
! [SV132: $i,SV99: $i] :
( ( ~ ( empty @ SV99 )
| ~ ( relation @ SV132 )
| ( empty @ ( relation_composition @ SV99 @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1011,plain,
! [SV133: $i,SV100: $i] :
( ( ~ ( empty @ SV100 )
| ~ ( relation @ SV133 )
| ( relation @ ( relation_composition @ SV100 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1012,plain,
! [SV101: $i,SV134: $i] :
( ( ~ ( function @ SV134 )
| ~ ( relation @ SV134 )
| ~ ( ~ ( in @ ( sK45_C @ SV134 @ SV101 ) @ SV101 )
| ~ ( ( ( apply @ SV134 @ ( sK45_C @ SV134 @ SV101 ) )
!= ( sK45_C @ SV134 @ SV101 ) ) ) )
| ( ( relation_dom @ SV134 )
!= SV101 )
| ( SV134
= ( identity_relation @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1013,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)],[922]) ).
thf(1014,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[922]) ).
thf(1015,plain,
( ( ~ ( empty @ sK5_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[923]) ).
thf(1016,plain,
( ( ~ ( relation @ sK5_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[923]) ).
thf(1017,plain,
! [SV102: $i] :
( ( ( ~ ( ~ ! [SY3338: $i,SY3339: $i] :
( ( sK28_B @ SV102 )
!= ( ordered_pair @ SY3338 @ SY3339 ) )
| ~ ( in @ ( sK28_B @ SV102 ) @ SV102 ) ) )
= $true )
| ( ( relation @ SV102 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[924]) ).
thf(1018,plain,
! [SV103: $i] :
( ( ( ~ ( relation @ SV103 ) )
= $true )
| ( ( ! [SY3340: $i] :
( ( SY3340
= ( ordered_pair @ ( sK26_C @ SY3340 @ SV103 ) @ ( sK27_SY3120 @ SY3340 @ SV103 ) ) )
| ~ ( in @ SY3340 @ SV103 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[925]) ).
thf(1019,plain,
! [SV135: $i,SV46: $i] :
( ( ! [SY3354: $i] :
( ~ ( relation @ SY3354 )
| ~ ( in @ ( ordered_pair @ SV46 @ SV135 ) @ SY3354 )
| ( in @ SV46 @ ( relation_field @ SY3354 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1020,plain,
! [SV136: $i,SV46: $i] :
( ( ! [SY3355: $i] :
( ~ ( relation @ SY3355 )
| ~ ( in @ ( ordered_pair @ SV46 @ SV136 ) @ SY3355 )
| ( in @ SV136 @ ( relation_field @ SY3355 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1021,plain,
! [SV81: $i,SV47: $i] :
( ( ! [SY3306: $i,SY3307: $i] :
( ~ ( relation @ SY3307 )
| ~ ( in @ SV47 @ SY3306 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ SY3307 )
| ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SY3306 ) @ SY3307 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[928]) ).
thf(1022,plain,
! [SV81: $i,SV47: $i] :
( ( ~ ( ~ ! [SY3308: $i,SY3309: $i] :
( ~ ( relation @ SY3309 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SY3308 ) @ SY3309 ) )
| ( in @ SV47 @ SY3308 ) )
| ~ ! [SY3310: $i,SY3311: $i] :
( ~ ( relation @ SY3311 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SY3310 ) @ SY3311 ) )
| ( in @ ( ordered_pair @ SV47 @ SV81 ) @ SY3311 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[929]) ).
thf(1023,plain,
! [SV104: $i] :
( ( ( ~ ( function @ SV104 )
| ~ ( relation @ SV104 ) )
= $true )
| ( ( function @ ( function_inverse @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[930]) ).
thf(1024,plain,
! [SV105: $i] :
( ( ( ~ ( function @ SV105 )
| ~ ( relation @ SV105 ) )
= $true )
| ( ( relation @ ( function_inverse @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[931]) ).
thf(1025,plain,
! [SV137: $i,SV48: $i] :
( ( ! [SY3356: $i] :
( ~ ( relation @ SY3356 )
| ~ ( in @ SV48 @ SV137 )
| ~ ( in @ SV48 @ ( relation_rng @ SY3356 ) )
| ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SV137 @ SY3356 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1026,plain,
! [SV48: $i] :
( ( ~ ! [SY3229: $i,SY3230: $i] :
( ~ ( relation @ SY3230 )
| ~ ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SY3229 @ SY3230 ) ) )
| ( in @ SV48 @ SY3229 ) )
| ~ ! [SY3231: $i,SY3232: $i] :
( ~ ( relation @ SY3232 )
| ~ ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SY3231 @ SY3232 ) ) )
| ( in @ SV48 @ ( relation_rng @ SY3232 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[933]) ).
thf(1027,plain,
! [SV106: $i] :
( ( ( ~ ( empty @ SV106 ) )
= $true )
| ( ( empty @ ( relation_inverse @ SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[934]) ).
thf(1028,plain,
! [SV107: $i] :
( ( ( ~ ( empty @ SV107 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[935]) ).
thf(1029,plain,
! [SV49: $i] :
( ( ( ~ ! [SY3233: $i] :
( ~ ( relation @ SY3233 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3233 @ SV49 ) @ ( sK25_SY3119 @ SY3233 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3233 @ SV49 ) @ ( sK25_SY3119 @ SY3233 @ SV49 ) ) @ SY3233 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK24_C @ SY3233 @ SV49 ) @ ( sK25_SY3119 @ SY3233 @ SV49 ) ) @ SV49 )
| ( in @ ( ordered_pair @ ( sK24_C @ SY3233 @ SV49 ) @ ( sK25_SY3119 @ SY3233 @ SV49 ) ) @ SY3233 ) ) )
| ( SV49 = SY3233 ) ) )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[936]) ).
thf(1030,plain,
! [SV49: $i] :
( ( ( ~ ! [SY3234: $i] :
( ~ ( relation @ SY3234 )
| ( SV49 != SY3234 )
| ~ ( ~ ! [SY3235: $i,SY3236: $i] :
( ~ ( in @ ( ordered_pair @ SY3235 @ SY3236 ) @ SV49 )
| ( in @ ( ordered_pair @ SY3235 @ SY3236 ) @ SY3234 ) )
| ~ ! [SY3237: $i,SY3238: $i] :
( ~ ( in @ ( ordered_pair @ SY3237 @ SY3238 ) @ SY3234 )
| ( in @ ( ordered_pair @ SY3237 @ SY3238 ) @ SV49 ) ) ) ) )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[936]) ).
thf(1031,plain,
! [SV108: $i] :
( ( ( ~ ( relation @ SV108 ) )
= $true )
| ( ( ( ( relation_dom @ SV108 )
!= empty_set )
| ( ( relation_rng @ SV108 )
= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[937]) ).
thf(1032,plain,
! [SV109: $i] :
( ( ( ~ ( relation @ SV109 ) )
= $true )
| ( ( ( ( relation_rng @ SV109 )
!= empty_set )
| ( ( relation_dom @ SV109 )
= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[938]) ).
thf(1033,plain,
! [SV50: $i] :
( ( ( ~ ! [SY3239: $i,SY3240: $i] :
( ~ ( ~ ( ! [SY3241: $i] :
( ~ ( in @ ( ordered_pair @ SY3241 @ ( sK33_D @ SY3240 @ SY3239 @ SV50 ) ) @ SV50 )
| ~ ( in @ SY3241 @ SY3239 ) )
| ~ ( in @ ( sK33_D @ SY3240 @ SY3239 @ SV50 ) @ SY3240 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK34_SY3126 @ SY3240 @ SY3239 @ SV50 ) @ ( sK33_D @ SY3240 @ SY3239 @ SV50 ) ) @ SV50 )
| ~ ( in @ ( sK34_SY3126 @ SY3240 @ SY3239 @ SV50 ) @ SY3239 ) )
| ( in @ ( sK33_D @ SY3240 @ SY3239 @ SV50 ) @ SY3240 ) ) )
| ( SY3240
= ( relation_image @ SV50 @ SY3239 ) ) ) )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[939]) ).
thf(1034,plain,
! [SV50: $i] :
( ( ( ~ ! [SY3242: $i,SY3243: $i] :
( ( SY3243
!= ( relation_image @ SV50 @ SY3242 ) )
| ~ ( ~ ! [SY3244: $i] :
( ! [SY3245: $i] :
( ~ ( in @ ( ordered_pair @ SY3245 @ SY3244 ) @ SV50 )
| ~ ( in @ SY3245 @ SY3242 ) )
| ( in @ SY3244 @ SY3243 ) )
| ~ ! [SY3246: $i] :
( ~ ( in @ SY3246 @ SY3243 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK32_E @ SY3246 @ SY3243 @ SY3242 @ SV50 ) @ SY3246 ) @ SV50 )
| ~ ( in @ ( sK32_E @ SY3246 @ SY3243 @ SY3242 @ SV50 ) @ SY3242 ) ) ) ) ) )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[939]) ).
thf(1035,plain,
! [SV138: $i,SV110: $i] :
( ( ~ ( function @ SV110 )
| ~ ( relation @ SV110 )
| ~ ( relation @ SV138 )
| ~ ( function @ SV138 )
| ( function @ ( relation_composition @ SV110 @ SV138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(1036,plain,
! [SV139: $i,SV111: $i] :
( ( ~ ( function @ SV111 )
| ~ ( relation @ SV111 )
| ~ ( relation @ SV139 )
| ~ ( function @ SV139 )
| ( relation @ ( relation_composition @ SV111 @ SV139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1037,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[942]) ).
thf(1038,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[942]) ).
thf(1039,plain,
! [SV112: $i] :
( ( ( ~ ( empty @ SV112 )
| ~ ( relation @ SV112 )
| ~ ( function @ SV112 ) )
= $true )
| ( ( one_to_one @ SV112 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[943]) ).
thf(1040,plain,
! [SV140: $i,SV51: $i] :
( ( ! [SY3357: $i] :
( ~ ( relation @ SY3357 )
| ! [SY3358: $i] :
( ~ ( in @ SY3358 @ ( relation_dom @ SY3357 ) )
| ~ ( in @ ( ordered_pair @ SY3358 @ SV51 ) @ SY3357 )
| ~ ( in @ SY3358 @ SV140 ) )
| ( in @ SV51 @ ( relation_image @ SY3357 @ SV140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(1041,plain,
! [SV141: $i,SV51: $i] :
( ( ! [SY3359: $i] :
( ~ ( relation @ SY3359 )
| ~ ( in @ SV51 @ ( relation_image @ SY3359 @ SV141 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK47_D @ SY3359 @ SV141 @ SV51 ) @ ( relation_dom @ SY3359 ) )
| ~ ( in @ ( ordered_pair @ ( sK47_D @ SY3359 @ SV141 @ SV51 ) @ SV51 ) @ SY3359 ) )
| ~ ( in @ ( sK47_D @ SY3359 @ SV141 @ SV51 ) @ SV141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1042,plain,
! [SV52: $i] :
( ( ( ~ ! [SY3252: $i] :
( ~ ( relation @ SY3252 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_C @ SY3252 @ SV52 ) @ ( sK15_SY3113 @ SY3252 @ SV52 ) ) @ SY3252 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY3113 @ SY3252 @ SV52 ) @ ( sK14_C @ SY3252 @ SV52 ) ) @ SV52 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SY3252 @ SV52 ) @ ( sK15_SY3113 @ SY3252 @ SV52 ) ) @ SY3252 )
| ( in @ ( ordered_pair @ ( sK15_SY3113 @ SY3252 @ SV52 ) @ ( sK14_C @ SY3252 @ SV52 ) ) @ SV52 ) ) )
| ( SY3252
= ( relation_inverse @ SV52 ) ) ) )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[948]) ).
thf(1043,plain,
! [SV52: $i] :
( ( ( ~ ! [SY3253: $i] :
( ~ ( relation @ SY3253 )
| ( SY3253
!= ( relation_inverse @ SV52 ) )
| ~ ( ~ ! [SY3254: $i,SY3255: $i] :
( ~ ( in @ ( ordered_pair @ SY3254 @ SY3255 ) @ SY3253 )
| ( in @ ( ordered_pair @ SY3255 @ SY3254 ) @ SV52 ) )
| ~ ! [SY3256: $i,SY3257: $i] :
( ~ ( in @ ( ordered_pair @ SY3257 @ SY3256 ) @ SV52 )
| ( in @ ( ordered_pair @ SY3256 @ SY3257 ) @ SY3253 ) ) ) ) )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[948]) ).
thf(1044,plain,
! [SV115: $i] :
( ( ( ~ ( function @ SV115 )
| ~ ( relation @ SV115 )
| ~ ( one_to_one @ SV115 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[949]) ).
thf(1045,plain,
! [SV116: $i] :
( ( ( ~ ( function @ SV116 )
| ~ ( relation @ SV116 )
| ~ ( one_to_one @ SV116 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[950]) ).
thf(1046,plain,
! [SV117: $i] :
( ( ( ~ ( relation @ SV117 ) )
= $true )
| ( ( ( ( relation_dom @ SV117 )
!= empty_set )
| ( SV117 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[951]) ).
thf(1047,plain,
! [SV118: $i] :
( ( ( ~ ( relation @ SV118 ) )
= $true )
| ( ( ( ( relation_rng @ SV118 )
!= empty_set )
| ( SV118 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[952]) ).
thf(1048,plain,
! [SV119: $i] :
( ( ( ~ ( empty @ SV119 ) )
= $true )
| ( ( empty @ ( relation_dom @ SV119 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[953]) ).
thf(1049,plain,
! [SV120: $i] :
( ( ( ~ ( empty @ SV120 ) )
= $true )
| ( ( relation @ ( relation_dom @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[954]) ).
thf(1050,plain,
! [SV121: $i] :
( ( ( ~ ( empty @ SV121 ) )
= $true )
| ( ( empty @ ( relation_rng @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[955]) ).
thf(1051,plain,
! [SV122: $i] :
( ( ( ~ ( empty @ SV122 ) )
= $true )
| ( ( relation @ ( relation_rng @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[956]) ).
thf(1052,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[958]) ).
thf(1053,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[958]) ).
thf(1054,plain,
! [SV123: $i,SV142: $i] :
( ( ~ ( relation @ SV142 )
| ~ ( ~ ( ( ( sK39_C @ SV142 @ SV123 )
!= ( sK40_SY3129 @ SV142 @ SV123 ) )
| ~ ( in @ ( sK39_C @ SV142 @ SV123 ) @ SV123 )
| ~ ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 ) )
| ~ ~ ( ~ ( ( ( sK39_C @ SV142 @ SV123 )
= ( sK40_SY3129 @ SV142 @ SV123 ) )
| ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 ) )
| ~ ( ( in @ ( sK39_C @ SV142 @ SV123 ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 ) ) ) )
| ( SV142
= ( identity_relation @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1055,plain,
! [SV124: $i,SV143: $i] :
( ( ~ ( relation @ SV143 )
| ( SV143
!= ( identity_relation @ SV124 ) )
| ~ ( ~ ! [SY3360: $i,SY3361: $i] :
( ( SY3360 != SY3361 )
| ~ ( in @ SY3360 @ SV124 )
| ( in @ ( ordered_pair @ SY3360 @ SY3361 ) @ SV143 ) )
| ~ ~ ( ~ ! [SY3362: $i,SY3363: $i] :
( ~ ( in @ ( ordered_pair @ SY3362 @ SY3363 ) @ SV143 )
| ( SY3362 = SY3363 ) )
| ~ ! [SY3364: $i] :
( ! [SY3365: $i] :
~ ( in @ ( ordered_pair @ SY3364 @ SY3365 ) @ SV143 )
| ( in @ SY3364 @ SV124 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1056,plain,
! [SV144: $i,SV125: $i] :
( ( ~ ( empty @ SV125 )
| ~ ( relation @ SV144 )
| ( empty @ ( relation_composition @ SV144 @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1057,plain,
! [SV145: $i,SV126: $i] :
( ( ~ ( empty @ SV126 )
| ~ ( relation @ SV145 )
| ( relation @ ( relation_composition @ SV145 @ SV126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1058,plain,
! [SV53: $i,SV82: $i] :
( ( ( ~ ! [SY3312: $i] :
( ~ ( relation @ SY3312 )
| ~ ( ~ ( ~ ( in @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) @ SV53 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SY3312 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) ) @ SV82 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SY3312 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) ) @ SY3312 ) )
| ~ ~ ( ~ ( ( in @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) @ SV53 )
| ( in @ ( ordered_pair @ ( sK35_D @ SY3312 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) ) @ SY3312 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SY3312 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) ) @ SV82 )
| ( in @ ( ordered_pair @ ( sK35_D @ SY3312 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) ) @ SY3312 ) ) ) )
| ( SY3312
= ( relation_rng_restriction @ SV53 @ SV82 ) ) )
| ~ ! [SY3313: $i] :
( ~ ( relation @ SY3313 )
| ( SY3313
!= ( relation_rng_restriction @ SV53 @ SV82 ) )
| ~ ( ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ SY3315 @ SV53 )
| ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV82 )
| ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SY3313 ) )
| ~ ~ ( ~ ! [SY3263: $i,SY3264: $i] :
( ~ ( in @ ( ordered_pair @ SY3263 @ SY3264 ) @ SY3313 )
| ( in @ SY3264 @ SV53 ) )
| ~ ! [SY3318: $i,SY3319: $i] :
( ~ ( in @ ( ordered_pair @ SY3318 @ SY3319 ) @ SY3313 )
| ( in @ ( ordered_pair @ SY3318 @ SY3319 ) @ SV82 ) ) ) ) ) )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[963]) ).
thf(1059,plain,
( ( ~ ( function @ sK3_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[964]) ).
thf(1060,plain,
( ( ~ ( relation @ sK3_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[964]) ).
thf(1061,plain,
! [SV54: $i] :
( ( ( ~ ! [SY3267: $i] :
( ~ ( relation @ SY3267 )
| ~ ( subset @ SV54 @ SY3267 )
| ( subset @ ( relation_dom @ SV54 ) @ ( relation_dom @ SY3267 ) ) ) )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[965]) ).
thf(1062,plain,
! [SV54: $i] :
( ( ( ~ ! [SY3268: $i] :
( ~ ( relation @ SY3268 )
| ~ ( subset @ SV54 @ SY3268 )
| ( subset @ ( relation_rng @ SV54 ) @ ( relation_rng @ SY3268 ) ) ) )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[965]) ).
thf(1063,plain,
! [SV55: $i,SV83: $i] :
( ( ( function @ SV83 )
= $false )
| ( ( ~ ( relation @ SV83 ) )
= $true )
| ( ( ~ ( ~ ! [SY3320: $i] :
( ~ ( function @ SY3320 )
| ~ ( relation @ SY3320 )
| ~ ( in @ SV55 @ ( relation_dom @ SY3320 ) )
| ~ ( in @ ( apply @ SY3320 @ SV55 ) @ ( relation_dom @ SV83 ) )
| ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3320 @ SV83 ) ) ) )
| ~ ~ ( ~ ! [SY3321: $i] :
( ~ ( function @ SY3321 )
| ~ ( relation @ SY3321 )
| ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3321 @ SV83 ) ) )
| ( in @ SV55 @ ( relation_dom @ SY3321 ) ) )
| ~ ! [SY3322: $i] :
( ~ ( function @ SY3322 )
| ~ ( relation @ SY3322 )
| ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3322 @ SV83 ) ) )
| ( in @ ( apply @ SY3322 @ SV55 ) @ ( relation_dom @ SV83 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(1064,plain,
! [SV146: $i,SV56: $i] :
( ( ! [SY3366: $i] :
( ~ ( relation @ SY3366 )
| ~ ( in @ SV56 @ SV146 )
| ~ ( in @ SV56 @ ( relation_dom @ SY3366 ) )
| ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SY3366 @ SV146 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1065,plain,
! [SV56: $i] :
( ( ~ ! [SY3275: $i,SY3276: $i] :
( ~ ( relation @ SY3276 )
| ~ ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SY3276 @ SY3275 ) ) )
| ( in @ SV56 @ SY3275 ) )
| ~ ! [SY3277: $i,SY3278: $i] :
( ~ ( relation @ SY3278 )
| ~ ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SY3278 @ SY3277 ) ) )
| ( in @ SV56 @ ( relation_dom @ SY3278 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[968]) ).
thf(1066,plain,
! [SV127: $i] :
( ( ( ~ ( relation @ SV127 ) )
= $true )
| ( ( ( relation_rng @ SV127 )
= ( relation_dom @ ( relation_inverse @ SV127 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[969]) ).
thf(1067,plain,
! [SV128: $i] :
( ( ( ~ ( relation @ SV128 ) )
= $true )
| ( ( ( relation_dom @ SV128 )
= ( relation_rng @ ( relation_inverse @ SV128 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[970]) ).
thf(1068,plain,
! [SV147: $i,SV57: $i] :
( ( ! [SY3367: $i] :
( ~ ( relation @ SY3367 )
| ~ ( in @ ( ordered_pair @ SV57 @ SV147 ) @ SY3367 )
| ( in @ SV57 @ ( relation_dom @ SY3367 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1069,plain,
! [SV148: $i,SV57: $i] :
( ( ! [SY3368: $i] :
( ~ ( relation @ SY3368 )
| ~ ( in @ ( ordered_pair @ SV57 @ SV148 ) @ SY3368 )
| ( in @ SV148 @ ( relation_rng @ SY3368 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1070,plain,
! [SV149: $i,SV58: $i] :
( ( ! [SY3369: $i] :
( ~ ( relation @ SY3369 )
| ! [SY3370: $i] :
( ~ ( in @ SY3370 @ ( relation_rng @ SY3369 ) )
| ~ ( in @ ( ordered_pair @ SV58 @ SY3370 ) @ SY3369 )
| ~ ( in @ SY3370 @ SV149 ) )
| ( in @ SV58 @ ( relation_inverse_image @ SY3369 @ SV149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1071,plain,
! [SV150: $i,SV58: $i] :
( ( ! [SY3371: $i] :
( ~ ( relation @ SY3371 )
| ~ ( in @ SV58 @ ( relation_inverse_image @ SY3371 @ SV150 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK46_D @ SY3371 @ SV150 @ SV58 ) @ ( relation_rng @ SY3371 ) )
| ~ ( in @ ( ordered_pair @ SV58 @ ( sK46_D @ SY3371 @ SV150 @ SV58 ) ) @ SY3371 ) )
| ~ ( in @ ( sK46_D @ SY3371 @ SV150 @ SV58 ) @ SV150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1072,plain,
! [SV59: $i] :
( ( ( ~ ! [SY3288: $i] :
( ~ ( relation @ SY3288 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SY3288 @ SV59 ) @ ( sK23_SY3118 @ SY3288 @ SV59 ) ) @ SV59 )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_C @ SY3288 @ SV59 ) @ ( sK23_SY3118 @ SY3288 @ SV59 ) ) @ SY3288 ) )
| ( subset @ SV59 @ SY3288 ) ) )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[975]) ).
thf(1073,plain,
! [SV59: $i] :
( ( ( ~ ! [SY3289: $i] :
( ~ ( relation @ SY3289 )
| ~ ( subset @ SV59 @ SY3289 )
| ! [SY3290: $i,SY3291: $i] :
( ~ ( in @ ( ordered_pair @ SY3290 @ SY3291 ) @ SV59 )
| ( in @ ( ordered_pair @ SY3290 @ SY3291 ) @ SY3289 ) ) ) )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[975]) ).
thf(1074,plain,
! [SV60: $i] :
( ( ( ~ ! [SY3292: $i,SY3293: $i] :
( ~ ( relation @ SY3293 )
| ~ ( ~ ( ~ ( in @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ SY3292 )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ ( sK38_SY3128 @ SY3293 @ SY3292 @ SV60 ) ) @ SV60 )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ ( sK38_SY3128 @ SY3293 @ SY3292 @ SV60 ) ) @ SY3293 ) )
| ~ ~ ( ~ ( ( in @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ SY3292 )
| ( in @ ( ordered_pair @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ ( sK38_SY3128 @ SY3293 @ SY3292 @ SV60 ) ) @ SY3293 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ ( sK38_SY3128 @ SY3293 @ SY3292 @ SV60 ) ) @ SV60 )
| ( in @ ( ordered_pair @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ ( sK38_SY3128 @ SY3293 @ SY3292 @ SV60 ) ) @ SY3293 ) ) ) )
| ( SY3293
= ( relation_dom_restriction @ SV60 @ SY3292 ) ) ) )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[976]) ).
thf(1075,plain,
! [SV60: $i] :
( ( ( ~ ! [SY3294: $i,SY3295: $i] :
( ~ ( relation @ SY3295 )
| ( SY3295
!= ( relation_dom_restriction @ SV60 @ SY3294 ) )
| ~ ( ~ ! [SY3296: $i,SY3297: $i] :
( ~ ( in @ SY3296 @ SY3294 )
| ~ ( in @ ( ordered_pair @ SY3296 @ SY3297 ) @ SV60 )
| ( in @ ( ordered_pair @ SY3296 @ SY3297 ) @ SY3295 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3295 )
| ( in @ SX3 @ SY3294 ) )
| ~ ! [SY3300: $i,SY3301: $i] :
( ~ ( in @ ( ordered_pair @ SY3300 @ SY3301 ) @ SY3295 )
| ( in @ ( ordered_pair @ SY3300 @ SY3301 ) @ SV60 ) ) ) ) ) )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[976]) ).
thf(1076,plain,
! [SV9: $i,SV86: $i] :
( ( ( relation @ SV86 )
= $false )
| ( ( ( relation_rng @ ( relation_composition @ SV9 @ SV86 ) )
= ( relation_image @ SV86 @ ( relation_rng @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[978]) ).
thf(1077,plain,
! [SV69: $i,SV11: $i] :
( ( ( SV11 = empty_set )
= $true )
| ( ( ~ ( subset @ SV11 @ ( relation_rng @ SV69 ) ) )
= $true )
| ( ( ( ( relation_inverse_image @ SV69 @ SV11 )
!= empty_set ) )
= $true )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[979]) ).
thf(1078,plain,
! [SV85: $i,SV70: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ SV70 ) )
= $true )
| ( ( subset @ ( relation_inverse_image @ SV85 @ SV12 ) @ ( relation_inverse_image @ SV85 @ SV70 ) )
= $true )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[980]) ).
thf(1079,plain,
! [SV14: $i,SV71: $i] :
( ( ( relation @ SV71 )
= $false )
| ( ( function @ SV71 )
= $false )
| ( ( ! [SY3304: $i] :
( ~ ( function @ SY3304 )
| ~ ( relation @ SY3304 )
| ~ ( in @ SV14 @ ( relation_dom @ ( relation_composition @ SY3304 @ SV71 ) ) )
| ( ( apply @ ( relation_composition @ SY3304 @ SV71 ) @ SV14 )
= ( apply @ SV71 @ ( apply @ SY3304 @ SV14 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[981]) ).
thf(1080,plain,
! [SV15: $i,SV72: $i] :
( ( ( relation @ SV72 )
= $false )
| ( ( function @ SV72 )
= $false )
| ( ( ! [SY3305: $i] :
( ~ ( function @ SY3305 )
| ~ ( relation @ SY3305 )
| ~ ( in @ SV15 @ ( relation_dom @ SV72 ) )
| ( ( apply @ ( relation_composition @ SV72 @ SY3305 ) @ SV15 )
= ( apply @ SY3305 @ ( apply @ SV72 @ SV15 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1081,plain,
! [SV16: $i,SV87: $i] :
( ( ( relation @ SV87 )
= $false )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV16 @ SV87 ) ) @ ( relation_dom @ SV16 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[983]) ).
thf(1082,plain,
! [SV17: $i,SV88: $i] :
( ( ( relation @ SV88 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV17 @ SV88 ) ) @ ( relation_rng @ SV88 ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[984]) ).
thf(1083,plain,
! [SV18: $i,SV89: $i] :
( ( ( relation @ SV89 )
= $false )
| ( ( ~ ( subset @ ( relation_rng @ SV18 ) @ ( relation_dom @ SV89 ) )
| ( ( relation_dom @ ( relation_composition @ SV18 @ SV89 ) )
= ( relation_dom @ SV18 ) ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[985]) ).
thf(1084,plain,
! [SV19: $i,SV90: $i] :
( ( ( relation @ SV90 )
= $false )
| ( ( ~ ( subset @ ( relation_dom @ SV19 ) @ ( relation_rng @ SV90 ) )
| ( ( relation_rng @ ( relation_composition @ SV90 @ SV19 ) )
= ( relation_rng @ SV19 ) ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[986]) ).
thf(1085,plain,
! [SV28: $i] :
( ( ( ~ ( one_to_one @ SV28 ) )
= $true )
| ( ( ( function_inverse @ SV28 )
= ( relation_inverse @ SV28 ) )
= $true )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[987]) ).
thf(1086,plain,
! [SV30: $i,SV77: $i] :
( ( ( relation @ SV77 )
= $false )
| ( ( relation @ SV30 )
= $false )
| ( ( relation @ ( relation_composition @ SV30 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[988]) ).
thf(1087,plain,
! [SV34: $i,SV79: $i] :
( ( ( relation @ SV79 )
= $false )
| ( ( relation @ SV34 )
= $false )
| ( ( relation @ ( set_intersection2 @ SV34 @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(1088,plain,
! [SV35: $i,SV80: $i] :
( ( ( relation @ SV80 )
= $false )
| ( ( relation @ SV35 )
= $false )
| ( ( relation @ ( set_union2 @ SV35 @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[990]) ).
thf(1089,plain,
! [SV39: $i,SV129: $i,SV151: $i] :
( ( ~ ( function @ SV151 )
| ~ ( relation @ SV151 )
| ( SV129
!= ( apply @ SV151 @ SV39 ) )
| ~ ( in @ SV39 @ ( relation_dom @ SV151 ) )
| ( in @ ( ordered_pair @ SV39 @ SV129 ) @ SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1090,plain,
! [SV39: $i] :
( ( ~ ! [SY3164: $i,SY3165: $i] :
( ~ ( function @ SY3165 )
| ~ ( relation @ SY3165 )
| ~ ( in @ ( ordered_pair @ SV39 @ SY3164 ) @ SY3165 )
| ( SY3164
= ( apply @ SY3165 @ SV39 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[994]) ).
thf(1091,plain,
! [SV39: $i] :
( ( ~ ! [SY3166: $i,SY3167: $i] :
( ~ ( function @ SY3167 )
| ~ ( relation @ SY3167 )
| ~ ( in @ ( ordered_pair @ SV39 @ SY3166 ) @ SY3167 )
| ( in @ SV39 @ ( relation_dom @ SY3167 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[994]) ).
thf(1092,plain,
! [SV40: $i] :
( ( ( ~ ( one_to_one @ SV40 ) )
= $true )
| ( ( ~ ( ~ ! [SY3168: $i] :
( ~ ( function @ SY3168 )
| ~ ( relation @ SY3168 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK44_SY3131 @ SY3168 @ SV40 )
= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ( ( sK43_C @ SY3168 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SY3168 @ SV40 )
= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SY3168 @ SV40 )
= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ( ( sK44_SY3131 @ SY3168 @ SV40 )
!= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK43_C @ SY3168 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK44_SY3131 @ SY3168 @ SV40 )
!= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK43_C @ SY3168 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK43_C @ SY3168 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SY3168 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SY3168 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK44_SY3131 @ SY3168 @ SV40 )
!= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ( ( relation_dom @ SY3168 )
!= ( relation_rng @ SV40 ) )
| ( SY3168
= ( function_inverse @ SV40 ) ) )
| ~ ~ ( ~ ! [SY3169: $i] :
( ~ ( function @ SY3169 )
| ~ ( relation @ SY3169 )
| ( SY3169
!= ( function_inverse @ SV40 ) )
| ~ ( ~ ~ ( ~ ! [SY3170: $i,SY3171: $i] :
( ( SY3171
!= ( apply @ SY3169 @ SY3170 ) )
| ~ ( in @ SY3170 @ ( relation_rng @ SV40 ) )
| ( SY3170
= ( apply @ SV40 @ SY3171 ) ) )
| ~ ! [SY3172: $i,SY3173: $i] :
( ( SY3173
!= ( apply @ SY3169 @ SY3172 ) )
| ~ ( in @ SY3172 @ ( relation_rng @ SV40 ) )
| ( in @ SY3173 @ ( relation_dom @ SV40 ) ) ) )
| ~ ~ ( ~ ! [SY3174: $i,SY3175: $i] :
( ( SY3174
!= ( apply @ SV40 @ SY3175 ) )
| ~ ( in @ SY3175 @ ( relation_dom @ SV40 ) )
| ( SY3175
= ( apply @ SY3169 @ SY3174 ) ) )
| ~ ! [SY3176: $i] :
( ! [SY3177: $i] :
( ( SY3176
!= ( apply @ SV40 @ SY3177 ) )
| ~ ( in @ SY3177 @ ( relation_dom @ SV40 ) ) )
| ( in @ SY3176 @ ( relation_rng @ SV40 ) ) ) ) ) )
| ~ ! [SY3178: $i] :
( ~ ( function @ SY3178 )
| ~ ( relation @ SY3178 )
| ( SY3178
!= ( function_inverse @ SV40 ) )
| ( ( relation_dom @ SY3178 )
= ( relation_rng @ SV40 ) ) ) ) ) )
= $true )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[995]) ).
thf(1093,plain,
! [SV41: $i] :
( ( ( ! [SY3179: $i,SY3180: $i] :
( ~ ( ~ ( ! [SY3181: $i] :
( ~ ( in @ ( ordered_pair @ ( sK30_D @ SY3180 @ SY3179 @ SV41 ) @ SY3181 ) @ SV41 )
| ~ ( in @ SY3181 @ SY3179 ) )
| ~ ( in @ ( sK30_D @ SY3180 @ SY3179 @ SV41 ) @ SY3180 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK30_D @ SY3180 @ SY3179 @ SV41 ) @ ( sK31_SY3124 @ SY3180 @ SY3179 @ SV41 ) ) @ SV41 )
| ~ ( in @ ( sK31_SY3124 @ SY3180 @ SY3179 @ SV41 ) @ SY3179 ) )
| ( in @ ( sK30_D @ SY3180 @ SY3179 @ SV41 ) @ SY3180 ) ) )
| ( SY3180
= ( relation_inverse_image @ SV41 @ SY3179 ) ) ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[996]) ).
thf(1094,plain,
! [SV41: $i] :
( ( ( ! [SY3182: $i,SY3183: $i] :
( ( SY3183
!= ( relation_inverse_image @ SV41 @ SY3182 ) )
| ~ ( ~ ! [SY3184: $i] :
( ! [SY3185: $i] :
( ~ ( in @ ( ordered_pair @ SY3184 @ SY3185 ) @ SV41 )
| ~ ( in @ SY3185 @ SY3182 ) )
| ( in @ SY3184 @ SY3183 ) )
| ~ ! [SY3186: $i] :
( ~ ( in @ SY3186 @ SY3183 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3186 @ ( sK29_E @ SY3186 @ SY3183 @ SY3182 @ SV41 ) ) @ SV41 )
| ~ ( in @ ( sK29_E @ SY3186 @ SY3183 @ SY3182 @ SV41 ) @ SY3182 ) ) ) ) ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[997]) ).
thf(1095,plain,
! [SV42: $i] :
( ( ( ! [SY3187: $i] :
( ~ ( ~ ( ! [SY3188: $i] :
~ ( in @ ( ordered_pair @ SY3188 @ ( sK17_C @ SY3187 @ SV42 ) ) @ SV42 )
| ~ ( in @ ( sK17_C @ SY3187 @ SV42 ) @ SY3187 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK18_SY3115 @ SY3187 @ SV42 ) @ ( sK17_C @ SY3187 @ SV42 ) ) @ SV42 )
| ( in @ ( sK17_C @ SY3187 @ SV42 ) @ SY3187 ) ) )
| ( SY3187
= ( relation_rng @ SV42 ) ) ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[998]) ).
thf(1096,plain,
! [SV42: $i] :
( ( ( ! [SY3189: $i] :
( ( SY3189
!= ( relation_rng @ SV42 ) )
| ~ ( ~ ! [SY3190: $i] :
( ! [SY3191: $i] :
~ ( in @ ( ordered_pair @ SY3191 @ SY3190 ) @ SV42 )
| ( in @ SY3190 @ SY3189 ) )
| ~ ! [SY3192: $i] :
( ~ ( in @ SY3192 @ SY3189 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3192 @ SY3189 @ SV42 ) @ SY3192 ) @ SV42 ) ) ) ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[999]) ).
thf(1097,plain,
! [SV92: $i] :
( ( ( ~ ( function @ SV92 ) )
= $true )
| ( ( ~ ( relation @ SV92 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK12_B @ SV92 ) @ ( relation_dom @ SV92 ) )
| ~ ( in @ ( sK13_SY3112 @ SV92 ) @ ( relation_dom @ SV92 ) ) )
| ( ( apply @ SV92 @ ( sK12_B @ SV92 ) )
!= ( apply @ SV92 @ ( sK13_SY3112 @ SV92 ) ) ) )
| ~ ( ( ( sK12_B @ SV92 )
!= ( sK13_SY3112 @ SV92 ) ) ) )
| ( one_to_one @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1000]) ).
thf(1098,plain,
! [SV93: $i] :
( ( ( ~ ( function @ SV93 ) )
= $true )
| ( ( ~ ( relation @ SV93 ) )
= $true )
| ( ( ~ ( one_to_one @ SV93 )
| ! [SY3323: $i,SY3324: $i] :
( ~ ( in @ SY3323 @ ( relation_dom @ SV93 ) )
| ~ ( in @ SY3324 @ ( relation_dom @ SV93 ) )
| ( ( apply @ SV93 @ SY3323 )
!= ( apply @ SV93 @ SY3324 ) )
| ( SY3323 = SY3324 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1001]) ).
thf(1099,plain,
! [SV43: $i,SV94: $i] :
( ( ( relation @ SV94 )
= $false )
| ( ( ~ ( ~ ! [SY3325: $i] :
( ~ ( relation @ SY3325 )
| ~ ( ~ ( ! [SY3326: $i] :
( ~ ( in @ ( ordered_pair @ ( sK9_D @ SY3325 @ SV94 @ SV43 ) @ SY3326 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3326 @ ( sK10_SY3107 @ SY3325 @ SV94 @ SV43 ) ) @ SV94 ) )
| ~ ( in @ ( ordered_pair @ ( sK9_D @ SY3325 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SY3325 @ SV94 @ SV43 ) ) @ SY3325 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK9_D @ SY3325 @ SV94 @ SV43 ) @ ( sK11_SY3111 @ SY3325 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY3111 @ SY3325 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SY3325 @ SV94 @ SV43 ) ) @ SV94 ) )
| ( in @ ( ordered_pair @ ( sK9_D @ SY3325 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SY3325 @ SV94 @ SV43 ) ) @ SY3325 ) ) )
| ( SY3325
= ( relation_composition @ SV43 @ SV94 ) ) )
| ~ ! [SY3327: $i] :
( ~ ( relation @ SY3327 )
| ( SY3327
!= ( relation_composition @ SV43 @ SV94 ) )
| ~ ( ~ ! [SY3328: $i,SY3329: $i] :
( ! [SY3330: $i] :
( ~ ( in @ ( ordered_pair @ SY3328 @ SY3330 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3330 @ SY3329 ) @ SV94 ) )
| ( in @ ( ordered_pair @ SY3328 @ SY3329 ) @ SY3327 ) )
| ~ ! [SY3331: $i,SY3332: $i] :
( ~ ( in @ ( ordered_pair @ SY3331 @ SY3332 ) @ SY3327 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3331 @ ( sK8_F @ SY3332 @ SY3331 @ SY3327 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK8_F @ SY3332 @ SY3331 @ SY3327 @ SV94 @ SV43 ) @ SY3332 ) @ SV94 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1002]) ).
thf(1100,plain,
! [SV44: $i] :
( ( ( ! [SY3202: $i] :
( ~ ( ~ ( ! [SY3203: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SY3202 @ SV44 ) @ SY3203 ) @ SV44 )
| ~ ( in @ ( sK20_C @ SY3202 @ SV44 ) @ SY3202 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SY3202 @ SV44 ) @ ( sK21_SY3117 @ SY3202 @ SV44 ) ) @ SV44 )
| ( in @ ( sK20_C @ SY3202 @ SV44 ) @ SY3202 ) ) )
| ( SY3202
= ( relation_dom @ SV44 ) ) ) )
= $true )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1003]) ).
thf(1101,plain,
! [SV44: $i] :
( ( ( ! [SY3204: $i] :
( ( SY3204
!= ( relation_dom @ SV44 ) )
| ~ ( ~ ! [SY3205: $i] :
( ! [SY3206: $i] :
~ ( in @ ( ordered_pair @ SY3205 @ SY3206 ) @ SV44 )
| ( in @ SY3205 @ SY3204 ) )
| ~ ! [SY3207: $i] :
( ~ ( in @ SY3207 @ SY3204 )
| ( in @ ( ordered_pair @ SY3207 @ ( sK19_D @ SY3207 @ SY3204 @ SV44 ) ) @ SV44 ) ) ) ) )
= $true )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1004]) ).
thf(1102,plain,
! [SV45: $i] :
( ( ( ~ ~ ( ~ ! [SY3208: $i] :
( ~ ( in @ SY3208 @ ( relation_dom @ SV45 ) )
| ! [SY3209: $i] :
( ( SY3209
!= ( apply @ SV45 @ SY3208 ) )
| ( in @ ( ordered_pair @ SY3208 @ SY3209 ) @ SV45 ) ) )
| ~ ! [SY3210: $i] :
( ~ ( in @ SY3210 @ ( relation_dom @ SV45 ) )
| ! [SY3211: $i] :
( ~ ( in @ ( ordered_pair @ SY3210 @ SY3211 ) @ SV45 )
| ( SY3211
= ( apply @ SV45 @ SY3210 ) ) ) ) )
| ~ ~ ( ~ ! [SY3212: $i] :
( ( in @ SY3212 @ ( relation_dom @ SV45 ) )
| ! [SY3213: $i] :
( ( SY3213
!= ( apply @ SV45 @ SY3212 ) )
| ( SY3213 = empty_set ) ) )
| ~ ! [SY3214: $i] :
( ( in @ SY3214 @ ( relation_dom @ SV45 ) )
| ! [SY3215: $i] :
( ( SY3215 != empty_set )
| ( SY3215
= ( apply @ SV45 @ SY3214 ) ) ) ) ) )
= $false )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1005]) ).
thf(1103,plain,
! [SV95: $i,SV130: $i] :
( ( ( ~ ( function @ SV130 )
| ~ ( relation @ SV130 ) )
= $true )
| ( ( ~ ( in @ SV95 @ ( relation_rng @ SV130 ) )
| ~ ( one_to_one @ SV130 )
| ( SV95
= ( apply @ SV130 @ ( apply @ ( function_inverse @ SV130 ) @ SV95 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1006]) ).
thf(1104,plain,
! [SV96: $i,SV131: $i] :
( ( ( ~ ( function @ SV131 )
| ~ ( relation @ SV131 ) )
= $true )
| ( ( ~ ( in @ SV96 @ ( relation_rng @ SV131 ) )
| ~ ( one_to_one @ SV131 )
| ( SV96
= ( apply @ ( relation_composition @ ( function_inverse @ SV131 ) @ SV131 ) @ SV96 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1007]) ).
thf(1105,plain,
! [SV97: $i] :
( ( ( ~ ( function @ SV97 ) )
= $true )
| ( ( ~ ( relation @ SV97 ) )
= $true )
| ( ( ~ ( one_to_one @ SV97 )
| ( ( relation_rng @ SV97 )
= ( relation_dom @ ( function_inverse @ SV97 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1008]) ).
thf(1106,plain,
! [SV98: $i] :
( ( ( ~ ( function @ SV98 ) )
= $true )
| ( ( ~ ( relation @ SV98 ) )
= $true )
| ( ( ~ ( one_to_one @ SV98 )
| ( ( relation_dom @ SV98 )
= ( relation_rng @ ( function_inverse @ SV98 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1009]) ).
thf(1107,plain,
! [SV132: $i,SV99: $i] :
( ( ( ~ ( empty @ SV99 )
| ~ ( relation @ SV132 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV99 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1010]) ).
thf(1108,plain,
! [SV133: $i,SV100: $i] :
( ( ( ~ ( empty @ SV100 )
| ~ ( relation @ SV133 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV100 @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1011]) ).
thf(1109,plain,
! [SV101: $i,SV134: $i] :
( ( ( ~ ( function @ SV134 )
| ~ ( relation @ SV134 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK45_C @ SV134 @ SV101 ) @ SV101 )
| ~ ( ( ( apply @ SV134 @ ( sK45_C @ SV134 @ SV101 ) )
!= ( sK45_C @ SV134 @ SV101 ) ) ) )
| ( ( relation_dom @ SV134 )
!= SV101 )
| ( SV134
= ( identity_relation @ SV101 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1012]) ).
thf(1110,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)],[1013]) ).
thf(1111,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1014]) ).
thf(1112,plain,
( ( empty @ sK5_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1015]) ).
thf(1113,plain,
( ( relation @ sK5_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1016]) ).
thf(1114,plain,
! [SV102: $i] :
( ( ( ~ ! [SY3338: $i,SY3339: $i] :
( ( sK28_B @ SV102 )
!= ( ordered_pair @ SY3338 @ SY3339 ) )
| ~ ( in @ ( sK28_B @ SV102 ) @ SV102 ) )
= $false )
| ( ( relation @ SV102 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1017]) ).
thf(1115,plain,
! [SV103: $i] :
( ( ( relation @ SV103 )
= $false )
| ( ( ! [SY3340: $i] :
( ( SY3340
= ( ordered_pair @ ( sK26_C @ SY3340 @ SV103 ) @ ( sK27_SY3120 @ SY3340 @ SV103 ) ) )
| ~ ( in @ SY3340 @ SV103 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1018]) ).
thf(1116,plain,
! [SV135: $i,SV46: $i,SV152: $i] :
( ( ~ ( relation @ SV152 )
| ~ ( in @ ( ordered_pair @ SV46 @ SV135 ) @ SV152 )
| ( in @ SV46 @ ( relation_field @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1117,plain,
! [SV136: $i,SV46: $i,SV153: $i] :
( ( ~ ( relation @ SV153 )
| ~ ( in @ ( ordered_pair @ SV46 @ SV136 ) @ SV153 )
| ( in @ SV136 @ ( relation_field @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1118,plain,
! [SV81: $i,SV154: $i,SV47: $i] :
( ( ! [SY3372: $i] :
( ~ ( relation @ SY3372 )
| ~ ( in @ SV47 @ SV154 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ SY3372 )
| ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SV154 ) @ SY3372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1119,plain,
! [SV81: $i,SV47: $i] :
( ( ~ ! [SY3308: $i,SY3309: $i] :
( ~ ( relation @ SY3309 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SY3308 ) @ SY3309 ) )
| ( in @ SV47 @ SY3308 ) )
| ~ ! [SY3310: $i,SY3311: $i] :
( ~ ( relation @ SY3311 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SY3310 ) @ SY3311 ) )
| ( in @ ( ordered_pair @ SV47 @ SV81 ) @ SY3311 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1120,plain,
! [SV104: $i] :
( ( ( ~ ( function @ SV104 ) )
= $true )
| ( ( ~ ( relation @ SV104 ) )
= $true )
| ( ( function @ ( function_inverse @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1023]) ).
thf(1121,plain,
! [SV105: $i] :
( ( ( ~ ( function @ SV105 ) )
= $true )
| ( ( ~ ( relation @ SV105 ) )
= $true )
| ( ( relation @ ( function_inverse @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1024]) ).
thf(1122,plain,
! [SV137: $i,SV48: $i,SV155: $i] :
( ( ~ ( relation @ SV155 )
| ~ ( in @ SV48 @ SV137 )
| ~ ( in @ SV48 @ ( relation_rng @ SV155 ) )
| ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SV137 @ SV155 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1123,plain,
! [SV48: $i] :
( ( ~ ! [SY3229: $i,SY3230: $i] :
( ~ ( relation @ SY3230 )
| ~ ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SY3229 @ SY3230 ) ) )
| ( in @ SV48 @ SY3229 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1026]) ).
thf(1124,plain,
! [SV48: $i] :
( ( ~ ! [SY3231: $i,SY3232: $i] :
( ~ ( relation @ SY3232 )
| ~ ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SY3231 @ SY3232 ) ) )
| ( in @ SV48 @ ( relation_rng @ SY3232 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1026]) ).
thf(1125,plain,
! [SV106: $i] :
( ( ( empty @ SV106 )
= $false )
| ( ( empty @ ( relation_inverse @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1027]) ).
thf(1126,plain,
! [SV107: $i] :
( ( ( empty @ SV107 )
= $false )
| ( ( relation @ ( relation_inverse @ SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1028]) ).
thf(1127,plain,
! [SV49: $i] :
( ( ( ! [SY3233: $i] :
( ~ ( relation @ SY3233 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3233 @ SV49 ) @ ( sK25_SY3119 @ SY3233 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3233 @ SV49 ) @ ( sK25_SY3119 @ SY3233 @ SV49 ) ) @ SY3233 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK24_C @ SY3233 @ SV49 ) @ ( sK25_SY3119 @ SY3233 @ SV49 ) ) @ SV49 )
| ( in @ ( ordered_pair @ ( sK24_C @ SY3233 @ SV49 ) @ ( sK25_SY3119 @ SY3233 @ SV49 ) ) @ SY3233 ) ) )
| ( SV49 = SY3233 ) ) )
= $true )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1029]) ).
thf(1128,plain,
! [SV49: $i] :
( ( ( ! [SY3234: $i] :
( ~ ( relation @ SY3234 )
| ( SV49 != SY3234 )
| ~ ( ~ ! [SY3235: $i,SY3236: $i] :
( ~ ( in @ ( ordered_pair @ SY3235 @ SY3236 ) @ SV49 )
| ( in @ ( ordered_pair @ SY3235 @ SY3236 ) @ SY3234 ) )
| ~ ! [SY3237: $i,SY3238: $i] :
( ~ ( in @ ( ordered_pair @ SY3237 @ SY3238 ) @ SY3234 )
| ( in @ ( ordered_pair @ SY3237 @ SY3238 ) @ SV49 ) ) ) ) )
= $true )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1030]) ).
thf(1129,plain,
! [SV108: $i] :
( ( ( relation @ SV108 )
= $false )
| ( ( ( ( relation_dom @ SV108 )
!= empty_set )
| ( ( relation_rng @ SV108 )
= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1031]) ).
thf(1130,plain,
! [SV109: $i] :
( ( ( relation @ SV109 )
= $false )
| ( ( ( ( relation_rng @ SV109 )
!= empty_set )
| ( ( relation_dom @ SV109 )
= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1032]) ).
thf(1131,plain,
! [SV50: $i] :
( ( ( ! [SY3239: $i,SY3240: $i] :
( ~ ( ~ ( ! [SY3241: $i] :
( ~ ( in @ ( ordered_pair @ SY3241 @ ( sK33_D @ SY3240 @ SY3239 @ SV50 ) ) @ SV50 )
| ~ ( in @ SY3241 @ SY3239 ) )
| ~ ( in @ ( sK33_D @ SY3240 @ SY3239 @ SV50 ) @ SY3240 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK34_SY3126 @ SY3240 @ SY3239 @ SV50 ) @ ( sK33_D @ SY3240 @ SY3239 @ SV50 ) ) @ SV50 )
| ~ ( in @ ( sK34_SY3126 @ SY3240 @ SY3239 @ SV50 ) @ SY3239 ) )
| ( in @ ( sK33_D @ SY3240 @ SY3239 @ SV50 ) @ SY3240 ) ) )
| ( SY3240
= ( relation_image @ SV50 @ SY3239 ) ) ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1033]) ).
thf(1132,plain,
! [SV50: $i] :
( ( ( ! [SY3242: $i,SY3243: $i] :
( ( SY3243
!= ( relation_image @ SV50 @ SY3242 ) )
| ~ ( ~ ! [SY3244: $i] :
( ! [SY3245: $i] :
( ~ ( in @ ( ordered_pair @ SY3245 @ SY3244 ) @ SV50 )
| ~ ( in @ SY3245 @ SY3242 ) )
| ( in @ SY3244 @ SY3243 ) )
| ~ ! [SY3246: $i] :
( ~ ( in @ SY3246 @ SY3243 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK32_E @ SY3246 @ SY3243 @ SY3242 @ SV50 ) @ SY3246 ) @ SV50 )
| ~ ( in @ ( sK32_E @ SY3246 @ SY3243 @ SY3242 @ SV50 ) @ SY3242 ) ) ) ) ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1034]) ).
thf(1133,plain,
! [SV138: $i,SV110: $i] :
( ( ( ~ ( function @ SV110 )
| ~ ( relation @ SV110 )
| ~ ( relation @ SV138 )
| ~ ( function @ SV138 ) )
= $true )
| ( ( function @ ( relation_composition @ SV110 @ SV138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1035]) ).
thf(1134,plain,
! [SV139: $i,SV111: $i] :
( ( ( ~ ( function @ SV111 )
| ~ ( relation @ SV111 )
| ~ ( relation @ SV139 )
| ~ ( function @ SV139 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV111 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1036]) ).
thf(1135,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1037]) ).
thf(1136,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1038]) ).
thf(1137,plain,
! [SV112: $i] :
( ( ( ~ ( empty @ SV112 )
| ~ ( relation @ SV112 ) )
= $true )
| ( ( ~ ( function @ SV112 ) )
= $true )
| ( ( one_to_one @ SV112 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1039]) ).
thf(1138,plain,
! [SV140: $i,SV51: $i,SV156: $i] :
( ( ~ ( relation @ SV156 )
| ! [SY3373: $i] :
( ~ ( in @ SY3373 @ ( relation_dom @ SV156 ) )
| ~ ( in @ ( ordered_pair @ SY3373 @ SV51 ) @ SV156 )
| ~ ( in @ SY3373 @ SV140 ) )
| ( in @ SV51 @ ( relation_image @ SV156 @ SV140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1139,plain,
! [SV141: $i,SV51: $i,SV157: $i] :
( ( ~ ( relation @ SV157 )
| ~ ( in @ SV51 @ ( relation_image @ SV157 @ SV141 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK47_D @ SV157 @ SV141 @ SV51 ) @ ( relation_dom @ SV157 ) )
| ~ ( in @ ( ordered_pair @ ( sK47_D @ SV157 @ SV141 @ SV51 ) @ SV51 ) @ SV157 ) )
| ~ ( in @ ( sK47_D @ SV157 @ SV141 @ SV51 ) @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1140,plain,
! [SV52: $i] :
( ( ( ! [SY3252: $i] :
( ~ ( relation @ SY3252 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_C @ SY3252 @ SV52 ) @ ( sK15_SY3113 @ SY3252 @ SV52 ) ) @ SY3252 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY3113 @ SY3252 @ SV52 ) @ ( sK14_C @ SY3252 @ SV52 ) ) @ SV52 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SY3252 @ SV52 ) @ ( sK15_SY3113 @ SY3252 @ SV52 ) ) @ SY3252 )
| ( in @ ( ordered_pair @ ( sK15_SY3113 @ SY3252 @ SV52 ) @ ( sK14_C @ SY3252 @ SV52 ) ) @ SV52 ) ) )
| ( SY3252
= ( relation_inverse @ SV52 ) ) ) )
= $true )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1042]) ).
thf(1141,plain,
! [SV52: $i] :
( ( ( ! [SY3253: $i] :
( ~ ( relation @ SY3253 )
| ( SY3253
!= ( relation_inverse @ SV52 ) )
| ~ ( ~ ! [SY3254: $i,SY3255: $i] :
( ~ ( in @ ( ordered_pair @ SY3254 @ SY3255 ) @ SY3253 )
| ( in @ ( ordered_pair @ SY3255 @ SY3254 ) @ SV52 ) )
| ~ ! [SY3256: $i,SY3257: $i] :
( ~ ( in @ ( ordered_pair @ SY3257 @ SY3256 ) @ SV52 )
| ( in @ ( ordered_pair @ SY3256 @ SY3257 ) @ SY3253 ) ) ) ) )
= $true )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1043]) ).
thf(1142,plain,
! [SV115: $i] :
( ( ( ~ ( function @ SV115 )
| ~ ( relation @ SV115 ) )
= $true )
| ( ( ~ ( one_to_one @ SV115 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1044]) ).
thf(1143,plain,
! [SV116: $i] :
( ( ( ~ ( function @ SV116 )
| ~ ( relation @ SV116 ) )
= $true )
| ( ( ~ ( one_to_one @ SV116 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1045]) ).
thf(1144,plain,
! [SV117: $i] :
( ( ( relation @ SV117 )
= $false )
| ( ( ( ( relation_dom @ SV117 )
!= empty_set )
| ( SV117 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1046]) ).
thf(1145,plain,
! [SV118: $i] :
( ( ( relation @ SV118 )
= $false )
| ( ( ( ( relation_rng @ SV118 )
!= empty_set )
| ( SV118 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1047]) ).
thf(1146,plain,
! [SV119: $i] :
( ( ( empty @ SV119 )
= $false )
| ( ( empty @ ( relation_dom @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1048]) ).
thf(1147,plain,
! [SV120: $i] :
( ( ( empty @ SV120 )
= $false )
| ( ( relation @ ( relation_dom @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1049]) ).
thf(1148,plain,
! [SV121: $i] :
( ( ( empty @ SV121 )
= $false )
| ( ( empty @ ( relation_rng @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1050]) ).
thf(1149,plain,
! [SV122: $i] :
( ( ( empty @ SV122 )
= $false )
| ( ( relation @ ( relation_rng @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1051]) ).
thf(1150,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1052]) ).
thf(1151,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1053]) ).
thf(1152,plain,
! [SV123: $i,SV142: $i] :
( ( ( ~ ( relation @ SV142 ) )
= $true )
| ( ( ~ ( ~ ( ( ( sK39_C @ SV142 @ SV123 )
!= ( sK40_SY3129 @ SV142 @ SV123 ) )
| ~ ( in @ ( sK39_C @ SV142 @ SV123 ) @ SV123 )
| ~ ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 ) )
| ~ ~ ( ~ ( ( ( sK39_C @ SV142 @ SV123 )
= ( sK40_SY3129 @ SV142 @ SV123 ) )
| ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 ) )
| ~ ( ( in @ ( sK39_C @ SV142 @ SV123 ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 ) ) ) )
| ( SV142
= ( identity_relation @ SV123 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1054]) ).
thf(1153,plain,
! [SV124: $i,SV143: $i] :
( ( ( ~ ( relation @ SV143 ) )
= $true )
| ( ( ( SV143
!= ( identity_relation @ SV124 ) )
| ~ ( ~ ! [SY3360: $i,SY3361: $i] :
( ( SY3360 != SY3361 )
| ~ ( in @ SY3360 @ SV124 )
| ( in @ ( ordered_pair @ SY3360 @ SY3361 ) @ SV143 ) )
| ~ ~ ( ~ ! [SY3362: $i,SY3363: $i] :
( ~ ( in @ ( ordered_pair @ SY3362 @ SY3363 ) @ SV143 )
| ( SY3362 = SY3363 ) )
| ~ ! [SY3364: $i] :
( ! [SY3365: $i] :
~ ( in @ ( ordered_pair @ SY3364 @ SY3365 ) @ SV143 )
| ( in @ SY3364 @ SV124 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1055]) ).
thf(1154,plain,
! [SV144: $i,SV125: $i] :
( ( ( ~ ( empty @ SV125 )
| ~ ( relation @ SV144 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV144 @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1056]) ).
thf(1155,plain,
! [SV145: $i,SV126: $i] :
( ( ( ~ ( empty @ SV126 )
| ~ ( relation @ SV145 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV145 @ SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1057]) ).
thf(1156,plain,
! [SV53: $i,SV82: $i] :
( ( ( ~ ! [SY3312: $i] :
( ~ ( relation @ SY3312 )
| ~ ( ~ ( ~ ( in @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) @ SV53 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SY3312 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) ) @ SV82 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SY3312 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) ) @ SY3312 ) )
| ~ ~ ( ~ ( ( in @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) @ SV53 )
| ( in @ ( ordered_pair @ ( sK35_D @ SY3312 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) ) @ SY3312 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SY3312 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) ) @ SV82 )
| ( in @ ( ordered_pair @ ( sK35_D @ SY3312 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) ) @ SY3312 ) ) ) )
| ( SY3312
= ( relation_rng_restriction @ SV53 @ SV82 ) ) ) )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1058]) ).
thf(1157,plain,
! [SV82: $i,SV53: $i] :
( ( ( ~ ! [SY3313: $i] :
( ~ ( relation @ SY3313 )
| ( SY3313
!= ( relation_rng_restriction @ SV53 @ SV82 ) )
| ~ ( ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ SY3315 @ SV53 )
| ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV82 )
| ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SY3313 ) )
| ~ ~ ( ~ ! [SY3263: $i,SY3264: $i] :
( ~ ( in @ ( ordered_pair @ SY3263 @ SY3264 ) @ SY3313 )
| ( in @ SY3264 @ SV53 ) )
| ~ ! [SY3318: $i,SY3319: $i] :
( ~ ( in @ ( ordered_pair @ SY3318 @ SY3319 ) @ SY3313 )
| ( in @ ( ordered_pair @ SY3318 @ SY3319 ) @ SV82 ) ) ) ) ) )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1058]) ).
thf(1158,plain,
( ( function @ sK3_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1059]) ).
thf(1159,plain,
( ( relation @ sK3_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1060]) ).
thf(1160,plain,
! [SV54: $i] :
( ( ( ! [SY3267: $i] :
( ~ ( relation @ SY3267 )
| ~ ( subset @ SV54 @ SY3267 )
| ( subset @ ( relation_dom @ SV54 ) @ ( relation_dom @ SY3267 ) ) ) )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1061]) ).
thf(1161,plain,
! [SV54: $i] :
( ( ( ! [SY3268: $i] :
( ~ ( relation @ SY3268 )
| ~ ( subset @ SV54 @ SY3268 )
| ( subset @ ( relation_rng @ SV54 ) @ ( relation_rng @ SY3268 ) ) ) )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1062]) ).
thf(1162,plain,
! [SV55: $i,SV83: $i] :
( ( ( relation @ SV83 )
= $false )
| ( ( function @ SV83 )
= $false )
| ( ( ~ ( ~ ! [SY3320: $i] :
( ~ ( function @ SY3320 )
| ~ ( relation @ SY3320 )
| ~ ( in @ SV55 @ ( relation_dom @ SY3320 ) )
| ~ ( in @ ( apply @ SY3320 @ SV55 ) @ ( relation_dom @ SV83 ) )
| ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3320 @ SV83 ) ) ) )
| ~ ~ ( ~ ! [SY3321: $i] :
( ~ ( function @ SY3321 )
| ~ ( relation @ SY3321 )
| ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3321 @ SV83 ) ) )
| ( in @ SV55 @ ( relation_dom @ SY3321 ) ) )
| ~ ! [SY3322: $i] :
( ~ ( function @ SY3322 )
| ~ ( relation @ SY3322 )
| ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3322 @ SV83 ) ) )
| ( in @ ( apply @ SY3322 @ SV55 ) @ ( relation_dom @ SV83 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1063]) ).
thf(1163,plain,
! [SV146: $i,SV56: $i,SV158: $i] :
( ( ~ ( relation @ SV158 )
| ~ ( in @ SV56 @ SV146 )
| ~ ( in @ SV56 @ ( relation_dom @ SV158 ) )
| ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SV158 @ SV146 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1164,plain,
! [SV56: $i] :
( ( ~ ! [SY3275: $i,SY3276: $i] :
( ~ ( relation @ SY3276 )
| ~ ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SY3276 @ SY3275 ) ) )
| ( in @ SV56 @ SY3275 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1065]) ).
thf(1165,plain,
! [SV56: $i] :
( ( ~ ! [SY3277: $i,SY3278: $i] :
( ~ ( relation @ SY3278 )
| ~ ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SY3278 @ SY3277 ) ) )
| ( in @ SV56 @ ( relation_dom @ SY3278 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1065]) ).
thf(1166,plain,
! [SV127: $i] :
( ( ( relation @ SV127 )
= $false )
| ( ( ( relation_rng @ SV127 )
= ( relation_dom @ ( relation_inverse @ SV127 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1066]) ).
thf(1167,plain,
! [SV128: $i] :
( ( ( relation @ SV128 )
= $false )
| ( ( ( relation_dom @ SV128 )
= ( relation_rng @ ( relation_inverse @ SV128 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1067]) ).
thf(1168,plain,
! [SV147: $i,SV57: $i,SV159: $i] :
( ( ~ ( relation @ SV159 )
| ~ ( in @ ( ordered_pair @ SV57 @ SV147 ) @ SV159 )
| ( in @ SV57 @ ( relation_dom @ SV159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1169,plain,
! [SV148: $i,SV57: $i,SV160: $i] :
( ( ~ ( relation @ SV160 )
| ~ ( in @ ( ordered_pair @ SV57 @ SV148 ) @ SV160 )
| ( in @ SV148 @ ( relation_rng @ SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1069]) ).
thf(1170,plain,
! [SV149: $i,SV58: $i,SV161: $i] :
( ( ~ ( relation @ SV161 )
| ! [SY3374: $i] :
( ~ ( in @ SY3374 @ ( relation_rng @ SV161 ) )
| ~ ( in @ ( ordered_pair @ SV58 @ SY3374 ) @ SV161 )
| ~ ( in @ SY3374 @ SV149 ) )
| ( in @ SV58 @ ( relation_inverse_image @ SV161 @ SV149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1171,plain,
! [SV150: $i,SV58: $i,SV162: $i] :
( ( ~ ( relation @ SV162 )
| ~ ( in @ SV58 @ ( relation_inverse_image @ SV162 @ SV150 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK46_D @ SV162 @ SV150 @ SV58 ) @ ( relation_rng @ SV162 ) )
| ~ ( in @ ( ordered_pair @ SV58 @ ( sK46_D @ SV162 @ SV150 @ SV58 ) ) @ SV162 ) )
| ~ ( in @ ( sK46_D @ SV162 @ SV150 @ SV58 ) @ SV150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1172,plain,
! [SV59: $i] :
( ( ( ! [SY3288: $i] :
( ~ ( relation @ SY3288 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SY3288 @ SV59 ) @ ( sK23_SY3118 @ SY3288 @ SV59 ) ) @ SV59 )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_C @ SY3288 @ SV59 ) @ ( sK23_SY3118 @ SY3288 @ SV59 ) ) @ SY3288 ) )
| ( subset @ SV59 @ SY3288 ) ) )
= $true )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1072]) ).
thf(1173,plain,
! [SV59: $i] :
( ( ( ! [SY3289: $i] :
( ~ ( relation @ SY3289 )
| ~ ( subset @ SV59 @ SY3289 )
| ! [SY3290: $i,SY3291: $i] :
( ~ ( in @ ( ordered_pair @ SY3290 @ SY3291 ) @ SV59 )
| ( in @ ( ordered_pair @ SY3290 @ SY3291 ) @ SY3289 ) ) ) )
= $true )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1073]) ).
thf(1174,plain,
! [SV60: $i] :
( ( ( ! [SY3292: $i,SY3293: $i] :
( ~ ( relation @ SY3293 )
| ~ ( ~ ( ~ ( in @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ SY3292 )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ ( sK38_SY3128 @ SY3293 @ SY3292 @ SV60 ) ) @ SV60 )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ ( sK38_SY3128 @ SY3293 @ SY3292 @ SV60 ) ) @ SY3293 ) )
| ~ ~ ( ~ ( ( in @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ SY3292 )
| ( in @ ( ordered_pair @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ ( sK38_SY3128 @ SY3293 @ SY3292 @ SV60 ) ) @ SY3293 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ ( sK38_SY3128 @ SY3293 @ SY3292 @ SV60 ) ) @ SV60 )
| ( in @ ( ordered_pair @ ( sK37_D @ SY3293 @ SY3292 @ SV60 ) @ ( sK38_SY3128 @ SY3293 @ SY3292 @ SV60 ) ) @ SY3293 ) ) ) )
| ( SY3293
= ( relation_dom_restriction @ SV60 @ SY3292 ) ) ) )
= $true )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1074]) ).
thf(1175,plain,
! [SV60: $i] :
( ( ( ! [SY3294: $i,SY3295: $i] :
( ~ ( relation @ SY3295 )
| ( SY3295
!= ( relation_dom_restriction @ SV60 @ SY3294 ) )
| ~ ( ~ ! [SY3296: $i,SY3297: $i] :
( ~ ( in @ SY3296 @ SY3294 )
| ~ ( in @ ( ordered_pair @ SY3296 @ SY3297 ) @ SV60 )
| ( in @ ( ordered_pair @ SY3296 @ SY3297 ) @ SY3295 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3295 )
| ( in @ SX3 @ SY3294 ) )
| ~ ! [SY3300: $i,SY3301: $i] :
( ~ ( in @ ( ordered_pair @ SY3300 @ SY3301 ) @ SY3295 )
| ( in @ ( ordered_pair @ SY3300 @ SY3301 ) @ SV60 ) ) ) ) ) )
= $true )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1075]) ).
thf(1176,plain,
! [SV69: $i,SV11: $i] :
( ( ( subset @ SV11 @ ( relation_rng @ SV69 ) )
= $false )
| ( ( SV11 = empty_set )
= $true )
| ( ( ( ( relation_inverse_image @ SV69 @ SV11 )
!= empty_set ) )
= $true )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1077]) ).
thf(1177,plain,
! [SV85: $i,SV70: $i,SV12: $i] :
( ( ( subset @ SV12 @ SV70 )
= $false )
| ( ( subset @ ( relation_inverse_image @ SV85 @ SV12 ) @ ( relation_inverse_image @ SV85 @ SV70 ) )
= $true )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1078]) ).
thf(1178,plain,
! [SV71: $i,SV14: $i,SV163: $i] :
( ( ( ~ ( function @ SV163 )
| ~ ( relation @ SV163 )
| ~ ( in @ SV14 @ ( relation_dom @ ( relation_composition @ SV163 @ SV71 ) ) )
| ( ( apply @ ( relation_composition @ SV163 @ SV71 ) @ SV14 )
= ( apply @ SV71 @ ( apply @ SV163 @ SV14 ) ) ) )
= $true )
| ( ( function @ SV71 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1179,plain,
! [SV72: $i,SV15: $i,SV164: $i] :
( ( ( ~ ( function @ SV164 )
| ~ ( relation @ SV164 )
| ~ ( in @ SV15 @ ( relation_dom @ SV72 ) )
| ( ( apply @ ( relation_composition @ SV72 @ SV164 ) @ SV15 )
= ( apply @ SV164 @ ( apply @ SV72 @ SV15 ) ) ) )
= $true )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1180,plain,
! [SV89: $i,SV18: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV18 ) @ ( relation_dom @ SV89 ) ) )
= $true )
| ( ( ( relation_dom @ ( relation_composition @ SV18 @ SV89 ) )
= ( relation_dom @ SV18 ) )
= $true )
| ( ( relation @ SV89 )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1083]) ).
thf(1181,plain,
! [SV90: $i,SV19: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV19 ) @ ( relation_rng @ SV90 ) ) )
= $true )
| ( ( ( relation_rng @ ( relation_composition @ SV90 @ SV19 ) )
= ( relation_rng @ SV19 ) )
= $true )
| ( ( relation @ SV90 )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1084]) ).
thf(1182,plain,
! [SV28: $i] :
( ( ( one_to_one @ SV28 )
= $false )
| ( ( ( function_inverse @ SV28 )
= ( relation_inverse @ SV28 ) )
= $true )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1085]) ).
thf(1183,plain,
! [SV39: $i,SV129: $i,SV151: $i] :
( ( ( ~ ( function @ SV151 )
| ~ ( relation @ SV151 ) )
= $true )
| ( ( ( SV129
!= ( apply @ SV151 @ SV39 ) )
| ~ ( in @ SV39 @ ( relation_dom @ SV151 ) )
| ( in @ ( ordered_pair @ SV39 @ SV129 ) @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1089]) ).
thf(1184,plain,
! [SV39: $i] :
( ( ! [SY3164: $i,SY3165: $i] :
( ~ ( function @ SY3165 )
| ~ ( relation @ SY3165 )
| ~ ( in @ ( ordered_pair @ SV39 @ SY3164 ) @ SY3165 )
| ( SY3164
= ( apply @ SY3165 @ SV39 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1090]) ).
thf(1185,plain,
! [SV39: $i] :
( ( ! [SY3166: $i,SY3167: $i] :
( ~ ( function @ SY3167 )
| ~ ( relation @ SY3167 )
| ~ ( in @ ( ordered_pair @ SV39 @ SY3166 ) @ SY3167 )
| ( in @ SV39 @ ( relation_dom @ SY3167 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1091]) ).
thf(1186,plain,
! [SV40: $i] :
( ( ( one_to_one @ SV40 )
= $false )
| ( ( ~ ( ~ ! [SY3168: $i] :
( ~ ( function @ SY3168 )
| ~ ( relation @ SY3168 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK44_SY3131 @ SY3168 @ SV40 )
= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ( ( sK43_C @ SY3168 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SY3168 @ SV40 )
= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SY3168 @ SV40 )
= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ( ( sK44_SY3131 @ SY3168 @ SV40 )
!= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK43_C @ SY3168 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK44_SY3131 @ SY3168 @ SV40 )
!= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK43_C @ SY3168 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK43_C @ SY3168 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SY3168 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SY3168 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK44_SY3131 @ SY3168 @ SV40 )
!= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ( ( relation_dom @ SY3168 )
!= ( relation_rng @ SV40 ) )
| ( SY3168
= ( function_inverse @ SV40 ) ) )
| ~ ~ ( ~ ! [SY3169: $i] :
( ~ ( function @ SY3169 )
| ~ ( relation @ SY3169 )
| ( SY3169
!= ( function_inverse @ SV40 ) )
| ~ ( ~ ~ ( ~ ! [SY3170: $i,SY3171: $i] :
( ( SY3171
!= ( apply @ SY3169 @ SY3170 ) )
| ~ ( in @ SY3170 @ ( relation_rng @ SV40 ) )
| ( SY3170
= ( apply @ SV40 @ SY3171 ) ) )
| ~ ! [SY3172: $i,SY3173: $i] :
( ( SY3173
!= ( apply @ SY3169 @ SY3172 ) )
| ~ ( in @ SY3172 @ ( relation_rng @ SV40 ) )
| ( in @ SY3173 @ ( relation_dom @ SV40 ) ) ) )
| ~ ~ ( ~ ! [SY3174: $i,SY3175: $i] :
( ( SY3174
!= ( apply @ SV40 @ SY3175 ) )
| ~ ( in @ SY3175 @ ( relation_dom @ SV40 ) )
| ( SY3175
= ( apply @ SY3169 @ SY3174 ) ) )
| ~ ! [SY3176: $i] :
( ! [SY3177: $i] :
( ( SY3176
!= ( apply @ SV40 @ SY3177 ) )
| ~ ( in @ SY3177 @ ( relation_dom @ SV40 ) ) )
| ( in @ SY3176 @ ( relation_rng @ SV40 ) ) ) ) ) )
| ~ ! [SY3178: $i] :
( ~ ( function @ SY3178 )
| ~ ( relation @ SY3178 )
| ( SY3178
!= ( function_inverse @ SV40 ) )
| ( ( relation_dom @ SY3178 )
= ( relation_rng @ SV40 ) ) ) ) ) )
= $true )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1092]) ).
thf(1187,plain,
! [SV41: $i,SV165: $i] :
( ( ( ! [SY3375: $i] :
( ~ ( ~ ( ! [SY3376: $i] :
( ~ ( in @ ( ordered_pair @ ( sK30_D @ SY3375 @ SV165 @ SV41 ) @ SY3376 ) @ SV41 )
| ~ ( in @ SY3376 @ SV165 ) )
| ~ ( in @ ( sK30_D @ SY3375 @ SV165 @ SV41 ) @ SY3375 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK30_D @ SY3375 @ SV165 @ SV41 ) @ ( sK31_SY3124 @ SY3375 @ SV165 @ SV41 ) ) @ SV41 )
| ~ ( in @ ( sK31_SY3124 @ SY3375 @ SV165 @ SV41 ) @ SV165 ) )
| ( in @ ( sK30_D @ SY3375 @ SV165 @ SV41 ) @ SY3375 ) ) )
| ( SY3375
= ( relation_inverse_image @ SV41 @ SV165 ) ) ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1093]) ).
thf(1188,plain,
! [SV166: $i,SV41: $i] :
( ( ( ! [SY3377: $i] :
( ( SY3377
!= ( relation_inverse_image @ SV41 @ SV166 ) )
| ~ ( ~ ! [SY3378: $i] :
( ! [SY3379: $i] :
( ~ ( in @ ( ordered_pair @ SY3378 @ SY3379 ) @ SV41 )
| ~ ( in @ SY3379 @ SV166 ) )
| ( in @ SY3378 @ SY3377 ) )
| ~ ! [SY3380: $i] :
( ~ ( in @ SY3380 @ SY3377 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3380 @ ( sK29_E @ SY3380 @ SY3377 @ SV166 @ SV41 ) ) @ SV41 )
| ~ ( in @ ( sK29_E @ SY3380 @ SY3377 @ SV166 @ SV41 ) @ SV166 ) ) ) ) ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1189,plain,
! [SV42: $i,SV167: $i] :
( ( ( ~ ( ~ ( ! [SY3381: $i] :
~ ( in @ ( ordered_pair @ SY3381 @ ( sK17_C @ SV167 @ SV42 ) ) @ SV42 )
| ~ ( in @ ( sK17_C @ SV167 @ SV42 ) @ SV167 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK18_SY3115 @ SV167 @ SV42 ) @ ( sK17_C @ SV167 @ SV42 ) ) @ SV42 )
| ( in @ ( sK17_C @ SV167 @ SV42 ) @ SV167 ) ) )
| ( SV167
= ( relation_rng @ SV42 ) ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1190,plain,
! [SV42: $i,SV168: $i] :
( ( ( ( SV168
!= ( relation_rng @ SV42 ) )
| ~ ( ~ ! [SY3382: $i] :
( ! [SY3191: $i] :
~ ( in @ ( ordered_pair @ SY3191 @ SY3382 ) @ SV42 )
| ( in @ SY3382 @ SV168 ) )
| ~ ! [SY3384: $i] :
( ~ ( in @ SY3384 @ SV168 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3384 @ SV168 @ SV42 ) @ SY3384 ) @ SV42 ) ) ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1191,plain,
! [SV92: $i] :
( ( ( function @ SV92 )
= $false )
| ( ( ~ ( relation @ SV92 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK12_B @ SV92 ) @ ( relation_dom @ SV92 ) )
| ~ ( in @ ( sK13_SY3112 @ SV92 ) @ ( relation_dom @ SV92 ) ) )
| ( ( apply @ SV92 @ ( sK12_B @ SV92 ) )
!= ( apply @ SV92 @ ( sK13_SY3112 @ SV92 ) ) ) )
| ~ ( ( ( sK12_B @ SV92 )
!= ( sK13_SY3112 @ SV92 ) ) ) )
| ( one_to_one @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1192,plain,
! [SV93: $i] :
( ( ( function @ SV93 )
= $false )
| ( ( ~ ( relation @ SV93 ) )
= $true )
| ( ( ~ ( one_to_one @ SV93 )
| ! [SY3323: $i,SY3324: $i] :
( ~ ( in @ SY3323 @ ( relation_dom @ SV93 ) )
| ~ ( in @ SY3324 @ ( relation_dom @ SV93 ) )
| ( ( apply @ SV93 @ SY3323 )
!= ( apply @ SV93 @ SY3324 ) )
| ( SY3323 = SY3324 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1098]) ).
thf(1193,plain,
! [SV43: $i,SV94: $i] :
( ( ( ~ ! [SY3325: $i] :
( ~ ( relation @ SY3325 )
| ~ ( ~ ( ! [SY3326: $i] :
( ~ ( in @ ( ordered_pair @ ( sK9_D @ SY3325 @ SV94 @ SV43 ) @ SY3326 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3326 @ ( sK10_SY3107 @ SY3325 @ SV94 @ SV43 ) ) @ SV94 ) )
| ~ ( in @ ( ordered_pair @ ( sK9_D @ SY3325 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SY3325 @ SV94 @ SV43 ) ) @ SY3325 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK9_D @ SY3325 @ SV94 @ SV43 ) @ ( sK11_SY3111 @ SY3325 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY3111 @ SY3325 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SY3325 @ SV94 @ SV43 ) ) @ SV94 ) )
| ( in @ ( ordered_pair @ ( sK9_D @ SY3325 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SY3325 @ SV94 @ SV43 ) ) @ SY3325 ) ) )
| ( SY3325
= ( relation_composition @ SV43 @ SV94 ) ) )
| ~ ! [SY3327: $i] :
( ~ ( relation @ SY3327 )
| ( SY3327
!= ( relation_composition @ SV43 @ SV94 ) )
| ~ ( ~ ! [SY3328: $i,SY3329: $i] :
( ! [SY3330: $i] :
( ~ ( in @ ( ordered_pair @ SY3328 @ SY3330 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3330 @ SY3329 ) @ SV94 ) )
| ( in @ ( ordered_pair @ SY3328 @ SY3329 ) @ SY3327 ) )
| ~ ! [SY3331: $i,SY3332: $i] :
( ~ ( in @ ( ordered_pair @ SY3331 @ SY3332 ) @ SY3327 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3331 @ ( sK8_F @ SY3332 @ SY3331 @ SY3327 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK8_F @ SY3332 @ SY3331 @ SY3327 @ SV94 @ SV43 ) @ SY3332 ) @ SV94 ) ) ) ) ) )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1099]) ).
thf(1194,plain,
! [SV44: $i,SV169: $i] :
( ( ( ~ ( ~ ( ! [SY3385: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SV169 @ SV44 ) @ SY3385 ) @ SV44 )
| ~ ( in @ ( sK20_C @ SV169 @ SV44 ) @ SV169 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SV169 @ SV44 ) @ ( sK21_SY3117 @ SV169 @ SV44 ) ) @ SV44 )
| ( in @ ( sK20_C @ SV169 @ SV44 ) @ SV169 ) ) )
| ( SV169
= ( relation_dom @ SV44 ) ) )
= $true )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1195,plain,
! [SV44: $i,SV170: $i] :
( ( ( ( SV170
!= ( relation_dom @ SV44 ) )
| ~ ( ~ ! [SY3386: $i] :
( ! [SY3206: $i] :
~ ( in @ ( ordered_pair @ SY3386 @ SY3206 ) @ SV44 )
| ( in @ SY3386 @ SV170 ) )
| ~ ! [SY3388: $i] :
( ~ ( in @ SY3388 @ SV170 )
| ( in @ ( ordered_pair @ SY3388 @ ( sK19_D @ SY3388 @ SV170 @ SV44 ) ) @ SV44 ) ) ) )
= $true )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1196,plain,
! [SV45: $i] :
( ( ( ~ ~ ( ~ ! [SY3208: $i] :
( ~ ( in @ SY3208 @ ( relation_dom @ SV45 ) )
| ! [SY3209: $i] :
( ( SY3209
!= ( apply @ SV45 @ SY3208 ) )
| ( in @ ( ordered_pair @ SY3208 @ SY3209 ) @ SV45 ) ) )
| ~ ! [SY3210: $i] :
( ~ ( in @ SY3210 @ ( relation_dom @ SV45 ) )
| ! [SY3211: $i] :
( ~ ( in @ ( ordered_pair @ SY3210 @ SY3211 ) @ SV45 )
| ( SY3211
= ( apply @ SV45 @ SY3210 ) ) ) ) ) )
= $false )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1102]) ).
thf(1197,plain,
! [SV45: $i] :
( ( ( ~ ~ ( ~ ! [SY3212: $i] :
( ( in @ SY3212 @ ( relation_dom @ SV45 ) )
| ! [SY3213: $i] :
( ( SY3213
!= ( apply @ SV45 @ SY3212 ) )
| ( SY3213 = empty_set ) ) )
| ~ ! [SY3214: $i] :
( ( in @ SY3214 @ ( relation_dom @ SV45 ) )
| ! [SY3215: $i] :
( ( SY3215 != empty_set )
| ( SY3215
= ( apply @ SV45 @ SY3214 ) ) ) ) ) )
= $false )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1102]) ).
thf(1198,plain,
! [SV95: $i,SV130: $i] :
( ( ( ~ ( function @ SV130 ) )
= $true )
| ( ( ~ ( relation @ SV130 ) )
= $true )
| ( ( ~ ( in @ SV95 @ ( relation_rng @ SV130 ) )
| ~ ( one_to_one @ SV130 )
| ( SV95
= ( apply @ SV130 @ ( apply @ ( function_inverse @ SV130 ) @ SV95 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1103]) ).
thf(1199,plain,
! [SV96: $i,SV131: $i] :
( ( ( ~ ( function @ SV131 ) )
= $true )
| ( ( ~ ( relation @ SV131 ) )
= $true )
| ( ( ~ ( in @ SV96 @ ( relation_rng @ SV131 ) )
| ~ ( one_to_one @ SV131 )
| ( SV96
= ( apply @ ( relation_composition @ ( function_inverse @ SV131 ) @ SV131 ) @ SV96 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1104]) ).
thf(1200,plain,
! [SV97: $i] :
( ( ( function @ SV97 )
= $false )
| ( ( ~ ( relation @ SV97 ) )
= $true )
| ( ( ~ ( one_to_one @ SV97 )
| ( ( relation_rng @ SV97 )
= ( relation_dom @ ( function_inverse @ SV97 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1105]) ).
thf(1201,plain,
! [SV98: $i] :
( ( ( function @ SV98 )
= $false )
| ( ( ~ ( relation @ SV98 ) )
= $true )
| ( ( ~ ( one_to_one @ SV98 )
| ( ( relation_dom @ SV98 )
= ( relation_rng @ ( function_inverse @ SV98 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1106]) ).
thf(1202,plain,
! [SV132: $i,SV99: $i] :
( ( ( ~ ( empty @ SV99 ) )
= $true )
| ( ( ~ ( relation @ SV132 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV99 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1107]) ).
thf(1203,plain,
! [SV133: $i,SV100: $i] :
( ( ( ~ ( empty @ SV100 ) )
= $true )
| ( ( ~ ( relation @ SV133 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV100 @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1108]) ).
thf(1204,plain,
! [SV101: $i,SV134: $i] :
( ( ( ~ ( function @ SV134 ) )
= $true )
| ( ( ~ ( relation @ SV134 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK45_C @ SV134 @ SV101 ) @ SV101 )
| ~ ( ( ( apply @ SV134 @ ( sK45_C @ SV134 @ SV101 ) )
!= ( sK45_C @ SV134 @ SV101 ) ) ) )
| ( ( relation_dom @ SV134 )
!= SV101 )
| ( SV134
= ( identity_relation @ SV101 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1109]) ).
thf(1205,plain,
! [SV171: $i] :
( ( ! [SY3389: $i] :
( ~ ( function @ SY3389 )
| ~ ( relation @ SY3389 )
| ( SY3389
!= ( identity_relation @ SV171 ) )
| ! [SY3390: $i] :
( ~ ( in @ SY3390 @ SV171 )
| ( ( apply @ SY3389 @ SY3390 )
= SY3390 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1206,plain,
! [SV172: $i] :
( ( ! [SY3391: $i] :
( ~ ( function @ SY3391 )
| ~ ( relation @ SY3391 )
| ( SY3391
!= ( identity_relation @ SV172 ) )
| ( ( relation_dom @ SY3391 )
= SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1207,plain,
! [SV102: $i] :
( ( ( ~ ! [SY3338: $i,SY3339: $i] :
( ( sK28_B @ SV102 )
!= ( ordered_pair @ SY3338 @ SY3339 ) ) )
= $false )
| ( ( relation @ SV102 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1114]) ).
thf(1208,plain,
! [SV102: $i] :
( ( ( ~ ( in @ ( sK28_B @ SV102 ) @ SV102 ) )
= $false )
| ( ( relation @ SV102 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1114]) ).
thf(1209,plain,
! [SV103: $i,SV173: $i] :
( ( ( ( SV173
= ( ordered_pair @ ( sK26_C @ SV173 @ SV103 ) @ ( sK27_SY3120 @ SV173 @ SV103 ) ) )
| ~ ( in @ SV173 @ SV103 ) )
= $true )
| ( ( relation @ SV103 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1210,plain,
! [SV135: $i,SV46: $i,SV152: $i] :
( ( ( ~ ( relation @ SV152 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV46 @ SV135 ) @ SV152 )
| ( in @ SV46 @ ( relation_field @ SV152 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1116]) ).
thf(1211,plain,
! [SV136: $i,SV46: $i,SV153: $i] :
( ( ( ~ ( relation @ SV153 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV46 @ SV136 ) @ SV153 )
| ( in @ SV136 @ ( relation_field @ SV153 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1117]) ).
thf(1212,plain,
! [SV81: $i,SV154: $i,SV47: $i,SV174: $i] :
( ( ~ ( relation @ SV174 )
| ~ ( in @ SV47 @ SV154 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ SV174 )
| ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SV154 ) @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1213,plain,
! [SV81: $i,SV47: $i] :
( ( ~ ! [SY3308: $i,SY3309: $i] :
( ~ ( relation @ SY3309 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SY3308 ) @ SY3309 ) )
| ( in @ SV47 @ SY3308 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1119]) ).
thf(1214,plain,
! [SV81: $i,SV47: $i] :
( ( ~ ! [SY3310: $i,SY3311: $i] :
( ~ ( relation @ SY3311 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SY3310 ) @ SY3311 ) )
| ( in @ ( ordered_pair @ SV47 @ SV81 ) @ SY3311 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1119]) ).
thf(1215,plain,
! [SV104: $i] :
( ( ( function @ SV104 )
= $false )
| ( ( ~ ( relation @ SV104 ) )
= $true )
| ( ( function @ ( function_inverse @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1120]) ).
thf(1216,plain,
! [SV105: $i] :
( ( ( function @ SV105 )
= $false )
| ( ( ~ ( relation @ SV105 ) )
= $true )
| ( ( relation @ ( function_inverse @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1121]) ).
thf(1217,plain,
! [SV137: $i,SV48: $i,SV155: $i] :
( ( ( ~ ( relation @ SV155 ) )
= $true )
| ( ( ~ ( in @ SV48 @ SV137 )
| ~ ( in @ SV48 @ ( relation_rng @ SV155 ) )
| ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SV137 @ SV155 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1122]) ).
thf(1218,plain,
! [SV48: $i] :
( ( ! [SY3229: $i,SY3230: $i] :
( ~ ( relation @ SY3230 )
| ~ ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SY3229 @ SY3230 ) ) )
| ( in @ SV48 @ SY3229 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1123]) ).
thf(1219,plain,
! [SV48: $i] :
( ( ! [SY3231: $i,SY3232: $i] :
( ~ ( relation @ SY3232 )
| ~ ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SY3231 @ SY3232 ) ) )
| ( in @ SV48 @ ( relation_rng @ SY3232 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1124]) ).
thf(1220,plain,
! [SV49: $i,SV175: $i] :
( ( ( ~ ( relation @ SV175 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV175 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV49 )
| ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV175 ) ) )
| ( SV49 = SV175 ) )
= $true )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1221,plain,
! [SV49: $i,SV176: $i] :
( ( ( ~ ( relation @ SV176 )
| ( SV49 != SV176 )
| ~ ( ~ ! [SY3392: $i,SY3393: $i] :
( ~ ( in @ ( ordered_pair @ SY3392 @ SY3393 ) @ SV49 )
| ( in @ ( ordered_pair @ SY3392 @ SY3393 ) @ SV176 ) )
| ~ ! [SY3394: $i,SY3395: $i] :
( ~ ( in @ ( ordered_pair @ SY3394 @ SY3395 ) @ SV176 )
| ( in @ ( ordered_pair @ SY3394 @ SY3395 ) @ SV49 ) ) ) )
= $true )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1222,plain,
! [SV108: $i] :
( ( ( ( ( relation_dom @ SV108 )
!= empty_set ) )
= $true )
| ( ( ( relation_rng @ SV108 )
= empty_set )
= $true )
| ( ( relation @ SV108 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1129]) ).
thf(1223,plain,
! [SV109: $i] :
( ( ( ( ( relation_rng @ SV109 )
!= empty_set ) )
= $true )
| ( ( ( relation_dom @ SV109 )
= empty_set )
= $true )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1130]) ).
thf(1224,plain,
! [SV50: $i,SV177: $i] :
( ( ( ! [SY3396: $i] :
( ~ ( ~ ( ! [SY3397: $i] :
( ~ ( in @ ( ordered_pair @ SY3397 @ ( sK33_D @ SY3396 @ SV177 @ SV50 ) ) @ SV50 )
| ~ ( in @ SY3397 @ SV177 ) )
| ~ ( in @ ( sK33_D @ SY3396 @ SV177 @ SV50 ) @ SY3396 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK34_SY3126 @ SY3396 @ SV177 @ SV50 ) @ ( sK33_D @ SY3396 @ SV177 @ SV50 ) ) @ SV50 )
| ~ ( in @ ( sK34_SY3126 @ SY3396 @ SV177 @ SV50 ) @ SV177 ) )
| ( in @ ( sK33_D @ SY3396 @ SV177 @ SV50 ) @ SY3396 ) ) )
| ( SY3396
= ( relation_image @ SV50 @ SV177 ) ) ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1225,plain,
! [SV178: $i,SV50: $i] :
( ( ( ! [SY3398: $i] :
( ( SY3398
!= ( relation_image @ SV50 @ SV178 ) )
| ~ ( ~ ! [SY3399: $i] :
( ! [SY3400: $i] :
( ~ ( in @ ( ordered_pair @ SY3400 @ SY3399 ) @ SV50 )
| ~ ( in @ SY3400 @ SV178 ) )
| ( in @ SY3399 @ SY3398 ) )
| ~ ! [SY3401: $i] :
( ~ ( in @ SY3401 @ SY3398 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK32_E @ SY3401 @ SY3398 @ SV178 @ SV50 ) @ SY3401 ) @ SV50 )
| ~ ( in @ ( sK32_E @ SY3401 @ SY3398 @ SV178 @ SV50 ) @ SV178 ) ) ) ) ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1226,plain,
! [SV138: $i,SV110: $i] :
( ( ( ~ ( function @ SV110 )
| ~ ( relation @ SV110 )
| ~ ( relation @ SV138 ) )
= $true )
| ( ( ~ ( function @ SV138 ) )
= $true )
| ( ( function @ ( relation_composition @ SV110 @ SV138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1133]) ).
thf(1227,plain,
! [SV139: $i,SV111: $i] :
( ( ( ~ ( function @ SV111 )
| ~ ( relation @ SV111 )
| ~ ( relation @ SV139 ) )
= $true )
| ( ( ~ ( function @ SV139 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV111 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1134]) ).
thf(1228,plain,
! [SV179: $i] :
( ( ~ ( empty @ SV179 )
| ~ ( relation @ SV179 )
| ~ ( function @ SV179 )
| ( function @ SV179 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1229,plain,
! [SV180: $i] :
( ( ~ ( empty @ SV180 )
| ~ ( relation @ SV180 )
| ~ ( function @ SV180 )
| ( relation @ SV180 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1136]) ).
thf(1230,plain,
! [SV112: $i] :
( ( ( ~ ( empty @ SV112 ) )
= $true )
| ( ( ~ ( relation @ SV112 ) )
= $true )
| ( ( ~ ( function @ SV112 ) )
= $true )
| ( ( one_to_one @ SV112 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1137]) ).
thf(1231,plain,
! [SV140: $i,SV51: $i,SV156: $i] :
( ( ( ~ ( relation @ SV156 ) )
= $true )
| ( ( ! [SY3373: $i] :
( ~ ( in @ SY3373 @ ( relation_dom @ SV156 ) )
| ~ ( in @ ( ordered_pair @ SY3373 @ SV51 ) @ SV156 )
| ~ ( in @ SY3373 @ SV140 ) )
| ( in @ SV51 @ ( relation_image @ SV156 @ SV140 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1138]) ).
thf(1232,plain,
! [SV141: $i,SV51: $i,SV157: $i] :
( ( ( ~ ( relation @ SV157 ) )
= $true )
| ( ( ~ ( in @ SV51 @ ( relation_image @ SV157 @ SV141 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK47_D @ SV157 @ SV141 @ SV51 ) @ ( relation_dom @ SV157 ) )
| ~ ( in @ ( ordered_pair @ ( sK47_D @ SV157 @ SV141 @ SV51 ) @ SV51 ) @ SV157 ) )
| ~ ( in @ ( sK47_D @ SV157 @ SV141 @ SV51 ) @ SV141 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1139]) ).
thf(1233,plain,
! [SV52: $i,SV181: $i] :
( ( ( ~ ( relation @ SV181 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_C @ SV181 @ SV52 ) @ ( sK15_SY3113 @ SV181 @ SV52 ) ) @ SV181 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY3113 @ SV181 @ SV52 ) @ ( sK14_C @ SV181 @ SV52 ) ) @ SV52 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SV181 @ SV52 ) @ ( sK15_SY3113 @ SV181 @ SV52 ) ) @ SV181 )
| ( in @ ( ordered_pair @ ( sK15_SY3113 @ SV181 @ SV52 ) @ ( sK14_C @ SV181 @ SV52 ) ) @ SV52 ) ) )
| ( SV181
= ( relation_inverse @ SV52 ) ) )
= $true )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1234,plain,
! [SV52: $i,SV182: $i] :
( ( ( ~ ( relation @ SV182 )
| ( SV182
!= ( relation_inverse @ SV52 ) )
| ~ ( ~ ! [SY3402: $i,SY3403: $i] :
( ~ ( in @ ( ordered_pair @ SY3402 @ SY3403 ) @ SV182 )
| ( in @ ( ordered_pair @ SY3403 @ SY3402 ) @ SV52 ) )
| ~ ! [SY3404: $i,SY3405: $i] :
( ~ ( in @ ( ordered_pair @ SY3405 @ SY3404 ) @ SV52 )
| ( in @ ( ordered_pair @ SY3404 @ SY3405 ) @ SV182 ) ) ) )
= $true )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1235,plain,
! [SV115: $i] :
( ( ( ~ ( function @ SV115 ) )
= $true )
| ( ( ~ ( relation @ SV115 ) )
= $true )
| ( ( ~ ( one_to_one @ SV115 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1142]) ).
thf(1236,plain,
! [SV116: $i] :
( ( ( ~ ( function @ SV116 ) )
= $true )
| ( ( ~ ( relation @ SV116 ) )
= $true )
| ( ( ~ ( one_to_one @ SV116 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1143]) ).
thf(1237,plain,
! [SV117: $i] :
( ( ( ( ( relation_dom @ SV117 )
!= empty_set ) )
= $true )
| ( ( SV117 = empty_set )
= $true )
| ( ( relation @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1144]) ).
thf(1238,plain,
! [SV118: $i] :
( ( ( ( ( relation_rng @ SV118 )
!= empty_set ) )
= $true )
| ( ( SV118 = empty_set )
= $true )
| ( ( relation @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1145]) ).
thf(1239,plain,
! [SV123: $i,SV142: $i] :
( ( ( relation @ SV142 )
= $false )
| ( ( ~ ( ~ ( ( ( sK39_C @ SV142 @ SV123 )
!= ( sK40_SY3129 @ SV142 @ SV123 ) )
| ~ ( in @ ( sK39_C @ SV142 @ SV123 ) @ SV123 )
| ~ ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 ) )
| ~ ~ ( ~ ( ( ( sK39_C @ SV142 @ SV123 )
= ( sK40_SY3129 @ SV142 @ SV123 ) )
| ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 ) )
| ~ ( ( in @ ( sK39_C @ SV142 @ SV123 ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 ) ) ) )
| ( SV142
= ( identity_relation @ SV123 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1152]) ).
thf(1240,plain,
! [SV124: $i,SV143: $i] :
( ( ( relation @ SV143 )
= $false )
| ( ( ( SV143
!= ( identity_relation @ SV124 ) )
| ~ ( ~ ! [SY3360: $i,SY3361: $i] :
( ( SY3360 != SY3361 )
| ~ ( in @ SY3360 @ SV124 )
| ( in @ ( ordered_pair @ SY3360 @ SY3361 ) @ SV143 ) )
| ~ ~ ( ~ ! [SY3362: $i,SY3363: $i] :
( ~ ( in @ ( ordered_pair @ SY3362 @ SY3363 ) @ SV143 )
| ( SY3362 = SY3363 ) )
| ~ ! [SY3364: $i] :
( ! [SY3365: $i] :
~ ( in @ ( ordered_pair @ SY3364 @ SY3365 ) @ SV143 )
| ( in @ SY3364 @ SV124 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1153]) ).
thf(1241,plain,
! [SV144: $i,SV125: $i] :
( ( ( ~ ( empty @ SV125 ) )
= $true )
| ( ( ~ ( relation @ SV144 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV144 @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1154]) ).
thf(1242,plain,
! [SV145: $i,SV126: $i] :
( ( ( ~ ( empty @ SV126 ) )
= $true )
| ( ( ~ ( relation @ SV145 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV145 @ SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1155]) ).
thf(1243,plain,
! [SV53: $i,SV82: $i] :
( ( ( ! [SY3312: $i] :
( ~ ( relation @ SY3312 )
| ~ ( ~ ( ~ ( in @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) @ SV53 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SY3312 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) ) @ SV82 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SY3312 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) ) @ SY3312 ) )
| ~ ~ ( ~ ( ( in @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) @ SV53 )
| ( in @ ( ordered_pair @ ( sK35_D @ SY3312 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) ) @ SY3312 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SY3312 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) ) @ SV82 )
| ( in @ ( ordered_pair @ ( sK35_D @ SY3312 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SY3312 @ SV82 @ SV53 ) ) @ SY3312 ) ) ) )
| ( SY3312
= ( relation_rng_restriction @ SV53 @ SV82 ) ) ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1156]) ).
thf(1244,plain,
! [SV82: $i,SV53: $i] :
( ( ( ! [SY3313: $i] :
( ~ ( relation @ SY3313 )
| ( SY3313
!= ( relation_rng_restriction @ SV53 @ SV82 ) )
| ~ ( ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ SY3315 @ SV53 )
| ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV82 )
| ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SY3313 ) )
| ~ ~ ( ~ ! [SY3263: $i,SY3264: $i] :
( ~ ( in @ ( ordered_pair @ SY3263 @ SY3264 ) @ SY3313 )
| ( in @ SY3264 @ SV53 ) )
| ~ ! [SY3318: $i,SY3319: $i] :
( ~ ( in @ ( ordered_pair @ SY3318 @ SY3319 ) @ SY3313 )
| ( in @ ( ordered_pair @ SY3318 @ SY3319 ) @ SV82 ) ) ) ) ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1157]) ).
thf(1245,plain,
! [SV54: $i,SV183: $i] :
( ( ( ~ ( relation @ SV183 )
| ~ ( subset @ SV54 @ SV183 )
| ( subset @ ( relation_dom @ SV54 ) @ ( relation_dom @ SV183 ) ) )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1160]) ).
thf(1246,plain,
! [SV54: $i,SV184: $i] :
( ( ( ~ ( relation @ SV184 )
| ~ ( subset @ SV54 @ SV184 )
| ( subset @ ( relation_rng @ SV54 ) @ ( relation_rng @ SV184 ) ) )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1247,plain,
! [SV83: $i,SV55: $i] :
( ( ( ~ ! [SY3320: $i] :
( ~ ( function @ SY3320 )
| ~ ( relation @ SY3320 )
| ~ ( in @ SV55 @ ( relation_dom @ SY3320 ) )
| ~ ( in @ ( apply @ SY3320 @ SV55 ) @ ( relation_dom @ SV83 ) )
| ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3320 @ SV83 ) ) ) )
| ~ ~ ( ~ ! [SY3321: $i] :
( ~ ( function @ SY3321 )
| ~ ( relation @ SY3321 )
| ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3321 @ SV83 ) ) )
| ( in @ SV55 @ ( relation_dom @ SY3321 ) ) )
| ~ ! [SY3322: $i] :
( ~ ( function @ SY3322 )
| ~ ( relation @ SY3322 )
| ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3322 @ SV83 ) ) )
| ( in @ ( apply @ SY3322 @ SV55 ) @ ( relation_dom @ SV83 ) ) ) ) )
= $false )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1162]) ).
thf(1248,plain,
! [SV146: $i,SV56: $i,SV158: $i] :
( ( ( ~ ( relation @ SV158 ) )
= $true )
| ( ( ~ ( in @ SV56 @ SV146 )
| ~ ( in @ SV56 @ ( relation_dom @ SV158 ) )
| ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SV158 @ SV146 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1163]) ).
thf(1249,plain,
! [SV56: $i] :
( ( ! [SY3275: $i,SY3276: $i] :
( ~ ( relation @ SY3276 )
| ~ ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SY3276 @ SY3275 ) ) )
| ( in @ SV56 @ SY3275 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1164]) ).
thf(1250,plain,
! [SV56: $i] :
( ( ! [SY3277: $i,SY3278: $i] :
( ~ ( relation @ SY3278 )
| ~ ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SY3278 @ SY3277 ) ) )
| ( in @ SV56 @ ( relation_dom @ SY3278 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1165]) ).
thf(1251,plain,
! [SV147: $i,SV57: $i,SV159: $i] :
( ( ( ~ ( relation @ SV159 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV57 @ SV147 ) @ SV159 )
| ( in @ SV57 @ ( relation_dom @ SV159 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1168]) ).
thf(1252,plain,
! [SV148: $i,SV57: $i,SV160: $i] :
( ( ( ~ ( relation @ SV160 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV57 @ SV148 ) @ SV160 )
| ( in @ SV148 @ ( relation_rng @ SV160 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1169]) ).
thf(1253,plain,
! [SV149: $i,SV58: $i,SV161: $i] :
( ( ( ~ ( relation @ SV161 ) )
= $true )
| ( ( ! [SY3374: $i] :
( ~ ( in @ SY3374 @ ( relation_rng @ SV161 ) )
| ~ ( in @ ( ordered_pair @ SV58 @ SY3374 ) @ SV161 )
| ~ ( in @ SY3374 @ SV149 ) )
| ( in @ SV58 @ ( relation_inverse_image @ SV161 @ SV149 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1170]) ).
thf(1254,plain,
! [SV150: $i,SV58: $i,SV162: $i] :
( ( ( ~ ( relation @ SV162 ) )
= $true )
| ( ( ~ ( in @ SV58 @ ( relation_inverse_image @ SV162 @ SV150 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK46_D @ SV162 @ SV150 @ SV58 ) @ ( relation_rng @ SV162 ) )
| ~ ( in @ ( ordered_pair @ SV58 @ ( sK46_D @ SV162 @ SV150 @ SV58 ) ) @ SV162 ) )
| ~ ( in @ ( sK46_D @ SV162 @ SV150 @ SV58 ) @ SV150 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1171]) ).
thf(1255,plain,
! [SV59: $i,SV185: $i] :
( ( ( ~ ( relation @ SV185 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SV185 @ SV59 ) @ ( sK23_SY3118 @ SV185 @ SV59 ) ) @ SV59 )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_C @ SV185 @ SV59 ) @ ( sK23_SY3118 @ SV185 @ SV59 ) ) @ SV185 ) )
| ( subset @ SV59 @ SV185 ) )
= $true )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1172]) ).
thf(1256,plain,
! [SV59: $i,SV186: $i] :
( ( ( ~ ( relation @ SV186 )
| ~ ( subset @ SV59 @ SV186 )
| ! [SY3406: $i,SY3407: $i] :
( ~ ( in @ ( ordered_pair @ SY3406 @ SY3407 ) @ SV59 )
| ( in @ ( ordered_pair @ SY3406 @ SY3407 ) @ SV186 ) ) )
= $true )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1257,plain,
! [SV60: $i,SV187: $i] :
( ( ( ! [SY3408: $i] :
( ~ ( relation @ SY3408 )
| ~ ( ~ ( ~ ( in @ ( sK37_D @ SY3408 @ SV187 @ SV60 ) @ SV187 )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ SY3408 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SY3408 @ SV187 @ SV60 ) ) @ SV60 )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ SY3408 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SY3408 @ SV187 @ SV60 ) ) @ SY3408 ) )
| ~ ~ ( ~ ( ( in @ ( sK37_D @ SY3408 @ SV187 @ SV60 ) @ SV187 )
| ( in @ ( ordered_pair @ ( sK37_D @ SY3408 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SY3408 @ SV187 @ SV60 ) ) @ SY3408 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK37_D @ SY3408 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SY3408 @ SV187 @ SV60 ) ) @ SV60 )
| ( in @ ( ordered_pair @ ( sK37_D @ SY3408 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SY3408 @ SV187 @ SV60 ) ) @ SY3408 ) ) ) )
| ( SY3408
= ( relation_dom_restriction @ SV60 @ SV187 ) ) ) )
= $true )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1258,plain,
! [SV188: $i,SV60: $i] :
( ( ( ! [SY3409: $i] :
( ~ ( relation @ SY3409 )
| ( SY3409
!= ( relation_dom_restriction @ SV60 @ SV188 ) )
| ~ ( ~ ! [SY3410: $i,SY3411: $i] :
( ~ ( in @ SY3410 @ SV188 )
| ~ ( in @ ( ordered_pair @ SY3410 @ SY3411 ) @ SV60 )
| ( in @ ( ordered_pair @ SY3410 @ SY3411 ) @ SY3409 ) )
| ~ ~ ( ~ ! [SY3412: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SY3412 @ SX4 ) @ SY3409 )
| ( in @ SY3412 @ SV188 ) )
| ~ ! [SY3300: $i,SY3301: $i] :
( ~ ( in @ ( ordered_pair @ SY3300 @ SY3301 ) @ SY3409 )
| ( in @ ( ordered_pair @ SY3300 @ SY3301 ) @ SV60 ) ) ) ) ) )
= $true )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1259,plain,
! [SV11: $i,SV69: $i] :
( ( ( ( relation_inverse_image @ SV69 @ SV11 )
= empty_set )
= $false )
| ( ( SV11 = empty_set )
= $true )
| ( ( subset @ SV11 @ ( relation_rng @ SV69 ) )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1260,plain,
! [SV71: $i,SV14: $i,SV163: $i] :
( ( ( ~ ( function @ SV163 )
| ~ ( relation @ SV163 ) )
= $true )
| ( ( ~ ( in @ SV14 @ ( relation_dom @ ( relation_composition @ SV163 @ SV71 ) ) )
| ( ( apply @ ( relation_composition @ SV163 @ SV71 ) @ SV14 )
= ( apply @ SV71 @ ( apply @ SV163 @ SV14 ) ) ) )
= $true )
| ( ( function @ SV71 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1178]) ).
thf(1261,plain,
! [SV72: $i,SV15: $i,SV164: $i] :
( ( ( ~ ( function @ SV164 )
| ~ ( relation @ SV164 ) )
= $true )
| ( ( ~ ( in @ SV15 @ ( relation_dom @ SV72 ) )
| ( ( apply @ ( relation_composition @ SV72 @ SV164 ) @ SV15 )
= ( apply @ SV164 @ ( apply @ SV72 @ SV15 ) ) ) )
= $true )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1179]) ).
thf(1262,plain,
! [SV89: $i,SV18: $i] :
( ( ( subset @ ( relation_rng @ SV18 ) @ ( relation_dom @ SV89 ) )
= $false )
| ( ( ( relation_dom @ ( relation_composition @ SV18 @ SV89 ) )
= ( relation_dom @ SV18 ) )
= $true )
| ( ( relation @ SV89 )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1180]) ).
thf(1263,plain,
! [SV90: $i,SV19: $i] :
( ( ( subset @ ( relation_dom @ SV19 ) @ ( relation_rng @ SV90 ) )
= $false )
| ( ( ( relation_rng @ ( relation_composition @ SV90 @ SV19 ) )
= ( relation_rng @ SV19 ) )
= $true )
| ( ( relation @ SV90 )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1181]) ).
thf(1264,plain,
! [SV39: $i,SV129: $i,SV151: $i] :
( ( ( ~ ( function @ SV151 ) )
= $true )
| ( ( ~ ( relation @ SV151 ) )
= $true )
| ( ( ( SV129
!= ( apply @ SV151 @ SV39 ) )
| ~ ( in @ SV39 @ ( relation_dom @ SV151 ) )
| ( in @ ( ordered_pair @ SV39 @ SV129 ) @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1183]) ).
thf(1265,plain,
! [SV189: $i,SV39: $i] :
( ( ! [SY3416: $i] :
( ~ ( function @ SY3416 )
| ~ ( relation @ SY3416 )
| ~ ( in @ ( ordered_pair @ SV39 @ SV189 ) @ SY3416 )
| ( SV189
= ( apply @ SY3416 @ SV39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1266,plain,
! [SV190: $i,SV39: $i] :
( ( ! [SY3417: $i] :
( ~ ( function @ SY3417 )
| ~ ( relation @ SY3417 )
| ~ ( in @ ( ordered_pair @ SV39 @ SV190 ) @ SY3417 )
| ( in @ SV39 @ ( relation_dom @ SY3417 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1267,plain,
! [SV40: $i] :
( ( ( ~ ! [SY3168: $i] :
( ~ ( function @ SY3168 )
| ~ ( relation @ SY3168 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK44_SY3131 @ SY3168 @ SV40 )
= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ( ( sK43_C @ SY3168 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SY3168 @ SV40 )
= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SY3168 @ SV40 )
= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ( ( sK44_SY3131 @ SY3168 @ SV40 )
!= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK43_C @ SY3168 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK44_SY3131 @ SY3168 @ SV40 )
!= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK43_C @ SY3168 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK43_C @ SY3168 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SY3168 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SY3168 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK44_SY3131 @ SY3168 @ SV40 )
!= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ( ( relation_dom @ SY3168 )
!= ( relation_rng @ SV40 ) )
| ( SY3168
= ( function_inverse @ SV40 ) ) )
| ~ ~ ( ~ ! [SY3169: $i] :
( ~ ( function @ SY3169 )
| ~ ( relation @ SY3169 )
| ( SY3169
!= ( function_inverse @ SV40 ) )
| ~ ( ~ ~ ( ~ ! [SY3170: $i,SY3171: $i] :
( ( SY3171
!= ( apply @ SY3169 @ SY3170 ) )
| ~ ( in @ SY3170 @ ( relation_rng @ SV40 ) )
| ( SY3170
= ( apply @ SV40 @ SY3171 ) ) )
| ~ ! [SY3172: $i,SY3173: $i] :
( ( SY3173
!= ( apply @ SY3169 @ SY3172 ) )
| ~ ( in @ SY3172 @ ( relation_rng @ SV40 ) )
| ( in @ SY3173 @ ( relation_dom @ SV40 ) ) ) )
| ~ ~ ( ~ ! [SY3174: $i,SY3175: $i] :
( ( SY3174
!= ( apply @ SV40 @ SY3175 ) )
| ~ ( in @ SY3175 @ ( relation_dom @ SV40 ) )
| ( SY3175
= ( apply @ SY3169 @ SY3174 ) ) )
| ~ ! [SY3176: $i] :
( ! [SY3177: $i] :
( ( SY3176
!= ( apply @ SV40 @ SY3177 ) )
| ~ ( in @ SY3177 @ ( relation_dom @ SV40 ) ) )
| ( in @ SY3176 @ ( relation_rng @ SV40 ) ) ) ) ) )
| ~ ! [SY3178: $i] :
( ~ ( function @ SY3178 )
| ~ ( relation @ SY3178 )
| ( SY3178
!= ( function_inverse @ SV40 ) )
| ( ( relation_dom @ SY3178 )
= ( relation_rng @ SV40 ) ) ) ) )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1186]) ).
thf(1268,plain,
! [SV41: $i,SV165: $i,SV191: $i] :
( ( ( ~ ( ~ ( ! [SY3418: $i] :
( ~ ( in @ ( ordered_pair @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SY3418 ) @ SV41 )
| ~ ( in @ SY3418 @ SV165 ) )
| ~ ( in @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SV191 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ ( sK31_SY3124 @ SV191 @ SV165 @ SV41 ) ) @ SV41 )
| ~ ( in @ ( sK31_SY3124 @ SV191 @ SV165 @ SV41 ) @ SV165 ) )
| ( in @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SV191 ) ) )
| ( SV191
= ( relation_inverse_image @ SV41 @ SV165 ) ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1187]) ).
thf(1269,plain,
! [SV166: $i,SV41: $i,SV192: $i] :
( ( ( ( SV192
!= ( relation_inverse_image @ SV41 @ SV166 ) )
| ~ ( ~ ! [SY3419: $i] :
( ! [SY3379: $i] :
( ~ ( in @ ( ordered_pair @ SY3419 @ SY3379 ) @ SV41 )
| ~ ( in @ SY3379 @ SV166 ) )
| ( in @ SY3419 @ SV192 ) )
| ~ ! [SY3421: $i] :
( ~ ( in @ SY3421 @ SV192 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3421 @ ( sK29_E @ SY3421 @ SV192 @ SV166 @ SV41 ) ) @ SV41 )
| ~ ( in @ ( sK29_E @ SY3421 @ SV192 @ SV166 @ SV41 ) @ SV166 ) ) ) ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1270,plain,
! [SV42: $i,SV167: $i] :
( ( ( ~ ( ~ ( ! [SY3381: $i] :
~ ( in @ ( ordered_pair @ SY3381 @ ( sK17_C @ SV167 @ SV42 ) ) @ SV42 )
| ~ ( in @ ( sK17_C @ SV167 @ SV42 ) @ SV167 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK18_SY3115 @ SV167 @ SV42 ) @ ( sK17_C @ SV167 @ SV42 ) ) @ SV42 )
| ( in @ ( sK17_C @ SV167 @ SV42 ) @ SV167 ) ) ) )
= $true )
| ( ( SV167
= ( relation_rng @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1189]) ).
thf(1271,plain,
! [SV42: $i,SV168: $i] :
( ( ( ( SV168
!= ( relation_rng @ SV42 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3382: $i] :
( ! [SY3191: $i] :
~ ( in @ ( ordered_pair @ SY3191 @ SY3382 ) @ SV42 )
| ( in @ SY3382 @ SV168 ) )
| ~ ! [SY3384: $i] :
( ~ ( in @ SY3384 @ SV168 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3384 @ SV168 @ SV42 ) @ SY3384 ) @ SV42 ) ) ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1190]) ).
thf(1272,plain,
! [SV92: $i] :
( ( ( relation @ SV92 )
= $false )
| ( ( function @ SV92 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK12_B @ SV92 ) @ ( relation_dom @ SV92 ) )
| ~ ( in @ ( sK13_SY3112 @ SV92 ) @ ( relation_dom @ SV92 ) ) )
| ( ( apply @ SV92 @ ( sK12_B @ SV92 ) )
!= ( apply @ SV92 @ ( sK13_SY3112 @ SV92 ) ) ) )
| ~ ( ( ( sK12_B @ SV92 )
!= ( sK13_SY3112 @ SV92 ) ) ) )
| ( one_to_one @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1191]) ).
thf(1273,plain,
! [SV93: $i] :
( ( ( relation @ SV93 )
= $false )
| ( ( function @ SV93 )
= $false )
| ( ( ~ ( one_to_one @ SV93 )
| ! [SY3323: $i,SY3324: $i] :
( ~ ( in @ SY3323 @ ( relation_dom @ SV93 ) )
| ~ ( in @ SY3324 @ ( relation_dom @ SV93 ) )
| ( ( apply @ SV93 @ SY3323 )
!= ( apply @ SV93 @ SY3324 ) )
| ( SY3323 = SY3324 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1192]) ).
thf(1274,plain,
! [SV43: $i,SV94: $i] :
( ( ( ~ ! [SY3325: $i] :
( ~ ( relation @ SY3325 )
| ~ ( ~ ( ! [SY3326: $i] :
( ~ ( in @ ( ordered_pair @ ( sK9_D @ SY3325 @ SV94 @ SV43 ) @ SY3326 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3326 @ ( sK10_SY3107 @ SY3325 @ SV94 @ SV43 ) ) @ SV94 ) )
| ~ ( in @ ( ordered_pair @ ( sK9_D @ SY3325 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SY3325 @ SV94 @ SV43 ) ) @ SY3325 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK9_D @ SY3325 @ SV94 @ SV43 ) @ ( sK11_SY3111 @ SY3325 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY3111 @ SY3325 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SY3325 @ SV94 @ SV43 ) ) @ SV94 ) )
| ( in @ ( ordered_pair @ ( sK9_D @ SY3325 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SY3325 @ SV94 @ SV43 ) ) @ SY3325 ) ) )
| ( SY3325
= ( relation_composition @ SV43 @ SV94 ) ) ) )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1193]) ).
thf(1275,plain,
! [SV94: $i,SV43: $i] :
( ( ( ~ ! [SY3327: $i] :
( ~ ( relation @ SY3327 )
| ( SY3327
!= ( relation_composition @ SV43 @ SV94 ) )
| ~ ( ~ ! [SY3328: $i,SY3329: $i] :
( ! [SY3330: $i] :
( ~ ( in @ ( ordered_pair @ SY3328 @ SY3330 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3330 @ SY3329 ) @ SV94 ) )
| ( in @ ( ordered_pair @ SY3328 @ SY3329 ) @ SY3327 ) )
| ~ ! [SY3331: $i,SY3332: $i] :
( ~ ( in @ ( ordered_pair @ SY3331 @ SY3332 ) @ SY3327 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3331 @ ( sK8_F @ SY3332 @ SY3331 @ SY3327 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK8_F @ SY3332 @ SY3331 @ SY3327 @ SV94 @ SV43 ) @ SY3332 ) @ SV94 ) ) ) ) ) )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1193]) ).
thf(1276,plain,
! [SV44: $i,SV169: $i] :
( ( ( ~ ( ~ ( ! [SY3385: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SV169 @ SV44 ) @ SY3385 ) @ SV44 )
| ~ ( in @ ( sK20_C @ SV169 @ SV44 ) @ SV169 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SV169 @ SV44 ) @ ( sK21_SY3117 @ SV169 @ SV44 ) ) @ SV44 )
| ( in @ ( sK20_C @ SV169 @ SV44 ) @ SV169 ) ) ) )
= $true )
| ( ( SV169
= ( relation_dom @ SV44 ) )
= $true )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1194]) ).
thf(1277,plain,
! [SV44: $i,SV170: $i] :
( ( ( ( SV170
!= ( relation_dom @ SV44 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3386: $i] :
( ! [SY3206: $i] :
~ ( in @ ( ordered_pair @ SY3386 @ SY3206 ) @ SV44 )
| ( in @ SY3386 @ SV170 ) )
| ~ ! [SY3388: $i] :
( ~ ( in @ SY3388 @ SV170 )
| ( in @ ( ordered_pair @ SY3388 @ ( sK19_D @ SY3388 @ SV170 @ SV44 ) ) @ SV44 ) ) ) )
= $true )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1195]) ).
thf(1278,plain,
! [SV45: $i] :
( ( ( ~ ( ~ ! [SY3208: $i] :
( ~ ( in @ SY3208 @ ( relation_dom @ SV45 ) )
| ! [SY3209: $i] :
( ( SY3209
!= ( apply @ SV45 @ SY3208 ) )
| ( in @ ( ordered_pair @ SY3208 @ SY3209 ) @ SV45 ) ) )
| ~ ! [SY3210: $i] :
( ~ ( in @ SY3210 @ ( relation_dom @ SV45 ) )
| ! [SY3211: $i] :
( ~ ( in @ ( ordered_pair @ SY3210 @ SY3211 ) @ SV45 )
| ( SY3211
= ( apply @ SV45 @ SY3210 ) ) ) ) ) )
= $true )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1196]) ).
thf(1279,plain,
! [SV45: $i] :
( ( ( ~ ( ~ ! [SY3212: $i] :
( ( in @ SY3212 @ ( relation_dom @ SV45 ) )
| ! [SY3213: $i] :
( ( SY3213
!= ( apply @ SV45 @ SY3212 ) )
| ( SY3213 = empty_set ) ) )
| ~ ! [SY3214: $i] :
( ( in @ SY3214 @ ( relation_dom @ SV45 ) )
| ! [SY3215: $i] :
( ( SY3215 != empty_set )
| ( SY3215
= ( apply @ SV45 @ SY3214 ) ) ) ) ) )
= $true )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1197]) ).
thf(1280,plain,
! [SV95: $i,SV130: $i] :
( ( ( function @ SV130 )
= $false )
| ( ( ~ ( relation @ SV130 ) )
= $true )
| ( ( ~ ( in @ SV95 @ ( relation_rng @ SV130 ) )
| ~ ( one_to_one @ SV130 )
| ( SV95
= ( apply @ SV130 @ ( apply @ ( function_inverse @ SV130 ) @ SV95 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1198]) ).
thf(1281,plain,
! [SV96: $i,SV131: $i] :
( ( ( function @ SV131 )
= $false )
| ( ( ~ ( relation @ SV131 ) )
= $true )
| ( ( ~ ( in @ SV96 @ ( relation_rng @ SV131 ) )
| ~ ( one_to_one @ SV131 )
| ( SV96
= ( apply @ ( relation_composition @ ( function_inverse @ SV131 ) @ SV131 ) @ SV96 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1199]) ).
thf(1282,plain,
! [SV97: $i] :
( ( ( relation @ SV97 )
= $false )
| ( ( function @ SV97 )
= $false )
| ( ( ~ ( one_to_one @ SV97 )
| ( ( relation_rng @ SV97 )
= ( relation_dom @ ( function_inverse @ SV97 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1200]) ).
thf(1283,plain,
! [SV98: $i] :
( ( ( relation @ SV98 )
= $false )
| ( ( function @ SV98 )
= $false )
| ( ( ~ ( one_to_one @ SV98 )
| ( ( relation_dom @ SV98 )
= ( relation_rng @ ( function_inverse @ SV98 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1201]) ).
thf(1284,plain,
! [SV132: $i,SV99: $i] :
( ( ( empty @ SV99 )
= $false )
| ( ( ~ ( relation @ SV132 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV99 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1202]) ).
thf(1285,plain,
! [SV133: $i,SV100: $i] :
( ( ( empty @ SV100 )
= $false )
| ( ( ~ ( relation @ SV133 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV100 @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1203]) ).
thf(1286,plain,
! [SV101: $i,SV134: $i] :
( ( ( function @ SV134 )
= $false )
| ( ( ~ ( relation @ SV134 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK45_C @ SV134 @ SV101 ) @ SV101 )
| ~ ( ( ( apply @ SV134 @ ( sK45_C @ SV134 @ SV101 ) )
!= ( sK45_C @ SV134 @ SV101 ) ) ) )
| ( ( relation_dom @ SV134 )
!= SV101 )
| ( SV134
= ( identity_relation @ SV101 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1204]) ).
thf(1287,plain,
! [SV171: $i,SV193: $i] :
( ( ~ ( function @ SV193 )
| ~ ( relation @ SV193 )
| ( SV193
!= ( identity_relation @ SV171 ) )
| ! [SY3422: $i] :
( ~ ( in @ SY3422 @ SV171 )
| ( ( apply @ SV193 @ SY3422 )
= SY3422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(1288,plain,
! [SV172: $i,SV194: $i] :
( ( ~ ( function @ SV194 )
| ~ ( relation @ SV194 )
| ( SV194
!= ( identity_relation @ SV172 ) )
| ( ( relation_dom @ SV194 )
= SV172 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1206]) ).
thf(1289,plain,
! [SV102: $i] :
( ( ( ! [SY3338: $i,SY3339: $i] :
( ( sK28_B @ SV102 )
!= ( ordered_pair @ SY3338 @ SY3339 ) ) )
= $true )
| ( ( relation @ SV102 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1207]) ).
thf(1290,plain,
! [SV102: $i] :
( ( ( in @ ( sK28_B @ SV102 ) @ SV102 )
= $true )
| ( ( relation @ SV102 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1208]) ).
thf(1291,plain,
! [SV103: $i,SV173: $i] :
( ( ( SV173
= ( ordered_pair @ ( sK26_C @ SV173 @ SV103 ) @ ( sK27_SY3120 @ SV173 @ SV103 ) ) )
= $true )
| ( ( ~ ( in @ SV173 @ SV103 ) )
= $true )
| ( ( relation @ SV103 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1209]) ).
thf(1292,plain,
! [SV135: $i,SV46: $i,SV152: $i] :
( ( ( relation @ SV152 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV46 @ SV135 ) @ SV152 )
| ( in @ SV46 @ ( relation_field @ SV152 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1210]) ).
thf(1293,plain,
! [SV136: $i,SV46: $i,SV153: $i] :
( ( ( relation @ SV153 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV46 @ SV136 ) @ SV153 )
| ( in @ SV136 @ ( relation_field @ SV153 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1211]) ).
thf(1294,plain,
! [SV81: $i,SV154: $i,SV47: $i,SV174: $i] :
( ( ( ~ ( relation @ SV174 ) )
= $true )
| ( ( ~ ( in @ SV47 @ SV154 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ SV174 )
| ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SV154 ) @ SV174 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1212]) ).
thf(1295,plain,
! [SV81: $i,SV47: $i] :
( ( ! [SY3308: $i,SY3309: $i] :
( ~ ( relation @ SY3309 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SY3308 ) @ SY3309 ) )
| ( in @ SV47 @ SY3308 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1213]) ).
thf(1296,plain,
! [SV81: $i,SV47: $i] :
( ( ! [SY3310: $i,SY3311: $i] :
( ~ ( relation @ SY3311 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SY3310 ) @ SY3311 ) )
| ( in @ ( ordered_pair @ SV47 @ SV81 ) @ SY3311 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1214]) ).
thf(1297,plain,
! [SV104: $i] :
( ( ( relation @ SV104 )
= $false )
| ( ( function @ SV104 )
= $false )
| ( ( function @ ( function_inverse @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1215]) ).
thf(1298,plain,
! [SV105: $i] :
( ( ( relation @ SV105 )
= $false )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ ( function_inverse @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1299,plain,
! [SV137: $i,SV48: $i,SV155: $i] :
( ( ( relation @ SV155 )
= $false )
| ( ( ~ ( in @ SV48 @ SV137 )
| ~ ( in @ SV48 @ ( relation_rng @ SV155 ) )
| ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SV137 @ SV155 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1217]) ).
thf(1300,plain,
! [SV195: $i,SV48: $i] :
( ( ! [SY3423: $i] :
( ~ ( relation @ SY3423 )
| ~ ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SV195 @ SY3423 ) ) )
| ( in @ SV48 @ SV195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1218]) ).
thf(1301,plain,
! [SV196: $i,SV48: $i] :
( ( ! [SY3424: $i] :
( ~ ( relation @ SY3424 )
| ~ ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SV196 @ SY3424 ) ) )
| ( in @ SV48 @ ( relation_rng @ SY3424 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1219]) ).
thf(1302,plain,
! [SV49: $i,SV175: $i] :
( ( ( ~ ( relation @ SV175 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV175 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV49 )
| ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV175 ) ) )
| ( SV49 = SV175 ) )
= $true )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1220]) ).
thf(1303,plain,
! [SV49: $i,SV176: $i] :
( ( ( ~ ( relation @ SV176 ) )
= $true )
| ( ( ( SV49 != SV176 )
| ~ ( ~ ! [SY3392: $i,SY3393: $i] :
( ~ ( in @ ( ordered_pair @ SY3392 @ SY3393 ) @ SV49 )
| ( in @ ( ordered_pair @ SY3392 @ SY3393 ) @ SV176 ) )
| ~ ! [SY3394: $i,SY3395: $i] :
( ~ ( in @ ( ordered_pair @ SY3394 @ SY3395 ) @ SV176 )
| ( in @ ( ordered_pair @ SY3394 @ SY3395 ) @ SV49 ) ) ) )
= $true )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1221]) ).
thf(1304,plain,
! [SV108: $i] :
( ( ( ( relation_dom @ SV108 )
= empty_set )
= $false )
| ( ( ( relation_rng @ SV108 )
= empty_set )
= $true )
| ( ( relation @ SV108 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1222]) ).
thf(1305,plain,
! [SV109: $i] :
( ( ( ( relation_rng @ SV109 )
= empty_set )
= $false )
| ( ( ( relation_dom @ SV109 )
= empty_set )
= $true )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1223]) ).
thf(1306,plain,
! [SV50: $i,SV177: $i,SV197: $i] :
( ( ( ~ ( ~ ( ! [SY3425: $i] :
( ~ ( in @ ( ordered_pair @ SY3425 @ ( sK33_D @ SV197 @ SV177 @ SV50 ) ) @ SV50 )
| ~ ( in @ SY3425 @ SV177 ) )
| ~ ( in @ ( sK33_D @ SV197 @ SV177 @ SV50 ) @ SV197 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK34_SY3126 @ SV197 @ SV177 @ SV50 ) @ ( sK33_D @ SV197 @ SV177 @ SV50 ) ) @ SV50 )
| ~ ( in @ ( sK34_SY3126 @ SV197 @ SV177 @ SV50 ) @ SV177 ) )
| ( in @ ( sK33_D @ SV197 @ SV177 @ SV50 ) @ SV197 ) ) )
| ( SV197
= ( relation_image @ SV50 @ SV177 ) ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1307,plain,
! [SV178: $i,SV50: $i,SV198: $i] :
( ( ( ( SV198
!= ( relation_image @ SV50 @ SV178 ) )
| ~ ( ~ ! [SY3426: $i] :
( ! [SY3400: $i] :
( ~ ( in @ ( ordered_pair @ SY3400 @ SY3426 ) @ SV50 )
| ~ ( in @ SY3400 @ SV178 ) )
| ( in @ SY3426 @ SV198 ) )
| ~ ! [SY3428: $i] :
( ~ ( in @ SY3428 @ SV198 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK32_E @ SY3428 @ SV198 @ SV178 @ SV50 ) @ SY3428 ) @ SV50 )
| ~ ( in @ ( sK32_E @ SY3428 @ SV198 @ SV178 @ SV50 ) @ SV178 ) ) ) ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1308,plain,
! [SV138: $i,SV110: $i] :
( ( ( ~ ( function @ SV110 )
| ~ ( relation @ SV110 ) )
= $true )
| ( ( ~ ( relation @ SV138 ) )
= $true )
| ( ( ~ ( function @ SV138 ) )
= $true )
| ( ( function @ ( relation_composition @ SV110 @ SV138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1226]) ).
thf(1309,plain,
! [SV139: $i,SV111: $i] :
( ( ( ~ ( function @ SV111 )
| ~ ( relation @ SV111 ) )
= $true )
| ( ( ~ ( relation @ SV139 ) )
= $true )
| ( ( ~ ( function @ SV139 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV111 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1227]) ).
thf(1310,plain,
! [SV179: $i] :
( ( ( ~ ( empty @ SV179 )
| ~ ( relation @ SV179 )
| ~ ( function @ SV179 ) )
= $true )
| ( ( function @ SV179 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1228]) ).
thf(1311,plain,
! [SV180: $i] :
( ( ( ~ ( empty @ SV180 )
| ~ ( relation @ SV180 )
| ~ ( function @ SV180 ) )
= $true )
| ( ( relation @ SV180 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1229]) ).
thf(1312,plain,
! [SV112: $i] :
( ( ( empty @ SV112 )
= $false )
| ( ( ~ ( relation @ SV112 ) )
= $true )
| ( ( ~ ( function @ SV112 ) )
= $true )
| ( ( one_to_one @ SV112 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1230]) ).
thf(1313,plain,
! [SV140: $i,SV51: $i,SV156: $i] :
( ( ( relation @ SV156 )
= $false )
| ( ( ! [SY3373: $i] :
( ~ ( in @ SY3373 @ ( relation_dom @ SV156 ) )
| ~ ( in @ ( ordered_pair @ SY3373 @ SV51 ) @ SV156 )
| ~ ( in @ SY3373 @ SV140 ) )
| ( in @ SV51 @ ( relation_image @ SV156 @ SV140 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1231]) ).
thf(1314,plain,
! [SV141: $i,SV51: $i,SV157: $i] :
( ( ( relation @ SV157 )
= $false )
| ( ( ~ ( in @ SV51 @ ( relation_image @ SV157 @ SV141 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK47_D @ SV157 @ SV141 @ SV51 ) @ ( relation_dom @ SV157 ) )
| ~ ( in @ ( ordered_pair @ ( sK47_D @ SV157 @ SV141 @ SV51 ) @ SV51 ) @ SV157 ) )
| ~ ( in @ ( sK47_D @ SV157 @ SV141 @ SV51 ) @ SV141 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1232]) ).
thf(1315,plain,
! [SV52: $i,SV181: $i] :
( ( ( ~ ( relation @ SV181 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_C @ SV181 @ SV52 ) @ ( sK15_SY3113 @ SV181 @ SV52 ) ) @ SV181 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY3113 @ SV181 @ SV52 ) @ ( sK14_C @ SV181 @ SV52 ) ) @ SV52 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SV181 @ SV52 ) @ ( sK15_SY3113 @ SV181 @ SV52 ) ) @ SV181 )
| ( in @ ( ordered_pair @ ( sK15_SY3113 @ SV181 @ SV52 ) @ ( sK14_C @ SV181 @ SV52 ) ) @ SV52 ) ) )
| ( SV181
= ( relation_inverse @ SV52 ) ) )
= $true )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1233]) ).
thf(1316,plain,
! [SV52: $i,SV182: $i] :
( ( ( ~ ( relation @ SV182 ) )
= $true )
| ( ( ( SV182
!= ( relation_inverse @ SV52 ) )
| ~ ( ~ ! [SY3402: $i,SY3403: $i] :
( ~ ( in @ ( ordered_pair @ SY3402 @ SY3403 ) @ SV182 )
| ( in @ ( ordered_pair @ SY3403 @ SY3402 ) @ SV52 ) )
| ~ ! [SY3404: $i,SY3405: $i] :
( ~ ( in @ ( ordered_pair @ SY3405 @ SY3404 ) @ SV52 )
| ( in @ ( ordered_pair @ SY3404 @ SY3405 ) @ SV182 ) ) ) )
= $true )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1234]) ).
thf(1317,plain,
! [SV115: $i] :
( ( ( function @ SV115 )
= $false )
| ( ( ~ ( relation @ SV115 ) )
= $true )
| ( ( ~ ( one_to_one @ SV115 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1235]) ).
thf(1318,plain,
! [SV116: $i] :
( ( ( function @ SV116 )
= $false )
| ( ( ~ ( relation @ SV116 ) )
= $true )
| ( ( ~ ( one_to_one @ SV116 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1236]) ).
thf(1319,plain,
! [SV117: $i] :
( ( ( ( relation_dom @ SV117 )
= empty_set )
= $false )
| ( ( SV117 = empty_set )
= $true )
| ( ( relation @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1237]) ).
thf(1320,plain,
! [SV118: $i] :
( ( ( ( relation_rng @ SV118 )
= empty_set )
= $false )
| ( ( SV118 = empty_set )
= $true )
| ( ( relation @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1238]) ).
thf(1321,plain,
! [SV123: $i,SV142: $i] :
( ( ( ~ ( ~ ( ( ( sK39_C @ SV142 @ SV123 )
!= ( sK40_SY3129 @ SV142 @ SV123 ) )
| ~ ( in @ ( sK39_C @ SV142 @ SV123 ) @ SV123 )
| ~ ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 ) )
| ~ ~ ( ~ ( ( ( sK39_C @ SV142 @ SV123 )
= ( sK40_SY3129 @ SV142 @ SV123 ) )
| ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 ) )
| ~ ( ( in @ ( sK39_C @ SV142 @ SV123 ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 ) ) ) ) )
= $true )
| ( ( SV142
= ( identity_relation @ SV123 ) )
= $true )
| ( ( relation @ SV142 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1239]) ).
thf(1322,plain,
! [SV124: $i,SV143: $i] :
( ( ( ( SV143
!= ( identity_relation @ SV124 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3360: $i,SY3361: $i] :
( ( SY3360 != SY3361 )
| ~ ( in @ SY3360 @ SV124 )
| ( in @ ( ordered_pair @ SY3360 @ SY3361 ) @ SV143 ) )
| ~ ~ ( ~ ! [SY3362: $i,SY3363: $i] :
( ~ ( in @ ( ordered_pair @ SY3362 @ SY3363 ) @ SV143 )
| ( SY3362 = SY3363 ) )
| ~ ! [SY3364: $i] :
( ! [SY3365: $i] :
~ ( in @ ( ordered_pair @ SY3364 @ SY3365 ) @ SV143 )
| ( in @ SY3364 @ SV124 ) ) ) ) )
= $true )
| ( ( relation @ SV143 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1240]) ).
thf(1323,plain,
! [SV144: $i,SV125: $i] :
( ( ( empty @ SV125 )
= $false )
| ( ( ~ ( relation @ SV144 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV144 @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1241]) ).
thf(1324,plain,
! [SV145: $i,SV126: $i] :
( ( ( empty @ SV126 )
= $false )
| ( ( ~ ( relation @ SV145 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV145 @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1242]) ).
thf(1325,plain,
! [SV53: $i,SV82: $i,SV199: $i] :
( ( ( ~ ( relation @ SV199 )
| ~ ( ~ ( ~ ( in @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) @ SV53 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV82 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 ) )
| ~ ~ ( ~ ( ( in @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) @ SV53 )
| ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV82 )
| ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 ) ) ) )
| ( SV199
= ( relation_rng_restriction @ SV53 @ SV82 ) ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1243]) ).
thf(1326,plain,
! [SV82: $i,SV53: $i,SV200: $i] :
( ( ( ~ ( relation @ SV200 )
| ( SV200
!= ( relation_rng_restriction @ SV53 @ SV82 ) )
| ~ ( ~ ! [SY3429: $i,SY3430: $i] :
( ~ ( in @ SY3430 @ SV53 )
| ~ ( in @ ( ordered_pair @ SY3429 @ SY3430 ) @ SV82 )
| ( in @ ( ordered_pair @ SY3429 @ SY3430 ) @ SV200 ) )
| ~ ~ ( ~ ! [SY3431: $i,SY3432: $i] :
( ~ ( in @ ( ordered_pair @ SY3431 @ SY3432 ) @ SV200 )
| ( in @ SY3432 @ SV53 ) )
| ~ ! [SY3433: $i,SY3434: $i] :
( ~ ( in @ ( ordered_pair @ SY3433 @ SY3434 ) @ SV200 )
| ( in @ ( ordered_pair @ SY3433 @ SY3434 ) @ SV82 ) ) ) ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1244]) ).
thf(1327,plain,
! [SV54: $i,SV183: $i] :
( ( ( ~ ( relation @ SV183 ) )
= $true )
| ( ( ~ ( subset @ SV54 @ SV183 )
| ( subset @ ( relation_dom @ SV54 ) @ ( relation_dom @ SV183 ) ) )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1245]) ).
thf(1328,plain,
! [SV54: $i,SV184: $i] :
( ( ( ~ ( relation @ SV184 ) )
= $true )
| ( ( ~ ( subset @ SV54 @ SV184 )
| ( subset @ ( relation_rng @ SV54 ) @ ( relation_rng @ SV184 ) ) )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1246]) ).
thf(1329,plain,
! [SV83: $i,SV55: $i] :
( ( ( ~ ! [SY3320: $i] :
( ~ ( function @ SY3320 )
| ~ ( relation @ SY3320 )
| ~ ( in @ SV55 @ ( relation_dom @ SY3320 ) )
| ~ ( in @ ( apply @ SY3320 @ SV55 ) @ ( relation_dom @ SV83 ) )
| ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3320 @ SV83 ) ) ) ) )
= $false )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1247]) ).
thf(1330,plain,
! [SV83: $i,SV55: $i] :
( ( ( ~ ~ ( ~ ! [SY3321: $i] :
( ~ ( function @ SY3321 )
| ~ ( relation @ SY3321 )
| ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3321 @ SV83 ) ) )
| ( in @ SV55 @ ( relation_dom @ SY3321 ) ) )
| ~ ! [SY3322: $i] :
( ~ ( function @ SY3322 )
| ~ ( relation @ SY3322 )
| ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3322 @ SV83 ) ) )
| ( in @ ( apply @ SY3322 @ SV55 ) @ ( relation_dom @ SV83 ) ) ) ) )
= $false )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1247]) ).
thf(1331,plain,
! [SV146: $i,SV56: $i,SV158: $i] :
( ( ( relation @ SV158 )
= $false )
| ( ( ~ ( in @ SV56 @ SV146 )
| ~ ( in @ SV56 @ ( relation_dom @ SV158 ) )
| ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SV158 @ SV146 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1248]) ).
thf(1332,plain,
! [SV201: $i,SV56: $i] :
( ( ! [SY3435: $i] :
( ~ ( relation @ SY3435 )
| ~ ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SY3435 @ SV201 ) ) )
| ( in @ SV56 @ SV201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1249]) ).
thf(1333,plain,
! [SV202: $i,SV56: $i] :
( ( ! [SY3436: $i] :
( ~ ( relation @ SY3436 )
| ~ ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SY3436 @ SV202 ) ) )
| ( in @ SV56 @ ( relation_dom @ SY3436 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1334,plain,
! [SV147: $i,SV57: $i,SV159: $i] :
( ( ( relation @ SV159 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV57 @ SV147 ) @ SV159 )
| ( in @ SV57 @ ( relation_dom @ SV159 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1251]) ).
thf(1335,plain,
! [SV148: $i,SV57: $i,SV160: $i] :
( ( ( relation @ SV160 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV57 @ SV148 ) @ SV160 )
| ( in @ SV148 @ ( relation_rng @ SV160 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1252]) ).
thf(1336,plain,
! [SV149: $i,SV58: $i,SV161: $i] :
( ( ( relation @ SV161 )
= $false )
| ( ( ! [SY3374: $i] :
( ~ ( in @ SY3374 @ ( relation_rng @ SV161 ) )
| ~ ( in @ ( ordered_pair @ SV58 @ SY3374 ) @ SV161 )
| ~ ( in @ SY3374 @ SV149 ) )
| ( in @ SV58 @ ( relation_inverse_image @ SV161 @ SV149 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1253]) ).
thf(1337,plain,
! [SV150: $i,SV58: $i,SV162: $i] :
( ( ( relation @ SV162 )
= $false )
| ( ( ~ ( in @ SV58 @ ( relation_inverse_image @ SV162 @ SV150 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK46_D @ SV162 @ SV150 @ SV58 ) @ ( relation_rng @ SV162 ) )
| ~ ( in @ ( ordered_pair @ SV58 @ ( sK46_D @ SV162 @ SV150 @ SV58 ) ) @ SV162 ) )
| ~ ( in @ ( sK46_D @ SV162 @ SV150 @ SV58 ) @ SV150 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1254]) ).
thf(1338,plain,
! [SV59: $i,SV185: $i] :
( ( ( ~ ( relation @ SV185 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SV185 @ SV59 ) @ ( sK23_SY3118 @ SV185 @ SV59 ) ) @ SV59 )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_C @ SV185 @ SV59 ) @ ( sK23_SY3118 @ SV185 @ SV59 ) ) @ SV185 ) )
| ( subset @ SV59 @ SV185 ) )
= $true )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1255]) ).
thf(1339,plain,
! [SV59: $i,SV186: $i] :
( ( ( ~ ( relation @ SV186 ) )
= $true )
| ( ( ~ ( subset @ SV59 @ SV186 )
| ! [SY3406: $i,SY3407: $i] :
( ~ ( in @ ( ordered_pair @ SY3406 @ SY3407 ) @ SV59 )
| ( in @ ( ordered_pair @ SY3406 @ SY3407 ) @ SV186 ) ) )
= $true )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1256]) ).
thf(1340,plain,
! [SV60: $i,SV187: $i,SV203: $i] :
( ( ( ~ ( relation @ SV203 )
| ~ ( ~ ( ~ ( in @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ SV187 )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV60 )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 ) )
| ~ ~ ( ~ ( ( in @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ SV187 )
| ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV60 )
| ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 ) ) ) )
| ( SV203
= ( relation_dom_restriction @ SV60 @ SV187 ) ) )
= $true )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1257]) ).
thf(1341,plain,
! [SV188: $i,SV60: $i,SV204: $i] :
( ( ( ~ ( relation @ SV204 )
| ( SV204
!= ( relation_dom_restriction @ SV60 @ SV188 ) )
| ~ ( ~ ! [SY3437: $i,SY3438: $i] :
( ~ ( in @ SY3437 @ SV188 )
| ~ ( in @ ( ordered_pair @ SY3437 @ SY3438 ) @ SV60 )
| ( in @ ( ordered_pair @ SY3437 @ SY3438 ) @ SV204 ) )
| ~ ~ ( ~ ! [SY3439: $i] :
( ! [SY3440: $i] :
~ ( in @ ( ordered_pair @ SY3439 @ SY3440 ) @ SV204 )
| ( in @ SY3439 @ SV188 ) )
| ~ ! [SY3441: $i,SY3442: $i] :
( ~ ( in @ ( ordered_pair @ SY3441 @ SY3442 ) @ SV204 )
| ( in @ ( ordered_pair @ SY3441 @ SY3442 ) @ SV60 ) ) ) ) )
= $true )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1258]) ).
thf(1342,plain,
! [SV71: $i,SV14: $i,SV163: $i] :
( ( ( ~ ( function @ SV163 ) )
= $true )
| ( ( ~ ( relation @ SV163 ) )
= $true )
| ( ( ~ ( in @ SV14 @ ( relation_dom @ ( relation_composition @ SV163 @ SV71 ) ) )
| ( ( apply @ ( relation_composition @ SV163 @ SV71 ) @ SV14 )
= ( apply @ SV71 @ ( apply @ SV163 @ SV14 ) ) ) )
= $true )
| ( ( function @ SV71 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1260]) ).
thf(1343,plain,
! [SV72: $i,SV15: $i,SV164: $i] :
( ( ( ~ ( function @ SV164 ) )
= $true )
| ( ( ~ ( relation @ SV164 ) )
= $true )
| ( ( ~ ( in @ SV15 @ ( relation_dom @ SV72 ) )
| ( ( apply @ ( relation_composition @ SV72 @ SV164 ) @ SV15 )
= ( apply @ SV164 @ ( apply @ SV72 @ SV15 ) ) ) )
= $true )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1261]) ).
thf(1344,plain,
! [SV39: $i,SV129: $i,SV151: $i] :
( ( ( function @ SV151 )
= $false )
| ( ( ~ ( relation @ SV151 ) )
= $true )
| ( ( ( SV129
!= ( apply @ SV151 @ SV39 ) )
| ~ ( in @ SV39 @ ( relation_dom @ SV151 ) )
| ( in @ ( ordered_pair @ SV39 @ SV129 ) @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1264]) ).
thf(1345,plain,
! [SV189: $i,SV39: $i,SV205: $i] :
( ( ~ ( function @ SV205 )
| ~ ( relation @ SV205 )
| ~ ( in @ ( ordered_pair @ SV39 @ SV189 ) @ SV205 )
| ( SV189
= ( apply @ SV205 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1346,plain,
! [SV190: $i,SV39: $i,SV206: $i] :
( ( ~ ( function @ SV206 )
| ~ ( relation @ SV206 )
| ~ ( in @ ( ordered_pair @ SV39 @ SV190 ) @ SV206 )
| ( in @ SV39 @ ( relation_dom @ SV206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1347,plain,
! [SV40: $i] :
( ( ( ~ ! [SY3168: $i] :
( ~ ( function @ SY3168 )
| ~ ( relation @ SY3168 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK44_SY3131 @ SY3168 @ SV40 )
= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ( ( sK43_C @ SY3168 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SY3168 @ SV40 )
= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SY3168 @ SV40 )
= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ( ( sK44_SY3131 @ SY3168 @ SV40 )
!= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK43_C @ SY3168 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK44_SY3131 @ SY3168 @ SV40 )
!= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK43_C @ SY3168 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK43_C @ SY3168 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SY3168 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SY3168 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK44_SY3131 @ SY3168 @ SV40 )
!= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ( ( relation_dom @ SY3168 )
!= ( relation_rng @ SV40 ) )
| ( SY3168
= ( function_inverse @ SV40 ) ) ) )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1267]) ).
thf(1348,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ! [SY3169: $i] :
( ~ ( function @ SY3169 )
| ~ ( relation @ SY3169 )
| ( SY3169
!= ( function_inverse @ SV40 ) )
| ~ ( ~ ~ ( ~ ! [SY3170: $i,SY3171: $i] :
( ( SY3171
!= ( apply @ SY3169 @ SY3170 ) )
| ~ ( in @ SY3170 @ ( relation_rng @ SV40 ) )
| ( SY3170
= ( apply @ SV40 @ SY3171 ) ) )
| ~ ! [SY3172: $i,SY3173: $i] :
( ( SY3173
!= ( apply @ SY3169 @ SY3172 ) )
| ~ ( in @ SY3172 @ ( relation_rng @ SV40 ) )
| ( in @ SY3173 @ ( relation_dom @ SV40 ) ) ) )
| ~ ~ ( ~ ! [SY3174: $i,SY3175: $i] :
( ( SY3174
!= ( apply @ SV40 @ SY3175 ) )
| ~ ( in @ SY3175 @ ( relation_dom @ SV40 ) )
| ( SY3175
= ( apply @ SY3169 @ SY3174 ) ) )
| ~ ! [SY3176: $i] :
( ! [SY3177: $i] :
( ( SY3176
!= ( apply @ SV40 @ SY3177 ) )
| ~ ( in @ SY3177 @ ( relation_dom @ SV40 ) ) )
| ( in @ SY3176 @ ( relation_rng @ SV40 ) ) ) ) ) )
| ~ ! [SY3178: $i] :
( ~ ( function @ SY3178 )
| ~ ( relation @ SY3178 )
| ( SY3178
!= ( function_inverse @ SV40 ) )
| ( ( relation_dom @ SY3178 )
= ( relation_rng @ SV40 ) ) ) ) )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1267]) ).
thf(1349,plain,
! [SV41: $i,SV165: $i,SV191: $i] :
( ( ( ~ ( ~ ( ! [SY3418: $i] :
( ~ ( in @ ( ordered_pair @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SY3418 ) @ SV41 )
| ~ ( in @ SY3418 @ SV165 ) )
| ~ ( in @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SV191 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ ( sK31_SY3124 @ SV191 @ SV165 @ SV41 ) ) @ SV41 )
| ~ ( in @ ( sK31_SY3124 @ SV191 @ SV165 @ SV41 ) @ SV165 ) )
| ( in @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SV191 ) ) ) )
= $true )
| ( ( SV191
= ( relation_inverse_image @ SV41 @ SV165 ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1268]) ).
thf(1350,plain,
! [SV166: $i,SV41: $i,SV192: $i] :
( ( ( ( SV192
!= ( relation_inverse_image @ SV41 @ SV166 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3419: $i] :
( ! [SY3379: $i] :
( ~ ( in @ ( ordered_pair @ SY3419 @ SY3379 ) @ SV41 )
| ~ ( in @ SY3379 @ SV166 ) )
| ( in @ SY3419 @ SV192 ) )
| ~ ! [SY3421: $i] :
( ~ ( in @ SY3421 @ SV192 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3421 @ ( sK29_E @ SY3421 @ SV192 @ SV166 @ SV41 ) ) @ SV41 )
| ~ ( in @ ( sK29_E @ SY3421 @ SV192 @ SV166 @ SV41 ) @ SV166 ) ) ) ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1269]) ).
thf(1351,plain,
! [SV42: $i,SV167: $i] :
( ( ( ~ ( ! [SY3381: $i] :
~ ( in @ ( ordered_pair @ SY3381 @ ( sK17_C @ SV167 @ SV42 ) ) @ SV42 )
| ~ ( in @ ( sK17_C @ SV167 @ SV42 ) @ SV167 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK18_SY3115 @ SV167 @ SV42 ) @ ( sK17_C @ SV167 @ SV42 ) ) @ SV42 )
| ( in @ ( sK17_C @ SV167 @ SV42 ) @ SV167 ) ) )
= $false )
| ( ( SV167
= ( relation_rng @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1270]) ).
thf(1352,plain,
! [SV42: $i,SV168: $i] :
( ( ( SV168
= ( relation_rng @ SV42 ) )
= $false )
| ( ( ~ ( ~ ! [SY3382: $i] :
( ! [SY3191: $i] :
~ ( in @ ( ordered_pair @ SY3191 @ SY3382 ) @ SV42 )
| ( in @ SY3382 @ SV168 ) )
| ~ ! [SY3384: $i] :
( ~ ( in @ SY3384 @ SV168 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3384 @ SV168 @ SV42 ) @ SY3384 ) @ SV42 ) ) ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1271]) ).
thf(1353,plain,
! [SV92: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK12_B @ SV92 ) @ ( relation_dom @ SV92 ) )
| ~ ( in @ ( sK13_SY3112 @ SV92 ) @ ( relation_dom @ SV92 ) ) )
| ( ( apply @ SV92 @ ( sK12_B @ SV92 ) )
!= ( apply @ SV92 @ ( sK13_SY3112 @ SV92 ) ) ) )
| ~ ( ( ( sK12_B @ SV92 )
!= ( sK13_SY3112 @ SV92 ) ) ) ) )
= $true )
| ( ( one_to_one @ SV92 )
= $true )
| ( ( function @ SV92 )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1272]) ).
thf(1354,plain,
! [SV93: $i] :
( ( ( ~ ( one_to_one @ SV93 ) )
= $true )
| ( ( ! [SY3323: $i,SY3324: $i] :
( ~ ( in @ SY3323 @ ( relation_dom @ SV93 ) )
| ~ ( in @ SY3324 @ ( relation_dom @ SV93 ) )
| ( ( apply @ SV93 @ SY3323 )
!= ( apply @ SV93 @ SY3324 ) )
| ( SY3323 = SY3324 ) ) )
= $true )
| ( ( function @ SV93 )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1273]) ).
thf(1355,plain,
! [SV43: $i,SV94: $i] :
( ( ( ! [SY3325: $i] :
( ~ ( relation @ SY3325 )
| ~ ( ~ ( ! [SY3326: $i] :
( ~ ( in @ ( ordered_pair @ ( sK9_D @ SY3325 @ SV94 @ SV43 ) @ SY3326 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3326 @ ( sK10_SY3107 @ SY3325 @ SV94 @ SV43 ) ) @ SV94 ) )
| ~ ( in @ ( ordered_pair @ ( sK9_D @ SY3325 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SY3325 @ SV94 @ SV43 ) ) @ SY3325 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK9_D @ SY3325 @ SV94 @ SV43 ) @ ( sK11_SY3111 @ SY3325 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY3111 @ SY3325 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SY3325 @ SV94 @ SV43 ) ) @ SV94 ) )
| ( in @ ( ordered_pair @ ( sK9_D @ SY3325 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SY3325 @ SV94 @ SV43 ) ) @ SY3325 ) ) )
| ( SY3325
= ( relation_composition @ SV43 @ SV94 ) ) ) )
= $true )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1274]) ).
thf(1356,plain,
! [SV94: $i,SV43: $i] :
( ( ( ! [SY3327: $i] :
( ~ ( relation @ SY3327 )
| ( SY3327
!= ( relation_composition @ SV43 @ SV94 ) )
| ~ ( ~ ! [SY3328: $i,SY3329: $i] :
( ! [SY3330: $i] :
( ~ ( in @ ( ordered_pair @ SY3328 @ SY3330 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3330 @ SY3329 ) @ SV94 ) )
| ( in @ ( ordered_pair @ SY3328 @ SY3329 ) @ SY3327 ) )
| ~ ! [SY3331: $i,SY3332: $i] :
( ~ ( in @ ( ordered_pair @ SY3331 @ SY3332 ) @ SY3327 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3331 @ ( sK8_F @ SY3332 @ SY3331 @ SY3327 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK8_F @ SY3332 @ SY3331 @ SY3327 @ SV94 @ SV43 ) @ SY3332 ) @ SV94 ) ) ) ) ) )
= $true )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1275]) ).
thf(1357,plain,
! [SV44: $i,SV169: $i] :
( ( ( ~ ( ! [SY3385: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SV169 @ SV44 ) @ SY3385 ) @ SV44 )
| ~ ( in @ ( sK20_C @ SV169 @ SV44 ) @ SV169 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SV169 @ SV44 ) @ ( sK21_SY3117 @ SV169 @ SV44 ) ) @ SV44 )
| ( in @ ( sK20_C @ SV169 @ SV44 ) @ SV169 ) ) )
= $false )
| ( ( SV169
= ( relation_dom @ SV44 ) )
= $true )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1276]) ).
thf(1358,plain,
! [SV44: $i,SV170: $i] :
( ( ( SV170
= ( relation_dom @ SV44 ) )
= $false )
| ( ( ~ ( ~ ! [SY3386: $i] :
( ! [SY3206: $i] :
~ ( in @ ( ordered_pair @ SY3386 @ SY3206 ) @ SV44 )
| ( in @ SY3386 @ SV170 ) )
| ~ ! [SY3388: $i] :
( ~ ( in @ SY3388 @ SV170 )
| ( in @ ( ordered_pair @ SY3388 @ ( sK19_D @ SY3388 @ SV170 @ SV44 ) ) @ SV44 ) ) ) )
= $true )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1277]) ).
thf(1359,plain,
! [SV45: $i] :
( ( ( ~ ! [SY3208: $i] :
( ~ ( in @ SY3208 @ ( relation_dom @ SV45 ) )
| ! [SY3209: $i] :
( ( SY3209
!= ( apply @ SV45 @ SY3208 ) )
| ( in @ ( ordered_pair @ SY3208 @ SY3209 ) @ SV45 ) ) )
| ~ ! [SY3210: $i] :
( ~ ( in @ SY3210 @ ( relation_dom @ SV45 ) )
| ! [SY3211: $i] :
( ~ ( in @ ( ordered_pair @ SY3210 @ SY3211 ) @ SV45 )
| ( SY3211
= ( apply @ SV45 @ SY3210 ) ) ) ) )
= $false )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1278]) ).
thf(1360,plain,
! [SV45: $i] :
( ( ( ~ ! [SY3212: $i] :
( ( in @ SY3212 @ ( relation_dom @ SV45 ) )
| ! [SY3213: $i] :
( ( SY3213
!= ( apply @ SV45 @ SY3212 ) )
| ( SY3213 = empty_set ) ) )
| ~ ! [SY3214: $i] :
( ( in @ SY3214 @ ( relation_dom @ SV45 ) )
| ! [SY3215: $i] :
( ( SY3215 != empty_set )
| ( SY3215
= ( apply @ SV45 @ SY3214 ) ) ) ) )
= $false )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1279]) ).
thf(1361,plain,
! [SV95: $i,SV130: $i] :
( ( ( relation @ SV130 )
= $false )
| ( ( function @ SV130 )
= $false )
| ( ( ~ ( in @ SV95 @ ( relation_rng @ SV130 ) )
| ~ ( one_to_one @ SV130 )
| ( SV95
= ( apply @ SV130 @ ( apply @ ( function_inverse @ SV130 ) @ SV95 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1280]) ).
thf(1362,plain,
! [SV96: $i,SV131: $i] :
( ( ( relation @ SV131 )
= $false )
| ( ( function @ SV131 )
= $false )
| ( ( ~ ( in @ SV96 @ ( relation_rng @ SV131 ) )
| ~ ( one_to_one @ SV131 )
| ( SV96
= ( apply @ ( relation_composition @ ( function_inverse @ SV131 ) @ SV131 ) @ SV96 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1281]) ).
thf(1363,plain,
! [SV97: $i] :
( ( ( ~ ( one_to_one @ SV97 ) )
= $true )
| ( ( ( relation_rng @ SV97 )
= ( relation_dom @ ( function_inverse @ SV97 ) ) )
= $true )
| ( ( function @ SV97 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1282]) ).
thf(1364,plain,
! [SV98: $i] :
( ( ( ~ ( one_to_one @ SV98 ) )
= $true )
| ( ( ( relation_dom @ SV98 )
= ( relation_rng @ ( function_inverse @ SV98 ) ) )
= $true )
| ( ( function @ SV98 )
= $false )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1283]) ).
thf(1365,plain,
! [SV99: $i,SV132: $i] :
( ( ( relation @ SV132 )
= $false )
| ( ( empty @ SV99 )
= $false )
| ( ( empty @ ( relation_composition @ SV99 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1284]) ).
thf(1366,plain,
! [SV100: $i,SV133: $i] :
( ( ( relation @ SV133 )
= $false )
| ( ( empty @ SV100 )
= $false )
| ( ( relation @ ( relation_composition @ SV100 @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1285]) ).
thf(1367,plain,
! [SV101: $i,SV134: $i] :
( ( ( relation @ SV134 )
= $false )
| ( ( function @ SV134 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK45_C @ SV134 @ SV101 ) @ SV101 )
| ~ ( ( ( apply @ SV134 @ ( sK45_C @ SV134 @ SV101 ) )
!= ( sK45_C @ SV134 @ SV101 ) ) ) )
| ( ( relation_dom @ SV134 )
!= SV101 )
| ( SV134
= ( identity_relation @ SV101 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1286]) ).
thf(1368,plain,
! [SV171: $i,SV193: $i] :
( ( ( ~ ( function @ SV193 )
| ~ ( relation @ SV193 ) )
= $true )
| ( ( ( SV193
!= ( identity_relation @ SV171 ) )
| ! [SY3422: $i] :
( ~ ( in @ SY3422 @ SV171 )
| ( ( apply @ SV193 @ SY3422 )
= SY3422 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1287]) ).
thf(1369,plain,
! [SV172: $i,SV194: $i] :
( ( ( ~ ( function @ SV194 )
| ~ ( relation @ SV194 ) )
= $true )
| ( ( ( SV194
!= ( identity_relation @ SV172 ) )
| ( ( relation_dom @ SV194 )
= SV172 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1288]) ).
thf(1370,plain,
! [SV207: $i,SV102: $i] :
( ( ( ! [SY3443: $i] :
( ( sK28_B @ SV102 )
!= ( ordered_pair @ SV207 @ SY3443 ) ) )
= $true )
| ( ( relation @ SV102 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1371,plain,
! [SV103: $i,SV173: $i] :
( ( ( in @ SV173 @ SV103 )
= $false )
| ( ( SV173
= ( ordered_pair @ ( sK26_C @ SV173 @ SV103 ) @ ( sK27_SY3120 @ SV173 @ SV103 ) ) )
= $true )
| ( ( relation @ SV103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1291]) ).
thf(1372,plain,
! [SV152: $i,SV135: $i,SV46: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV46 @ SV135 ) @ SV152 ) )
= $true )
| ( ( in @ SV46 @ ( relation_field @ SV152 ) )
= $true )
| ( ( relation @ SV152 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1292]) ).
thf(1373,plain,
! [SV153: $i,SV136: $i,SV46: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV46 @ SV136 ) @ SV153 ) )
= $true )
| ( ( in @ SV136 @ ( relation_field @ SV153 ) )
= $true )
| ( ( relation @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1293]) ).
thf(1374,plain,
! [SV81: $i,SV154: $i,SV47: $i,SV174: $i] :
( ( ( relation @ SV174 )
= $false )
| ( ( ~ ( in @ SV47 @ SV154 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ SV174 )
| ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SV154 ) @ SV174 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1294]) ).
thf(1375,plain,
! [SV208: $i,SV81: $i,SV47: $i] :
( ( ! [SY3444: $i] :
( ~ ( relation @ SY3444 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SV208 ) @ SY3444 ) )
| ( in @ SV47 @ SV208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1295]) ).
thf(1376,plain,
! [SV209: $i,SV81: $i,SV47: $i] :
( ( ! [SY3445: $i] :
( ~ ( relation @ SY3445 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SV209 ) @ SY3445 ) )
| ( in @ ( ordered_pair @ SV47 @ SV81 ) @ SY3445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1296]) ).
thf(1377,plain,
! [SV155: $i,SV137: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ SV137 )
| ~ ( in @ SV48 @ ( relation_rng @ SV155 ) ) )
= $true )
| ( ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SV137 @ SV155 ) ) )
= $true )
| ( ( relation @ SV155 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1299]) ).
thf(1378,plain,
! [SV195: $i,SV48: $i,SV210: $i] :
( ( ~ ( relation @ SV210 )
| ~ ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SV195 @ SV210 ) ) )
| ( in @ SV48 @ SV195 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1379,plain,
! [SV196: $i,SV48: $i,SV211: $i] :
( ( ~ ( relation @ SV211 )
| ~ ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SV196 @ SV211 ) ) )
| ( in @ SV48 @ ( relation_rng @ SV211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1380,plain,
! [SV49: $i,SV175: $i] :
( ( ( relation @ SV175 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV175 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV49 )
| ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV175 ) ) )
| ( SV49 = SV175 ) )
= $true )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1302]) ).
thf(1381,plain,
! [SV49: $i,SV176: $i] :
( ( ( relation @ SV176 )
= $false )
| ( ( ( SV49 != SV176 )
| ~ ( ~ ! [SY3392: $i,SY3393: $i] :
( ~ ( in @ ( ordered_pair @ SY3392 @ SY3393 ) @ SV49 )
| ( in @ ( ordered_pair @ SY3392 @ SY3393 ) @ SV176 ) )
| ~ ! [SY3394: $i,SY3395: $i] :
( ~ ( in @ ( ordered_pair @ SY3394 @ SY3395 ) @ SV176 )
| ( in @ ( ordered_pair @ SY3394 @ SY3395 ) @ SV49 ) ) ) )
= $true )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1303]) ).
thf(1382,plain,
! [SV50: $i,SV177: $i,SV197: $i] :
( ( ( ~ ( ~ ( ! [SY3425: $i] :
( ~ ( in @ ( ordered_pair @ SY3425 @ ( sK33_D @ SV197 @ SV177 @ SV50 ) ) @ SV50 )
| ~ ( in @ SY3425 @ SV177 ) )
| ~ ( in @ ( sK33_D @ SV197 @ SV177 @ SV50 ) @ SV197 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK34_SY3126 @ SV197 @ SV177 @ SV50 ) @ ( sK33_D @ SV197 @ SV177 @ SV50 ) ) @ SV50 )
| ~ ( in @ ( sK34_SY3126 @ SV197 @ SV177 @ SV50 ) @ SV177 ) )
| ( in @ ( sK33_D @ SV197 @ SV177 @ SV50 ) @ SV197 ) ) ) )
= $true )
| ( ( SV197
= ( relation_image @ SV50 @ SV177 ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1306]) ).
thf(1383,plain,
! [SV178: $i,SV50: $i,SV198: $i] :
( ( ( ( SV198
!= ( relation_image @ SV50 @ SV178 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3426: $i] :
( ! [SY3400: $i] :
( ~ ( in @ ( ordered_pair @ SY3400 @ SY3426 ) @ SV50 )
| ~ ( in @ SY3400 @ SV178 ) )
| ( in @ SY3426 @ SV198 ) )
| ~ ! [SY3428: $i] :
( ~ ( in @ SY3428 @ SV198 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK32_E @ SY3428 @ SV198 @ SV178 @ SV50 ) @ SY3428 ) @ SV50 )
| ~ ( in @ ( sK32_E @ SY3428 @ SV198 @ SV178 @ SV50 ) @ SV178 ) ) ) ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1307]) ).
thf(1384,plain,
! [SV138: $i,SV110: $i] :
( ( ( ~ ( function @ SV110 ) )
= $true )
| ( ( ~ ( relation @ SV110 ) )
= $true )
| ( ( ~ ( relation @ SV138 ) )
= $true )
| ( ( ~ ( function @ SV138 ) )
= $true )
| ( ( function @ ( relation_composition @ SV110 @ SV138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1308]) ).
thf(1385,plain,
! [SV139: $i,SV111: $i] :
( ( ( ~ ( function @ SV111 ) )
= $true )
| ( ( ~ ( relation @ SV111 ) )
= $true )
| ( ( ~ ( relation @ SV139 ) )
= $true )
| ( ( ~ ( function @ SV139 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV111 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1309]) ).
thf(1386,plain,
! [SV179: $i] :
( ( ( ~ ( empty @ SV179 )
| ~ ( relation @ SV179 ) )
= $true )
| ( ( ~ ( function @ SV179 ) )
= $true )
| ( ( function @ SV179 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1310]) ).
thf(1387,plain,
! [SV180: $i] :
( ( ( ~ ( empty @ SV180 )
| ~ ( relation @ SV180 ) )
= $true )
| ( ( ~ ( function @ SV180 ) )
= $true )
| ( ( relation @ SV180 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1311]) ).
thf(1388,plain,
! [SV112: $i] :
( ( ( relation @ SV112 )
= $false )
| ( ( empty @ SV112 )
= $false )
| ( ( ~ ( function @ SV112 ) )
= $true )
| ( ( one_to_one @ SV112 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1312]) ).
thf(1389,plain,
! [SV140: $i,SV51: $i,SV156: $i] :
( ( ( ! [SY3373: $i] :
( ~ ( in @ SY3373 @ ( relation_dom @ SV156 ) )
| ~ ( in @ ( ordered_pair @ SY3373 @ SV51 ) @ SV156 )
| ~ ( in @ SY3373 @ SV140 ) ) )
= $true )
| ( ( in @ SV51 @ ( relation_image @ SV156 @ SV140 ) )
= $true )
| ( ( relation @ SV156 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1313]) ).
thf(1390,plain,
! [SV141: $i,SV157: $i,SV51: $i] :
( ( ( ~ ( in @ SV51 @ ( relation_image @ SV157 @ SV141 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK47_D @ SV157 @ SV141 @ SV51 ) @ ( relation_dom @ SV157 ) )
| ~ ( in @ ( ordered_pair @ ( sK47_D @ SV157 @ SV141 @ SV51 ) @ SV51 ) @ SV157 ) )
| ~ ( in @ ( sK47_D @ SV157 @ SV141 @ SV51 ) @ SV141 ) ) )
= $true )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1314]) ).
thf(1391,plain,
! [SV52: $i,SV181: $i] :
( ( ( relation @ SV181 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_C @ SV181 @ SV52 ) @ ( sK15_SY3113 @ SV181 @ SV52 ) ) @ SV181 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY3113 @ SV181 @ SV52 ) @ ( sK14_C @ SV181 @ SV52 ) ) @ SV52 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SV181 @ SV52 ) @ ( sK15_SY3113 @ SV181 @ SV52 ) ) @ SV181 )
| ( in @ ( ordered_pair @ ( sK15_SY3113 @ SV181 @ SV52 ) @ ( sK14_C @ SV181 @ SV52 ) ) @ SV52 ) ) )
| ( SV181
= ( relation_inverse @ SV52 ) ) )
= $true )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1315]) ).
thf(1392,plain,
! [SV52: $i,SV182: $i] :
( ( ( relation @ SV182 )
= $false )
| ( ( ( SV182
!= ( relation_inverse @ SV52 ) )
| ~ ( ~ ! [SY3402: $i,SY3403: $i] :
( ~ ( in @ ( ordered_pair @ SY3402 @ SY3403 ) @ SV182 )
| ( in @ ( ordered_pair @ SY3403 @ SY3402 ) @ SV52 ) )
| ~ ! [SY3404: $i,SY3405: $i] :
( ~ ( in @ ( ordered_pair @ SY3405 @ SY3404 ) @ SV52 )
| ( in @ ( ordered_pair @ SY3404 @ SY3405 ) @ SV182 ) ) ) )
= $true )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1316]) ).
thf(1393,plain,
! [SV115: $i] :
( ( ( relation @ SV115 )
= $false )
| ( ( function @ SV115 )
= $false )
| ( ( ~ ( one_to_one @ SV115 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1317]) ).
thf(1394,plain,
! [SV116: $i] :
( ( ( relation @ SV116 )
= $false )
| ( ( function @ SV116 )
= $false )
| ( ( ~ ( one_to_one @ SV116 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1318]) ).
thf(1395,plain,
! [SV123: $i,SV142: $i] :
( ( ( ~ ( ( ( sK39_C @ SV142 @ SV123 )
!= ( sK40_SY3129 @ SV142 @ SV123 ) )
| ~ ( in @ ( sK39_C @ SV142 @ SV123 ) @ SV123 )
| ~ ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 ) )
| ~ ~ ( ~ ( ( ( sK39_C @ SV142 @ SV123 )
= ( sK40_SY3129 @ SV142 @ SV123 ) )
| ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 ) )
| ~ ( ( in @ ( sK39_C @ SV142 @ SV123 ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 ) ) ) )
= $false )
| ( ( SV142
= ( identity_relation @ SV123 ) )
= $true )
| ( ( relation @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1321]) ).
thf(1396,plain,
! [SV124: $i,SV143: $i] :
( ( ( SV143
= ( identity_relation @ SV124 ) )
= $false )
| ( ( ~ ( ~ ! [SY3360: $i,SY3361: $i] :
( ( SY3360 != SY3361 )
| ~ ( in @ SY3360 @ SV124 )
| ( in @ ( ordered_pair @ SY3360 @ SY3361 ) @ SV143 ) )
| ~ ~ ( ~ ! [SY3362: $i,SY3363: $i] :
( ~ ( in @ ( ordered_pair @ SY3362 @ SY3363 ) @ SV143 )
| ( SY3362 = SY3363 ) )
| ~ ! [SY3364: $i] :
( ! [SY3365: $i] :
~ ( in @ ( ordered_pair @ SY3364 @ SY3365 ) @ SV143 )
| ( in @ SY3364 @ SV124 ) ) ) ) )
= $true )
| ( ( relation @ SV143 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1322]) ).
thf(1397,plain,
! [SV125: $i,SV144: $i] :
( ( ( relation @ SV144 )
= $false )
| ( ( empty @ SV125 )
= $false )
| ( ( empty @ ( relation_composition @ SV144 @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1323]) ).
thf(1398,plain,
! [SV126: $i,SV145: $i] :
( ( ( relation @ SV145 )
= $false )
| ( ( empty @ SV126 )
= $false )
| ( ( relation @ ( relation_composition @ SV145 @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1324]) ).
thf(1399,plain,
! [SV53: $i,SV82: $i,SV199: $i] :
( ( ( ~ ( relation @ SV199 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) @ SV53 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV82 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 ) )
| ~ ~ ( ~ ( ( in @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) @ SV53 )
| ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV82 )
| ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 ) ) ) )
| ( SV199
= ( relation_rng_restriction @ SV53 @ SV82 ) ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1325]) ).
thf(1400,plain,
! [SV82: $i,SV53: $i,SV200: $i] :
( ( ( ~ ( relation @ SV200 ) )
= $true )
| ( ( ( SV200
!= ( relation_rng_restriction @ SV53 @ SV82 ) )
| ~ ( ~ ! [SY3429: $i,SY3430: $i] :
( ~ ( in @ SY3430 @ SV53 )
| ~ ( in @ ( ordered_pair @ SY3429 @ SY3430 ) @ SV82 )
| ( in @ ( ordered_pair @ SY3429 @ SY3430 ) @ SV200 ) )
| ~ ~ ( ~ ! [SY3431: $i,SY3432: $i] :
( ~ ( in @ ( ordered_pair @ SY3431 @ SY3432 ) @ SV200 )
| ( in @ SY3432 @ SV53 ) )
| ~ ! [SY3433: $i,SY3434: $i] :
( ~ ( in @ ( ordered_pair @ SY3433 @ SY3434 ) @ SV200 )
| ( in @ ( ordered_pair @ SY3433 @ SY3434 ) @ SV82 ) ) ) ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1326]) ).
thf(1401,plain,
! [SV54: $i,SV183: $i] :
( ( ( relation @ SV183 )
= $false )
| ( ( ~ ( subset @ SV54 @ SV183 )
| ( subset @ ( relation_dom @ SV54 ) @ ( relation_dom @ SV183 ) ) )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1327]) ).
thf(1402,plain,
! [SV54: $i,SV184: $i] :
( ( ( relation @ SV184 )
= $false )
| ( ( ~ ( subset @ SV54 @ SV184 )
| ( subset @ ( relation_rng @ SV54 ) @ ( relation_rng @ SV184 ) ) )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1328]) ).
thf(1403,plain,
! [SV83: $i,SV55: $i] :
( ( ( ! [SY3320: $i] :
( ~ ( function @ SY3320 )
| ~ ( relation @ SY3320 )
| ~ ( in @ SV55 @ ( relation_dom @ SY3320 ) )
| ~ ( in @ ( apply @ SY3320 @ SV55 ) @ ( relation_dom @ SV83 ) )
| ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3320 @ SV83 ) ) ) ) )
= $true )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1329]) ).
thf(1404,plain,
! [SV83: $i,SV55: $i] :
( ( ( ~ ( ~ ! [SY3321: $i] :
( ~ ( function @ SY3321 )
| ~ ( relation @ SY3321 )
| ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3321 @ SV83 ) ) )
| ( in @ SV55 @ ( relation_dom @ SY3321 ) ) )
| ~ ! [SY3322: $i] :
( ~ ( function @ SY3322 )
| ~ ( relation @ SY3322 )
| ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3322 @ SV83 ) ) )
| ( in @ ( apply @ SY3322 @ SV55 ) @ ( relation_dom @ SV83 ) ) ) ) )
= $true )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1330]) ).
thf(1405,plain,
! [SV158: $i,SV146: $i,SV56: $i] :
( ( ( ~ ( in @ SV56 @ SV146 )
| ~ ( in @ SV56 @ ( relation_dom @ SV158 ) ) )
= $true )
| ( ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SV158 @ SV146 ) ) )
= $true )
| ( ( relation @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1331]) ).
thf(1406,plain,
! [SV201: $i,SV56: $i,SV212: $i] :
( ( ~ ( relation @ SV212 )
| ~ ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SV212 @ SV201 ) ) )
| ( in @ SV56 @ SV201 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1332]) ).
thf(1407,plain,
! [SV202: $i,SV56: $i,SV213: $i] :
( ( ~ ( relation @ SV213 )
| ~ ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SV213 @ SV202 ) ) )
| ( in @ SV56 @ ( relation_dom @ SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1333]) ).
thf(1408,plain,
! [SV159: $i,SV147: $i,SV57: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV57 @ SV147 ) @ SV159 ) )
= $true )
| ( ( in @ SV57 @ ( relation_dom @ SV159 ) )
= $true )
| ( ( relation @ SV159 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1334]) ).
thf(1409,plain,
! [SV160: $i,SV148: $i,SV57: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV57 @ SV148 ) @ SV160 ) )
= $true )
| ( ( in @ SV148 @ ( relation_rng @ SV160 ) )
= $true )
| ( ( relation @ SV160 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1335]) ).
thf(1410,plain,
! [SV149: $i,SV58: $i,SV161: $i] :
( ( ( ! [SY3374: $i] :
( ~ ( in @ SY3374 @ ( relation_rng @ SV161 ) )
| ~ ( in @ ( ordered_pair @ SV58 @ SY3374 ) @ SV161 )
| ~ ( in @ SY3374 @ SV149 ) ) )
= $true )
| ( ( in @ SV58 @ ( relation_inverse_image @ SV161 @ SV149 ) )
= $true )
| ( ( relation @ SV161 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1336]) ).
thf(1411,plain,
! [SV150: $i,SV162: $i,SV58: $i] :
( ( ( ~ ( in @ SV58 @ ( relation_inverse_image @ SV162 @ SV150 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK46_D @ SV162 @ SV150 @ SV58 ) @ ( relation_rng @ SV162 ) )
| ~ ( in @ ( ordered_pair @ SV58 @ ( sK46_D @ SV162 @ SV150 @ SV58 ) ) @ SV162 ) )
| ~ ( in @ ( sK46_D @ SV162 @ SV150 @ SV58 ) @ SV150 ) ) )
= $true )
| ( ( relation @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1337]) ).
thf(1412,plain,
! [SV59: $i,SV185: $i] :
( ( ( relation @ SV185 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SV185 @ SV59 ) @ ( sK23_SY3118 @ SV185 @ SV59 ) ) @ SV59 )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_C @ SV185 @ SV59 ) @ ( sK23_SY3118 @ SV185 @ SV59 ) ) @ SV185 ) )
| ( subset @ SV59 @ SV185 ) )
= $true )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1338]) ).
thf(1413,plain,
! [SV59: $i,SV186: $i] :
( ( ( relation @ SV186 )
= $false )
| ( ( ~ ( subset @ SV59 @ SV186 )
| ! [SY3406: $i,SY3407: $i] :
( ~ ( in @ ( ordered_pair @ SY3406 @ SY3407 ) @ SV59 )
| ( in @ ( ordered_pair @ SY3406 @ SY3407 ) @ SV186 ) ) )
= $true )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1339]) ).
thf(1414,plain,
! [SV60: $i,SV187: $i,SV203: $i] :
( ( ( ~ ( relation @ SV203 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ SV187 )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV60 )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 ) )
| ~ ~ ( ~ ( ( in @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ SV187 )
| ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV60 )
| ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 ) ) ) )
| ( SV203
= ( relation_dom_restriction @ SV60 @ SV187 ) ) )
= $true )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1340]) ).
thf(1415,plain,
! [SV188: $i,SV60: $i,SV204: $i] :
( ( ( ~ ( relation @ SV204 ) )
= $true )
| ( ( ( SV204
!= ( relation_dom_restriction @ SV60 @ SV188 ) )
| ~ ( ~ ! [SY3437: $i,SY3438: $i] :
( ~ ( in @ SY3437 @ SV188 )
| ~ ( in @ ( ordered_pair @ SY3437 @ SY3438 ) @ SV60 )
| ( in @ ( ordered_pair @ SY3437 @ SY3438 ) @ SV204 ) )
| ~ ~ ( ~ ! [SY3439: $i] :
( ! [SY3440: $i] :
~ ( in @ ( ordered_pair @ SY3439 @ SY3440 ) @ SV204 )
| ( in @ SY3439 @ SV188 ) )
| ~ ! [SY3441: $i,SY3442: $i] :
( ~ ( in @ ( ordered_pair @ SY3441 @ SY3442 ) @ SV204 )
| ( in @ ( ordered_pair @ SY3441 @ SY3442 ) @ SV60 ) ) ) ) )
= $true )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1341]) ).
thf(1416,plain,
! [SV71: $i,SV14: $i,SV163: $i] :
( ( ( function @ SV163 )
= $false )
| ( ( ~ ( relation @ SV163 ) )
= $true )
| ( ( ~ ( in @ SV14 @ ( relation_dom @ ( relation_composition @ SV163 @ SV71 ) ) )
| ( ( apply @ ( relation_composition @ SV163 @ SV71 ) @ SV14 )
= ( apply @ SV71 @ ( apply @ SV163 @ SV14 ) ) ) )
= $true )
| ( ( function @ SV71 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1342]) ).
thf(1417,plain,
! [SV72: $i,SV15: $i,SV164: $i] :
( ( ( function @ SV164 )
= $false )
| ( ( ~ ( relation @ SV164 ) )
= $true )
| ( ( ~ ( in @ SV15 @ ( relation_dom @ SV72 ) )
| ( ( apply @ ( relation_composition @ SV72 @ SV164 ) @ SV15 )
= ( apply @ SV164 @ ( apply @ SV72 @ SV15 ) ) ) )
= $true )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1343]) ).
thf(1418,plain,
! [SV39: $i,SV129: $i,SV151: $i] :
( ( ( relation @ SV151 )
= $false )
| ( ( function @ SV151 )
= $false )
| ( ( ( SV129
!= ( apply @ SV151 @ SV39 ) )
| ~ ( in @ SV39 @ ( relation_dom @ SV151 ) )
| ( in @ ( ordered_pair @ SV39 @ SV129 ) @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1344]) ).
thf(1419,plain,
! [SV189: $i,SV39: $i,SV205: $i] :
( ( ( ~ ( function @ SV205 )
| ~ ( relation @ SV205 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV39 @ SV189 ) @ SV205 )
| ( SV189
= ( apply @ SV205 @ SV39 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1345]) ).
thf(1420,plain,
! [SV190: $i,SV39: $i,SV206: $i] :
( ( ( ~ ( function @ SV206 )
| ~ ( relation @ SV206 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV39 @ SV190 ) @ SV206 )
| ( in @ SV39 @ ( relation_dom @ SV206 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1346]) ).
thf(1421,plain,
! [SV40: $i] :
( ( ( ! [SY3168: $i] :
( ~ ( function @ SY3168 )
| ~ ( relation @ SY3168 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK44_SY3131 @ SY3168 @ SV40 )
= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ( ( sK43_C @ SY3168 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SY3168 @ SV40 )
= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SY3168 @ SV40 )
= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ( ( sK44_SY3131 @ SY3168 @ SV40 )
!= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK43_C @ SY3168 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK44_SY3131 @ SY3168 @ SV40 )
!= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK43_C @ SY3168 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK43_C @ SY3168 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SY3168 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SY3168 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SY3168 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK44_SY3131 @ SY3168 @ SV40 )
!= ( apply @ SY3168 @ ( sK43_C @ SY3168 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SY3168 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ( ( relation_dom @ SY3168 )
!= ( relation_rng @ SV40 ) )
| ( SY3168
= ( function_inverse @ SV40 ) ) ) )
= $true )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1347]) ).
thf(1422,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ! [SY3169: $i] :
( ~ ( function @ SY3169 )
| ~ ( relation @ SY3169 )
| ( SY3169
!= ( function_inverse @ SV40 ) )
| ~ ( ~ ~ ( ~ ! [SY3170: $i,SY3171: $i] :
( ( SY3171
!= ( apply @ SY3169 @ SY3170 ) )
| ~ ( in @ SY3170 @ ( relation_rng @ SV40 ) )
| ( SY3170
= ( apply @ SV40 @ SY3171 ) ) )
| ~ ! [SY3172: $i,SY3173: $i] :
( ( SY3173
!= ( apply @ SY3169 @ SY3172 ) )
| ~ ( in @ SY3172 @ ( relation_rng @ SV40 ) )
| ( in @ SY3173 @ ( relation_dom @ SV40 ) ) ) )
| ~ ~ ( ~ ! [SY3174: $i,SY3175: $i] :
( ( SY3174
!= ( apply @ SV40 @ SY3175 ) )
| ~ ( in @ SY3175 @ ( relation_dom @ SV40 ) )
| ( SY3175
= ( apply @ SY3169 @ SY3174 ) ) )
| ~ ! [SY3176: $i] :
( ! [SY3177: $i] :
( ( SY3176
!= ( apply @ SV40 @ SY3177 ) )
| ~ ( in @ SY3177 @ ( relation_dom @ SV40 ) ) )
| ( in @ SY3176 @ ( relation_rng @ SV40 ) ) ) ) ) )
| ~ ! [SY3178: $i] :
( ~ ( function @ SY3178 )
| ~ ( relation @ SY3178 )
| ( SY3178
!= ( function_inverse @ SV40 ) )
| ( ( relation_dom @ SY3178 )
= ( relation_rng @ SV40 ) ) ) ) )
= $true )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1348]) ).
thf(1423,plain,
! [SV41: $i,SV165: $i,SV191: $i] :
( ( ( ~ ( ! [SY3418: $i] :
( ~ ( in @ ( ordered_pair @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SY3418 ) @ SV41 )
| ~ ( in @ SY3418 @ SV165 ) )
| ~ ( in @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SV191 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ ( sK31_SY3124 @ SV191 @ SV165 @ SV41 ) ) @ SV41 )
| ~ ( in @ ( sK31_SY3124 @ SV191 @ SV165 @ SV41 ) @ SV165 ) )
| ( in @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SV191 ) ) )
= $false )
| ( ( SV191
= ( relation_inverse_image @ SV41 @ SV165 ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1349]) ).
thf(1424,plain,
! [SV166: $i,SV41: $i,SV192: $i] :
( ( ( SV192
= ( relation_inverse_image @ SV41 @ SV166 ) )
= $false )
| ( ( ~ ( ~ ! [SY3419: $i] :
( ! [SY3379: $i] :
( ~ ( in @ ( ordered_pair @ SY3419 @ SY3379 ) @ SV41 )
| ~ ( in @ SY3379 @ SV166 ) )
| ( in @ SY3419 @ SV192 ) )
| ~ ! [SY3421: $i] :
( ~ ( in @ SY3421 @ SV192 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3421 @ ( sK29_E @ SY3421 @ SV192 @ SV166 @ SV41 ) ) @ SV41 )
| ~ ( in @ ( sK29_E @ SY3421 @ SV192 @ SV166 @ SV41 ) @ SV166 ) ) ) ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1350]) ).
thf(1425,plain,
! [SV42: $i,SV167: $i] :
( ( ( ~ ( ! [SY3381: $i] :
~ ( in @ ( ordered_pair @ SY3381 @ ( sK17_C @ SV167 @ SV42 ) ) @ SV42 )
| ~ ( in @ ( sK17_C @ SV167 @ SV42 ) @ SV167 ) ) )
= $false )
| ( ( SV167
= ( relation_rng @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1351]) ).
thf(1426,plain,
! [SV42: $i,SV167: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK18_SY3115 @ SV167 @ SV42 ) @ ( sK17_C @ SV167 @ SV42 ) ) @ SV42 )
| ( in @ ( sK17_C @ SV167 @ SV42 ) @ SV167 ) ) )
= $false )
| ( ( SV167
= ( relation_rng @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1351]) ).
thf(1427,plain,
! [SV168: $i,SV42: $i] :
( ( ( ~ ! [SY3382: $i] :
( ! [SY3191: $i] :
~ ( in @ ( ordered_pair @ SY3191 @ SY3382 ) @ SV42 )
| ( in @ SY3382 @ SV168 ) )
| ~ ! [SY3384: $i] :
( ~ ( in @ SY3384 @ SV168 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3384 @ SV168 @ SV42 ) @ SY3384 ) @ SV42 ) ) )
= $false )
| ( ( SV168
= ( relation_rng @ SV42 ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1352]) ).
thf(1428,plain,
! [SV92: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK12_B @ SV92 ) @ ( relation_dom @ SV92 ) )
| ~ ( in @ ( sK13_SY3112 @ SV92 ) @ ( relation_dom @ SV92 ) ) )
| ( ( apply @ SV92 @ ( sK12_B @ SV92 ) )
!= ( apply @ SV92 @ ( sK13_SY3112 @ SV92 ) ) ) )
| ~ ( ( ( sK12_B @ SV92 )
!= ( sK13_SY3112 @ SV92 ) ) ) )
= $false )
| ( ( one_to_one @ SV92 )
= $true )
| ( ( function @ SV92 )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1353]) ).
thf(1429,plain,
! [SV93: $i] :
( ( ( one_to_one @ SV93 )
= $false )
| ( ( ! [SY3323: $i,SY3324: $i] :
( ~ ( in @ SY3323 @ ( relation_dom @ SV93 ) )
| ~ ( in @ SY3324 @ ( relation_dom @ SV93 ) )
| ( ( apply @ SV93 @ SY3323 )
!= ( apply @ SV93 @ SY3324 ) )
| ( SY3323 = SY3324 ) ) )
= $true )
| ( ( function @ SV93 )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1354]) ).
thf(1430,plain,
! [SV43: $i,SV94: $i,SV214: $i] :
( ( ( ~ ( relation @ SV214 )
| ~ ( ~ ( ! [SY3446: $i] :
( ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ SY3446 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3446 @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV94 ) )
| ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV214 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK11_SY3111 @ SV214 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY3111 @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV94 ) )
| ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV214 ) ) )
| ( SV214
= ( relation_composition @ SV43 @ SV94 ) ) )
= $true )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1355]) ).
thf(1431,plain,
! [SV94: $i,SV43: $i,SV215: $i] :
( ( ( ~ ( relation @ SV215 )
| ( SV215
!= ( relation_composition @ SV43 @ SV94 ) )
| ~ ( ~ ! [SY3447: $i,SY3448: $i] :
( ! [SY3330: $i] :
( ~ ( in @ ( ordered_pair @ SY3447 @ SY3330 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3330 @ SY3448 ) @ SV94 ) )
| ( in @ ( ordered_pair @ SY3447 @ SY3448 ) @ SV215 ) )
| ~ ! [SY3450: $i,SY3451: $i] :
( ~ ( in @ ( ordered_pair @ SY3450 @ SY3451 ) @ SV215 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3450 @ ( sK8_F @ SY3451 @ SY3450 @ SV215 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK8_F @ SY3451 @ SY3450 @ SV215 @ SV94 @ SV43 ) @ SY3451 ) @ SV94 ) ) ) ) )
= $true )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1356]) ).
thf(1432,plain,
! [SV44: $i,SV169: $i] :
( ( ( ~ ( ! [SY3385: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SV169 @ SV44 ) @ SY3385 ) @ SV44 )
| ~ ( in @ ( sK20_C @ SV169 @ SV44 ) @ SV169 ) ) )
= $false )
| ( ( SV169
= ( relation_dom @ SV44 ) )
= $true )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1357]) ).
thf(1433,plain,
! [SV44: $i,SV169: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK20_C @ SV169 @ SV44 ) @ ( sK21_SY3117 @ SV169 @ SV44 ) ) @ SV44 )
| ( in @ ( sK20_C @ SV169 @ SV44 ) @ SV169 ) ) )
= $false )
| ( ( SV169
= ( relation_dom @ SV44 ) )
= $true )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1357]) ).
thf(1434,plain,
! [SV170: $i,SV44: $i] :
( ( ( ~ ! [SY3386: $i] :
( ! [SY3206: $i] :
~ ( in @ ( ordered_pair @ SY3386 @ SY3206 ) @ SV44 )
| ( in @ SY3386 @ SV170 ) )
| ~ ! [SY3388: $i] :
( ~ ( in @ SY3388 @ SV170 )
| ( in @ ( ordered_pair @ SY3388 @ ( sK19_D @ SY3388 @ SV170 @ SV44 ) ) @ SV44 ) ) )
= $false )
| ( ( SV170
= ( relation_dom @ SV44 ) )
= $false )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1358]) ).
thf(1435,plain,
! [SV45: $i] :
( ( ( ~ ! [SY3208: $i] :
( ~ ( in @ SY3208 @ ( relation_dom @ SV45 ) )
| ! [SY3209: $i] :
( ( SY3209
!= ( apply @ SV45 @ SY3208 ) )
| ( in @ ( ordered_pair @ SY3208 @ SY3209 ) @ SV45 ) ) ) )
= $false )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1359]) ).
thf(1436,plain,
! [SV45: $i] :
( ( ( ~ ! [SY3210: $i] :
( ~ ( in @ SY3210 @ ( relation_dom @ SV45 ) )
| ! [SY3211: $i] :
( ~ ( in @ ( ordered_pair @ SY3210 @ SY3211 ) @ SV45 )
| ( SY3211
= ( apply @ SV45 @ SY3210 ) ) ) ) )
= $false )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1359]) ).
thf(1437,plain,
! [SV45: $i] :
( ( ( ~ ! [SY3212: $i] :
( ( in @ SY3212 @ ( relation_dom @ SV45 ) )
| ! [SY3213: $i] :
( ( SY3213
!= ( apply @ SV45 @ SY3212 ) )
| ( SY3213 = empty_set ) ) ) )
= $false )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1360]) ).
thf(1438,plain,
! [SV45: $i] :
( ( ( ~ ! [SY3214: $i] :
( ( in @ SY3214 @ ( relation_dom @ SV45 ) )
| ! [SY3215: $i] :
( ( SY3215 != empty_set )
| ( SY3215
= ( apply @ SV45 @ SY3214 ) ) ) ) )
= $false )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1360]) ).
thf(1439,plain,
! [SV130: $i,SV95: $i] :
( ( ( ~ ( in @ SV95 @ ( relation_rng @ SV130 ) )
| ~ ( one_to_one @ SV130 ) )
= $true )
| ( ( SV95
= ( apply @ SV130 @ ( apply @ ( function_inverse @ SV130 ) @ SV95 ) ) )
= $true )
| ( ( function @ SV130 )
= $false )
| ( ( relation @ SV130 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1361]) ).
thf(1440,plain,
! [SV131: $i,SV96: $i] :
( ( ( ~ ( in @ SV96 @ ( relation_rng @ SV131 ) )
| ~ ( one_to_one @ SV131 ) )
= $true )
| ( ( SV96
= ( apply @ ( relation_composition @ ( function_inverse @ SV131 ) @ SV131 ) @ SV96 ) )
= $true )
| ( ( function @ SV131 )
= $false )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1362]) ).
thf(1441,plain,
! [SV97: $i] :
( ( ( one_to_one @ SV97 )
= $false )
| ( ( ( relation_rng @ SV97 )
= ( relation_dom @ ( function_inverse @ SV97 ) ) )
= $true )
| ( ( function @ SV97 )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1363]) ).
thf(1442,plain,
! [SV98: $i] :
( ( ( one_to_one @ SV98 )
= $false )
| ( ( ( relation_dom @ SV98 )
= ( relation_rng @ ( function_inverse @ SV98 ) ) )
= $true )
| ( ( function @ SV98 )
= $false )
| ( ( relation @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1364]) ).
thf(1443,plain,
! [SV101: $i,SV134: $i] :
( ( ( ~ ( ~ ( in @ ( sK45_C @ SV134 @ SV101 ) @ SV101 )
| ~ ( ( ( apply @ SV134 @ ( sK45_C @ SV134 @ SV101 ) )
!= ( sK45_C @ SV134 @ SV101 ) ) ) )
| ( ( relation_dom @ SV134 )
!= SV101 ) )
= $true )
| ( ( SV134
= ( identity_relation @ SV101 ) )
= $true )
| ( ( function @ SV134 )
= $false )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1367]) ).
thf(1444,plain,
! [SV171: $i,SV193: $i] :
( ( ( ~ ( function @ SV193 ) )
= $true )
| ( ( ~ ( relation @ SV193 ) )
= $true )
| ( ( ( SV193
!= ( identity_relation @ SV171 ) )
| ! [SY3422: $i] :
( ~ ( in @ SY3422 @ SV171 )
| ( ( apply @ SV193 @ SY3422 )
= SY3422 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1368]) ).
thf(1445,plain,
! [SV172: $i,SV194: $i] :
( ( ( ~ ( function @ SV194 ) )
= $true )
| ( ( ~ ( relation @ SV194 ) )
= $true )
| ( ( ( SV194
!= ( identity_relation @ SV172 ) )
| ( ( relation_dom @ SV194 )
= SV172 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1369]) ).
thf(1446,plain,
! [SV216: $i,SV207: $i,SV102: $i] :
( ( ( ( ( sK28_B @ SV102 )
!= ( ordered_pair @ SV207 @ SV216 ) ) )
= $true )
| ( ( relation @ SV102 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1447,plain,
! [SV152: $i,SV135: $i,SV46: $i] :
( ( ( in @ ( ordered_pair @ SV46 @ SV135 ) @ SV152 )
= $false )
| ( ( in @ SV46 @ ( relation_field @ SV152 ) )
= $true )
| ( ( relation @ SV152 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1372]) ).
thf(1448,plain,
! [SV153: $i,SV136: $i,SV46: $i] :
( ( ( in @ ( ordered_pair @ SV46 @ SV136 ) @ SV153 )
= $false )
| ( ( in @ SV136 @ ( relation_field @ SV153 ) )
= $true )
| ( ( relation @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1373]) ).
thf(1449,plain,
! [SV174: $i,SV81: $i,SV154: $i,SV47: $i] :
( ( ( ~ ( in @ SV47 @ SV154 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ SV174 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SV154 ) @ SV174 ) )
= $true )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1374]) ).
thf(1450,plain,
! [SV208: $i,SV81: $i,SV47: $i,SV217: $i] :
( ( ~ ( relation @ SV217 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SV208 ) @ SV217 ) )
| ( in @ SV47 @ SV208 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1375]) ).
thf(1451,plain,
! [SV209: $i,SV81: $i,SV47: $i,SV218: $i] :
( ( ~ ( relation @ SV218 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SV209 ) @ SV218 ) )
| ( in @ ( ordered_pair @ SV47 @ SV81 ) @ SV218 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1376]) ).
thf(1452,plain,
! [SV155: $i,SV137: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ SV137 ) )
= $true )
| ( ( ~ ( in @ SV48 @ ( relation_rng @ SV155 ) ) )
= $true )
| ( ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SV137 @ SV155 ) ) )
= $true )
| ( ( relation @ SV155 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1377]) ).
thf(1453,plain,
! [SV195: $i,SV48: $i,SV210: $i] :
( ( ( ~ ( relation @ SV210 ) )
= $true )
| ( ( ~ ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SV195 @ SV210 ) ) )
| ( in @ SV48 @ SV195 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1378]) ).
thf(1454,plain,
! [SV196: $i,SV48: $i,SV211: $i] :
( ( ( ~ ( relation @ SV211 ) )
= $true )
| ( ( ~ ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SV196 @ SV211 ) ) )
| ( in @ SV48 @ ( relation_rng @ SV211 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1379]) ).
thf(1455,plain,
! [SV49: $i,SV175: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV175 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV49 )
| ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV175 ) ) ) )
= $true )
| ( ( SV49 = SV175 )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1380]) ).
thf(1456,plain,
! [SV176: $i,SV49: $i] :
( ( ( ( SV49 != SV176 ) )
= $true )
| ( ( ~ ( ~ ! [SY3392: $i,SY3393: $i] :
( ~ ( in @ ( ordered_pair @ SY3392 @ SY3393 ) @ SV49 )
| ( in @ ( ordered_pair @ SY3392 @ SY3393 ) @ SV176 ) )
| ~ ! [SY3394: $i,SY3395: $i] :
( ~ ( in @ ( ordered_pair @ SY3394 @ SY3395 ) @ SV176 )
| ( in @ ( ordered_pair @ SY3394 @ SY3395 ) @ SV49 ) ) ) )
= $true )
| ( ( relation @ SV176 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1381]) ).
thf(1457,plain,
! [SV50: $i,SV177: $i,SV197: $i] :
( ( ( ~ ( ! [SY3425: $i] :
( ~ ( in @ ( ordered_pair @ SY3425 @ ( sK33_D @ SV197 @ SV177 @ SV50 ) ) @ SV50 )
| ~ ( in @ SY3425 @ SV177 ) )
| ~ ( in @ ( sK33_D @ SV197 @ SV177 @ SV50 ) @ SV197 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK34_SY3126 @ SV197 @ SV177 @ SV50 ) @ ( sK33_D @ SV197 @ SV177 @ SV50 ) ) @ SV50 )
| ~ ( in @ ( sK34_SY3126 @ SV197 @ SV177 @ SV50 ) @ SV177 ) )
| ( in @ ( sK33_D @ SV197 @ SV177 @ SV50 ) @ SV197 ) ) )
= $false )
| ( ( SV197
= ( relation_image @ SV50 @ SV177 ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1382]) ).
thf(1458,plain,
! [SV178: $i,SV50: $i,SV198: $i] :
( ( ( SV198
= ( relation_image @ SV50 @ SV178 ) )
= $false )
| ( ( ~ ( ~ ! [SY3426: $i] :
( ! [SY3400: $i] :
( ~ ( in @ ( ordered_pair @ SY3400 @ SY3426 ) @ SV50 )
| ~ ( in @ SY3400 @ SV178 ) )
| ( in @ SY3426 @ SV198 ) )
| ~ ! [SY3428: $i] :
( ~ ( in @ SY3428 @ SV198 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK32_E @ SY3428 @ SV198 @ SV178 @ SV50 ) @ SY3428 ) @ SV50 )
| ~ ( in @ ( sK32_E @ SY3428 @ SV198 @ SV178 @ SV50 ) @ SV178 ) ) ) ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1383]) ).
thf(1459,plain,
! [SV138: $i,SV110: $i] :
( ( ( function @ SV110 )
= $false )
| ( ( ~ ( relation @ SV110 ) )
= $true )
| ( ( ~ ( relation @ SV138 ) )
= $true )
| ( ( ~ ( function @ SV138 ) )
= $true )
| ( ( function @ ( relation_composition @ SV110 @ SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1384]) ).
thf(1460,plain,
! [SV139: $i,SV111: $i] :
( ( ( function @ SV111 )
= $false )
| ( ( ~ ( relation @ SV111 ) )
= $true )
| ( ( ~ ( relation @ SV139 ) )
= $true )
| ( ( ~ ( function @ SV139 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV111 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1385]) ).
thf(1461,plain,
! [SV179: $i] :
( ( ( ~ ( empty @ SV179 ) )
= $true )
| ( ( ~ ( relation @ SV179 ) )
= $true )
| ( ( ~ ( function @ SV179 ) )
= $true )
| ( ( function @ SV179 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1386]) ).
thf(1462,plain,
! [SV180: $i] :
( ( ( ~ ( empty @ SV180 ) )
= $true )
| ( ( ~ ( relation @ SV180 ) )
= $true )
| ( ( ~ ( function @ SV180 ) )
= $true )
| ( ( relation @ SV180 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1387]) ).
thf(1463,plain,
! [SV112: $i] :
( ( ( function @ SV112 )
= $false )
| ( ( empty @ SV112 )
= $false )
| ( ( relation @ SV112 )
= $false )
| ( ( one_to_one @ SV112 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1388]) ).
thf(1464,plain,
! [SV140: $i,SV51: $i,SV156: $i,SV219: $i] :
( ( ( ~ ( in @ SV219 @ ( relation_dom @ SV156 ) )
| ~ ( in @ ( ordered_pair @ SV219 @ SV51 ) @ SV156 )
| ~ ( in @ SV219 @ SV140 ) )
= $true )
| ( ( in @ SV51 @ ( relation_image @ SV156 @ SV140 ) )
= $true )
| ( ( relation @ SV156 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1389]) ).
thf(1465,plain,
! [SV141: $i,SV157: $i,SV51: $i] :
( ( ( in @ SV51 @ ( relation_image @ SV157 @ SV141 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK47_D @ SV157 @ SV141 @ SV51 ) @ ( relation_dom @ SV157 ) )
| ~ ( in @ ( ordered_pair @ ( sK47_D @ SV157 @ SV141 @ SV51 ) @ SV51 ) @ SV157 ) )
| ~ ( in @ ( sK47_D @ SV157 @ SV141 @ SV51 ) @ SV141 ) ) )
= $true )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1390]) ).
thf(1466,plain,
! [SV52: $i,SV181: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_C @ SV181 @ SV52 ) @ ( sK15_SY3113 @ SV181 @ SV52 ) ) @ SV181 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY3113 @ SV181 @ SV52 ) @ ( sK14_C @ SV181 @ SV52 ) ) @ SV52 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SV181 @ SV52 ) @ ( sK15_SY3113 @ SV181 @ SV52 ) ) @ SV181 )
| ( in @ ( ordered_pair @ ( sK15_SY3113 @ SV181 @ SV52 ) @ ( sK14_C @ SV181 @ SV52 ) ) @ SV52 ) ) ) )
= $true )
| ( ( SV181
= ( relation_inverse @ SV52 ) )
= $true )
| ( ( relation @ SV181 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1391]) ).
thf(1467,plain,
! [SV52: $i,SV182: $i] :
( ( ( ( SV182
!= ( relation_inverse @ SV52 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3402: $i,SY3403: $i] :
( ~ ( in @ ( ordered_pair @ SY3402 @ SY3403 ) @ SV182 )
| ( in @ ( ordered_pair @ SY3403 @ SY3402 ) @ SV52 ) )
| ~ ! [SY3404: $i,SY3405: $i] :
( ~ ( in @ ( ordered_pair @ SY3405 @ SY3404 ) @ SV52 )
| ( in @ ( ordered_pair @ SY3404 @ SY3405 ) @ SV182 ) ) ) )
= $true )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1392]) ).
thf(1468,plain,
! [SV115: $i] :
( ( ( one_to_one @ SV115 )
= $false )
| ( ( function @ SV115 )
= $false )
| ( ( relation @ SV115 )
= $false )
| ( ( function @ ( relation_inverse @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1393]) ).
thf(1469,plain,
! [SV116: $i] :
( ( ( one_to_one @ SV116 )
= $false )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false )
| ( ( relation @ ( relation_inverse @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1394]) ).
thf(1470,plain,
! [SV123: $i,SV142: $i] :
( ( ( ~ ( ( ( sK39_C @ SV142 @ SV123 )
!= ( sK40_SY3129 @ SV142 @ SV123 ) )
| ~ ( in @ ( sK39_C @ SV142 @ SV123 ) @ SV123 )
| ~ ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 ) ) )
= $false )
| ( ( SV142
= ( identity_relation @ SV123 ) )
= $true )
| ( ( relation @ SV142 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1395]) ).
thf(1471,plain,
! [SV123: $i,SV142: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK39_C @ SV142 @ SV123 )
= ( sK40_SY3129 @ SV142 @ SV123 ) )
| ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 ) )
| ~ ( ( in @ ( sK39_C @ SV142 @ SV123 ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 ) ) ) )
= $false )
| ( ( SV142
= ( identity_relation @ SV123 ) )
= $true )
| ( ( relation @ SV142 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1395]) ).
thf(1472,plain,
! [SV143: $i,SV124: $i] :
( ( ( ~ ! [SY3360: $i,SY3361: $i] :
( ( SY3360 != SY3361 )
| ~ ( in @ SY3360 @ SV124 )
| ( in @ ( ordered_pair @ SY3360 @ SY3361 ) @ SV143 ) )
| ~ ~ ( ~ ! [SY3362: $i,SY3363: $i] :
( ~ ( in @ ( ordered_pair @ SY3362 @ SY3363 ) @ SV143 )
| ( SY3362 = SY3363 ) )
| ~ ! [SY3364: $i] :
( ! [SY3365: $i] :
~ ( in @ ( ordered_pair @ SY3364 @ SY3365 ) @ SV143 )
| ( in @ SY3364 @ SV124 ) ) ) )
= $false )
| ( ( SV143
= ( identity_relation @ SV124 ) )
= $false )
| ( ( relation @ SV143 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1396]) ).
thf(1473,plain,
! [SV53: $i,SV82: $i,SV199: $i] :
( ( ( relation @ SV199 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) @ SV53 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV82 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 ) )
| ~ ~ ( ~ ( ( in @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) @ SV53 )
| ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV82 )
| ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 ) ) ) )
| ( SV199
= ( relation_rng_restriction @ SV53 @ SV82 ) ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1399]) ).
thf(1474,plain,
! [SV82: $i,SV53: $i,SV200: $i] :
( ( ( relation @ SV200 )
= $false )
| ( ( ( SV200
!= ( relation_rng_restriction @ SV53 @ SV82 ) )
| ~ ( ~ ! [SY3429: $i,SY3430: $i] :
( ~ ( in @ SY3430 @ SV53 )
| ~ ( in @ ( ordered_pair @ SY3429 @ SY3430 ) @ SV82 )
| ( in @ ( ordered_pair @ SY3429 @ SY3430 ) @ SV200 ) )
| ~ ~ ( ~ ! [SY3431: $i,SY3432: $i] :
( ~ ( in @ ( ordered_pair @ SY3431 @ SY3432 ) @ SV200 )
| ( in @ SY3432 @ SV53 ) )
| ~ ! [SY3433: $i,SY3434: $i] :
( ~ ( in @ ( ordered_pair @ SY3433 @ SY3434 ) @ SV200 )
| ( in @ ( ordered_pair @ SY3433 @ SY3434 ) @ SV82 ) ) ) ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1400]) ).
thf(1475,plain,
! [SV183: $i,SV54: $i] :
( ( ( ~ ( subset @ SV54 @ SV183 ) )
= $true )
| ( ( subset @ ( relation_dom @ SV54 ) @ ( relation_dom @ SV183 ) )
= $true )
| ( ( relation @ SV183 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1401]) ).
thf(1476,plain,
! [SV184: $i,SV54: $i] :
( ( ( ~ ( subset @ SV54 @ SV184 ) )
= $true )
| ( ( subset @ ( relation_rng @ SV54 ) @ ( relation_rng @ SV184 ) )
= $true )
| ( ( relation @ SV184 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1402]) ).
thf(1477,plain,
! [SV83: $i,SV55: $i,SV220: $i] :
( ( ( ~ ( function @ SV220 )
| ~ ( relation @ SV220 )
| ~ ( in @ SV55 @ ( relation_dom @ SV220 ) )
| ~ ( in @ ( apply @ SV220 @ SV55 ) @ ( relation_dom @ SV83 ) )
| ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SV220 @ SV83 ) ) ) )
= $true )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1403]) ).
thf(1478,plain,
! [SV83: $i,SV55: $i] :
( ( ( ~ ! [SY3321: $i] :
( ~ ( function @ SY3321 )
| ~ ( relation @ SY3321 )
| ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3321 @ SV83 ) ) )
| ( in @ SV55 @ ( relation_dom @ SY3321 ) ) )
| ~ ! [SY3322: $i] :
( ~ ( function @ SY3322 )
| ~ ( relation @ SY3322 )
| ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3322 @ SV83 ) ) )
| ( in @ ( apply @ SY3322 @ SV55 ) @ ( relation_dom @ SV83 ) ) ) )
= $false )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1404]) ).
thf(1479,plain,
! [SV158: $i,SV146: $i,SV56: $i] :
( ( ( ~ ( in @ SV56 @ SV146 ) )
= $true )
| ( ( ~ ( in @ SV56 @ ( relation_dom @ SV158 ) ) )
= $true )
| ( ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SV158 @ SV146 ) ) )
= $true )
| ( ( relation @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1405]) ).
thf(1480,plain,
! [SV201: $i,SV56: $i,SV212: $i] :
( ( ( ~ ( relation @ SV212 ) )
= $true )
| ( ( ~ ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SV212 @ SV201 ) ) )
| ( in @ SV56 @ SV201 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1406]) ).
thf(1481,plain,
! [SV202: $i,SV56: $i,SV213: $i] :
( ( ( ~ ( relation @ SV213 ) )
= $true )
| ( ( ~ ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SV213 @ SV202 ) ) )
| ( in @ SV56 @ ( relation_dom @ SV213 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1407]) ).
thf(1482,plain,
! [SV159: $i,SV147: $i,SV57: $i] :
( ( ( in @ ( ordered_pair @ SV57 @ SV147 ) @ SV159 )
= $false )
| ( ( in @ SV57 @ ( relation_dom @ SV159 ) )
= $true )
| ( ( relation @ SV159 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1408]) ).
thf(1483,plain,
! [SV160: $i,SV148: $i,SV57: $i] :
( ( ( in @ ( ordered_pair @ SV57 @ SV148 ) @ SV160 )
= $false )
| ( ( in @ SV148 @ ( relation_rng @ SV160 ) )
= $true )
| ( ( relation @ SV160 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1409]) ).
thf(1484,plain,
! [SV149: $i,SV58: $i,SV161: $i,SV221: $i] :
( ( ( ~ ( in @ SV221 @ ( relation_rng @ SV161 ) )
| ~ ( in @ ( ordered_pair @ SV58 @ SV221 ) @ SV161 )
| ~ ( in @ SV221 @ SV149 ) )
= $true )
| ( ( in @ SV58 @ ( relation_inverse_image @ SV161 @ SV149 ) )
= $true )
| ( ( relation @ SV161 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1410]) ).
thf(1485,plain,
! [SV150: $i,SV162: $i,SV58: $i] :
( ( ( in @ SV58 @ ( relation_inverse_image @ SV162 @ SV150 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK46_D @ SV162 @ SV150 @ SV58 ) @ ( relation_rng @ SV162 ) )
| ~ ( in @ ( ordered_pair @ SV58 @ ( sK46_D @ SV162 @ SV150 @ SV58 ) ) @ SV162 ) )
| ~ ( in @ ( sK46_D @ SV162 @ SV150 @ SV58 ) @ SV150 ) ) )
= $true )
| ( ( relation @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1411]) ).
thf(1486,plain,
! [SV59: $i,SV185: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SV185 @ SV59 ) @ ( sK23_SY3118 @ SV185 @ SV59 ) ) @ SV59 )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_C @ SV185 @ SV59 ) @ ( sK23_SY3118 @ SV185 @ SV59 ) ) @ SV185 ) ) )
= $true )
| ( ( subset @ SV59 @ SV185 )
= $true )
| ( ( relation @ SV185 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1412]) ).
thf(1487,plain,
! [SV186: $i,SV59: $i] :
( ( ( ~ ( subset @ SV59 @ SV186 ) )
= $true )
| ( ( ! [SY3406: $i,SY3407: $i] :
( ~ ( in @ ( ordered_pair @ SY3406 @ SY3407 ) @ SV59 )
| ( in @ ( ordered_pair @ SY3406 @ SY3407 ) @ SV186 ) ) )
= $true )
| ( ( relation @ SV186 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1413]) ).
thf(1488,plain,
! [SV60: $i,SV187: $i,SV203: $i] :
( ( ( relation @ SV203 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ SV187 )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV60 )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 ) )
| ~ ~ ( ~ ( ( in @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ SV187 )
| ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV60 )
| ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 ) ) ) )
| ( SV203
= ( relation_dom_restriction @ SV60 @ SV187 ) ) )
= $true )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1414]) ).
thf(1489,plain,
! [SV188: $i,SV60: $i,SV204: $i] :
( ( ( relation @ SV204 )
= $false )
| ( ( ( SV204
!= ( relation_dom_restriction @ SV60 @ SV188 ) )
| ~ ( ~ ! [SY3437: $i,SY3438: $i] :
( ~ ( in @ SY3437 @ SV188 )
| ~ ( in @ ( ordered_pair @ SY3437 @ SY3438 ) @ SV60 )
| ( in @ ( ordered_pair @ SY3437 @ SY3438 ) @ SV204 ) )
| ~ ~ ( ~ ! [SY3439: $i] :
( ! [SY3440: $i] :
~ ( in @ ( ordered_pair @ SY3439 @ SY3440 ) @ SV204 )
| ( in @ SY3439 @ SV188 ) )
| ~ ! [SY3441: $i,SY3442: $i] :
( ~ ( in @ ( ordered_pair @ SY3441 @ SY3442 ) @ SV204 )
| ( in @ ( ordered_pair @ SY3441 @ SY3442 ) @ SV60 ) ) ) ) )
= $true )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1415]) ).
thf(1490,plain,
! [SV71: $i,SV14: $i,SV163: $i] :
( ( ( relation @ SV163 )
= $false )
| ( ( function @ SV163 )
= $false )
| ( ( ~ ( in @ SV14 @ ( relation_dom @ ( relation_composition @ SV163 @ SV71 ) ) )
| ( ( apply @ ( relation_composition @ SV163 @ SV71 ) @ SV14 )
= ( apply @ SV71 @ ( apply @ SV163 @ SV14 ) ) ) )
= $true )
| ( ( function @ SV71 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1416]) ).
thf(1491,plain,
! [SV72: $i,SV15: $i,SV164: $i] :
( ( ( relation @ SV164 )
= $false )
| ( ( function @ SV164 )
= $false )
| ( ( ~ ( in @ SV15 @ ( relation_dom @ SV72 ) )
| ( ( apply @ ( relation_composition @ SV72 @ SV164 ) @ SV15 )
= ( apply @ SV164 @ ( apply @ SV72 @ SV15 ) ) ) )
= $true )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1417]) ).
thf(1492,plain,
! [SV39: $i,SV151: $i,SV129: $i] :
( ( ( ( SV129
!= ( apply @ SV151 @ SV39 ) )
| ~ ( in @ SV39 @ ( relation_dom @ SV151 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV39 @ SV129 ) @ SV151 )
= $true )
| ( ( function @ SV151 )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1418]) ).
thf(1493,plain,
! [SV189: $i,SV39: $i,SV205: $i] :
( ( ( ~ ( function @ SV205 ) )
= $true )
| ( ( ~ ( relation @ SV205 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV39 @ SV189 ) @ SV205 )
| ( SV189
= ( apply @ SV205 @ SV39 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1419]) ).
thf(1494,plain,
! [SV190: $i,SV39: $i,SV206: $i] :
( ( ( ~ ( function @ SV206 ) )
= $true )
| ( ( ~ ( relation @ SV206 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV39 @ SV190 ) @ SV206 )
| ( in @ SV39 @ ( relation_dom @ SV206 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1420]) ).
thf(1495,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ( function @ SV222 )
| ~ ( relation @ SV222 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) )
| ( SV222
= ( function_inverse @ SV40 ) ) )
= $true )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1421]) ).
thf(1496,plain,
! [SV40: $i] :
( ( ( ~ ! [SY3169: $i] :
( ~ ( function @ SY3169 )
| ~ ( relation @ SY3169 )
| ( SY3169
!= ( function_inverse @ SV40 ) )
| ~ ( ~ ~ ( ~ ! [SY3170: $i,SY3171: $i] :
( ( SY3171
!= ( apply @ SY3169 @ SY3170 ) )
| ~ ( in @ SY3170 @ ( relation_rng @ SV40 ) )
| ( SY3170
= ( apply @ SV40 @ SY3171 ) ) )
| ~ ! [SY3172: $i,SY3173: $i] :
( ( SY3173
!= ( apply @ SY3169 @ SY3172 ) )
| ~ ( in @ SY3172 @ ( relation_rng @ SV40 ) )
| ( in @ SY3173 @ ( relation_dom @ SV40 ) ) ) )
| ~ ~ ( ~ ! [SY3174: $i,SY3175: $i] :
( ( SY3174
!= ( apply @ SV40 @ SY3175 ) )
| ~ ( in @ SY3175 @ ( relation_dom @ SV40 ) )
| ( SY3175
= ( apply @ SY3169 @ SY3174 ) ) )
| ~ ! [SY3176: $i] :
( ! [SY3177: $i] :
( ( SY3176
!= ( apply @ SV40 @ SY3177 ) )
| ~ ( in @ SY3177 @ ( relation_dom @ SV40 ) ) )
| ( in @ SY3176 @ ( relation_rng @ SV40 ) ) ) ) ) )
| ~ ! [SY3178: $i] :
( ~ ( function @ SY3178 )
| ~ ( relation @ SY3178 )
| ( SY3178
!= ( function_inverse @ SV40 ) )
| ( ( relation_dom @ SY3178 )
= ( relation_rng @ SV40 ) ) ) )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1422]) ).
thf(1497,plain,
! [SV41: $i,SV165: $i,SV191: $i] :
( ( ( ~ ( ! [SY3418: $i] :
( ~ ( in @ ( ordered_pair @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SY3418 ) @ SV41 )
| ~ ( in @ SY3418 @ SV165 ) )
| ~ ( in @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SV191 ) ) )
= $false )
| ( ( SV191
= ( relation_inverse_image @ SV41 @ SV165 ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1423]) ).
thf(1498,plain,
! [SV41: $i,SV165: $i,SV191: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ ( sK31_SY3124 @ SV191 @ SV165 @ SV41 ) ) @ SV41 )
| ~ ( in @ ( sK31_SY3124 @ SV191 @ SV165 @ SV41 ) @ SV165 ) )
| ( in @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SV191 ) ) )
= $false )
| ( ( SV191
= ( relation_inverse_image @ SV41 @ SV165 ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1423]) ).
thf(1499,plain,
! [SV192: $i,SV166: $i,SV41: $i] :
( ( ( ~ ! [SY3419: $i] :
( ! [SY3379: $i] :
( ~ ( in @ ( ordered_pair @ SY3419 @ SY3379 ) @ SV41 )
| ~ ( in @ SY3379 @ SV166 ) )
| ( in @ SY3419 @ SV192 ) )
| ~ ! [SY3421: $i] :
( ~ ( in @ SY3421 @ SV192 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3421 @ ( sK29_E @ SY3421 @ SV192 @ SV166 @ SV41 ) ) @ SV41 )
| ~ ( in @ ( sK29_E @ SY3421 @ SV192 @ SV166 @ SV41 ) @ SV166 ) ) ) )
= $false )
| ( ( SV192
= ( relation_inverse_image @ SV41 @ SV166 ) )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1424]) ).
thf(1500,plain,
! [SV42: $i,SV167: $i] :
( ( ( ! [SY3381: $i] :
~ ( in @ ( ordered_pair @ SY3381 @ ( sK17_C @ SV167 @ SV42 ) ) @ SV42 )
| ~ ( in @ ( sK17_C @ SV167 @ SV42 ) @ SV167 ) )
= $true )
| ( ( SV167
= ( relation_rng @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1425]) ).
thf(1501,plain,
! [SV42: $i,SV167: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK18_SY3115 @ SV167 @ SV42 ) @ ( sK17_C @ SV167 @ SV42 ) ) @ SV42 )
| ( in @ ( sK17_C @ SV167 @ SV42 ) @ SV167 ) )
= $true )
| ( ( SV167
= ( relation_rng @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1426]) ).
thf(1502,plain,
! [SV168: $i,SV42: $i] :
( ( ( ~ ! [SY3382: $i] :
( ! [SY3191: $i] :
~ ( in @ ( ordered_pair @ SY3191 @ SY3382 ) @ SV42 )
| ( in @ SY3382 @ SV168 ) ) )
= $false )
| ( ( SV168
= ( relation_rng @ SV42 ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1427]) ).
thf(1503,plain,
! [SV42: $i,SV168: $i] :
( ( ( ~ ! [SY3384: $i] :
( ~ ( in @ SY3384 @ SV168 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3384 @ SV168 @ SV42 ) @ SY3384 ) @ SV42 ) ) )
= $false )
| ( ( SV168
= ( relation_rng @ SV42 ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1427]) ).
thf(1504,plain,
! [SV92: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK12_B @ SV92 ) @ ( relation_dom @ SV92 ) )
| ~ ( in @ ( sK13_SY3112 @ SV92 ) @ ( relation_dom @ SV92 ) ) )
| ( ( apply @ SV92 @ ( sK12_B @ SV92 ) )
!= ( apply @ SV92 @ ( sK13_SY3112 @ SV92 ) ) ) ) )
= $false )
| ( ( one_to_one @ SV92 )
= $true )
| ( ( function @ SV92 )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1428]) ).
thf(1505,plain,
! [SV92: $i] :
( ( ( ~ ( ( ( sK12_B @ SV92 )
!= ( sK13_SY3112 @ SV92 ) ) ) )
= $false )
| ( ( one_to_one @ SV92 )
= $true )
| ( ( function @ SV92 )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1428]) ).
thf(1506,plain,
! [SV93: $i,SV223: $i] :
( ( ( ! [SY3452: $i] :
( ~ ( in @ SV223 @ ( relation_dom @ SV93 ) )
| ~ ( in @ SY3452 @ ( relation_dom @ SV93 ) )
| ( ( apply @ SV93 @ SV223 )
!= ( apply @ SV93 @ SY3452 ) )
| ( SV223 = SY3452 ) ) )
= $true )
| ( ( one_to_one @ SV93 )
= $false )
| ( ( function @ SV93 )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1429]) ).
thf(1507,plain,
! [SV43: $i,SV94: $i,SV214: $i] :
( ( ( ~ ( relation @ SV214 ) )
= $true )
| ( ( ~ ( ~ ( ! [SY3446: $i] :
( ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ SY3446 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3446 @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV94 ) )
| ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV214 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK11_SY3111 @ SV214 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY3111 @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV94 ) )
| ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV214 ) ) )
| ( SV214
= ( relation_composition @ SV43 @ SV94 ) ) )
= $true )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1430]) ).
thf(1508,plain,
! [SV94: $i,SV43: $i,SV215: $i] :
( ( ( ~ ( relation @ SV215 ) )
= $true )
| ( ( ( SV215
!= ( relation_composition @ SV43 @ SV94 ) )
| ~ ( ~ ! [SY3447: $i,SY3448: $i] :
( ! [SY3330: $i] :
( ~ ( in @ ( ordered_pair @ SY3447 @ SY3330 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3330 @ SY3448 ) @ SV94 ) )
| ( in @ ( ordered_pair @ SY3447 @ SY3448 ) @ SV215 ) )
| ~ ! [SY3450: $i,SY3451: $i] :
( ~ ( in @ ( ordered_pair @ SY3450 @ SY3451 ) @ SV215 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3450 @ ( sK8_F @ SY3451 @ SY3450 @ SV215 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK8_F @ SY3451 @ SY3450 @ SV215 @ SV94 @ SV43 ) @ SY3451 ) @ SV94 ) ) ) ) )
= $true )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1431]) ).
thf(1509,plain,
! [SV44: $i,SV169: $i] :
( ( ( ! [SY3385: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SV169 @ SV44 ) @ SY3385 ) @ SV44 )
| ~ ( in @ ( sK20_C @ SV169 @ SV44 ) @ SV169 ) )
= $true )
| ( ( SV169
= ( relation_dom @ SV44 ) )
= $true )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1432]) ).
thf(1510,plain,
! [SV44: $i,SV169: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK20_C @ SV169 @ SV44 ) @ ( sK21_SY3117 @ SV169 @ SV44 ) ) @ SV44 )
| ( in @ ( sK20_C @ SV169 @ SV44 ) @ SV169 ) )
= $true )
| ( ( SV169
= ( relation_dom @ SV44 ) )
= $true )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1433]) ).
thf(1511,plain,
! [SV170: $i,SV44: $i] :
( ( ( ~ ! [SY3386: $i] :
( ! [SY3206: $i] :
~ ( in @ ( ordered_pair @ SY3386 @ SY3206 ) @ SV44 )
| ( in @ SY3386 @ SV170 ) ) )
= $false )
| ( ( SV170
= ( relation_dom @ SV44 ) )
= $false )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1434]) ).
thf(1512,plain,
! [SV44: $i,SV170: $i] :
( ( ( ~ ! [SY3388: $i] :
( ~ ( in @ SY3388 @ SV170 )
| ( in @ ( ordered_pair @ SY3388 @ ( sK19_D @ SY3388 @ SV170 @ SV44 ) ) @ SV44 ) ) )
= $false )
| ( ( SV170
= ( relation_dom @ SV44 ) )
= $false )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1434]) ).
thf(1513,plain,
! [SV45: $i] :
( ( ( ! [SY3208: $i] :
( ~ ( in @ SY3208 @ ( relation_dom @ SV45 ) )
| ! [SY3209: $i] :
( ( SY3209
!= ( apply @ SV45 @ SY3208 ) )
| ( in @ ( ordered_pair @ SY3208 @ SY3209 ) @ SV45 ) ) ) )
= $true )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1435]) ).
thf(1514,plain,
! [SV45: $i] :
( ( ( ! [SY3210: $i] :
( ~ ( in @ SY3210 @ ( relation_dom @ SV45 ) )
| ! [SY3211: $i] :
( ~ ( in @ ( ordered_pair @ SY3210 @ SY3211 ) @ SV45 )
| ( SY3211
= ( apply @ SV45 @ SY3210 ) ) ) ) )
= $true )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1436]) ).
thf(1515,plain,
! [SV45: $i] :
( ( ( ! [SY3212: $i] :
( ( in @ SY3212 @ ( relation_dom @ SV45 ) )
| ! [SY3213: $i] :
( ( SY3213
!= ( apply @ SV45 @ SY3212 ) )
| ( SY3213 = empty_set ) ) ) )
= $true )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1437]) ).
thf(1516,plain,
! [SV45: $i] :
( ( ( ! [SY3214: $i] :
( ( in @ SY3214 @ ( relation_dom @ SV45 ) )
| ! [SY3215: $i] :
( ( SY3215 != empty_set )
| ( SY3215
= ( apply @ SV45 @ SY3214 ) ) ) ) )
= $true )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1438]) ).
thf(1517,plain,
! [SV130: $i,SV95: $i] :
( ( ( ~ ( in @ SV95 @ ( relation_rng @ SV130 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV130 ) )
= $true )
| ( ( SV95
= ( apply @ SV130 @ ( apply @ ( function_inverse @ SV130 ) @ SV95 ) ) )
= $true )
| ( ( function @ SV130 )
= $false )
| ( ( relation @ SV130 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1439]) ).
thf(1518,plain,
! [SV131: $i,SV96: $i] :
( ( ( ~ ( in @ SV96 @ ( relation_rng @ SV131 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV131 ) )
= $true )
| ( ( SV96
= ( apply @ ( relation_composition @ ( function_inverse @ SV131 ) @ SV131 ) @ SV96 ) )
= $true )
| ( ( function @ SV131 )
= $false )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1440]) ).
thf(1519,plain,
! [SV101: $i,SV134: $i] :
( ( ( ~ ( ~ ( in @ ( sK45_C @ SV134 @ SV101 ) @ SV101 )
| ~ ( ( ( apply @ SV134 @ ( sK45_C @ SV134 @ SV101 ) )
!= ( sK45_C @ SV134 @ SV101 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV134 )
!= SV101 ) )
= $true )
| ( ( SV134
= ( identity_relation @ SV101 ) )
= $true )
| ( ( function @ SV134 )
= $false )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1443]) ).
thf(1520,plain,
! [SV171: $i,SV193: $i] :
( ( ( function @ SV193 )
= $false )
| ( ( ~ ( relation @ SV193 ) )
= $true )
| ( ( ( SV193
!= ( identity_relation @ SV171 ) )
| ! [SY3422: $i] :
( ~ ( in @ SY3422 @ SV171 )
| ( ( apply @ SV193 @ SY3422 )
= SY3422 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1444]) ).
thf(1521,plain,
! [SV172: $i,SV194: $i] :
( ( ( function @ SV194 )
= $false )
| ( ( ~ ( relation @ SV194 ) )
= $true )
| ( ( ( SV194
!= ( identity_relation @ SV172 ) )
| ( ( relation_dom @ SV194 )
= SV172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1445]) ).
thf(1522,plain,
! [SV216: $i,SV207: $i,SV102: $i] :
( ( ( ( sK28_B @ SV102 )
= ( ordered_pair @ SV207 @ SV216 ) )
= $false )
| ( ( relation @ SV102 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1446]) ).
thf(1523,plain,
! [SV174: $i,SV81: $i,SV154: $i,SV47: $i] :
( ( ( ~ ( in @ SV47 @ SV154 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ SV174 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SV154 ) @ SV174 ) )
= $true )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1449]) ).
thf(1524,plain,
! [SV208: $i,SV81: $i,SV47: $i,SV217: $i] :
( ( ( ~ ( relation @ SV217 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SV208 ) @ SV217 ) )
| ( in @ SV47 @ SV208 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1450]) ).
thf(1525,plain,
! [SV209: $i,SV81: $i,SV47: $i,SV218: $i] :
( ( ( ~ ( relation @ SV218 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SV209 ) @ SV218 ) )
| ( in @ ( ordered_pair @ SV47 @ SV81 ) @ SV218 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1451]) ).
thf(1526,plain,
! [SV155: $i,SV137: $i,SV48: $i] :
( ( ( in @ SV48 @ SV137 )
= $false )
| ( ( ~ ( in @ SV48 @ ( relation_rng @ SV155 ) ) )
= $true )
| ( ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SV137 @ SV155 ) ) )
= $true )
| ( ( relation @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1452]) ).
thf(1527,plain,
! [SV195: $i,SV48: $i,SV210: $i] :
( ( ( relation @ SV210 )
= $false )
| ( ( ~ ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SV195 @ SV210 ) ) )
| ( in @ SV48 @ SV195 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1453]) ).
thf(1528,plain,
! [SV196: $i,SV48: $i,SV211: $i] :
( ( ( relation @ SV211 )
= $false )
| ( ( ~ ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SV196 @ SV211 ) ) )
| ( in @ SV48 @ ( relation_rng @ SV211 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1454]) ).
thf(1529,plain,
! [SV49: $i,SV175: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV175 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV49 )
| ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV175 ) ) )
= $false )
| ( ( SV49 = SV175 )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1455]) ).
thf(1530,plain,
! [SV176: $i,SV49: $i] :
( ( ( SV49 = SV176 )
= $false )
| ( ( ~ ( ~ ! [SY3392: $i,SY3393: $i] :
( ~ ( in @ ( ordered_pair @ SY3392 @ SY3393 ) @ SV49 )
| ( in @ ( ordered_pair @ SY3392 @ SY3393 ) @ SV176 ) )
| ~ ! [SY3394: $i,SY3395: $i] :
( ~ ( in @ ( ordered_pair @ SY3394 @ SY3395 ) @ SV176 )
| ( in @ ( ordered_pair @ SY3394 @ SY3395 ) @ SV49 ) ) ) )
= $true )
| ( ( relation @ SV176 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1456]) ).
thf(1531,plain,
! [SV50: $i,SV177: $i,SV197: $i] :
( ( ( ~ ( ! [SY3425: $i] :
( ~ ( in @ ( ordered_pair @ SY3425 @ ( sK33_D @ SV197 @ SV177 @ SV50 ) ) @ SV50 )
| ~ ( in @ SY3425 @ SV177 ) )
| ~ ( in @ ( sK33_D @ SV197 @ SV177 @ SV50 ) @ SV197 ) ) )
= $false )
| ( ( SV197
= ( relation_image @ SV50 @ SV177 ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1457]) ).
thf(1532,plain,
! [SV50: $i,SV177: $i,SV197: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK34_SY3126 @ SV197 @ SV177 @ SV50 ) @ ( sK33_D @ SV197 @ SV177 @ SV50 ) ) @ SV50 )
| ~ ( in @ ( sK34_SY3126 @ SV197 @ SV177 @ SV50 ) @ SV177 ) )
| ( in @ ( sK33_D @ SV197 @ SV177 @ SV50 ) @ SV197 ) ) )
= $false )
| ( ( SV197
= ( relation_image @ SV50 @ SV177 ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1457]) ).
thf(1533,plain,
! [SV198: $i,SV178: $i,SV50: $i] :
( ( ( ~ ! [SY3426: $i] :
( ! [SY3400: $i] :
( ~ ( in @ ( ordered_pair @ SY3400 @ SY3426 ) @ SV50 )
| ~ ( in @ SY3400 @ SV178 ) )
| ( in @ SY3426 @ SV198 ) )
| ~ ! [SY3428: $i] :
( ~ ( in @ SY3428 @ SV198 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK32_E @ SY3428 @ SV198 @ SV178 @ SV50 ) @ SY3428 ) @ SV50 )
| ~ ( in @ ( sK32_E @ SY3428 @ SV198 @ SV178 @ SV50 ) @ SV178 ) ) ) )
= $false )
| ( ( SV198
= ( relation_image @ SV50 @ SV178 ) )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1458]) ).
thf(1534,plain,
! [SV138: $i,SV110: $i] :
( ( ( relation @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( ~ ( relation @ SV138 ) )
= $true )
| ( ( ~ ( function @ SV138 ) )
= $true )
| ( ( function @ ( relation_composition @ SV110 @ SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1459]) ).
thf(1535,plain,
! [SV139: $i,SV111: $i] :
( ( ( relation @ SV111 )
= $false )
| ( ( function @ SV111 )
= $false )
| ( ( ~ ( relation @ SV139 ) )
= $true )
| ( ( ~ ( function @ SV139 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV111 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1460]) ).
thf(1536,plain,
! [SV179: $i] :
( ( ( empty @ SV179 )
= $false )
| ( ( ~ ( relation @ SV179 ) )
= $true )
| ( ( ~ ( function @ SV179 ) )
= $true )
| ( ( function @ SV179 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1461]) ).
thf(1537,plain,
! [SV180: $i] :
( ( ( empty @ SV180 )
= $false )
| ( ( ~ ( relation @ SV180 ) )
= $true )
| ( ( ~ ( function @ SV180 ) )
= $true )
| ( ( relation @ SV180 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1462]) ).
thf(1538,plain,
! [SV140: $i,SV51: $i,SV156: $i,SV219: $i] :
( ( ( ~ ( in @ SV219 @ ( relation_dom @ SV156 ) )
| ~ ( in @ ( ordered_pair @ SV219 @ SV51 ) @ SV156 ) )
= $true )
| ( ( ~ ( in @ SV219 @ SV140 ) )
= $true )
| ( ( in @ SV51 @ ( relation_image @ SV156 @ SV140 ) )
= $true )
| ( ( relation @ SV156 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1464]) ).
thf(1539,plain,
! [SV51: $i,SV141: $i,SV157: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK47_D @ SV157 @ SV141 @ SV51 ) @ ( relation_dom @ SV157 ) )
| ~ ( in @ ( ordered_pair @ ( sK47_D @ SV157 @ SV141 @ SV51 ) @ SV51 ) @ SV157 ) )
| ~ ( in @ ( sK47_D @ SV157 @ SV141 @ SV51 ) @ SV141 ) )
= $false )
| ( ( in @ SV51 @ ( relation_image @ SV157 @ SV141 ) )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1465]) ).
thf(1540,plain,
! [SV52: $i,SV181: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_C @ SV181 @ SV52 ) @ ( sK15_SY3113 @ SV181 @ SV52 ) ) @ SV181 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY3113 @ SV181 @ SV52 ) @ ( sK14_C @ SV181 @ SV52 ) ) @ SV52 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SV181 @ SV52 ) @ ( sK15_SY3113 @ SV181 @ SV52 ) ) @ SV181 )
| ( in @ ( ordered_pair @ ( sK15_SY3113 @ SV181 @ SV52 ) @ ( sK14_C @ SV181 @ SV52 ) ) @ SV52 ) ) )
= $false )
| ( ( SV181
= ( relation_inverse @ SV52 ) )
= $true )
| ( ( relation @ SV181 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1466]) ).
thf(1541,plain,
! [SV52: $i,SV182: $i] :
( ( ( SV182
= ( relation_inverse @ SV52 ) )
= $false )
| ( ( ~ ( ~ ! [SY3402: $i,SY3403: $i] :
( ~ ( in @ ( ordered_pair @ SY3402 @ SY3403 ) @ SV182 )
| ( in @ ( ordered_pair @ SY3403 @ SY3402 ) @ SV52 ) )
| ~ ! [SY3404: $i,SY3405: $i] :
( ~ ( in @ ( ordered_pair @ SY3405 @ SY3404 ) @ SV52 )
| ( in @ ( ordered_pair @ SY3404 @ SY3405 ) @ SV182 ) ) ) )
= $true )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1467]) ).
thf(1542,plain,
! [SV123: $i,SV142: $i] :
( ( ( ( ( sK39_C @ SV142 @ SV123 )
!= ( sK40_SY3129 @ SV142 @ SV123 ) )
| ~ ( in @ ( sK39_C @ SV142 @ SV123 ) @ SV123 )
| ~ ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 ) )
= $true )
| ( ( SV142
= ( identity_relation @ SV123 ) )
= $true )
| ( ( relation @ SV142 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1470]) ).
thf(1543,plain,
! [SV123: $i,SV142: $i] :
( ( ( ~ ( ~ ( ( ( sK39_C @ SV142 @ SV123 )
= ( sK40_SY3129 @ SV142 @ SV123 ) )
| ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 ) )
| ~ ( ( in @ ( sK39_C @ SV142 @ SV123 ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 ) ) ) )
= $true )
| ( ( SV142
= ( identity_relation @ SV123 ) )
= $true )
| ( ( relation @ SV142 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1471]) ).
thf(1544,plain,
! [SV143: $i,SV124: $i] :
( ( ( ~ ! [SY3360: $i,SY3361: $i] :
( ( SY3360 != SY3361 )
| ~ ( in @ SY3360 @ SV124 )
| ( in @ ( ordered_pair @ SY3360 @ SY3361 ) @ SV143 ) ) )
= $false )
| ( ( SV143
= ( identity_relation @ SV124 ) )
= $false )
| ( ( relation @ SV143 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1545,plain,
! [SV124: $i,SV143: $i] :
( ( ( ~ ~ ( ~ ! [SY3362: $i,SY3363: $i] :
( ~ ( in @ ( ordered_pair @ SY3362 @ SY3363 ) @ SV143 )
| ( SY3362 = SY3363 ) )
| ~ ! [SY3364: $i] :
( ! [SY3365: $i] :
~ ( in @ ( ordered_pair @ SY3364 @ SY3365 ) @ SV143 )
| ( in @ SY3364 @ SV124 ) ) ) )
= $false )
| ( ( SV143
= ( identity_relation @ SV124 ) )
= $false )
| ( ( relation @ SV143 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1546,plain,
! [SV53: $i,SV82: $i,SV199: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) @ SV53 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV82 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 ) )
| ~ ~ ( ~ ( ( in @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) @ SV53 )
| ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV82 )
| ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 ) ) ) ) )
= $true )
| ( ( SV199
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $true )
| ( ( relation @ SV199 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1473]) ).
thf(1547,plain,
! [SV82: $i,SV53: $i,SV200: $i] :
( ( ( ( SV200
!= ( relation_rng_restriction @ SV53 @ SV82 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3429: $i,SY3430: $i] :
( ~ ( in @ SY3430 @ SV53 )
| ~ ( in @ ( ordered_pair @ SY3429 @ SY3430 ) @ SV82 )
| ( in @ ( ordered_pair @ SY3429 @ SY3430 ) @ SV200 ) )
| ~ ~ ( ~ ! [SY3431: $i,SY3432: $i] :
( ~ ( in @ ( ordered_pair @ SY3431 @ SY3432 ) @ SV200 )
| ( in @ SY3432 @ SV53 ) )
| ~ ! [SY3433: $i,SY3434: $i] :
( ~ ( in @ ( ordered_pair @ SY3433 @ SY3434 ) @ SV200 )
| ( in @ ( ordered_pair @ SY3433 @ SY3434 ) @ SV82 ) ) ) ) )
= $true )
| ( ( relation @ SV200 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1474]) ).
thf(1548,plain,
! [SV183: $i,SV54: $i] :
( ( ( subset @ SV54 @ SV183 )
= $false )
| ( ( subset @ ( relation_dom @ SV54 ) @ ( relation_dom @ SV183 ) )
= $true )
| ( ( relation @ SV183 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1475]) ).
thf(1549,plain,
! [SV184: $i,SV54: $i] :
( ( ( subset @ SV54 @ SV184 )
= $false )
| ( ( subset @ ( relation_rng @ SV54 ) @ ( relation_rng @ SV184 ) )
= $true )
| ( ( relation @ SV184 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1476]) ).
thf(1550,plain,
! [SV83: $i,SV55: $i,SV220: $i] :
( ( ( ~ ( function @ SV220 )
| ~ ( relation @ SV220 ) )
= $true )
| ( ( ~ ( in @ SV55 @ ( relation_dom @ SV220 ) )
| ~ ( in @ ( apply @ SV220 @ SV55 ) @ ( relation_dom @ SV83 ) )
| ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SV220 @ SV83 ) ) ) )
= $true )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1477]) ).
thf(1551,plain,
! [SV83: $i,SV55: $i] :
( ( ( ~ ! [SY3321: $i] :
( ~ ( function @ SY3321 )
| ~ ( relation @ SY3321 )
| ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3321 @ SV83 ) ) )
| ( in @ SV55 @ ( relation_dom @ SY3321 ) ) ) )
= $false )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1478]) ).
thf(1552,plain,
! [SV83: $i,SV55: $i] :
( ( ( ~ ! [SY3322: $i] :
( ~ ( function @ SY3322 )
| ~ ( relation @ SY3322 )
| ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3322 @ SV83 ) ) )
| ( in @ ( apply @ SY3322 @ SV55 ) @ ( relation_dom @ SV83 ) ) ) )
= $false )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1478]) ).
thf(1553,plain,
! [SV158: $i,SV146: $i,SV56: $i] :
( ( ( in @ SV56 @ SV146 )
= $false )
| ( ( ~ ( in @ SV56 @ ( relation_dom @ SV158 ) ) )
= $true )
| ( ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SV158 @ SV146 ) ) )
= $true )
| ( ( relation @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1479]) ).
thf(1554,plain,
! [SV201: $i,SV56: $i,SV212: $i] :
( ( ( relation @ SV212 )
= $false )
| ( ( ~ ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SV212 @ SV201 ) ) )
| ( in @ SV56 @ SV201 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1480]) ).
thf(1555,plain,
! [SV202: $i,SV56: $i,SV213: $i] :
( ( ( relation @ SV213 )
= $false )
| ( ( ~ ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SV213 @ SV202 ) ) )
| ( in @ SV56 @ ( relation_dom @ SV213 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1481]) ).
thf(1556,plain,
! [SV149: $i,SV58: $i,SV161: $i,SV221: $i] :
( ( ( ~ ( in @ SV221 @ ( relation_rng @ SV161 ) )
| ~ ( in @ ( ordered_pair @ SV58 @ SV221 ) @ SV161 ) )
= $true )
| ( ( ~ ( in @ SV221 @ SV149 ) )
= $true )
| ( ( in @ SV58 @ ( relation_inverse_image @ SV161 @ SV149 ) )
= $true )
| ( ( relation @ SV161 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1484]) ).
thf(1557,plain,
! [SV58: $i,SV150: $i,SV162: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK46_D @ SV162 @ SV150 @ SV58 ) @ ( relation_rng @ SV162 ) )
| ~ ( in @ ( ordered_pair @ SV58 @ ( sK46_D @ SV162 @ SV150 @ SV58 ) ) @ SV162 ) )
| ~ ( in @ ( sK46_D @ SV162 @ SV150 @ SV58 ) @ SV150 ) )
= $false )
| ( ( in @ SV58 @ ( relation_inverse_image @ SV162 @ SV150 ) )
= $false )
| ( ( relation @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1485]) ).
thf(1558,plain,
! [SV59: $i,SV185: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SV185 @ SV59 ) @ ( sK23_SY3118 @ SV185 @ SV59 ) ) @ SV59 )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_C @ SV185 @ SV59 ) @ ( sK23_SY3118 @ SV185 @ SV59 ) ) @ SV185 ) )
= $false )
| ( ( subset @ SV59 @ SV185 )
= $true )
| ( ( relation @ SV185 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1486]) ).
thf(1559,plain,
! [SV186: $i,SV59: $i] :
( ( ( subset @ SV59 @ SV186 )
= $false )
| ( ( ! [SY3406: $i,SY3407: $i] :
( ~ ( in @ ( ordered_pair @ SY3406 @ SY3407 ) @ SV59 )
| ( in @ ( ordered_pair @ SY3406 @ SY3407 ) @ SV186 ) ) )
= $true )
| ( ( relation @ SV186 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1487]) ).
thf(1560,plain,
! [SV60: $i,SV187: $i,SV203: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ SV187 )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV60 )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 ) )
| ~ ~ ( ~ ( ( in @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ SV187 )
| ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV60 )
| ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 ) ) ) ) )
= $true )
| ( ( SV203
= ( relation_dom_restriction @ SV60 @ SV187 ) )
= $true )
| ( ( relation @ SV203 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1488]) ).
thf(1561,plain,
! [SV188: $i,SV60: $i,SV204: $i] :
( ( ( ( SV204
!= ( relation_dom_restriction @ SV60 @ SV188 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3437: $i,SY3438: $i] :
( ~ ( in @ SY3437 @ SV188 )
| ~ ( in @ ( ordered_pair @ SY3437 @ SY3438 ) @ SV60 )
| ( in @ ( ordered_pair @ SY3437 @ SY3438 ) @ SV204 ) )
| ~ ~ ( ~ ! [SY3439: $i] :
( ! [SY3440: $i] :
~ ( in @ ( ordered_pair @ SY3439 @ SY3440 ) @ SV204 )
| ( in @ SY3439 @ SV188 ) )
| ~ ! [SY3441: $i,SY3442: $i] :
( ~ ( in @ ( ordered_pair @ SY3441 @ SY3442 ) @ SV204 )
| ( in @ ( ordered_pair @ SY3441 @ SY3442 ) @ SV60 ) ) ) ) )
= $true )
| ( ( relation @ SV204 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1489]) ).
thf(1562,plain,
! [SV71: $i,SV163: $i,SV14: $i] :
( ( ( ~ ( in @ SV14 @ ( relation_dom @ ( relation_composition @ SV163 @ SV71 ) ) ) )
= $true )
| ( ( ( apply @ ( relation_composition @ SV163 @ SV71 ) @ SV14 )
= ( apply @ SV71 @ ( apply @ SV163 @ SV14 ) ) )
= $true )
| ( ( function @ SV163 )
= $false )
| ( ( relation @ SV163 )
= $false )
| ( ( function @ SV71 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1490]) ).
thf(1563,plain,
! [SV164: $i,SV72: $i,SV15: $i] :
( ( ( ~ ( in @ SV15 @ ( relation_dom @ SV72 ) ) )
= $true )
| ( ( ( apply @ ( relation_composition @ SV72 @ SV164 ) @ SV15 )
= ( apply @ SV164 @ ( apply @ SV72 @ SV15 ) ) )
= $true )
| ( ( function @ SV164 )
= $false )
| ( ( relation @ SV164 )
= $false )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1491]) ).
thf(1564,plain,
! [SV39: $i,SV151: $i,SV129: $i] :
( ( ( ( SV129
!= ( apply @ SV151 @ SV39 ) ) )
= $true )
| ( ( ~ ( in @ SV39 @ ( relation_dom @ SV151 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV39 @ SV129 ) @ SV151 )
= $true )
| ( ( function @ SV151 )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1492]) ).
thf(1565,plain,
! [SV189: $i,SV39: $i,SV205: $i] :
( ( ( function @ SV205 )
= $false )
| ( ( ~ ( relation @ SV205 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV39 @ SV189 ) @ SV205 )
| ( SV189
= ( apply @ SV205 @ SV39 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1493]) ).
thf(1566,plain,
! [SV190: $i,SV39: $i,SV206: $i] :
( ( ( function @ SV206 )
= $false )
| ( ( ~ ( relation @ SV206 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV39 @ SV190 ) @ SV206 )
| ( in @ SV39 @ ( relation_dom @ SV206 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1494]) ).
thf(1567,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ( function @ SV222 )
| ~ ( relation @ SV222 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) )
| ( SV222
= ( function_inverse @ SV40 ) ) )
= $true )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1495]) ).
thf(1568,plain,
! [SV40: $i] :
( ( ( ~ ! [SY3169: $i] :
( ~ ( function @ SY3169 )
| ~ ( relation @ SY3169 )
| ( SY3169
!= ( function_inverse @ SV40 ) )
| ~ ( ~ ~ ( ~ ! [SY3170: $i,SY3171: $i] :
( ( SY3171
!= ( apply @ SY3169 @ SY3170 ) )
| ~ ( in @ SY3170 @ ( relation_rng @ SV40 ) )
| ( SY3170
= ( apply @ SV40 @ SY3171 ) ) )
| ~ ! [SY3172: $i,SY3173: $i] :
( ( SY3173
!= ( apply @ SY3169 @ SY3172 ) )
| ~ ( in @ SY3172 @ ( relation_rng @ SV40 ) )
| ( in @ SY3173 @ ( relation_dom @ SV40 ) ) ) )
| ~ ~ ( ~ ! [SY3174: $i,SY3175: $i] :
( ( SY3174
!= ( apply @ SV40 @ SY3175 ) )
| ~ ( in @ SY3175 @ ( relation_dom @ SV40 ) )
| ( SY3175
= ( apply @ SY3169 @ SY3174 ) ) )
| ~ ! [SY3176: $i] :
( ! [SY3177: $i] :
( ( SY3176
!= ( apply @ SV40 @ SY3177 ) )
| ~ ( in @ SY3177 @ ( relation_dom @ SV40 ) ) )
| ( in @ SY3176 @ ( relation_rng @ SV40 ) ) ) ) ) ) )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1496]) ).
thf(1569,plain,
! [SV40: $i] :
( ( ( ~ ! [SY3178: $i] :
( ~ ( function @ SY3178 )
| ~ ( relation @ SY3178 )
| ( SY3178
!= ( function_inverse @ SV40 ) )
| ( ( relation_dom @ SY3178 )
= ( relation_rng @ SV40 ) ) ) )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1496]) ).
thf(1570,plain,
! [SV41: $i,SV165: $i,SV191: $i] :
( ( ( ! [SY3418: $i] :
( ~ ( in @ ( ordered_pair @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SY3418 ) @ SV41 )
| ~ ( in @ SY3418 @ SV165 ) )
| ~ ( in @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SV191 ) )
= $true )
| ( ( SV191
= ( relation_inverse_image @ SV41 @ SV165 ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1497]) ).
thf(1571,plain,
! [SV41: $i,SV165: $i,SV191: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ ( sK31_SY3124 @ SV191 @ SV165 @ SV41 ) ) @ SV41 )
| ~ ( in @ ( sK31_SY3124 @ SV191 @ SV165 @ SV41 ) @ SV165 ) )
| ( in @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SV191 ) )
= $true )
| ( ( SV191
= ( relation_inverse_image @ SV41 @ SV165 ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1498]) ).
thf(1572,plain,
! [SV192: $i,SV166: $i,SV41: $i] :
( ( ( ~ ! [SY3419: $i] :
( ! [SY3379: $i] :
( ~ ( in @ ( ordered_pair @ SY3419 @ SY3379 ) @ SV41 )
| ~ ( in @ SY3379 @ SV166 ) )
| ( in @ SY3419 @ SV192 ) ) )
= $false )
| ( ( SV192
= ( relation_inverse_image @ SV41 @ SV166 ) )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1499]) ).
thf(1573,plain,
! [SV41: $i,SV166: $i,SV192: $i] :
( ( ( ~ ! [SY3421: $i] :
( ~ ( in @ SY3421 @ SV192 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3421 @ ( sK29_E @ SY3421 @ SV192 @ SV166 @ SV41 ) ) @ SV41 )
| ~ ( in @ ( sK29_E @ SY3421 @ SV192 @ SV166 @ SV41 ) @ SV166 ) ) ) )
= $false )
| ( ( SV192
= ( relation_inverse_image @ SV41 @ SV166 ) )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1499]) ).
thf(1574,plain,
! [SV42: $i,SV167: $i] :
( ( ( ! [SY3381: $i] :
~ ( in @ ( ordered_pair @ SY3381 @ ( sK17_C @ SV167 @ SV42 ) ) @ SV42 ) )
= $true )
| ( ( ~ ( in @ ( sK17_C @ SV167 @ SV42 ) @ SV167 ) )
= $true )
| ( ( SV167
= ( relation_rng @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1500]) ).
thf(1575,plain,
! [SV42: $i,SV167: $i] :
( ( ( in @ ( ordered_pair @ ( sK18_SY3115 @ SV167 @ SV42 ) @ ( sK17_C @ SV167 @ SV42 ) ) @ SV42 )
= $true )
| ( ( in @ ( sK17_C @ SV167 @ SV42 ) @ SV167 )
= $true )
| ( ( SV167
= ( relation_rng @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1501]) ).
thf(1576,plain,
! [SV168: $i,SV42: $i] :
( ( ( ! [SY3382: $i] :
( ! [SY3191: $i] :
~ ( in @ ( ordered_pair @ SY3191 @ SY3382 ) @ SV42 )
| ( in @ SY3382 @ SV168 ) ) )
= $true )
| ( ( SV168
= ( relation_rng @ SV42 ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1502]) ).
thf(1577,plain,
! [SV42: $i,SV168: $i] :
( ( ( ! [SY3384: $i] :
( ~ ( in @ SY3384 @ SV168 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3384 @ SV168 @ SV42 ) @ SY3384 ) @ SV42 ) ) )
= $true )
| ( ( SV168
= ( relation_rng @ SV42 ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1503]) ).
thf(1578,plain,
! [SV92: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK12_B @ SV92 ) @ ( relation_dom @ SV92 ) )
| ~ ( in @ ( sK13_SY3112 @ SV92 ) @ ( relation_dom @ SV92 ) ) )
| ( ( apply @ SV92 @ ( sK12_B @ SV92 ) )
!= ( apply @ SV92 @ ( sK13_SY3112 @ SV92 ) ) ) ) )
= $true )
| ( ( one_to_one @ SV92 )
= $true )
| ( ( function @ SV92 )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1504]) ).
thf(1579,plain,
! [SV92: $i] :
( ( ( ( ( sK12_B @ SV92 )
!= ( sK13_SY3112 @ SV92 ) ) )
= $true )
| ( ( one_to_one @ SV92 )
= $true )
| ( ( function @ SV92 )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1505]) ).
thf(1580,plain,
! [SV224: $i,SV93: $i,SV223: $i] :
( ( ( ~ ( in @ SV223 @ ( relation_dom @ SV93 ) )
| ~ ( in @ SV224 @ ( relation_dom @ SV93 ) )
| ( ( apply @ SV93 @ SV223 )
!= ( apply @ SV93 @ SV224 ) )
| ( SV223 = SV224 ) )
= $true )
| ( ( one_to_one @ SV93 )
= $false )
| ( ( function @ SV93 )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(1581,plain,
! [SV43: $i,SV94: $i,SV214: $i] :
( ( ( relation @ SV214 )
= $false )
| ( ( ~ ( ~ ( ! [SY3446: $i] :
( ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ SY3446 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3446 @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV94 ) )
| ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV214 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK11_SY3111 @ SV214 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY3111 @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV94 ) )
| ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV214 ) ) )
| ( SV214
= ( relation_composition @ SV43 @ SV94 ) ) )
= $true )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1507]) ).
thf(1582,plain,
! [SV94: $i,SV43: $i,SV215: $i] :
( ( ( relation @ SV215 )
= $false )
| ( ( ( SV215
!= ( relation_composition @ SV43 @ SV94 ) )
| ~ ( ~ ! [SY3447: $i,SY3448: $i] :
( ! [SY3330: $i] :
( ~ ( in @ ( ordered_pair @ SY3447 @ SY3330 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3330 @ SY3448 ) @ SV94 ) )
| ( in @ ( ordered_pair @ SY3447 @ SY3448 ) @ SV215 ) )
| ~ ! [SY3450: $i,SY3451: $i] :
( ~ ( in @ ( ordered_pair @ SY3450 @ SY3451 ) @ SV215 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3450 @ ( sK8_F @ SY3451 @ SY3450 @ SV215 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK8_F @ SY3451 @ SY3450 @ SV215 @ SV94 @ SV43 ) @ SY3451 ) @ SV94 ) ) ) ) )
= $true )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1508]) ).
thf(1583,plain,
! [SV44: $i,SV169: $i] :
( ( ( ! [SY3385: $i] :
~ ( in @ ( ordered_pair @ ( sK20_C @ SV169 @ SV44 ) @ SY3385 ) @ SV44 ) )
= $true )
| ( ( ~ ( in @ ( sK20_C @ SV169 @ SV44 ) @ SV169 ) )
= $true )
| ( ( SV169
= ( relation_dom @ SV44 ) )
= $true )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1509]) ).
thf(1584,plain,
! [SV44: $i,SV169: $i] :
( ( ( in @ ( ordered_pair @ ( sK20_C @ SV169 @ SV44 ) @ ( sK21_SY3117 @ SV169 @ SV44 ) ) @ SV44 )
= $true )
| ( ( in @ ( sK20_C @ SV169 @ SV44 ) @ SV169 )
= $true )
| ( ( SV169
= ( relation_dom @ SV44 ) )
= $true )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1510]) ).
thf(1585,plain,
! [SV170: $i,SV44: $i] :
( ( ( ! [SY3386: $i] :
( ! [SY3206: $i] :
~ ( in @ ( ordered_pair @ SY3386 @ SY3206 ) @ SV44 )
| ( in @ SY3386 @ SV170 ) ) )
= $true )
| ( ( SV170
= ( relation_dom @ SV44 ) )
= $false )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1511]) ).
thf(1586,plain,
! [SV44: $i,SV170: $i] :
( ( ( ! [SY3388: $i] :
( ~ ( in @ SY3388 @ SV170 )
| ( in @ ( ordered_pair @ SY3388 @ ( sK19_D @ SY3388 @ SV170 @ SV44 ) ) @ SV44 ) ) )
= $true )
| ( ( SV170
= ( relation_dom @ SV44 ) )
= $false )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1512]) ).
thf(1587,plain,
! [SV45: $i,SV225: $i] :
( ( ( ~ ( in @ SV225 @ ( relation_dom @ SV45 ) )
| ! [SY3453: $i] :
( ( SY3453
!= ( apply @ SV45 @ SV225 ) )
| ( in @ ( ordered_pair @ SV225 @ SY3453 ) @ SV45 ) ) )
= $true )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1513]) ).
thf(1588,plain,
! [SV45: $i,SV226: $i] :
( ( ( ~ ( in @ SV226 @ ( relation_dom @ SV45 ) )
| ! [SY3454: $i] :
( ~ ( in @ ( ordered_pair @ SV226 @ SY3454 ) @ SV45 )
| ( SY3454
= ( apply @ SV45 @ SV226 ) ) ) )
= $true )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1514]) ).
thf(1589,plain,
! [SV45: $i,SV227: $i] :
( ( ( ( in @ SV227 @ ( relation_dom @ SV45 ) )
| ! [SY3455: $i] :
( ( SY3455
!= ( apply @ SV45 @ SV227 ) )
| ( SY3455 = empty_set ) ) )
= $true )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1515]) ).
thf(1590,plain,
! [SV45: $i,SV228: $i] :
( ( ( ( in @ SV228 @ ( relation_dom @ SV45 ) )
| ! [SY3456: $i] :
( ( SY3456 != empty_set )
| ( SY3456
= ( apply @ SV45 @ SV228 ) ) ) )
= $true )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1516]) ).
thf(1591,plain,
! [SV130: $i,SV95: $i] :
( ( ( in @ SV95 @ ( relation_rng @ SV130 ) )
= $false )
| ( ( ~ ( one_to_one @ SV130 ) )
= $true )
| ( ( SV95
= ( apply @ SV130 @ ( apply @ ( function_inverse @ SV130 ) @ SV95 ) ) )
= $true )
| ( ( function @ SV130 )
= $false )
| ( ( relation @ SV130 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1517]) ).
thf(1592,plain,
! [SV131: $i,SV96: $i] :
( ( ( in @ SV96 @ ( relation_rng @ SV131 ) )
= $false )
| ( ( ~ ( one_to_one @ SV131 ) )
= $true )
| ( ( SV96
= ( apply @ ( relation_composition @ ( function_inverse @ SV131 ) @ SV131 ) @ SV96 ) )
= $true )
| ( ( function @ SV131 )
= $false )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1518]) ).
thf(1593,plain,
! [SV101: $i,SV134: $i] :
( ( ( ~ ( in @ ( sK45_C @ SV134 @ SV101 ) @ SV101 )
| ~ ( ( ( apply @ SV134 @ ( sK45_C @ SV134 @ SV101 ) )
!= ( sK45_C @ SV134 @ SV101 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV134 )
!= SV101 ) )
= $true )
| ( ( SV134
= ( identity_relation @ SV101 ) )
= $true )
| ( ( function @ SV134 )
= $false )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1519]) ).
thf(1594,plain,
! [SV171: $i,SV193: $i] :
( ( ( relation @ SV193 )
= $false )
| ( ( function @ SV193 )
= $false )
| ( ( ( SV193
!= ( identity_relation @ SV171 ) )
| ! [SY3422: $i] :
( ~ ( in @ SY3422 @ SV171 )
| ( ( apply @ SV193 @ SY3422 )
= SY3422 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1520]) ).
thf(1595,plain,
! [SV172: $i,SV194: $i] :
( ( ( relation @ SV194 )
= $false )
| ( ( function @ SV194 )
= $false )
| ( ( ( SV194
!= ( identity_relation @ SV172 ) )
| ( ( relation_dom @ SV194 )
= SV172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1521]) ).
thf(1596,plain,
! [SV174: $i,SV81: $i,SV154: $i,SV47: $i] :
( ( ( in @ SV47 @ SV154 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ SV174 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SV154 ) @ SV174 ) )
= $true )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1523]) ).
thf(1597,plain,
! [SV208: $i,SV81: $i,SV47: $i,SV217: $i] :
( ( ( relation @ SV217 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SV208 ) @ SV217 ) )
| ( in @ SV47 @ SV208 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1524]) ).
thf(1598,plain,
! [SV209: $i,SV81: $i,SV47: $i,SV218: $i] :
( ( ( relation @ SV218 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SV209 ) @ SV218 ) )
| ( in @ ( ordered_pair @ SV47 @ SV81 ) @ SV218 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1525]) ).
thf(1599,plain,
! [SV137: $i,SV155: $i,SV48: $i] :
( ( ( in @ SV48 @ ( relation_rng @ SV155 ) )
= $false )
| ( ( in @ SV48 @ SV137 )
= $false )
| ( ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SV137 @ SV155 ) ) )
= $true )
| ( ( relation @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1526]) ).
thf(1600,plain,
! [SV210: $i,SV195: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SV195 @ SV210 ) ) ) )
= $true )
| ( ( in @ SV48 @ SV195 )
= $true )
| ( ( relation @ SV210 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1527]) ).
thf(1601,plain,
! [SV211: $i,SV196: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SV196 @ SV211 ) ) ) )
= $true )
| ( ( in @ SV48 @ ( relation_rng @ SV211 ) )
= $true )
| ( ( relation @ SV211 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1528]) ).
thf(1602,plain,
! [SV49: $i,SV175: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV175 ) ) )
= $false )
| ( ( SV49 = SV175 )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1529]) ).
thf(1603,plain,
! [SV49: $i,SV175: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV49 )
| ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV175 ) ) )
= $false )
| ( ( SV49 = SV175 )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1529]) ).
thf(1604,plain,
! [SV176: $i,SV49: $i] :
( ( ( ~ ! [SY3392: $i,SY3393: $i] :
( ~ ( in @ ( ordered_pair @ SY3392 @ SY3393 ) @ SV49 )
| ( in @ ( ordered_pair @ SY3392 @ SY3393 ) @ SV176 ) )
| ~ ! [SY3394: $i,SY3395: $i] :
( ~ ( in @ ( ordered_pair @ SY3394 @ SY3395 ) @ SV176 )
| ( in @ ( ordered_pair @ SY3394 @ SY3395 ) @ SV49 ) ) )
= $false )
| ( ( SV49 = SV176 )
= $false )
| ( ( relation @ SV176 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1530]) ).
thf(1605,plain,
! [SV50: $i,SV177: $i,SV197: $i] :
( ( ( ! [SY3425: $i] :
( ~ ( in @ ( ordered_pair @ SY3425 @ ( sK33_D @ SV197 @ SV177 @ SV50 ) ) @ SV50 )
| ~ ( in @ SY3425 @ SV177 ) )
| ~ ( in @ ( sK33_D @ SV197 @ SV177 @ SV50 ) @ SV197 ) )
= $true )
| ( ( SV197
= ( relation_image @ SV50 @ SV177 ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1531]) ).
thf(1606,plain,
! [SV50: $i,SV177: $i,SV197: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK34_SY3126 @ SV197 @ SV177 @ SV50 ) @ ( sK33_D @ SV197 @ SV177 @ SV50 ) ) @ SV50 )
| ~ ( in @ ( sK34_SY3126 @ SV197 @ SV177 @ SV50 ) @ SV177 ) )
| ( in @ ( sK33_D @ SV197 @ SV177 @ SV50 ) @ SV197 ) )
= $true )
| ( ( SV197
= ( relation_image @ SV50 @ SV177 ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1532]) ).
thf(1607,plain,
! [SV198: $i,SV178: $i,SV50: $i] :
( ( ( ~ ! [SY3426: $i] :
( ! [SY3400: $i] :
( ~ ( in @ ( ordered_pair @ SY3400 @ SY3426 ) @ SV50 )
| ~ ( in @ SY3400 @ SV178 ) )
| ( in @ SY3426 @ SV198 ) ) )
= $false )
| ( ( SV198
= ( relation_image @ SV50 @ SV178 ) )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1533]) ).
thf(1608,plain,
! [SV50: $i,SV178: $i,SV198: $i] :
( ( ( ~ ! [SY3428: $i] :
( ~ ( in @ SY3428 @ SV198 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK32_E @ SY3428 @ SV198 @ SV178 @ SV50 ) @ SY3428 ) @ SV50 )
| ~ ( in @ ( sK32_E @ SY3428 @ SV198 @ SV178 @ SV50 ) @ SV178 ) ) ) )
= $false )
| ( ( SV198
= ( relation_image @ SV50 @ SV178 ) )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1533]) ).
thf(1609,plain,
! [SV110: $i,SV138: $i] :
( ( ( relation @ SV138 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false )
| ( ( ~ ( function @ SV138 ) )
= $true )
| ( ( function @ ( relation_composition @ SV110 @ SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1534]) ).
thf(1610,plain,
! [SV111: $i,SV139: $i] :
( ( ( relation @ SV139 )
= $false )
| ( ( function @ SV111 )
= $false )
| ( ( relation @ SV111 )
= $false )
| ( ( ~ ( function @ SV139 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV111 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1535]) ).
thf(1611,plain,
! [SV179: $i] :
( ( ( relation @ SV179 )
= $false )
| ( ( empty @ SV179 )
= $false )
| ( ( ~ ( function @ SV179 ) )
= $true )
| ( ( function @ SV179 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1536]) ).
thf(1612,plain,
! [SV180: $i] :
( ( ( relation @ SV180 )
= $false )
| ( ( empty @ SV180 )
= $false )
| ( ( ~ ( function @ SV180 ) )
= $true )
| ( ( relation @ SV180 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1537]) ).
thf(1613,plain,
! [SV140: $i,SV51: $i,SV156: $i,SV219: $i] :
( ( ( ~ ( in @ SV219 @ ( relation_dom @ SV156 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV219 @ SV51 ) @ SV156 ) )
= $true )
| ( ( ~ ( in @ SV219 @ SV140 ) )
= $true )
| ( ( in @ SV51 @ ( relation_image @ SV156 @ SV140 ) )
= $true )
| ( ( relation @ SV156 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1538]) ).
thf(1614,plain,
! [SV51: $i,SV141: $i,SV157: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK47_D @ SV157 @ SV141 @ SV51 ) @ ( relation_dom @ SV157 ) )
| ~ ( in @ ( ordered_pair @ ( sK47_D @ SV157 @ SV141 @ SV51 ) @ SV51 ) @ SV157 ) ) )
= $false )
| ( ( in @ SV51 @ ( relation_image @ SV157 @ SV141 ) )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1539]) ).
thf(1615,plain,
! [SV51: $i,SV141: $i,SV157: $i] :
( ( ( ~ ( in @ ( sK47_D @ SV157 @ SV141 @ SV51 ) @ SV141 ) )
= $false )
| ( ( in @ SV51 @ ( relation_image @ SV157 @ SV141 ) )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1539]) ).
thf(1616,plain,
! [SV52: $i,SV181: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_C @ SV181 @ SV52 ) @ ( sK15_SY3113 @ SV181 @ SV52 ) ) @ SV181 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY3113 @ SV181 @ SV52 ) @ ( sK14_C @ SV181 @ SV52 ) ) @ SV52 ) ) )
= $false )
| ( ( SV181
= ( relation_inverse @ SV52 ) )
= $true )
| ( ( relation @ SV181 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1540]) ).
thf(1617,plain,
! [SV52: $i,SV181: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SV181 @ SV52 ) @ ( sK15_SY3113 @ SV181 @ SV52 ) ) @ SV181 )
| ( in @ ( ordered_pair @ ( sK15_SY3113 @ SV181 @ SV52 ) @ ( sK14_C @ SV181 @ SV52 ) ) @ SV52 ) ) )
= $false )
| ( ( SV181
= ( relation_inverse @ SV52 ) )
= $true )
| ( ( relation @ SV181 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1540]) ).
thf(1618,plain,
! [SV52: $i,SV182: $i] :
( ( ( ~ ! [SY3402: $i,SY3403: $i] :
( ~ ( in @ ( ordered_pair @ SY3402 @ SY3403 ) @ SV182 )
| ( in @ ( ordered_pair @ SY3403 @ SY3402 ) @ SV52 ) )
| ~ ! [SY3404: $i,SY3405: $i] :
( ~ ( in @ ( ordered_pair @ SY3405 @ SY3404 ) @ SV52 )
| ( in @ ( ordered_pair @ SY3404 @ SY3405 ) @ SV182 ) ) )
= $false )
| ( ( SV182
= ( relation_inverse @ SV52 ) )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1541]) ).
thf(1619,plain,
! [SV123: $i,SV142: $i] :
( ( ( ( ( sK39_C @ SV142 @ SV123 )
!= ( sK40_SY3129 @ SV142 @ SV123 ) )
| ~ ( in @ ( sK39_C @ SV142 @ SV123 ) @ SV123 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 ) )
= $true )
| ( ( SV142
= ( identity_relation @ SV123 ) )
= $true )
| ( ( relation @ SV142 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1542]) ).
thf(1620,plain,
! [SV123: $i,SV142: $i] :
( ( ( ~ ( ( ( sK39_C @ SV142 @ SV123 )
= ( sK40_SY3129 @ SV142 @ SV123 ) )
| ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 ) )
| ~ ( ( in @ ( sK39_C @ SV142 @ SV123 ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 ) ) )
= $false )
| ( ( SV142
= ( identity_relation @ SV123 ) )
= $true )
| ( ( relation @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1543]) ).
thf(1621,plain,
! [SV143: $i,SV124: $i] :
( ( ( ! [SY3360: $i,SY3361: $i] :
( ( SY3360 != SY3361 )
| ~ ( in @ SY3360 @ SV124 )
| ( in @ ( ordered_pair @ SY3360 @ SY3361 ) @ SV143 ) ) )
= $true )
| ( ( SV143
= ( identity_relation @ SV124 ) )
= $false )
| ( ( relation @ SV143 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1544]) ).
thf(1622,plain,
! [SV124: $i,SV143: $i] :
( ( ( ~ ( ~ ! [SY3362: $i,SY3363: $i] :
( ~ ( in @ ( ordered_pair @ SY3362 @ SY3363 ) @ SV143 )
| ( SY3362 = SY3363 ) )
| ~ ! [SY3364: $i] :
( ! [SY3365: $i] :
~ ( in @ ( ordered_pair @ SY3364 @ SY3365 ) @ SV143 )
| ( in @ SY3364 @ SV124 ) ) ) )
= $true )
| ( ( SV143
= ( identity_relation @ SV124 ) )
= $false )
| ( ( relation @ SV143 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1545]) ).
thf(1623,plain,
! [SV53: $i,SV82: $i,SV199: $i] :
( ( ( ~ ( ~ ( in @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) @ SV53 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV82 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 ) )
| ~ ~ ( ~ ( ( in @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) @ SV53 )
| ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV82 )
| ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 ) ) ) )
= $false )
| ( ( SV199
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $true )
| ( ( relation @ SV199 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1546]) ).
thf(1624,plain,
! [SV82: $i,SV53: $i,SV200: $i] :
( ( ( SV200
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $false )
| ( ( ~ ( ~ ! [SY3429: $i,SY3430: $i] :
( ~ ( in @ SY3430 @ SV53 )
| ~ ( in @ ( ordered_pair @ SY3429 @ SY3430 ) @ SV82 )
| ( in @ ( ordered_pair @ SY3429 @ SY3430 ) @ SV200 ) )
| ~ ~ ( ~ ! [SY3431: $i,SY3432: $i] :
( ~ ( in @ ( ordered_pair @ SY3431 @ SY3432 ) @ SV200 )
| ( in @ SY3432 @ SV53 ) )
| ~ ! [SY3433: $i,SY3434: $i] :
( ~ ( in @ ( ordered_pair @ SY3433 @ SY3434 ) @ SV200 )
| ( in @ ( ordered_pair @ SY3433 @ SY3434 ) @ SV82 ) ) ) ) )
= $true )
| ( ( relation @ SV200 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1547]) ).
thf(1625,plain,
! [SV83: $i,SV55: $i,SV220: $i] :
( ( ( ~ ( function @ SV220 ) )
= $true )
| ( ( ~ ( relation @ SV220 ) )
= $true )
| ( ( ~ ( in @ SV55 @ ( relation_dom @ SV220 ) )
| ~ ( in @ ( apply @ SV220 @ SV55 ) @ ( relation_dom @ SV83 ) )
| ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SV220 @ SV83 ) ) ) )
= $true )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1550]) ).
thf(1626,plain,
! [SV83: $i,SV55: $i] :
( ( ( ! [SY3321: $i] :
( ~ ( function @ SY3321 )
| ~ ( relation @ SY3321 )
| ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3321 @ SV83 ) ) )
| ( in @ SV55 @ ( relation_dom @ SY3321 ) ) ) )
= $true )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1551]) ).
thf(1627,plain,
! [SV83: $i,SV55: $i] :
( ( ( ! [SY3322: $i] :
( ~ ( function @ SY3322 )
| ~ ( relation @ SY3322 )
| ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SY3322 @ SV83 ) ) )
| ( in @ ( apply @ SY3322 @ SV55 ) @ ( relation_dom @ SV83 ) ) ) )
= $true )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1552]) ).
thf(1628,plain,
! [SV146: $i,SV158: $i,SV56: $i] :
( ( ( in @ SV56 @ ( relation_dom @ SV158 ) )
= $false )
| ( ( in @ SV56 @ SV146 )
= $false )
| ( ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SV158 @ SV146 ) ) )
= $true )
| ( ( relation @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1553]) ).
thf(1629,plain,
! [SV201: $i,SV212: $i,SV56: $i] :
( ( ( ~ ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SV212 @ SV201 ) ) ) )
= $true )
| ( ( in @ SV56 @ SV201 )
= $true )
| ( ( relation @ SV212 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1554]) ).
thf(1630,plain,
! [SV202: $i,SV213: $i,SV56: $i] :
( ( ( ~ ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SV213 @ SV202 ) ) ) )
= $true )
| ( ( in @ SV56 @ ( relation_dom @ SV213 ) )
= $true )
| ( ( relation @ SV213 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1555]) ).
thf(1631,plain,
! [SV149: $i,SV58: $i,SV161: $i,SV221: $i] :
( ( ( ~ ( in @ SV221 @ ( relation_rng @ SV161 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV58 @ SV221 ) @ SV161 ) )
= $true )
| ( ( ~ ( in @ SV221 @ SV149 ) )
= $true )
| ( ( in @ SV58 @ ( relation_inverse_image @ SV161 @ SV149 ) )
= $true )
| ( ( relation @ SV161 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1556]) ).
thf(1632,plain,
! [SV58: $i,SV150: $i,SV162: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK46_D @ SV162 @ SV150 @ SV58 ) @ ( relation_rng @ SV162 ) )
| ~ ( in @ ( ordered_pair @ SV58 @ ( sK46_D @ SV162 @ SV150 @ SV58 ) ) @ SV162 ) ) )
= $false )
| ( ( in @ SV58 @ ( relation_inverse_image @ SV162 @ SV150 ) )
= $false )
| ( ( relation @ SV162 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1557]) ).
thf(1633,plain,
! [SV58: $i,SV150: $i,SV162: $i] :
( ( ( ~ ( in @ ( sK46_D @ SV162 @ SV150 @ SV58 ) @ SV150 ) )
= $false )
| ( ( in @ SV58 @ ( relation_inverse_image @ SV162 @ SV150 ) )
= $false )
| ( ( relation @ SV162 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1557]) ).
thf(1634,plain,
! [SV59: $i,SV185: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SV185 @ SV59 ) @ ( sK23_SY3118 @ SV185 @ SV59 ) ) @ SV59 ) )
= $false )
| ( ( subset @ SV59 @ SV185 )
= $true )
| ( ( relation @ SV185 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1558]) ).
thf(1635,plain,
! [SV59: $i,SV185: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK22_C @ SV185 @ SV59 ) @ ( sK23_SY3118 @ SV185 @ SV59 ) ) @ SV185 ) )
= $false )
| ( ( subset @ SV59 @ SV185 )
= $true )
| ( ( relation @ SV185 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1558]) ).
thf(1636,plain,
! [SV186: $i,SV59: $i,SV229: $i] :
( ( ( ! [SY3457: $i] :
( ~ ( in @ ( ordered_pair @ SV229 @ SY3457 ) @ SV59 )
| ( in @ ( ordered_pair @ SV229 @ SY3457 ) @ SV186 ) ) )
= $true )
| ( ( subset @ SV59 @ SV186 )
= $false )
| ( ( relation @ SV186 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1559]) ).
thf(1637,plain,
! [SV60: $i,SV187: $i,SV203: $i] :
( ( ( ~ ( ~ ( in @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ SV187 )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV60 )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 ) )
| ~ ~ ( ~ ( ( in @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ SV187 )
| ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV60 )
| ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 ) ) ) )
= $false )
| ( ( SV203
= ( relation_dom_restriction @ SV60 @ SV187 ) )
= $true )
| ( ( relation @ SV203 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1560]) ).
thf(1638,plain,
! [SV188: $i,SV60: $i,SV204: $i] :
( ( ( SV204
= ( relation_dom_restriction @ SV60 @ SV188 ) )
= $false )
| ( ( ~ ( ~ ! [SY3437: $i,SY3438: $i] :
( ~ ( in @ SY3437 @ SV188 )
| ~ ( in @ ( ordered_pair @ SY3437 @ SY3438 ) @ SV60 )
| ( in @ ( ordered_pair @ SY3437 @ SY3438 ) @ SV204 ) )
| ~ ~ ( ~ ! [SY3439: $i] :
( ! [SY3440: $i] :
~ ( in @ ( ordered_pair @ SY3439 @ SY3440 ) @ SV204 )
| ( in @ SY3439 @ SV188 ) )
| ~ ! [SY3441: $i,SY3442: $i] :
( ~ ( in @ ( ordered_pair @ SY3441 @ SY3442 ) @ SV204 )
| ( in @ ( ordered_pair @ SY3441 @ SY3442 ) @ SV60 ) ) ) ) )
= $true )
| ( ( relation @ SV204 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1561]) ).
thf(1639,plain,
! [SV71: $i,SV163: $i,SV14: $i] :
( ( ( in @ SV14 @ ( relation_dom @ ( relation_composition @ SV163 @ SV71 ) ) )
= $false )
| ( ( ( apply @ ( relation_composition @ SV163 @ SV71 ) @ SV14 )
= ( apply @ SV71 @ ( apply @ SV163 @ SV14 ) ) )
= $true )
| ( ( function @ SV163 )
= $false )
| ( ( relation @ SV163 )
= $false )
| ( ( function @ SV71 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1562]) ).
thf(1640,plain,
! [SV164: $i,SV72: $i,SV15: $i] :
( ( ( in @ SV15 @ ( relation_dom @ SV72 ) )
= $false )
| ( ( ( apply @ ( relation_composition @ SV72 @ SV164 ) @ SV15 )
= ( apply @ SV164 @ ( apply @ SV72 @ SV15 ) ) )
= $true )
| ( ( function @ SV164 )
= $false )
| ( ( relation @ SV164 )
= $false )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1563]) ).
thf(1641,plain,
! [SV39: $i,SV151: $i,SV129: $i] :
( ( ( SV129
= ( apply @ SV151 @ SV39 ) )
= $false )
| ( ( ~ ( in @ SV39 @ ( relation_dom @ SV151 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV39 @ SV129 ) @ SV151 )
= $true )
| ( ( function @ SV151 )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1564]) ).
thf(1642,plain,
! [SV189: $i,SV39: $i,SV205: $i] :
( ( ( relation @ SV205 )
= $false )
| ( ( function @ SV205 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV39 @ SV189 ) @ SV205 )
| ( SV189
= ( apply @ SV205 @ SV39 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1565]) ).
thf(1643,plain,
! [SV190: $i,SV39: $i,SV206: $i] :
( ( ( relation @ SV206 )
= $false )
| ( ( function @ SV206 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV39 @ SV190 ) @ SV206 )
| ( in @ SV39 @ ( relation_dom @ SV206 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1566]) ).
thf(1644,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ( function @ SV222 ) )
= $true )
| ( ( ~ ( relation @ SV222 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) )
| ( SV222
= ( function_inverse @ SV40 ) ) )
= $true )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1567]) ).
thf(1645,plain,
! [SV40: $i] :
( ( ( ! [SY3169: $i] :
( ~ ( function @ SY3169 )
| ~ ( relation @ SY3169 )
| ( SY3169
!= ( function_inverse @ SV40 ) )
| ~ ( ~ ~ ( ~ ! [SY3170: $i,SY3171: $i] :
( ( SY3171
!= ( apply @ SY3169 @ SY3170 ) )
| ~ ( in @ SY3170 @ ( relation_rng @ SV40 ) )
| ( SY3170
= ( apply @ SV40 @ SY3171 ) ) )
| ~ ! [SY3172: $i,SY3173: $i] :
( ( SY3173
!= ( apply @ SY3169 @ SY3172 ) )
| ~ ( in @ SY3172 @ ( relation_rng @ SV40 ) )
| ( in @ SY3173 @ ( relation_dom @ SV40 ) ) ) )
| ~ ~ ( ~ ! [SY3174: $i,SY3175: $i] :
( ( SY3174
!= ( apply @ SV40 @ SY3175 ) )
| ~ ( in @ SY3175 @ ( relation_dom @ SV40 ) )
| ( SY3175
= ( apply @ SY3169 @ SY3174 ) ) )
| ~ ! [SY3176: $i] :
( ! [SY3177: $i] :
( ( SY3176
!= ( apply @ SV40 @ SY3177 ) )
| ~ ( in @ SY3177 @ ( relation_dom @ SV40 ) ) )
| ( in @ SY3176 @ ( relation_rng @ SV40 ) ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1568]) ).
thf(1646,plain,
! [SV40: $i] :
( ( ( ! [SY3178: $i] :
( ~ ( function @ SY3178 )
| ~ ( relation @ SY3178 )
| ( SY3178
!= ( function_inverse @ SV40 ) )
| ( ( relation_dom @ SY3178 )
= ( relation_rng @ SV40 ) ) ) )
= $true )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1569]) ).
thf(1647,plain,
! [SV41: $i,SV165: $i,SV191: $i] :
( ( ( ! [SY3418: $i] :
( ~ ( in @ ( ordered_pair @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SY3418 ) @ SV41 )
| ~ ( in @ SY3418 @ SV165 ) ) )
= $true )
| ( ( ~ ( in @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SV191 ) )
= $true )
| ( ( SV191
= ( relation_inverse_image @ SV41 @ SV165 ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1570]) ).
thf(1648,plain,
! [SV41: $i,SV165: $i,SV191: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ ( sK31_SY3124 @ SV191 @ SV165 @ SV41 ) ) @ SV41 )
| ~ ( in @ ( sK31_SY3124 @ SV191 @ SV165 @ SV41 ) @ SV165 ) ) )
= $true )
| ( ( in @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SV191 )
= $true )
| ( ( SV191
= ( relation_inverse_image @ SV41 @ SV165 ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1571]) ).
thf(1649,plain,
! [SV192: $i,SV166: $i,SV41: $i] :
( ( ( ! [SY3419: $i] :
( ! [SY3379: $i] :
( ~ ( in @ ( ordered_pair @ SY3419 @ SY3379 ) @ SV41 )
| ~ ( in @ SY3379 @ SV166 ) )
| ( in @ SY3419 @ SV192 ) ) )
= $true )
| ( ( SV192
= ( relation_inverse_image @ SV41 @ SV166 ) )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1572]) ).
thf(1650,plain,
! [SV41: $i,SV166: $i,SV192: $i] :
( ( ( ! [SY3421: $i] :
( ~ ( in @ SY3421 @ SV192 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3421 @ ( sK29_E @ SY3421 @ SV192 @ SV166 @ SV41 ) ) @ SV41 )
| ~ ( in @ ( sK29_E @ SY3421 @ SV192 @ SV166 @ SV41 ) @ SV166 ) ) ) )
= $true )
| ( ( SV192
= ( relation_inverse_image @ SV41 @ SV166 ) )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1573]) ).
thf(1651,plain,
! [SV42: $i,SV167: $i,SV230: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV230 @ ( sK17_C @ SV167 @ SV42 ) ) @ SV42 ) )
= $true )
| ( ( ~ ( in @ ( sK17_C @ SV167 @ SV42 ) @ SV167 ) )
= $true )
| ( ( SV167
= ( relation_rng @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1574]) ).
thf(1652,plain,
! [SV168: $i,SV42: $i,SV231: $i] :
( ( ( ! [SY3458: $i] :
~ ( in @ ( ordered_pair @ SY3458 @ SV231 ) @ SV42 )
| ( in @ SV231 @ SV168 ) )
= $true )
| ( ( SV168
= ( relation_rng @ SV42 ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1576]) ).
thf(1653,plain,
! [SV42: $i,SV168: $i,SV232: $i] :
( ( ( ~ ( in @ SV232 @ SV168 )
| ( in @ ( ordered_pair @ ( sK16_D @ SV232 @ SV168 @ SV42 ) @ SV232 ) @ SV42 ) )
= $true )
| ( ( SV168
= ( relation_rng @ SV42 ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1577]) ).
thf(1654,plain,
! [SV92: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK12_B @ SV92 ) @ ( relation_dom @ SV92 ) )
| ~ ( in @ ( sK13_SY3112 @ SV92 ) @ ( relation_dom @ SV92 ) ) )
| ( ( apply @ SV92 @ ( sK12_B @ SV92 ) )
!= ( apply @ SV92 @ ( sK13_SY3112 @ SV92 ) ) ) )
= $false )
| ( ( one_to_one @ SV92 )
= $true )
| ( ( function @ SV92 )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1578]) ).
thf(1655,plain,
! [SV92: $i] :
( ( ( ( sK12_B @ SV92 )
= ( sK13_SY3112 @ SV92 ) )
= $false )
| ( ( one_to_one @ SV92 )
= $true )
| ( ( function @ SV92 )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1579]) ).
thf(1656,plain,
! [SV224: $i,SV93: $i,SV223: $i] :
( ( ( ~ ( in @ SV223 @ ( relation_dom @ SV93 ) )
| ~ ( in @ SV224 @ ( relation_dom @ SV93 ) )
| ( ( apply @ SV93 @ SV223 )
!= ( apply @ SV93 @ SV224 ) ) )
= $true )
| ( ( SV223 = SV224 )
= $true )
| ( ( one_to_one @ SV93 )
= $false )
| ( ( function @ SV93 )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1580]) ).
thf(1657,plain,
! [SV43: $i,SV94: $i,SV214: $i] :
( ( ( ~ ( ~ ( ! [SY3446: $i] :
( ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ SY3446 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3446 @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV94 ) )
| ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV214 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK11_SY3111 @ SV214 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY3111 @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV94 ) )
| ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV214 ) ) ) )
= $true )
| ( ( SV214
= ( relation_composition @ SV43 @ SV94 ) )
= $true )
| ( ( relation @ SV214 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1581]) ).
thf(1658,plain,
! [SV94: $i,SV43: $i,SV215: $i] :
( ( ( ( SV215
!= ( relation_composition @ SV43 @ SV94 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3447: $i,SY3448: $i] :
( ! [SY3330: $i] :
( ~ ( in @ ( ordered_pair @ SY3447 @ SY3330 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3330 @ SY3448 ) @ SV94 ) )
| ( in @ ( ordered_pair @ SY3447 @ SY3448 ) @ SV215 ) )
| ~ ! [SY3450: $i,SY3451: $i] :
( ~ ( in @ ( ordered_pair @ SY3450 @ SY3451 ) @ SV215 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3450 @ ( sK8_F @ SY3451 @ SY3450 @ SV215 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK8_F @ SY3451 @ SY3450 @ SV215 @ SV94 @ SV43 ) @ SY3451 ) @ SV94 ) ) ) ) )
= $true )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1582]) ).
thf(1659,plain,
! [SV233: $i,SV44: $i,SV169: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK20_C @ SV169 @ SV44 ) @ SV233 ) @ SV44 ) )
= $true )
| ( ( ~ ( in @ ( sK20_C @ SV169 @ SV44 ) @ SV169 ) )
= $true )
| ( ( SV169
= ( relation_dom @ SV44 ) )
= $true )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1583]) ).
thf(1660,plain,
! [SV170: $i,SV44: $i,SV234: $i] :
( ( ( ! [SY3459: $i] :
~ ( in @ ( ordered_pair @ SV234 @ SY3459 ) @ SV44 )
| ( in @ SV234 @ SV170 ) )
= $true )
| ( ( SV170
= ( relation_dom @ SV44 ) )
= $false )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1585]) ).
thf(1661,plain,
! [SV44: $i,SV170: $i,SV235: $i] :
( ( ( ~ ( in @ SV235 @ SV170 )
| ( in @ ( ordered_pair @ SV235 @ ( sK19_D @ SV235 @ SV170 @ SV44 ) ) @ SV44 ) )
= $true )
| ( ( SV170
= ( relation_dom @ SV44 ) )
= $false )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1586]) ).
thf(1662,plain,
! [SV45: $i,SV225: $i] :
( ( ( ~ ( in @ SV225 @ ( relation_dom @ SV45 ) ) )
= $true )
| ( ( ! [SY3453: $i] :
( ( SY3453
!= ( apply @ SV45 @ SV225 ) )
| ( in @ ( ordered_pair @ SV225 @ SY3453 ) @ SV45 ) ) )
= $true )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1587]) ).
thf(1663,plain,
! [SV45: $i,SV226: $i] :
( ( ( ~ ( in @ SV226 @ ( relation_dom @ SV45 ) ) )
= $true )
| ( ( ! [SY3454: $i] :
( ~ ( in @ ( ordered_pair @ SV226 @ SY3454 ) @ SV45 )
| ( SY3454
= ( apply @ SV45 @ SV226 ) ) ) )
= $true )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1588]) ).
thf(1664,plain,
! [SV45: $i,SV227: $i] :
( ( ( in @ SV227 @ ( relation_dom @ SV45 ) )
= $true )
| ( ( ! [SY3455: $i] :
( ( SY3455
!= ( apply @ SV45 @ SV227 ) )
| ( SY3455 = empty_set ) ) )
= $true )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1589]) ).
thf(1665,plain,
! [SV45: $i,SV228: $i] :
( ( ( in @ SV228 @ ( relation_dom @ SV45 ) )
= $true )
| ( ( ! [SY3456: $i] :
( ( SY3456 != empty_set )
| ( SY3456
= ( apply @ SV45 @ SV228 ) ) ) )
= $true )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1590]) ).
thf(1666,plain,
! [SV95: $i,SV130: $i] :
( ( ( one_to_one @ SV130 )
= $false )
| ( ( in @ SV95 @ ( relation_rng @ SV130 ) )
= $false )
| ( ( SV95
= ( apply @ SV130 @ ( apply @ ( function_inverse @ SV130 ) @ SV95 ) ) )
= $true )
| ( ( function @ SV130 )
= $false )
| ( ( relation @ SV130 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1591]) ).
thf(1667,plain,
! [SV96: $i,SV131: $i] :
( ( ( one_to_one @ SV131 )
= $false )
| ( ( in @ SV96 @ ( relation_rng @ SV131 ) )
= $false )
| ( ( SV96
= ( apply @ ( relation_composition @ ( function_inverse @ SV131 ) @ SV131 ) @ SV96 ) )
= $true )
| ( ( function @ SV131 )
= $false )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1592]) ).
thf(1668,plain,
! [SV101: $i,SV134: $i] :
( ( ( ~ ( in @ ( sK45_C @ SV134 @ SV101 ) @ SV101 ) )
= $false )
| ( ( ( ( relation_dom @ SV134 )
!= SV101 ) )
= $true )
| ( ( SV134
= ( identity_relation @ SV101 ) )
= $true )
| ( ( function @ SV134 )
= $false )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1593]) ).
thf(1669,plain,
! [SV101: $i,SV134: $i] :
( ( ( ~ ( ( ( apply @ SV134 @ ( sK45_C @ SV134 @ SV101 ) )
!= ( sK45_C @ SV134 @ SV101 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV134 )
!= SV101 ) )
= $true )
| ( ( SV134
= ( identity_relation @ SV101 ) )
= $true )
| ( ( function @ SV134 )
= $false )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1593]) ).
thf(1670,plain,
! [SV171: $i,SV193: $i] :
( ( ( ( SV193
!= ( identity_relation @ SV171 ) ) )
= $true )
| ( ( ! [SY3422: $i] :
( ~ ( in @ SY3422 @ SV171 )
| ( ( apply @ SV193 @ SY3422 )
= SY3422 ) ) )
= $true )
| ( ( function @ SV193 )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1594]) ).
thf(1671,plain,
! [SV172: $i,SV194: $i] :
( ( ( ( SV194
!= ( identity_relation @ SV172 ) ) )
= $true )
| ( ( ( relation_dom @ SV194 )
= SV172 )
= $true )
| ( ( function @ SV194 )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1595]) ).
thf(1672,plain,
! [SV154: $i,SV174: $i,SV81: $i,SV47: $i] :
( ( ( in @ ( ordered_pair @ SV47 @ SV81 ) @ SV174 )
= $false )
| ( ( in @ SV47 @ SV154 )
= $false )
| ( ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SV154 ) @ SV174 ) )
= $true )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1596]) ).
thf(1673,plain,
! [SV217: $i,SV208: $i,SV81: $i,SV47: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SV208 ) @ SV217 ) ) )
= $true )
| ( ( in @ SV47 @ SV208 )
= $true )
| ( ( relation @ SV217 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1597]) ).
thf(1674,plain,
! [SV218: $i,SV209: $i,SV81: $i,SV47: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SV209 ) @ SV218 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV47 @ SV81 ) @ SV218 )
= $true )
| ( ( relation @ SV218 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1598]) ).
thf(1675,plain,
! [SV210: $i,SV195: $i,SV48: $i] :
( ( ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SV195 @ SV210 ) ) )
= $false )
| ( ( in @ SV48 @ SV195 )
= $true )
| ( ( relation @ SV210 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1600]) ).
thf(1676,plain,
! [SV211: $i,SV196: $i,SV48: $i] :
( ( ( in @ SV48 @ ( relation_rng @ ( relation_rng_restriction @ SV196 @ SV211 ) ) )
= $false )
| ( ( in @ SV48 @ ( relation_rng @ SV211 ) )
= $true )
| ( ( relation @ SV211 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1601]) ).
thf(1677,plain,
! [SV49: $i,SV175: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV175 ) )
= $true )
| ( ( SV49 = SV175 )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1602]) ).
thf(1678,plain,
! [SV49: $i,SV175: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV49 )
| ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV175 ) )
= $true )
| ( ( SV49 = SV175 )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1603]) ).
thf(1679,plain,
! [SV176: $i,SV49: $i] :
( ( ( ~ ! [SY3392: $i,SY3393: $i] :
( ~ ( in @ ( ordered_pair @ SY3392 @ SY3393 ) @ SV49 )
| ( in @ ( ordered_pair @ SY3392 @ SY3393 ) @ SV176 ) ) )
= $false )
| ( ( SV49 = SV176 )
= $false )
| ( ( relation @ SV176 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1604]) ).
thf(1680,plain,
! [SV49: $i,SV176: $i] :
( ( ( ~ ! [SY3394: $i,SY3395: $i] :
( ~ ( in @ ( ordered_pair @ SY3394 @ SY3395 ) @ SV176 )
| ( in @ ( ordered_pair @ SY3394 @ SY3395 ) @ SV49 ) ) )
= $false )
| ( ( SV49 = SV176 )
= $false )
| ( ( relation @ SV176 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1604]) ).
thf(1681,plain,
! [SV50: $i,SV177: $i,SV197: $i] :
( ( ( ! [SY3425: $i] :
( ~ ( in @ ( ordered_pair @ SY3425 @ ( sK33_D @ SV197 @ SV177 @ SV50 ) ) @ SV50 )
| ~ ( in @ SY3425 @ SV177 ) ) )
= $true )
| ( ( ~ ( in @ ( sK33_D @ SV197 @ SV177 @ SV50 ) @ SV197 ) )
= $true )
| ( ( SV197
= ( relation_image @ SV50 @ SV177 ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1605]) ).
thf(1682,plain,
! [SV50: $i,SV177: $i,SV197: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK34_SY3126 @ SV197 @ SV177 @ SV50 ) @ ( sK33_D @ SV197 @ SV177 @ SV50 ) ) @ SV50 )
| ~ ( in @ ( sK34_SY3126 @ SV197 @ SV177 @ SV50 ) @ SV177 ) ) )
= $true )
| ( ( in @ ( sK33_D @ SV197 @ SV177 @ SV50 ) @ SV197 )
= $true )
| ( ( SV197
= ( relation_image @ SV50 @ SV177 ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1606]) ).
thf(1683,plain,
! [SV198: $i,SV178: $i,SV50: $i] :
( ( ( ! [SY3426: $i] :
( ! [SY3400: $i] :
( ~ ( in @ ( ordered_pair @ SY3400 @ SY3426 ) @ SV50 )
| ~ ( in @ SY3400 @ SV178 ) )
| ( in @ SY3426 @ SV198 ) ) )
= $true )
| ( ( SV198
= ( relation_image @ SV50 @ SV178 ) )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1607]) ).
thf(1684,plain,
! [SV50: $i,SV178: $i,SV198: $i] :
( ( ( ! [SY3428: $i] :
( ~ ( in @ SY3428 @ SV198 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK32_E @ SY3428 @ SV198 @ SV178 @ SV50 ) @ SY3428 ) @ SV50 )
| ~ ( in @ ( sK32_E @ SY3428 @ SV198 @ SV178 @ SV50 ) @ SV178 ) ) ) )
= $true )
| ( ( SV198
= ( relation_image @ SV50 @ SV178 ) )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1608]) ).
thf(1685,plain,
! [SV110: $i,SV138: $i] :
( ( ( function @ SV138 )
= $false )
| ( ( relation @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV138 )
= $false )
| ( ( function @ ( relation_composition @ SV110 @ SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1609]) ).
thf(1686,plain,
! [SV111: $i,SV139: $i] :
( ( ( function @ SV139 )
= $false )
| ( ( relation @ SV111 )
= $false )
| ( ( function @ SV111 )
= $false )
| ( ( relation @ SV139 )
= $false )
| ( ( relation @ ( relation_composition @ SV111 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1610]) ).
thf(1687,plain,
! [SV179: $i] :
( ( ( function @ SV179 )
= $false )
| ( ( empty @ SV179 )
= $false )
| ( ( relation @ SV179 )
= $false )
| ( ( function @ SV179 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1611]) ).
thf(1688,plain,
! [SV180: $i] :
( ( ( function @ SV180 )
= $false )
| ( ( empty @ SV180 )
= $false )
| ( ( relation @ SV180 )
= $false )
| ( ( relation @ SV180 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1612]) ).
thf(1689,plain,
! [SV140: $i,SV51: $i,SV156: $i,SV219: $i] :
( ( ( in @ SV219 @ ( relation_dom @ SV156 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV219 @ SV51 ) @ SV156 ) )
= $true )
| ( ( ~ ( in @ SV219 @ SV140 ) )
= $true )
| ( ( in @ SV51 @ ( relation_image @ SV156 @ SV140 ) )
= $true )
| ( ( relation @ SV156 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1613]) ).
thf(1690,plain,
! [SV51: $i,SV141: $i,SV157: $i] :
( ( ( ~ ( ~ ( in @ ( sK47_D @ SV157 @ SV141 @ SV51 ) @ ( relation_dom @ SV157 ) )
| ~ ( in @ ( ordered_pair @ ( sK47_D @ SV157 @ SV141 @ SV51 ) @ SV51 ) @ SV157 ) ) )
= $true )
| ( ( in @ SV51 @ ( relation_image @ SV157 @ SV141 ) )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1614]) ).
thf(1691,plain,
! [SV51: $i,SV141: $i,SV157: $i] :
( ( ( in @ ( sK47_D @ SV157 @ SV141 @ SV51 ) @ SV141 )
= $true )
| ( ( in @ SV51 @ ( relation_image @ SV157 @ SV141 ) )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1615]) ).
thf(1692,plain,
! [SV52: $i,SV181: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK14_C @ SV181 @ SV52 ) @ ( sK15_SY3113 @ SV181 @ SV52 ) ) @ SV181 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY3113 @ SV181 @ SV52 ) @ ( sK14_C @ SV181 @ SV52 ) ) @ SV52 ) )
= $true )
| ( ( SV181
= ( relation_inverse @ SV52 ) )
= $true )
| ( ( relation @ SV181 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1616]) ).
thf(1693,plain,
! [SV52: $i,SV181: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK14_C @ SV181 @ SV52 ) @ ( sK15_SY3113 @ SV181 @ SV52 ) ) @ SV181 )
| ( in @ ( ordered_pair @ ( sK15_SY3113 @ SV181 @ SV52 ) @ ( sK14_C @ SV181 @ SV52 ) ) @ SV52 ) )
= $true )
| ( ( SV181
= ( relation_inverse @ SV52 ) )
= $true )
| ( ( relation @ SV181 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1617]) ).
thf(1694,plain,
! [SV52: $i,SV182: $i] :
( ( ( ~ ! [SY3402: $i,SY3403: $i] :
( ~ ( in @ ( ordered_pair @ SY3402 @ SY3403 ) @ SV182 )
| ( in @ ( ordered_pair @ SY3403 @ SY3402 ) @ SV52 ) ) )
= $false )
| ( ( SV182
= ( relation_inverse @ SV52 ) )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1618]) ).
thf(1695,plain,
! [SV182: $i,SV52: $i] :
( ( ( ~ ! [SY3404: $i,SY3405: $i] :
( ~ ( in @ ( ordered_pair @ SY3405 @ SY3404 ) @ SV52 )
| ( in @ ( ordered_pair @ SY3404 @ SY3405 ) @ SV182 ) ) )
= $false )
| ( ( SV182
= ( relation_inverse @ SV52 ) )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1618]) ).
thf(1696,plain,
! [SV123: $i,SV142: $i] :
( ( ( ( ( sK39_C @ SV142 @ SV123 )
!= ( sK40_SY3129 @ SV142 @ SV123 ) ) )
= $true )
| ( ( ~ ( in @ ( sK39_C @ SV142 @ SV123 ) @ SV123 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 ) )
= $true )
| ( ( SV142
= ( identity_relation @ SV123 ) )
= $true )
| ( ( relation @ SV142 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1619]) ).
thf(1697,plain,
! [SV123: $i,SV142: $i] :
( ( ( ~ ( ( ( sK39_C @ SV142 @ SV123 )
= ( sK40_SY3129 @ SV142 @ SV123 ) )
| ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 ) ) )
= $false )
| ( ( SV142
= ( identity_relation @ SV123 ) )
= $true )
| ( ( relation @ SV142 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1620]) ).
thf(1698,plain,
! [SV123: $i,SV142: $i] :
( ( ( ~ ( ( in @ ( sK39_C @ SV142 @ SV123 ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 ) ) )
= $false )
| ( ( SV142
= ( identity_relation @ SV123 ) )
= $true )
| ( ( relation @ SV142 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1620]) ).
thf(1699,plain,
! [SV143: $i,SV124: $i,SV236: $i] :
( ( ( ! [SY3460: $i] :
( ( SV236 != SY3460 )
| ~ ( in @ SV236 @ SV124 )
| ( in @ ( ordered_pair @ SV236 @ SY3460 ) @ SV143 ) ) )
= $true )
| ( ( SV143
= ( identity_relation @ SV124 ) )
= $false )
| ( ( relation @ SV143 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1621]) ).
thf(1700,plain,
! [SV124: $i,SV143: $i] :
( ( ( ~ ! [SY3362: $i,SY3363: $i] :
( ~ ( in @ ( ordered_pair @ SY3362 @ SY3363 ) @ SV143 )
| ( SY3362 = SY3363 ) )
| ~ ! [SY3364: $i] :
( ! [SY3365: $i] :
~ ( in @ ( ordered_pair @ SY3364 @ SY3365 ) @ SV143 )
| ( in @ SY3364 @ SV124 ) ) )
= $false )
| ( ( SV143
= ( identity_relation @ SV124 ) )
= $false )
| ( ( relation @ SV143 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1622]) ).
thf(1701,plain,
! [SV53: $i,SV82: $i,SV199: $i] :
( ( ( ~ ( ~ ( in @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) @ SV53 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV82 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 ) ) )
= $false )
| ( ( SV199
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $true )
| ( ( relation @ SV199 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1623]) ).
thf(1702,plain,
! [SV53: $i,SV82: $i,SV199: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) @ SV53 )
| ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV82 )
| ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 ) ) ) )
= $false )
| ( ( SV199
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $true )
| ( ( relation @ SV199 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1623]) ).
thf(1703,plain,
! [SV200: $i,SV82: $i,SV53: $i] :
( ( ( ~ ! [SY3429: $i,SY3430: $i] :
( ~ ( in @ SY3430 @ SV53 )
| ~ ( in @ ( ordered_pair @ SY3429 @ SY3430 ) @ SV82 )
| ( in @ ( ordered_pair @ SY3429 @ SY3430 ) @ SV200 ) )
| ~ ~ ( ~ ! [SY3431: $i,SY3432: $i] :
( ~ ( in @ ( ordered_pair @ SY3431 @ SY3432 ) @ SV200 )
| ( in @ SY3432 @ SV53 ) )
| ~ ! [SY3433: $i,SY3434: $i] :
( ~ ( in @ ( ordered_pair @ SY3433 @ SY3434 ) @ SV200 )
| ( in @ ( ordered_pair @ SY3433 @ SY3434 ) @ SV82 ) ) ) )
= $false )
| ( ( SV200
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $false )
| ( ( relation @ SV200 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1624]) ).
thf(1704,plain,
! [SV83: $i,SV55: $i,SV220: $i] :
( ( ( function @ SV220 )
= $false )
| ( ( ~ ( relation @ SV220 ) )
= $true )
| ( ( ~ ( in @ SV55 @ ( relation_dom @ SV220 ) )
| ~ ( in @ ( apply @ SV220 @ SV55 ) @ ( relation_dom @ SV83 ) )
| ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SV220 @ SV83 ) ) ) )
= $true )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1625]) ).
thf(1705,plain,
! [SV83: $i,SV55: $i,SV237: $i] :
( ( ( ~ ( function @ SV237 )
| ~ ( relation @ SV237 )
| ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SV237 @ SV83 ) ) )
| ( in @ SV55 @ ( relation_dom @ SV237 ) ) )
= $true )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1626]) ).
thf(1706,plain,
! [SV83: $i,SV55: $i,SV238: $i] :
( ( ( ~ ( function @ SV238 )
| ~ ( relation @ SV238 )
| ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SV238 @ SV83 ) ) )
| ( in @ ( apply @ SV238 @ SV55 ) @ ( relation_dom @ SV83 ) ) )
= $true )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1627]) ).
thf(1707,plain,
! [SV201: $i,SV212: $i,SV56: $i] :
( ( ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SV212 @ SV201 ) ) )
= $false )
| ( ( in @ SV56 @ SV201 )
= $true )
| ( ( relation @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1629]) ).
thf(1708,plain,
! [SV202: $i,SV213: $i,SV56: $i] :
( ( ( in @ SV56 @ ( relation_dom @ ( relation_dom_restriction @ SV213 @ SV202 ) ) )
= $false )
| ( ( in @ SV56 @ ( relation_dom @ SV213 ) )
= $true )
| ( ( relation @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1630]) ).
thf(1709,plain,
! [SV149: $i,SV58: $i,SV161: $i,SV221: $i] :
( ( ( in @ SV221 @ ( relation_rng @ SV161 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV58 @ SV221 ) @ SV161 ) )
= $true )
| ( ( ~ ( in @ SV221 @ SV149 ) )
= $true )
| ( ( in @ SV58 @ ( relation_inverse_image @ SV161 @ SV149 ) )
= $true )
| ( ( relation @ SV161 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1631]) ).
thf(1710,plain,
! [SV58: $i,SV150: $i,SV162: $i] :
( ( ( ~ ( ~ ( in @ ( sK46_D @ SV162 @ SV150 @ SV58 ) @ ( relation_rng @ SV162 ) )
| ~ ( in @ ( ordered_pair @ SV58 @ ( sK46_D @ SV162 @ SV150 @ SV58 ) ) @ SV162 ) ) )
= $true )
| ( ( in @ SV58 @ ( relation_inverse_image @ SV162 @ SV150 ) )
= $false )
| ( ( relation @ SV162 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1632]) ).
thf(1711,plain,
! [SV58: $i,SV150: $i,SV162: $i] :
( ( ( in @ ( sK46_D @ SV162 @ SV150 @ SV58 ) @ SV150 )
= $true )
| ( ( in @ SV58 @ ( relation_inverse_image @ SV162 @ SV150 ) )
= $false )
| ( ( relation @ SV162 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1633]) ).
thf(1712,plain,
! [SV59: $i,SV185: $i] :
( ( ( in @ ( ordered_pair @ ( sK22_C @ SV185 @ SV59 ) @ ( sK23_SY3118 @ SV185 @ SV59 ) ) @ SV59 )
= $true )
| ( ( subset @ SV59 @ SV185 )
= $true )
| ( ( relation @ SV185 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1634]) ).
thf(1713,plain,
! [SV59: $i,SV185: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SV185 @ SV59 ) @ ( sK23_SY3118 @ SV185 @ SV59 ) ) @ SV185 ) )
= $true )
| ( ( subset @ SV59 @ SV185 )
= $true )
| ( ( relation @ SV185 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1635]) ).
thf(1714,plain,
! [SV186: $i,SV59: $i,SV239: $i,SV229: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV229 @ SV239 ) @ SV59 )
| ( in @ ( ordered_pair @ SV229 @ SV239 ) @ SV186 ) )
= $true )
| ( ( subset @ SV59 @ SV186 )
= $false )
| ( ( relation @ SV186 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1636]) ).
thf(1715,plain,
! [SV60: $i,SV187: $i,SV203: $i] :
( ( ( ~ ( ~ ( in @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ SV187 )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV60 )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 ) ) )
= $false )
| ( ( SV203
= ( relation_dom_restriction @ SV60 @ SV187 ) )
= $true )
| ( ( relation @ SV203 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1637]) ).
thf(1716,plain,
! [SV60: $i,SV187: $i,SV203: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ SV187 )
| ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV60 )
| ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 ) ) ) )
= $false )
| ( ( SV203
= ( relation_dom_restriction @ SV60 @ SV187 ) )
= $true )
| ( ( relation @ SV203 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1637]) ).
thf(1717,plain,
! [SV204: $i,SV60: $i,SV188: $i] :
( ( ( ~ ! [SY3437: $i,SY3438: $i] :
( ~ ( in @ SY3437 @ SV188 )
| ~ ( in @ ( ordered_pair @ SY3437 @ SY3438 ) @ SV60 )
| ( in @ ( ordered_pair @ SY3437 @ SY3438 ) @ SV204 ) )
| ~ ~ ( ~ ! [SY3439: $i] :
( ! [SY3440: $i] :
~ ( in @ ( ordered_pair @ SY3439 @ SY3440 ) @ SV204 )
| ( in @ SY3439 @ SV188 ) )
| ~ ! [SY3441: $i,SY3442: $i] :
( ~ ( in @ ( ordered_pair @ SY3441 @ SY3442 ) @ SV204 )
| ( in @ ( ordered_pair @ SY3441 @ SY3442 ) @ SV60 ) ) ) )
= $false )
| ( ( SV204
= ( relation_dom_restriction @ SV60 @ SV188 ) )
= $false )
| ( ( relation @ SV204 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1638]) ).
thf(1718,plain,
! [SV129: $i,SV151: $i,SV39: $i] :
( ( ( in @ SV39 @ ( relation_dom @ SV151 ) )
= $false )
| ( ( SV129
= ( apply @ SV151 @ SV39 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV39 @ SV129 ) @ SV151 )
= $true )
| ( ( function @ SV151 )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1641]) ).
thf(1719,plain,
! [SV205: $i,SV189: $i,SV39: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV39 @ SV189 ) @ SV205 ) )
= $true )
| ( ( SV189
= ( apply @ SV205 @ SV39 ) )
= $true )
| ( ( function @ SV205 )
= $false )
| ( ( relation @ SV205 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1642]) ).
thf(1720,plain,
! [SV206: $i,SV190: $i,SV39: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV39 @ SV190 ) @ SV206 ) )
= $true )
| ( ( in @ SV39 @ ( relation_dom @ SV206 ) )
= $true )
| ( ( function @ SV206 )
= $false )
| ( ( relation @ SV206 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1643]) ).
thf(1721,plain,
! [SV40: $i,SV222: $i] :
( ( ( function @ SV222 )
= $false )
| ( ( ~ ( relation @ SV222 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) )
| ( SV222
= ( function_inverse @ SV40 ) ) )
= $true )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1644]) ).
thf(1722,plain,
! [SV40: $i,SV240: $i] :
( ( ( ~ ( function @ SV240 )
| ~ ( relation @ SV240 )
| ( SV240
!= ( function_inverse @ SV40 ) )
| ~ ( ~ ~ ( ~ ! [SY3461: $i,SY3462: $i] :
( ( SY3462
!= ( apply @ SV240 @ SY3461 ) )
| ~ ( in @ SY3461 @ ( relation_rng @ SV40 ) )
| ( SY3461
= ( apply @ SV40 @ SY3462 ) ) )
| ~ ! [SY3463: $i,SY3464: $i] :
( ( SY3464
!= ( apply @ SV240 @ SY3463 ) )
| ~ ( in @ SY3463 @ ( relation_rng @ SV40 ) )
| ( in @ SY3464 @ ( relation_dom @ SV40 ) ) ) )
| ~ ~ ( ~ ! [SY3465: $i,SY3466: $i] :
( ( SY3465
!= ( apply @ SV40 @ SY3466 ) )
| ~ ( in @ SY3466 @ ( relation_dom @ SV40 ) )
| ( SY3466
= ( apply @ SV240 @ SY3465 ) ) )
| ~ ! [SY3176: $i] :
( ! [SY3177: $i] :
( ( SY3176
!= ( apply @ SV40 @ SY3177 ) )
| ~ ( in @ SY3177 @ ( relation_dom @ SV40 ) ) )
| ( in @ SY3176 @ ( relation_rng @ SV40 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1645]) ).
thf(1723,plain,
! [SV40: $i,SV241: $i] :
( ( ( ~ ( function @ SV241 )
| ~ ( relation @ SV241 )
| ( SV241
!= ( function_inverse @ SV40 ) )
| ( ( relation_dom @ SV241 )
= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1646]) ).
thf(1724,plain,
! [SV242: $i,SV41: $i,SV165: $i,SV191: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SV242 ) @ SV41 )
| ~ ( in @ SV242 @ SV165 ) )
= $true )
| ( ( ~ ( in @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SV191 ) )
= $true )
| ( ( SV191
= ( relation_inverse_image @ SV41 @ SV165 ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1647]) ).
thf(1725,plain,
! [SV41: $i,SV165: $i,SV191: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ ( sK31_SY3124 @ SV191 @ SV165 @ SV41 ) ) @ SV41 )
| ~ ( in @ ( sK31_SY3124 @ SV191 @ SV165 @ SV41 ) @ SV165 ) )
= $false )
| ( ( in @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SV191 )
= $true )
| ( ( SV191
= ( relation_inverse_image @ SV41 @ SV165 ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1648]) ).
thf(1726,plain,
! [SV192: $i,SV166: $i,SV41: $i,SV243: $i] :
( ( ( ! [SY3469: $i] :
( ~ ( in @ ( ordered_pair @ SV243 @ SY3469 ) @ SV41 )
| ~ ( in @ SY3469 @ SV166 ) )
| ( in @ SV243 @ SV192 ) )
= $true )
| ( ( SV192
= ( relation_inverse_image @ SV41 @ SV166 ) )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1649]) ).
thf(1727,plain,
! [SV41: $i,SV166: $i,SV192: $i,SV244: $i] :
( ( ( ~ ( in @ SV244 @ SV192 )
| ~ ( ~ ( in @ ( ordered_pair @ SV244 @ ( sK29_E @ SV244 @ SV192 @ SV166 @ SV41 ) ) @ SV41 )
| ~ ( in @ ( sK29_E @ SV244 @ SV192 @ SV166 @ SV41 ) @ SV166 ) ) )
= $true )
| ( ( SV192
= ( relation_inverse_image @ SV41 @ SV166 ) )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(1728,plain,
! [SV42: $i,SV167: $i,SV230: $i] :
( ( ( in @ ( ordered_pair @ SV230 @ ( sK17_C @ SV167 @ SV42 ) ) @ SV42 )
= $false )
| ( ( ~ ( in @ ( sK17_C @ SV167 @ SV42 ) @ SV167 ) )
= $true )
| ( ( SV167
= ( relation_rng @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1651]) ).
thf(1729,plain,
! [SV168: $i,SV42: $i,SV231: $i] :
( ( ( ! [SY3458: $i] :
~ ( in @ ( ordered_pair @ SY3458 @ SV231 ) @ SV42 ) )
= $true )
| ( ( in @ SV231 @ SV168 )
= $true )
| ( ( SV168
= ( relation_rng @ SV42 ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1652]) ).
thf(1730,plain,
! [SV42: $i,SV168: $i,SV232: $i] :
( ( ( ~ ( in @ SV232 @ SV168 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK16_D @ SV232 @ SV168 @ SV42 ) @ SV232 ) @ SV42 )
= $true )
| ( ( SV168
= ( relation_rng @ SV42 ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1653]) ).
thf(1731,plain,
! [SV92: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK12_B @ SV92 ) @ ( relation_dom @ SV92 ) )
| ~ ( in @ ( sK13_SY3112 @ SV92 ) @ ( relation_dom @ SV92 ) ) ) )
= $false )
| ( ( one_to_one @ SV92 )
= $true )
| ( ( function @ SV92 )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1654]) ).
thf(1732,plain,
! [SV92: $i] :
( ( ( ( ( apply @ SV92 @ ( sK12_B @ SV92 ) )
!= ( apply @ SV92 @ ( sK13_SY3112 @ SV92 ) ) ) )
= $false )
| ( ( one_to_one @ SV92 )
= $true )
| ( ( function @ SV92 )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1654]) ).
thf(1733,plain,
! [SV224: $i,SV93: $i,SV223: $i] :
( ( ( ~ ( in @ SV223 @ ( relation_dom @ SV93 ) )
| ~ ( in @ SV224 @ ( relation_dom @ SV93 ) ) )
= $true )
| ( ( ( ( apply @ SV93 @ SV223 )
!= ( apply @ SV93 @ SV224 ) ) )
= $true )
| ( ( SV223 = SV224 )
= $true )
| ( ( one_to_one @ SV93 )
= $false )
| ( ( function @ SV93 )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1656]) ).
thf(1734,plain,
! [SV43: $i,SV94: $i,SV214: $i] :
( ( ( ~ ( ! [SY3446: $i] :
( ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ SY3446 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3446 @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV94 ) )
| ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV214 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK11_SY3111 @ SV214 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY3111 @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV94 ) )
| ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV214 ) ) )
= $false )
| ( ( SV214
= ( relation_composition @ SV43 @ SV94 ) )
= $true )
| ( ( relation @ SV214 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1657]) ).
thf(1735,plain,
! [SV94: $i,SV43: $i,SV215: $i] :
( ( ( SV215
= ( relation_composition @ SV43 @ SV94 ) )
= $false )
| ( ( ~ ( ~ ! [SY3447: $i,SY3448: $i] :
( ! [SY3330: $i] :
( ~ ( in @ ( ordered_pair @ SY3447 @ SY3330 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3330 @ SY3448 ) @ SV94 ) )
| ( in @ ( ordered_pair @ SY3447 @ SY3448 ) @ SV215 ) )
| ~ ! [SY3450: $i,SY3451: $i] :
( ~ ( in @ ( ordered_pair @ SY3450 @ SY3451 ) @ SV215 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3450 @ ( sK8_F @ SY3451 @ SY3450 @ SV215 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK8_F @ SY3451 @ SY3450 @ SV215 @ SV94 @ SV43 ) @ SY3451 ) @ SV94 ) ) ) ) )
= $true )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1658]) ).
thf(1736,plain,
! [SV233: $i,SV44: $i,SV169: $i] :
( ( ( in @ ( ordered_pair @ ( sK20_C @ SV169 @ SV44 ) @ SV233 ) @ SV44 )
= $false )
| ( ( ~ ( in @ ( sK20_C @ SV169 @ SV44 ) @ SV169 ) )
= $true )
| ( ( SV169
= ( relation_dom @ SV44 ) )
= $true )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1659]) ).
thf(1737,plain,
! [SV170: $i,SV44: $i,SV234: $i] :
( ( ( ! [SY3459: $i] :
~ ( in @ ( ordered_pair @ SV234 @ SY3459 ) @ SV44 ) )
= $true )
| ( ( in @ SV234 @ SV170 )
= $true )
| ( ( SV170
= ( relation_dom @ SV44 ) )
= $false )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1660]) ).
thf(1738,plain,
! [SV44: $i,SV170: $i,SV235: $i] :
( ( ( ~ ( in @ SV235 @ SV170 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV235 @ ( sK19_D @ SV235 @ SV170 @ SV44 ) ) @ SV44 )
= $true )
| ( ( SV170
= ( relation_dom @ SV44 ) )
= $false )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1661]) ).
thf(1739,plain,
! [SV45: $i,SV225: $i] :
( ( ( in @ SV225 @ ( relation_dom @ SV45 ) )
= $false )
| ( ( ! [SY3453: $i] :
( ( SY3453
!= ( apply @ SV45 @ SV225 ) )
| ( in @ ( ordered_pair @ SV225 @ SY3453 ) @ SV45 ) ) )
= $true )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1662]) ).
thf(1740,plain,
! [SV45: $i,SV226: $i] :
( ( ( in @ SV226 @ ( relation_dom @ SV45 ) )
= $false )
| ( ( ! [SY3454: $i] :
( ~ ( in @ ( ordered_pair @ SV226 @ SY3454 ) @ SV45 )
| ( SY3454
= ( apply @ SV45 @ SV226 ) ) ) )
= $true )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1663]) ).
thf(1741,plain,
! [SV227: $i,SV45: $i,SV245: $i] :
( ( ( ( SV245
!= ( apply @ SV45 @ SV227 ) )
| ( SV245 = empty_set ) )
= $true )
| ( ( in @ SV227 @ ( relation_dom @ SV45 ) )
= $true )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1664]) ).
thf(1742,plain,
! [SV228: $i,SV45: $i,SV246: $i] :
( ( ( ( SV246 != empty_set )
| ( SV246
= ( apply @ SV45 @ SV228 ) ) )
= $true )
| ( ( in @ SV228 @ ( relation_dom @ SV45 ) )
= $true )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1665]) ).
thf(1743,plain,
! [SV101: $i,SV134: $i] :
( ( ( in @ ( sK45_C @ SV134 @ SV101 ) @ SV101 )
= $true )
| ( ( ( ( relation_dom @ SV134 )
!= SV101 ) )
= $true )
| ( ( SV134
= ( identity_relation @ SV101 ) )
= $true )
| ( ( function @ SV134 )
= $false )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1668]) ).
thf(1744,plain,
! [SV101: $i,SV134: $i] :
( ( ( ( ( apply @ SV134 @ ( sK45_C @ SV134 @ SV101 ) )
!= ( sK45_C @ SV134 @ SV101 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV134 )
!= SV101 ) )
= $true )
| ( ( SV134
= ( identity_relation @ SV101 ) )
= $true )
| ( ( function @ SV134 )
= $false )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1669]) ).
thf(1745,plain,
! [SV171: $i,SV193: $i] :
( ( ( SV193
= ( identity_relation @ SV171 ) )
= $false )
| ( ( ! [SY3422: $i] :
( ~ ( in @ SY3422 @ SV171 )
| ( ( apply @ SV193 @ SY3422 )
= SY3422 ) ) )
= $true )
| ( ( function @ SV193 )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1670]) ).
thf(1746,plain,
! [SV172: $i,SV194: $i] :
( ( ( SV194
= ( identity_relation @ SV172 ) )
= $false )
| ( ( ( relation_dom @ SV194 )
= SV172 )
= $true )
| ( ( function @ SV194 )
= $false )
| ( ( relation @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1671]) ).
thf(1747,plain,
! [SV217: $i,SV208: $i,SV81: $i,SV47: $i] :
( ( ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SV208 ) @ SV217 ) )
= $false )
| ( ( in @ SV47 @ SV208 )
= $true )
| ( ( relation @ SV217 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1673]) ).
thf(1748,plain,
! [SV218: $i,SV209: $i,SV81: $i,SV47: $i] :
( ( ( in @ ( ordered_pair @ SV47 @ SV81 ) @ ( relation_composition @ ( identity_relation @ SV209 ) @ SV218 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV47 @ SV81 ) @ SV218 )
= $true )
| ( ( relation @ SV218 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1674]) ).
thf(1749,plain,
! [SV49: $i,SV175: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV49 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV175 ) )
= $true )
| ( ( SV49 = SV175 )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1677]) ).
thf(1750,plain,
! [SV49: $i,SV175: $i] :
( ( ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV49 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV175 )
= $true )
| ( ( SV49 = SV175 )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1678]) ).
thf(1751,plain,
! [SV176: $i,SV49: $i] :
( ( ( ! [SY3392: $i,SY3393: $i] :
( ~ ( in @ ( ordered_pair @ SY3392 @ SY3393 ) @ SV49 )
| ( in @ ( ordered_pair @ SY3392 @ SY3393 ) @ SV176 ) ) )
= $true )
| ( ( SV49 = SV176 )
= $false )
| ( ( relation @ SV176 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1679]) ).
thf(1752,plain,
! [SV49: $i,SV176: $i] :
( ( ( ! [SY3394: $i,SY3395: $i] :
( ~ ( in @ ( ordered_pair @ SY3394 @ SY3395 ) @ SV176 )
| ( in @ ( ordered_pair @ SY3394 @ SY3395 ) @ SV49 ) ) )
= $true )
| ( ( SV49 = SV176 )
= $false )
| ( ( relation @ SV176 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1680]) ).
thf(1753,plain,
! [SV50: $i,SV177: $i,SV197: $i,SV247: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV247 @ ( sK33_D @ SV197 @ SV177 @ SV50 ) ) @ SV50 )
| ~ ( in @ SV247 @ SV177 ) )
= $true )
| ( ( ~ ( in @ ( sK33_D @ SV197 @ SV177 @ SV50 ) @ SV197 ) )
= $true )
| ( ( SV197
= ( relation_image @ SV50 @ SV177 ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1681]) ).
thf(1754,plain,
! [SV50: $i,SV177: $i,SV197: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK34_SY3126 @ SV197 @ SV177 @ SV50 ) @ ( sK33_D @ SV197 @ SV177 @ SV50 ) ) @ SV50 )
| ~ ( in @ ( sK34_SY3126 @ SV197 @ SV177 @ SV50 ) @ SV177 ) )
= $false )
| ( ( in @ ( sK33_D @ SV197 @ SV177 @ SV50 ) @ SV197 )
= $true )
| ( ( SV197
= ( relation_image @ SV50 @ SV177 ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1682]) ).
thf(1755,plain,
! [SV198: $i,SV178: $i,SV50: $i,SV248: $i] :
( ( ( ! [SY3470: $i] :
( ~ ( in @ ( ordered_pair @ SY3470 @ SV248 ) @ SV50 )
| ~ ( in @ SY3470 @ SV178 ) )
| ( in @ SV248 @ SV198 ) )
= $true )
| ( ( SV198
= ( relation_image @ SV50 @ SV178 ) )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1683]) ).
thf(1756,plain,
! [SV50: $i,SV178: $i,SV198: $i,SV249: $i] :
( ( ( ~ ( in @ SV249 @ SV198 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK32_E @ SV249 @ SV198 @ SV178 @ SV50 ) @ SV249 ) @ SV50 )
| ~ ( in @ ( sK32_E @ SV249 @ SV198 @ SV178 @ SV50 ) @ SV178 ) ) )
= $true )
| ( ( SV198
= ( relation_image @ SV50 @ SV178 ) )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1684]) ).
thf(1757,plain,
! [SV140: $i,SV156: $i,SV51: $i,SV219: $i] :
( ( ( in @ ( ordered_pair @ SV219 @ SV51 ) @ SV156 )
= $false )
| ( ( in @ SV219 @ ( relation_dom @ SV156 ) )
= $false )
| ( ( ~ ( in @ SV219 @ SV140 ) )
= $true )
| ( ( in @ SV51 @ ( relation_image @ SV156 @ SV140 ) )
= $true )
| ( ( relation @ SV156 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1689]) ).
thf(1758,plain,
! [SV51: $i,SV141: $i,SV157: $i] :
( ( ( ~ ( in @ ( sK47_D @ SV157 @ SV141 @ SV51 ) @ ( relation_dom @ SV157 ) )
| ~ ( in @ ( ordered_pair @ ( sK47_D @ SV157 @ SV141 @ SV51 ) @ SV51 ) @ SV157 ) )
= $false )
| ( ( in @ SV51 @ ( relation_image @ SV157 @ SV141 ) )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1690]) ).
thf(1759,plain,
! [SV52: $i,SV181: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK14_C @ SV181 @ SV52 ) @ ( sK15_SY3113 @ SV181 @ SV52 ) ) @ SV181 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK15_SY3113 @ SV181 @ SV52 ) @ ( sK14_C @ SV181 @ SV52 ) ) @ SV52 ) )
= $true )
| ( ( SV181
= ( relation_inverse @ SV52 ) )
= $true )
| ( ( relation @ SV181 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1692]) ).
thf(1760,plain,
! [SV52: $i,SV181: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_C @ SV181 @ SV52 ) @ ( sK15_SY3113 @ SV181 @ SV52 ) ) @ SV181 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK15_SY3113 @ SV181 @ SV52 ) @ ( sK14_C @ SV181 @ SV52 ) ) @ SV52 )
= $true )
| ( ( SV181
= ( relation_inverse @ SV52 ) )
= $true )
| ( ( relation @ SV181 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1693]) ).
thf(1761,plain,
! [SV52: $i,SV182: $i] :
( ( ( ! [SY3402: $i,SY3403: $i] :
( ~ ( in @ ( ordered_pair @ SY3402 @ SY3403 ) @ SV182 )
| ( in @ ( ordered_pair @ SY3403 @ SY3402 ) @ SV52 ) ) )
= $true )
| ( ( SV182
= ( relation_inverse @ SV52 ) )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1694]) ).
thf(1762,plain,
! [SV182: $i,SV52: $i] :
( ( ( ! [SY3404: $i,SY3405: $i] :
( ~ ( in @ ( ordered_pair @ SY3405 @ SY3404 ) @ SV52 )
| ( in @ ( ordered_pair @ SY3404 @ SY3405 ) @ SV182 ) ) )
= $true )
| ( ( SV182
= ( relation_inverse @ SV52 ) )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1695]) ).
thf(1763,plain,
! [SV123: $i,SV142: $i] :
( ( ( ( sK39_C @ SV142 @ SV123 )
= ( sK40_SY3129 @ SV142 @ SV123 ) )
= $false )
| ( ( ~ ( in @ ( sK39_C @ SV142 @ SV123 ) @ SV123 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 ) )
= $true )
| ( ( SV142
= ( identity_relation @ SV123 ) )
= $true )
| ( ( relation @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1696]) ).
thf(1764,plain,
! [SV123: $i,SV142: $i] :
( ( ( ( ( sK39_C @ SV142 @ SV123 )
= ( sK40_SY3129 @ SV142 @ SV123 ) )
| ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 ) )
= $true )
| ( ( SV142
= ( identity_relation @ SV123 ) )
= $true )
| ( ( relation @ SV142 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1697]) ).
thf(1765,plain,
! [SV123: $i,SV142: $i] :
( ( ( ( in @ ( sK39_C @ SV142 @ SV123 ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 ) )
= $true )
| ( ( SV142
= ( identity_relation @ SV123 ) )
= $true )
| ( ( relation @ SV142 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1698]) ).
thf(1766,plain,
! [SV143: $i,SV124: $i,SV250: $i,SV236: $i] :
( ( ( ( SV236 != SV250 )
| ~ ( in @ SV236 @ SV124 )
| ( in @ ( ordered_pair @ SV236 @ SV250 ) @ SV143 ) )
= $true )
| ( ( SV143
= ( identity_relation @ SV124 ) )
= $false )
| ( ( relation @ SV143 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1699]) ).
thf(1767,plain,
! [SV124: $i,SV143: $i] :
( ( ( ~ ! [SY3362: $i,SY3363: $i] :
( ~ ( in @ ( ordered_pair @ SY3362 @ SY3363 ) @ SV143 )
| ( SY3362 = SY3363 ) ) )
= $false )
| ( ( SV143
= ( identity_relation @ SV124 ) )
= $false )
| ( ( relation @ SV143 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1700]) ).
thf(1768,plain,
! [SV124: $i,SV143: $i] :
( ( ( ~ ! [SY3364: $i] :
( ! [SY3365: $i] :
~ ( in @ ( ordered_pair @ SY3364 @ SY3365 ) @ SV143 )
| ( in @ SY3364 @ SV124 ) ) )
= $false )
| ( ( SV143
= ( identity_relation @ SV124 ) )
= $false )
| ( ( relation @ SV143 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1700]) ).
thf(1769,plain,
! [SV53: $i,SV82: $i,SV199: $i] :
( ( ( ~ ( in @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) @ SV53 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV82 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 ) )
= $true )
| ( ( SV199
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $true )
| ( ( relation @ SV199 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1701]) ).
thf(1770,plain,
! [SV53: $i,SV82: $i,SV199: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) @ SV53 )
| ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV82 )
| ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 ) ) ) )
= $true )
| ( ( SV199
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $true )
| ( ( relation @ SV199 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1702]) ).
thf(1771,plain,
! [SV200: $i,SV82: $i,SV53: $i] :
( ( ( ~ ! [SY3429: $i,SY3430: $i] :
( ~ ( in @ SY3430 @ SV53 )
| ~ ( in @ ( ordered_pair @ SY3429 @ SY3430 ) @ SV82 )
| ( in @ ( ordered_pair @ SY3429 @ SY3430 ) @ SV200 ) ) )
= $false )
| ( ( SV200
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $false )
| ( ( relation @ SV200 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1703]) ).
thf(1772,plain,
! [SV82: $i,SV53: $i,SV200: $i] :
( ( ( ~ ~ ( ~ ! [SY3431: $i,SY3432: $i] :
( ~ ( in @ ( ordered_pair @ SY3431 @ SY3432 ) @ SV200 )
| ( in @ SY3432 @ SV53 ) )
| ~ ! [SY3433: $i,SY3434: $i] :
( ~ ( in @ ( ordered_pair @ SY3433 @ SY3434 ) @ SV200 )
| ( in @ ( ordered_pair @ SY3433 @ SY3434 ) @ SV82 ) ) ) )
= $false )
| ( ( SV200
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $false )
| ( ( relation @ SV200 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1703]) ).
thf(1773,plain,
! [SV83: $i,SV55: $i,SV220: $i] :
( ( ( relation @ SV220 )
= $false )
| ( ( function @ SV220 )
= $false )
| ( ( ~ ( in @ SV55 @ ( relation_dom @ SV220 ) )
| ~ ( in @ ( apply @ SV220 @ SV55 ) @ ( relation_dom @ SV83 ) )
| ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SV220 @ SV83 ) ) ) )
= $true )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1704]) ).
thf(1774,plain,
! [SV83: $i,SV55: $i,SV237: $i] :
( ( ( ~ ( function @ SV237 )
| ~ ( relation @ SV237 ) )
= $true )
| ( ( ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SV237 @ SV83 ) ) )
| ( in @ SV55 @ ( relation_dom @ SV237 ) ) )
= $true )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1705]) ).
thf(1775,plain,
! [SV83: $i,SV55: $i,SV238: $i] :
( ( ( ~ ( function @ SV238 )
| ~ ( relation @ SV238 ) )
= $true )
| ( ( ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SV238 @ SV83 ) ) )
| ( in @ ( apply @ SV238 @ SV55 ) @ ( relation_dom @ SV83 ) ) )
= $true )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1706]) ).
thf(1776,plain,
! [SV149: $i,SV161: $i,SV221: $i,SV58: $i] :
( ( ( in @ ( ordered_pair @ SV58 @ SV221 ) @ SV161 )
= $false )
| ( ( in @ SV221 @ ( relation_rng @ SV161 ) )
= $false )
| ( ( ~ ( in @ SV221 @ SV149 ) )
= $true )
| ( ( in @ SV58 @ ( relation_inverse_image @ SV161 @ SV149 ) )
= $true )
| ( ( relation @ SV161 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1709]) ).
thf(1777,plain,
! [SV58: $i,SV150: $i,SV162: $i] :
( ( ( ~ ( in @ ( sK46_D @ SV162 @ SV150 @ SV58 ) @ ( relation_rng @ SV162 ) )
| ~ ( in @ ( ordered_pair @ SV58 @ ( sK46_D @ SV162 @ SV150 @ SV58 ) ) @ SV162 ) )
= $false )
| ( ( in @ SV58 @ ( relation_inverse_image @ SV162 @ SV150 ) )
= $false )
| ( ( relation @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1710]) ).
thf(1778,plain,
! [SV59: $i,SV185: $i] :
( ( ( in @ ( ordered_pair @ ( sK22_C @ SV185 @ SV59 ) @ ( sK23_SY3118 @ SV185 @ SV59 ) ) @ SV185 )
= $false )
| ( ( subset @ SV59 @ SV185 )
= $true )
| ( ( relation @ SV185 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1713]) ).
thf(1779,plain,
! [SV186: $i,SV59: $i,SV239: $i,SV229: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV229 @ SV239 ) @ SV59 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV229 @ SV239 ) @ SV186 )
= $true )
| ( ( subset @ SV59 @ SV186 )
= $false )
| ( ( relation @ SV186 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1714]) ).
thf(1780,plain,
! [SV60: $i,SV187: $i,SV203: $i] :
( ( ( ~ ( in @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ SV187 )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV60 )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 ) )
= $true )
| ( ( SV203
= ( relation_dom_restriction @ SV60 @ SV187 ) )
= $true )
| ( ( relation @ SV203 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1715]) ).
thf(1781,plain,
! [SV60: $i,SV187: $i,SV203: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ SV187 )
| ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV60 )
| ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 ) ) ) )
= $true )
| ( ( SV203
= ( relation_dom_restriction @ SV60 @ SV187 ) )
= $true )
| ( ( relation @ SV203 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1716]) ).
thf(1782,plain,
! [SV204: $i,SV60: $i,SV188: $i] :
( ( ( ~ ! [SY3437: $i,SY3438: $i] :
( ~ ( in @ SY3437 @ SV188 )
| ~ ( in @ ( ordered_pair @ SY3437 @ SY3438 ) @ SV60 )
| ( in @ ( ordered_pair @ SY3437 @ SY3438 ) @ SV204 ) ) )
= $false )
| ( ( SV204
= ( relation_dom_restriction @ SV60 @ SV188 ) )
= $false )
| ( ( relation @ SV204 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1717]) ).
thf(1783,plain,
! [SV60: $i,SV188: $i,SV204: $i] :
( ( ( ~ ~ ( ~ ! [SY3439: $i] :
( ! [SY3440: $i] :
~ ( in @ ( ordered_pair @ SY3439 @ SY3440 ) @ SV204 )
| ( in @ SY3439 @ SV188 ) )
| ~ ! [SY3441: $i,SY3442: $i] :
( ~ ( in @ ( ordered_pair @ SY3441 @ SY3442 ) @ SV204 )
| ( in @ ( ordered_pair @ SY3441 @ SY3442 ) @ SV60 ) ) ) )
= $false )
| ( ( SV204
= ( relation_dom_restriction @ SV60 @ SV188 ) )
= $false )
| ( ( relation @ SV204 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1717]) ).
thf(1784,plain,
! [SV205: $i,SV189: $i,SV39: $i] :
( ( ( in @ ( ordered_pair @ SV39 @ SV189 ) @ SV205 )
= $false )
| ( ( SV189
= ( apply @ SV205 @ SV39 ) )
= $true )
| ( ( function @ SV205 )
= $false )
| ( ( relation @ SV205 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1719]) ).
thf(1785,plain,
! [SV206: $i,SV190: $i,SV39: $i] :
( ( ( in @ ( ordered_pair @ SV39 @ SV190 ) @ SV206 )
= $false )
| ( ( in @ SV39 @ ( relation_dom @ SV206 ) )
= $true )
| ( ( function @ SV206 )
= $false )
| ( ( relation @ SV206 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1720]) ).
thf(1786,plain,
! [SV40: $i,SV222: $i] :
( ( ( relation @ SV222 )
= $false )
| ( ( function @ SV222 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) )
| ( SV222
= ( function_inverse @ SV40 ) ) )
= $true )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1721]) ).
thf(1787,plain,
! [SV40: $i,SV240: $i] :
( ( ( ~ ( function @ SV240 )
| ~ ( relation @ SV240 ) )
= $true )
| ( ( ( SV240
!= ( function_inverse @ SV40 ) )
| ~ ( ~ ~ ( ~ ! [SY3461: $i,SY3462: $i] :
( ( SY3462
!= ( apply @ SV240 @ SY3461 ) )
| ~ ( in @ SY3461 @ ( relation_rng @ SV40 ) )
| ( SY3461
= ( apply @ SV40 @ SY3462 ) ) )
| ~ ! [SY3463: $i,SY3464: $i] :
( ( SY3464
!= ( apply @ SV240 @ SY3463 ) )
| ~ ( in @ SY3463 @ ( relation_rng @ SV40 ) )
| ( in @ SY3464 @ ( relation_dom @ SV40 ) ) ) )
| ~ ~ ( ~ ! [SY3465: $i,SY3466: $i] :
( ( SY3465
!= ( apply @ SV40 @ SY3466 ) )
| ~ ( in @ SY3466 @ ( relation_dom @ SV40 ) )
| ( SY3466
= ( apply @ SV240 @ SY3465 ) ) )
| ~ ! [SY3176: $i] :
( ! [SY3177: $i] :
( ( SY3176
!= ( apply @ SV40 @ SY3177 ) )
| ~ ( in @ SY3177 @ ( relation_dom @ SV40 ) ) )
| ( in @ SY3176 @ ( relation_rng @ SV40 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1722]) ).
thf(1788,plain,
! [SV40: $i,SV241: $i] :
( ( ( ~ ( function @ SV241 )
| ~ ( relation @ SV241 ) )
= $true )
| ( ( ( SV241
!= ( function_inverse @ SV40 ) )
| ( ( relation_dom @ SV241 )
= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1723]) ).
thf(1789,plain,
! [SV242: $i,SV41: $i,SV165: $i,SV191: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SV242 ) @ SV41 ) )
= $true )
| ( ( ~ ( in @ SV242 @ SV165 ) )
= $true )
| ( ( ~ ( in @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SV191 ) )
= $true )
| ( ( SV191
= ( relation_inverse_image @ SV41 @ SV165 ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1724]) ).
thf(1790,plain,
! [SV41: $i,SV165: $i,SV191: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ ( sK31_SY3124 @ SV191 @ SV165 @ SV41 ) ) @ SV41 ) )
= $false )
| ( ( in @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SV191 )
= $true )
| ( ( SV191
= ( relation_inverse_image @ SV41 @ SV165 ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1725]) ).
thf(1791,plain,
! [SV41: $i,SV165: $i,SV191: $i] :
( ( ( ~ ( in @ ( sK31_SY3124 @ SV191 @ SV165 @ SV41 ) @ SV165 ) )
= $false )
| ( ( in @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SV191 )
= $true )
| ( ( SV191
= ( relation_inverse_image @ SV41 @ SV165 ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1725]) ).
thf(1792,plain,
! [SV192: $i,SV166: $i,SV41: $i,SV243: $i] :
( ( ( ! [SY3469: $i] :
( ~ ( in @ ( ordered_pair @ SV243 @ SY3469 ) @ SV41 )
| ~ ( in @ SY3469 @ SV166 ) ) )
= $true )
| ( ( in @ SV243 @ SV192 )
= $true )
| ( ( SV192
= ( relation_inverse_image @ SV41 @ SV166 ) )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1726]) ).
thf(1793,plain,
! [SV41: $i,SV166: $i,SV192: $i,SV244: $i] :
( ( ( ~ ( in @ SV244 @ SV192 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV244 @ ( sK29_E @ SV244 @ SV192 @ SV166 @ SV41 ) ) @ SV41 )
| ~ ( in @ ( sK29_E @ SV244 @ SV192 @ SV166 @ SV41 ) @ SV166 ) ) )
= $true )
| ( ( SV192
= ( relation_inverse_image @ SV41 @ SV166 ) )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1727]) ).
thf(1794,plain,
! [SV230: $i,SV42: $i,SV167: $i] :
( ( ( in @ ( sK17_C @ SV167 @ SV42 ) @ SV167 )
= $false )
| ( ( in @ ( ordered_pair @ SV230 @ ( sK17_C @ SV167 @ SV42 ) ) @ SV42 )
= $false )
| ( ( SV167
= ( relation_rng @ SV42 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1728]) ).
thf(1795,plain,
! [SV168: $i,SV42: $i,SV231: $i,SV251: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV251 @ SV231 ) @ SV42 ) )
= $true )
| ( ( in @ SV231 @ SV168 )
= $true )
| ( ( SV168
= ( relation_rng @ SV42 ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1729]) ).
thf(1796,plain,
! [SV42: $i,SV168: $i,SV232: $i] :
( ( ( in @ SV232 @ SV168 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK16_D @ SV232 @ SV168 @ SV42 ) @ SV232 ) @ SV42 )
= $true )
| ( ( SV168
= ( relation_rng @ SV42 ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1730]) ).
thf(1797,plain,
! [SV92: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_B @ SV92 ) @ ( relation_dom @ SV92 ) )
| ~ ( in @ ( sK13_SY3112 @ SV92 ) @ ( relation_dom @ SV92 ) ) ) )
= $true )
| ( ( one_to_one @ SV92 )
= $true )
| ( ( function @ SV92 )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1731]) ).
thf(1798,plain,
! [SV92: $i] :
( ( ( ( apply @ SV92 @ ( sK12_B @ SV92 ) )
= ( apply @ SV92 @ ( sK13_SY3112 @ SV92 ) ) )
= $true )
| ( ( one_to_one @ SV92 )
= $true )
| ( ( function @ SV92 )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1732]) ).
thf(1799,plain,
! [SV224: $i,SV93: $i,SV223: $i] :
( ( ( ~ ( in @ SV223 @ ( relation_dom @ SV93 ) ) )
= $true )
| ( ( ~ ( in @ SV224 @ ( relation_dom @ SV93 ) ) )
= $true )
| ( ( ( ( apply @ SV93 @ SV223 )
!= ( apply @ SV93 @ SV224 ) ) )
= $true )
| ( ( SV223 = SV224 )
= $true )
| ( ( one_to_one @ SV93 )
= $false )
| ( ( function @ SV93 )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1733]) ).
thf(1800,plain,
! [SV43: $i,SV94: $i,SV214: $i] :
( ( ( ~ ( ! [SY3446: $i] :
( ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ SY3446 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3446 @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV94 ) )
| ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV214 ) ) )
= $false )
| ( ( SV214
= ( relation_composition @ SV43 @ SV94 ) )
= $true )
| ( ( relation @ SV214 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1734]) ).
thf(1801,plain,
! [SV43: $i,SV94: $i,SV214: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK11_SY3111 @ SV214 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY3111 @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV94 ) )
| ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV214 ) ) )
= $false )
| ( ( SV214
= ( relation_composition @ SV43 @ SV94 ) )
= $true )
| ( ( relation @ SV214 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1734]) ).
thf(1802,plain,
! [SV215: $i,SV94: $i,SV43: $i] :
( ( ( ~ ! [SY3447: $i,SY3448: $i] :
( ! [SY3330: $i] :
( ~ ( in @ ( ordered_pair @ SY3447 @ SY3330 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3330 @ SY3448 ) @ SV94 ) )
| ( in @ ( ordered_pair @ SY3447 @ SY3448 ) @ SV215 ) )
| ~ ! [SY3450: $i,SY3451: $i] :
( ~ ( in @ ( ordered_pair @ SY3450 @ SY3451 ) @ SV215 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3450 @ ( sK8_F @ SY3451 @ SY3450 @ SV215 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK8_F @ SY3451 @ SY3450 @ SV215 @ SV94 @ SV43 ) @ SY3451 ) @ SV94 ) ) ) )
= $false )
| ( ( SV215
= ( relation_composition @ SV43 @ SV94 ) )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1735]) ).
thf(1803,plain,
! [SV233: $i,SV44: $i,SV169: $i] :
( ( ( in @ ( sK20_C @ SV169 @ SV44 ) @ SV169 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK20_C @ SV169 @ SV44 ) @ SV233 ) @ SV44 )
= $false )
| ( ( SV169
= ( relation_dom @ SV44 ) )
= $true )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1736]) ).
thf(1804,plain,
! [SV170: $i,SV44: $i,SV252: $i,SV234: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV234 @ SV252 ) @ SV44 ) )
= $true )
| ( ( in @ SV234 @ SV170 )
= $true )
| ( ( SV170
= ( relation_dom @ SV44 ) )
= $false )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1737]) ).
thf(1805,plain,
! [SV44: $i,SV170: $i,SV235: $i] :
( ( ( in @ SV235 @ SV170 )
= $false )
| ( ( in @ ( ordered_pair @ SV235 @ ( sK19_D @ SV235 @ SV170 @ SV44 ) ) @ SV44 )
= $true )
| ( ( SV170
= ( relation_dom @ SV44 ) )
= $false )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1738]) ).
thf(1806,plain,
! [SV225: $i,SV45: $i,SV253: $i] :
( ( ( ( SV253
!= ( apply @ SV45 @ SV225 ) )
| ( in @ ( ordered_pair @ SV225 @ SV253 ) @ SV45 ) )
= $true )
| ( ( in @ SV225 @ ( relation_dom @ SV45 ) )
= $false )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1739]) ).
thf(1807,plain,
! [SV45: $i,SV254: $i,SV226: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV226 @ SV254 ) @ SV45 )
| ( SV254
= ( apply @ SV45 @ SV226 ) ) )
= $true )
| ( ( in @ SV226 @ ( relation_dom @ SV45 ) )
= $false )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1740]) ).
thf(1808,plain,
! [SV227: $i,SV45: $i,SV245: $i] :
( ( ( ( SV245
!= ( apply @ SV45 @ SV227 ) ) )
= $true )
| ( ( SV245 = empty_set )
= $true )
| ( ( in @ SV227 @ ( relation_dom @ SV45 ) )
= $true )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1741]) ).
thf(1809,plain,
! [SV228: $i,SV45: $i,SV246: $i] :
( ( ( ( SV246 != empty_set ) )
= $true )
| ( ( SV246
= ( apply @ SV45 @ SV228 ) )
= $true )
| ( ( in @ SV228 @ ( relation_dom @ SV45 ) )
= $true )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1742]) ).
thf(1810,plain,
! [SV101: $i,SV134: $i] :
( ( ( ( relation_dom @ SV134 )
= SV101 )
= $false )
| ( ( in @ ( sK45_C @ SV134 @ SV101 ) @ SV101 )
= $true )
| ( ( SV134
= ( identity_relation @ SV101 ) )
= $true )
| ( ( function @ SV134 )
= $false )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1743]) ).
thf(1811,plain,
! [SV101: $i,SV134: $i] :
( ( ( ( apply @ SV134 @ ( sK45_C @ SV134 @ SV101 ) )
= ( sK45_C @ SV134 @ SV101 ) )
= $false )
| ( ( ( ( relation_dom @ SV134 )
!= SV101 ) )
= $true )
| ( ( SV134
= ( identity_relation @ SV101 ) )
= $true )
| ( ( function @ SV134 )
= $false )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1744]) ).
thf(1812,plain,
! [SV193: $i,SV171: $i,SV255: $i] :
( ( ( ~ ( in @ SV255 @ SV171 )
| ( ( apply @ SV193 @ SV255 )
= SV255 ) )
= $true )
| ( ( SV193
= ( identity_relation @ SV171 ) )
= $false )
| ( ( function @ SV193 )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1745]) ).
thf(1813,plain,
! [SV49: $i,SV175: $i] :
( ( ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV49 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV175 ) )
= $true )
| ( ( SV49 = SV175 )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1749]) ).
thf(1814,plain,
! [SV176: $i,SV49: $i,SV256: $i] :
( ( ( ! [SY3471: $i] :
( ~ ( in @ ( ordered_pair @ SV256 @ SY3471 ) @ SV49 )
| ( in @ ( ordered_pair @ SV256 @ SY3471 ) @ SV176 ) ) )
= $true )
| ( ( SV49 = SV176 )
= $false )
| ( ( relation @ SV176 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1751]) ).
thf(1815,plain,
! [SV49: $i,SV176: $i,SV257: $i] :
( ( ( ! [SY3472: $i] :
( ~ ( in @ ( ordered_pair @ SV257 @ SY3472 ) @ SV176 )
| ( in @ ( ordered_pair @ SV257 @ SY3472 ) @ SV49 ) ) )
= $true )
| ( ( SV49 = SV176 )
= $false )
| ( ( relation @ SV176 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(1816,plain,
! [SV50: $i,SV177: $i,SV197: $i,SV247: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV247 @ ( sK33_D @ SV197 @ SV177 @ SV50 ) ) @ SV50 ) )
= $true )
| ( ( ~ ( in @ SV247 @ SV177 ) )
= $true )
| ( ( ~ ( in @ ( sK33_D @ SV197 @ SV177 @ SV50 ) @ SV197 ) )
= $true )
| ( ( SV197
= ( relation_image @ SV50 @ SV177 ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1753]) ).
thf(1817,plain,
! [SV50: $i,SV177: $i,SV197: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK34_SY3126 @ SV197 @ SV177 @ SV50 ) @ ( sK33_D @ SV197 @ SV177 @ SV50 ) ) @ SV50 ) )
= $false )
| ( ( in @ ( sK33_D @ SV197 @ SV177 @ SV50 ) @ SV197 )
= $true )
| ( ( SV197
= ( relation_image @ SV50 @ SV177 ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1754]) ).
thf(1818,plain,
! [SV50: $i,SV177: $i,SV197: $i] :
( ( ( ~ ( in @ ( sK34_SY3126 @ SV197 @ SV177 @ SV50 ) @ SV177 ) )
= $false )
| ( ( in @ ( sK33_D @ SV197 @ SV177 @ SV50 ) @ SV197 )
= $true )
| ( ( SV197
= ( relation_image @ SV50 @ SV177 ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1754]) ).
thf(1819,plain,
! [SV198: $i,SV178: $i,SV50: $i,SV248: $i] :
( ( ( ! [SY3470: $i] :
( ~ ( in @ ( ordered_pair @ SY3470 @ SV248 ) @ SV50 )
| ~ ( in @ SY3470 @ SV178 ) ) )
= $true )
| ( ( in @ SV248 @ SV198 )
= $true )
| ( ( SV198
= ( relation_image @ SV50 @ SV178 ) )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1755]) ).
thf(1820,plain,
! [SV50: $i,SV178: $i,SV198: $i,SV249: $i] :
( ( ( ~ ( in @ SV249 @ SV198 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK32_E @ SV249 @ SV198 @ SV178 @ SV50 ) @ SV249 ) @ SV50 )
| ~ ( in @ ( sK32_E @ SV249 @ SV198 @ SV178 @ SV50 ) @ SV178 ) ) )
= $true )
| ( ( SV198
= ( relation_image @ SV50 @ SV178 ) )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1756]) ).
thf(1821,plain,
! [SV51: $i,SV156: $i,SV140: $i,SV219: $i] :
( ( ( in @ SV219 @ SV140 )
= $false )
| ( ( in @ SV219 @ ( relation_dom @ SV156 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV219 @ SV51 ) @ SV156 )
= $false )
| ( ( in @ SV51 @ ( relation_image @ SV156 @ SV140 ) )
= $true )
| ( ( relation @ SV156 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1757]) ).
thf(1822,plain,
! [SV51: $i,SV141: $i,SV157: $i] :
( ( ( ~ ( in @ ( sK47_D @ SV157 @ SV141 @ SV51 ) @ ( relation_dom @ SV157 ) ) )
= $false )
| ( ( in @ SV51 @ ( relation_image @ SV157 @ SV141 ) )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1758]) ).
thf(1823,plain,
! [SV51: $i,SV141: $i,SV157: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV157 @ SV141 @ SV51 ) @ SV51 ) @ SV157 ) )
= $false )
| ( ( in @ SV51 @ ( relation_image @ SV157 @ SV141 ) )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1758]) ).
thf(1824,plain,
! [SV52: $i,SV181: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_C @ SV181 @ SV52 ) @ ( sK15_SY3113 @ SV181 @ SV52 ) ) @ SV181 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK15_SY3113 @ SV181 @ SV52 ) @ ( sK14_C @ SV181 @ SV52 ) ) @ SV52 ) )
= $true )
| ( ( SV181
= ( relation_inverse @ SV52 ) )
= $true )
| ( ( relation @ SV181 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1759]) ).
thf(1825,plain,
! [SV52: $i,SV182: $i,SV258: $i] :
( ( ( ! [SY3473: $i] :
( ~ ( in @ ( ordered_pair @ SV258 @ SY3473 ) @ SV182 )
| ( in @ ( ordered_pair @ SY3473 @ SV258 ) @ SV52 ) ) )
= $true )
| ( ( SV182
= ( relation_inverse @ SV52 ) )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1761]) ).
thf(1826,plain,
! [SV182: $i,SV52: $i,SV259: $i] :
( ( ( ! [SY3474: $i] :
( ~ ( in @ ( ordered_pair @ SY3474 @ SV259 ) @ SV52 )
| ( in @ ( ordered_pair @ SV259 @ SY3474 ) @ SV182 ) ) )
= $true )
| ( ( SV182
= ( relation_inverse @ SV52 ) )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1762]) ).
thf(1827,plain,
! [SV123: $i,SV142: $i] :
( ( ( in @ ( sK39_C @ SV142 @ SV123 ) @ SV123 )
= $false )
| ( ( ( sK39_C @ SV142 @ SV123 )
= ( sK40_SY3129 @ SV142 @ SV123 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 ) )
= $true )
| ( ( SV142
= ( identity_relation @ SV123 ) )
= $true )
| ( ( relation @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1763]) ).
thf(1828,plain,
! [SV123: $i,SV142: $i] :
( ( ( ( sK39_C @ SV142 @ SV123 )
= ( sK40_SY3129 @ SV142 @ SV123 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 )
= $true )
| ( ( SV142
= ( identity_relation @ SV123 ) )
= $true )
| ( ( relation @ SV142 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1764]) ).
thf(1829,plain,
! [SV123: $i,SV142: $i] :
( ( ( in @ ( sK39_C @ SV142 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 )
= $true )
| ( ( SV142
= ( identity_relation @ SV123 ) )
= $true )
| ( ( relation @ SV142 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1765]) ).
thf(1830,plain,
! [SV143: $i,SV124: $i,SV250: $i,SV236: $i] :
( ( ( ( SV236 != SV250 )
| ~ ( in @ SV236 @ SV124 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV236 @ SV250 ) @ SV143 )
= $true )
| ( ( SV143
= ( identity_relation @ SV124 ) )
= $false )
| ( ( relation @ SV143 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1766]) ).
thf(1831,plain,
! [SV124: $i,SV143: $i] :
( ( ( ! [SY3362: $i,SY3363: $i] :
( ~ ( in @ ( ordered_pair @ SY3362 @ SY3363 ) @ SV143 )
| ( SY3362 = SY3363 ) ) )
= $true )
| ( ( SV143
= ( identity_relation @ SV124 ) )
= $false )
| ( ( relation @ SV143 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1767]) ).
thf(1832,plain,
! [SV124: $i,SV143: $i] :
( ( ( ! [SY3364: $i] :
( ! [SY3365: $i] :
~ ( in @ ( ordered_pair @ SY3364 @ SY3365 ) @ SV143 )
| ( in @ SY3364 @ SV124 ) ) )
= $true )
| ( ( SV143
= ( identity_relation @ SV124 ) )
= $false )
| ( ( relation @ SV143 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1768]) ).
thf(1833,plain,
! [SV53: $i,SV82: $i,SV199: $i] :
( ( ( ~ ( in @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) @ SV53 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV82 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 ) )
= $true )
| ( ( SV199
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $true )
| ( ( relation @ SV199 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1769]) ).
thf(1834,plain,
! [SV53: $i,SV82: $i,SV199: $i] :
( ( ( ~ ( ( in @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) @ SV53 )
| ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV82 )
| ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 ) ) )
= $false )
| ( ( SV199
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $true )
| ( ( relation @ SV199 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1770]) ).
thf(1835,plain,
! [SV200: $i,SV82: $i,SV53: $i] :
( ( ( ! [SY3429: $i,SY3430: $i] :
( ~ ( in @ SY3430 @ SV53 )
| ~ ( in @ ( ordered_pair @ SY3429 @ SY3430 ) @ SV82 )
| ( in @ ( ordered_pair @ SY3429 @ SY3430 ) @ SV200 ) ) )
= $true )
| ( ( SV200
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $false )
| ( ( relation @ SV200 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1771]) ).
thf(1836,plain,
! [SV82: $i,SV53: $i,SV200: $i] :
( ( ( ~ ( ~ ! [SY3431: $i,SY3432: $i] :
( ~ ( in @ ( ordered_pair @ SY3431 @ SY3432 ) @ SV200 )
| ( in @ SY3432 @ SV53 ) )
| ~ ! [SY3433: $i,SY3434: $i] :
( ~ ( in @ ( ordered_pair @ SY3433 @ SY3434 ) @ SV200 )
| ( in @ ( ordered_pair @ SY3433 @ SY3434 ) @ SV82 ) ) ) )
= $true )
| ( ( SV200
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $false )
| ( ( relation @ SV200 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1772]) ).
thf(1837,plain,
! [SV83: $i,SV220: $i,SV55: $i] :
( ( ( ~ ( in @ SV55 @ ( relation_dom @ SV220 ) )
| ~ ( in @ ( apply @ SV220 @ SV55 ) @ ( relation_dom @ SV83 ) ) )
= $true )
| ( ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SV220 @ SV83 ) ) )
= $true )
| ( ( function @ SV220 )
= $false )
| ( ( relation @ SV220 )
= $false )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1773]) ).
thf(1838,plain,
! [SV83: $i,SV55: $i,SV237: $i] :
( ( ( ~ ( function @ SV237 ) )
= $true )
| ( ( ~ ( relation @ SV237 ) )
= $true )
| ( ( ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SV237 @ SV83 ) ) )
| ( in @ SV55 @ ( relation_dom @ SV237 ) ) )
= $true )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1774]) ).
thf(1839,plain,
! [SV83: $i,SV55: $i,SV238: $i] :
( ( ( ~ ( function @ SV238 ) )
= $true )
| ( ( ~ ( relation @ SV238 ) )
= $true )
| ( ( ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SV238 @ SV83 ) ) )
| ( in @ ( apply @ SV238 @ SV55 ) @ ( relation_dom @ SV83 ) ) )
= $true )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1775]) ).
thf(1840,plain,
! [SV58: $i,SV161: $i,SV149: $i,SV221: $i] :
( ( ( in @ SV221 @ SV149 )
= $false )
| ( ( in @ SV221 @ ( relation_rng @ SV161 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV58 @ SV221 ) @ SV161 )
= $false )
| ( ( in @ SV58 @ ( relation_inverse_image @ SV161 @ SV149 ) )
= $true )
| ( ( relation @ SV161 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1776]) ).
thf(1841,plain,
! [SV58: $i,SV150: $i,SV162: $i] :
( ( ( ~ ( in @ ( sK46_D @ SV162 @ SV150 @ SV58 ) @ ( relation_rng @ SV162 ) ) )
= $false )
| ( ( in @ SV58 @ ( relation_inverse_image @ SV162 @ SV150 ) )
= $false )
| ( ( relation @ SV162 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1777]) ).
thf(1842,plain,
! [SV150: $i,SV162: $i,SV58: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV58 @ ( sK46_D @ SV162 @ SV150 @ SV58 ) ) @ SV162 ) )
= $false )
| ( ( in @ SV58 @ ( relation_inverse_image @ SV162 @ SV150 ) )
= $false )
| ( ( relation @ SV162 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1777]) ).
thf(1843,plain,
! [SV186: $i,SV59: $i,SV239: $i,SV229: $i] :
( ( ( in @ ( ordered_pair @ SV229 @ SV239 ) @ SV59 )
= $false )
| ( ( in @ ( ordered_pair @ SV229 @ SV239 ) @ SV186 )
= $true )
| ( ( subset @ SV59 @ SV186 )
= $false )
| ( ( relation @ SV186 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1779]) ).
thf(1844,plain,
! [SV60: $i,SV187: $i,SV203: $i] :
( ( ( ~ ( in @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ SV187 )
| ~ ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV60 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 ) )
= $true )
| ( ( SV203
= ( relation_dom_restriction @ SV60 @ SV187 ) )
= $true )
| ( ( relation @ SV203 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1780]) ).
thf(1845,plain,
! [SV60: $i,SV187: $i,SV203: $i] :
( ( ( ~ ( ( in @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ SV187 )
| ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV60 )
| ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 ) ) )
= $false )
| ( ( SV203
= ( relation_dom_restriction @ SV60 @ SV187 ) )
= $true )
| ( ( relation @ SV203 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1781]) ).
thf(1846,plain,
! [SV204: $i,SV60: $i,SV188: $i] :
( ( ( ! [SY3437: $i,SY3438: $i] :
( ~ ( in @ SY3437 @ SV188 )
| ~ ( in @ ( ordered_pair @ SY3437 @ SY3438 ) @ SV60 )
| ( in @ ( ordered_pair @ SY3437 @ SY3438 ) @ SV204 ) ) )
= $true )
| ( ( SV204
= ( relation_dom_restriction @ SV60 @ SV188 ) )
= $false )
| ( ( relation @ SV204 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1782]) ).
thf(1847,plain,
! [SV60: $i,SV188: $i,SV204: $i] :
( ( ( ~ ( ~ ! [SY3439: $i] :
( ! [SY3440: $i] :
~ ( in @ ( ordered_pair @ SY3439 @ SY3440 ) @ SV204 )
| ( in @ SY3439 @ SV188 ) )
| ~ ! [SY3441: $i,SY3442: $i] :
( ~ ( in @ ( ordered_pair @ SY3441 @ SY3442 ) @ SV204 )
| ( in @ ( ordered_pair @ SY3441 @ SY3442 ) @ SV60 ) ) ) )
= $true )
| ( ( SV204
= ( relation_dom_restriction @ SV60 @ SV188 ) )
= $false )
| ( ( relation @ SV204 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1783]) ).
thf(1848,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1786]) ).
thf(1849,plain,
! [SV40: $i,SV240: $i] :
( ( ( ~ ( function @ SV240 ) )
= $true )
| ( ( ~ ( relation @ SV240 ) )
= $true )
| ( ( ( SV240
!= ( function_inverse @ SV40 ) )
| ~ ( ~ ~ ( ~ ! [SY3461: $i,SY3462: $i] :
( ( SY3462
!= ( apply @ SV240 @ SY3461 ) )
| ~ ( in @ SY3461 @ ( relation_rng @ SV40 ) )
| ( SY3461
= ( apply @ SV40 @ SY3462 ) ) )
| ~ ! [SY3463: $i,SY3464: $i] :
( ( SY3464
!= ( apply @ SV240 @ SY3463 ) )
| ~ ( in @ SY3463 @ ( relation_rng @ SV40 ) )
| ( in @ SY3464 @ ( relation_dom @ SV40 ) ) ) )
| ~ ~ ( ~ ! [SY3465: $i,SY3466: $i] :
( ( SY3465
!= ( apply @ SV40 @ SY3466 ) )
| ~ ( in @ SY3466 @ ( relation_dom @ SV40 ) )
| ( SY3466
= ( apply @ SV240 @ SY3465 ) ) )
| ~ ! [SY3176: $i] :
( ! [SY3177: $i] :
( ( SY3176
!= ( apply @ SV40 @ SY3177 ) )
| ~ ( in @ SY3177 @ ( relation_dom @ SV40 ) ) )
| ( in @ SY3176 @ ( relation_rng @ SV40 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1787]) ).
thf(1850,plain,
! [SV40: $i,SV241: $i] :
( ( ( ~ ( function @ SV241 ) )
= $true )
| ( ( ~ ( relation @ SV241 ) )
= $true )
| ( ( ( SV241
!= ( function_inverse @ SV40 ) )
| ( ( relation_dom @ SV241 )
= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1788]) ).
thf(1851,plain,
! [SV242: $i,SV41: $i,SV165: $i,SV191: $i] :
( ( ( in @ ( ordered_pair @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SV242 ) @ SV41 )
= $false )
| ( ( ~ ( in @ SV242 @ SV165 ) )
= $true )
| ( ( ~ ( in @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SV191 ) )
= $true )
| ( ( SV191
= ( relation_inverse_image @ SV41 @ SV165 ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1789]) ).
thf(1852,plain,
! [SV41: $i,SV165: $i,SV191: $i] :
( ( ( in @ ( ordered_pair @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ ( sK31_SY3124 @ SV191 @ SV165 @ SV41 ) ) @ SV41 )
= $true )
| ( ( in @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SV191 )
= $true )
| ( ( SV191
= ( relation_inverse_image @ SV41 @ SV165 ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1790]) ).
thf(1853,plain,
! [SV41: $i,SV165: $i,SV191: $i] :
( ( ( in @ ( sK31_SY3124 @ SV191 @ SV165 @ SV41 ) @ SV165 )
= $true )
| ( ( in @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SV191 )
= $true )
| ( ( SV191
= ( relation_inverse_image @ SV41 @ SV165 ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1791]) ).
thf(1854,plain,
! [SV192: $i,SV166: $i,SV41: $i,SV260: $i,SV243: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV243 @ SV260 ) @ SV41 )
| ~ ( in @ SV260 @ SV166 ) )
= $true )
| ( ( in @ SV243 @ SV192 )
= $true )
| ( ( SV192
= ( relation_inverse_image @ SV41 @ SV166 ) )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1792]) ).
thf(1855,plain,
! [SV41: $i,SV166: $i,SV192: $i,SV244: $i] :
( ( ( in @ SV244 @ SV192 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV244 @ ( sK29_E @ SV244 @ SV192 @ SV166 @ SV41 ) ) @ SV41 )
| ~ ( in @ ( sK29_E @ SV244 @ SV192 @ SV166 @ SV41 ) @ SV166 ) ) )
= $true )
| ( ( SV192
= ( relation_inverse_image @ SV41 @ SV166 ) )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1793]) ).
thf(1856,plain,
! [SV168: $i,SV42: $i,SV231: $i,SV251: $i] :
( ( ( in @ ( ordered_pair @ SV251 @ SV231 ) @ SV42 )
= $false )
| ( ( in @ SV231 @ SV168 )
= $true )
| ( ( SV168
= ( relation_rng @ SV42 ) )
= $false )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1795]) ).
thf(1857,plain,
! [SV92: $i] :
( ( ( ~ ( in @ ( sK12_B @ SV92 ) @ ( relation_dom @ SV92 ) )
| ~ ( in @ ( sK13_SY3112 @ SV92 ) @ ( relation_dom @ SV92 ) ) )
= $false )
| ( ( one_to_one @ SV92 )
= $true )
| ( ( function @ SV92 )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1797]) ).
thf(1858,plain,
! [SV224: $i,SV93: $i,SV223: $i] :
( ( ( in @ SV223 @ ( relation_dom @ SV93 ) )
= $false )
| ( ( ~ ( in @ SV224 @ ( relation_dom @ SV93 ) ) )
= $true )
| ( ( ( ( apply @ SV93 @ SV223 )
!= ( apply @ SV93 @ SV224 ) ) )
= $true )
| ( ( SV223 = SV224 )
= $true )
| ( ( one_to_one @ SV93 )
= $false )
| ( ( function @ SV93 )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1799]) ).
thf(1859,plain,
! [SV43: $i,SV94: $i,SV214: $i] :
( ( ( ! [SY3446: $i] :
( ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ SY3446 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3446 @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV94 ) )
| ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV214 ) )
= $true )
| ( ( SV214
= ( relation_composition @ SV43 @ SV94 ) )
= $true )
| ( ( relation @ SV214 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1800]) ).
thf(1860,plain,
! [SV43: $i,SV94: $i,SV214: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK11_SY3111 @ SV214 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY3111 @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV94 ) )
| ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV214 ) )
= $true )
| ( ( SV214
= ( relation_composition @ SV43 @ SV94 ) )
= $true )
| ( ( relation @ SV214 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1801]) ).
thf(1861,plain,
! [SV215: $i,SV94: $i,SV43: $i] :
( ( ( ~ ! [SY3447: $i,SY3448: $i] :
( ! [SY3330: $i] :
( ~ ( in @ ( ordered_pair @ SY3447 @ SY3330 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3330 @ SY3448 ) @ SV94 ) )
| ( in @ ( ordered_pair @ SY3447 @ SY3448 ) @ SV215 ) ) )
= $false )
| ( ( SV215
= ( relation_composition @ SV43 @ SV94 ) )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1802]) ).
thf(1862,plain,
! [SV43: $i,SV94: $i,SV215: $i] :
( ( ( ~ ! [SY3450: $i,SY3451: $i] :
( ~ ( in @ ( ordered_pair @ SY3450 @ SY3451 ) @ SV215 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3450 @ ( sK8_F @ SY3451 @ SY3450 @ SV215 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK8_F @ SY3451 @ SY3450 @ SV215 @ SV94 @ SV43 ) @ SY3451 ) @ SV94 ) ) ) )
= $false )
| ( ( SV215
= ( relation_composition @ SV43 @ SV94 ) )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1802]) ).
thf(1863,plain,
! [SV170: $i,SV44: $i,SV252: $i,SV234: $i] :
( ( ( in @ ( ordered_pair @ SV234 @ SV252 ) @ SV44 )
= $false )
| ( ( in @ SV234 @ SV170 )
= $true )
| ( ( SV170
= ( relation_dom @ SV44 ) )
= $false )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1804]) ).
thf(1864,plain,
! [SV225: $i,SV45: $i,SV253: $i] :
( ( ( ( SV253
!= ( apply @ SV45 @ SV225 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV225 @ SV253 ) @ SV45 )
= $true )
| ( ( in @ SV225 @ ( relation_dom @ SV45 ) )
= $false )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1806]) ).
thf(1865,plain,
! [SV45: $i,SV254: $i,SV226: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV226 @ SV254 ) @ SV45 ) )
= $true )
| ( ( SV254
= ( apply @ SV45 @ SV226 ) )
= $true )
| ( ( in @ SV226 @ ( relation_dom @ SV45 ) )
= $false )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1807]) ).
thf(1866,plain,
! [SV227: $i,SV45: $i,SV245: $i] :
( ( ( SV245
= ( apply @ SV45 @ SV227 ) )
= $false )
| ( ( SV245 = empty_set )
= $true )
| ( ( in @ SV227 @ ( relation_dom @ SV45 ) )
= $true )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1808]) ).
thf(1867,plain,
! [SV228: $i,SV45: $i,SV246: $i] :
( ( ( SV246 = empty_set )
= $false )
| ( ( SV246
= ( apply @ SV45 @ SV228 ) )
= $true )
| ( ( in @ SV228 @ ( relation_dom @ SV45 ) )
= $true )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1809]) ).
thf(1868,plain,
! [SV101: $i,SV134: $i] :
( ( ( ( relation_dom @ SV134 )
= SV101 )
= $false )
| ( ( ( apply @ SV134 @ ( sK45_C @ SV134 @ SV101 ) )
= ( sK45_C @ SV134 @ SV101 ) )
= $false )
| ( ( SV134
= ( identity_relation @ SV101 ) )
= $true )
| ( ( function @ SV134 )
= $false )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1811]) ).
thf(1869,plain,
! [SV193: $i,SV171: $i,SV255: $i] :
( ( ( ~ ( in @ SV255 @ SV171 ) )
= $true )
| ( ( ( apply @ SV193 @ SV255 )
= SV255 )
= $true )
| ( ( SV193
= ( identity_relation @ SV171 ) )
= $false )
| ( ( function @ SV193 )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1812]) ).
thf(1870,plain,
! [SV49: $i,SV175: $i] :
( ( ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV175 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK24_C @ SV175 @ SV49 ) @ ( sK25_SY3119 @ SV175 @ SV49 ) ) @ SV49 )
= $false )
| ( ( SV49 = SV175 )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1813]) ).
thf(1871,plain,
! [SV176: $i,SV49: $i,SV261: $i,SV256: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV256 @ SV261 ) @ SV49 )
| ( in @ ( ordered_pair @ SV256 @ SV261 ) @ SV176 ) )
= $true )
| ( ( SV49 = SV176 )
= $false )
| ( ( relation @ SV176 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1814]) ).
thf(1872,plain,
! [SV49: $i,SV176: $i,SV262: $i,SV257: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV257 @ SV262 ) @ SV176 )
| ( in @ ( ordered_pair @ SV257 @ SV262 ) @ SV49 ) )
= $true )
| ( ( SV49 = SV176 )
= $false )
| ( ( relation @ SV176 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1815]) ).
thf(1873,plain,
! [SV50: $i,SV177: $i,SV197: $i,SV247: $i] :
( ( ( in @ ( ordered_pair @ SV247 @ ( sK33_D @ SV197 @ SV177 @ SV50 ) ) @ SV50 )
= $false )
| ( ( ~ ( in @ SV247 @ SV177 ) )
= $true )
| ( ( ~ ( in @ ( sK33_D @ SV197 @ SV177 @ SV50 ) @ SV197 ) )
= $true )
| ( ( SV197
= ( relation_image @ SV50 @ SV177 ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1816]) ).
thf(1874,plain,
! [SV50: $i,SV177: $i,SV197: $i] :
( ( ( in @ ( ordered_pair @ ( sK34_SY3126 @ SV197 @ SV177 @ SV50 ) @ ( sK33_D @ SV197 @ SV177 @ SV50 ) ) @ SV50 )
= $true )
| ( ( in @ ( sK33_D @ SV197 @ SV177 @ SV50 ) @ SV197 )
= $true )
| ( ( SV197
= ( relation_image @ SV50 @ SV177 ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1817]) ).
thf(1875,plain,
! [SV50: $i,SV177: $i,SV197: $i] :
( ( ( in @ ( sK34_SY3126 @ SV197 @ SV177 @ SV50 ) @ SV177 )
= $true )
| ( ( in @ ( sK33_D @ SV197 @ SV177 @ SV50 ) @ SV197 )
= $true )
| ( ( SV197
= ( relation_image @ SV50 @ SV177 ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1818]) ).
thf(1876,plain,
! [SV198: $i,SV178: $i,SV50: $i,SV248: $i,SV263: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV263 @ SV248 ) @ SV50 )
| ~ ( in @ SV263 @ SV178 ) )
= $true )
| ( ( in @ SV248 @ SV198 )
= $true )
| ( ( SV198
= ( relation_image @ SV50 @ SV178 ) )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1819]) ).
thf(1877,plain,
! [SV50: $i,SV178: $i,SV198: $i,SV249: $i] :
( ( ( in @ SV249 @ SV198 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK32_E @ SV249 @ SV198 @ SV178 @ SV50 ) @ SV249 ) @ SV50 )
| ~ ( in @ ( sK32_E @ SV249 @ SV198 @ SV178 @ SV50 ) @ SV178 ) ) )
= $true )
| ( ( SV198
= ( relation_image @ SV50 @ SV178 ) )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1820]) ).
thf(1878,plain,
! [SV51: $i,SV141: $i,SV157: $i] :
( ( ( in @ ( sK47_D @ SV157 @ SV141 @ SV51 ) @ ( relation_dom @ SV157 ) )
= $true )
| ( ( in @ SV51 @ ( relation_image @ SV157 @ SV141 ) )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1822]) ).
thf(1879,plain,
! [SV51: $i,SV141: $i,SV157: $i] :
( ( ( in @ ( ordered_pair @ ( sK47_D @ SV157 @ SV141 @ SV51 ) @ SV51 ) @ SV157 )
= $true )
| ( ( in @ SV51 @ ( relation_image @ SV157 @ SV141 ) )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1823]) ).
thf(1880,plain,
! [SV52: $i,SV181: $i] :
( ( ( in @ ( ordered_pair @ ( sK15_SY3113 @ SV181 @ SV52 ) @ ( sK14_C @ SV181 @ SV52 ) ) @ SV52 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK14_C @ SV181 @ SV52 ) @ ( sK15_SY3113 @ SV181 @ SV52 ) ) @ SV181 )
= $false )
| ( ( SV181
= ( relation_inverse @ SV52 ) )
= $true )
| ( ( relation @ SV181 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1824]) ).
thf(1881,plain,
! [SV52: $i,SV182: $i,SV264: $i,SV258: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV258 @ SV264 ) @ SV182 )
| ( in @ ( ordered_pair @ SV264 @ SV258 ) @ SV52 ) )
= $true )
| ( ( SV182
= ( relation_inverse @ SV52 ) )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1825]) ).
thf(1882,plain,
! [SV182: $i,SV52: $i,SV259: $i,SV265: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV265 @ SV259 ) @ SV52 )
| ( in @ ( ordered_pair @ SV259 @ SV265 ) @ SV182 ) )
= $true )
| ( ( SV182
= ( relation_inverse @ SV52 ) )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(1883,plain,
! [SV123: $i,SV142: $i] :
( ( ( in @ ( ordered_pair @ ( sK39_C @ SV142 @ SV123 ) @ ( sK40_SY3129 @ SV142 @ SV123 ) ) @ SV142 )
= $false )
| ( ( ( sK39_C @ SV142 @ SV123 )
= ( sK40_SY3129 @ SV142 @ SV123 ) )
= $false )
| ( ( in @ ( sK39_C @ SV142 @ SV123 ) @ SV123 )
= $false )
| ( ( SV142
= ( identity_relation @ SV123 ) )
= $true )
| ( ( relation @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1827]) ).
thf(1884,plain,
! [SV143: $i,SV124: $i,SV250: $i,SV236: $i] :
( ( ( ( SV236 != SV250 ) )
= $true )
| ( ( ~ ( in @ SV236 @ SV124 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV236 @ SV250 ) @ SV143 )
= $true )
| ( ( SV143
= ( identity_relation @ SV124 ) )
= $false )
| ( ( relation @ SV143 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1830]) ).
thf(1885,plain,
! [SV124: $i,SV143: $i,SV266: $i] :
( ( ( ! [SY3475: $i] :
( ~ ( in @ ( ordered_pair @ SV266 @ SY3475 ) @ SV143 )
| ( SV266 = SY3475 ) ) )
= $true )
| ( ( SV143
= ( identity_relation @ SV124 ) )
= $false )
| ( ( relation @ SV143 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1831]) ).
thf(1886,plain,
! [SV124: $i,SV143: $i,SV267: $i] :
( ( ( ! [SY3476: $i] :
~ ( in @ ( ordered_pair @ SV267 @ SY3476 ) @ SV143 )
| ( in @ SV267 @ SV124 ) )
= $true )
| ( ( SV143
= ( identity_relation @ SV124 ) )
= $false )
| ( ( relation @ SV143 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1832]) ).
thf(1887,plain,
! [SV53: $i,SV82: $i,SV199: $i] :
( ( ( ~ ( in @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) @ SV53 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV82 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 ) )
= $true )
| ( ( SV199
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $true )
| ( ( relation @ SV199 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1833]) ).
thf(1888,plain,
! [SV53: $i,SV82: $i,SV199: $i] :
( ( ( ~ ( ( in @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) @ SV53 )
| ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 ) ) )
= $false )
| ( ( SV199
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $true )
| ( ( relation @ SV199 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1834]) ).
thf(1889,plain,
! [SV53: $i,SV82: $i,SV199: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV82 )
| ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 ) ) )
= $false )
| ( ( SV199
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $true )
| ( ( relation @ SV199 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1834]) ).
thf(1890,plain,
! [SV200: $i,SV82: $i,SV268: $i,SV53: $i] :
( ( ( ! [SY3477: $i] :
( ~ ( in @ SY3477 @ SV53 )
| ~ ( in @ ( ordered_pair @ SV268 @ SY3477 ) @ SV82 )
| ( in @ ( ordered_pair @ SV268 @ SY3477 ) @ SV200 ) ) )
= $true )
| ( ( SV200
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $false )
| ( ( relation @ SV200 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1835]) ).
thf(1891,plain,
! [SV82: $i,SV53: $i,SV200: $i] :
( ( ( ~ ! [SY3431: $i,SY3432: $i] :
( ~ ( in @ ( ordered_pair @ SY3431 @ SY3432 ) @ SV200 )
| ( in @ SY3432 @ SV53 ) )
| ~ ! [SY3433: $i,SY3434: $i] :
( ~ ( in @ ( ordered_pair @ SY3433 @ SY3434 ) @ SV200 )
| ( in @ ( ordered_pair @ SY3433 @ SY3434 ) @ SV82 ) ) )
= $false )
| ( ( SV200
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $false )
| ( ( relation @ SV200 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1836]) ).
thf(1892,plain,
! [SV83: $i,SV220: $i,SV55: $i] :
( ( ( ~ ( in @ SV55 @ ( relation_dom @ SV220 ) ) )
= $true )
| ( ( ~ ( in @ ( apply @ SV220 @ SV55 ) @ ( relation_dom @ SV83 ) ) )
= $true )
| ( ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SV220 @ SV83 ) ) )
= $true )
| ( ( function @ SV220 )
= $false )
| ( ( relation @ SV220 )
= $false )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1837]) ).
thf(1893,plain,
! [SV83: $i,SV55: $i,SV237: $i] :
( ( ( function @ SV237 )
= $false )
| ( ( ~ ( relation @ SV237 ) )
= $true )
| ( ( ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SV237 @ SV83 ) ) )
| ( in @ SV55 @ ( relation_dom @ SV237 ) ) )
= $true )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1838]) ).
thf(1894,plain,
! [SV83: $i,SV55: $i,SV238: $i] :
( ( ( function @ SV238 )
= $false )
| ( ( ~ ( relation @ SV238 ) )
= $true )
| ( ( ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SV238 @ SV83 ) ) )
| ( in @ ( apply @ SV238 @ SV55 ) @ ( relation_dom @ SV83 ) ) )
= $true )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1839]) ).
thf(1895,plain,
! [SV58: $i,SV150: $i,SV162: $i] :
( ( ( in @ ( sK46_D @ SV162 @ SV150 @ SV58 ) @ ( relation_rng @ SV162 ) )
= $true )
| ( ( in @ SV58 @ ( relation_inverse_image @ SV162 @ SV150 ) )
= $false )
| ( ( relation @ SV162 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1841]) ).
thf(1896,plain,
! [SV150: $i,SV162: $i,SV58: $i] :
( ( ( in @ ( ordered_pair @ SV58 @ ( sK46_D @ SV162 @ SV150 @ SV58 ) ) @ SV162 )
= $true )
| ( ( in @ SV58 @ ( relation_inverse_image @ SV162 @ SV150 ) )
= $false )
| ( ( relation @ SV162 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1842]) ).
thf(1897,plain,
! [SV60: $i,SV187: $i,SV203: $i] :
( ( ( ~ ( in @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ SV187 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV60 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 ) )
= $true )
| ( ( SV203
= ( relation_dom_restriction @ SV60 @ SV187 ) )
= $true )
| ( ( relation @ SV203 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1844]) ).
thf(1898,plain,
! [SV60: $i,SV187: $i,SV203: $i] :
( ( ( ~ ( ( in @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ SV187 )
| ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 ) ) )
= $false )
| ( ( SV203
= ( relation_dom_restriction @ SV60 @ SV187 ) )
= $true )
| ( ( relation @ SV203 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1845]) ).
thf(1899,plain,
! [SV60: $i,SV187: $i,SV203: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV60 )
| ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 ) ) )
= $false )
| ( ( SV203
= ( relation_dom_restriction @ SV60 @ SV187 ) )
= $true )
| ( ( relation @ SV203 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1845]) ).
thf(1900,plain,
! [SV204: $i,SV60: $i,SV188: $i,SV269: $i] :
( ( ( ! [SY3478: $i] :
( ~ ( in @ SV269 @ SV188 )
| ~ ( in @ ( ordered_pair @ SV269 @ SY3478 ) @ SV60 )
| ( in @ ( ordered_pair @ SV269 @ SY3478 ) @ SV204 ) ) )
= $true )
| ( ( SV204
= ( relation_dom_restriction @ SV60 @ SV188 ) )
= $false )
| ( ( relation @ SV204 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1846]) ).
thf(1901,plain,
! [SV60: $i,SV188: $i,SV204: $i] :
( ( ( ~ ! [SY3439: $i] :
( ! [SY3440: $i] :
~ ( in @ ( ordered_pair @ SY3439 @ SY3440 ) @ SV204 )
| ( in @ SY3439 @ SV188 ) )
| ~ ! [SY3441: $i,SY3442: $i] :
( ~ ( in @ ( ordered_pair @ SY3441 @ SY3442 ) @ SV204 )
| ( in @ ( ordered_pair @ SY3441 @ SY3442 ) @ SV60 ) ) )
= $false )
| ( ( SV204
= ( relation_dom_restriction @ SV60 @ SV188 ) )
= $false )
| ( ( relation @ SV204 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1847]) ).
thf(1902,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1848]) ).
thf(1903,plain,
! [SV40: $i,SV240: $i] :
( ( ( function @ SV240 )
= $false )
| ( ( ~ ( relation @ SV240 ) )
= $true )
| ( ( ( SV240
!= ( function_inverse @ SV40 ) )
| ~ ( ~ ~ ( ~ ! [SY3461: $i,SY3462: $i] :
( ( SY3462
!= ( apply @ SV240 @ SY3461 ) )
| ~ ( in @ SY3461 @ ( relation_rng @ SV40 ) )
| ( SY3461
= ( apply @ SV40 @ SY3462 ) ) )
| ~ ! [SY3463: $i,SY3464: $i] :
( ( SY3464
!= ( apply @ SV240 @ SY3463 ) )
| ~ ( in @ SY3463 @ ( relation_rng @ SV40 ) )
| ( in @ SY3464 @ ( relation_dom @ SV40 ) ) ) )
| ~ ~ ( ~ ! [SY3465: $i,SY3466: $i] :
( ( SY3465
!= ( apply @ SV40 @ SY3466 ) )
| ~ ( in @ SY3466 @ ( relation_dom @ SV40 ) )
| ( SY3466
= ( apply @ SV240 @ SY3465 ) ) )
| ~ ! [SY3176: $i] :
( ! [SY3177: $i] :
( ( SY3176
!= ( apply @ SV40 @ SY3177 ) )
| ~ ( in @ SY3177 @ ( relation_dom @ SV40 ) ) )
| ( in @ SY3176 @ ( relation_rng @ SV40 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1849]) ).
thf(1904,plain,
! [SV40: $i,SV241: $i] :
( ( ( function @ SV241 )
= $false )
| ( ( ~ ( relation @ SV241 ) )
= $true )
| ( ( ( SV241
!= ( function_inverse @ SV40 ) )
| ( ( relation_dom @ SV241 )
= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1850]) ).
thf(1905,plain,
! [SV41: $i,SV191: $i,SV165: $i,SV242: $i] :
( ( ( in @ SV242 @ SV165 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SV242 ) @ SV41 )
= $false )
| ( ( ~ ( in @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SV191 ) )
= $true )
| ( ( SV191
= ( relation_inverse_image @ SV41 @ SV165 ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1851]) ).
thf(1906,plain,
! [SV192: $i,SV166: $i,SV41: $i,SV260: $i,SV243: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV243 @ SV260 ) @ SV41 ) )
= $true )
| ( ( ~ ( in @ SV260 @ SV166 ) )
= $true )
| ( ( in @ SV243 @ SV192 )
= $true )
| ( ( SV192
= ( relation_inverse_image @ SV41 @ SV166 ) )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1854]) ).
thf(1907,plain,
! [SV41: $i,SV166: $i,SV192: $i,SV244: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV244 @ ( sK29_E @ SV244 @ SV192 @ SV166 @ SV41 ) ) @ SV41 )
| ~ ( in @ ( sK29_E @ SV244 @ SV192 @ SV166 @ SV41 ) @ SV166 ) )
= $false )
| ( ( in @ SV244 @ SV192 )
= $false )
| ( ( SV192
= ( relation_inverse_image @ SV41 @ SV166 ) )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1855]) ).
thf(1908,plain,
! [SV92: $i] :
( ( ( ~ ( in @ ( sK12_B @ SV92 ) @ ( relation_dom @ SV92 ) ) )
= $false )
| ( ( one_to_one @ SV92 )
= $true )
| ( ( function @ SV92 )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1857]) ).
thf(1909,plain,
! [SV92: $i] :
( ( ( ~ ( in @ ( sK13_SY3112 @ SV92 ) @ ( relation_dom @ SV92 ) ) )
= $false )
| ( ( one_to_one @ SV92 )
= $true )
| ( ( function @ SV92 )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1857]) ).
thf(1910,plain,
! [SV223: $i,SV93: $i,SV224: $i] :
( ( ( in @ SV224 @ ( relation_dom @ SV93 ) )
= $false )
| ( ( in @ SV223 @ ( relation_dom @ SV93 ) )
= $false )
| ( ( ( ( apply @ SV93 @ SV223 )
!= ( apply @ SV93 @ SV224 ) ) )
= $true )
| ( ( SV223 = SV224 )
= $true )
| ( ( one_to_one @ SV93 )
= $false )
| ( ( function @ SV93 )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1858]) ).
thf(1911,plain,
! [SV43: $i,SV94: $i,SV214: $i] :
( ( ( ! [SY3446: $i] :
( ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ SY3446 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3446 @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV94 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV214 ) )
= $true )
| ( ( SV214
= ( relation_composition @ SV43 @ SV94 ) )
= $true )
| ( ( relation @ SV214 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1859]) ).
thf(1912,plain,
! [SV43: $i,SV94: $i,SV214: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK11_SY3111 @ SV214 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY3111 @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV94 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV214 )
= $true )
| ( ( SV214
= ( relation_composition @ SV43 @ SV94 ) )
= $true )
| ( ( relation @ SV214 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1860]) ).
thf(1913,plain,
! [SV215: $i,SV94: $i,SV43: $i] :
( ( ( ! [SY3447: $i,SY3448: $i] :
( ! [SY3330: $i] :
( ~ ( in @ ( ordered_pair @ SY3447 @ SY3330 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3330 @ SY3448 ) @ SV94 ) )
| ( in @ ( ordered_pair @ SY3447 @ SY3448 ) @ SV215 ) ) )
= $true )
| ( ( SV215
= ( relation_composition @ SV43 @ SV94 ) )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1861]) ).
thf(1914,plain,
! [SV43: $i,SV94: $i,SV215: $i] :
( ( ( ! [SY3450: $i,SY3451: $i] :
( ~ ( in @ ( ordered_pair @ SY3450 @ SY3451 ) @ SV215 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3450 @ ( sK8_F @ SY3451 @ SY3450 @ SV215 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK8_F @ SY3451 @ SY3450 @ SV215 @ SV94 @ SV43 ) @ SY3451 ) @ SV94 ) ) ) )
= $true )
| ( ( SV215
= ( relation_composition @ SV43 @ SV94 ) )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1862]) ).
thf(1915,plain,
! [SV225: $i,SV45: $i,SV253: $i] :
( ( ( SV253
= ( apply @ SV45 @ SV225 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV225 @ SV253 ) @ SV45 )
= $true )
| ( ( in @ SV225 @ ( relation_dom @ SV45 ) )
= $false )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1864]) ).
thf(1916,plain,
! [SV45: $i,SV254: $i,SV226: $i] :
( ( ( in @ ( ordered_pair @ SV226 @ SV254 ) @ SV45 )
= $false )
| ( ( SV254
= ( apply @ SV45 @ SV226 ) )
= $true )
| ( ( in @ SV226 @ ( relation_dom @ SV45 ) )
= $false )
| ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1865]) ).
thf(1917,plain,
! [SV193: $i,SV171: $i,SV255: $i] :
( ( ( in @ SV255 @ SV171 )
= $false )
| ( ( ( apply @ SV193 @ SV255 )
= SV255 )
= $true )
| ( ( SV193
= ( identity_relation @ SV171 ) )
= $false )
| ( ( function @ SV193 )
= $false )
| ( ( relation @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1869]) ).
thf(1918,plain,
! [SV176: $i,SV49: $i,SV261: $i,SV256: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV256 @ SV261 ) @ SV49 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV256 @ SV261 ) @ SV176 )
= $true )
| ( ( SV49 = SV176 )
= $false )
| ( ( relation @ SV176 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1871]) ).
thf(1919,plain,
! [SV49: $i,SV176: $i,SV262: $i,SV257: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV257 @ SV262 ) @ SV176 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV257 @ SV262 ) @ SV49 )
= $true )
| ( ( SV49 = SV176 )
= $false )
| ( ( relation @ SV176 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1872]) ).
thf(1920,plain,
! [SV50: $i,SV197: $i,SV177: $i,SV247: $i] :
( ( ( in @ SV247 @ SV177 )
= $false )
| ( ( in @ ( ordered_pair @ SV247 @ ( sK33_D @ SV197 @ SV177 @ SV50 ) ) @ SV50 )
= $false )
| ( ( ~ ( in @ ( sK33_D @ SV197 @ SV177 @ SV50 ) @ SV197 ) )
= $true )
| ( ( SV197
= ( relation_image @ SV50 @ SV177 ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1873]) ).
thf(1921,plain,
! [SV198: $i,SV178: $i,SV50: $i,SV248: $i,SV263: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV263 @ SV248 ) @ SV50 ) )
= $true )
| ( ( ~ ( in @ SV263 @ SV178 ) )
= $true )
| ( ( in @ SV248 @ SV198 )
= $true )
| ( ( SV198
= ( relation_image @ SV50 @ SV178 ) )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1876]) ).
thf(1922,plain,
! [SV50: $i,SV178: $i,SV198: $i,SV249: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK32_E @ SV249 @ SV198 @ SV178 @ SV50 ) @ SV249 ) @ SV50 )
| ~ ( in @ ( sK32_E @ SV249 @ SV198 @ SV178 @ SV50 ) @ SV178 ) )
= $false )
| ( ( in @ SV249 @ SV198 )
= $false )
| ( ( SV198
= ( relation_image @ SV50 @ SV178 ) )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1877]) ).
thf(1923,plain,
! [SV52: $i,SV182: $i,SV264: $i,SV258: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV258 @ SV264 ) @ SV182 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV264 @ SV258 ) @ SV52 )
= $true )
| ( ( SV182
= ( relation_inverse @ SV52 ) )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1881]) ).
thf(1924,plain,
! [SV182: $i,SV52: $i,SV259: $i,SV265: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV265 @ SV259 ) @ SV52 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV259 @ SV265 ) @ SV182 )
= $true )
| ( ( SV182
= ( relation_inverse @ SV52 ) )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1882]) ).
thf(1925,plain,
! [SV143: $i,SV124: $i,SV250: $i,SV236: $i] :
( ( ( SV236 = SV250 )
= $false )
| ( ( ~ ( in @ SV236 @ SV124 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV236 @ SV250 ) @ SV143 )
= $true )
| ( ( SV143
= ( identity_relation @ SV124 ) )
= $false )
| ( ( relation @ SV143 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1884]) ).
thf(1926,plain,
! [SV124: $i,SV143: $i,SV270: $i,SV266: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV266 @ SV270 ) @ SV143 )
| ( SV266 = SV270 ) )
= $true )
| ( ( SV143
= ( identity_relation @ SV124 ) )
= $false )
| ( ( relation @ SV143 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(1927,plain,
! [SV124: $i,SV143: $i,SV267: $i] :
( ( ( ! [SY3476: $i] :
~ ( in @ ( ordered_pair @ SV267 @ SY3476 ) @ SV143 ) )
= $true )
| ( ( in @ SV267 @ SV124 )
= $true )
| ( ( SV143
= ( identity_relation @ SV124 ) )
= $false )
| ( ( relation @ SV143 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1886]) ).
thf(1928,plain,
! [SV53: $i,SV82: $i,SV199: $i] :
( ( ( in @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) @ SV53 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV82 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 ) )
= $true )
| ( ( SV199
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $true )
| ( ( relation @ SV199 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1887]) ).
thf(1929,plain,
! [SV53: $i,SV82: $i,SV199: $i] :
( ( ( ( in @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) @ SV53 )
| ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 ) )
= $true )
| ( ( SV199
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $true )
| ( ( relation @ SV199 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1888]) ).
thf(1930,plain,
! [SV53: $i,SV82: $i,SV199: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV82 )
| ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 ) )
= $true )
| ( ( SV199
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $true )
| ( ( relation @ SV199 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1889]) ).
thf(1931,plain,
! [SV200: $i,SV82: $i,SV268: $i,SV53: $i,SV271: $i] :
( ( ( ~ ( in @ SV271 @ SV53 )
| ~ ( in @ ( ordered_pair @ SV268 @ SV271 ) @ SV82 )
| ( in @ ( ordered_pair @ SV268 @ SV271 ) @ SV200 ) )
= $true )
| ( ( SV200
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $false )
| ( ( relation @ SV200 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1890]) ).
thf(1932,plain,
! [SV82: $i,SV53: $i,SV200: $i] :
( ( ( ~ ! [SY3431: $i,SY3432: $i] :
( ~ ( in @ ( ordered_pair @ SY3431 @ SY3432 ) @ SV200 )
| ( in @ SY3432 @ SV53 ) ) )
= $false )
| ( ( SV200
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $false )
| ( ( relation @ SV200 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1891]) ).
thf(1933,plain,
! [SV53: $i,SV82: $i,SV200: $i] :
( ( ( ~ ! [SY3433: $i,SY3434: $i] :
( ~ ( in @ ( ordered_pair @ SY3433 @ SY3434 ) @ SV200 )
| ( in @ ( ordered_pair @ SY3433 @ SY3434 ) @ SV82 ) ) )
= $false )
| ( ( SV200
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $false )
| ( ( relation @ SV200 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1891]) ).
thf(1934,plain,
! [SV83: $i,SV220: $i,SV55: $i] :
( ( ( in @ SV55 @ ( relation_dom @ SV220 ) )
= $false )
| ( ( ~ ( in @ ( apply @ SV220 @ SV55 ) @ ( relation_dom @ SV83 ) ) )
= $true )
| ( ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SV220 @ SV83 ) ) )
= $true )
| ( ( function @ SV220 )
= $false )
| ( ( relation @ SV220 )
= $false )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1892]) ).
thf(1935,plain,
! [SV83: $i,SV55: $i,SV237: $i] :
( ( ( relation @ SV237 )
= $false )
| ( ( function @ SV237 )
= $false )
| ( ( ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SV237 @ SV83 ) ) )
| ( in @ SV55 @ ( relation_dom @ SV237 ) ) )
= $true )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1893]) ).
thf(1936,plain,
! [SV83: $i,SV55: $i,SV238: $i] :
( ( ( relation @ SV238 )
= $false )
| ( ( function @ SV238 )
= $false )
| ( ( ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SV238 @ SV83 ) ) )
| ( in @ ( apply @ SV238 @ SV55 ) @ ( relation_dom @ SV83 ) ) )
= $true )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1894]) ).
thf(1937,plain,
! [SV60: $i,SV187: $i,SV203: $i] :
( ( ( in @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ SV187 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV60 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 ) )
= $true )
| ( ( SV203
= ( relation_dom_restriction @ SV60 @ SV187 ) )
= $true )
| ( ( relation @ SV203 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1897]) ).
thf(1938,plain,
! [SV60: $i,SV187: $i,SV203: $i] :
( ( ( ( in @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ SV187 )
| ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 ) )
= $true )
| ( ( SV203
= ( relation_dom_restriction @ SV60 @ SV187 ) )
= $true )
| ( ( relation @ SV203 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1898]) ).
thf(1939,plain,
! [SV60: $i,SV187: $i,SV203: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV60 )
| ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 ) )
= $true )
| ( ( SV203
= ( relation_dom_restriction @ SV60 @ SV187 ) )
= $true )
| ( ( relation @ SV203 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1899]) ).
thf(1940,plain,
! [SV204: $i,SV60: $i,SV272: $i,SV188: $i,SV269: $i] :
( ( ( ~ ( in @ SV269 @ SV188 )
| ~ ( in @ ( ordered_pair @ SV269 @ SV272 ) @ SV60 )
| ( in @ ( ordered_pair @ SV269 @ SV272 ) @ SV204 ) )
= $true )
| ( ( SV204
= ( relation_dom_restriction @ SV60 @ SV188 ) )
= $false )
| ( ( relation @ SV204 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1900]) ).
thf(1941,plain,
! [SV60: $i,SV188: $i,SV204: $i] :
( ( ( ~ ! [SY3439: $i] :
( ! [SY3440: $i] :
~ ( in @ ( ordered_pair @ SY3439 @ SY3440 ) @ SV204 )
| ( in @ SY3439 @ SV188 ) ) )
= $false )
| ( ( SV204
= ( relation_dom_restriction @ SV60 @ SV188 ) )
= $false )
| ( ( relation @ SV204 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1901]) ).
thf(1942,plain,
! [SV188: $i,SV60: $i,SV204: $i] :
( ( ( ~ ! [SY3441: $i,SY3442: $i] :
( ~ ( in @ ( ordered_pair @ SY3441 @ SY3442 ) @ SV204 )
| ( in @ ( ordered_pair @ SY3441 @ SY3442 ) @ SV60 ) ) )
= $false )
| ( ( SV204
= ( relation_dom_restriction @ SV60 @ SV188 ) )
= $false )
| ( ( relation @ SV204 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1901]) ).
thf(1943,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1902]) ).
thf(1944,plain,
! [SV40: $i,SV240: $i] :
( ( ( relation @ SV240 )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( ( SV240
!= ( function_inverse @ SV40 ) )
| ~ ( ~ ~ ( ~ ! [SY3461: $i,SY3462: $i] :
( ( SY3462
!= ( apply @ SV240 @ SY3461 ) )
| ~ ( in @ SY3461 @ ( relation_rng @ SV40 ) )
| ( SY3461
= ( apply @ SV40 @ SY3462 ) ) )
| ~ ! [SY3463: $i,SY3464: $i] :
( ( SY3464
!= ( apply @ SV240 @ SY3463 ) )
| ~ ( in @ SY3463 @ ( relation_rng @ SV40 ) )
| ( in @ SY3464 @ ( relation_dom @ SV40 ) ) ) )
| ~ ~ ( ~ ! [SY3465: $i,SY3466: $i] :
( ( SY3465
!= ( apply @ SV40 @ SY3466 ) )
| ~ ( in @ SY3466 @ ( relation_dom @ SV40 ) )
| ( SY3466
= ( apply @ SV240 @ SY3465 ) ) )
| ~ ! [SY3176: $i] :
( ! [SY3177: $i] :
( ( SY3176
!= ( apply @ SV40 @ SY3177 ) )
| ~ ( in @ SY3177 @ ( relation_dom @ SV40 ) ) )
| ( in @ SY3176 @ ( relation_rng @ SV40 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1903]) ).
thf(1945,plain,
! [SV40: $i,SV241: $i] :
( ( ( relation @ SV241 )
= $false )
| ( ( function @ SV241 )
= $false )
| ( ( ( SV241
!= ( function_inverse @ SV40 ) )
| ( ( relation_dom @ SV241 )
= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1904]) ).
thf(1946,plain,
! [SV242: $i,SV41: $i,SV165: $i,SV191: $i] :
( ( ( in @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SV191 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK30_D @ SV191 @ SV165 @ SV41 ) @ SV242 ) @ SV41 )
= $false )
| ( ( in @ SV242 @ SV165 )
= $false )
| ( ( SV191
= ( relation_inverse_image @ SV41 @ SV165 ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1905]) ).
thf(1947,plain,
! [SV192: $i,SV166: $i,SV41: $i,SV260: $i,SV243: $i] :
( ( ( in @ ( ordered_pair @ SV243 @ SV260 ) @ SV41 )
= $false )
| ( ( ~ ( in @ SV260 @ SV166 ) )
= $true )
| ( ( in @ SV243 @ SV192 )
= $true )
| ( ( SV192
= ( relation_inverse_image @ SV41 @ SV166 ) )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1906]) ).
thf(1948,plain,
! [SV41: $i,SV166: $i,SV192: $i,SV244: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV244 @ ( sK29_E @ SV244 @ SV192 @ SV166 @ SV41 ) ) @ SV41 ) )
= $false )
| ( ( in @ SV244 @ SV192 )
= $false )
| ( ( SV192
= ( relation_inverse_image @ SV41 @ SV166 ) )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1907]) ).
thf(1949,plain,
! [SV41: $i,SV166: $i,SV192: $i,SV244: $i] :
( ( ( ~ ( in @ ( sK29_E @ SV244 @ SV192 @ SV166 @ SV41 ) @ SV166 ) )
= $false )
| ( ( in @ SV244 @ SV192 )
= $false )
| ( ( SV192
= ( relation_inverse_image @ SV41 @ SV166 ) )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1907]) ).
thf(1950,plain,
! [SV92: $i] :
( ( ( in @ ( sK12_B @ SV92 ) @ ( relation_dom @ SV92 ) )
= $true )
| ( ( one_to_one @ SV92 )
= $true )
| ( ( function @ SV92 )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1908]) ).
thf(1951,plain,
! [SV92: $i] :
( ( ( in @ ( sK13_SY3112 @ SV92 ) @ ( relation_dom @ SV92 ) )
= $true )
| ( ( one_to_one @ SV92 )
= $true )
| ( ( function @ SV92 )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1909]) ).
thf(1952,plain,
! [SV224: $i,SV223: $i,SV93: $i] :
( ( ( ( apply @ SV93 @ SV223 )
= ( apply @ SV93 @ SV224 ) )
= $false )
| ( ( in @ SV223 @ ( relation_dom @ SV93 ) )
= $false )
| ( ( in @ SV224 @ ( relation_dom @ SV93 ) )
= $false )
| ( ( SV223 = SV224 )
= $true )
| ( ( one_to_one @ SV93 )
= $false )
| ( ( function @ SV93 )
= $false )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1910]) ).
thf(1953,plain,
! [SV273: $i,SV43: $i,SV94: $i,SV214: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ SV273 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SV273 @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV94 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV214 ) )
= $true )
| ( ( SV214
= ( relation_composition @ SV43 @ SV94 ) )
= $true )
| ( ( relation @ SV214 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1911]) ).
thf(1954,plain,
! [SV43: $i,SV94: $i,SV214: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK11_SY3111 @ SV214 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK11_SY3111 @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV94 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV214 )
= $true )
| ( ( SV214
= ( relation_composition @ SV43 @ SV94 ) )
= $true )
| ( ( relation @ SV214 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1912]) ).
thf(1955,plain,
! [SV215: $i,SV94: $i,SV43: $i,SV274: $i] :
( ( ( ! [SY3479: $i] :
( ! [SY3480: $i] :
( ~ ( in @ ( ordered_pair @ SV274 @ SY3480 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3480 @ SY3479 ) @ SV94 ) )
| ( in @ ( ordered_pair @ SV274 @ SY3479 ) @ SV215 ) ) )
= $true )
| ( ( SV215
= ( relation_composition @ SV43 @ SV94 ) )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(1956,plain,
! [SV43: $i,SV94: $i,SV215: $i,SV275: $i] :
( ( ( ! [SY3481: $i] :
( ~ ( in @ ( ordered_pair @ SV275 @ SY3481 ) @ SV215 )
| ~ ( ~ ( in @ ( ordered_pair @ SV275 @ ( sK8_F @ SY3481 @ SV275 @ SV215 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK8_F @ SY3481 @ SV275 @ SV215 @ SV94 @ SV43 ) @ SY3481 ) @ SV94 ) ) ) )
= $true )
| ( ( SV215
= ( relation_composition @ SV43 @ SV94 ) )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1914]) ).
thf(1957,plain,
! [SV176: $i,SV49: $i,SV261: $i,SV256: $i] :
( ( ( in @ ( ordered_pair @ SV256 @ SV261 ) @ SV49 )
= $false )
| ( ( in @ ( ordered_pair @ SV256 @ SV261 ) @ SV176 )
= $true )
| ( ( SV49 = SV176 )
= $false )
| ( ( relation @ SV176 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1918]) ).
thf(1958,plain,
! [SV49: $i,SV176: $i,SV262: $i,SV257: $i] :
( ( ( in @ ( ordered_pair @ SV257 @ SV262 ) @ SV176 )
= $false )
| ( ( in @ ( ordered_pair @ SV257 @ SV262 ) @ SV49 )
= $true )
| ( ( SV49 = SV176 )
= $false )
| ( ( relation @ SV176 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1919]) ).
thf(1959,plain,
! [SV247: $i,SV50: $i,SV177: $i,SV197: $i] :
( ( ( in @ ( sK33_D @ SV197 @ SV177 @ SV50 ) @ SV197 )
= $false )
| ( ( in @ ( ordered_pair @ SV247 @ ( sK33_D @ SV197 @ SV177 @ SV50 ) ) @ SV50 )
= $false )
| ( ( in @ SV247 @ SV177 )
= $false )
| ( ( SV197
= ( relation_image @ SV50 @ SV177 ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1920]) ).
thf(1960,plain,
! [SV198: $i,SV178: $i,SV50: $i,SV248: $i,SV263: $i] :
( ( ( in @ ( ordered_pair @ SV263 @ SV248 ) @ SV50 )
= $false )
| ( ( ~ ( in @ SV263 @ SV178 ) )
= $true )
| ( ( in @ SV248 @ SV198 )
= $true )
| ( ( SV198
= ( relation_image @ SV50 @ SV178 ) )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1921]) ).
thf(1961,plain,
! [SV50: $i,SV178: $i,SV198: $i,SV249: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK32_E @ SV249 @ SV198 @ SV178 @ SV50 ) @ SV249 ) @ SV50 ) )
= $false )
| ( ( in @ SV249 @ SV198 )
= $false )
| ( ( SV198
= ( relation_image @ SV50 @ SV178 ) )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1922]) ).
thf(1962,plain,
! [SV50: $i,SV178: $i,SV198: $i,SV249: $i] :
( ( ( ~ ( in @ ( sK32_E @ SV249 @ SV198 @ SV178 @ SV50 ) @ SV178 ) )
= $false )
| ( ( in @ SV249 @ SV198 )
= $false )
| ( ( SV198
= ( relation_image @ SV50 @ SV178 ) )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1922]) ).
thf(1963,plain,
! [SV52: $i,SV182: $i,SV264: $i,SV258: $i] :
( ( ( in @ ( ordered_pair @ SV258 @ SV264 ) @ SV182 )
= $false )
| ( ( in @ ( ordered_pair @ SV264 @ SV258 ) @ SV52 )
= $true )
| ( ( SV182
= ( relation_inverse @ SV52 ) )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1923]) ).
thf(1964,plain,
! [SV182: $i,SV52: $i,SV259: $i,SV265: $i] :
( ( ( in @ ( ordered_pair @ SV265 @ SV259 ) @ SV52 )
= $false )
| ( ( in @ ( ordered_pair @ SV259 @ SV265 ) @ SV182 )
= $true )
| ( ( SV182
= ( relation_inverse @ SV52 ) )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1924]) ).
thf(1965,plain,
! [SV143: $i,SV250: $i,SV124: $i,SV236: $i] :
( ( ( in @ SV236 @ SV124 )
= $false )
| ( ( SV236 = SV250 )
= $false )
| ( ( in @ ( ordered_pair @ SV236 @ SV250 ) @ SV143 )
= $true )
| ( ( SV143
= ( identity_relation @ SV124 ) )
= $false )
| ( ( relation @ SV143 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1925]) ).
thf(1966,plain,
! [SV124: $i,SV143: $i,SV270: $i,SV266: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV266 @ SV270 ) @ SV143 ) )
= $true )
| ( ( SV266 = SV270 )
= $true )
| ( ( SV143
= ( identity_relation @ SV124 ) )
= $false )
| ( ( relation @ SV143 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1926]) ).
thf(1967,plain,
! [SV124: $i,SV143: $i,SV276: $i,SV267: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV267 @ SV276 ) @ SV143 ) )
= $true )
| ( ( in @ SV267 @ SV124 )
= $true )
| ( ( SV143
= ( identity_relation @ SV124 ) )
= $false )
| ( ( relation @ SV143 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1927]) ).
thf(1968,plain,
! [SV53: $i,SV82: $i,SV199: $i] :
( ( ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV82 )
= $false )
| ( ( in @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) @ SV53 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 ) )
= $true )
| ( ( SV199
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $true )
| ( ( relation @ SV199 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1928]) ).
thf(1969,plain,
! [SV53: $i,SV82: $i,SV199: $i] :
( ( ( in @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) @ SV53 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 )
= $true )
| ( ( SV199
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $true )
| ( ( relation @ SV199 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1929]) ).
thf(1970,plain,
! [SV53: $i,SV82: $i,SV199: $i] :
( ( ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV82 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 )
= $true )
| ( ( SV199
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $true )
| ( ( relation @ SV199 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1930]) ).
thf(1971,plain,
! [SV200: $i,SV82: $i,SV268: $i,SV53: $i,SV271: $i] :
( ( ( ~ ( in @ SV271 @ SV53 )
| ~ ( in @ ( ordered_pair @ SV268 @ SV271 ) @ SV82 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV268 @ SV271 ) @ SV200 )
= $true )
| ( ( SV200
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $false )
| ( ( relation @ SV200 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1931]) ).
thf(1972,plain,
! [SV82: $i,SV53: $i,SV200: $i] :
( ( ( ! [SY3431: $i,SY3432: $i] :
( ~ ( in @ ( ordered_pair @ SY3431 @ SY3432 ) @ SV200 )
| ( in @ SY3432 @ SV53 ) ) )
= $true )
| ( ( SV200
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $false )
| ( ( relation @ SV200 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1932]) ).
thf(1973,plain,
! [SV53: $i,SV82: $i,SV200: $i] :
( ( ( ! [SY3433: $i,SY3434: $i] :
( ~ ( in @ ( ordered_pair @ SY3433 @ SY3434 ) @ SV200 )
| ( in @ ( ordered_pair @ SY3433 @ SY3434 ) @ SV82 ) ) )
= $true )
| ( ( SV200
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $false )
| ( ( relation @ SV200 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1933]) ).
thf(1974,plain,
! [SV83: $i,SV55: $i,SV220: $i] :
( ( ( in @ ( apply @ SV220 @ SV55 ) @ ( relation_dom @ SV83 ) )
= $false )
| ( ( in @ SV55 @ ( relation_dom @ SV220 ) )
= $false )
| ( ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SV220 @ SV83 ) ) )
= $true )
| ( ( function @ SV220 )
= $false )
| ( ( relation @ SV220 )
= $false )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1934]) ).
thf(1975,plain,
! [SV83: $i,SV237: $i,SV55: $i] :
( ( ( ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SV237 @ SV83 ) ) ) )
= $true )
| ( ( in @ SV55 @ ( relation_dom @ SV237 ) )
= $true )
| ( ( function @ SV237 )
= $false )
| ( ( relation @ SV237 )
= $false )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1935]) ).
thf(1976,plain,
! [SV83: $i,SV238: $i,SV55: $i] :
( ( ( ~ ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SV238 @ SV83 ) ) ) )
= $true )
| ( ( in @ ( apply @ SV238 @ SV55 ) @ ( relation_dom @ SV83 ) )
= $true )
| ( ( function @ SV238 )
= $false )
| ( ( relation @ SV238 )
= $false )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1936]) ).
thf(1977,plain,
! [SV60: $i,SV187: $i,SV203: $i] :
( ( ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV60 )
= $false )
| ( ( in @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ SV187 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 ) )
= $true )
| ( ( SV203
= ( relation_dom_restriction @ SV60 @ SV187 ) )
= $true )
| ( ( relation @ SV203 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1937]) ).
thf(1978,plain,
! [SV60: $i,SV187: $i,SV203: $i] :
( ( ( in @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ SV187 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 )
= $true )
| ( ( SV203
= ( relation_dom_restriction @ SV60 @ SV187 ) )
= $true )
| ( ( relation @ SV203 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1938]) ).
thf(1979,plain,
! [SV60: $i,SV187: $i,SV203: $i] :
( ( ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV60 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 )
= $true )
| ( ( SV203
= ( relation_dom_restriction @ SV60 @ SV187 ) )
= $true )
| ( ( relation @ SV203 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1939]) ).
thf(1980,plain,
! [SV204: $i,SV60: $i,SV272: $i,SV188: $i,SV269: $i] :
( ( ( ~ ( in @ SV269 @ SV188 )
| ~ ( in @ ( ordered_pair @ SV269 @ SV272 ) @ SV60 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV269 @ SV272 ) @ SV204 )
= $true )
| ( ( SV204
= ( relation_dom_restriction @ SV60 @ SV188 ) )
= $false )
| ( ( relation @ SV204 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1940]) ).
thf(1981,plain,
! [SV60: $i,SV188: $i,SV204: $i] :
( ( ( ! [SY3439: $i] :
( ! [SY3440: $i] :
~ ( in @ ( ordered_pair @ SY3439 @ SY3440 ) @ SV204 )
| ( in @ SY3439 @ SV188 ) ) )
= $true )
| ( ( SV204
= ( relation_dom_restriction @ SV60 @ SV188 ) )
= $false )
| ( ( relation @ SV204 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1941]) ).
thf(1982,plain,
! [SV188: $i,SV60: $i,SV204: $i] :
( ( ( ! [SY3441: $i,SY3442: $i] :
( ~ ( in @ ( ordered_pair @ SY3441 @ SY3442 ) @ SV204 )
| ( in @ ( ordered_pair @ SY3441 @ SY3442 ) @ SV60 ) ) )
= $true )
| ( ( SV204
= ( relation_dom_restriction @ SV60 @ SV188 ) )
= $false )
| ( ( relation @ SV204 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1942]) ).
thf(1983,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1943]) ).
thf(1984,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1943]) ).
thf(1985,plain,
! [SV40: $i,SV240: $i] :
( ( ( ( SV240
!= ( function_inverse @ SV40 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY3461: $i,SY3462: $i] :
( ( SY3462
!= ( apply @ SV240 @ SY3461 ) )
| ~ ( in @ SY3461 @ ( relation_rng @ SV40 ) )
| ( SY3461
= ( apply @ SV40 @ SY3462 ) ) )
| ~ ! [SY3463: $i,SY3464: $i] :
( ( SY3464
!= ( apply @ SV240 @ SY3463 ) )
| ~ ( in @ SY3463 @ ( relation_rng @ SV40 ) )
| ( in @ SY3464 @ ( relation_dom @ SV40 ) ) ) )
| ~ ~ ( ~ ! [SY3465: $i,SY3466: $i] :
( ( SY3465
!= ( apply @ SV40 @ SY3466 ) )
| ~ ( in @ SY3466 @ ( relation_dom @ SV40 ) )
| ( SY3466
= ( apply @ SV240 @ SY3465 ) ) )
| ~ ! [SY3176: $i] :
( ! [SY3177: $i] :
( ( SY3176
!= ( apply @ SV40 @ SY3177 ) )
| ~ ( in @ SY3177 @ ( relation_dom @ SV40 ) ) )
| ( in @ SY3176 @ ( relation_rng @ SV40 ) ) ) ) ) )
= $true )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1944]) ).
thf(1986,plain,
! [SV40: $i,SV241: $i] :
( ( ( ( SV241
!= ( function_inverse @ SV40 ) ) )
= $true )
| ( ( ( relation_dom @ SV241 )
= ( relation_rng @ SV40 ) )
= $true )
| ( ( function @ SV241 )
= $false )
| ( ( relation @ SV241 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1945]) ).
thf(1987,plain,
! [SV192: $i,SV41: $i,SV243: $i,SV166: $i,SV260: $i] :
( ( ( in @ SV260 @ SV166 )
= $false )
| ( ( in @ ( ordered_pair @ SV243 @ SV260 ) @ SV41 )
= $false )
| ( ( in @ SV243 @ SV192 )
= $true )
| ( ( SV192
= ( relation_inverse_image @ SV41 @ SV166 ) )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1947]) ).
thf(1988,plain,
! [SV41: $i,SV166: $i,SV192: $i,SV244: $i] :
( ( ( in @ ( ordered_pair @ SV244 @ ( sK29_E @ SV244 @ SV192 @ SV166 @ SV41 ) ) @ SV41 )
= $true )
| ( ( in @ SV244 @ SV192 )
= $false )
| ( ( SV192
= ( relation_inverse_image @ SV41 @ SV166 ) )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1948]) ).
thf(1989,plain,
! [SV41: $i,SV166: $i,SV192: $i,SV244: $i] :
( ( ( in @ ( sK29_E @ SV244 @ SV192 @ SV166 @ SV41 ) @ SV166 )
= $true )
| ( ( in @ SV244 @ SV192 )
= $false )
| ( ( SV192
= ( relation_inverse_image @ SV41 @ SV166 ) )
= $false )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1949]) ).
thf(1990,plain,
! [SV273: $i,SV43: $i,SV94: $i,SV214: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ SV273 ) @ SV43 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV273 @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV94 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV214 ) )
= $true )
| ( ( SV214
= ( relation_composition @ SV43 @ SV94 ) )
= $true )
| ( ( relation @ SV214 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1953]) ).
thf(1991,plain,
! [SV43: $i,SV94: $i,SV214: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK11_SY3111 @ SV214 @ SV94 @ SV43 ) ) @ SV43 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV214 )
= $true )
| ( ( SV214
= ( relation_composition @ SV43 @ SV94 ) )
= $true )
| ( ( relation @ SV214 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1954]) ).
thf(1992,plain,
! [SV43: $i,SV94: $i,SV214: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK11_SY3111 @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV94 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV214 )
= $true )
| ( ( SV214
= ( relation_composition @ SV43 @ SV94 ) )
= $true )
| ( ( relation @ SV214 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1954]) ).
thf(1993,plain,
! [SV215: $i,SV94: $i,SV277: $i,SV43: $i,SV274: $i] :
( ( ( ! [SY3482: $i] :
( ~ ( in @ ( ordered_pair @ SV274 @ SY3482 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3482 @ SV277 ) @ SV94 ) )
| ( in @ ( ordered_pair @ SV274 @ SV277 ) @ SV215 ) )
= $true )
| ( ( SV215
= ( relation_composition @ SV43 @ SV94 ) )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1955]) ).
thf(1994,plain,
! [SV43: $i,SV94: $i,SV215: $i,SV278: $i,SV275: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV275 @ SV278 ) @ SV215 )
| ~ ( ~ ( in @ ( ordered_pair @ SV275 @ ( sK8_F @ SV278 @ SV275 @ SV215 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK8_F @ SV278 @ SV275 @ SV215 @ SV94 @ SV43 ) @ SV278 ) @ SV94 ) ) )
= $true )
| ( ( SV215
= ( relation_composition @ SV43 @ SV94 ) )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1956]) ).
thf(1995,plain,
! [SV198: $i,SV50: $i,SV248: $i,SV178: $i,SV263: $i] :
( ( ( in @ SV263 @ SV178 )
= $false )
| ( ( in @ ( ordered_pair @ SV263 @ SV248 ) @ SV50 )
= $false )
| ( ( in @ SV248 @ SV198 )
= $true )
| ( ( SV198
= ( relation_image @ SV50 @ SV178 ) )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1960]) ).
thf(1996,plain,
! [SV50: $i,SV178: $i,SV198: $i,SV249: $i] :
( ( ( in @ ( ordered_pair @ ( sK32_E @ SV249 @ SV198 @ SV178 @ SV50 ) @ SV249 ) @ SV50 )
= $true )
| ( ( in @ SV249 @ SV198 )
= $false )
| ( ( SV198
= ( relation_image @ SV50 @ SV178 ) )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1961]) ).
thf(1997,plain,
! [SV50: $i,SV178: $i,SV198: $i,SV249: $i] :
( ( ( in @ ( sK32_E @ SV249 @ SV198 @ SV178 @ SV50 ) @ SV178 )
= $true )
| ( ( in @ SV249 @ SV198 )
= $false )
| ( ( SV198
= ( relation_image @ SV50 @ SV178 ) )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1962]) ).
thf(1998,plain,
! [SV124: $i,SV143: $i,SV270: $i,SV266: $i] :
( ( ( in @ ( ordered_pair @ SV266 @ SV270 ) @ SV143 )
= $false )
| ( ( SV266 = SV270 )
= $true )
| ( ( SV143
= ( identity_relation @ SV124 ) )
= $false )
| ( ( relation @ SV143 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1966]) ).
thf(1999,plain,
! [SV124: $i,SV143: $i,SV276: $i,SV267: $i] :
( ( ( in @ ( ordered_pair @ SV267 @ SV276 ) @ SV143 )
= $false )
| ( ( in @ SV267 @ SV124 )
= $true )
| ( ( SV143
= ( identity_relation @ SV124 ) )
= $false )
| ( ( relation @ SV143 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1967]) ).
thf(2000,plain,
! [SV53: $i,SV82: $i,SV199: $i] :
( ( ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV199 )
= $false )
| ( ( in @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) @ SV53 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK35_D @ SV199 @ SV82 @ SV53 ) @ ( sK36_SY3127 @ SV199 @ SV82 @ SV53 ) ) @ SV82 )
= $false )
| ( ( SV199
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $true )
| ( ( relation @ SV199 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1968]) ).
thf(2001,plain,
! [SV200: $i,SV82: $i,SV268: $i,SV53: $i,SV271: $i] :
( ( ( ~ ( in @ SV271 @ SV53 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV268 @ SV271 ) @ SV82 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV268 @ SV271 ) @ SV200 )
= $true )
| ( ( SV200
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $false )
| ( ( relation @ SV200 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1971]) ).
thf(2002,plain,
! [SV82: $i,SV53: $i,SV200: $i,SV279: $i] :
( ( ( ! [SY3483: $i] :
( ~ ( in @ ( ordered_pair @ SV279 @ SY3483 ) @ SV200 )
| ( in @ SY3483 @ SV53 ) ) )
= $true )
| ( ( SV200
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $false )
| ( ( relation @ SV200 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1972]) ).
thf(2003,plain,
! [SV53: $i,SV82: $i,SV200: $i,SV280: $i] :
( ( ( ! [SY3484: $i] :
( ~ ( in @ ( ordered_pair @ SV280 @ SY3484 ) @ SV200 )
| ( in @ ( ordered_pair @ SV280 @ SY3484 ) @ SV82 ) ) )
= $true )
| ( ( SV200
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $false )
| ( ( relation @ SV200 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1973]) ).
thf(2004,plain,
! [SV83: $i,SV237: $i,SV55: $i] :
( ( ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SV237 @ SV83 ) ) )
= $false )
| ( ( in @ SV55 @ ( relation_dom @ SV237 ) )
= $true )
| ( ( function @ SV237 )
= $false )
| ( ( relation @ SV237 )
= $false )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1975]) ).
thf(2005,plain,
! [SV83: $i,SV238: $i,SV55: $i] :
( ( ( in @ SV55 @ ( relation_dom @ ( relation_composition @ SV238 @ SV83 ) ) )
= $false )
| ( ( in @ ( apply @ SV238 @ SV55 ) @ ( relation_dom @ SV83 ) )
= $true )
| ( ( function @ SV238 )
= $false )
| ( ( relation @ SV238 )
= $false )
| ( ( function @ SV83 )
= $false )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1976]) ).
thf(2006,plain,
! [SV60: $i,SV187: $i,SV203: $i] :
( ( ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV203 )
= $false )
| ( ( in @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ SV187 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK37_D @ SV203 @ SV187 @ SV60 ) @ ( sK38_SY3128 @ SV203 @ SV187 @ SV60 ) ) @ SV60 )
= $false )
| ( ( SV203
= ( relation_dom_restriction @ SV60 @ SV187 ) )
= $true )
| ( ( relation @ SV203 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1977]) ).
thf(2007,plain,
! [SV204: $i,SV60: $i,SV272: $i,SV188: $i,SV269: $i] :
( ( ( ~ ( in @ SV269 @ SV188 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV269 @ SV272 ) @ SV60 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV269 @ SV272 ) @ SV204 )
= $true )
| ( ( SV204
= ( relation_dom_restriction @ SV60 @ SV188 ) )
= $false )
| ( ( relation @ SV204 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1980]) ).
thf(2008,plain,
! [SV60: $i,SV188: $i,SV204: $i,SV281: $i] :
( ( ( ! [SY3485: $i] :
~ ( in @ ( ordered_pair @ SV281 @ SY3485 ) @ SV204 )
| ( in @ SV281 @ SV188 ) )
= $true )
| ( ( SV204
= ( relation_dom_restriction @ SV60 @ SV188 ) )
= $false )
| ( ( relation @ SV204 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1981]) ).
thf(2009,plain,
! [SV188: $i,SV60: $i,SV204: $i,SV282: $i] :
( ( ( ! [SY3486: $i] :
( ~ ( in @ ( ordered_pair @ SV282 @ SY3486 ) @ SV204 )
| ( in @ ( ordered_pair @ SV282 @ SY3486 ) @ SV60 ) ) )
= $true )
| ( ( SV204
= ( relation_dom_restriction @ SV60 @ SV188 ) )
= $false )
| ( ( relation @ SV204 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1982]) ).
thf(2010,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1983]) ).
thf(2011,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1984]) ).
thf(2012,plain,
! [SV40: $i,SV240: $i] :
( ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY3461: $i,SY3462: $i] :
( ( SY3462
!= ( apply @ SV240 @ SY3461 ) )
| ~ ( in @ SY3461 @ ( relation_rng @ SV40 ) )
| ( SY3461
= ( apply @ SV40 @ SY3462 ) ) )
| ~ ! [SY3463: $i,SY3464: $i] :
( ( SY3464
!= ( apply @ SV240 @ SY3463 ) )
| ~ ( in @ SY3463 @ ( relation_rng @ SV40 ) )
| ( in @ SY3464 @ ( relation_dom @ SV40 ) ) ) )
| ~ ~ ( ~ ! [SY3465: $i,SY3466: $i] :
( ( SY3465
!= ( apply @ SV40 @ SY3466 ) )
| ~ ( in @ SY3466 @ ( relation_dom @ SV40 ) )
| ( SY3466
= ( apply @ SV240 @ SY3465 ) ) )
| ~ ! [SY3176: $i] :
( ! [SY3177: $i] :
( ( SY3176
!= ( apply @ SV40 @ SY3177 ) )
| ~ ( in @ SY3177 @ ( relation_dom @ SV40 ) ) )
| ( in @ SY3176 @ ( relation_rng @ SV40 ) ) ) ) ) )
= $true )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1985]) ).
thf(2013,plain,
! [SV40: $i,SV241: $i] :
( ( ( SV241
= ( function_inverse @ SV40 ) )
= $false )
| ( ( ( relation_dom @ SV241 )
= ( relation_rng @ SV40 ) )
= $true )
| ( ( function @ SV241 )
= $false )
| ( ( relation @ SV241 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1986]) ).
thf(2014,plain,
! [SV273: $i,SV43: $i,SV94: $i,SV214: $i] :
( ( ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ SV273 ) @ SV43 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV273 @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV94 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV214 ) )
= $true )
| ( ( SV214
= ( relation_composition @ SV43 @ SV94 ) )
= $true )
| ( ( relation @ SV214 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1990]) ).
thf(2015,plain,
! [SV43: $i,SV94: $i,SV214: $i] :
( ( ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK11_SY3111 @ SV214 @ SV94 @ SV43 ) ) @ SV43 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV214 )
= $true )
| ( ( SV214
= ( relation_composition @ SV43 @ SV94 ) )
= $true )
| ( ( relation @ SV214 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1991]) ).
thf(2016,plain,
! [SV43: $i,SV94: $i,SV214: $i] :
( ( ( in @ ( ordered_pair @ ( sK11_SY3111 @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV94 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV214 )
= $true )
| ( ( SV214
= ( relation_composition @ SV43 @ SV94 ) )
= $true )
| ( ( relation @ SV214 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1992]) ).
thf(2017,plain,
! [SV215: $i,SV94: $i,SV277: $i,SV43: $i,SV274: $i] :
( ( ( ! [SY3482: $i] :
( ~ ( in @ ( ordered_pair @ SV274 @ SY3482 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY3482 @ SV277 ) @ SV94 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV274 @ SV277 ) @ SV215 )
= $true )
| ( ( SV215
= ( relation_composition @ SV43 @ SV94 ) )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1993]) ).
thf(2018,plain,
! [SV43: $i,SV94: $i,SV215: $i,SV278: $i,SV275: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV275 @ SV278 ) @ SV215 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV275 @ ( sK8_F @ SV278 @ SV275 @ SV215 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK8_F @ SV278 @ SV275 @ SV215 @ SV94 @ SV43 ) @ SV278 ) @ SV94 ) ) )
= $true )
| ( ( SV215
= ( relation_composition @ SV43 @ SV94 ) )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1994]) ).
thf(2019,plain,
! [SV200: $i,SV82: $i,SV268: $i,SV53: $i,SV271: $i] :
( ( ( in @ SV271 @ SV53 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV268 @ SV271 ) @ SV82 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV268 @ SV271 ) @ SV200 )
= $true )
| ( ( SV200
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $false )
| ( ( relation @ SV200 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2001]) ).
thf(2020,plain,
! [SV82: $i,SV53: $i,SV200: $i,SV283: $i,SV279: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV279 @ SV283 ) @ SV200 )
| ( in @ SV283 @ SV53 ) )
= $true )
| ( ( SV200
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $false )
| ( ( relation @ SV200 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2002]) ).
thf(2021,plain,
! [SV53: $i,SV82: $i,SV200: $i,SV284: $i,SV280: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV280 @ SV284 ) @ SV200 )
| ( in @ ( ordered_pair @ SV280 @ SV284 ) @ SV82 ) )
= $true )
| ( ( SV200
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $false )
| ( ( relation @ SV200 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2003]) ).
thf(2022,plain,
! [SV204: $i,SV60: $i,SV272: $i,SV188: $i,SV269: $i] :
( ( ( in @ SV269 @ SV188 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV269 @ SV272 ) @ SV60 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV269 @ SV272 ) @ SV204 )
= $true )
| ( ( SV204
= ( relation_dom_restriction @ SV60 @ SV188 ) )
= $false )
| ( ( relation @ SV204 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2007]) ).
thf(2023,plain,
! [SV60: $i,SV188: $i,SV204: $i,SV281: $i] :
( ( ( ! [SY3485: $i] :
~ ( in @ ( ordered_pair @ SV281 @ SY3485 ) @ SV204 ) )
= $true )
| ( ( in @ SV281 @ SV188 )
= $true )
| ( ( SV204
= ( relation_dom_restriction @ SV60 @ SV188 ) )
= $false )
| ( ( relation @ SV204 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2008]) ).
thf(2024,plain,
! [SV188: $i,SV60: $i,SV204: $i,SV285: $i,SV282: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV282 @ SV285 ) @ SV204 )
| ( in @ ( ordered_pair @ SV282 @ SV285 ) @ SV60 ) )
= $true )
| ( ( SV204
= ( relation_dom_restriction @ SV60 @ SV188 ) )
= $false )
| ( ( relation @ SV204 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2009]) ).
thf(2025,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2010]) ).
thf(2026,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2011]) ).
thf(2027,plain,
! [SV40: $i,SV240: $i] :
( ( ( ~ ~ ( ~ ! [SY3461: $i,SY3462: $i] :
( ( SY3462
!= ( apply @ SV240 @ SY3461 ) )
| ~ ( in @ SY3461 @ ( relation_rng @ SV40 ) )
| ( SY3461
= ( apply @ SV40 @ SY3462 ) ) )
| ~ ! [SY3463: $i,SY3464: $i] :
( ( SY3464
!= ( apply @ SV240 @ SY3463 ) )
| ~ ( in @ SY3463 @ ( relation_rng @ SV40 ) )
| ( in @ SY3464 @ ( relation_dom @ SV40 ) ) ) )
| ~ ~ ( ~ ! [SY3465: $i,SY3466: $i] :
( ( SY3465
!= ( apply @ SV40 @ SY3466 ) )
| ~ ( in @ SY3466 @ ( relation_dom @ SV40 ) )
| ( SY3466
= ( apply @ SV240 @ SY3465 ) ) )
| ~ ! [SY3176: $i] :
( ! [SY3177: $i] :
( ( SY3176
!= ( apply @ SV40 @ SY3177 ) )
| ~ ( in @ SY3177 @ ( relation_dom @ SV40 ) ) )
| ( in @ SY3176 @ ( relation_rng @ SV40 ) ) ) ) )
= $false )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2012]) ).
thf(2028,plain,
! [SV43: $i,SV94: $i,SV214: $i,SV273: $i] :
( ( ( in @ ( ordered_pair @ SV273 @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV94 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ SV273 ) @ SV43 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV214 ) )
= $true )
| ( ( SV214
= ( relation_composition @ SV43 @ SV94 ) )
= $true )
| ( ( relation @ SV214 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2014]) ).
thf(2029,plain,
! [SV215: $i,SV94: $i,SV277: $i,SV43: $i,SV286: $i,SV274: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV274 @ SV286 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SV286 @ SV277 ) @ SV94 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV274 @ SV277 ) @ SV215 )
= $true )
| ( ( SV215
= ( relation_composition @ SV43 @ SV94 ) )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2017]) ).
thf(2030,plain,
! [SV43: $i,SV94: $i,SV215: $i,SV278: $i,SV275: $i] :
( ( ( in @ ( ordered_pair @ SV275 @ SV278 ) @ SV215 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV275 @ ( sK8_F @ SV278 @ SV275 @ SV215 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK8_F @ SV278 @ SV275 @ SV215 @ SV94 @ SV43 ) @ SV278 ) @ SV94 ) ) )
= $true )
| ( ( SV215
= ( relation_composition @ SV43 @ SV94 ) )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2018]) ).
thf(2031,plain,
! [SV200: $i,SV53: $i,SV82: $i,SV271: $i,SV268: $i] :
( ( ( in @ ( ordered_pair @ SV268 @ SV271 ) @ SV82 )
= $false )
| ( ( in @ SV271 @ SV53 )
= $false )
| ( ( in @ ( ordered_pair @ SV268 @ SV271 ) @ SV200 )
= $true )
| ( ( SV200
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $false )
| ( ( relation @ SV200 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2019]) ).
thf(2032,plain,
! [SV82: $i,SV53: $i,SV200: $i,SV283: $i,SV279: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV279 @ SV283 ) @ SV200 ) )
= $true )
| ( ( in @ SV283 @ SV53 )
= $true )
| ( ( SV200
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $false )
| ( ( relation @ SV200 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2020]) ).
thf(2033,plain,
! [SV53: $i,SV82: $i,SV200: $i,SV284: $i,SV280: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV280 @ SV284 ) @ SV200 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV280 @ SV284 ) @ SV82 )
= $true )
| ( ( SV200
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $false )
| ( ( relation @ SV200 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2021]) ).
thf(2034,plain,
! [SV204: $i,SV188: $i,SV60: $i,SV272: $i,SV269: $i] :
( ( ( in @ ( ordered_pair @ SV269 @ SV272 ) @ SV60 )
= $false )
| ( ( in @ SV269 @ SV188 )
= $false )
| ( ( in @ ( ordered_pair @ SV269 @ SV272 ) @ SV204 )
= $true )
| ( ( SV204
= ( relation_dom_restriction @ SV60 @ SV188 ) )
= $false )
| ( ( relation @ SV204 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2022]) ).
thf(2035,plain,
! [SV60: $i,SV188: $i,SV204: $i,SV287: $i,SV281: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV281 @ SV287 ) @ SV204 ) )
= $true )
| ( ( in @ SV281 @ SV188 )
= $true )
| ( ( SV204
= ( relation_dom_restriction @ SV60 @ SV188 ) )
= $false )
| ( ( relation @ SV204 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2036,plain,
! [SV188: $i,SV60: $i,SV204: $i,SV285: $i,SV282: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV282 @ SV285 ) @ SV204 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV282 @ SV285 ) @ SV60 )
= $true )
| ( ( SV204
= ( relation_dom_restriction @ SV60 @ SV188 ) )
= $false )
| ( ( relation @ SV204 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2024]) ).
thf(2037,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2025]) ).
thf(2038,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2025]) ).
thf(2039,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2026]) ).
thf(2040,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2026]) ).
thf(2041,plain,
! [SV40: $i,SV240: $i] :
( ( ( ~ ~ ( ~ ! [SY3461: $i,SY3462: $i] :
( ( SY3462
!= ( apply @ SV240 @ SY3461 ) )
| ~ ( in @ SY3461 @ ( relation_rng @ SV40 ) )
| ( SY3461
= ( apply @ SV40 @ SY3462 ) ) )
| ~ ! [SY3463: $i,SY3464: $i] :
( ( SY3464
!= ( apply @ SV240 @ SY3463 ) )
| ~ ( in @ SY3463 @ ( relation_rng @ SV40 ) )
| ( in @ SY3464 @ ( relation_dom @ SV40 ) ) ) ) )
= $false )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2027]) ).
thf(2042,plain,
! [SV240: $i,SV40: $i] :
( ( ( ~ ~ ( ~ ! [SY3465: $i,SY3466: $i] :
( ( SY3465
!= ( apply @ SV40 @ SY3466 ) )
| ~ ( in @ SY3466 @ ( relation_dom @ SV40 ) )
| ( SY3466
= ( apply @ SV240 @ SY3465 ) ) )
| ~ ! [SY3176: $i] :
( ! [SY3177: $i] :
( ( SY3176
!= ( apply @ SV40 @ SY3177 ) )
| ~ ( in @ SY3177 @ ( relation_dom @ SV40 ) ) )
| ( in @ SY3176 @ ( relation_rng @ SV40 ) ) ) ) )
= $false )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2027]) ).
thf(2043,plain,
! [SV273: $i,SV43: $i,SV94: $i,SV214: $i] :
( ( ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV214 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK9_D @ SV214 @ SV94 @ SV43 ) @ SV273 ) @ SV43 )
= $false )
| ( ( in @ ( ordered_pair @ SV273 @ ( sK10_SY3107 @ SV214 @ SV94 @ SV43 ) ) @ SV94 )
= $false )
| ( ( SV214
= ( relation_composition @ SV43 @ SV94 ) )
= $true )
| ( ( relation @ SV214 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2028]) ).
thf(2044,plain,
! [SV215: $i,SV94: $i,SV277: $i,SV43: $i,SV286: $i,SV274: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV274 @ SV286 ) @ SV43 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV286 @ SV277 ) @ SV94 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV274 @ SV277 ) @ SV215 )
= $true )
| ( ( SV215
= ( relation_composition @ SV43 @ SV94 ) )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2029]) ).
thf(2045,plain,
! [SV43: $i,SV94: $i,SV215: $i,SV278: $i,SV275: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV275 @ ( sK8_F @ SV278 @ SV275 @ SV215 @ SV94 @ SV43 ) ) @ SV43 )
| ~ ( in @ ( ordered_pair @ ( sK8_F @ SV278 @ SV275 @ SV215 @ SV94 @ SV43 ) @ SV278 ) @ SV94 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV275 @ SV278 ) @ SV215 )
= $false )
| ( ( SV215
= ( relation_composition @ SV43 @ SV94 ) )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2030]) ).
thf(2046,plain,
! [SV82: $i,SV53: $i,SV200: $i,SV283: $i,SV279: $i] :
( ( ( in @ ( ordered_pair @ SV279 @ SV283 ) @ SV200 )
= $false )
| ( ( in @ SV283 @ SV53 )
= $true )
| ( ( SV200
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $false )
| ( ( relation @ SV200 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2032]) ).
thf(2047,plain,
! [SV53: $i,SV82: $i,SV200: $i,SV284: $i,SV280: $i] :
( ( ( in @ ( ordered_pair @ SV280 @ SV284 ) @ SV200 )
= $false )
| ( ( in @ ( ordered_pair @ SV280 @ SV284 ) @ SV82 )
= $true )
| ( ( SV200
= ( relation_rng_restriction @ SV53 @ SV82 ) )
= $false )
| ( ( relation @ SV200 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2033]) ).
thf(2048,plain,
! [SV60: $i,SV188: $i,SV204: $i,SV287: $i,SV281: $i] :
( ( ( in @ ( ordered_pair @ SV281 @ SV287 ) @ SV204 )
= $false )
| ( ( in @ SV281 @ SV188 )
= $true )
| ( ( SV204
= ( relation_dom_restriction @ SV60 @ SV188 ) )
= $false )
| ( ( relation @ SV204 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2035]) ).
thf(2049,plain,
! [SV188: $i,SV60: $i,SV204: $i,SV285: $i,SV282: $i] :
( ( ( in @ ( ordered_pair @ SV282 @ SV285 ) @ SV204 )
= $false )
| ( ( in @ ( ordered_pair @ SV282 @ SV285 ) @ SV60 )
= $true )
| ( ( SV204
= ( relation_dom_restriction @ SV60 @ SV188 ) )
= $false )
| ( ( relation @ SV204 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2036]) ).
thf(2050,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2037]) ).
thf(2051,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2038]) ).
thf(2052,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ( ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2039]) ).
thf(2053,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2040]) ).
thf(2054,plain,
! [SV40: $i,SV240: $i] :
( ( ( ~ ( ~ ! [SY3461: $i,SY3462: $i] :
( ( SY3462
!= ( apply @ SV240 @ SY3461 ) )
| ~ ( in @ SY3461 @ ( relation_rng @ SV40 ) )
| ( SY3461
= ( apply @ SV40 @ SY3462 ) ) )
| ~ ! [SY3463: $i,SY3464: $i] :
( ( SY3464
!= ( apply @ SV240 @ SY3463 ) )
| ~ ( in @ SY3463 @ ( relation_rng @ SV40 ) )
| ( in @ SY3464 @ ( relation_dom @ SV40 ) ) ) ) )
= $true )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2041]) ).
thf(2055,plain,
! [SV240: $i,SV40: $i] :
( ( ( ~ ( ~ ! [SY3465: $i,SY3466: $i] :
( ( SY3465
!= ( apply @ SV40 @ SY3466 ) )
| ~ ( in @ SY3466 @ ( relation_dom @ SV40 ) )
| ( SY3466
= ( apply @ SV240 @ SY3465 ) ) )
| ~ ! [SY3176: $i] :
( ! [SY3177: $i] :
( ( SY3176
!= ( apply @ SV40 @ SY3177 ) )
| ~ ( in @ SY3177 @ ( relation_dom @ SV40 ) ) )
| ( in @ SY3176 @ ( relation_rng @ SV40 ) ) ) ) )
= $true )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2042]) ).
thf(2056,plain,
! [SV215: $i,SV94: $i,SV277: $i,SV43: $i,SV286: $i,SV274: $i] :
( ( ( in @ ( ordered_pair @ SV274 @ SV286 ) @ SV43 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV286 @ SV277 ) @ SV94 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV274 @ SV277 ) @ SV215 )
= $true )
| ( ( SV215
= ( relation_composition @ SV43 @ SV94 ) )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2044]) ).
thf(2057,plain,
! [SV43: $i,SV94: $i,SV215: $i,SV278: $i,SV275: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV275 @ ( sK8_F @ SV278 @ SV275 @ SV215 @ SV94 @ SV43 ) ) @ SV43 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV275 @ SV278 ) @ SV215 )
= $false )
| ( ( SV215
= ( relation_composition @ SV43 @ SV94 ) )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2045]) ).
thf(2058,plain,
! [SV43: $i,SV94: $i,SV215: $i,SV275: $i,SV278: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK8_F @ SV278 @ SV275 @ SV215 @ SV94 @ SV43 ) @ SV278 ) @ SV94 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV275 @ SV278 ) @ SV215 )
= $false )
| ( ( SV215
= ( relation_composition @ SV43 @ SV94 ) )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2045]) ).
thf(2059,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2050]) ).
thf(2060,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2051]) ).
thf(2061,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2052]) ).
thf(2062,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) )
= $true )
| ( ( ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2053]) ).
thf(2063,plain,
! [SV40: $i,SV240: $i] :
( ( ( ~ ! [SY3461: $i,SY3462: $i] :
( ( SY3462
!= ( apply @ SV240 @ SY3461 ) )
| ~ ( in @ SY3461 @ ( relation_rng @ SV40 ) )
| ( SY3461
= ( apply @ SV40 @ SY3462 ) ) )
| ~ ! [SY3463: $i,SY3464: $i] :
( ( SY3464
!= ( apply @ SV240 @ SY3463 ) )
| ~ ( in @ SY3463 @ ( relation_rng @ SV40 ) )
| ( in @ SY3464 @ ( relation_dom @ SV40 ) ) ) )
= $false )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2054]) ).
thf(2064,plain,
! [SV240: $i,SV40: $i] :
( ( ( ~ ! [SY3465: $i,SY3466: $i] :
( ( SY3465
!= ( apply @ SV40 @ SY3466 ) )
| ~ ( in @ SY3466 @ ( relation_dom @ SV40 ) )
| ( SY3466
= ( apply @ SV240 @ SY3465 ) ) )
| ~ ! [SY3176: $i] :
( ! [SY3177: $i] :
( ( SY3176
!= ( apply @ SV40 @ SY3177 ) )
| ~ ( in @ SY3177 @ ( relation_dom @ SV40 ) ) )
| ( in @ SY3176 @ ( relation_rng @ SV40 ) ) ) )
= $false )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2055]) ).
thf(2065,plain,
! [SV215: $i,SV43: $i,SV274: $i,SV94: $i,SV277: $i,SV286: $i] :
( ( ( in @ ( ordered_pair @ SV286 @ SV277 ) @ SV94 )
= $false )
| ( ( in @ ( ordered_pair @ SV274 @ SV286 ) @ SV43 )
= $false )
| ( ( in @ ( ordered_pair @ SV274 @ SV277 ) @ SV215 )
= $true )
| ( ( SV215
= ( relation_composition @ SV43 @ SV94 ) )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2056]) ).
thf(2066,plain,
! [SV43: $i,SV94: $i,SV215: $i,SV278: $i,SV275: $i] :
( ( ( in @ ( ordered_pair @ SV275 @ ( sK8_F @ SV278 @ SV275 @ SV215 @ SV94 @ SV43 ) ) @ SV43 )
= $true )
| ( ( in @ ( ordered_pair @ SV275 @ SV278 ) @ SV215 )
= $false )
| ( ( SV215
= ( relation_composition @ SV43 @ SV94 ) )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2057]) ).
thf(2067,plain,
! [SV43: $i,SV94: $i,SV215: $i,SV275: $i,SV278: $i] :
( ( ( in @ ( ordered_pair @ ( sK8_F @ SV278 @ SV275 @ SV215 @ SV94 @ SV43 ) @ SV278 ) @ SV94 )
= $true )
| ( ( in @ ( ordered_pair @ SV275 @ SV278 ) @ SV215 )
= $false )
| ( ( SV215
= ( relation_composition @ SV43 @ SV94 ) )
= $false )
| ( ( relation @ SV215 )
= $false )
| ( ( relation @ SV94 )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2058]) ).
thf(2068,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2059]) ).
thf(2069,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2059]) ).
thf(2070,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2060]) ).
thf(2071,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2060]) ).
thf(2072,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2061]) ).
thf(2073,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2061]) ).
thf(2074,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) )
= $true )
| ( ( ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2062]) ).
thf(2075,plain,
! [SV40: $i,SV240: $i] :
( ( ( ~ ! [SY3461: $i,SY3462: $i] :
( ( SY3462
!= ( apply @ SV240 @ SY3461 ) )
| ~ ( in @ SY3461 @ ( relation_rng @ SV40 ) )
| ( SY3461
= ( apply @ SV40 @ SY3462 ) ) ) )
= $false )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2063]) ).
thf(2076,plain,
! [SV40: $i,SV240: $i] :
( ( ( ~ ! [SY3463: $i,SY3464: $i] :
( ( SY3464
!= ( apply @ SV240 @ SY3463 ) )
| ~ ( in @ SY3463 @ ( relation_rng @ SV40 ) )
| ( in @ SY3464 @ ( relation_dom @ SV40 ) ) ) )
= $false )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2063]) ).
thf(2077,plain,
! [SV240: $i,SV40: $i] :
( ( ( ~ ! [SY3465: $i,SY3466: $i] :
( ( SY3465
!= ( apply @ SV40 @ SY3466 ) )
| ~ ( in @ SY3466 @ ( relation_dom @ SV40 ) )
| ( SY3466
= ( apply @ SV240 @ SY3465 ) ) ) )
= $false )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2064]) ).
thf(2078,plain,
! [SV240: $i,SV40: $i] :
( ( ( ~ ! [SY3176: $i] :
( ! [SY3177: $i] :
( ( SY3176
!= ( apply @ SV40 @ SY3177 ) )
| ~ ( in @ SY3177 @ ( relation_dom @ SV40 ) ) )
| ( in @ SY3176 @ ( relation_rng @ SV40 ) ) ) )
= $false )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2064]) ).
thf(2079,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ( ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2068]) ).
thf(2080,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2069]) ).
thf(2081,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2070]) ).
thf(2082,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2071]) ).
thf(2083,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2072]) ).
thf(2084,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2073]) ).
thf(2085,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
= $false )
| ( ( ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) )
= $true )
| ( ( ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2074]) ).
thf(2086,plain,
! [SV40: $i,SV240: $i] :
( ( ( ! [SY3461: $i,SY3462: $i] :
( ( SY3462
!= ( apply @ SV240 @ SY3461 ) )
| ~ ( in @ SY3461 @ ( relation_rng @ SV40 ) )
| ( SY3461
= ( apply @ SV40 @ SY3462 ) ) ) )
= $true )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2075]) ).
thf(2087,plain,
! [SV40: $i,SV240: $i] :
( ( ( ! [SY3463: $i,SY3464: $i] :
( ( SY3464
!= ( apply @ SV240 @ SY3463 ) )
| ~ ( in @ SY3463 @ ( relation_rng @ SV40 ) )
| ( in @ SY3464 @ ( relation_dom @ SV40 ) ) ) )
= $true )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2076]) ).
thf(2088,plain,
! [SV240: $i,SV40: $i] :
( ( ( ! [SY3465: $i,SY3466: $i] :
( ( SY3465
!= ( apply @ SV40 @ SY3466 ) )
| ~ ( in @ SY3466 @ ( relation_dom @ SV40 ) )
| ( SY3466
= ( apply @ SV240 @ SY3465 ) ) ) )
= $true )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2077]) ).
thf(2089,plain,
! [SV240: $i,SV40: $i] :
( ( ( ! [SY3176: $i] :
( ! [SY3177: $i] :
( ( SY3176
!= ( apply @ SV40 @ SY3177 ) )
| ~ ( in @ SY3177 @ ( relation_dom @ SV40 ) ) )
| ( in @ SY3176 @ ( relation_rng @ SV40 ) ) ) )
= $true )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2078]) ).
thf(2090,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2079]) ).
thf(2091,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
= $true )
| ( ( ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2080]) ).
thf(2092,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
| ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2081]) ).
thf(2093,plain,
! [SV40: $i,SV222: $i] :
( ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
= $true )
| ( ( ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2082]) ).
thf(2094,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) )
= $true )
| ( ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2083]) ).
thf(2095,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) )
= $true )
| ( ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2084]) ).
thf(2096,plain,
! [SV40: $i,SV222: $i] :
( ( ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
= $false )
| ( ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
= $false )
| ( ( ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2085]) ).
thf(2097,plain,
! [SV40: $i,SV288: $i,SV240: $i] :
( ( ( ! [SY3487: $i] :
( ( SY3487
!= ( apply @ SV240 @ SV288 ) )
| ~ ( in @ SV288 @ ( relation_rng @ SV40 ) )
| ( SV288
= ( apply @ SV40 @ SY3487 ) ) ) )
= $true )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2086]) ).
thf(2098,plain,
! [SV40: $i,SV289: $i,SV240: $i] :
( ( ( ! [SY3488: $i] :
( ( SY3488
!= ( apply @ SV240 @ SV289 ) )
| ~ ( in @ SV289 @ ( relation_rng @ SV40 ) )
| ( in @ SY3488 @ ( relation_dom @ SV40 ) ) ) )
= $true )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2087]) ).
thf(2099,plain,
! [SV240: $i,SV40: $i,SV290: $i] :
( ( ( ! [SY3489: $i] :
( ( SV290
!= ( apply @ SV40 @ SY3489 ) )
| ~ ( in @ SY3489 @ ( relation_dom @ SV40 ) )
| ( SY3489
= ( apply @ SV240 @ SV290 ) ) ) )
= $true )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2088]) ).
thf(2100,plain,
! [SV240: $i,SV40: $i,SV291: $i] :
( ( ( ! [SY3490: $i] :
( ( SV291
!= ( apply @ SV40 @ SY3490 ) )
| ~ ( in @ SY3490 @ ( relation_dom @ SV40 ) ) )
| ( in @ SV291 @ ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2089]) ).
thf(2101,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2090]) ).
thf(2102,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2090]) ).
thf(2103,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) )
= $true )
| ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2091]) ).
thf(2104,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2092]) ).
thf(2105,plain,
! [SV40: $i,SV222: $i] :
( ( ( ~ ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2092]) ).
thf(2106,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) )
= $true )
| ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2093]) ).
thf(2107,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) )
= $true )
| ( ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2094]) ).
thf(2108,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( ( sK43_C @ SV222 @ SV40 )
!= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) )
= $true )
| ( ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2095]) ).
thf(2109,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( ( sK44_SY3131 @ SV222 @ SV40 )
!= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) )
= $true )
| ( ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
= $false )
| ( ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
= $false )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2096]) ).
thf(2110,plain,
! [SV40: $i,SV288: $i,SV240: $i,SV292: $i] :
( ( ( ( SV292
!= ( apply @ SV240 @ SV288 ) )
| ~ ( in @ SV288 @ ( relation_rng @ SV40 ) )
| ( SV288
= ( apply @ SV40 @ SV292 ) ) )
= $true )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2097]) ).
thf(2111,plain,
! [SV40: $i,SV289: $i,SV240: $i,SV293: $i] :
( ( ( ( SV293
!= ( apply @ SV240 @ SV289 ) )
| ~ ( in @ SV289 @ ( relation_rng @ SV40 ) )
| ( in @ SV293 @ ( relation_dom @ SV40 ) ) )
= $true )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2098]) ).
thf(2112,plain,
! [SV240: $i,SV294: $i,SV40: $i,SV290: $i] :
( ( ( ( SV290
!= ( apply @ SV40 @ SV294 ) )
| ~ ( in @ SV294 @ ( relation_dom @ SV40 ) )
| ( SV294
= ( apply @ SV240 @ SV290 ) ) )
= $true )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2099]) ).
thf(2113,plain,
! [SV240: $i,SV40: $i,SV291: $i] :
( ( ( ! [SY3490: $i] :
( ( SV291
!= ( apply @ SV40 @ SY3490 ) )
| ~ ( in @ SY3490 @ ( relation_dom @ SV40 ) ) ) )
= $true )
| ( ( in @ SV291 @ ( relation_rng @ SV40 ) )
= $true )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2100]) ).
thf(2114,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2101]) ).
thf(2115,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2102]) ).
thf(2116,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
= $false )
| ( ( ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) )
= $true )
| ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2103]) ).
thf(2117,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2104]) ).
thf(2118,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
| ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2105]) ).
thf(2119,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
= $false )
| ( ( ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) )
= $true )
| ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2106]) ).
thf(2120,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
= $false )
| ( ( ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) )
= $true )
| ( ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2107]) ).
thf(2121,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
= $false )
| ( ( ~ ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) ) )
= $true )
| ( ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2108]) ).
thf(2122,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
= $false )
| ( ( ~ ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) ) )
= $true )
| ( ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
= $false )
| ( ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
= $false )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2109]) ).
thf(2123,plain,
! [SV40: $i,SV288: $i,SV240: $i,SV292: $i] :
( ( ( ( SV292
!= ( apply @ SV240 @ SV288 ) )
| ~ ( in @ SV288 @ ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV288
= ( apply @ SV40 @ SV292 ) )
= $true )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2110]) ).
thf(2124,plain,
! [SV40: $i,SV289: $i,SV240: $i,SV293: $i] :
( ( ( ( SV293
!= ( apply @ SV240 @ SV289 ) )
| ~ ( in @ SV289 @ ( relation_rng @ SV40 ) ) )
= $true )
| ( ( in @ SV293 @ ( relation_dom @ SV40 ) )
= $true )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2111]) ).
thf(2125,plain,
! [SV240: $i,SV294: $i,SV40: $i,SV290: $i] :
( ( ( ( SV290
!= ( apply @ SV40 @ SV294 ) )
| ~ ( in @ SV294 @ ( relation_dom @ SV40 ) ) )
= $true )
| ( ( SV294
= ( apply @ SV240 @ SV290 ) )
= $true )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2112]) ).
thf(2126,plain,
! [SV240: $i,SV295: $i,SV40: $i,SV291: $i] :
( ( ( ( SV291
!= ( apply @ SV40 @ SV295 ) )
| ~ ( in @ SV295 @ ( relation_dom @ SV40 ) ) )
= $true )
| ( ( in @ SV291 @ ( relation_rng @ SV40 ) )
= $true )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2113]) ).
thf(2127,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
= $true )
| ( ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2114]) ).
thf(2128,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
= $true )
| ( ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2115]) ).
thf(2129,plain,
! [SV40: $i,SV222: $i] :
( ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
= $false )
| ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
= $false )
| ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2116]) ).
thf(2130,plain,
! [SV40: $i,SV222: $i] :
( ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
= $true )
| ( ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2117]) ).
thf(2131,plain,
! [SV40: $i,SV222: $i] :
( ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
= $true )
| ( ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2118]) ).
thf(2132,plain,
! [SV40: $i,SV222: $i] :
( ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
= $false )
| ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
= $false )
| ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2119]) ).
thf(2133,plain,
! [SV40: $i,SV222: $i] :
( ( ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
= $false )
| ( ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
= $false )
| ( ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2120]) ).
thf(2134,plain,
! [SV40: $i,SV222: $i] :
( ( ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
= $false )
| ( ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
= $false )
| ( ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
= $true )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2121]) ).
thf(2135,plain,
! [SV40: $i,SV222: $i] :
( ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
= $false )
| ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
= $false )
| ( ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
= $false )
| ( ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
= $false )
| ( ( ( ( relation_dom @ SV222 )
!= ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2122]) ).
thf(2136,plain,
! [SV40: $i,SV288: $i,SV240: $i,SV292: $i] :
( ( ( ( SV292
!= ( apply @ SV240 @ SV288 ) ) )
= $true )
| ( ( ~ ( in @ SV288 @ ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV288
= ( apply @ SV40 @ SV292 ) )
= $true )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2123]) ).
thf(2137,plain,
! [SV40: $i,SV289: $i,SV240: $i,SV293: $i] :
( ( ( ( SV293
!= ( apply @ SV240 @ SV289 ) ) )
= $true )
| ( ( ~ ( in @ SV289 @ ( relation_rng @ SV40 ) ) )
= $true )
| ( ( in @ SV293 @ ( relation_dom @ SV40 ) )
= $true )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2124]) ).
thf(2138,plain,
! [SV240: $i,SV294: $i,SV40: $i,SV290: $i] :
( ( ( ( SV290
!= ( apply @ SV40 @ SV294 ) ) )
= $true )
| ( ( ~ ( in @ SV294 @ ( relation_dom @ SV40 ) ) )
= $true )
| ( ( SV294
= ( apply @ SV240 @ SV290 ) )
= $true )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2125]) ).
thf(2139,plain,
! [SV240: $i,SV295: $i,SV40: $i,SV291: $i] :
( ( ( ( SV291
!= ( apply @ SV40 @ SV295 ) ) )
= $true )
| ( ( ~ ( in @ SV295 @ ( relation_dom @ SV40 ) ) )
= $true )
| ( ( in @ SV291 @ ( relation_rng @ SV40 ) )
= $true )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2126]) ).
thf(2140,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( relation_dom @ SV222 )
= ( relation_rng @ SV40 ) )
= $false )
| ( ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
= $true )
| ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2127]) ).
thf(2141,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( relation_dom @ SV222 )
= ( relation_rng @ SV40 ) )
= $false )
| ( ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
= $true )
| ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2128]) ).
thf(2142,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( relation_dom @ SV222 )
= ( relation_rng @ SV40 ) )
= $false )
| ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
= $true )
| ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
= $false )
| ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
= $false )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2129]) ).
thf(2143,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( relation_dom @ SV222 )
= ( relation_rng @ SV40 ) )
= $false )
| ( ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
= $true )
| ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2130]) ).
thf(2144,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( relation_dom @ SV222 )
= ( relation_rng @ SV40 ) )
= $false )
| ( ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
= $true )
| ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
= $true )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2131]) ).
thf(2145,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( relation_dom @ SV222 )
= ( relation_rng @ SV40 ) )
= $false )
| ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
= $true )
| ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
= $false )
| ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
= $false )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2132]) ).
thf(2146,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( relation_dom @ SV222 )
= ( relation_rng @ SV40 ) )
= $false )
| ( ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
= $true )
| ( ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
= $false )
| ( ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
= $false )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2133]) ).
thf(2147,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( relation_dom @ SV222 )
= ( relation_rng @ SV40 ) )
= $false )
| ( ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
= $true )
| ( ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
= $false )
| ( ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
= $false )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2134]) ).
thf(2148,plain,
! [SV40: $i,SV222: $i] :
( ( ( ( relation_dom @ SV222 )
= ( relation_rng @ SV40 ) )
= $false )
| ( ( in @ ( sK44_SY3131 @ SV222 @ SV40 ) @ ( relation_dom @ SV40 ) )
= $false )
| ( ( ( sK43_C @ SV222 @ SV40 )
= ( apply @ SV40 @ ( sK44_SY3131 @ SV222 @ SV40 ) ) )
= $false )
| ( ( ( sK44_SY3131 @ SV222 @ SV40 )
= ( apply @ SV222 @ ( sK43_C @ SV222 @ SV40 ) ) )
= $false )
| ( ( in @ ( sK43_C @ SV222 @ SV40 ) @ ( relation_rng @ SV40 ) )
= $false )
| ( ( SV222
= ( function_inverse @ SV40 ) )
= $true )
| ( ( function @ SV222 )
= $false )
| ( ( relation @ SV222 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2135]) ).
thf(2149,plain,
! [SV40: $i,SV288: $i,SV240: $i,SV292: $i] :
( ( ( SV292
= ( apply @ SV240 @ SV288 ) )
= $false )
| ( ( ~ ( in @ SV288 @ ( relation_rng @ SV40 ) ) )
= $true )
| ( ( SV288
= ( apply @ SV40 @ SV292 ) )
= $true )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2136]) ).
thf(2150,plain,
! [SV40: $i,SV289: $i,SV240: $i,SV293: $i] :
( ( ( SV293
= ( apply @ SV240 @ SV289 ) )
= $false )
| ( ( ~ ( in @ SV289 @ ( relation_rng @ SV40 ) ) )
= $true )
| ( ( in @ SV293 @ ( relation_dom @ SV40 ) )
= $true )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2137]) ).
thf(2151,plain,
! [SV240: $i,SV294: $i,SV40: $i,SV290: $i] :
( ( ( SV290
= ( apply @ SV40 @ SV294 ) )
= $false )
| ( ( ~ ( in @ SV294 @ ( relation_dom @ SV40 ) ) )
= $true )
| ( ( SV294
= ( apply @ SV240 @ SV290 ) )
= $true )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2138]) ).
thf(2152,plain,
! [SV240: $i,SV295: $i,SV40: $i,SV291: $i] :
( ( ( SV291
= ( apply @ SV40 @ SV295 ) )
= $false )
| ( ( ~ ( in @ SV295 @ ( relation_dom @ SV40 ) ) )
= $true )
| ( ( in @ SV291 @ ( relation_rng @ SV40 ) )
= $true )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2139]) ).
thf(2153,plain,
! [SV240: $i,SV292: $i,SV40: $i,SV288: $i] :
( ( ( in @ SV288 @ ( relation_rng @ SV40 ) )
= $false )
| ( ( SV292
= ( apply @ SV240 @ SV288 ) )
= $false )
| ( ( SV288
= ( apply @ SV40 @ SV292 ) )
= $true )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2149]) ).
thf(2154,plain,
! [SV240: $i,SV293: $i,SV40: $i,SV289: $i] :
( ( ( in @ SV289 @ ( relation_rng @ SV40 ) )
= $false )
| ( ( SV293
= ( apply @ SV240 @ SV289 ) )
= $false )
| ( ( in @ SV293 @ ( relation_dom @ SV40 ) )
= $true )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2150]) ).
thf(2155,plain,
! [SV240: $i,SV290: $i,SV40: $i,SV294: $i] :
( ( ( in @ SV294 @ ( relation_dom @ SV40 ) )
= $false )
| ( ( SV290
= ( apply @ SV40 @ SV294 ) )
= $false )
| ( ( SV294
= ( apply @ SV240 @ SV290 ) )
= $true )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2151]) ).
thf(2156,plain,
! [SV240: $i,SV291: $i,SV40: $i,SV295: $i] :
( ( ( in @ SV295 @ ( relation_dom @ SV40 ) )
= $false )
| ( ( SV291
= ( apply @ SV40 @ SV295 ) )
= $false )
| ( ( in @ SV291 @ ( relation_rng @ SV40 ) )
= $true )
| ( ( SV240
= ( function_inverse @ SV40 ) )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false )
| ( ( one_to_one @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2152]) ).
thf(2157,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[501,2156,2155,2154,2153,2148,2147,2146,2145,2144,2143,2142,2141,2140,2067,2066,2065,2049,2048,2047,2046,2043,2034,2031,2016,2015,2013,2006,2005,2004,2000,1999,1998,1997,1996,1995,1989,1988,1987,1979,1978,1974,1970,1969,1965,1964,1963,1959,1958,1957,1952,1951,1950,1946,1917,1916,1915,1896,1895,1883,1880,1879,1878,1875,1874,1870,1868,1867,1866,1863,1856,1853,1852,1843,1840,1829,1828,1821,1810,1805,1803,1798,1796,1794,1785,1784,1778,1760,1750,1748,1747,1746,1718,1712,1711,1708,1707,1691,1688,1687,1686,1685,1676,1675,1672,1667,1666,1655,1640,1639,1628,1599,1584,1575,1549,1548,1522,1483,1482,1469,1468,1463,1448,1447,1442,1441,1398,1397,1371,1366,1365,1320,1319,1305,1304,1298,1297,1290,1263,1262,1259,1182,1177,1167,1166,1159,1158,1151,1150,1149,1148,1147,1146,1126,1125,1113,1112,1088,1087,1086,1082,1081,1076,992,991,977,957,947,946,900,899,896,895,894,893,892,883,881,880,878,877,876,875,873,872,860,853,851,832,831,826,825,813,805,804,791,783,781,780,779,767,762,592,584,503,502]) ).
thf(2158,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU221+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 : n015.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 : Sun Jun 19 06:58:14 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.48 ......
% 0.38/0.60
% 0.38/0.60 No.of.Axioms: 233
% 0.38/0.60
% 0.38/0.60 Length.of.Defs: 0
% 0.38/0.60
% 0.38/0.60 Contains.Choice.Funs: false
% 0.53/0.70 ..............
% 0.65/0.82 (rf:2,axioms:170,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:235,loop_count:0,foatp_calls:0,translation:fof_full).............................................................................................................................................................................................................................................................................eprover: CPU time limit exceeded, terminating
% 75.34/75.67 ..........ignored arguments false
% 75.47/75.78 .......
% 75.57/75.88 (rf:0,axioms:233,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:235,loop_count:0,foatp_calls:0,translation:fof_full)..................................................................................................................................................................................................................................................................................................eprover: CPU time limit exceeded, terminating
% 150.10/150.45 ..................................
% 150.35/150.72 (rf:2,axioms:170,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:235,loop_count:0,foatp_calls:0,translation:fof_full).............................................................................................................................................................................................................................................................................eprover: CPU time limit exceeded, terminating
% 224.94/225.27 ............................
% 225.39/225.71 (rf:-1,axioms:87,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:235,loop_count:0,foatp_calls:0,translation:fof_full)..............................................................................................................................................................
% 226.71/227.02
% 226.71/227.02 ********************************
% 226.71/227.02 * All subproblems solved! *
% 226.71/227.02 ********************************
% 226.71/227.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:-1,axioms:90,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2157,loop_count:0,foatp_calls:1,translation:fof_full)
% 228.28/228.61
% 228.28/228.61 %**** Beginning of derivation protocol ****
% 228.28/228.61 % SZS output start CNFRefutation
% See solution above
% 228.28/228.63
% 228.28/228.63 %**** End of derivation protocol ****
% 228.28/228.63 %**** no. of clauses in derivation: 2012 ****
% 228.28/228.63 %**** clause counter: 2157 ****
% 228.28/228.63
% 228.28/228.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:-1,axioms:90,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2157,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------