TSTP Solution File: SEU217+2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU217+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 : n026.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 12:08:20 EDT 2022
% Result : Theorem 13.36s 13.55s
% Output : CNFRefutation 16.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 306
% Syntax : Number of formulae : 3494 (1562 unt; 111 typ; 0 def)
% Number of atoms : 27725 (9502 equ; 0 cnn)
% Maximal formula atoms : 11 ( 8 avg)
% Number of connectives : 63200 (10256 ~;10221 |; 586 &;41668 @)
% ( 146 <=>; 323 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 217 ( 217 >; 0 *; 0 +; 0 <<)
% Number of symbols : 114 ( 111 usr; 11 con; 0-5 aty)
% Number of variables : 10695 ( 0 ^10649 !; 46 ?;10695 :)
% 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_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_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_A,type,
sK10_A: $i ).
thf(tp_sK11_B,type,
sK11_B: $i > $i ).
thf(tp_sK12_F,type,
sK12_F: $i > $i > $i > $i > $i > $i ).
thf(tp_sK13_D,type,
sK13_D: $i > $i > $i > $i ).
thf(tp_sK14_SY457,type,
sK14_SY457: $i > $i > $i > $i ).
thf(tp_sK15_SY461,type,
sK15_SY461: $i > $i > $i > $i ).
thf(tp_sK16_C,type,
sK16_C: $i > $i > $i ).
thf(tp_sK17_SY462,type,
sK17_SY462: $i > $i > $i ).
thf(tp_sK18_D,type,
sK18_D: $i > $i > $i > $i ).
thf(tp_sK19_C,type,
sK19_C: $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_SY464,type,
sK20_SY464: $i > $i > $i ).
thf(tp_sK21_D,type,
sK21_D: $i > $i > $i > $i ).
thf(tp_sK22_C,type,
sK22_C: $i > $i > $i ).
thf(tp_sK23_SY466,type,
sK23_SY466: $i > $i > $i ).
thf(tp_sK24_C,type,
sK24_C: $i > $i > $i ).
thf(tp_sK25_SY467,type,
sK25_SY467: $i > $i > $i ).
thf(tp_sK26_E,type,
sK26_E: $i > $i > $i > $i > $i ).
thf(tp_sK27_D,type,
sK27_D: $i > $i > $i > $i ).
thf(tp_sK28_SY469,type,
sK28_SY469: $i > $i > $i > $i ).
thf(tp_sK29_E,type,
sK29_E: $i > $i > $i > $i > $i ).
thf(tp_sK2_SY456,type,
sK2_SY456: $i ).
thf(tp_sK30_D,type,
sK30_D: $i > $i > $i > $i ).
thf(tp_sK31_SY471,type,
sK31_SY471: $i > $i > $i > $i ).
thf(tp_sK32_D,type,
sK32_D: $i > $i > $i > $i ).
thf(tp_sK33_SY472,type,
sK33_SY472: $i > $i > $i > $i ).
thf(tp_sK34_D,type,
sK34_D: $i > $i > $i > $i ).
thf(tp_sK35_SY473,type,
sK35_SY473: $i > $i > $i > $i ).
thf(tp_sK36_B,type,
sK36_B: $i > $i ).
thf(tp_sK37_SY474,type,
sK37_SY474: $i > $i ).
thf(tp_sK38_C,type,
sK38_C: $i > $i > $i ).
thf(tp_sK39_D,type,
sK39_D: $i > $i > $i > $i ).
thf(tp_sK3_A,type,
sK3_A: $i ).
thf(tp_sK40_D,type,
sK40_D: $i > $i > $i > $i ).
thf(tp_sK41_B,type,
sK41_B: $i > $i ).
thf(tp_sK42_B,type,
sK42_B: $i > $i ).
thf(tp_sK43_SY481,type,
sK43_SY481: $i > $i > $i ).
thf(tp_sK44_C,type,
sK44_C: $i > $i > $i ).
thf(tp_sK45_D,type,
sK45_D: $i > $i > $i > $i ).
thf(tp_sK46_D,type,
sK46_D: $i > $i > $i > $i ).
thf(tp_sK47_C,type,
sK47_C: $i > $i > $i ).
thf(tp_sK48_SY487,type,
sK48_SY487: $i > $i > $i ).
thf(tp_sK49_D,type,
sK49_D: $i > $i > $i > $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_sK50_C,type,
sK50_C: $i > $i > $i ).
thf(tp_sK51_E,type,
sK51_E: $i > $i > $i > $i > $i ).
thf(tp_sK52_SY488,type,
sK52_SY488: $i > $i > $i > $i > $i ).
thf(tp_sK53_D,type,
sK53_D: $i > $i > $i > $i ).
thf(tp_sK54_SY491,type,
sK54_SY491: $i > $i > $i > $i ).
thf(tp_sK55_SY493,type,
sK55_SY493: $i > $i > $i > $i ).
thf(tp_sK56_D,type,
sK56_D: $i > $i > $i > $i ).
thf(tp_sK57_D,type,
sK57_D: $i > $i > $i > $i ).
thf(tp_sK58_C,type,
sK58_C: $i > $i > $i ).
thf(tp_sK59_SY494,type,
sK59_SY494: $i > $i > $i ).
thf(tp_sK5_B,type,
sK5_B: $i > $i ).
thf(tp_sK60_C,type,
sK60_C: $i > $i > $i ).
thf(tp_sK61_B,type,
sK61_B: $i > $i ).
thf(tp_sK62_C,type,
sK62_C: $i > $i > $i ).
thf(tp_sK63_D,type,
sK63_D: $i > $i > $i > $i ).
thf(tp_sK64_C,type,
sK64_C: $i > $i > $i ).
thf(tp_sK65_SY495,type,
sK65_SY495: $i > $i > $i ).
thf(tp_sK66_C,type,
sK66_C: $i > $i > $i ).
thf(tp_sK67_SY497,type,
sK67_SY497: $i > $i > $i ).
thf(tp_sK68_B,type,
sK68_B: $i > $i ).
thf(tp_sK69_C,type,
sK69_C: $i > $i > $i ).
thf(tp_sK6_A,type,
sK6_A: $i ).
thf(tp_sK70_SY500,type,
sK70_SY500: $i > $i > $i ).
thf(tp_sK71_C,type,
sK71_C: $i > $i > $i ).
thf(tp_sK72_C,type,
sK72_C: $i > $i > $i ).
thf(tp_sK73_C,type,
sK73_C: $i > $i > $i ).
thf(tp_sK7_A,type,
sK7_A: $i ).
thf(tp_sK8_B,type,
sK8_B: $i > $i ).
thf(tp_sK9_A,type,
sK9_A: $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(tp_set_meet,type,
set_meet: $i > $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subset_complement,type,
subset_complement: $i > $i > $i ).
thf(tp_subset_difference,type,
subset_difference: $i > $i > $i > $i ).
thf(tp_union,type,
union: $i > $i ).
thf(tp_union_of_subsets,type,
union_of_subsets: $i > $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
( ( subset @ E @ C )
=> ( in @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_tarski) ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(4,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(7,axiom,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(9,axiom,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(12,axiom,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(14,axiom,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(16,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( meet_of_subsets @ A @ B )
= ( set_meet @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( union_of_subsets @ A @ B )
= ( union @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
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] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(22,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(23,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(24,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(25,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(26,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(27,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
thf(30,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(34,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(35,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(36,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(37,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(38,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(40,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(42,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(44,axiom,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(45,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(46,axiom,
! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
thf(47,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(48,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(49,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(50,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(51,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(52,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(53,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(54,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(57,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(58,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
thf(59,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(60,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(61,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
thf(62,axiom,
! [A: $i] : ( relation @ ( identity_relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
thf(64,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(67,axiom,
! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(70,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(75,axiom,
! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_subset_1) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
thf(86,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(87,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(88,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(89,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(90,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(91,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
thf(92,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(93,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(94,axiom,
! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
thf(96,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(97,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(98,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(99,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(100,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(101,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
thf(104,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
thf(105,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(106,axiom,
! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(107,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(108,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(109,axiom,
! [A: $i,B: $i] :
( ( ( A != empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ C @ D ) ) ) ) )
& ( ( A = empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ( B = empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_setfam_1) ).
thf(110,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(111,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(112,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(113,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(114,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(115,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(116,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(117,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(118,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(119,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(120,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(121,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(123,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(125,axiom,
! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(126,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(128,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(129,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(130,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(132,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(133,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(134,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(135,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_difference @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(136,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(137,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(138,axiom,
! [A: $i] :
( ( ( relation_dom @ ( identity_relation @ A ) )
= A )
& ( ( relation_rng @ ( identity_relation @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_relat_1) ).
thf(139,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(140,axiom,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
thf(141,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(142,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(143,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(144,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(145,axiom,
! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(146,axiom,
( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1) ).
thf(147,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(148,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).
thf(149,axiom,
! [A: $i] :
( ( A != empty_set )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ A )
=> ( ~ ( in @ C @ B )
=> ( in @ C @ ( subset_complement @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).
thf(150,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(151,axiom,
! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(154,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(155,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_zfmisc_1) ).
thf(156,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_setfam_1) ).
thf(157,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(158,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_xboole_1) ).
thf(159,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(160,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(161,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ( ( disjoint @ B @ C )
<=> ( subset @ B @ ( subset_complement @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_subset_1) ).
thf(162,axiom,
! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_xboole_1) ).
thf(163,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(164,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(165,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(166,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
thf(167,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(168,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(169,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(170,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(171,axiom,
! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(172,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(173,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(174,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(175,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(176,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(177,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(179,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(180,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(181,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(182,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(183,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(184,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(185,axiom,
( ( powerset @ empty_set )
= ( singleton @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(186,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(188,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(189,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(190,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(191,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(192,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(194,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(195,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(196,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(197,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(199,axiom,
! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( powerset @ C ) @ B ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(200,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(201,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(202,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(203,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(204,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(205,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(206,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(207,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(208,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( unordered_pair @ A @ B )
= ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(209,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(210,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l71_subset_1) ).
thf(211,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
thf(212,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(213,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_zfmisc_1) ).
thf(215,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_subset_1) ).
thf(216,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_xboole_1) ).
thf(217,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(218,axiom,
! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
thf(219,axiom,
! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).
thf(220,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l23_zfmisc_1) ).
thf(221,axiom,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(222,conjecture,
! [A: $i,B: $i] :
( ( in @ B @ A )
=> ( ( apply @ ( identity_relation @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_1) ).
thf(223,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( in @ B @ A )
=> ( ( apply @ ( identity_relation @ A ) @ B )
= B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[222]) ).
thf(224,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ A )
=> ( ( apply @ ( identity_relation @ A ) @ B )
= B ) ) )
= $false ),
inference(unfold_def,[status(thm)],[223]) ).
thf(225,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(226,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(227,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(228,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(229,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(230,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(231,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(232,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(233,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(234,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(235,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(236,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( meet_of_subsets @ A @ B )
= ( set_meet @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(237,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( union_of_subsets @ A @ B )
= ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(238,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(239,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(240,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(241,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(242,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(243,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(244,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(245,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(246,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(247,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(248,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(249,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(250,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(251,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)],[34]) ).
thf(252,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(253,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(254,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(255,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(256,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(257,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(258,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(259,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(260,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(261,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(262,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(263,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(264,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(265,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(266,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(267,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)],[51]) ).
thf(268,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(269,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)],[53]) ).
thf(270,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(271,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(272,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(273,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(274,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(275,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(276,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(277,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(278,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(279,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(280,plain,
( ( ! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(281,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(282,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)],[86]) ).
thf(283,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(284,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)],[88]) ).
thf(285,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(286,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(287,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(288,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)],[92]) ).
thf(289,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)],[96]) ).
thf(290,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)],[97]) ).
thf(291,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)],[100]) ).
thf(292,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_inverse_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ A )
& ( in @ E @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(293,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ ( ordered_pair @ E @ D ) @ A )
& ( in @ E @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(294,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)],[113]) ).
thf(295,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)],[114]) ).
thf(296,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(297,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(298,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(299,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(300,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(301,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(302,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(303,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(304,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(305,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)],[129]) ).
thf(306,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(307,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(308,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)],[132]) ).
thf(309,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(310,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)],[134]) ).
thf(311,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(312,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(313,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)],[137]) ).
thf(314,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(315,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(316,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_dom @ A )
= empty_set )
<=> ( ( relation_rng @ A )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(317,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
=> ( A = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(318,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(319,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(320,plain,
( ( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(321,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(322,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
& ( in @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(323,plain,
( ( ! [A: $i] :
( ( A != empty_set )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ A )
=> ( ~ ( in @ C @ B )
=> ( in @ C @ ( subset_complement @ A @ B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(324,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(325,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)],[154]) ).
thf(326,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(327,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)],[157]) ).
thf(328,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(329,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)],[159]) ).
thf(330,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)],[160]) ).
thf(331,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ( ( disjoint @ B @ C )
<=> ( subset @ B @ ( subset_complement @ A @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(332,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(333,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(334,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(335,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(336,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(337,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)],[170]) ).
thf(338,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(339,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)],[172]) ).
thf(340,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(341,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(342,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)],[175]) ).
thf(343,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(344,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(345,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(346,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)],[179]) ).
thf(347,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)],[180]) ).
thf(348,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)],[181]) ).
thf(349,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(350,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)],[183]) ).
thf(351,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)],[184]) ).
thf(352,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(353,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(354,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(355,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(356,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)],[189]) ).
thf(357,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)],[190]) ).
thf(358,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(359,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)],[192]) ).
thf(360,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(361,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)],[195]) ).
thf(362,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(363,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)],[197]) ).
thf(364,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( powerset @ C ) @ B ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(365,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(366,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(367,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)],[202]) ).
thf(368,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(369,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(370,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(371,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(372,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)],[207]) ).
thf(373,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( unordered_pair @ A @ B )
= ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(374,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(375,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(376,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(377,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(378,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
( ( subset @ E @ C )
=> ( in @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(379,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(380,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(381,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(382,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(383,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(384,plain,
( ( ! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(385,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(386,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(387,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(388,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(389,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(390,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(391,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(392,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(393,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(394,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)],[105]) ).
thf(395,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(396,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(397,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(398,plain,
( ( ! [A: $i,B: $i] :
( ( ( A != empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ C @ D ) ) ) ) )
& ( ( A = empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ( B = empty_set ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(399,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)],[110]) ).
thf(400,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)],[116]) ).
thf(401,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(402,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(403,plain,
( ( ! [A: $i] :
( ( ( relation_dom @ ( identity_relation @ A ) )
= A )
& ( ( relation_rng @ ( identity_relation @ A ) )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(404,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(405,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(406,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(407,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(408,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(409,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(410,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(411,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(412,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(413,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(414,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(415,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(416,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(417,plain,
( ( ! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(418,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(419,plain,
( ( ! [SY456: $i] :
( ( in @ SY456 @ sK1_A )
=> ( ( apply @ ( identity_relation @ sK1_A ) @ SY456 )
= SY456 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[224]) ).
thf(420,plain,
( ( ( in @ sK2_SY456 @ sK1_A )
=> ( ( apply @ ( identity_relation @ sK1_A ) @ sK2_SY456 )
= sK2_SY456 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[419]) ).
thf(421,plain,
( ( in @ sK2_SY456 @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[420]) ).
thf(422,plain,
( ( ( apply @ ( identity_relation @ sK1_A ) @ sK2_SY456 )
= sK2_SY456 )
= $false ),
inference(standard_cnf,[status(thm)],[420]) ).
thf(423,plain,
( ( ( ( apply @ ( identity_relation @ sK1_A ) @ sK2_SY456 )
!= sK2_SY456 ) )
= $true ),
inference(polarity_switch,[status(thm)],[422]) ).
thf(424,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[225]) ).
thf(425,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[226]) ).
thf(426,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[227]) ).
thf(427,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[229]) ).
thf(428,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[233]) ).
thf(429,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[234]) ).
thf(430,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ~ ( element @ C @ ( powerset @ A ) )
| ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[235]) ).
thf(431,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ( meet_of_subsets @ A @ B )
= ( set_meet @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[236]) ).
thf(432,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ( union_of_subsets @ A @ B )
= ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[237]) ).
thf(433,plain,
( ( ( relation @ sK3_A )
& ( relation_empty_yielding @ sK3_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[238]) ).
thf(434,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[239]) ).
thf(435,plain,
( ( ! [A: $i] :
( ( element @ ( sK5_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK5_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[240]) ).
thf(436,plain,
( ( ~ ( empty @ sK6_A )
& ( relation @ sK6_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[241]) ).
thf(437,plain,
( ( empty @ sK7_A )
= $true ),
inference(extcnf_combined,[status(esa)],[242]) ).
thf(438,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK8_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK8_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[243]) ).
thf(439,plain,
( ( ( empty @ sK9_A )
& ( relation @ sK9_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[244]) ).
thf(440,plain,
( ( ( function @ sK10_A )
& ( relation @ sK10_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[245]) ).
thf(441,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[246]) ).
thf(442,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[247]) ).
thf(443,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[248]) ).
thf(444,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[249]) ).
thf(445,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[250]) ).
thf(446,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)],[251]) ).
thf(447,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[252]) ).
thf(448,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[253]) ).
thf(449,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[254]) ).
thf(450,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[255]) ).
thf(451,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[256]) ).
thf(452,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[258]) ).
thf(453,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[260]) ).
thf(454,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[262]) ).
thf(455,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[266]) ).
thf(456,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)],[267]) ).
thf(457,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)],[269]) ).
thf(458,plain,
( ( ! [A: $i] : ( element @ ( sK11_B @ A ) @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[270]) ).
thf(459,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[271]) ).
thf(460,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[272]) ).
thf(461,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[273]) ).
thf(462,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ~ ( element @ C @ ( powerset @ A ) )
| ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[274]) ).
thf(463,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[275]) ).
thf(464,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[276]) ).
thf(465,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[277]) ).
thf(466,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[278]) ).
thf(467,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[279]) ).
thf(468,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ( proper_subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( A != B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[281]) ).
thf(469,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ! [SY460: $i] :
( ~ ( in @ ( ordered_pair @ ( sK13_D @ C @ B @ A ) @ SY460 ) @ A )
| ~ ( in @ ( ordered_pair @ SY460 @ ( sK14_SY457 @ C @ B @ A ) ) @ B ) )
| ~ ( in @ ( ordered_pair @ ( sK13_D @ C @ B @ A ) @ ( sK14_SY457 @ C @ B @ A ) ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK13_D @ C @ B @ A ) @ ( sK15_SY461 @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK15_SY461 @ C @ B @ A ) @ ( sK14_SY457 @ C @ B @ A ) ) @ B ) )
| ( in @ ( ordered_pair @ ( sK13_D @ C @ B @ A ) @ ( sK14_SY457 @ 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 @ ( sK12_F @ E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK12_F @ E @ D @ C @ B @ A ) @ E ) @ B ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[282]) ).
thf(470,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_intersection2 @ A @ B )
!= empty_set )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[283]) ).
thf(471,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK16_C @ B @ A ) @ ( sK17_SY462 @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK17_SY462 @ B @ A ) @ ( sK16_C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( sK16_C @ B @ A ) @ ( sK17_SY462 @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK17_SY462 @ B @ A ) @ ( sK16_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)],[284]) ).
thf(472,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[285]) ).
thf(473,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[287]) ).
thf(474,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY463: $i] :
~ ( in @ ( ordered_pair @ SY463 @ ( sK19_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK19_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK20_SY464 @ B @ A ) @ ( sK19_C @ B @ A ) ) @ A )
| ( in @ ( sK19_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 @ ( sK18_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[288]) ).
thf(475,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY465: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ B @ A ) @ SY465 ) @ A )
| ~ ( in @ ( sK22_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK22_C @ B @ A ) @ ( sK23_SY466 @ B @ A ) ) @ A )
| ( in @ ( sK22_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 @ ( sK21_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[289]) ).
thf(476,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)],[290]) ).
thf(477,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( in @ ( ordered_pair @ ( sK24_C @ B @ A ) @ ( sK25_SY467 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK24_C @ B @ A ) @ ( sK25_SY467 @ 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)],[291]) ).
thf(478,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY468: $i] :
( ~ ( in @ ( ordered_pair @ ( sK27_D @ C @ B @ A ) @ SY468 ) @ A )
| ~ ( in @ SY468 @ B ) )
| ~ ( in @ ( sK27_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK27_D @ C @ B @ A ) @ ( sK28_SY469 @ C @ B @ A ) ) @ A )
& ( in @ ( sK28_SY469 @ C @ B @ A ) @ B ) )
| ( in @ ( sK27_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 @ ( sK26_E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( sK26_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[292]) ).
thf(479,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY470: $i] :
( ~ ( in @ ( ordered_pair @ SY470 @ ( sK30_D @ C @ B @ A ) ) @ A )
| ~ ( in @ SY470 @ B ) )
| ~ ( in @ ( sK30_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK31_SY471 @ C @ B @ A ) @ ( sK30_D @ C @ B @ A ) ) @ A )
& ( in @ ( sK31_SY471 @ C @ B @ A ) @ B ) )
| ( in @ ( sK30_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 @ ( sK29_E @ D @ C @ B @ A ) @ D ) @ A )
& ( in @ ( sK29_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[293]) ).
thf(480,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK33_SY472 @ C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ C @ B @ A ) @ ( sK33_SY472 @ C @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ C @ B @ A ) @ ( sK33_SY472 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK33_SY472 @ C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK32_D @ C @ B @ A ) @ ( sK33_SY472 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK32_D @ C @ B @ A ) @ ( sK33_SY472 @ C @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK32_D @ C @ B @ A ) @ ( sK33_SY472 @ 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)],[294]) ).
thf(481,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK34_D @ C @ B @ A ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ C @ B @ A ) @ ( sK35_SY473 @ C @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ C @ B @ A ) @ ( sK35_SY473 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK34_D @ C @ B @ A ) @ B )
| ( in @ ( ordered_pair @ ( sK34_D @ C @ B @ A ) @ ( sK35_SY473 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK34_D @ C @ B @ A ) @ ( sK35_SY473 @ C @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK34_D @ C @ B @ A ) @ ( sK35_SY473 @ 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)],[295]) ).
thf(482,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[296]) ).
thf(483,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[300]) ).
thf(484,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[301]) ).
thf(485,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[302]) ).
thf(486,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[304]) ).
thf(487,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)],[305]) ).
thf(488,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[306]) ).
thf(489,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[307]) ).
thf(490,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)],[308]) ).
thf(491,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[309]) ).
thf(492,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)],[310]) ).
thf(493,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= A )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[311]) ).
thf(494,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)],[313]) ).
thf(495,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[314]) ).
thf(496,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)],[316]) ).
thf(497,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)],[317]) ).
thf(498,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[318]) ).
thf(499,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[319]) ).
thf(500,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK36_B @ A ) @ ( sK37_SY474 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[321]) ).
thf(501,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( in @ B @ ( subset_complement @ A @ C ) )
| ~ ( in @ B @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[322]) ).
thf(502,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( element @ C @ A )
| ( in @ C @ B )
| ( in @ C @ ( subset_complement @ A @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[323]) ).
thf(503,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)],[325]) ).
thf(504,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( B = empty_set )
| ( ( complements_of_subsets @ A @ B )
!= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[326]) ).
thf(505,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)],[327]) ).
thf(506,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[328]) ).
thf(507,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)],[329]) ).
thf(508,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)],[330]) ).
thf(509,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( disjoint @ B @ C )
| ( subset @ B @ ( subset_complement @ A @ C ) ) )
& ! [C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( subset @ B @ ( subset_complement @ A @ C ) )
| ( disjoint @ B @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[331]) ).
thf(510,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[333]) ).
thf(511,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[334]) ).
thf(512,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[336]) ).
thf(513,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)],[337]) ).
thf(514,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ( in @ ( sK38_C @ B @ A ) @ A )
& ( ( apply @ B @ ( sK38_C @ B @ A ) )
!= ( sK38_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)],[339]) ).
thf(515,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ! [D: $i] :
( ( ordered_pair @ A @ B )
!= ( ordered_pair @ C @ D ) )
| ( A = C ) )
& ! [C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
!= ( ordered_pair @ C @ D ) )
| ( B = D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[340]) ).
thf(516,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[341]) ).
thf(517,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)],[342]) ).
thf(518,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[344]) ).
thf(519,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[345]) ).
thf(520,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)],[346]) ).
thf(521,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)],[347]) ).
thf(522,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)],[348]) ).
thf(523,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[349]) ).
thf(524,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)],[350]) ).
thf(525,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)],[351]) ).
thf(526,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[353]) ).
thf(527,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[354]) ).
thf(528,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)],[356]) ).
thf(529,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)],[357]) ).
thf(530,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[358]) ).
thf(531,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 @ ( sK39_D @ C @ B @ A ) @ ( relation_rng @ C ) )
& ( in @ ( ordered_pair @ A @ ( sK39_D @ C @ B @ A ) ) @ C )
& ( in @ ( sK39_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[359]) ).
thf(532,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[360]) ).
thf(533,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)],[361]) ).
thf(534,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[362]) ).
thf(535,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 @ ( sK40_D @ C @ B @ A ) @ ( relation_dom @ C ) )
& ( in @ ( ordered_pair @ ( sK40_D @ C @ B @ A ) @ A ) @ C )
& ( in @ ( sK40_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[363]) ).
thf(536,plain,
( ( ! [A: $i] :
( ! [SY475: $i] :
( ~ ( subset @ SY475 @ ( sK41_B @ A ) )
| ( are_equipotent @ SY475 @ ( sK41_B @ A ) )
| ( in @ SY475 @ ( sK41_B @ A ) ) )
& ! [SY476: $i] :
( ~ ( in @ SY476 @ ( sK41_B @ A ) )
| ( in @ ( powerset @ SY476 ) @ ( sK41_B @ A ) ) )
& ! [SY477: $i,SY478: $i] :
( ~ ( in @ SY477 @ ( sK41_B @ A ) )
| ~ ( subset @ SY478 @ SY477 )
| ( in @ SY478 @ ( sK41_B @ A ) ) )
& ( in @ A @ ( sK41_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[364]) ).
thf(537,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[365]) ).
thf(538,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ D )
| ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[366]) ).
thf(539,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)],[367]) ).
thf(540,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) )
& ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[368]) ).
thf(541,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[369]) ).
thf(542,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[370]) ).
thf(543,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[371]) ).
thf(544,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)],[372]) ).
thf(545,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( A = D )
| ( A = C )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ C @ D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[373]) ).
thf(546,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[374]) ).
thf(547,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[375]) ).
thf(548,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[376]) ).
thf(549,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(extcnf_combined,[status(esa)],[377]) ).
thf(550,plain,
( ( ! [A: $i] :
( ! [SY479: $i] :
( ~ ( subset @ SY479 @ ( sK42_B @ A ) )
| ( are_equipotent @ SY479 @ ( sK42_B @ A ) )
| ( in @ SY479 @ ( sK42_B @ A ) ) )
& ! [SY480: $i] :
( ( ! [SY485: $i] :
( ~ ( subset @ SY485 @ SY480 )
| ( in @ SY485 @ ( sK43_SY481 @ SY480 @ A ) ) )
& ( in @ ( sK43_SY481 @ SY480 @ A ) @ ( sK42_B @ A ) ) )
| ~ ( in @ SY480 @ ( sK42_B @ A ) ) )
& ! [SY483: $i,SY484: $i] :
( ~ ( in @ SY483 @ ( sK42_B @ A ) )
| ~ ( subset @ SY484 @ SY483 )
| ( in @ SY484 @ ( sK42_B @ A ) ) )
& ( in @ A @ ( sK42_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[378]) ).
thf(551,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[379]) ).
thf(552,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[380]) ).
thf(553,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK44_C @ B @ A ) @ A )
| ~ ( in @ ( sK44_C @ B @ A ) @ B ) )
& ( ( in @ ( sK44_C @ B @ A ) @ A )
| ( in @ ( sK44_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[381]) ).
thf(554,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[382]) ).
thf(555,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[383]) ).
thf(556,plain,
( ( ! [A: $i] : ( function @ ( identity_relation @ A ) )
& ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[384]) ).
thf(557,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK45_D @ C @ B @ A ) @ A )
| ( in @ ( sK45_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK45_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK45_D @ C @ B @ A ) @ A )
| ( in @ ( sK45_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK45_D @ C @ B @ A ) @ B )
| ( in @ ( sK45_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_difference @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_difference @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ~ ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[386]) ).
thf(558,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY486: $i] :
( ~ ( in @ ( sK47_C @ B @ A ) @ SY486 )
| ~ ( in @ SY486 @ A ) )
| ~ ( in @ ( sK47_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK47_C @ B @ A ) @ ( sK48_SY487 @ B @ A ) )
& ( in @ ( sK48_SY487 @ B @ A ) @ A ) )
| ( in @ ( sK47_C @ B @ A ) @ B ) ) )
| ( B
= ( union @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( union @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
( ~ ( in @ C @ D )
| ~ ( in @ D @ A ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( ( in @ C @ ( sK46_D @ C @ B @ A ) )
& ( in @ ( sK46_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[387]) ).
thf(559,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK49_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK49_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK49_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK49_D @ C @ B @ A ) @ A )
| ( in @ ( sK49_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK49_D @ C @ B @ A ) @ B )
| ( in @ ( sK49_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_intersection2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_intersection2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ~ ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[388]) ).
thf(560,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK50_C @ B @ A ) @ A )
& ~ ( in @ ( sK50_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[389]) ).
thf(561,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY489: $i,SY490: $i] :
( ~ ( in @ SY489 @ A )
| ~ ( in @ SY490 @ B )
| ( ( sK53_D @ C @ B @ A )
!= ( ordered_pair @ SY489 @ SY490 ) ) )
| ~ ( in @ ( sK53_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK54_SY491 @ C @ B @ A ) @ A )
& ( in @ ( sK55_SY493 @ C @ B @ A ) @ B )
& ( ( sK53_D @ C @ B @ A )
= ( ordered_pair @ ( sK54_SY491 @ C @ B @ A ) @ ( sK55_SY493 @ C @ B @ A ) ) ) )
| ( in @ ( sK53_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( cartesian_product2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( cartesian_product2 @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i,F: $i] :
( ~ ( in @ E @ A )
| ~ ( in @ F @ B )
| ( D
!= ( ordered_pair @ E @ F ) ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( sK51_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK52_SY488 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK51_E @ D @ C @ B @ A ) @ ( sK52_SY488 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[390]) ).
thf(562,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK56_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK56_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK56_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK56_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK56_D @ C @ B @ A ) @ C )
| ( in @ ( sK56_D @ C @ B @ A ) @ A )
| ( in @ ( sK56_D @ C @ B @ A ) @ B ) ) )
| ( C
= ( set_union2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A )
| ( in @ D @ B ) )
& ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[391]) ).
thf(563,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK57_D @ C @ B @ A ) @ C )
| ( ( sK57_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK57_D @ C @ B @ A ) @ C )
| ( ( sK57_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK57_D @ C @ B @ A ) @ C )
| ( ( sK57_D @ C @ B @ A )
= A )
| ( ( sK57_D @ C @ B @ A )
= B ) ) )
| ( C
= ( unordered_pair @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( unordered_pair @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( D = A )
| ( D = B ) )
& ! [D: $i] :
( ( D != A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ( D != B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[392]) ).
thf(564,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( in @ B @ A ) ) )
& ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( in @ B @ A )
| ( element @ B @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( empty @ B ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( empty @ B )
| ( element @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[393]) ).
thf(565,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK58_C @ B @ A ) @ ( sK59_SY494 @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK58_C @ B @ A ) @ ( sK59_SY494 @ B @ A ) ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK58_C @ B @ A ) @ ( sK59_SY494 @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK58_C @ B @ A ) @ ( sK59_SY494 @ 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)],[394]) ).
thf(566,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK60_C @ B @ A ) @ B )
| ~ ( subset @ ( sK60_C @ B @ A ) @ A ) )
& ( ( in @ ( sK60_C @ B @ A ) @ B )
| ( subset @ ( sK60_C @ B @ A ) @ A ) ) )
| ( B
= ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( in @ C @ B )
| ( subset @ C @ A ) )
& ! [C: $i] :
( ~ ( subset @ C @ A )
| ( in @ C @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[395]) ).
thf(567,plain,
( ( ! [A: $i] :
( ( in @ ( sK61_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[396]) ).
thf(568,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK62_C @ B @ A )
!= A )
| ~ ( in @ ( sK62_C @ B @ A ) @ B ) )
& ( ( ( sK62_C @ B @ A )
= A )
| ( in @ ( sK62_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[397]) ).
thf(569,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( ( ( ( in @ ( sK65_SY495 @ B @ A ) @ A )
& ~ ( in @ ( sK64_C @ B @ A ) @ ( sK65_SY495 @ B @ A ) ) )
| ~ ( in @ ( sK64_C @ B @ A ) @ B ) )
& ( ! [SY496: $i] :
( ~ ( in @ SY496 @ A )
| ( in @ ( sK64_C @ B @ A ) @ SY496 ) )
| ( in @ ( sK64_C @ B @ A ) @ B ) ) )
| ( B
= ( set_meet @ A ) ) ) )
& ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( ! [C: $i] :
( ( ( in @ ( sK63_D @ C @ B @ A ) @ A )
& ~ ( in @ C @ ( sK63_D @ C @ B @ A ) ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ C @ D ) ) ) ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( B = empty_set ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
( ( B != empty_set )
| ( B
= ( set_meet @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[398]) ).
thf(570,plain,
( ( ! [A: $i] :
( ( ! [SY498: $i,SY499: $i] :
( ( sK68_B @ A )
!= ( ordered_pair @ SY498 @ SY499 ) )
& ( in @ ( sK68_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK66_C @ B @ A ) @ ( sK67_SY497 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[399]) ).
thf(571,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( ( ( sK69_C @ B @ A )
!= ( sK70_SY500 @ B @ A ) )
| ~ ( in @ ( sK69_C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK69_C @ B @ A ) @ ( sK70_SY500 @ B @ A ) ) @ B ) )
& ( ( ( sK69_C @ B @ A )
= ( sK70_SY500 @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK69_C @ B @ A ) @ ( sK70_SY500 @ B @ A ) ) @ B ) )
& ( ( in @ ( sK69_C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK69_C @ B @ A ) @ ( sK70_SY500 @ 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)],[400]) ).
thf(572,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[401]) ).
thf(573,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[402]) ).
thf(574,plain,
( ( ! [A: $i] :
( ( relation_dom @ ( identity_relation @ A ) )
= A )
& ! [A: $i] :
( ( relation_rng @ ( identity_relation @ A ) )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[403]) ).
thf(575,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
!= A )
| ~ ( in @ B @ A ) )
& ! [A: $i,B: $i] :
( ( in @ B @ A )
| ( ( set_difference @ A @ ( singleton @ B ) )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[404]) ).
thf(576,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK71_C @ B @ A ) @ ( set_intersection2 @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[405]) ).
thf(577,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[406]) ).
thf(578,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK72_C @ B @ A ) @ A )
& ( in @ ( sK72_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[407]) ).
thf(579,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ C )
| ( subset @ ( unordered_pair @ A @ B ) @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ A @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[408]) ).
thf(580,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[409]) ).
thf(581,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) )
& ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ A @ C ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ B @ D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[410]) ).
thf(582,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK73_C @ B @ A ) @ A )
& ~ ( in @ ( sK73_C @ B @ A ) @ B ) )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[411]) ).
thf(583,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) )
& ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ A @ C ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ B @ D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[412]) ).
thf(584,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[413]) ).
thf(585,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[414]) ).
thf(586,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[415]) ).
thf(587,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[416]) ).
thf(588,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[417]) ).
thf(589,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[418]) ).
thf(590,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[589]) ).
thf(591,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[588]) ).
thf(592,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[587]) ).
thf(593,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[586]) ).
thf(594,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[585]) ).
thf(595,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[584]) ).
thf(596,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) )
& ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ A @ C ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[583]) ).
thf(597,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK73_C @ B @ A ) @ A )
& ~ ( in @ ( sK73_C @ B @ A ) @ B ) )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[582]) ).
thf(598,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) )
& ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ A @ C ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[581]) ).
thf(599,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[580]) ).
thf(600,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ C )
| ( subset @ ( unordered_pair @ A @ B ) @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ A @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[579]) ).
thf(601,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK72_C @ B @ A ) @ A )
& ( in @ ( sK72_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[578]) ).
thf(602,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[577]) ).
thf(603,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK71_C @ B @ A ) @ ( set_intersection2 @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[576]) ).
thf(604,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
!= A )
| ~ ( in @ B @ A ) )
& ! [A: $i,B: $i] :
( ( in @ B @ A )
| ( ( set_difference @ A @ ( singleton @ B ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[575]) ).
thf(605,plain,
( ( ! [A: $i] :
( ( relation_dom @ ( identity_relation @ A ) )
= A )
& ! [A: $i] :
( ( relation_rng @ ( identity_relation @ A ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[574]) ).
thf(606,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[573]) ).
thf(607,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[572]) ).
thf(608,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( ( ( sK69_C @ B @ A )
!= ( sK70_SY500 @ B @ A ) )
| ~ ( in @ ( sK69_C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK69_C @ B @ A ) @ ( sK70_SY500 @ B @ A ) ) @ B ) )
& ( ( ( sK69_C @ B @ A )
= ( sK70_SY500 @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK69_C @ B @ A ) @ ( sK70_SY500 @ B @ A ) ) @ B ) )
& ( ( in @ ( sK69_C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK69_C @ B @ A ) @ ( sK70_SY500 @ 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)],[571]) ).
thf(609,plain,
( ( ! [A: $i] :
( ( ! [SY498: $i,SY499: $i] :
( ( sK68_B @ A )
!= ( ordered_pair @ SY498 @ SY499 ) )
& ( in @ ( sK68_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK66_C @ B @ A ) @ ( sK67_SY497 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[570]) ).
thf(610,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( ( ( ( in @ ( sK65_SY495 @ B @ A ) @ A )
& ~ ( in @ ( sK64_C @ B @ A ) @ ( sK65_SY495 @ B @ A ) ) )
| ~ ( in @ ( sK64_C @ B @ A ) @ B ) )
& ( ! [SY496: $i] :
( ~ ( in @ SY496 @ A )
| ( in @ ( sK64_C @ B @ A ) @ SY496 ) )
| ( in @ ( sK64_C @ B @ A ) @ B ) ) )
| ( B
= ( set_meet @ A ) ) ) )
& ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( ! [C: $i] :
( ( ( in @ ( sK63_D @ C @ B @ A ) @ A )
& ~ ( in @ C @ ( sK63_D @ C @ B @ A ) ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ C @ D ) ) ) ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( B = empty_set ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
( ( B != empty_set )
| ( B
= ( set_meet @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[569]) ).
thf(611,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK62_C @ B @ A )
!= A )
| ~ ( in @ ( sK62_C @ B @ A ) @ B ) )
& ( ( ( sK62_C @ B @ A )
= A )
| ( in @ ( sK62_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[568]) ).
thf(612,plain,
( ( ! [A: $i] :
( ( in @ ( sK61_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[567]) ).
thf(613,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK60_C @ B @ A ) @ B )
| ~ ( subset @ ( sK60_C @ B @ A ) @ A ) )
& ( ( in @ ( sK60_C @ B @ A ) @ B )
| ( subset @ ( sK60_C @ B @ A ) @ A ) ) )
| ( B
= ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( in @ C @ B )
| ( subset @ C @ A ) )
& ! [C: $i] :
( ~ ( subset @ C @ A )
| ( in @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[566]) ).
thf(614,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK58_C @ B @ A ) @ ( sK59_SY494 @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK58_C @ B @ A ) @ ( sK59_SY494 @ B @ A ) ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK58_C @ B @ A ) @ ( sK59_SY494 @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK58_C @ B @ A ) @ ( sK59_SY494 @ 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)],[565]) ).
thf(615,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( in @ B @ A ) ) )
& ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( in @ B @ A )
| ( element @ B @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( empty @ B ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( empty @ B )
| ( element @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[564]) ).
thf(616,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK57_D @ C @ B @ A ) @ C )
| ( ( sK57_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK57_D @ C @ B @ A ) @ C )
| ( ( sK57_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK57_D @ C @ B @ A ) @ C )
| ( ( sK57_D @ C @ B @ A )
= A )
| ( ( sK57_D @ C @ B @ A )
= B ) ) )
| ( C
= ( unordered_pair @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( unordered_pair @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( D = A )
| ( D = B ) )
& ! [D: $i] :
( ( D != A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ( D != B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[563]) ).
thf(617,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK56_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK56_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK56_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK56_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK56_D @ C @ B @ A ) @ C )
| ( in @ ( sK56_D @ C @ B @ A ) @ A )
| ( in @ ( sK56_D @ C @ B @ A ) @ B ) ) )
| ( C
= ( set_union2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A )
| ( in @ D @ B ) )
& ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[562]) ).
thf(618,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY489: $i,SY490: $i] :
( ~ ( in @ SY489 @ A )
| ~ ( in @ SY490 @ B )
| ( ( sK53_D @ C @ B @ A )
!= ( ordered_pair @ SY489 @ SY490 ) ) )
| ~ ( in @ ( sK53_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK54_SY491 @ C @ B @ A ) @ A )
& ( in @ ( sK55_SY493 @ C @ B @ A ) @ B )
& ( ( sK53_D @ C @ B @ A )
= ( ordered_pair @ ( sK54_SY491 @ C @ B @ A ) @ ( sK55_SY493 @ C @ B @ A ) ) ) )
| ( in @ ( sK53_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( cartesian_product2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( cartesian_product2 @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i,F: $i] :
( ~ ( in @ E @ A )
| ~ ( in @ F @ B )
| ( D
!= ( ordered_pair @ E @ F ) ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( sK51_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK52_SY488 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK51_E @ D @ C @ B @ A ) @ ( sK52_SY488 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[561]) ).
thf(619,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK50_C @ B @ A ) @ A )
& ~ ( in @ ( sK50_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[560]) ).
thf(620,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK49_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK49_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK49_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK49_D @ C @ B @ A ) @ A )
| ( in @ ( sK49_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK49_D @ C @ B @ A ) @ B )
| ( in @ ( sK49_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_intersection2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_intersection2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ~ ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[559]) ).
thf(621,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY486: $i] :
( ~ ( in @ ( sK47_C @ B @ A ) @ SY486 )
| ~ ( in @ SY486 @ A ) )
| ~ ( in @ ( sK47_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK47_C @ B @ A ) @ ( sK48_SY487 @ B @ A ) )
& ( in @ ( sK48_SY487 @ B @ A ) @ A ) )
| ( in @ ( sK47_C @ B @ A ) @ B ) ) )
| ( B
= ( union @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( union @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
( ~ ( in @ C @ D )
| ~ ( in @ D @ A ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( ( in @ C @ ( sK46_D @ C @ B @ A ) )
& ( in @ ( sK46_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[558]) ).
thf(622,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK45_D @ C @ B @ A ) @ A )
| ( in @ ( sK45_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK45_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK45_D @ C @ B @ A ) @ A )
| ( in @ ( sK45_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK45_D @ C @ B @ A ) @ B )
| ( in @ ( sK45_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_difference @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_difference @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ~ ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[557]) ).
thf(623,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[385]) ).
thf(624,plain,
( ( ! [A: $i] : ( function @ ( identity_relation @ A ) )
& ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[556]) ).
thf(625,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[555]) ).
thf(626,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[554]) ).
thf(627,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK44_C @ B @ A ) @ A )
| ~ ( in @ ( sK44_C @ B @ A ) @ B ) )
& ( ( in @ ( sK44_C @ B @ A ) @ A )
| ( in @ ( sK44_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[553]) ).
thf(628,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[552]) ).
thf(629,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[551]) ).
thf(630,plain,
( ( ! [A: $i] :
( ! [SY479: $i] :
( ~ ( subset @ SY479 @ ( sK42_B @ A ) )
| ( are_equipotent @ SY479 @ ( sK42_B @ A ) )
| ( in @ SY479 @ ( sK42_B @ A ) ) )
& ! [SY480: $i] :
( ( ! [SY485: $i] :
( ~ ( subset @ SY485 @ SY480 )
| ( in @ SY485 @ ( sK43_SY481 @ SY480 @ A ) ) )
& ( in @ ( sK43_SY481 @ SY480 @ A ) @ ( sK42_B @ A ) ) )
| ~ ( in @ SY480 @ ( sK42_B @ A ) ) )
& ! [SY483: $i,SY484: $i] :
( ~ ( in @ SY483 @ ( sK42_B @ A ) )
| ~ ( subset @ SY484 @ SY483 )
| ( in @ SY484 @ ( sK42_B @ A ) ) )
& ( in @ A @ ( sK42_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[550]) ).
thf(631,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[549]) ).
thf(632,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[548]) ).
thf(633,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[547]) ).
thf(634,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[546]) ).
thf(635,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( A = D )
| ( A = C )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ C @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[545]) ).
thf(636,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)],[544]) ).
thf(637,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[543]) ).
thf(638,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[542]) ).
thf(639,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[541]) ).
thf(640,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) )
& ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[540]) ).
thf(641,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)],[539]) ).
thf(642,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ D )
| ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[538]) ).
thf(643,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[537]) ).
thf(644,plain,
( ( ! [A: $i] :
( ! [SY475: $i] :
( ~ ( subset @ SY475 @ ( sK41_B @ A ) )
| ( are_equipotent @ SY475 @ ( sK41_B @ A ) )
| ( in @ SY475 @ ( sK41_B @ A ) ) )
& ! [SY476: $i] :
( ~ ( in @ SY476 @ ( sK41_B @ A ) )
| ( in @ ( powerset @ SY476 ) @ ( sK41_B @ A ) ) )
& ! [SY477: $i,SY478: $i] :
( ~ ( in @ SY477 @ ( sK41_B @ A ) )
| ~ ( subset @ SY478 @ SY477 )
| ( in @ SY478 @ ( sK41_B @ A ) ) )
& ( in @ A @ ( sK41_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[536]) ).
thf(645,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 @ ( sK40_D @ C @ B @ A ) @ ( relation_dom @ C ) )
& ( in @ ( ordered_pair @ ( sK40_D @ C @ B @ A ) @ A ) @ C )
& ( in @ ( sK40_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[535]) ).
thf(646,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[534]) ).
thf(647,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)],[533]) ).
thf(648,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[532]) ).
thf(649,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 @ ( sK39_D @ C @ B @ A ) @ ( relation_rng @ C ) )
& ( in @ ( ordered_pair @ A @ ( sK39_D @ C @ B @ A ) ) @ C )
& ( in @ ( sK39_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[531]) ).
thf(650,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[530]) ).
thf(651,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)],[529]) ).
thf(652,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)],[528]) ).
thf(653,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[355]) ).
thf(654,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[527]) ).
thf(655,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[526]) ).
thf(656,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[352]) ).
thf(657,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)],[525]) ).
thf(658,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)],[524]) ).
thf(659,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[523]) ).
thf(660,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)],[522]) ).
thf(661,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)],[521]) ).
thf(662,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)],[520]) ).
thf(663,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[519]) ).
thf(664,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[518]) ).
thf(665,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[343]) ).
thf(666,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)],[517]) ).
thf(667,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[516]) ).
thf(668,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ! [D: $i] :
( ( ordered_pair @ A @ B )
!= ( ordered_pair @ C @ D ) )
| ( A = C ) )
& ! [C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
!= ( ordered_pair @ C @ D ) )
| ( B = D ) ) ) )
= $true ),
inference(copy,[status(thm)],[515]) ).
thf(669,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ( in @ ( sK38_C @ B @ A ) @ A )
& ( ( apply @ B @ ( sK38_C @ B @ A ) )
!= ( sK38_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)],[514]) ).
thf(670,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[338]) ).
thf(671,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)],[513]) ).
thf(672,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[512]) ).
thf(673,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[335]) ).
thf(674,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[511]) ).
thf(675,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[510]) ).
thf(676,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[332]) ).
thf(677,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( disjoint @ B @ C )
| ( subset @ B @ ( subset_complement @ A @ C ) ) )
& ! [C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( subset @ B @ ( subset_complement @ A @ C ) )
| ( disjoint @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[509]) ).
thf(678,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[508]) ).
thf(679,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[507]) ).
thf(680,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[506]) ).
thf(681,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)],[505]) ).
thf(682,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( B = empty_set )
| ( ( complements_of_subsets @ A @ B )
!= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[504]) ).
thf(683,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)],[503]) ).
thf(684,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[324]) ).
thf(685,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( element @ C @ A )
| ( in @ C @ B )
| ( in @ C @ ( subset_complement @ A @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[502]) ).
thf(686,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( in @ B @ ( subset_complement @ A @ C ) )
| ~ ( in @ B @ C ) ) )
= $true ),
inference(copy,[status(thm)],[501]) ).
thf(687,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK36_B @ A ) @ ( sK37_SY474 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[500]) ).
thf(688,plain,
( ( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[320]) ).
thf(689,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[499]) ).
thf(690,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[498]) ).
thf(691,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)],[497]) ).
thf(692,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)],[496]) ).
thf(693,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[315]) ).
thf(694,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[495]) ).
thf(695,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)],[494]) ).
thf(696,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[312]) ).
thf(697,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= A )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[493]) ).
thf(698,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)],[492]) ).
thf(699,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[491]) ).
thf(700,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)],[490]) ).
thf(701,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[489]) ).
thf(702,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[488]) ).
thf(703,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)],[487]) ).
thf(704,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[486]) ).
thf(705,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[303]) ).
thf(706,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[485]) ).
thf(707,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[484]) ).
thf(708,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[483]) ).
thf(709,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[299]) ).
thf(710,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[298]) ).
thf(711,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[297]) ).
thf(712,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[482]) ).
thf(713,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK34_D @ C @ B @ A ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ C @ B @ A ) @ ( sK35_SY473 @ C @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ C @ B @ A ) @ ( sK35_SY473 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK34_D @ C @ B @ A ) @ B )
| ( in @ ( ordered_pair @ ( sK34_D @ C @ B @ A ) @ ( sK35_SY473 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK34_D @ C @ B @ A ) @ ( sK35_SY473 @ C @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK34_D @ C @ B @ A ) @ ( sK35_SY473 @ 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)],[481]) ).
thf(714,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK33_SY472 @ C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ C @ B @ A ) @ ( sK33_SY472 @ C @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ C @ B @ A ) @ ( sK33_SY472 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK33_SY472 @ C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK32_D @ C @ B @ A ) @ ( sK33_SY472 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK32_D @ C @ B @ A ) @ ( sK33_SY472 @ C @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK32_D @ C @ B @ A ) @ ( sK33_SY472 @ 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)],[480]) ).
thf(715,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY470: $i] :
( ~ ( in @ ( ordered_pair @ SY470 @ ( sK30_D @ C @ B @ A ) ) @ A )
| ~ ( in @ SY470 @ B ) )
| ~ ( in @ ( sK30_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK31_SY471 @ C @ B @ A ) @ ( sK30_D @ C @ B @ A ) ) @ A )
& ( in @ ( sK31_SY471 @ C @ B @ A ) @ B ) )
| ( in @ ( sK30_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 @ ( sK29_E @ D @ C @ B @ A ) @ D ) @ A )
& ( in @ ( sK29_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[479]) ).
thf(716,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY468: $i] :
( ~ ( in @ ( ordered_pair @ ( sK27_D @ C @ B @ A ) @ SY468 ) @ A )
| ~ ( in @ SY468 @ B ) )
| ~ ( in @ ( sK27_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK27_D @ C @ B @ A ) @ ( sK28_SY469 @ C @ B @ A ) ) @ A )
& ( in @ ( sK28_SY469 @ C @ B @ A ) @ B ) )
| ( in @ ( sK27_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 @ ( sK26_E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( sK26_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[478]) ).
thf(717,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( in @ ( ordered_pair @ ( sK24_C @ B @ A ) @ ( sK25_SY467 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK24_C @ B @ A ) @ ( sK25_SY467 @ 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)],[477]) ).
thf(718,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)],[476]) ).
thf(719,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY465: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ B @ A ) @ SY465 ) @ A )
| ~ ( in @ ( sK22_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK22_C @ B @ A ) @ ( sK23_SY466 @ B @ A ) ) @ A )
| ( in @ ( sK22_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 @ ( sK21_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[475]) ).
thf(720,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY463: $i] :
~ ( in @ ( ordered_pair @ SY463 @ ( sK19_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK19_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK20_SY464 @ B @ A ) @ ( sK19_C @ B @ A ) ) @ A )
| ( in @ ( sK19_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 @ ( sK18_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[474]) ).
thf(721,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[473]) ).
thf(722,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[286]) ).
thf(723,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[472]) ).
thf(724,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK16_C @ B @ A ) @ ( sK17_SY462 @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK17_SY462 @ B @ A ) @ ( sK16_C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( sK16_C @ B @ A ) @ ( sK17_SY462 @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK17_SY462 @ B @ A ) @ ( sK16_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)],[471]) ).
thf(725,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_intersection2 @ A @ B )
!= empty_set )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[470]) ).
thf(726,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ! [SY460: $i] :
( ~ ( in @ ( ordered_pair @ ( sK13_D @ C @ B @ A ) @ SY460 ) @ A )
| ~ ( in @ ( ordered_pair @ SY460 @ ( sK14_SY457 @ C @ B @ A ) ) @ B ) )
| ~ ( in @ ( ordered_pair @ ( sK13_D @ C @ B @ A ) @ ( sK14_SY457 @ C @ B @ A ) ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK13_D @ C @ B @ A ) @ ( sK15_SY461 @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK15_SY461 @ C @ B @ A ) @ ( sK14_SY457 @ C @ B @ A ) ) @ B ) )
| ( in @ ( ordered_pair @ ( sK13_D @ C @ B @ A ) @ ( sK14_SY457 @ 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 @ ( sK12_F @ E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK12_F @ E @ D @ C @ B @ A ) @ E ) @ B ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[469]) ).
thf(727,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ( proper_subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( A != B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[468]) ).
thf(728,plain,
( ( ! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[280]) ).
thf(729,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[467]) ).
thf(730,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[466]) ).
thf(731,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[465]) ).
thf(732,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[464]) ).
thf(733,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[463]) ).
thf(734,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ~ ( element @ C @ ( powerset @ A ) )
| ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[462]) ).
thf(735,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[461]) ).
thf(736,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[460]) ).
thf(737,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[459]) ).
thf(738,plain,
( ( ! [A: $i] : ( element @ ( sK11_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[458]) ).
thf(739,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)],[457]) ).
thf(740,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[268]) ).
thf(741,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)],[456]) ).
thf(742,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[455]) ).
thf(743,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[265]) ).
thf(744,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[264]) ).
thf(745,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[263]) ).
thf(746,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[454]) ).
thf(747,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[261]) ).
thf(748,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[453]) ).
thf(749,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[259]) ).
thf(750,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[452]) ).
thf(751,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[257]) ).
thf(752,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[451]) ).
thf(753,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[450]) ).
thf(754,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[449]) ).
thf(755,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[448]) ).
thf(756,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[447]) ).
thf(757,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)],[446]) ).
thf(758,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[445]) ).
thf(759,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[444]) ).
thf(760,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[443]) ).
thf(761,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[442]) ).
thf(762,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[441]) ).
thf(763,plain,
( ( ( function @ sK10_A )
& ( relation @ sK10_A ) )
= $true ),
inference(copy,[status(thm)],[440]) ).
thf(764,plain,
( ( ( empty @ sK9_A )
& ( relation @ sK9_A ) )
= $true ),
inference(copy,[status(thm)],[439]) ).
thf(765,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK8_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK8_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[438]) ).
thf(766,plain,
( ( empty @ sK7_A )
= $true ),
inference(copy,[status(thm)],[437]) ).
thf(767,plain,
( ( ~ ( empty @ sK6_A )
& ( relation @ sK6_A ) )
= $true ),
inference(copy,[status(thm)],[436]) ).
thf(768,plain,
( ( ! [A: $i] :
( ( element @ ( sK5_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK5_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(769,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[434]) ).
thf(770,plain,
( ( ( relation @ sK3_A )
& ( relation_empty_yielding @ sK3_A ) )
= $true ),
inference(copy,[status(thm)],[433]) ).
thf(771,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ( union_of_subsets @ A @ B )
= ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[432]) ).
thf(772,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ( meet_of_subsets @ A @ B )
= ( set_meet @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[431]) ).
thf(773,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ~ ( element @ C @ ( powerset @ A ) )
| ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[430]) ).
thf(774,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[429]) ).
thf(775,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[428]) ).
thf(776,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[232]) ).
thf(777,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[231]) ).
thf(778,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(779,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[427]) ).
thf(780,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(781,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(782,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[425]) ).
thf(783,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[424]) ).
thf(784,plain,
( ( in @ sK2_SY456 @ sK1_A )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(785,plain,
( ( ( ( apply @ ( identity_relation @ sK1_A ) @ sK2_SY456 )
!= sK2_SY456 ) )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(786,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK49_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK49_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK49_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK49_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ( in @ ( sK49_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK49_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[620]) ).
thf(787,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK47_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK47_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK47_C @ SX1 @ SX0 ) @ ( sK48_SY487 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK48_SY487 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK47_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK46_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK46_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[621]) ).
thf(788,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ ( sK33_SY472 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ SX2 @ SX1 @ SX0 ) @ ( sK33_SY472 @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ SX2 @ SX1 @ SX0 ) @ ( sK33_SY472 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK33_SY472 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK32_D @ SX2 @ SX1 @ SX0 ) @ ( sK33_SY472 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_D @ SX2 @ SX1 @ SX0 ) @ ( sK33_SY472 @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK32_D @ SX2 @ SX1 @ SX0 ) @ ( sK33_SY472 @ 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)],[714]) ).
thf(789,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)],[739]) ).
thf(790,plain,
( ( ~ ( ~ ( relation @ sK3_A )
| ~ ( relation_empty_yielding @ sK3_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[770]) ).
thf(791,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ( in @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[598]) ).
thf(792,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK72_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK72_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[601]) ).
thf(793,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK62_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK62_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK62_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK62_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[611]) ).
thf(794,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( in @ ( sK61_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[612]) ).
thf(795,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX1 @ ( sK42_B @ SX0 ) )
| ( are_equipotent @ SX1 @ ( sK42_B @ SX0 ) )
| ( in @ SX1 @ ( sK42_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK43_SY481 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK43_SY481 @ SX1 @ SX0 ) @ ( sK42_B @ SX0 ) ) )
| ~ ( in @ SX1 @ ( sK42_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK42_B @ SX0 ) )
| ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK42_B @ SX0 ) ) )
| ~ ( in @ SX0 @ ( sK42_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[630]) ).
thf(796,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[674]) ).
thf(797,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)],[718]) ).
thf(798,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i,SX4: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX4 @ SX1 )
| ( ( sK53_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ SX3 @ SX4 ) ) )
| ~ ( in @ ( sK53_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK54_SY491 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK55_SY493 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( sK53_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ ( sK54_SY491 @ SX2 @ SX1 @ SX0 ) @ ( sK55_SY493 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( in @ ( sK53_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ( SX2
= ( cartesian_product2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( cartesian_product2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i,SX5: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ~ ( ~ ( in @ ( sK51_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK52_SY488 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( SX3
!= ( ordered_pair @ ( sK51_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK52_SY488 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[618]) ).
thf(799,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[632]) ).
thf(800,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)],[692]) ).
thf(801,plain,
( ( ~ ( ~ ( function @ sK10_A )
| ~ ( relation @ sK10_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[763]) ).
thf(802,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)],[700]) ).
thf(803,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[751]) ).
thf(804,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK69_C @ SX1 @ SX0 )
!= ( sK70_SY500 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK69_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK69_C @ SX1 @ SX0 ) @ ( sK70_SY500 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK69_C @ SX1 @ SX0 )
= ( sK70_SY500 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK69_C @ SX1 @ SX0 ) @ ( sK70_SY500 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK69_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK69_C @ SX1 @ SX0 ) @ ( sK70_SY500 @ 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)],[608]) ).
thf(805,plain,
( ( ! [SX0: $i] :
~ ( ~ ( element @ ( sK5_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ( empty @ ( sK5_B @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[768]) ).
thf(806,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ ( sK13_D @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ ( sK14_SY457 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_D @ SX2 @ SX1 @ SX0 ) @ ( sK14_SY457 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_D @ SX2 @ SX1 @ SX0 ) @ ( sK15_SY461 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY461 @ SX2 @ SX1 @ SX0 ) @ ( sK14_SY457 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( in @ ( ordered_pair @ ( sK13_D @ SX2 @ SX1 @ SX0 ) @ ( sK14_SY457 @ 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 @ ( sK12_F @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK12_F @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX4 ) @ SX1 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[726]) ).
thf(807,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ SX0 ) )
| ~ ( disjoint @ SX1 @ SX2 )
| ( subset @ SX1 @ ( subset_complement @ SX0 @ SX2 ) ) )
| ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ SX0 ) )
| ~ ( subset @ SX1 @ ( subset_complement @ SX0 @ SX2 ) )
| ( disjoint @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[677]) ).
thf(808,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)],[636]) ).
thf(809,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ ( sK34_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ SX2 @ SX1 @ SX0 ) @ ( sK35_SY473 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ SX2 @ SX1 @ SX0 ) @ ( sK35_SY473 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK34_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK34_D @ SX2 @ SX1 @ SX0 ) @ ( sK35_SY473 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK34_D @ SX2 @ SX1 @ SX0 ) @ ( sK35_SY473 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK34_D @ SX2 @ SX1 @ SX0 ) @ ( sK35_SY473 @ 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)],[713]) ).
thf(810,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_C @ SX1 @ SX0 ) @ ( sK17_SY462 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK17_SY462 @ SX1 @ SX0 ) @ ( sK16_C @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK16_C @ SX1 @ SX0 ) @ ( sK17_SY462 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK17_SY462 @ SX1 @ SX0 ) @ ( sK16_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)],[724]) ).
thf(811,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[779]) ).
thf(812,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[599]) ).
thf(813,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[725]) ).
thf(814,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK38_C @ SX1 @ SX0 ) )
!= ( sK38_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)],[669]) ).
thf(815,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[672]) ).
thf(816,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[712]) ).
thf(817,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ ( sK30_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ~ ( in @ ( sK30_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_SY471 @ SX2 @ SX1 @ SX0 ) @ ( sK30_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK31_SY471 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( in @ ( sK30_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 @ ( sK29_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ ( sK29_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[715]) ).
thf(818,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)],[666]) ).
thf(819,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)],[695]) ).
thf(820,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[593]) ).
thf(821,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX2 )
| ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[600]) ).
thf(822,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[615]) ).
thf(823,plain,
( ( ~ ( ~ ( empty @ sK9_A )
| ~ ( relation @ sK9_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[764]) ).
thf(824,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ SX2 @ ( sK19_C @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK19_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_SY464 @ SX1 @ SX0 ) @ ( sK19_C @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK19_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 @ ( sK18_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[720]) ).
thf(825,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[740]) ).
thf(826,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[604]) ).
thf(827,plain,
( ( ~ ( ~ ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) )
| ~ ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[624]) ).
thf(828,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK71_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[603]) ).
thf(829,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK73_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK73_C @ SX1 @ SX0 ) @ SX1 ) )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[597]) ).
thf(830,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ ( sK27_D @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ~ ( in @ ( sK27_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK27_D @ SX2 @ SX1 @ SX0 ) @ ( sK28_SY469 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK28_SY469 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( in @ ( sK27_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 @ ( sK26_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK26_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[716]) ).
thf(831,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[697]) ).
thf(832,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK68_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK68_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK66_C @ SX1 @ SX0 ) @ ( sK67_SY497 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[609]) ).
thf(833,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)],[698]) ).
thf(834,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)],[657]) ).
thf(835,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SX1 @ SX0 ) @ SX2 ) @ SX0 )
| ~ ( in @ ( sK22_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SX1 @ SX0 ) @ ( sK23_SY466 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK22_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 @ ( sK21_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[719]) ).
thf(836,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK57_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK57_D @ SX2 @ SX1 @ SX0 )
!= SX0 ) )
| ~ ( ~ ( in @ ( sK57_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK57_D @ SX2 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ( ( in @ ( sK57_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK57_D @ SX2 @ SX1 @ SX0 )
= SX0 )
| ( ( sK57_D @ SX2 @ SX1 @ SX0 )
= SX1 ) ) )
| ( SX2
= ( unordered_pair @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( unordered_pair @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ( SX3 != SX0 )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[616]) ).
thf(837,plain,
( ( ~ ( ( ( relation_dom @ empty_set )
!= empty_set )
| ( ( relation_rng @ empty_set )
!= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[688]) ).
thf(838,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK58_C @ SX1 @ SX0 ) @ ( sK59_SY494 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK58_C @ SX1 @ SX0 ) @ ( sK59_SY494 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_C @ SX1 @ SX0 ) @ ( sK59_SY494 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK58_C @ SX1 @ SX0 ) @ ( sK59_SY494 @ 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)],[614]) ).
thf(839,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)],[741]) ).
thf(840,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)],[658]) ).
thf(841,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX1 @ ( sK41_B @ SX0 ) )
| ( are_equipotent @ SX1 @ ( sK41_B @ SX0 ) )
| ( in @ SX1 @ ( sK41_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK41_B @ SX0 ) )
| ( in @ ( powerset @ SX1 ) @ ( sK41_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK41_B @ SX0 ) )
| ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK41_B @ SX0 ) ) )
| ~ ( in @ SX0 @ ( sK41_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[644]) ).
thf(842,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SX1 @ SX0 ) @ ( sK25_SY467 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SX1 @ SX0 ) @ ( sK25_SY467 @ 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)],[717]) ).
thf(843,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK60_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK60_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK60_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK60_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[613]) ).
thf(844,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)],[757]) ).
thf(845,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)],[662]) ).
thf(846,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ( element @ ( sK8_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK8_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[765]) ).
thf(847,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 @ ( sK39_D @ SX2 @ SX1 @ SX0 ) @ ( relation_rng @ SX2 ) )
| ~ ( in @ ( ordered_pair @ SX0 @ ( sK39_D @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( in @ ( sK39_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[649]) ).
thf(848,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK65_SY495 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK64_C @ SX1 @ SX0 ) @ ( sK65_SY495 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK64_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK64_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK64_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK63_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK63_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[610]) ).
thf(849,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)],[671]) ).
thf(850,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( relation_dom @ ( identity_relation @ SX0 ) )
= SX0 )
| ~ ! [SX0: $i] :
( ( relation_rng @ ( identity_relation @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[605]) ).
thf(851,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[727]) ).
thf(852,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ( in @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[596]) ).
thf(853,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK56_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK56_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ~ ( in @ ( sK56_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK56_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ( ( in @ ( sK56_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( in @ ( sK56_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK56_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX2
= ( set_union2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_union2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[617]) ).
thf(854,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[755]) ).
thf(855,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 @ ( sK40_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX2 ) )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) @ SX2 ) )
| ~ ( in @ ( sK40_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[645]) ).
thf(856,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] : ( subset @ ( cartesian_product2 @ SX0 @ SX2 ) @ ( cartesian_product2 @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] : ( subset @ ( cartesian_product2 @ SX2 @ SX0 ) @ ( cartesian_product2 @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[640]) ).
thf(857,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK44_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[627]) ).
thf(858,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[634]) ).
thf(859,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ( ordered_pair @ SX0 @ SX1 )
!= ( ordered_pair @ SX2 @ SX3 ) )
| ( SX0 = SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( ( ordered_pair @ SX0 @ SX1 )
!= ( ordered_pair @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[668]) ).
thf(860,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK50_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK50_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[619]) ).
thf(861,plain,
( ( ~ ( ~ ~ ( empty @ sK6_A )
| ~ ( relation @ sK6_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[767]) ).
thf(862,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)],[691]) ).
thf(863,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[756]) ).
thf(864,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK45_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK45_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK45_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK45_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK45_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( in @ ( sK45_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK45_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( set_difference @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_difference @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( in @ SX3 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[622]) ).
thf(865,plain,
! [SV1: $i] :
( ( ! [SY501: $i] :
( ~ ( in @ SV1 @ SY501 )
| ( ( set_union2 @ ( singleton @ SV1 ) @ SY501 )
= SY501 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(866,plain,
! [SV2: $i] :
( ( ! [SY502: $i] :
( ~ ( disjoint @ ( singleton @ SV2 ) @ SY502 )
| ~ ( in @ SV2 @ SY502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(867,plain,
! [SV3: $i] :
( ( ! [SY503: $i] :
( ( in @ SV3 @ SY503 )
| ( disjoint @ ( singleton @ SV3 ) @ SY503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(868,plain,
! [SV4: $i] :
( ( ! [SY504: $i] :
( ~ ( element @ SY504 @ ( powerset @ SV4 ) )
| ! [SY505: $i] :
( ~ ( in @ SY505 @ SY504 )
| ( in @ SY505 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(869,plain,
! [SV5: $i] :
( ( ! [SY506: $i] :
( ~ ( in @ SV5 @ SY506 )
| ( subset @ SV5 @ ( union @ SY506 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(870,plain,
! [SV6: $i] :
( ( ! [SY507: $i] :
( ~ ( in @ SV6 @ SY507 )
| ( ( set_union2 @ ( singleton @ SV6 ) @ SY507 )
= SY507 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(871,plain,
! [SV7: $i] :
( ( ! [SY508: $i] :
( ~ ( in @ SV7 @ SY508 )
| ( subset @ SV7 @ ( union @ SY508 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(872,plain,
! [SV8: $i] :
( ( ! [SY509: $i] :
( ~ ( in @ SV8 @ SY509 )
| ~ ( in @ SY509 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(873,plain,
! [SV9: $i] :
( ( relation @ ( identity_relation @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(874,plain,
! [SV10: $i] :
( ( ! [SY510: $i] :
( ~ ( in @ SV10 @ SY510 )
| ( element @ SV10 @ SY510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(875,plain,
! [SV11: $i] :
( ( ! [SY511: $i] :
( ~ ( element @ SV11 @ SY511 )
| ( empty @ SY511 )
| ( in @ SV11 @ SY511 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(876,plain,
! [SV12: $i] :
( ( ! [SY512: $i,SY513: $i] :
( ~ ( element @ SY512 @ ( powerset @ SY513 ) )
| ~ ( in @ SV12 @ SY512 )
| ( element @ SV12 @ SY513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(877,plain,
! [SV13: $i] :
( ( ! [SY514: $i] :
( ~ ( empty @ SY514 )
| ~ ( in @ SV13 @ SY514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(878,plain,
! [SV14: $i] :
( ( ( ( singleton @ SV14 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(879,plain,
! [SV15: $i] :
( ( ! [SY515: $i] :
( ~ ( subset @ SV15 @ SY515 )
| ! [SY516: $i] :
( ( in @ SY516 @ SV15 )
| ( subset @ SV15 @ ( set_difference @ SY515 @ ( singleton @ SY516 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(880,plain,
! [SV16: $i] :
( ( ! [SY517: $i,SY518: $i,SY519: $i] :
( ( SV16 = SY519 )
| ( SV16 = SY518 )
| ( ( unordered_pair @ SV16 @ SY517 )
!= ( unordered_pair @ SY518 @ SY519 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(881,plain,
! [SV17: $i] :
( ( ! [SY520: $i] :
( ~ ( relation @ SY520 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV17 @ SY520 ) ) @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(882,plain,
! [SV18: $i] :
( ( ! [SY521: $i] :
( ~ ( relation @ SY521 )
| ( subset @ ( relation_rng_restriction @ SV18 @ SY521 ) @ SY521 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(883,plain,
! [SV19: $i] :
( ( ! [SY522: $i] :
( ~ ( relation @ SY522 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV19 @ SY522 ) ) @ ( relation_rng @ SY522 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(884,plain,
! [SV20: $i] :
( ( ! [SY523: $i] :
( ~ ( relation @ SY523 )
| ( ( relation_rng @ ( relation_rng_restriction @ SV20 @ SY523 ) )
= ( set_intersection2 @ ( relation_rng @ SY523 ) @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(885,plain,
! [SV21: $i] :
( ( ! [SY524: $i,SY525: $i,SY526: $i] :
( ~ ( subset @ SV21 @ SY524 )
| ~ ( subset @ SY525 @ SY526 )
| ( subset @ ( cartesian_product2 @ SV21 @ SY525 ) @ ( cartesian_product2 @ SY524 @ SY526 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(886,plain,
! [SV22: $i] :
( ( ! [SY527: $i] :
( ~ ( subset @ SV22 @ SY527 )
| ( ( set_union2 @ SV22 @ SY527 )
= SY527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(887,plain,
! [SV23: $i] :
( ( ! [SY528: $i] :
( ~ ( relation @ SY528 )
| ( subset @ ( relation_image @ SY528 @ SV23 ) @ ( relation_rng @ SY528 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(888,plain,
! [SV24: $i] :
( ( ! [SY529: $i] :
( ~ ( relation @ SY529 )
| ( ( relation_image @ SY529 @ SV24 )
= ( relation_image @ SY529 @ ( set_intersection2 @ ( relation_dom @ SY529 ) @ SV24 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(889,plain,
! [SV25: $i] :
( ( ~ ( relation @ SV25 )
| ( ( relation_image @ SV25 @ ( relation_dom @ SV25 ) )
= ( relation_rng @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(890,plain,
! [SV26: $i] :
( ( ! [SY530: $i] :
( ~ ( relation @ SY530 )
| ( subset @ ( relation_inverse_image @ SY530 @ SV26 ) @ ( relation_dom @ SY530 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(891,plain,
! [SV27: $i] :
( ( ! [SY531: $i] :
( ~ ( relation @ SY531 )
| ( SV27 = empty_set )
| ~ ( subset @ SV27 @ ( relation_rng @ SY531 ) )
| ( ( relation_inverse_image @ SY531 @ SV27 )
!= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(892,plain,
! [SV28: $i] :
( ( ! [SY532: $i,SY533: $i] :
( ~ ( relation @ SY533 )
| ~ ( subset @ SV28 @ SY532 )
| ( subset @ ( relation_inverse_image @ SY533 @ SV28 ) @ ( relation_inverse_image @ SY533 @ SY532 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(893,plain,
! [SV29: $i] :
( ( ! [SY534: $i] : ( subset @ ( set_intersection2 @ SV29 @ SY534 ) @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(894,plain,
! [SV30: $i] :
( ( ! [SY535: $i,SY536: $i] :
( ~ ( subset @ SV30 @ SY535 )
| ~ ( subset @ SV30 @ SY536 )
| ( subset @ SV30 @ ( set_intersection2 @ SY535 @ SY536 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(895,plain,
! [SV31: $i] :
( ( ! [SY537: $i,SY538: $i] :
( ~ ( subset @ SV31 @ SY537 )
| ~ ( subset @ SY537 @ SY538 )
| ( subset @ SV31 @ SY538 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(896,plain,
! [SV32: $i] :
( ( ~ ( relation @ SV32 )
| ( subset @ SV32 @ ( cartesian_product2 @ ( relation_dom @ SV32 ) @ ( relation_rng @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(897,plain,
! [SV33: $i] :
( ( ! [SY539: $i] :
( ~ ( function @ SY539 )
| ~ ( relation @ SY539 )
| ! [SY540: $i] :
( ~ ( function @ SY540 )
| ~ ( relation @ SY540 )
| ~ ( in @ SV33 @ ( relation_dom @ ( relation_composition @ SY540 @ SY539 ) ) )
| ( ( apply @ ( relation_composition @ SY540 @ SY539 ) @ SV33 )
= ( apply @ SY539 @ ( apply @ SY540 @ SV33 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(898,plain,
! [SV34: $i] :
( ( ! [SY541: $i] :
( ~ ( function @ SY541 )
| ~ ( relation @ SY541 )
| ! [SY542: $i] :
( ~ ( function @ SY542 )
| ~ ( relation @ SY542 )
| ~ ( in @ SV34 @ ( relation_dom @ SY541 ) )
| ( ( apply @ ( relation_composition @ SY541 @ SY542 ) @ SV34 )
= ( apply @ SY542 @ ( apply @ SY541 @ SV34 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(899,plain,
! [SV35: $i] :
( ( ! [SY543: $i] :
( ~ ( subset @ SV35 @ SY543 )
| ! [SY544: $i] : ( subset @ ( set_intersection2 @ SV35 @ SY544 ) @ ( set_intersection2 @ SY543 @ SY544 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(900,plain,
! [SV36: $i] :
( ( ! [SY545: $i] :
( ~ ( subset @ SV36 @ SY545 )
| ( ( set_intersection2 @ SV36 @ SY545 )
= SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(901,plain,
! [SV37: $i] :
( ( subset @ empty_set @ SV37 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(902,plain,
! [SV38: $i] :
( ( ! [SY546: $i] :
( ~ ( subset @ SV38 @ SY546 )
| ! [SY547: $i] : ( subset @ ( set_difference @ SV38 @ SY547 ) @ ( set_difference @ SY546 @ SY547 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(903,plain,
! [SV39: $i] :
( ( ! [SY548: $i] : ( subset @ ( set_difference @ SV39 @ SY548 ) @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(904,plain,
! [SV40: $i] :
( ( ! [SY549: $i] :
( ( set_union2 @ SV40 @ ( set_difference @ SY549 @ SV40 ) )
= ( set_union2 @ SV40 @ SY549 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(905,plain,
! [SV41: $i] :
( ( ~ ( subset @ SV41 @ empty_set )
| ( SV41 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(906,plain,
! [SV42: $i] :
( ( ! [SY550: $i] :
( ( set_difference @ ( set_union2 @ SV42 @ SY550 ) @ SY550 )
= ( set_difference @ SV42 @ SY550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(907,plain,
! [SV43: $i] :
( ( ~ ( relation @ SV43 )
| ! [SY551: $i] :
( ~ ( relation @ SY551 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV43 @ SY551 ) ) @ ( relation_dom @ SV43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(908,plain,
! [SV44: $i] :
( ( ~ ( relation @ SV44 )
| ! [SY552: $i] :
( ~ ( relation @ SY552 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV44 @ SY552 ) ) @ ( relation_rng @ SY552 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(909,plain,
! [SV45: $i] :
( ( ! [SY553: $i] :
( ~ ( subset @ SV45 @ SY553 )
| ( SY553
= ( set_union2 @ SV45 @ ( set_difference @ SY553 @ SV45 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(910,plain,
! [SV46: $i] :
( ( ~ ( relation @ SV46 )
| ! [SY554: $i] :
( ~ ( relation @ SY554 )
| ~ ( subset @ ( relation_rng @ SV46 ) @ ( relation_dom @ SY554 ) )
| ( ( relation_dom @ ( relation_composition @ SV46 @ SY554 ) )
= ( relation_dom @ SV46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(911,plain,
! [SV47: $i] :
( ( ! [SY555: $i] :
( ~ ( element @ SY555 @ ( powerset @ ( powerset @ SV47 ) ) )
| ( SY555 = empty_set )
| ( ( complements_of_subsets @ SV47 @ SY555 )
!= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(912,plain,
! [SV48: $i] :
( ( ~ ( relation @ SV48 )
| ! [SY556: $i] :
( ~ ( relation @ SY556 )
| ~ ( subset @ ( relation_dom @ SV48 ) @ ( relation_rng @ SY556 ) )
| ( ( relation_rng @ ( relation_composition @ SY556 @ SV48 ) )
= ( relation_rng @ SV48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(913,plain,
! [SV49: $i] :
( ( ! [SY557: $i] :
( ( set_difference @ SV49 @ ( set_difference @ SV49 @ SY557 ) )
= ( set_intersection2 @ SV49 @ SY557 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(914,plain,
! [SV50: $i] :
( ( ( SV50 = empty_set )
| ! [SY558: $i] :
( ~ ( element @ SY558 @ ( powerset @ SV50 ) )
| ! [SY559: $i] :
( ~ ( element @ SY559 @ SV50 )
| ( in @ SY559 @ SY558 )
| ( in @ SY559 @ ( subset_complement @ SV50 @ SY558 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(915,plain,
! [SV51: $i] :
( ( ! [SY560: $i,SY561: $i] :
( ~ ( element @ SY561 @ ( powerset @ SV51 ) )
| ~ ( in @ SY560 @ ( subset_complement @ SV51 @ SY561 ) )
| ~ ( in @ SY560 @ SY561 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(916,plain,
! [SV52: $i] :
( ( ~ ( relation @ SV52 )
| ( in @ ( ordered_pair @ ( sK36_B @ SV52 ) @ ( sK37_SY474 @ SV52 ) ) @ SV52 )
| ( SV52 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(917,plain,
! [SV53: $i] :
( ( ! [SY562: $i] :
( ~ ( proper_subset @ SY562 @ SV53 )
| ~ ( subset @ SV53 @ SY562 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(918,plain,
! [SV54: $i] :
( ( ! [SY563: $i,SY564: $i] :
( ~ ( disjoint @ SY563 @ SY564 )
| ~ ( subset @ SV54 @ SY563 )
| ( disjoint @ SV54 @ SY564 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(919,plain,
! [SV55: $i] :
( ( ( unordered_pair @ SV55 @ SV55 )
= ( singleton @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(920,plain,
! [SV56: $i] :
( ( ! [SY565: $i] :
( ~ ( subset @ ( singleton @ SV56 ) @ ( singleton @ SY565 ) )
| ( SV56 = SY565 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(921,plain,
! [SV57: $i] :
( ( ! [SY566: $i] : ( subset @ SV57 @ ( set_union2 @ SV57 @ SY566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(922,plain,
! [SV58: $i] :
( ( ! [SY567: $i] :
( ~ ( relation @ SY567 )
| ( subset @ ( relation_dom_restriction @ SY567 @ SV58 ) @ SY567 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(923,plain,
! [SV59: $i] :
( ( ! [SY568: $i,SY569: $i] :
( ~ ( subset @ SV59 @ SY568 )
| ~ ( subset @ SY569 @ SY568 )
| ( subset @ ( set_union2 @ SV59 @ SY569 ) @ SY568 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(924,plain,
! [SV60: $i] :
( ( ! [SY570: $i] :
( ! [SY571: $i] :
( ( singleton @ SV60 )
!= ( unordered_pair @ SY570 @ SY571 ) )
| ( SV60 = SY570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(925,plain,
! [SV61: $i] :
( ( ! [SY572: $i] :
( ~ ( relation @ SY572 )
| ( ( relation_dom @ ( relation_dom_restriction @ SY572 @ SV61 ) )
= ( set_intersection2 @ ( relation_dom @ SY572 ) @ SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(926,plain,
! [SV62: $i] :
( ( ! [SY573: $i] :
( ~ ( relation @ SY573 )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ SY573 @ SV62 ) ) @ ( relation_rng @ SY573 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(927,plain,
! [SV63: $i] :
( ( ( union @ ( powerset @ SV63 ) )
= SV63 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(928,plain,
! [SV64: $i] :
( ( ! [SY574: $i,SY575: $i] :
( ( ( singleton @ SV64 )
!= ( unordered_pair @ SY574 @ SY575 ) )
| ( SY574 = SY575 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(929,plain,
! [SV65: $i] :
( ( ~ ( empty @ SV65 )
| ( function @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(930,plain,
! [SV66: $i] :
( ( ~ ( empty @ SV66 )
| ( relation @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(931,plain,
! [SV67: $i] :
( ( ! [SY576: $i] :
( ( unordered_pair @ SV67 @ SY576 )
= ( unordered_pair @ SY576 @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(932,plain,
! [SV68: $i] :
( ( ! [SY577: $i] :
( ( set_union2 @ SV68 @ SY577 )
= ( set_union2 @ SY577 @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(933,plain,
! [SV69: $i] :
( ( ! [SY578: $i] :
( ( set_intersection2 @ SV69 @ SY578 )
= ( set_intersection2 @ SY578 @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(934,plain,
! [SV70: $i] :
( ( ! [SY579: $i] :
( ~ ( element @ SY579 @ ( powerset @ SV70 ) )
| ( ( subset_complement @ SV70 @ SY579 )
= ( set_difference @ SV70 @ SY579 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(935,plain,
! [SV71: $i] :
( ( ! [SY580: $i] :
( ( ordered_pair @ SV71 @ SY580 )
= ( unordered_pair @ ( unordered_pair @ SV71 @ SY580 ) @ ( singleton @ SV71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(936,plain,
! [SV72: $i] :
( ( ~ ( relation @ SV72 )
| ( ( relation_field @ SV72 )
= ( set_union2 @ ( relation_dom @ SV72 ) @ ( relation_rng @ SV72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(937,plain,
! [SV73: $i] :
( ( element @ ( cast_to_subset @ SV73 ) @ ( powerset @ SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(938,plain,
! [SV74: $i] :
( ( ! [SY581: $i] :
( ~ ( element @ SY581 @ ( powerset @ SV74 ) )
| ( element @ ( subset_complement @ SV74 @ SY581 ) @ ( powerset @ SV74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(939,plain,
! [SV75: $i] :
( ( ~ ( relation @ SV75 )
| ( relation @ ( relation_inverse @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(940,plain,
! [SV76: $i] :
( ( ! [SY582: $i] :
( ~ ( relation @ SV76 )
| ~ ( relation @ SY582 )
| ( relation @ ( relation_composition @ SV76 @ SY582 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(941,plain,
! [SV77: $i] :
( ( ! [SY583: $i] :
( ~ ( element @ SY583 @ ( powerset @ ( powerset @ SV77 ) ) )
| ( element @ ( union_of_subsets @ SV77 @ SY583 ) @ ( powerset @ SV77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(942,plain,
! [SV78: $i] :
( ( ! [SY584: $i] :
( ~ ( element @ SY584 @ ( powerset @ ( powerset @ SV78 ) ) )
| ( element @ ( meet_of_subsets @ SV78 @ SY584 ) @ ( powerset @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(943,plain,
! [SV79: $i] :
( ( ! [SY585: $i,SY586: $i] :
( ~ ( element @ SY585 @ ( powerset @ SV79 ) )
| ~ ( element @ SY586 @ ( powerset @ SV79 ) )
| ( element @ ( subset_difference @ SV79 @ SY585 @ SY586 ) @ ( powerset @ SV79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(944,plain,
! [SV80: $i] :
( ( ~ ( relation @ SV80 )
| ! [SY587: $i] : ( relation @ ( relation_dom_restriction @ SV80 @ SY587 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(945,plain,
! [SV81: $i] :
( ( ! [SY588: $i] :
( ~ ( element @ SY588 @ ( powerset @ ( powerset @ SV81 ) ) )
| ( element @ ( complements_of_subsets @ SV81 @ SY588 ) @ ( powerset @ ( powerset @ SV81 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(946,plain,
! [SV82: $i] :
( ( ! [SY589: $i] :
( ~ ( relation @ SY589 )
| ( relation @ ( relation_rng_restriction @ SV82 @ SY589 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(947,plain,
! [SV83: $i] :
( ( element @ ( sK11_B @ SV83 ) @ SV83 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(948,plain,
! [SV84: $i] :
( ( ! [SY590: $i] :
( ~ ( relation @ SV84 )
| ~ ( relation @ SY590 )
| ( relation @ ( set_intersection2 @ SV84 @ SY590 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(949,plain,
! [SV85: $i] :
( ( ~ ( empty @ ( powerset @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(950,plain,
! [SV86: $i] :
( ( ! [SY591: $i] :
~ ( empty @ ( ordered_pair @ SV86 @ SY591 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(951,plain,
! [SV87: $i] :
( ( ! [SY592: $i] :
( ~ ( relation @ SV87 )
| ~ ( relation @ SY592 )
| ( relation @ ( set_union2 @ SV87 @ SY592 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(952,plain,
! [SV88: $i] :
( ( ~ ( empty @ ( singleton @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(953,plain,
! [SV89: $i] :
( ( ( empty @ SV89 )
| ! [SY593: $i] :
~ ( empty @ ( set_union2 @ SV89 @ SY593 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(954,plain,
! [SV90: $i] :
( ( ! [SY594: $i] :
~ ( empty @ ( unordered_pair @ SV90 @ SY594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(955,plain,
! [SV91: $i] :
( ( ( empty @ SV91 )
| ! [SY595: $i] :
~ ( empty @ ( set_union2 @ SY595 @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(956,plain,
! [SV92: $i] :
( ( ! [SY596: $i] :
( ( empty @ SV92 )
| ( empty @ SY596 )
| ~ ( empty @ ( cartesian_product2 @ SV92 @ SY596 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(957,plain,
! [SV93: $i] :
( ( ( empty @ SV93 )
| ~ ( relation @ SV93 )
| ~ ( empty @ ( relation_dom @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(958,plain,
! [SV94: $i] :
( ( ( empty @ SV94 )
| ~ ( relation @ SV94 )
| ~ ( empty @ ( relation_rng @ SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(959,plain,
! [SV95: $i] :
( ( ( set_union2 @ SV95 @ SV95 )
= SV95 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(960,plain,
! [SV96: $i] :
( ( ( set_intersection2 @ SV96 @ SV96 )
= SV96 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(961,plain,
! [SV97: $i] :
( ( ! [SY597: $i] :
( ~ ( element @ SY597 @ ( powerset @ SV97 ) )
| ( ( subset_complement @ SV97 @ ( subset_complement @ SV97 @ SY597 ) )
= SY597 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(962,plain,
! [SV98: $i] :
( ( ~ ( relation @ SV98 )
| ( ( relation_inverse @ ( relation_inverse @ SV98 ) )
= SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(963,plain,
! [SV99: $i] :
( ( ! [SY598: $i] :
( ~ ( element @ SY598 @ ( powerset @ ( powerset @ SV99 ) ) )
| ( ( complements_of_subsets @ SV99 @ ( complements_of_subsets @ SV99 @ SY598 ) )
= SY598 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(964,plain,
( ( empty @ sK4_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[769]) ).
thf(965,plain,
! [SV100: $i] :
( ( ! [SY599: $i] :
( ~ ( element @ SY599 @ ( powerset @ ( powerset @ SV100 ) ) )
| ( ( union_of_subsets @ SV100 @ SY599 )
= ( union @ SY599 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(966,plain,
! [SV101: $i] :
( ( ! [SY600: $i] :
( ~ ( element @ SY600 @ ( powerset @ ( powerset @ SV101 ) ) )
| ( ( meet_of_subsets @ SV101 @ SY600 )
= ( set_meet @ SY600 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(967,plain,
! [SV102: $i] :
( ( ! [SY601: $i,SY602: $i] :
( ~ ( element @ SY601 @ ( powerset @ SV102 ) )
| ~ ( element @ SY602 @ ( powerset @ SV102 ) )
| ( ( subset_difference @ SV102 @ SY601 @ SY602 )
= ( set_difference @ SY601 @ SY602 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(968,plain,
! [SV103: $i] :
( ( subset @ SV103 @ SV103 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(969,plain,
! [SV104: $i] :
( ( ! [SY603: $i] :
( ~ ( disjoint @ SV104 @ SY603 )
| ( disjoint @ SY603 @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(970,plain,
! [SV105: $i] :
( ( ( set_union2 @ SV105 @ empty_set )
= SV105 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(971,plain,
! [SV106: $i] :
( ( ( set_intersection2 @ SV106 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(972,plain,
! [SV107: $i] :
( ( ( set_difference @ SV107 @ empty_set )
= SV107 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(973,plain,
! [SV108: $i] :
( ( ( set_difference @ empty_set @ SV108 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(974,plain,
! [SV109: $i] :
( ( ! [SY604: $i,SY605: $i] :
( ~ ( element @ SY604 @ ( powerset @ SY605 ) )
| ~ ( in @ SV109 @ SY604 )
| ~ ( empty @ SY605 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(975,plain,
! [SV110: $i] :
( ( ~ ( empty @ SV110 )
| ( SV110 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(976,plain,
! [SV111: $i] :
( ( ! [SY606: $i] :
( ( SV111 = SY606 )
| ~ ( empty @ SV111 )
| ~ ( empty @ SY606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(977,plain,
( ( ( apply @ ( identity_relation @ sK1_A ) @ sK2_SY456 )
= sK2_SY456 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[785]) ).
thf(978,plain,
! [SV112: $i] :
( ( ~ ( ~ ! [SY607: $i,SY608: $i] :
( ~ ( ~ ( ~ ( in @ ( sK49_D @ SY608 @ SY607 @ SV112 ) @ SV112 )
| ~ ( in @ ( sK49_D @ SY608 @ SY607 @ SV112 ) @ SY607 )
| ~ ( in @ ( sK49_D @ SY608 @ SY607 @ SV112 ) @ SY608 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_D @ SY608 @ SY607 @ SV112 ) @ SV112 )
| ( in @ ( sK49_D @ SY608 @ SY607 @ SV112 ) @ SY608 ) )
| ~ ( ( in @ ( sK49_D @ SY608 @ SY607 @ SV112 ) @ SY607 )
| ( in @ ( sK49_D @ SY608 @ SY607 @ SV112 ) @ SY608 ) ) ) )
| ( SY608
= ( set_intersection2 @ SV112 @ SY607 ) ) )
| ~ ! [SY609: $i,SY610: $i] :
( ( SY610
!= ( set_intersection2 @ SV112 @ SY609 ) )
| ~ ( ~ ! [SY611: $i] :
( ~ ( in @ SY611 @ SV112 )
| ~ ( in @ SY611 @ SY609 )
| ( in @ SY611 @ SY610 ) )
| ~ ~ ( ~ ! [SY612: $i] :
( ~ ( in @ SY612 @ SY610 )
| ( in @ SY612 @ SV112 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY610 )
| ( in @ SX3 @ SY609 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(979,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK47_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK47_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK47_C @ SX1 @ SX0 ) @ ( sK48_SY487 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK48_SY487 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK47_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK46_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK46_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[787]) ).
thf(980,plain,
! [SV113: $i] :
( ( ! [SY614: $i] :
( ~ ( relation @ SY614 )
| ~ ( ~ ! [SY615: $i] :
( ~ ( relation @ SY615 )
| ~ ( ~ ( ~ ( in @ ( sK33_SY472 @ SY615 @ SY614 @ SV113 ) @ SV113 )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ SY615 @ SY614 @ SV113 ) @ ( sK33_SY472 @ SY615 @ SY614 @ SV113 ) ) @ SY614 )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ SY615 @ SY614 @ SV113 ) @ ( sK33_SY472 @ SY615 @ SY614 @ SV113 ) ) @ SY615 ) )
| ~ ~ ( ~ ( ( in @ ( sK33_SY472 @ SY615 @ SY614 @ SV113 ) @ SV113 )
| ( in @ ( ordered_pair @ ( sK32_D @ SY615 @ SY614 @ SV113 ) @ ( sK33_SY472 @ SY615 @ SY614 @ SV113 ) ) @ SY615 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_D @ SY615 @ SY614 @ SV113 ) @ ( sK33_SY472 @ SY615 @ SY614 @ SV113 ) ) @ SY614 )
| ( in @ ( ordered_pair @ ( sK32_D @ SY615 @ SY614 @ SV113 ) @ ( sK33_SY472 @ SY615 @ SY614 @ SV113 ) ) @ SY615 ) ) ) )
| ( SY615
= ( relation_rng_restriction @ SV113 @ SY614 ) ) )
| ~ ! [SY616: $i] :
( ~ ( relation @ SY616 )
| ( SY616
!= ( relation_rng_restriction @ SV113 @ SY614 ) )
| ~ ( ~ ! [SY617: $i,SY618: $i] :
( ~ ( in @ SY618 @ SV113 )
| ~ ( in @ ( ordered_pair @ SY617 @ SY618 ) @ SY614 )
| ( in @ ( ordered_pair @ SY617 @ SY618 ) @ SY616 ) )
| ~ ~ ( ~ ! [SY619: $i,SY620: $i] :
( ~ ( in @ ( ordered_pair @ SY619 @ SY620 ) @ SY616 )
| ( in @ SY620 @ SV113 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY616 )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY614 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(981,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)],[789]) ).
thf(982,plain,
( ( ~ ( relation @ sK3_A )
| ~ ( relation_empty_yielding @ sK3_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[790]) ).
thf(983,plain,
! [SV114: $i] :
( ( ! [SY623: $i] :
~ ( ~ ! [SY624: $i,SY625: $i] :
( ~ ( in @ SV114 @ SY624 )
| ~ ( in @ SY623 @ SY625 )
| ( in @ ( ordered_pair @ SV114 @ SY623 ) @ ( cartesian_product2 @ SY624 @ SY625 ) ) )
| ~ ~ ( ~ ! [SY626: $i] :
( ! [SY627: $i] :
~ ( in @ ( ordered_pair @ SV114 @ SY623 ) @ ( cartesian_product2 @ SY626 @ SY627 ) )
| ( in @ SV114 @ SY626 ) )
| ~ ! [SY628: $i,SY629: $i] :
( ~ ( in @ ( ordered_pair @ SV114 @ SY623 ) @ ( cartesian_product2 @ SY628 @ SY629 ) )
| ( in @ SY623 @ SY629 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(984,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK72_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK72_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[792]) ).
thf(985,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK62_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK62_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK62_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK62_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[793]) ).
thf(986,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK61_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[794]) ).
thf(987,plain,
! [SV115: $i] :
( ( ~ ( ~ ! [SY630: $i] :
( ~ ( subset @ SY630 @ ( sK42_B @ SV115 ) )
| ( are_equipotent @ SY630 @ ( sK42_B @ SV115 ) )
| ( in @ SY630 @ ( sK42_B @ SV115 ) ) )
| ~ ~ ( ~ ! [SY631: $i] :
( ~ ( ~ ! [SY632: $i] :
( ~ ( subset @ SY632 @ SY631 )
| ( in @ SY632 @ ( sK43_SY481 @ SY631 @ SV115 ) ) )
| ~ ( in @ ( sK43_SY481 @ SY631 @ SV115 ) @ ( sK42_B @ SV115 ) ) )
| ~ ( in @ SY631 @ ( sK42_B @ SV115 ) ) )
| ~ ~ ( ~ ! [SY633: $i,SY634: $i] :
( ~ ( in @ SY633 @ ( sK42_B @ SV115 ) )
| ~ ( subset @ SY634 @ SY633 )
| ( in @ SY634 @ ( sK42_B @ SV115 ) ) )
| ~ ( in @ SV115 @ ( sK42_B @ SV115 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(988,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[796]) ).
thf(989,plain,
! [SV116: $i] :
( ( ~ ( function @ SV116 )
| ~ ( relation @ SV116 )
| ~ ( ~ ~ ( ~ ! [SY635: $i] :
( ~ ( in @ SY635 @ ( relation_dom @ SV116 ) )
| ! [SY636: $i] :
( ( SY636
!= ( apply @ SV116 @ SY635 ) )
| ( in @ ( ordered_pair @ SY635 @ SY636 ) @ SV116 ) ) )
| ~ ! [SY637: $i] :
( ~ ( in @ SY637 @ ( relation_dom @ SV116 ) )
| ! [SY638: $i] :
( ~ ( in @ ( ordered_pair @ SY637 @ SY638 ) @ SV116 )
| ( SY638
= ( apply @ SV116 @ SY637 ) ) ) ) )
| ~ ~ ( ~ ! [SY639: $i] :
( ( in @ SY639 @ ( relation_dom @ SV116 ) )
| ! [SY640: $i] :
( ( SY640
!= ( apply @ SV116 @ SY639 ) )
| ( SY640 = empty_set ) ) )
| ~ ! [SY641: $i] :
( ( in @ SY641 @ ( relation_dom @ SV116 ) )
| ! [SY642: $i] :
( ( SY642 != empty_set )
| ( SY642
= ( apply @ SV116 @ SY641 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(990,plain,
! [SV117: $i] :
( ( ~ ( ~ ! [SY643: $i,SY644: $i] :
( ~ ( ~ ( ! [SY645: $i,SY646: $i] :
( ~ ( in @ SY645 @ SV117 )
| ~ ( in @ SY646 @ SY643 )
| ( ( sK53_D @ SY644 @ SY643 @ SV117 )
!= ( ordered_pair @ SY645 @ SY646 ) ) )
| ~ ( in @ ( sK53_D @ SY644 @ SY643 @ SV117 ) @ SY644 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK54_SY491 @ SY644 @ SY643 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK55_SY493 @ SY644 @ SY643 @ SV117 ) @ SY643 ) )
| ( ( sK53_D @ SY644 @ SY643 @ SV117 )
!= ( ordered_pair @ ( sK54_SY491 @ SY644 @ SY643 @ SV117 ) @ ( sK55_SY493 @ SY644 @ SY643 @ SV117 ) ) ) )
| ( in @ ( sK53_D @ SY644 @ SY643 @ SV117 ) @ SY644 ) ) )
| ( SY644
= ( cartesian_product2 @ SV117 @ SY643 ) ) )
| ~ ! [SY647: $i,SY648: $i] :
( ( SY648
!= ( cartesian_product2 @ SV117 @ SY647 ) )
| ~ ( ~ ! [SY649: $i] :
( ! [SY650: $i,SY651: $i] :
( ~ ( in @ SY650 @ SV117 )
| ~ ( in @ SY651 @ SY647 )
| ( SY649
!= ( ordered_pair @ SY650 @ SY651 ) ) )
| ( in @ SY649 @ SY648 ) )
| ~ ! [SY652: $i] :
( ~ ( in @ SY652 @ SY648 )
| ~ ( ~ ~ ( ~ ( in @ ( sK51_E @ SY652 @ SY648 @ SY647 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK52_SY488 @ SY652 @ SY648 @ SY647 @ SV117 ) @ SY647 ) )
| ( SY652
!= ( ordered_pair @ ( sK51_E @ SY652 @ SY648 @ SY647 @ SV117 ) @ ( sK52_SY488 @ SY652 @ SY648 @ SY647 @ SV117 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(991,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[799]) ).
thf(992,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)],[800]) ).
thf(993,plain,
( ( ~ ( function @ sK10_A )
| ~ ( relation @ sK10_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[801]) ).
thf(994,plain,
! [SV118: $i] :
( ( ~ ( ~ ! [SY653: $i,SY654: $i] :
( ~ ( function @ SY654 )
| ~ ( relation @ SY654 )
| ( SY653
!= ( apply @ SY654 @ SV118 ) )
| ~ ( in @ SV118 @ ( relation_dom @ SY654 ) )
| ( in @ ( ordered_pair @ SV118 @ SY653 ) @ SY654 ) )
| ~ ~ ( ~ ! [SY655: $i,SY656: $i] :
( ~ ( function @ SY656 )
| ~ ( relation @ SY656 )
| ~ ( in @ ( ordered_pair @ SV118 @ SY655 ) @ SY656 )
| ( SY655
= ( apply @ SY656 @ SV118 ) ) )
| ~ ! [SY657: $i,SY658: $i] :
( ~ ( function @ SY658 )
| ~ ( relation @ SY658 )
| ~ ( in @ ( ordered_pair @ SV118 @ SY657 ) @ SY658 )
| ( in @ SV118 @ ( relation_dom @ SY658 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(995,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[803]) ).
thf(996,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK69_C @ SX1 @ SX0 )
!= ( sK70_SY500 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK69_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK69_C @ SX1 @ SX0 ) @ ( sK70_SY500 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK69_C @ SX1 @ SX0 )
= ( sK70_SY500 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK69_C @ SX1 @ SX0 ) @ ( sK70_SY500 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK69_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK69_C @ SX1 @ SX0 ) @ ( sK70_SY500 @ 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)],[804]) ).
thf(997,plain,
! [SV119: $i] :
( ( ~ ( ~ ( element @ ( sK5_B @ SV119 ) @ ( powerset @ SV119 ) )
| ~ ( empty @ ( sK5_B @ SV119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(998,plain,
! [SV120: $i] :
( ( ~ ( relation @ SV120 )
| ! [SY659: $i] :
( ~ ( relation @ SY659 )
| ~ ( ~ ! [SY660: $i] :
( ~ ( relation @ SY660 )
| ~ ( ~ ( ! [SY661: $i] :
( ~ ( in @ ( ordered_pair @ ( sK13_D @ SY660 @ SY659 @ SV120 ) @ SY661 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY661 @ ( sK14_SY457 @ SY660 @ SY659 @ SV120 ) ) @ SY659 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_D @ SY660 @ SY659 @ SV120 ) @ ( sK14_SY457 @ SY660 @ SY659 @ SV120 ) ) @ SY660 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_D @ SY660 @ SY659 @ SV120 ) @ ( sK15_SY461 @ SY660 @ SY659 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY461 @ SY660 @ SY659 @ SV120 ) @ ( sK14_SY457 @ SY660 @ SY659 @ SV120 ) ) @ SY659 ) )
| ( in @ ( ordered_pair @ ( sK13_D @ SY660 @ SY659 @ SV120 ) @ ( sK14_SY457 @ SY660 @ SY659 @ SV120 ) ) @ SY660 ) ) )
| ( SY660
= ( relation_composition @ SV120 @ SY659 ) ) )
| ~ ! [SY662: $i] :
( ~ ( relation @ SY662 )
| ( SY662
!= ( relation_composition @ SV120 @ SY659 ) )
| ~ ( ~ ! [SY663: $i,SY664: $i] :
( ! [SY665: $i] :
( ~ ( in @ ( ordered_pair @ SY663 @ SY665 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY665 @ SY664 ) @ SY659 ) )
| ( in @ ( ordered_pair @ SY663 @ SY664 ) @ SY662 ) )
| ~ ! [SY666: $i,SY667: $i] :
( ~ ( in @ ( ordered_pair @ SY666 @ SY667 ) @ SY662 )
| ~ ( ~ ( in @ ( ordered_pair @ SY666 @ ( sK12_F @ SY667 @ SY666 @ SY662 @ SY659 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK12_F @ SY667 @ SY666 @ SY662 @ SY659 @ SV120 ) @ SY667 ) @ SY659 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(999,plain,
! [SV121: $i] :
( ( ! [SY668: $i] :
( ~ ( element @ SY668 @ ( powerset @ SV121 ) )
| ~ ( ~ ! [SY669: $i] :
( ~ ( element @ SY669 @ ( powerset @ SV121 ) )
| ~ ( disjoint @ SY668 @ SY669 )
| ( subset @ SY668 @ ( subset_complement @ SV121 @ SY669 ) ) )
| ~ ! [SY670: $i] :
( ~ ( element @ SY670 @ ( powerset @ SV121 ) )
| ~ ( subset @ SY668 @ ( subset_complement @ SV121 @ SY670 ) )
| ( disjoint @ SY668 @ SY670 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(1000,plain,
! [SV122: $i] :
( ( ~ ( ~ ! [SY671: $i,SY672: $i] :
( ~ ( relation @ SY672 )
| ~ ( in @ SV122 @ SY671 )
| ~ ( in @ SV122 @ ( relation_rng @ SY672 ) )
| ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SY671 @ SY672 ) ) ) )
| ~ ~ ( ~ ! [SY673: $i,SY674: $i] :
( ~ ( relation @ SY674 )
| ~ ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SY673 @ SY674 ) ) )
| ( in @ SV122 @ SY673 ) )
| ~ ! [SY675: $i,SY676: $i] :
( ~ ( relation @ SY676 )
| ~ ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SY675 @ SY676 ) ) )
| ( in @ SV122 @ ( relation_rng @ SY676 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(1001,plain,
! [SV123: $i] :
( ( ~ ( relation @ SV123 )
| ~ ( ~ ! [SY677: $i,SY678: $i] :
( ~ ( relation @ SY678 )
| ~ ( ~ ( ~ ( in @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ SY677 )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ ( sK35_SY473 @ SY678 @ SY677 @ SV123 ) ) @ SV123 )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ ( sK35_SY473 @ SY678 @ SY677 @ SV123 ) ) @ SY678 ) )
| ~ ~ ( ~ ( ( in @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ SY677 )
| ( in @ ( ordered_pair @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ ( sK35_SY473 @ SY678 @ SY677 @ SV123 ) ) @ SY678 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ ( sK35_SY473 @ SY678 @ SY677 @ SV123 ) ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ ( sK35_SY473 @ SY678 @ SY677 @ SV123 ) ) @ SY678 ) ) ) )
| ( SY678
= ( relation_dom_restriction @ SV123 @ SY677 ) ) )
| ~ ! [SY679: $i,SY680: $i] :
( ~ ( relation @ SY680 )
| ( SY680
!= ( relation_dom_restriction @ SV123 @ SY679 ) )
| ~ ( ~ ! [SY681: $i,SY682: $i] :
( ~ ( in @ SY681 @ SY679 )
| ~ ( in @ ( ordered_pair @ SY681 @ SY682 ) @ SV123 )
| ( in @ ( ordered_pair @ SY681 @ SY682 ) @ SY680 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY680 )
| ( in @ SX3 @ SY679 ) )
| ~ ! [SY685: $i,SY686: $i] :
( ~ ( in @ ( ordered_pair @ SY685 @ SY686 ) @ SY680 )
| ( in @ ( ordered_pair @ SY685 @ SY686 ) @ SV123 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(1002,plain,
! [SV124: $i] :
( ( ~ ( relation @ SV124 )
| ~ ( ~ ! [SY687: $i] :
( ~ ( relation @ SY687 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_C @ SY687 @ SV124 ) @ ( sK17_SY462 @ SY687 @ SV124 ) ) @ SY687 )
| ~ ( in @ ( ordered_pair @ ( sK17_SY462 @ SY687 @ SV124 ) @ ( sK16_C @ SY687 @ SV124 ) ) @ SV124 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK16_C @ SY687 @ SV124 ) @ ( sK17_SY462 @ SY687 @ SV124 ) ) @ SY687 )
| ( in @ ( ordered_pair @ ( sK17_SY462 @ SY687 @ SV124 ) @ ( sK16_C @ SY687 @ SV124 ) ) @ SV124 ) ) )
| ( SY687
= ( relation_inverse @ SV124 ) ) )
| ~ ! [SY688: $i] :
( ~ ( relation @ SY688 )
| ( SY688
!= ( relation_inverse @ SV124 ) )
| ~ ( ~ ! [SY689: $i,SY690: $i] :
( ~ ( in @ ( ordered_pair @ SY689 @ SY690 ) @ SY688 )
| ( in @ ( ordered_pair @ SY690 @ SY689 ) @ SV124 ) )
| ~ ! [SY691: $i,SY692: $i] :
( ~ ( in @ ( ordered_pair @ SY692 @ SY691 ) @ SV124 )
| ( in @ ( ordered_pair @ SY691 @ SY692 ) @ SY688 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(1003,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[811]) ).
thf(1004,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[812]) ).
thf(1005,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[813]) ).
thf(1006,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK38_C @ SX1 @ SX0 ) )
!= ( sK38_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)],[814]) ).
thf(1007,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[815]) ).
thf(1008,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[816]) ).
thf(1009,plain,
! [SV125: $i] :
( ( ~ ( relation @ SV125 )
| ~ ( ~ ! [SY693: $i,SY694: $i] :
( ~ ( ~ ( ! [SY695: $i] :
( ~ ( in @ ( ordered_pair @ SY695 @ ( sK30_D @ SY694 @ SY693 @ SV125 ) ) @ SV125 )
| ~ ( in @ SY695 @ SY693 ) )
| ~ ( in @ ( sK30_D @ SY694 @ SY693 @ SV125 ) @ SY694 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_SY471 @ SY694 @ SY693 @ SV125 ) @ ( sK30_D @ SY694 @ SY693 @ SV125 ) ) @ SV125 )
| ~ ( in @ ( sK31_SY471 @ SY694 @ SY693 @ SV125 ) @ SY693 ) )
| ( in @ ( sK30_D @ SY694 @ SY693 @ SV125 ) @ SY694 ) ) )
| ( SY694
= ( relation_image @ SV125 @ SY693 ) ) )
| ~ ! [SY696: $i,SY697: $i] :
( ( SY697
!= ( relation_image @ SV125 @ SY696 ) )
| ~ ( ~ ! [SY698: $i] :
( ! [SY699: $i] :
( ~ ( in @ ( ordered_pair @ SY699 @ SY698 ) @ SV125 )
| ~ ( in @ SY699 @ SY696 ) )
| ( in @ SY698 @ SY697 ) )
| ~ ! [SY700: $i] :
( ~ ( in @ SY700 @ SY697 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK29_E @ SY700 @ SY697 @ SY696 @ SV125 ) @ SY700 ) @ SV125 )
| ~ ( in @ ( sK29_E @ SY700 @ SY697 @ SY696 @ SV125 ) @ SY696 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(1010,plain,
! [SV126: $i] :
( ( ~ ( ~ ! [SY701: $i,SY702: $i] :
( ~ ( relation @ SY702 )
| ~ ( in @ ( ordered_pair @ SV126 @ SY701 ) @ SY702 )
| ( in @ SV126 @ ( relation_field @ SY702 ) ) )
| ~ ! [SY703: $i,SY704: $i] :
( ~ ( relation @ SY704 )
| ~ ( in @ ( ordered_pair @ SV126 @ SY703 ) @ SY704 )
| ( in @ SY703 @ ( relation_field @ SY704 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(1011,plain,
! [SV127: $i] :
( ( ! [SY705: $i] :
~ ( ~ ! [SY706: $i,SY707: $i] :
( ~ ( relation @ SY707 )
| ~ ( in @ SV127 @ SY706 )
| ~ ( in @ ( ordered_pair @ SV127 @ SY705 ) @ SY707 )
| ( in @ ( ordered_pair @ SV127 @ SY705 ) @ ( relation_composition @ ( identity_relation @ SY706 ) @ SY707 ) ) )
| ~ ~ ( ~ ! [SY708: $i,SY709: $i] :
( ~ ( relation @ SY709 )
| ~ ( in @ ( ordered_pair @ SV127 @ SY705 ) @ ( relation_composition @ ( identity_relation @ SY708 ) @ SY709 ) )
| ( in @ SV127 @ SY708 ) )
| ~ ! [SY710: $i,SY711: $i] :
( ~ ( relation @ SY711 )
| ~ ( in @ ( ordered_pair @ SV127 @ SY705 ) @ ( relation_composition @ ( identity_relation @ SY710 ) @ SY711 ) )
| ( in @ ( ordered_pair @ SV127 @ SY705 ) @ SY711 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(1012,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[820]) ).
thf(1013,plain,
! [SV128: $i] :
( ( ~ ( ~ ! [SY712: $i,SY713: $i] :
( ~ ( in @ SV128 @ SY713 )
| ~ ( in @ SY712 @ SY713 )
| ( subset @ ( unordered_pair @ SV128 @ SY712 ) @ SY713 ) )
| ~ ~ ( ~ ! [SY714: $i,SY715: $i] :
( ~ ( subset @ ( unordered_pair @ SV128 @ SY714 ) @ SY715 )
| ( in @ SV128 @ SY715 ) )
| ~ ! [SY716: $i,SY717: $i] :
( ~ ( subset @ ( unordered_pair @ SV128 @ SY716 ) @ SY717 )
| ( in @ SY716 @ SY717 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(1014,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[822]) ).
thf(1015,plain,
( ( ~ ( empty @ sK9_A )
| ~ ( relation @ sK9_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[823]) ).
thf(1016,plain,
! [SV129: $i] :
( ( ~ ( relation @ SV129 )
| ~ ( ~ ! [SY718: $i] :
( ~ ( ~ ( ! [SY719: $i] :
~ ( in @ ( ordered_pair @ SY719 @ ( sK19_C @ SY718 @ SV129 ) ) @ SV129 )
| ~ ( in @ ( sK19_C @ SY718 @ SV129 ) @ SY718 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_SY464 @ SY718 @ SV129 ) @ ( sK19_C @ SY718 @ SV129 ) ) @ SV129 )
| ( in @ ( sK19_C @ SY718 @ SV129 ) @ SY718 ) ) )
| ( SY718
= ( relation_rng @ SV129 ) ) )
| ~ ! [SY720: $i] :
( ( SY720
!= ( relation_rng @ SV129 ) )
| ~ ( ~ ! [SY721: $i] :
( ! [SY722: $i] :
~ ( in @ ( ordered_pair @ SY722 @ SY721 ) @ SV129 )
| ( in @ SY721 @ SY720 ) )
| ~ ! [SY723: $i] :
( ~ ( in @ SY723 @ SY720 )
| ( in @ ( ordered_pair @ ( sK18_D @ SY723 @ SY720 @ SV129 ) @ SY723 ) @ SV129 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(1017,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[825]) ).
thf(1018,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[826]) ).
thf(1019,plain,
( ( ~ ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) )
| ~ ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[827]) ).
thf(1020,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK71_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[828]) ).
thf(1021,plain,
! [SV130: $i] :
( ( ! [SY724: $i] :
( ~ ( ~ ( in @ ( sK73_C @ SY724 @ SV130 ) @ SV130 )
| ~ ~ ( in @ ( sK73_C @ SY724 @ SV130 ) @ SY724 ) )
| ( element @ SV130 @ ( powerset @ SY724 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(1022,plain,
! [SV131: $i] :
( ( ~ ( relation @ SV131 )
| ~ ( ~ ! [SY725: $i,SY726: $i] :
( ~ ( ~ ( ! [SY727: $i] :
( ~ ( in @ ( ordered_pair @ ( sK27_D @ SY726 @ SY725 @ SV131 ) @ SY727 ) @ SV131 )
| ~ ( in @ SY727 @ SY725 ) )
| ~ ( in @ ( sK27_D @ SY726 @ SY725 @ SV131 ) @ SY726 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK27_D @ SY726 @ SY725 @ SV131 ) @ ( sK28_SY469 @ SY726 @ SY725 @ SV131 ) ) @ SV131 )
| ~ ( in @ ( sK28_SY469 @ SY726 @ SY725 @ SV131 ) @ SY725 ) )
| ( in @ ( sK27_D @ SY726 @ SY725 @ SV131 ) @ SY726 ) ) )
| ( SY726
= ( relation_inverse_image @ SV131 @ SY725 ) ) )
| ~ ! [SY728: $i,SY729: $i] :
( ( SY729
!= ( relation_inverse_image @ SV131 @ SY728 ) )
| ~ ( ~ ! [SY730: $i] :
( ! [SY731: $i] :
( ~ ( in @ ( ordered_pair @ SY730 @ SY731 ) @ SV131 )
| ~ ( in @ SY731 @ SY728 ) )
| ( in @ SY730 @ SY729 ) )
| ~ ! [SY732: $i] :
( ~ ( in @ SY732 @ SY729 )
| ~ ( ~ ( in @ ( ordered_pair @ SY732 @ ( sK26_E @ SY732 @ SY729 @ SY728 @ SV131 ) ) @ SV131 )
| ~ ( in @ ( sK26_E @ SY732 @ SY729 @ SY728 @ SV131 ) @ SY728 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(1023,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[831]) ).
thf(1024,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK68_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK68_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK66_C @ SX1 @ SX0 ) @ ( sK67_SY497 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[832]) ).
thf(1025,plain,
! [SV132: $i] :
( ( ~ ( ~ ! [SY733: $i,SY734: $i] :
( ~ ( relation @ SY734 )
| ~ ( in @ SV132 @ SY733 )
| ~ ( in @ SV132 @ ( relation_dom @ SY734 ) )
| ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SY734 @ SY733 ) ) ) )
| ~ ~ ( ~ ! [SY735: $i,SY736: $i] :
( ~ ( relation @ SY736 )
| ~ ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SY736 @ SY735 ) ) )
| ( in @ SV132 @ SY735 ) )
| ~ ! [SY737: $i,SY738: $i] :
( ~ ( relation @ SY738 )
| ~ ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SY738 @ SY737 ) ) )
| ( in @ SV132 @ ( relation_dom @ SY738 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(1026,plain,
! [SV133: $i] :
( ( ~ ( ~ ! [SY739: $i,SY740: $i] :
( ~ ( relation @ SY740 )
| ~ ( in @ ( ordered_pair @ SV133 @ SY739 ) @ SY740 )
| ( in @ SV133 @ ( relation_dom @ SY740 ) ) )
| ~ ! [SY741: $i,SY742: $i] :
( ~ ( relation @ SY742 )
| ~ ( in @ ( ordered_pair @ SV133 @ SY741 ) @ SY742 )
| ( in @ SY741 @ ( relation_rng @ SY742 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(1027,plain,
! [SV134: $i] :
( ( ~ ( relation @ SV134 )
| ~ ( ~ ! [SY743: $i] :
( ~ ( ~ ( ! [SY744: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SY743 @ SV134 ) @ SY744 ) @ SV134 )
| ~ ( in @ ( sK22_C @ SY743 @ SV134 ) @ SY743 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SY743 @ SV134 ) @ ( sK23_SY466 @ SY743 @ SV134 ) ) @ SV134 )
| ( in @ ( sK22_C @ SY743 @ SV134 ) @ SY743 ) ) )
| ( SY743
= ( relation_dom @ SV134 ) ) )
| ~ ! [SY745: $i] :
( ( SY745
!= ( relation_dom @ SV134 ) )
| ~ ( ~ ! [SY746: $i] :
( ! [SY747: $i] :
~ ( in @ ( ordered_pair @ SY746 @ SY747 ) @ SV134 )
| ( in @ SY746 @ SY745 ) )
| ~ ! [SY748: $i] :
( ~ ( in @ SY748 @ SY745 )
| ( in @ ( ordered_pair @ SY748 @ ( sK21_D @ SY748 @ SY745 @ SV134 ) ) @ SV134 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(1028,plain,
! [SV135: $i] :
( ( ~ ( ~ ! [SY749: $i,SY750: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK57_D @ SY750 @ SY749 @ SV135 ) @ SY750 )
| ( ( sK57_D @ SY750 @ SY749 @ SV135 )
!= SV135 ) )
| ~ ( ~ ( in @ ( sK57_D @ SY750 @ SY749 @ SV135 ) @ SY750 )
| ( ( sK57_D @ SY750 @ SY749 @ SV135 )
!= SY749 ) ) )
| ~ ( ( in @ ( sK57_D @ SY750 @ SY749 @ SV135 ) @ SY750 )
| ( ( sK57_D @ SY750 @ SY749 @ SV135 )
= SV135 )
| ( ( sK57_D @ SY750 @ SY749 @ SV135 )
= SY749 ) ) )
| ( SY750
= ( unordered_pair @ SV135 @ SY749 ) ) )
| ~ ! [SY751: $i,SY752: $i] :
( ( SY752
!= ( unordered_pair @ SV135 @ SY751 ) )
| ~ ( ~ ! [SY753: $i] :
( ~ ( in @ SY753 @ SY752 )
| ( SY753 = SV135 )
| ( SY753 = SY751 ) )
| ~ ~ ( ~ ! [SY754: $i] :
( ( SY754 != SV135 )
| ( in @ SY754 @ SY752 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY751 )
| ( in @ SX3 @ SY752 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(1029,plain,
( ( ( ( relation_dom @ empty_set )
!= empty_set )
| ( ( relation_rng @ empty_set )
!= empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[837]) ).
thf(1030,plain,
! [SV136: $i] :
( ( ~ ( relation @ SV136 )
| ~ ( ~ ! [SY756: $i] :
( ~ ( relation @ SY756 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK58_C @ SY756 @ SV136 ) @ ( sK59_SY494 @ SY756 @ SV136 ) ) @ SV136 )
| ~ ( in @ ( ordered_pair @ ( sK58_C @ SY756 @ SV136 ) @ ( sK59_SY494 @ SY756 @ SV136 ) ) @ SY756 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_C @ SY756 @ SV136 ) @ ( sK59_SY494 @ SY756 @ SV136 ) ) @ SV136 )
| ( in @ ( ordered_pair @ ( sK58_C @ SY756 @ SV136 ) @ ( sK59_SY494 @ SY756 @ SV136 ) ) @ SY756 ) ) )
| ( SV136 = SY756 ) )
| ~ ! [SY757: $i] :
( ~ ( relation @ SY757 )
| ( SV136 != SY757 )
| ~ ( ~ ! [SY758: $i,SY759: $i] :
( ~ ( in @ ( ordered_pair @ SY758 @ SY759 ) @ SV136 )
| ( in @ ( ordered_pair @ SY758 @ SY759 ) @ SY757 ) )
| ~ ! [SY760: $i,SY761: $i] :
( ~ ( in @ ( ordered_pair @ SY760 @ SY761 ) @ SY757 )
| ( in @ ( ordered_pair @ SY760 @ SY761 ) @ SV136 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(1031,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)],[839]) ).
thf(1032,plain,
! [SV137: $i] :
( ( ! [SY762: $i] :
( ~ ( function @ SY762 )
| ~ ( relation @ SY762 )
| ~ ( ~ ! [SY763: $i] :
( ~ ( function @ SY763 )
| ~ ( relation @ SY763 )
| ~ ( in @ SV137 @ ( relation_dom @ SY763 ) )
| ~ ( in @ ( apply @ SY763 @ SV137 ) @ ( relation_dom @ SY762 ) )
| ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY763 @ SY762 ) ) ) )
| ~ ~ ( ~ ! [SY764: $i] :
( ~ ( function @ SY764 )
| ~ ( relation @ SY764 )
| ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY764 @ SY762 ) ) )
| ( in @ SV137 @ ( relation_dom @ SY764 ) ) )
| ~ ! [SY765: $i] :
( ~ ( function @ SY765 )
| ~ ( relation @ SY765 )
| ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY765 @ SY762 ) ) )
| ( in @ ( apply @ SY765 @ SV137 ) @ ( relation_dom @ SY762 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(1033,plain,
! [SV138: $i] :
( ( ~ ( ~ ! [SY766: $i] :
( ~ ( subset @ SY766 @ ( sK41_B @ SV138 ) )
| ( are_equipotent @ SY766 @ ( sK41_B @ SV138 ) )
| ( in @ SY766 @ ( sK41_B @ SV138 ) ) )
| ~ ~ ( ~ ! [SY767: $i] :
( ~ ( in @ SY767 @ ( sK41_B @ SV138 ) )
| ( in @ ( powerset @ SY767 ) @ ( sK41_B @ SV138 ) ) )
| ~ ~ ( ~ ! [SY768: $i,SY769: $i] :
( ~ ( in @ SY768 @ ( sK41_B @ SV138 ) )
| ~ ( subset @ SY769 @ SY768 )
| ( in @ SY769 @ ( sK41_B @ SV138 ) ) )
| ~ ( in @ SV138 @ ( sK41_B @ SV138 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(1034,plain,
! [SV139: $i] :
( ( ~ ( relation @ SV139 )
| ~ ( ~ ! [SY770: $i] :
( ~ ( relation @ SY770 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SY770 @ SV139 ) @ ( sK25_SY467 @ SY770 @ SV139 ) ) @ SV139 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SY770 @ SV139 ) @ ( sK25_SY467 @ SY770 @ SV139 ) ) @ SY770 ) )
| ( subset @ SV139 @ SY770 ) )
| ~ ! [SY771: $i] :
( ~ ( relation @ SY771 )
| ~ ( subset @ SV139 @ SY771 )
| ! [SY772: $i,SY773: $i] :
( ~ ( in @ ( ordered_pair @ SY772 @ SY773 ) @ SV139 )
| ( in @ ( ordered_pair @ SY772 @ SY773 ) @ SY771 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(1035,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK60_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK60_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK60_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK60_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[843]) ).
thf(1036,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)],[844]) ).
thf(1037,plain,
! [SV140: $i] :
( ( ~ ( relation @ SV140 )
| ~ ( ~ ! [SY774: $i] :
( ~ ( relation @ SY774 )
| ~ ( subset @ SV140 @ SY774 )
| ( subset @ ( relation_dom @ SV140 ) @ ( relation_dom @ SY774 ) ) )
| ~ ! [SY775: $i] :
( ~ ( relation @ SY775 )
| ~ ( subset @ SV140 @ SY775 )
| ( subset @ ( relation_rng @ SV140 ) @ ( relation_rng @ SY775 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(1038,plain,
! [SV141: $i] :
( ( ( empty @ SV141 )
| ~ ( ~ ( element @ ( sK8_B @ SV141 ) @ ( powerset @ SV141 ) )
| ~ ~ ( empty @ ( sK8_B @ SV141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(1039,plain,
! [SV142: $i] :
( ( ~ ( ~ ! [SY776: $i,SY777: $i] :
( ~ ( relation @ SY777 )
| ! [SY778: $i] :
( ~ ( in @ SY778 @ ( relation_rng @ SY777 ) )
| ~ ( in @ ( ordered_pair @ SV142 @ SY778 ) @ SY777 )
| ~ ( in @ SY778 @ SY776 ) )
| ( in @ SV142 @ ( relation_inverse_image @ SY777 @ SY776 ) ) )
| ~ ! [SY779: $i,SY780: $i] :
( ~ ( relation @ SY780 )
| ~ ( in @ SV142 @ ( relation_inverse_image @ SY780 @ SY779 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK39_D @ SY780 @ SY779 @ SV142 ) @ ( relation_rng @ SY780 ) )
| ~ ( in @ ( ordered_pair @ SV142 @ ( sK39_D @ SY780 @ SY779 @ SV142 ) ) @ SY780 ) )
| ~ ( in @ ( sK39_D @ SY780 @ SY779 @ SV142 ) @ SY779 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(1040,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK65_SY495 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK64_C @ SX1 @ SX0 ) @ ( sK65_SY495 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK64_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK64_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK64_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK63_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK63_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[848]) ).
thf(1041,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)],[849]) ).
thf(1042,plain,
( ( ~ ! [SX0: $i] :
( ( relation_dom @ ( identity_relation @ SX0 ) )
= SX0 )
| ~ ! [SX0: $i] :
( ( relation_rng @ ( identity_relation @ SX0 ) )
= SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[850]) ).
thf(1043,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[851]) ).
thf(1044,plain,
! [SV143: $i] :
( ( ! [SY781: $i] :
~ ( ~ ! [SY782: $i,SY783: $i] :
( ~ ( in @ SV143 @ SY782 )
| ~ ( in @ SY781 @ SY783 )
| ( in @ ( ordered_pair @ SV143 @ SY781 ) @ ( cartesian_product2 @ SY782 @ SY783 ) ) )
| ~ ~ ( ~ ! [SY784: $i] :
( ! [SY785: $i] :
~ ( in @ ( ordered_pair @ SV143 @ SY781 ) @ ( cartesian_product2 @ SY784 @ SY785 ) )
| ( in @ SV143 @ SY784 ) )
| ~ ! [SY786: $i,SY787: $i] :
( ~ ( in @ ( ordered_pair @ SV143 @ SY781 ) @ ( cartesian_product2 @ SY786 @ SY787 ) )
| ( in @ SY781 @ SY787 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(1045,plain,
! [SV144: $i] :
( ( ~ ( ~ ! [SY788: $i,SY789: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK56_D @ SY789 @ SY788 @ SV144 ) @ SY789 )
| ~ ( in @ ( sK56_D @ SY789 @ SY788 @ SV144 ) @ SV144 ) )
| ~ ( ~ ( in @ ( sK56_D @ SY789 @ SY788 @ SV144 ) @ SY789 )
| ~ ( in @ ( sK56_D @ SY789 @ SY788 @ SV144 ) @ SY788 ) ) )
| ~ ( ( in @ ( sK56_D @ SY789 @ SY788 @ SV144 ) @ SY789 )
| ( in @ ( sK56_D @ SY789 @ SY788 @ SV144 ) @ SV144 )
| ( in @ ( sK56_D @ SY789 @ SY788 @ SV144 ) @ SY788 ) ) )
| ( SY789
= ( set_union2 @ SV144 @ SY788 ) ) )
| ~ ! [SY790: $i,SY791: $i] :
( ( SY791
!= ( set_union2 @ SV144 @ SY790 ) )
| ~ ( ~ ! [SY792: $i] :
( ~ ( in @ SY792 @ SY791 )
| ( in @ SY792 @ SV144 )
| ( in @ SY792 @ SY790 ) )
| ~ ~ ( ~ ! [SY793: $i] :
( ~ ( in @ SY793 @ SV144 )
| ( in @ SY793 @ SY791 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY790 )
| ( in @ SX3 @ SY791 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(1046,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[854]) ).
thf(1047,plain,
! [SV145: $i] :
( ( ~ ( ~ ! [SY795: $i,SY796: $i] :
( ~ ( relation @ SY796 )
| ! [SY797: $i] :
( ~ ( in @ SY797 @ ( relation_dom @ SY796 ) )
| ~ ( in @ ( ordered_pair @ SY797 @ SV145 ) @ SY796 )
| ~ ( in @ SY797 @ SY795 ) )
| ( in @ SV145 @ ( relation_image @ SY796 @ SY795 ) ) )
| ~ ! [SY798: $i,SY799: $i] :
( ~ ( relation @ SY799 )
| ~ ( in @ SV145 @ ( relation_image @ SY799 @ SY798 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK40_D @ SY799 @ SY798 @ SV145 ) @ ( relation_dom @ SY799 ) )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY799 @ SY798 @ SV145 ) @ SV145 ) @ SY799 ) )
| ~ ( in @ ( sK40_D @ SY799 @ SY798 @ SV145 ) @ SY798 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(1048,plain,
! [SV146: $i] :
( ( ~ ( ~ ! [SY800: $i] :
( ~ ( subset @ SV146 @ SY800 )
| ! [SY801: $i] : ( subset @ ( cartesian_product2 @ SV146 @ SY801 ) @ ( cartesian_product2 @ SY800 @ SY801 ) ) )
| ~ ! [SY802: $i] :
( ~ ( subset @ SV146 @ SY802 )
| ! [SY803: $i] : ( subset @ ( cartesian_product2 @ SY803 @ SV146 ) @ ( cartesian_product2 @ SY803 @ SY802 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(1049,plain,
! [SV147: $i] :
( ( ! [SY804: $i] :
( ~ ( ~ ( ~ ( in @ ( sK44_C @ SY804 @ SV147 ) @ SV147 )
| ~ ( in @ ( sK44_C @ SY804 @ SV147 ) @ SY804 ) )
| ~ ( ( in @ ( sK44_C @ SY804 @ SV147 ) @ SV147 )
| ( in @ ( sK44_C @ SY804 @ SV147 ) @ SY804 ) ) )
| ( SV147 = SY804 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(1050,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[858]) ).
thf(1051,plain,
! [SV148: $i] :
( ( ! [SY805: $i] :
~ ( ~ ! [SY806: $i] :
( ! [SY807: $i] :
( ( ordered_pair @ SV148 @ SY805 )
!= ( ordered_pair @ SY806 @ SY807 ) )
| ( SV148 = SY806 ) )
| ~ ! [SY808: $i,SY809: $i] :
( ( ( ordered_pair @ SV148 @ SY805 )
!= ( ordered_pair @ SY808 @ SY809 ) )
| ( SY805 = SY809 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(1052,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK50_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK50_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(1053,plain,
( ( ~ ~ ( empty @ sK6_A )
| ~ ( relation @ sK6_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[861]) ).
thf(1054,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)],[862]) ).
thf(1055,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[863]) ).
thf(1056,plain,
! [SV149: $i] :
( ( ~ ( ~ ! [SY810: $i,SY811: $i] :
( ~ ( ~ ( ~ ( in @ ( sK45_D @ SY811 @ SY810 @ SV149 ) @ SV149 )
| ( in @ ( sK45_D @ SY811 @ SY810 @ SV149 ) @ SY810 )
| ~ ( in @ ( sK45_D @ SY811 @ SY810 @ SV149 ) @ SY811 ) )
| ~ ~ ( ~ ( ( in @ ( sK45_D @ SY811 @ SY810 @ SV149 ) @ SV149 )
| ( in @ ( sK45_D @ SY811 @ SY810 @ SV149 ) @ SY811 ) )
| ~ ( ~ ( in @ ( sK45_D @ SY811 @ SY810 @ SV149 ) @ SY810 )
| ( in @ ( sK45_D @ SY811 @ SY810 @ SV149 ) @ SY811 ) ) ) )
| ( SY811
= ( set_difference @ SV149 @ SY810 ) ) )
| ~ ! [SY812: $i,SY813: $i] :
( ( SY813
!= ( set_difference @ SV149 @ SY812 ) )
| ~ ( ~ ! [SY814: $i] :
( ~ ( in @ SY814 @ SV149 )
| ( in @ SY814 @ SY812 )
| ( in @ SY814 @ SY813 ) )
| ~ ~ ( ~ ! [SY815: $i] :
( ~ ( in @ SY815 @ SY813 )
| ( in @ SY815 @ SV149 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY813 )
| ~ ( in @ SX3 @ SY812 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(1057,plain,
! [SV150: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV150 )
| ( ( set_union2 @ ( singleton @ SV1 ) @ SV150 )
= SV150 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(1058,plain,
! [SV151: $i,SV2: $i] :
( ( ~ ( disjoint @ ( singleton @ SV2 ) @ SV151 )
| ~ ( in @ SV2 @ SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(1059,plain,
! [SV152: $i,SV3: $i] :
( ( ( in @ SV3 @ SV152 )
| ( disjoint @ ( singleton @ SV3 ) @ SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(1060,plain,
! [SV4: $i,SV153: $i] :
( ( ~ ( element @ SV153 @ ( powerset @ SV4 ) )
| ! [SY817: $i] :
( ~ ( in @ SY817 @ SV153 )
| ( in @ SY817 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(1061,plain,
! [SV154: $i,SV5: $i] :
( ( ~ ( in @ SV5 @ SV154 )
| ( subset @ SV5 @ ( union @ SV154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(1062,plain,
! [SV155: $i,SV6: $i] :
( ( ~ ( in @ SV6 @ SV155 )
| ( ( set_union2 @ ( singleton @ SV6 ) @ SV155 )
= SV155 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[870]) ).
thf(1063,plain,
! [SV156: $i,SV7: $i] :
( ( ~ ( in @ SV7 @ SV156 )
| ( subset @ SV7 @ ( union @ SV156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(1064,plain,
! [SV157: $i,SV8: $i] :
( ( ~ ( in @ SV8 @ SV157 )
| ~ ( in @ SV157 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(1065,plain,
! [SV158: $i,SV10: $i] :
( ( ~ ( in @ SV10 @ SV158 )
| ( element @ SV10 @ SV158 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(1066,plain,
! [SV159: $i,SV11: $i] :
( ( ~ ( element @ SV11 @ SV159 )
| ( empty @ SV159 )
| ( in @ SV11 @ SV159 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(1067,plain,
! [SV12: $i,SV160: $i] :
( ( ! [SY818: $i] :
( ~ ( element @ SV160 @ ( powerset @ SY818 ) )
| ~ ( in @ SV12 @ SV160 )
| ( element @ SV12 @ SY818 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(1068,plain,
! [SV13: $i,SV161: $i] :
( ( ~ ( empty @ SV161 )
| ~ ( in @ SV13 @ SV161 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[877]) ).
thf(1069,plain,
! [SV14: $i] :
( ( ( singleton @ SV14 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[878]) ).
thf(1070,plain,
! [SV162: $i,SV15: $i] :
( ( ~ ( subset @ SV15 @ SV162 )
| ! [SY819: $i] :
( ( in @ SY819 @ SV15 )
| ( subset @ SV15 @ ( set_difference @ SV162 @ ( singleton @ SY819 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(1071,plain,
! [SV163: $i,SV16: $i] :
( ( ! [SY820: $i,SY821: $i] :
( ( SV16 = SY821 )
| ( SV16 = SY820 )
| ( ( unordered_pair @ SV16 @ SV163 )
!= ( unordered_pair @ SY820 @ SY821 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(1072,plain,
! [SV17: $i,SV164: $i] :
( ( ~ ( relation @ SV164 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV17 @ SV164 ) ) @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(1073,plain,
! [SV18: $i,SV165: $i] :
( ( ~ ( relation @ SV165 )
| ( subset @ ( relation_rng_restriction @ SV18 @ SV165 ) @ SV165 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(1074,plain,
! [SV19: $i,SV166: $i] :
( ( ~ ( relation @ SV166 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV19 @ SV166 ) ) @ ( relation_rng @ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(1075,plain,
! [SV20: $i,SV167: $i] :
( ( ~ ( relation @ SV167 )
| ( ( relation_rng @ ( relation_rng_restriction @ SV20 @ SV167 ) )
= ( set_intersection2 @ ( relation_rng @ SV167 ) @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(1076,plain,
! [SV168: $i,SV21: $i] :
( ( ! [SY822: $i,SY823: $i] :
( ~ ( subset @ SV21 @ SV168 )
| ~ ( subset @ SY822 @ SY823 )
| ( subset @ ( cartesian_product2 @ SV21 @ SY822 ) @ ( cartesian_product2 @ SV168 @ SY823 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[885]) ).
thf(1077,plain,
! [SV169: $i,SV22: $i] :
( ( ~ ( subset @ SV22 @ SV169 )
| ( ( set_union2 @ SV22 @ SV169 )
= SV169 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(1078,plain,
! [SV23: $i,SV170: $i] :
( ( ~ ( relation @ SV170 )
| ( subset @ ( relation_image @ SV170 @ SV23 ) @ ( relation_rng @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(1079,plain,
! [SV24: $i,SV171: $i] :
( ( ~ ( relation @ SV171 )
| ( ( relation_image @ SV171 @ SV24 )
= ( relation_image @ SV171 @ ( set_intersection2 @ ( relation_dom @ SV171 ) @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[888]) ).
thf(1080,plain,
! [SV25: $i] :
( ( ( ~ ( relation @ SV25 ) )
= $true )
| ( ( ( relation_image @ SV25 @ ( relation_dom @ SV25 ) )
= ( relation_rng @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[889]) ).
thf(1081,plain,
! [SV26: $i,SV172: $i] :
( ( ~ ( relation @ SV172 )
| ( subset @ ( relation_inverse_image @ SV172 @ SV26 ) @ ( relation_dom @ SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(1082,plain,
! [SV27: $i,SV173: $i] :
( ( ~ ( relation @ SV173 )
| ( SV27 = empty_set )
| ~ ( subset @ SV27 @ ( relation_rng @ SV173 ) )
| ( ( relation_inverse_image @ SV173 @ SV27 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(1083,plain,
! [SV174: $i,SV28: $i] :
( ( ! [SY824: $i] :
( ~ ( relation @ SY824 )
| ~ ( subset @ SV28 @ SV174 )
| ( subset @ ( relation_inverse_image @ SY824 @ SV28 ) @ ( relation_inverse_image @ SY824 @ SV174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(1084,plain,
! [SV175: $i,SV29: $i] :
( ( subset @ ( set_intersection2 @ SV29 @ SV175 ) @ SV29 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(1085,plain,
! [SV176: $i,SV30: $i] :
( ( ! [SY825: $i] :
( ~ ( subset @ SV30 @ SV176 )
| ~ ( subset @ SV30 @ SY825 )
| ( subset @ SV30 @ ( set_intersection2 @ SV176 @ SY825 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(1086,plain,
! [SV177: $i,SV31: $i] :
( ( ! [SY826: $i] :
( ~ ( subset @ SV31 @ SV177 )
| ~ ( subset @ SV177 @ SY826 )
| ( subset @ SV31 @ SY826 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(1087,plain,
! [SV32: $i] :
( ( ( ~ ( relation @ SV32 ) )
= $true )
| ( ( subset @ SV32 @ ( cartesian_product2 @ ( relation_dom @ SV32 ) @ ( relation_rng @ SV32 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[896]) ).
thf(1088,plain,
! [SV33: $i,SV178: $i] :
( ( ~ ( function @ SV178 )
| ~ ( relation @ SV178 )
| ! [SY827: $i] :
( ~ ( function @ SY827 )
| ~ ( relation @ SY827 )
| ~ ( in @ SV33 @ ( relation_dom @ ( relation_composition @ SY827 @ SV178 ) ) )
| ( ( apply @ ( relation_composition @ SY827 @ SV178 ) @ SV33 )
= ( apply @ SV178 @ ( apply @ SY827 @ SV33 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(1089,plain,
! [SV34: $i,SV179: $i] :
( ( ~ ( function @ SV179 )
| ~ ( relation @ SV179 )
| ! [SY828: $i] :
( ~ ( function @ SY828 )
| ~ ( relation @ SY828 )
| ~ ( in @ SV34 @ ( relation_dom @ SV179 ) )
| ( ( apply @ ( relation_composition @ SV179 @ SY828 ) @ SV34 )
= ( apply @ SY828 @ ( apply @ SV179 @ SV34 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(1090,plain,
! [SV180: $i,SV35: $i] :
( ( ~ ( subset @ SV35 @ SV180 )
| ! [SY829: $i] : ( subset @ ( set_intersection2 @ SV35 @ SY829 ) @ ( set_intersection2 @ SV180 @ SY829 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(1091,plain,
! [SV181: $i,SV36: $i] :
( ( ~ ( subset @ SV36 @ SV181 )
| ( ( set_intersection2 @ SV36 @ SV181 )
= SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(1092,plain,
! [SV182: $i,SV38: $i] :
( ( ~ ( subset @ SV38 @ SV182 )
| ! [SY830: $i] : ( subset @ ( set_difference @ SV38 @ SY830 ) @ ( set_difference @ SV182 @ SY830 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[902]) ).
thf(1093,plain,
! [SV183: $i,SV39: $i] :
( ( subset @ ( set_difference @ SV39 @ SV183 ) @ SV39 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(1094,plain,
! [SV184: $i,SV40: $i] :
( ( ( set_union2 @ SV40 @ ( set_difference @ SV184 @ SV40 ) )
= ( set_union2 @ SV40 @ SV184 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[904]) ).
thf(1095,plain,
! [SV41: $i] :
( ( ( ~ ( subset @ SV41 @ empty_set ) )
= $true )
| ( ( SV41 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[905]) ).
thf(1096,plain,
! [SV185: $i,SV42: $i] :
( ( ( set_difference @ ( set_union2 @ SV42 @ SV185 ) @ SV185 )
= ( set_difference @ SV42 @ SV185 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(1097,plain,
! [SV43: $i] :
( ( ( ~ ( relation @ SV43 ) )
= $true )
| ( ( ! [SY551: $i] :
( ~ ( relation @ SY551 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV43 @ SY551 ) ) @ ( relation_dom @ SV43 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[907]) ).
thf(1098,plain,
! [SV44: $i] :
( ( ( ~ ( relation @ SV44 ) )
= $true )
| ( ( ! [SY552: $i] :
( ~ ( relation @ SY552 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV44 @ SY552 ) ) @ ( relation_rng @ SY552 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[908]) ).
thf(1099,plain,
! [SV186: $i,SV45: $i] :
( ( ~ ( subset @ SV45 @ SV186 )
| ( SV186
= ( set_union2 @ SV45 @ ( set_difference @ SV186 @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(1100,plain,
! [SV46: $i] :
( ( ( ~ ( relation @ SV46 ) )
= $true )
| ( ( ! [SY554: $i] :
( ~ ( relation @ SY554 )
| ~ ( subset @ ( relation_rng @ SV46 ) @ ( relation_dom @ SY554 ) )
| ( ( relation_dom @ ( relation_composition @ SV46 @ SY554 ) )
= ( relation_dom @ SV46 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[910]) ).
thf(1101,plain,
! [SV47: $i,SV187: $i] :
( ( ~ ( element @ SV187 @ ( powerset @ ( powerset @ SV47 ) ) )
| ( SV187 = empty_set )
| ( ( complements_of_subsets @ SV47 @ SV187 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(1102,plain,
! [SV48: $i] :
( ( ( ~ ( relation @ SV48 ) )
= $true )
| ( ( ! [SY556: $i] :
( ~ ( relation @ SY556 )
| ~ ( subset @ ( relation_dom @ SV48 ) @ ( relation_rng @ SY556 ) )
| ( ( relation_rng @ ( relation_composition @ SY556 @ SV48 ) )
= ( relation_rng @ SV48 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[912]) ).
thf(1103,plain,
! [SV188: $i,SV49: $i] :
( ( ( set_difference @ SV49 @ ( set_difference @ SV49 @ SV188 ) )
= ( set_intersection2 @ SV49 @ SV188 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(1104,plain,
! [SV50: $i] :
( ( ( SV50 = empty_set )
= $true )
| ( ( ! [SY558: $i] :
( ~ ( element @ SY558 @ ( powerset @ SV50 ) )
| ! [SY559: $i] :
( ~ ( element @ SY559 @ SV50 )
| ( in @ SY559 @ SY558 )
| ( in @ SY559 @ ( subset_complement @ SV50 @ SY558 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[914]) ).
thf(1105,plain,
! [SV189: $i,SV51: $i] :
( ( ! [SY831: $i] :
( ~ ( element @ SY831 @ ( powerset @ SV51 ) )
| ~ ( in @ SV189 @ ( subset_complement @ SV51 @ SY831 ) )
| ~ ( in @ SV189 @ SY831 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1106,plain,
! [SV52: $i] :
( ( ( ~ ( relation @ SV52 ) )
= $true )
| ( ( ( in @ ( ordered_pair @ ( sK36_B @ SV52 ) @ ( sK37_SY474 @ SV52 ) ) @ SV52 )
| ( SV52 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[916]) ).
thf(1107,plain,
! [SV53: $i,SV190: $i] :
( ( ~ ( proper_subset @ SV190 @ SV53 )
| ~ ( subset @ SV53 @ SV190 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(1108,plain,
! [SV54: $i,SV191: $i] :
( ( ! [SY832: $i] :
( ~ ( disjoint @ SV191 @ SY832 )
| ~ ( subset @ SV54 @ SV191 )
| ( disjoint @ SV54 @ SY832 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(1109,plain,
! [SV192: $i,SV56: $i] :
( ( ~ ( subset @ ( singleton @ SV56 ) @ ( singleton @ SV192 ) )
| ( SV56 = SV192 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1110,plain,
! [SV193: $i,SV57: $i] :
( ( subset @ SV57 @ ( set_union2 @ SV57 @ SV193 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1111,plain,
! [SV58: $i,SV194: $i] :
( ( ~ ( relation @ SV194 )
| ( subset @ ( relation_dom_restriction @ SV194 @ SV58 ) @ SV194 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[922]) ).
thf(1112,plain,
! [SV195: $i,SV59: $i] :
( ( ! [SY833: $i] :
( ~ ( subset @ SV59 @ SV195 )
| ~ ( subset @ SY833 @ SV195 )
| ( subset @ ( set_union2 @ SV59 @ SY833 ) @ SV195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(1113,plain,
! [SV196: $i,SV60: $i] :
( ( ! [SY834: $i] :
( ( singleton @ SV60 )
!= ( unordered_pair @ SV196 @ SY834 ) )
| ( SV60 = SV196 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1114,plain,
! [SV61: $i,SV197: $i] :
( ( ~ ( relation @ SV197 )
| ( ( relation_dom @ ( relation_dom_restriction @ SV197 @ SV61 ) )
= ( set_intersection2 @ ( relation_dom @ SV197 ) @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1115,plain,
! [SV62: $i,SV198: $i] :
( ( ~ ( relation @ SV198 )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV198 @ SV62 ) ) @ ( relation_rng @ SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1116,plain,
! [SV199: $i,SV64: $i] :
( ( ! [SY835: $i] :
( ( ( singleton @ SV64 )
!= ( unordered_pair @ SV199 @ SY835 ) )
| ( SV199 = SY835 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(1117,plain,
! [SV65: $i] :
( ( ( ~ ( empty @ SV65 ) )
= $true )
| ( ( function @ SV65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[929]) ).
thf(1118,plain,
! [SV66: $i] :
( ( ( ~ ( empty @ SV66 ) )
= $true )
| ( ( relation @ SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[930]) ).
thf(1119,plain,
! [SV200: $i,SV67: $i] :
( ( ( unordered_pair @ SV67 @ SV200 )
= ( unordered_pair @ SV200 @ SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1120,plain,
! [SV201: $i,SV68: $i] :
( ( ( set_union2 @ SV68 @ SV201 )
= ( set_union2 @ SV201 @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1121,plain,
! [SV202: $i,SV69: $i] :
( ( ( set_intersection2 @ SV69 @ SV202 )
= ( set_intersection2 @ SV202 @ SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1122,plain,
! [SV70: $i,SV203: $i] :
( ( ~ ( element @ SV203 @ ( powerset @ SV70 ) )
| ( ( subset_complement @ SV70 @ SV203 )
= ( set_difference @ SV70 @ SV203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1123,plain,
! [SV204: $i,SV71: $i] :
( ( ( ordered_pair @ SV71 @ SV204 )
= ( unordered_pair @ ( unordered_pair @ SV71 @ SV204 ) @ ( singleton @ SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1124,plain,
! [SV72: $i] :
( ( ( ~ ( relation @ SV72 ) )
= $true )
| ( ( ( relation_field @ SV72 )
= ( set_union2 @ ( relation_dom @ SV72 ) @ ( relation_rng @ SV72 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[936]) ).
thf(1125,plain,
! [SV74: $i,SV205: $i] :
( ( ~ ( element @ SV205 @ ( powerset @ SV74 ) )
| ( element @ ( subset_complement @ SV74 @ SV205 ) @ ( powerset @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1126,plain,
! [SV75: $i] :
( ( ( ~ ( relation @ SV75 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV75 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[939]) ).
thf(1127,plain,
! [SV206: $i,SV76: $i] :
( ( ~ ( relation @ SV76 )
| ~ ( relation @ SV206 )
| ( relation @ ( relation_composition @ SV76 @ SV206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(1128,plain,
! [SV77: $i,SV207: $i] :
( ( ~ ( element @ SV207 @ ( powerset @ ( powerset @ SV77 ) ) )
| ( element @ ( union_of_subsets @ SV77 @ SV207 ) @ ( powerset @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1129,plain,
! [SV78: $i,SV208: $i] :
( ( ~ ( element @ SV208 @ ( powerset @ ( powerset @ SV78 ) ) )
| ( element @ ( meet_of_subsets @ SV78 @ SV208 ) @ ( powerset @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1130,plain,
! [SV79: $i,SV209: $i] :
( ( ! [SY836: $i] :
( ~ ( element @ SV209 @ ( powerset @ SV79 ) )
| ~ ( element @ SY836 @ ( powerset @ SV79 ) )
| ( element @ ( subset_difference @ SV79 @ SV209 @ SY836 ) @ ( powerset @ SV79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1131,plain,
! [SV80: $i] :
( ( ( ~ ( relation @ SV80 ) )
= $true )
| ( ( ! [SY587: $i] : ( relation @ ( relation_dom_restriction @ SV80 @ SY587 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[944]) ).
thf(1132,plain,
! [SV81: $i,SV210: $i] :
( ( ~ ( element @ SV210 @ ( powerset @ ( powerset @ SV81 ) ) )
| ( element @ ( complements_of_subsets @ SV81 @ SV210 ) @ ( powerset @ ( powerset @ SV81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1133,plain,
! [SV82: $i,SV211: $i] :
( ( ~ ( relation @ SV211 )
| ( relation @ ( relation_rng_restriction @ SV82 @ SV211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(1134,plain,
! [SV212: $i,SV84: $i] :
( ( ~ ( relation @ SV84 )
| ~ ( relation @ SV212 )
| ( relation @ ( set_intersection2 @ SV84 @ SV212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1135,plain,
! [SV85: $i] :
( ( empty @ ( powerset @ SV85 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[949]) ).
thf(1136,plain,
! [SV213: $i,SV86: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV86 @ SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1137,plain,
! [SV214: $i,SV87: $i] :
( ( ~ ( relation @ SV87 )
| ~ ( relation @ SV214 )
| ( relation @ ( set_union2 @ SV87 @ SV214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1138,plain,
! [SV88: $i] :
( ( empty @ ( singleton @ SV88 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[952]) ).
thf(1139,plain,
! [SV89: $i] :
( ( ( empty @ SV89 )
= $true )
| ( ( ! [SY593: $i] :
~ ( empty @ ( set_union2 @ SV89 @ SY593 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[953]) ).
thf(1140,plain,
! [SV215: $i,SV90: $i] :
( ( ~ ( empty @ ( unordered_pair @ SV90 @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1141,plain,
! [SV91: $i] :
( ( ( empty @ SV91 )
= $true )
| ( ( ! [SY595: $i] :
~ ( empty @ ( set_union2 @ SY595 @ SV91 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[955]) ).
thf(1142,plain,
! [SV216: $i,SV92: $i] :
( ( ( empty @ SV92 )
| ( empty @ SV216 )
| ~ ( empty @ ( cartesian_product2 @ SV92 @ SV216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1143,plain,
! [SV93: $i] :
( ( ( ( empty @ SV93 )
| ~ ( relation @ SV93 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV93 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[957]) ).
thf(1144,plain,
! [SV94: $i] :
( ( ( ( empty @ SV94 )
| ~ ( relation @ SV94 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV94 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[958]) ).
thf(1145,plain,
! [SV97: $i,SV217: $i] :
( ( ~ ( element @ SV217 @ ( powerset @ SV97 ) )
| ( ( subset_complement @ SV97 @ ( subset_complement @ SV97 @ SV217 ) )
= SV217 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1146,plain,
! [SV98: $i] :
( ( ( ~ ( relation @ SV98 ) )
= $true )
| ( ( ( relation_inverse @ ( relation_inverse @ SV98 ) )
= SV98 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[962]) ).
thf(1147,plain,
! [SV99: $i,SV218: $i] :
( ( ~ ( element @ SV218 @ ( powerset @ ( powerset @ SV99 ) ) )
| ( ( complements_of_subsets @ SV99 @ ( complements_of_subsets @ SV99 @ SV218 ) )
= SV218 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[963]) ).
thf(1148,plain,
! [SV100: $i,SV219: $i] :
( ( ~ ( element @ SV219 @ ( powerset @ ( powerset @ SV100 ) ) )
| ( ( union_of_subsets @ SV100 @ SV219 )
= ( union @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1149,plain,
! [SV101: $i,SV220: $i] :
( ( ~ ( element @ SV220 @ ( powerset @ ( powerset @ SV101 ) ) )
| ( ( meet_of_subsets @ SV101 @ SV220 )
= ( set_meet @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1150,plain,
! [SV102: $i,SV221: $i] :
( ( ! [SY837: $i] :
( ~ ( element @ SV221 @ ( powerset @ SV102 ) )
| ~ ( element @ SY837 @ ( powerset @ SV102 ) )
| ( ( subset_difference @ SV102 @ SV221 @ SY837 )
= ( set_difference @ SV221 @ SY837 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1151,plain,
! [SV222: $i,SV104: $i] :
( ( ~ ( disjoint @ SV104 @ SV222 )
| ( disjoint @ SV222 @ SV104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1152,plain,
! [SV109: $i,SV223: $i] :
( ( ! [SY838: $i] :
( ~ ( element @ SV223 @ ( powerset @ SY838 ) )
| ~ ( in @ SV109 @ SV223 )
| ~ ( empty @ SY838 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1153,plain,
! [SV110: $i] :
( ( ( ~ ( empty @ SV110 ) )
= $true )
| ( ( SV110 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[975]) ).
thf(1154,plain,
! [SV224: $i,SV111: $i] :
( ( ( SV111 = SV224 )
| ~ ( empty @ SV111 )
| ~ ( empty @ SV224 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1155,plain,
! [SV112: $i] :
( ( ~ ! [SY607: $i,SY608: $i] :
( ~ ( ~ ( ~ ( in @ ( sK49_D @ SY608 @ SY607 @ SV112 ) @ SV112 )
| ~ ( in @ ( sK49_D @ SY608 @ SY607 @ SV112 ) @ SY607 )
| ~ ( in @ ( sK49_D @ SY608 @ SY607 @ SV112 ) @ SY608 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_D @ SY608 @ SY607 @ SV112 ) @ SV112 )
| ( in @ ( sK49_D @ SY608 @ SY607 @ SV112 ) @ SY608 ) )
| ~ ( ( in @ ( sK49_D @ SY608 @ SY607 @ SV112 ) @ SY607 )
| ( in @ ( sK49_D @ SY608 @ SY607 @ SV112 ) @ SY608 ) ) ) )
| ( SY608
= ( set_intersection2 @ SV112 @ SY607 ) ) )
| ~ ! [SY609: $i,SY610: $i] :
( ( SY610
!= ( set_intersection2 @ SV112 @ SY609 ) )
| ~ ( ~ ! [SY611: $i] :
( ~ ( in @ SY611 @ SV112 )
| ~ ( in @ SY611 @ SY609 )
| ( in @ SY611 @ SY610 ) )
| ~ ~ ( ~ ! [SY612: $i] :
( ~ ( in @ SY612 @ SY610 )
| ( in @ SY612 @ SV112 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY610 )
| ( in @ SX3 @ SY609 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[978]) ).
thf(1156,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK47_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK47_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK47_C @ SX1 @ SX0 ) @ ( sK48_SY487 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK48_SY487 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK47_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[979]) ).
thf(1157,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK46_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK46_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[979]) ).
thf(1158,plain,
! [SV113: $i,SV225: $i] :
( ( ~ ( relation @ SV225 )
| ~ ( ~ ! [SY839: $i] :
( ~ ( relation @ SY839 )
| ~ ( ~ ( ~ ( in @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) @ SV113 )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ SY839 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) ) @ SV225 )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ SY839 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) ) @ SY839 ) )
| ~ ~ ( ~ ( ( in @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) @ SV113 )
| ( in @ ( ordered_pair @ ( sK32_D @ SY839 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) ) @ SY839 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_D @ SY839 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) ) @ SV225 )
| ( in @ ( ordered_pair @ ( sK32_D @ SY839 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) ) @ SY839 ) ) ) )
| ( SY839
= ( relation_rng_restriction @ SV113 @ SV225 ) ) )
| ~ ! [SY840: $i] :
( ~ ( relation @ SY840 )
| ( SY840
!= ( relation_rng_restriction @ SV113 @ SV225 ) )
| ~ ( ~ ! [SY841: $i,SY842: $i] :
( ~ ( in @ SY842 @ SV113 )
| ~ ( in @ ( ordered_pair @ SY841 @ SY842 ) @ SV225 )
| ( in @ ( ordered_pair @ SY841 @ SY842 ) @ SY840 ) )
| ~ ~ ( ~ ! [SY619: $i,SY620: $i] :
( ~ ( in @ ( ordered_pair @ SY619 @ SY620 ) @ SY840 )
| ( in @ SY620 @ SV113 ) )
| ~ ! [SY845: $i,SY846: $i] :
( ~ ( in @ ( ordered_pair @ SY845 @ SY846 ) @ SY840 )
| ( in @ ( ordered_pair @ SY845 @ SY846 ) @ SV225 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1159,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[981]) ).
thf(1160,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[981]) ).
thf(1161,plain,
( ( ~ ( relation @ sK3_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[982]) ).
thf(1162,plain,
( ( ~ ( relation_empty_yielding @ sK3_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[982]) ).
thf(1163,plain,
! [SV226: $i,SV114: $i] :
( ( ~ ( ~ ! [SY847: $i,SY848: $i] :
( ~ ( in @ SV114 @ SY847 )
| ~ ( in @ SV226 @ SY848 )
| ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SY847 @ SY848 ) ) )
| ~ ~ ( ~ ! [SY849: $i] :
( ! [SY850: $i] :
~ ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SY849 @ SY850 ) )
| ( in @ SV114 @ SY849 ) )
| ~ ! [SY851: $i,SY852: $i] :
( ~ ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SY851 @ SY852 ) )
| ( in @ SV226 @ SY852 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1164,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK72_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK72_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[984]) ).
thf(1165,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[984]) ).
thf(1166,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK62_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK62_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK62_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK62_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[985]) ).
thf(1167,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[985]) ).
thf(1168,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK61_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[986]) ).
thf(1169,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[986]) ).
thf(1170,plain,
! [SV115: $i] :
( ( ~ ! [SY630: $i] :
( ~ ( subset @ SY630 @ ( sK42_B @ SV115 ) )
| ( are_equipotent @ SY630 @ ( sK42_B @ SV115 ) )
| ( in @ SY630 @ ( sK42_B @ SV115 ) ) )
| ~ ~ ( ~ ! [SY631: $i] :
( ~ ( ~ ! [SY632: $i] :
( ~ ( subset @ SY632 @ SY631 )
| ( in @ SY632 @ ( sK43_SY481 @ SY631 @ SV115 ) ) )
| ~ ( in @ ( sK43_SY481 @ SY631 @ SV115 ) @ ( sK42_B @ SV115 ) ) )
| ~ ( in @ SY631 @ ( sK42_B @ SV115 ) ) )
| ~ ~ ( ~ ! [SY633: $i,SY634: $i] :
( ~ ( in @ SY633 @ ( sK42_B @ SV115 ) )
| ~ ( subset @ SY634 @ SY633 )
| ( in @ SY634 @ ( sK42_B @ SV115 ) ) )
| ~ ( in @ SV115 @ ( sK42_B @ SV115 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[987]) ).
thf(1171,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[988]) ).
thf(1172,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[988]) ).
thf(1173,plain,
! [SV116: $i] :
( ( ( ~ ( function @ SV116 )
| ~ ( relation @ SV116 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY635: $i] :
( ~ ( in @ SY635 @ ( relation_dom @ SV116 ) )
| ! [SY636: $i] :
( ( SY636
!= ( apply @ SV116 @ SY635 ) )
| ( in @ ( ordered_pair @ SY635 @ SY636 ) @ SV116 ) ) )
| ~ ! [SY637: $i] :
( ~ ( in @ SY637 @ ( relation_dom @ SV116 ) )
| ! [SY638: $i] :
( ~ ( in @ ( ordered_pair @ SY637 @ SY638 ) @ SV116 )
| ( SY638
= ( apply @ SV116 @ SY637 ) ) ) ) )
| ~ ~ ( ~ ! [SY639: $i] :
( ( in @ SY639 @ ( relation_dom @ SV116 ) )
| ! [SY640: $i] :
( ( SY640
!= ( apply @ SV116 @ SY639 ) )
| ( SY640 = empty_set ) ) )
| ~ ! [SY641: $i] :
( ( in @ SY641 @ ( relation_dom @ SV116 ) )
| ! [SY642: $i] :
( ( SY642 != empty_set )
| ( SY642
= ( apply @ SV116 @ SY641 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[989]) ).
thf(1174,plain,
! [SV117: $i] :
( ( ~ ! [SY643: $i,SY644: $i] :
( ~ ( ~ ( ! [SY645: $i,SY646: $i] :
( ~ ( in @ SY645 @ SV117 )
| ~ ( in @ SY646 @ SY643 )
| ( ( sK53_D @ SY644 @ SY643 @ SV117 )
!= ( ordered_pair @ SY645 @ SY646 ) ) )
| ~ ( in @ ( sK53_D @ SY644 @ SY643 @ SV117 ) @ SY644 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK54_SY491 @ SY644 @ SY643 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK55_SY493 @ SY644 @ SY643 @ SV117 ) @ SY643 ) )
| ( ( sK53_D @ SY644 @ SY643 @ SV117 )
!= ( ordered_pair @ ( sK54_SY491 @ SY644 @ SY643 @ SV117 ) @ ( sK55_SY493 @ SY644 @ SY643 @ SV117 ) ) ) )
| ( in @ ( sK53_D @ SY644 @ SY643 @ SV117 ) @ SY644 ) ) )
| ( SY644
= ( cartesian_product2 @ SV117 @ SY643 ) ) )
| ~ ! [SY647: $i,SY648: $i] :
( ( SY648
!= ( cartesian_product2 @ SV117 @ SY647 ) )
| ~ ( ~ ! [SY649: $i] :
( ! [SY650: $i,SY651: $i] :
( ~ ( in @ SY650 @ SV117 )
| ~ ( in @ SY651 @ SY647 )
| ( SY649
!= ( ordered_pair @ SY650 @ SY651 ) ) )
| ( in @ SY649 @ SY648 ) )
| ~ ! [SY652: $i] :
( ~ ( in @ SY652 @ SY648 )
| ~ ( ~ ~ ( ~ ( in @ ( sK51_E @ SY652 @ SY648 @ SY647 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK52_SY488 @ SY652 @ SY648 @ SY647 @ SV117 ) @ SY647 ) )
| ( SY652
!= ( ordered_pair @ ( sK51_E @ SY652 @ SY648 @ SY647 @ SV117 ) @ ( sK52_SY488 @ SY652 @ SY648 @ SY647 @ SV117 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[990]) ).
thf(1175,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[991]) ).
thf(1176,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[991]) ).
thf(1177,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( ( relation_rng @ SX0 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[992]) ).
thf(1178,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( ( relation_dom @ SX0 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[992]) ).
thf(1179,plain,
( ( ~ ( function @ sK10_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[993]) ).
thf(1180,plain,
( ( ~ ( relation @ sK10_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[993]) ).
thf(1181,plain,
! [SV118: $i] :
( ( ~ ! [SY653: $i,SY654: $i] :
( ~ ( function @ SY654 )
| ~ ( relation @ SY654 )
| ( SY653
!= ( apply @ SY654 @ SV118 ) )
| ~ ( in @ SV118 @ ( relation_dom @ SY654 ) )
| ( in @ ( ordered_pair @ SV118 @ SY653 ) @ SY654 ) )
| ~ ~ ( ~ ! [SY655: $i,SY656: $i] :
( ~ ( function @ SY656 )
| ~ ( relation @ SY656 )
| ~ ( in @ ( ordered_pair @ SV118 @ SY655 ) @ SY656 )
| ( SY655
= ( apply @ SY656 @ SV118 ) ) )
| ~ ! [SY657: $i,SY658: $i] :
( ~ ( function @ SY658 )
| ~ ( relation @ SY658 )
| ~ ( in @ ( ordered_pair @ SV118 @ SY657 ) @ SY658 )
| ( in @ SV118 @ ( relation_dom @ SY658 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[994]) ).
thf(1182,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[995]) ).
thf(1183,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[995]) ).
thf(1184,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK69_C @ SX1 @ SX0 )
!= ( sK70_SY500 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK69_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK69_C @ SX1 @ SX0 ) @ ( sK70_SY500 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK69_C @ SX1 @ SX0 )
= ( sK70_SY500 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK69_C @ SX1 @ SX0 ) @ ( sK70_SY500 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK69_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK69_C @ SX1 @ SX0 ) @ ( sK70_SY500 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[996]) ).
thf(1185,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)],[996]) ).
thf(1186,plain,
! [SV119: $i] :
( ( ~ ( element @ ( sK5_B @ SV119 ) @ ( powerset @ SV119 ) )
| ~ ( empty @ ( sK5_B @ SV119 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[997]) ).
thf(1187,plain,
! [SV120: $i] :
( ( ( ~ ( relation @ SV120 ) )
= $true )
| ( ( ! [SY659: $i] :
( ~ ( relation @ SY659 )
| ~ ( ~ ! [SY660: $i] :
( ~ ( relation @ SY660 )
| ~ ( ~ ( ! [SY661: $i] :
( ~ ( in @ ( ordered_pair @ ( sK13_D @ SY660 @ SY659 @ SV120 ) @ SY661 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY661 @ ( sK14_SY457 @ SY660 @ SY659 @ SV120 ) ) @ SY659 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_D @ SY660 @ SY659 @ SV120 ) @ ( sK14_SY457 @ SY660 @ SY659 @ SV120 ) ) @ SY660 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_D @ SY660 @ SY659 @ SV120 ) @ ( sK15_SY461 @ SY660 @ SY659 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY461 @ SY660 @ SY659 @ SV120 ) @ ( sK14_SY457 @ SY660 @ SY659 @ SV120 ) ) @ SY659 ) )
| ( in @ ( ordered_pair @ ( sK13_D @ SY660 @ SY659 @ SV120 ) @ ( sK14_SY457 @ SY660 @ SY659 @ SV120 ) ) @ SY660 ) ) )
| ( SY660
= ( relation_composition @ SV120 @ SY659 ) ) )
| ~ ! [SY662: $i] :
( ~ ( relation @ SY662 )
| ( SY662
!= ( relation_composition @ SV120 @ SY659 ) )
| ~ ( ~ ! [SY663: $i,SY664: $i] :
( ! [SY665: $i] :
( ~ ( in @ ( ordered_pair @ SY663 @ SY665 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY665 @ SY664 ) @ SY659 ) )
| ( in @ ( ordered_pair @ SY663 @ SY664 ) @ SY662 ) )
| ~ ! [SY666: $i,SY667: $i] :
( ~ ( in @ ( ordered_pair @ SY666 @ SY667 ) @ SY662 )
| ~ ( ~ ( in @ ( ordered_pair @ SY666 @ ( sK12_F @ SY667 @ SY666 @ SY662 @ SY659 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK12_F @ SY667 @ SY666 @ SY662 @ SY659 @ SV120 ) @ SY667 ) @ SY659 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[998]) ).
thf(1188,plain,
! [SV121: $i,SV227: $i] :
( ( ~ ( element @ SV227 @ ( powerset @ SV121 ) )
| ~ ( ~ ! [SY853: $i] :
( ~ ( element @ SY853 @ ( powerset @ SV121 ) )
| ~ ( disjoint @ SV227 @ SY853 )
| ( subset @ SV227 @ ( subset_complement @ SV121 @ SY853 ) ) )
| ~ ! [SY854: $i] :
( ~ ( element @ SY854 @ ( powerset @ SV121 ) )
| ~ ( subset @ SV227 @ ( subset_complement @ SV121 @ SY854 ) )
| ( disjoint @ SV227 @ SY854 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1189,plain,
! [SV122: $i] :
( ( ~ ! [SY671: $i,SY672: $i] :
( ~ ( relation @ SY672 )
| ~ ( in @ SV122 @ SY671 )
| ~ ( in @ SV122 @ ( relation_rng @ SY672 ) )
| ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SY671 @ SY672 ) ) ) )
| ~ ~ ( ~ ! [SY673: $i,SY674: $i] :
( ~ ( relation @ SY674 )
| ~ ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SY673 @ SY674 ) ) )
| ( in @ SV122 @ SY673 ) )
| ~ ! [SY675: $i,SY676: $i] :
( ~ ( relation @ SY676 )
| ~ ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SY675 @ SY676 ) ) )
| ( in @ SV122 @ ( relation_rng @ SY676 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1000]) ).
thf(1190,plain,
! [SV123: $i] :
( ( ( ~ ( relation @ SV123 ) )
= $true )
| ( ( ~ ( ~ ! [SY677: $i,SY678: $i] :
( ~ ( relation @ SY678 )
| ~ ( ~ ( ~ ( in @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ SY677 )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ ( sK35_SY473 @ SY678 @ SY677 @ SV123 ) ) @ SV123 )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ ( sK35_SY473 @ SY678 @ SY677 @ SV123 ) ) @ SY678 ) )
| ~ ~ ( ~ ( ( in @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ SY677 )
| ( in @ ( ordered_pair @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ ( sK35_SY473 @ SY678 @ SY677 @ SV123 ) ) @ SY678 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ ( sK35_SY473 @ SY678 @ SY677 @ SV123 ) ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ ( sK35_SY473 @ SY678 @ SY677 @ SV123 ) ) @ SY678 ) ) ) )
| ( SY678
= ( relation_dom_restriction @ SV123 @ SY677 ) ) )
| ~ ! [SY679: $i,SY680: $i] :
( ~ ( relation @ SY680 )
| ( SY680
!= ( relation_dom_restriction @ SV123 @ SY679 ) )
| ~ ( ~ ! [SY681: $i,SY682: $i] :
( ~ ( in @ SY681 @ SY679 )
| ~ ( in @ ( ordered_pair @ SY681 @ SY682 ) @ SV123 )
| ( in @ ( ordered_pair @ SY681 @ SY682 ) @ SY680 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY680 )
| ( in @ SX3 @ SY679 ) )
| ~ ! [SY685: $i,SY686: $i] :
( ~ ( in @ ( ordered_pair @ SY685 @ SY686 ) @ SY680 )
| ( in @ ( ordered_pair @ SY685 @ SY686 ) @ SV123 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1001]) ).
thf(1191,plain,
! [SV124: $i] :
( ( ( ~ ( relation @ SV124 ) )
= $true )
| ( ( ~ ( ~ ! [SY687: $i] :
( ~ ( relation @ SY687 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_C @ SY687 @ SV124 ) @ ( sK17_SY462 @ SY687 @ SV124 ) ) @ SY687 )
| ~ ( in @ ( ordered_pair @ ( sK17_SY462 @ SY687 @ SV124 ) @ ( sK16_C @ SY687 @ SV124 ) ) @ SV124 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK16_C @ SY687 @ SV124 ) @ ( sK17_SY462 @ SY687 @ SV124 ) ) @ SY687 )
| ( in @ ( ordered_pair @ ( sK17_SY462 @ SY687 @ SV124 ) @ ( sK16_C @ SY687 @ SV124 ) ) @ SV124 ) ) )
| ( SY687
= ( relation_inverse @ SV124 ) ) )
| ~ ! [SY688: $i] :
( ~ ( relation @ SY688 )
| ( SY688
!= ( relation_inverse @ SV124 ) )
| ~ ( ~ ! [SY689: $i,SY690: $i] :
( ~ ( in @ ( ordered_pair @ SY689 @ SY690 ) @ SY688 )
| ( in @ ( ordered_pair @ SY690 @ SY689 ) @ SV124 ) )
| ~ ! [SY691: $i,SY692: $i] :
( ~ ( in @ ( ordered_pair @ SY692 @ SY691 ) @ SV124 )
| ( in @ ( ordered_pair @ SY691 @ SY692 ) @ SY688 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1002]) ).
thf(1192,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1003]) ).
thf(1193,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1003]) ).
thf(1194,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1004]) ).
thf(1195,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1004]) ).
thf(1196,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1005]) ).
thf(1197,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1005]) ).
thf(1198,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK38_C @ SX1 @ SX0 ) )
!= ( sK38_C @ SX1 @ SX0 ) ) ) )
| ( ( relation_dom @ SX1 )
!= SX0 )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1006]) ).
thf(1199,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)],[1006]) ).
thf(1200,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1007]) ).
thf(1201,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1007]) ).
thf(1202,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1008]) ).
thf(1203,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1008]) ).
thf(1204,plain,
! [SV125: $i] :
( ( ( ~ ( relation @ SV125 ) )
= $true )
| ( ( ~ ( ~ ! [SY693: $i,SY694: $i] :
( ~ ( ~ ( ! [SY695: $i] :
( ~ ( in @ ( ordered_pair @ SY695 @ ( sK30_D @ SY694 @ SY693 @ SV125 ) ) @ SV125 )
| ~ ( in @ SY695 @ SY693 ) )
| ~ ( in @ ( sK30_D @ SY694 @ SY693 @ SV125 ) @ SY694 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_SY471 @ SY694 @ SY693 @ SV125 ) @ ( sK30_D @ SY694 @ SY693 @ SV125 ) ) @ SV125 )
| ~ ( in @ ( sK31_SY471 @ SY694 @ SY693 @ SV125 ) @ SY693 ) )
| ( in @ ( sK30_D @ SY694 @ SY693 @ SV125 ) @ SY694 ) ) )
| ( SY694
= ( relation_image @ SV125 @ SY693 ) ) )
| ~ ! [SY696: $i,SY697: $i] :
( ( SY697
!= ( relation_image @ SV125 @ SY696 ) )
| ~ ( ~ ! [SY698: $i] :
( ! [SY699: $i] :
( ~ ( in @ ( ordered_pair @ SY699 @ SY698 ) @ SV125 )
| ~ ( in @ SY699 @ SY696 ) )
| ( in @ SY698 @ SY697 ) )
| ~ ! [SY700: $i] :
( ~ ( in @ SY700 @ SY697 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK29_E @ SY700 @ SY697 @ SY696 @ SV125 ) @ SY700 ) @ SV125 )
| ~ ( in @ ( sK29_E @ SY700 @ SY697 @ SY696 @ SV125 ) @ SY696 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1009]) ).
thf(1205,plain,
! [SV126: $i] :
( ( ~ ! [SY701: $i,SY702: $i] :
( ~ ( relation @ SY702 )
| ~ ( in @ ( ordered_pair @ SV126 @ SY701 ) @ SY702 )
| ( in @ SV126 @ ( relation_field @ SY702 ) ) )
| ~ ! [SY703: $i,SY704: $i] :
( ~ ( relation @ SY704 )
| ~ ( in @ ( ordered_pair @ SV126 @ SY703 ) @ SY704 )
| ( in @ SY703 @ ( relation_field @ SY704 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1010]) ).
thf(1206,plain,
! [SV228: $i,SV127: $i] :
( ( ~ ( ~ ! [SY855: $i,SY856: $i] :
( ~ ( relation @ SY856 )
| ~ ( in @ SV127 @ SY855 )
| ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ SY856 )
| ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SY855 ) @ SY856 ) ) )
| ~ ~ ( ~ ! [SY857: $i,SY858: $i] :
( ~ ( relation @ SY858 )
| ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SY857 ) @ SY858 ) )
| ( in @ SV127 @ SY857 ) )
| ~ ! [SY859: $i,SY860: $i] :
( ~ ( relation @ SY860 )
| ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SY859 ) @ SY860 ) )
| ( in @ ( ordered_pair @ SV127 @ SV228 ) @ SY860 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1207,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1012]) ).
thf(1208,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1012]) ).
thf(1209,plain,
! [SV128: $i] :
( ( ~ ! [SY712: $i,SY713: $i] :
( ~ ( in @ SV128 @ SY713 )
| ~ ( in @ SY712 @ SY713 )
| ( subset @ ( unordered_pair @ SV128 @ SY712 ) @ SY713 ) )
| ~ ~ ( ~ ! [SY714: $i,SY715: $i] :
( ~ ( subset @ ( unordered_pair @ SV128 @ SY714 ) @ SY715 )
| ( in @ SV128 @ SY715 ) )
| ~ ! [SY716: $i,SY717: $i] :
( ~ ( subset @ ( unordered_pair @ SV128 @ SY716 ) @ SY717 )
| ( in @ SY716 @ SY717 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1013]) ).
thf(1210,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1014]) ).
thf(1211,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1014]) ).
thf(1212,plain,
( ( ~ ( empty @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1015]) ).
thf(1213,plain,
( ( ~ ( relation @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1015]) ).
thf(1214,plain,
! [SV129: $i] :
( ( ( ~ ( relation @ SV129 ) )
= $true )
| ( ( ~ ( ~ ! [SY718: $i] :
( ~ ( ~ ( ! [SY719: $i] :
~ ( in @ ( ordered_pair @ SY719 @ ( sK19_C @ SY718 @ SV129 ) ) @ SV129 )
| ~ ( in @ ( sK19_C @ SY718 @ SV129 ) @ SY718 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_SY464 @ SY718 @ SV129 ) @ ( sK19_C @ SY718 @ SV129 ) ) @ SV129 )
| ( in @ ( sK19_C @ SY718 @ SV129 ) @ SY718 ) ) )
| ( SY718
= ( relation_rng @ SV129 ) ) )
| ~ ! [SY720: $i] :
( ( SY720
!= ( relation_rng @ SV129 ) )
| ~ ( ~ ! [SY721: $i] :
( ! [SY722: $i] :
~ ( in @ ( ordered_pair @ SY722 @ SY721 ) @ SV129 )
| ( in @ SY721 @ SY720 ) )
| ~ ! [SY723: $i] :
( ~ ( in @ SY723 @ SY720 )
| ( in @ ( ordered_pair @ ( sK18_D @ SY723 @ SY720 @ SV129 ) @ SY723 ) @ SV129 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1016]) ).
thf(1215,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1017]) ).
thf(1216,plain,
( ( ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1017]) ).
thf(1217,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1018]) ).
thf(1218,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1018]) ).
thf(1219,plain,
( ( ~ ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1019]) ).
thf(1220,plain,
( ( ~ ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1019]) ).
thf(1221,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK71_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1020]) ).
thf(1222,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1020]) ).
thf(1223,plain,
! [SV130: $i,SV229: $i] :
( ( ~ ( ~ ( in @ ( sK73_C @ SV229 @ SV130 ) @ SV130 )
| ~ ~ ( in @ ( sK73_C @ SV229 @ SV130 ) @ SV229 ) )
| ( element @ SV130 @ ( powerset @ SV229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1224,plain,
! [SV131: $i] :
( ( ( ~ ( relation @ SV131 ) )
= $true )
| ( ( ~ ( ~ ! [SY725: $i,SY726: $i] :
( ~ ( ~ ( ! [SY727: $i] :
( ~ ( in @ ( ordered_pair @ ( sK27_D @ SY726 @ SY725 @ SV131 ) @ SY727 ) @ SV131 )
| ~ ( in @ SY727 @ SY725 ) )
| ~ ( in @ ( sK27_D @ SY726 @ SY725 @ SV131 ) @ SY726 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK27_D @ SY726 @ SY725 @ SV131 ) @ ( sK28_SY469 @ SY726 @ SY725 @ SV131 ) ) @ SV131 )
| ~ ( in @ ( sK28_SY469 @ SY726 @ SY725 @ SV131 ) @ SY725 ) )
| ( in @ ( sK27_D @ SY726 @ SY725 @ SV131 ) @ SY726 ) ) )
| ( SY726
= ( relation_inverse_image @ SV131 @ SY725 ) ) )
| ~ ! [SY728: $i,SY729: $i] :
( ( SY729
!= ( relation_inverse_image @ SV131 @ SY728 ) )
| ~ ( ~ ! [SY730: $i] :
( ! [SY731: $i] :
( ~ ( in @ ( ordered_pair @ SY730 @ SY731 ) @ SV131 )
| ~ ( in @ SY731 @ SY728 ) )
| ( in @ SY730 @ SY729 ) )
| ~ ! [SY732: $i] :
( ~ ( in @ SY732 @ SY729 )
| ~ ( ~ ( in @ ( ordered_pair @ SY732 @ ( sK26_E @ SY732 @ SY729 @ SY728 @ SV131 ) ) @ SV131 )
| ~ ( in @ ( sK26_E @ SY732 @ SY729 @ SY728 @ SV131 ) @ SY728 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1022]) ).
thf(1225,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1023]) ).
thf(1226,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1023]) ).
thf(1227,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK68_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK68_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1024]) ).
thf(1228,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK66_C @ SX1 @ SX0 ) @ ( sK67_SY497 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1024]) ).
thf(1229,plain,
! [SV132: $i] :
( ( ~ ! [SY733: $i,SY734: $i] :
( ~ ( relation @ SY734 )
| ~ ( in @ SV132 @ SY733 )
| ~ ( in @ SV132 @ ( relation_dom @ SY734 ) )
| ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SY734 @ SY733 ) ) ) )
| ~ ~ ( ~ ! [SY735: $i,SY736: $i] :
( ~ ( relation @ SY736 )
| ~ ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SY736 @ SY735 ) ) )
| ( in @ SV132 @ SY735 ) )
| ~ ! [SY737: $i,SY738: $i] :
( ~ ( relation @ SY738 )
| ~ ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SY738 @ SY737 ) ) )
| ( in @ SV132 @ ( relation_dom @ SY738 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1025]) ).
thf(1230,plain,
! [SV133: $i] :
( ( ~ ! [SY739: $i,SY740: $i] :
( ~ ( relation @ SY740 )
| ~ ( in @ ( ordered_pair @ SV133 @ SY739 ) @ SY740 )
| ( in @ SV133 @ ( relation_dom @ SY740 ) ) )
| ~ ! [SY741: $i,SY742: $i] :
( ~ ( relation @ SY742 )
| ~ ( in @ ( ordered_pair @ SV133 @ SY741 ) @ SY742 )
| ( in @ SY741 @ ( relation_rng @ SY742 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1026]) ).
thf(1231,plain,
! [SV134: $i] :
( ( ( ~ ( relation @ SV134 ) )
= $true )
| ( ( ~ ( ~ ! [SY743: $i] :
( ~ ( ~ ( ! [SY744: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SY743 @ SV134 ) @ SY744 ) @ SV134 )
| ~ ( in @ ( sK22_C @ SY743 @ SV134 ) @ SY743 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SY743 @ SV134 ) @ ( sK23_SY466 @ SY743 @ SV134 ) ) @ SV134 )
| ( in @ ( sK22_C @ SY743 @ SV134 ) @ SY743 ) ) )
| ( SY743
= ( relation_dom @ SV134 ) ) )
| ~ ! [SY745: $i] :
( ( SY745
!= ( relation_dom @ SV134 ) )
| ~ ( ~ ! [SY746: $i] :
( ! [SY747: $i] :
~ ( in @ ( ordered_pair @ SY746 @ SY747 ) @ SV134 )
| ( in @ SY746 @ SY745 ) )
| ~ ! [SY748: $i] :
( ~ ( in @ SY748 @ SY745 )
| ( in @ ( ordered_pair @ SY748 @ ( sK21_D @ SY748 @ SY745 @ SV134 ) ) @ SV134 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1027]) ).
thf(1232,plain,
! [SV135: $i] :
( ( ~ ! [SY749: $i,SY750: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK57_D @ SY750 @ SY749 @ SV135 ) @ SY750 )
| ( ( sK57_D @ SY750 @ SY749 @ SV135 )
!= SV135 ) )
| ~ ( ~ ( in @ ( sK57_D @ SY750 @ SY749 @ SV135 ) @ SY750 )
| ( ( sK57_D @ SY750 @ SY749 @ SV135 )
!= SY749 ) ) )
| ~ ( ( in @ ( sK57_D @ SY750 @ SY749 @ SV135 ) @ SY750 )
| ( ( sK57_D @ SY750 @ SY749 @ SV135 )
= SV135 )
| ( ( sK57_D @ SY750 @ SY749 @ SV135 )
= SY749 ) ) )
| ( SY750
= ( unordered_pair @ SV135 @ SY749 ) ) )
| ~ ! [SY751: $i,SY752: $i] :
( ( SY752
!= ( unordered_pair @ SV135 @ SY751 ) )
| ~ ( ~ ! [SY753: $i] :
( ~ ( in @ SY753 @ SY752 )
| ( SY753 = SV135 )
| ( SY753 = SY751 ) )
| ~ ~ ( ~ ! [SY754: $i] :
( ( SY754 != SV135 )
| ( in @ SY754 @ SY752 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY751 )
| ( in @ SX3 @ SY752 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1028]) ).
thf(1233,plain,
( ( ( ( relation_dom @ empty_set )
!= empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1029]) ).
thf(1234,plain,
( ( ( ( relation_rng @ empty_set )
!= empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1029]) ).
thf(1235,plain,
! [SV136: $i] :
( ( ( ~ ( relation @ SV136 ) )
= $true )
| ( ( ~ ( ~ ! [SY756: $i] :
( ~ ( relation @ SY756 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK58_C @ SY756 @ SV136 ) @ ( sK59_SY494 @ SY756 @ SV136 ) ) @ SV136 )
| ~ ( in @ ( ordered_pair @ ( sK58_C @ SY756 @ SV136 ) @ ( sK59_SY494 @ SY756 @ SV136 ) ) @ SY756 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_C @ SY756 @ SV136 ) @ ( sK59_SY494 @ SY756 @ SV136 ) ) @ SV136 )
| ( in @ ( ordered_pair @ ( sK58_C @ SY756 @ SV136 ) @ ( sK59_SY494 @ SY756 @ SV136 ) ) @ SY756 ) ) )
| ( SV136 = SY756 ) )
| ~ ! [SY757: $i] :
( ~ ( relation @ SY757 )
| ( SV136 != SY757 )
| ~ ( ~ ! [SY758: $i,SY759: $i] :
( ~ ( in @ ( ordered_pair @ SY758 @ SY759 ) @ SV136 )
| ( in @ ( ordered_pair @ SY758 @ SY759 ) @ SY757 ) )
| ~ ! [SY760: $i,SY761: $i] :
( ~ ( in @ ( ordered_pair @ SY760 @ SY761 ) @ SY757 )
| ( in @ ( ordered_pair @ SY760 @ SY761 ) @ SV136 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1030]) ).
thf(1236,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)],[1031]) ).
thf(1237,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)],[1031]) ).
thf(1238,plain,
! [SV137: $i,SV230: $i] :
( ( ~ ( function @ SV230 )
| ~ ( relation @ SV230 )
| ~ ( ~ ! [SY861: $i] :
( ~ ( function @ SY861 )
| ~ ( relation @ SY861 )
| ~ ( in @ SV137 @ ( relation_dom @ SY861 ) )
| ~ ( in @ ( apply @ SY861 @ SV137 ) @ ( relation_dom @ SV230 ) )
| ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY861 @ SV230 ) ) ) )
| ~ ~ ( ~ ! [SY862: $i] :
( ~ ( function @ SY862 )
| ~ ( relation @ SY862 )
| ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY862 @ SV230 ) ) )
| ( in @ SV137 @ ( relation_dom @ SY862 ) ) )
| ~ ! [SY863: $i] :
( ~ ( function @ SY863 )
| ~ ( relation @ SY863 )
| ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY863 @ SV230 ) ) )
| ( in @ ( apply @ SY863 @ SV137 ) @ ( relation_dom @ SV230 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1239,plain,
! [SV138: $i] :
( ( ~ ! [SY766: $i] :
( ~ ( subset @ SY766 @ ( sK41_B @ SV138 ) )
| ( are_equipotent @ SY766 @ ( sK41_B @ SV138 ) )
| ( in @ SY766 @ ( sK41_B @ SV138 ) ) )
| ~ ~ ( ~ ! [SY767: $i] :
( ~ ( in @ SY767 @ ( sK41_B @ SV138 ) )
| ( in @ ( powerset @ SY767 ) @ ( sK41_B @ SV138 ) ) )
| ~ ~ ( ~ ! [SY768: $i,SY769: $i] :
( ~ ( in @ SY768 @ ( sK41_B @ SV138 ) )
| ~ ( subset @ SY769 @ SY768 )
| ( in @ SY769 @ ( sK41_B @ SV138 ) ) )
| ~ ( in @ SV138 @ ( sK41_B @ SV138 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1033]) ).
thf(1240,plain,
! [SV139: $i] :
( ( ( ~ ( relation @ SV139 ) )
= $true )
| ( ( ~ ( ~ ! [SY770: $i] :
( ~ ( relation @ SY770 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SY770 @ SV139 ) @ ( sK25_SY467 @ SY770 @ SV139 ) ) @ SV139 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SY770 @ SV139 ) @ ( sK25_SY467 @ SY770 @ SV139 ) ) @ SY770 ) )
| ( subset @ SV139 @ SY770 ) )
| ~ ! [SY771: $i] :
( ~ ( relation @ SY771 )
| ~ ( subset @ SV139 @ SY771 )
| ! [SY772: $i,SY773: $i] :
( ~ ( in @ ( ordered_pair @ SY772 @ SY773 ) @ SV139 )
| ( in @ ( ordered_pair @ SY772 @ SY773 ) @ SY771 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1034]) ).
thf(1241,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK60_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK60_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK60_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK60_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1035]) ).
thf(1242,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1035]) ).
thf(1243,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1036]) ).
thf(1244,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1036]) ).
thf(1245,plain,
! [SV140: $i] :
( ( ( ~ ( relation @ SV140 ) )
= $true )
| ( ( ~ ( ~ ! [SY774: $i] :
( ~ ( relation @ SY774 )
| ~ ( subset @ SV140 @ SY774 )
| ( subset @ ( relation_dom @ SV140 ) @ ( relation_dom @ SY774 ) ) )
| ~ ! [SY775: $i] :
( ~ ( relation @ SY775 )
| ~ ( subset @ SV140 @ SY775 )
| ( subset @ ( relation_rng @ SV140 ) @ ( relation_rng @ SY775 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1037]) ).
thf(1246,plain,
! [SV141: $i] :
( ( ( empty @ SV141 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK8_B @ SV141 ) @ ( powerset @ SV141 ) )
| ~ ~ ( empty @ ( sK8_B @ SV141 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1038]) ).
thf(1247,plain,
! [SV142: $i] :
( ( ~ ! [SY776: $i,SY777: $i] :
( ~ ( relation @ SY777 )
| ! [SY778: $i] :
( ~ ( in @ SY778 @ ( relation_rng @ SY777 ) )
| ~ ( in @ ( ordered_pair @ SV142 @ SY778 ) @ SY777 )
| ~ ( in @ SY778 @ SY776 ) )
| ( in @ SV142 @ ( relation_inverse_image @ SY777 @ SY776 ) ) )
| ~ ! [SY779: $i,SY780: $i] :
( ~ ( relation @ SY780 )
| ~ ( in @ SV142 @ ( relation_inverse_image @ SY780 @ SY779 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK39_D @ SY780 @ SY779 @ SV142 ) @ ( relation_rng @ SY780 ) )
| ~ ( in @ ( ordered_pair @ SV142 @ ( sK39_D @ SY780 @ SY779 @ SV142 ) ) @ SY780 ) )
| ~ ( in @ ( sK39_D @ SY780 @ SY779 @ SV142 ) @ SY779 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1039]) ).
thf(1248,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK65_SY495 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK64_C @ SX1 @ SX0 ) @ ( sK65_SY495 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK64_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK64_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK64_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK63_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK63_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1040]) ).
thf(1249,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1040]) ).
thf(1250,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1041]) ).
thf(1251,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1041]) ).
thf(1252,plain,
( ( ~ ! [SX0: $i] :
( ( relation_dom @ ( identity_relation @ SX0 ) )
= SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1042]) ).
thf(1253,plain,
( ( ~ ! [SX0: $i] :
( ( relation_rng @ ( identity_relation @ SX0 ) )
= SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1042]) ).
thf(1254,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1043]) ).
thf(1255,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1043]) ).
thf(1256,plain,
! [SV231: $i,SV143: $i] :
( ( ~ ( ~ ! [SY864: $i,SY865: $i] :
( ~ ( in @ SV143 @ SY864 )
| ~ ( in @ SV231 @ SY865 )
| ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SY864 @ SY865 ) ) )
| ~ ~ ( ~ ! [SY866: $i] :
( ! [SY867: $i] :
~ ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SY866 @ SY867 ) )
| ( in @ SV143 @ SY866 ) )
| ~ ! [SY868: $i,SY869: $i] :
( ~ ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SY868 @ SY869 ) )
| ( in @ SV231 @ SY869 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1257,plain,
! [SV144: $i] :
( ( ~ ! [SY788: $i,SY789: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK56_D @ SY789 @ SY788 @ SV144 ) @ SY789 )
| ~ ( in @ ( sK56_D @ SY789 @ SY788 @ SV144 ) @ SV144 ) )
| ~ ( ~ ( in @ ( sK56_D @ SY789 @ SY788 @ SV144 ) @ SY789 )
| ~ ( in @ ( sK56_D @ SY789 @ SY788 @ SV144 ) @ SY788 ) ) )
| ~ ( ( in @ ( sK56_D @ SY789 @ SY788 @ SV144 ) @ SY789 )
| ( in @ ( sK56_D @ SY789 @ SY788 @ SV144 ) @ SV144 )
| ( in @ ( sK56_D @ SY789 @ SY788 @ SV144 ) @ SY788 ) ) )
| ( SY789
= ( set_union2 @ SV144 @ SY788 ) ) )
| ~ ! [SY790: $i,SY791: $i] :
( ( SY791
!= ( set_union2 @ SV144 @ SY790 ) )
| ~ ( ~ ! [SY792: $i] :
( ~ ( in @ SY792 @ SY791 )
| ( in @ SY792 @ SV144 )
| ( in @ SY792 @ SY790 ) )
| ~ ~ ( ~ ! [SY793: $i] :
( ~ ( in @ SY793 @ SV144 )
| ( in @ SY793 @ SY791 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY790 )
| ( in @ SX3 @ SY791 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1045]) ).
thf(1258,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1046]) ).
thf(1259,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1046]) ).
thf(1260,plain,
! [SV145: $i] :
( ( ~ ! [SY795: $i,SY796: $i] :
( ~ ( relation @ SY796 )
| ! [SY797: $i] :
( ~ ( in @ SY797 @ ( relation_dom @ SY796 ) )
| ~ ( in @ ( ordered_pair @ SY797 @ SV145 ) @ SY796 )
| ~ ( in @ SY797 @ SY795 ) )
| ( in @ SV145 @ ( relation_image @ SY796 @ SY795 ) ) )
| ~ ! [SY798: $i,SY799: $i] :
( ~ ( relation @ SY799 )
| ~ ( in @ SV145 @ ( relation_image @ SY799 @ SY798 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK40_D @ SY799 @ SY798 @ SV145 ) @ ( relation_dom @ SY799 ) )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY799 @ SY798 @ SV145 ) @ SV145 ) @ SY799 ) )
| ~ ( in @ ( sK40_D @ SY799 @ SY798 @ SV145 ) @ SY798 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1047]) ).
thf(1261,plain,
! [SV146: $i] :
( ( ~ ! [SY800: $i] :
( ~ ( subset @ SV146 @ SY800 )
| ! [SY801: $i] : ( subset @ ( cartesian_product2 @ SV146 @ SY801 ) @ ( cartesian_product2 @ SY800 @ SY801 ) ) )
| ~ ! [SY802: $i] :
( ~ ( subset @ SV146 @ SY802 )
| ! [SY803: $i] : ( subset @ ( cartesian_product2 @ SY803 @ SV146 ) @ ( cartesian_product2 @ SY803 @ SY802 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1048]) ).
thf(1262,plain,
! [SV147: $i,SV232: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK44_C @ SV232 @ SV147 ) @ SV147 )
| ~ ( in @ ( sK44_C @ SV232 @ SV147 ) @ SV232 ) )
| ~ ( ( in @ ( sK44_C @ SV232 @ SV147 ) @ SV147 )
| ( in @ ( sK44_C @ SV232 @ SV147 ) @ SV232 ) ) )
| ( SV147 = SV232 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1263,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1050]) ).
thf(1264,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1050]) ).
thf(1265,plain,
! [SV233: $i,SV148: $i] :
( ( ~ ( ~ ! [SY870: $i] :
( ! [SY871: $i] :
( ( ordered_pair @ SV148 @ SV233 )
!= ( ordered_pair @ SY870 @ SY871 ) )
| ( SV148 = SY870 ) )
| ~ ! [SY872: $i,SY873: $i] :
( ( ( ordered_pair @ SV148 @ SV233 )
!= ( ordered_pair @ SY872 @ SY873 ) )
| ( SV233 = SY873 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1266,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK50_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK50_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1052]) ).
thf(1267,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1052]) ).
thf(1268,plain,
( ( ~ ~ ( empty @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1053]) ).
thf(1269,plain,
( ( ~ ( relation @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1053]) ).
thf(1270,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1054]) ).
thf(1271,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1054]) ).
thf(1272,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1055]) ).
thf(1273,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1055]) ).
thf(1274,plain,
! [SV149: $i] :
( ( ~ ! [SY810: $i,SY811: $i] :
( ~ ( ~ ( ~ ( in @ ( sK45_D @ SY811 @ SY810 @ SV149 ) @ SV149 )
| ( in @ ( sK45_D @ SY811 @ SY810 @ SV149 ) @ SY810 )
| ~ ( in @ ( sK45_D @ SY811 @ SY810 @ SV149 ) @ SY811 ) )
| ~ ~ ( ~ ( ( in @ ( sK45_D @ SY811 @ SY810 @ SV149 ) @ SV149 )
| ( in @ ( sK45_D @ SY811 @ SY810 @ SV149 ) @ SY811 ) )
| ~ ( ~ ( in @ ( sK45_D @ SY811 @ SY810 @ SV149 ) @ SY810 )
| ( in @ ( sK45_D @ SY811 @ SY810 @ SV149 ) @ SY811 ) ) ) )
| ( SY811
= ( set_difference @ SV149 @ SY810 ) ) )
| ~ ! [SY812: $i,SY813: $i] :
( ( SY813
!= ( set_difference @ SV149 @ SY812 ) )
| ~ ( ~ ! [SY814: $i] :
( ~ ( in @ SY814 @ SV149 )
| ( in @ SY814 @ SY812 )
| ( in @ SY814 @ SY813 ) )
| ~ ~ ( ~ ! [SY815: $i] :
( ~ ( in @ SY815 @ SY813 )
| ( in @ SY815 @ SV149 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY813 )
| ~ ( in @ SX3 @ SY812 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1056]) ).
thf(1275,plain,
! [SV150: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV150 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV1 ) @ SV150 )
= SV150 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1057]) ).
thf(1276,plain,
! [SV151: $i,SV2: $i] :
( ( ( ~ ( disjoint @ ( singleton @ SV2 ) @ SV151 ) )
= $true )
| ( ( ~ ( in @ SV2 @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1058]) ).
thf(1277,plain,
! [SV152: $i,SV3: $i] :
( ( ( in @ SV3 @ SV152 )
= $true )
| ( ( disjoint @ ( singleton @ SV3 ) @ SV152 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1059]) ).
thf(1278,plain,
! [SV4: $i,SV153: $i] :
( ( ( ~ ( element @ SV153 @ ( powerset @ SV4 ) ) )
= $true )
| ( ( ! [SY817: $i] :
( ~ ( in @ SY817 @ SV153 )
| ( in @ SY817 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1060]) ).
thf(1279,plain,
! [SV154: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ SV154 ) )
= $true )
| ( ( subset @ SV5 @ ( union @ SV154 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1061]) ).
thf(1280,plain,
! [SV155: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV155 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV6 ) @ SV155 )
= SV155 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1062]) ).
thf(1281,plain,
! [SV156: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV156 ) )
= $true )
| ( ( subset @ SV7 @ ( union @ SV156 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1063]) ).
thf(1282,plain,
! [SV157: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV157 ) )
= $true )
| ( ( ~ ( in @ SV157 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1064]) ).
thf(1283,plain,
! [SV158: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV158 ) )
= $true )
| ( ( element @ SV10 @ SV158 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1065]) ).
thf(1284,plain,
! [SV159: $i,SV11: $i] :
( ( ( ~ ( element @ SV11 @ SV159 ) )
= $true )
| ( ( ( empty @ SV159 )
| ( in @ SV11 @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1066]) ).
thf(1285,plain,
! [SV12: $i,SV234: $i,SV160: $i] :
( ( ~ ( element @ SV160 @ ( powerset @ SV234 ) )
| ~ ( in @ SV12 @ SV160 )
| ( element @ SV12 @ SV234 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1286,plain,
! [SV13: $i,SV161: $i] :
( ( ( ~ ( empty @ SV161 ) )
= $true )
| ( ( ~ ( in @ SV13 @ SV161 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1068]) ).
thf(1287,plain,
! [SV162: $i,SV15: $i] :
( ( ( ~ ( subset @ SV15 @ SV162 ) )
= $true )
| ( ( ! [SY819: $i] :
( ( in @ SY819 @ SV15 )
| ( subset @ SV15 @ ( set_difference @ SV162 @ ( singleton @ SY819 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1070]) ).
thf(1288,plain,
! [SV163: $i,SV235: $i,SV16: $i] :
( ( ! [SY874: $i] :
( ( SV16 = SY874 )
| ( SV16 = SV235 )
| ( ( unordered_pair @ SV16 @ SV163 )
!= ( unordered_pair @ SV235 @ SY874 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1289,plain,
! [SV17: $i,SV164: $i] :
( ( ( ~ ( relation @ SV164 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV17 @ SV164 ) ) @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1072]) ).
thf(1290,plain,
! [SV18: $i,SV165: $i] :
( ( ( ~ ( relation @ SV165 ) )
= $true )
| ( ( subset @ ( relation_rng_restriction @ SV18 @ SV165 ) @ SV165 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1073]) ).
thf(1291,plain,
! [SV19: $i,SV166: $i] :
( ( ( ~ ( relation @ SV166 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV19 @ SV166 ) ) @ ( relation_rng @ SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1074]) ).
thf(1292,plain,
! [SV20: $i,SV167: $i] :
( ( ( ~ ( relation @ SV167 ) )
= $true )
| ( ( ( relation_rng @ ( relation_rng_restriction @ SV20 @ SV167 ) )
= ( set_intersection2 @ ( relation_rng @ SV167 ) @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1075]) ).
thf(1293,plain,
! [SV236: $i,SV168: $i,SV21: $i] :
( ( ! [SY875: $i] :
( ~ ( subset @ SV21 @ SV168 )
| ~ ( subset @ SV236 @ SY875 )
| ( subset @ ( cartesian_product2 @ SV21 @ SV236 ) @ ( cartesian_product2 @ SV168 @ SY875 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1294,plain,
! [SV169: $i,SV22: $i] :
( ( ( ~ ( subset @ SV22 @ SV169 ) )
= $true )
| ( ( ( set_union2 @ SV22 @ SV169 )
= SV169 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1077]) ).
thf(1295,plain,
! [SV23: $i,SV170: $i] :
( ( ( ~ ( relation @ SV170 ) )
= $true )
| ( ( subset @ ( relation_image @ SV170 @ SV23 ) @ ( relation_rng @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1078]) ).
thf(1296,plain,
! [SV24: $i,SV171: $i] :
( ( ( ~ ( relation @ SV171 ) )
= $true )
| ( ( ( relation_image @ SV171 @ SV24 )
= ( relation_image @ SV171 @ ( set_intersection2 @ ( relation_dom @ SV171 ) @ SV24 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1079]) ).
thf(1297,plain,
! [SV25: $i] :
( ( ( relation @ SV25 )
= $false )
| ( ( ( relation_image @ SV25 @ ( relation_dom @ SV25 ) )
= ( relation_rng @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1080]) ).
thf(1298,plain,
! [SV26: $i,SV172: $i] :
( ( ( ~ ( relation @ SV172 ) )
= $true )
| ( ( subset @ ( relation_inverse_image @ SV172 @ SV26 ) @ ( relation_dom @ SV172 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1081]) ).
thf(1299,plain,
! [SV27: $i,SV173: $i] :
( ( ( ~ ( relation @ SV173 ) )
= $true )
| ( ( ( SV27 = empty_set )
| ~ ( subset @ SV27 @ ( relation_rng @ SV173 ) )
| ( ( relation_inverse_image @ SV173 @ SV27 )
!= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1082]) ).
thf(1300,plain,
! [SV174: $i,SV28: $i,SV237: $i] :
( ( ~ ( relation @ SV237 )
| ~ ( subset @ SV28 @ SV174 )
| ( subset @ ( relation_inverse_image @ SV237 @ SV28 ) @ ( relation_inverse_image @ SV237 @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1301,plain,
! [SV238: $i,SV176: $i,SV30: $i] :
( ( ~ ( subset @ SV30 @ SV176 )
| ~ ( subset @ SV30 @ SV238 )
| ( subset @ SV30 @ ( set_intersection2 @ SV176 @ SV238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1302,plain,
! [SV239: $i,SV177: $i,SV31: $i] :
( ( ~ ( subset @ SV31 @ SV177 )
| ~ ( subset @ SV177 @ SV239 )
| ( subset @ SV31 @ SV239 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1303,plain,
! [SV32: $i] :
( ( ( relation @ SV32 )
= $false )
| ( ( subset @ SV32 @ ( cartesian_product2 @ ( relation_dom @ SV32 ) @ ( relation_rng @ SV32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1087]) ).
thf(1304,plain,
! [SV33: $i,SV178: $i] :
( ( ( ~ ( function @ SV178 )
| ~ ( relation @ SV178 ) )
= $true )
| ( ( ! [SY827: $i] :
( ~ ( function @ SY827 )
| ~ ( relation @ SY827 )
| ~ ( in @ SV33 @ ( relation_dom @ ( relation_composition @ SY827 @ SV178 ) ) )
| ( ( apply @ ( relation_composition @ SY827 @ SV178 ) @ SV33 )
= ( apply @ SV178 @ ( apply @ SY827 @ SV33 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1088]) ).
thf(1305,plain,
! [SV34: $i,SV179: $i] :
( ( ( ~ ( function @ SV179 )
| ~ ( relation @ SV179 ) )
= $true )
| ( ( ! [SY828: $i] :
( ~ ( function @ SY828 )
| ~ ( relation @ SY828 )
| ~ ( in @ SV34 @ ( relation_dom @ SV179 ) )
| ( ( apply @ ( relation_composition @ SV179 @ SY828 ) @ SV34 )
= ( apply @ SY828 @ ( apply @ SV179 @ SV34 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1089]) ).
thf(1306,plain,
! [SV180: $i,SV35: $i] :
( ( ( ~ ( subset @ SV35 @ SV180 ) )
= $true )
| ( ( ! [SY829: $i] : ( subset @ ( set_intersection2 @ SV35 @ SY829 ) @ ( set_intersection2 @ SV180 @ SY829 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1090]) ).
thf(1307,plain,
! [SV181: $i,SV36: $i] :
( ( ( ~ ( subset @ SV36 @ SV181 ) )
= $true )
| ( ( ( set_intersection2 @ SV36 @ SV181 )
= SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1091]) ).
thf(1308,plain,
! [SV182: $i,SV38: $i] :
( ( ( ~ ( subset @ SV38 @ SV182 ) )
= $true )
| ( ( ! [SY830: $i] : ( subset @ ( set_difference @ SV38 @ SY830 ) @ ( set_difference @ SV182 @ SY830 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1092]) ).
thf(1309,plain,
! [SV41: $i] :
( ( ( subset @ SV41 @ empty_set )
= $false )
| ( ( SV41 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1095]) ).
thf(1310,plain,
! [SV43: $i] :
( ( ( relation @ SV43 )
= $false )
| ( ( ! [SY551: $i] :
( ~ ( relation @ SY551 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV43 @ SY551 ) ) @ ( relation_dom @ SV43 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1311,plain,
! [SV44: $i] :
( ( ( relation @ SV44 )
= $false )
| ( ( ! [SY552: $i] :
( ~ ( relation @ SY552 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV44 @ SY552 ) ) @ ( relation_rng @ SY552 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1098]) ).
thf(1312,plain,
! [SV186: $i,SV45: $i] :
( ( ( ~ ( subset @ SV45 @ SV186 ) )
= $true )
| ( ( SV186
= ( set_union2 @ SV45 @ ( set_difference @ SV186 @ SV45 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1099]) ).
thf(1313,plain,
! [SV46: $i] :
( ( ( relation @ SV46 )
= $false )
| ( ( ! [SY554: $i] :
( ~ ( relation @ SY554 )
| ~ ( subset @ ( relation_rng @ SV46 ) @ ( relation_dom @ SY554 ) )
| ( ( relation_dom @ ( relation_composition @ SV46 @ SY554 ) )
= ( relation_dom @ SV46 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1100]) ).
thf(1314,plain,
! [SV47: $i,SV187: $i] :
( ( ( ~ ( element @ SV187 @ ( powerset @ ( powerset @ SV47 ) ) ) )
= $true )
| ( ( ( SV187 = empty_set )
| ( ( complements_of_subsets @ SV47 @ SV187 )
!= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1101]) ).
thf(1315,plain,
! [SV48: $i] :
( ( ( relation @ SV48 )
= $false )
| ( ( ! [SY556: $i] :
( ~ ( relation @ SY556 )
| ~ ( subset @ ( relation_dom @ SV48 ) @ ( relation_rng @ SY556 ) )
| ( ( relation_rng @ ( relation_composition @ SY556 @ SV48 ) )
= ( relation_rng @ SV48 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1102]) ).
thf(1316,plain,
! [SV50: $i,SV240: $i] :
( ( ( ~ ( element @ SV240 @ ( powerset @ SV50 ) )
| ! [SY876: $i] :
( ~ ( element @ SY876 @ SV50 )
| ( in @ SY876 @ SV240 )
| ( in @ SY876 @ ( subset_complement @ SV50 @ SV240 ) ) ) )
= $true )
| ( ( SV50 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1317,plain,
! [SV189: $i,SV51: $i,SV241: $i] :
( ( ~ ( element @ SV241 @ ( powerset @ SV51 ) )
| ~ ( in @ SV189 @ ( subset_complement @ SV51 @ SV241 ) )
| ~ ( in @ SV189 @ SV241 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1105]) ).
thf(1318,plain,
! [SV52: $i] :
( ( ( relation @ SV52 )
= $false )
| ( ( ( in @ ( ordered_pair @ ( sK36_B @ SV52 ) @ ( sK37_SY474 @ SV52 ) ) @ SV52 )
| ( SV52 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1106]) ).
thf(1319,plain,
! [SV53: $i,SV190: $i] :
( ( ( ~ ( proper_subset @ SV190 @ SV53 ) )
= $true )
| ( ( ~ ( subset @ SV53 @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1107]) ).
thf(1320,plain,
! [SV54: $i,SV242: $i,SV191: $i] :
( ( ~ ( disjoint @ SV191 @ SV242 )
| ~ ( subset @ SV54 @ SV191 )
| ( disjoint @ SV54 @ SV242 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1321,plain,
! [SV192: $i,SV56: $i] :
( ( ( ~ ( subset @ ( singleton @ SV56 ) @ ( singleton @ SV192 ) ) )
= $true )
| ( ( SV56 = SV192 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1109]) ).
thf(1322,plain,
! [SV58: $i,SV194: $i] :
( ( ( ~ ( relation @ SV194 ) )
= $true )
| ( ( subset @ ( relation_dom_restriction @ SV194 @ SV58 ) @ SV194 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1111]) ).
thf(1323,plain,
! [SV243: $i,SV195: $i,SV59: $i] :
( ( ~ ( subset @ SV59 @ SV195 )
| ~ ( subset @ SV243 @ SV195 )
| ( subset @ ( set_union2 @ SV59 @ SV243 ) @ SV195 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1324,plain,
! [SV196: $i,SV60: $i] :
( ( ( ! [SY834: $i] :
( ( singleton @ SV60 )
!= ( unordered_pair @ SV196 @ SY834 ) ) )
= $true )
| ( ( SV60 = SV196 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1113]) ).
thf(1325,plain,
! [SV61: $i,SV197: $i] :
( ( ( ~ ( relation @ SV197 ) )
= $true )
| ( ( ( relation_dom @ ( relation_dom_restriction @ SV197 @ SV61 ) )
= ( set_intersection2 @ ( relation_dom @ SV197 ) @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1114]) ).
thf(1326,plain,
! [SV62: $i,SV198: $i] :
( ( ( ~ ( relation @ SV198 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV198 @ SV62 ) ) @ ( relation_rng @ SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1115]) ).
thf(1327,plain,
! [SV244: $i,SV199: $i,SV64: $i] :
( ( ( ( singleton @ SV64 )
!= ( unordered_pair @ SV199 @ SV244 ) )
| ( SV199 = SV244 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1328,plain,
! [SV65: $i] :
( ( ( empty @ SV65 )
= $false )
| ( ( function @ SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1117]) ).
thf(1329,plain,
! [SV66: $i] :
( ( ( empty @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1118]) ).
thf(1330,plain,
! [SV70: $i,SV203: $i] :
( ( ( ~ ( element @ SV203 @ ( powerset @ SV70 ) ) )
= $true )
| ( ( ( subset_complement @ SV70 @ SV203 )
= ( set_difference @ SV70 @ SV203 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1122]) ).
thf(1331,plain,
! [SV72: $i] :
( ( ( relation @ SV72 )
= $false )
| ( ( ( relation_field @ SV72 )
= ( set_union2 @ ( relation_dom @ SV72 ) @ ( relation_rng @ SV72 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1124]) ).
thf(1332,plain,
! [SV74: $i,SV205: $i] :
( ( ( ~ ( element @ SV205 @ ( powerset @ SV74 ) ) )
= $true )
| ( ( element @ ( subset_complement @ SV74 @ SV205 ) @ ( powerset @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1125]) ).
thf(1333,plain,
! [SV75: $i] :
( ( ( relation @ SV75 )
= $false )
| ( ( relation @ ( relation_inverse @ SV75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1126]) ).
thf(1334,plain,
! [SV206: $i,SV76: $i] :
( ( ( ~ ( relation @ SV76 )
| ~ ( relation @ SV206 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV76 @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1127]) ).
thf(1335,plain,
! [SV77: $i,SV207: $i] :
( ( ( ~ ( element @ SV207 @ ( powerset @ ( powerset @ SV77 ) ) ) )
= $true )
| ( ( element @ ( union_of_subsets @ SV77 @ SV207 ) @ ( powerset @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1128]) ).
thf(1336,plain,
! [SV78: $i,SV208: $i] :
( ( ( ~ ( element @ SV208 @ ( powerset @ ( powerset @ SV78 ) ) ) )
= $true )
| ( ( element @ ( meet_of_subsets @ SV78 @ SV208 ) @ ( powerset @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1129]) ).
thf(1337,plain,
! [SV245: $i,SV79: $i,SV209: $i] :
( ( ~ ( element @ SV209 @ ( powerset @ SV79 ) )
| ~ ( element @ SV245 @ ( powerset @ SV79 ) )
| ( element @ ( subset_difference @ SV79 @ SV209 @ SV245 ) @ ( powerset @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1338,plain,
! [SV80: $i] :
( ( ( relation @ SV80 )
= $false )
| ( ( ! [SY587: $i] : ( relation @ ( relation_dom_restriction @ SV80 @ SY587 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1131]) ).
thf(1339,plain,
! [SV81: $i,SV210: $i] :
( ( ( ~ ( element @ SV210 @ ( powerset @ ( powerset @ SV81 ) ) ) )
= $true )
| ( ( element @ ( complements_of_subsets @ SV81 @ SV210 ) @ ( powerset @ ( powerset @ SV81 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1132]) ).
thf(1340,plain,
! [SV82: $i,SV211: $i] :
( ( ( ~ ( relation @ SV211 ) )
= $true )
| ( ( relation @ ( relation_rng_restriction @ SV82 @ SV211 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1133]) ).
thf(1341,plain,
! [SV212: $i,SV84: $i] :
( ( ( ~ ( relation @ SV84 )
| ~ ( relation @ SV212 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV84 @ SV212 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1134]) ).
thf(1342,plain,
! [SV213: $i,SV86: $i] :
( ( empty @ ( ordered_pair @ SV86 @ SV213 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1136]) ).
thf(1343,plain,
! [SV214: $i,SV87: $i] :
( ( ( ~ ( relation @ SV87 )
| ~ ( relation @ SV214 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV87 @ SV214 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1137]) ).
thf(1344,plain,
! [SV246: $i,SV89: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV89 @ SV246 ) ) )
= $true )
| ( ( empty @ SV89 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1139]) ).
thf(1345,plain,
! [SV215: $i,SV90: $i] :
( ( empty @ ( unordered_pair @ SV90 @ SV215 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1140]) ).
thf(1346,plain,
! [SV91: $i,SV247: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV247 @ SV91 ) ) )
= $true )
| ( ( empty @ SV91 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1347,plain,
! [SV216: $i,SV92: $i] :
( ( ( ( empty @ SV92 )
| ( empty @ SV216 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV92 @ SV216 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1142]) ).
thf(1348,plain,
! [SV93: $i] :
( ( ( empty @ SV93 )
= $true )
| ( ( ~ ( relation @ SV93 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV93 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1143]) ).
thf(1349,plain,
! [SV94: $i] :
( ( ( empty @ SV94 )
= $true )
| ( ( ~ ( relation @ SV94 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV94 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1144]) ).
thf(1350,plain,
! [SV97: $i,SV217: $i] :
( ( ( ~ ( element @ SV217 @ ( powerset @ SV97 ) ) )
= $true )
| ( ( ( subset_complement @ SV97 @ ( subset_complement @ SV97 @ SV217 ) )
= SV217 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1145]) ).
thf(1351,plain,
! [SV98: $i] :
( ( ( relation @ SV98 )
= $false )
| ( ( ( relation_inverse @ ( relation_inverse @ SV98 ) )
= SV98 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1146]) ).
thf(1352,plain,
! [SV99: $i,SV218: $i] :
( ( ( ~ ( element @ SV218 @ ( powerset @ ( powerset @ SV99 ) ) ) )
= $true )
| ( ( ( complements_of_subsets @ SV99 @ ( complements_of_subsets @ SV99 @ SV218 ) )
= SV218 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1147]) ).
thf(1353,plain,
! [SV100: $i,SV219: $i] :
( ( ( ~ ( element @ SV219 @ ( powerset @ ( powerset @ SV100 ) ) ) )
= $true )
| ( ( ( union_of_subsets @ SV100 @ SV219 )
= ( union @ SV219 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1148]) ).
thf(1354,plain,
! [SV101: $i,SV220: $i] :
( ( ( ~ ( element @ SV220 @ ( powerset @ ( powerset @ SV101 ) ) ) )
= $true )
| ( ( ( meet_of_subsets @ SV101 @ SV220 )
= ( set_meet @ SV220 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1149]) ).
thf(1355,plain,
! [SV248: $i,SV102: $i,SV221: $i] :
( ( ~ ( element @ SV221 @ ( powerset @ SV102 ) )
| ~ ( element @ SV248 @ ( powerset @ SV102 ) )
| ( ( subset_difference @ SV102 @ SV221 @ SV248 )
= ( set_difference @ SV221 @ SV248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1150]) ).
thf(1356,plain,
! [SV222: $i,SV104: $i] :
( ( ( ~ ( disjoint @ SV104 @ SV222 ) )
= $true )
| ( ( disjoint @ SV222 @ SV104 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1151]) ).
thf(1357,plain,
! [SV109: $i,SV249: $i,SV223: $i] :
( ( ~ ( element @ SV223 @ ( powerset @ SV249 ) )
| ~ ( in @ SV109 @ SV223 )
| ~ ( empty @ SV249 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1358,plain,
! [SV110: $i] :
( ( ( empty @ SV110 )
= $false )
| ( ( SV110 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1153]) ).
thf(1359,plain,
! [SV224: $i,SV111: $i] :
( ( ( ( SV111 = SV224 )
| ~ ( empty @ SV111 ) )
= $true )
| ( ( ~ ( empty @ SV224 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1154]) ).
thf(1360,plain,
! [SV112: $i] :
( ( ~ ! [SY607: $i,SY608: $i] :
( ~ ( ~ ( ~ ( in @ ( sK49_D @ SY608 @ SY607 @ SV112 ) @ SV112 )
| ~ ( in @ ( sK49_D @ SY608 @ SY607 @ SV112 ) @ SY607 )
| ~ ( in @ ( sK49_D @ SY608 @ SY607 @ SV112 ) @ SY608 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_D @ SY608 @ SY607 @ SV112 ) @ SV112 )
| ( in @ ( sK49_D @ SY608 @ SY607 @ SV112 ) @ SY608 ) )
| ~ ( ( in @ ( sK49_D @ SY608 @ SY607 @ SV112 ) @ SY607 )
| ( in @ ( sK49_D @ SY608 @ SY607 @ SV112 ) @ SY608 ) ) ) )
| ( SY608
= ( set_intersection2 @ SV112 @ SY607 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1155]) ).
thf(1361,plain,
! [SV112: $i] :
( ( ~ ! [SY609: $i,SY610: $i] :
( ( SY610
!= ( set_intersection2 @ SV112 @ SY609 ) )
| ~ ( ~ ! [SY611: $i] :
( ~ ( in @ SY611 @ SV112 )
| ~ ( in @ SY611 @ SY609 )
| ( in @ SY611 @ SY610 ) )
| ~ ~ ( ~ ! [SY612: $i] :
( ~ ( in @ SY612 @ SY610 )
| ( in @ SY612 @ SV112 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY610 )
| ( in @ SX3 @ SY609 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1155]) ).
thf(1362,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK47_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK47_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK47_C @ SX1 @ SX0 ) @ ( sK48_SY487 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK48_SY487 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK47_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1156]) ).
thf(1363,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK46_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK46_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1157]) ).
thf(1364,plain,
! [SV113: $i,SV225: $i] :
( ( ( ~ ( relation @ SV225 ) )
= $true )
| ( ( ~ ( ~ ! [SY839: $i] :
( ~ ( relation @ SY839 )
| ~ ( ~ ( ~ ( in @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) @ SV113 )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ SY839 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) ) @ SV225 )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ SY839 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) ) @ SY839 ) )
| ~ ~ ( ~ ( ( in @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) @ SV113 )
| ( in @ ( ordered_pair @ ( sK32_D @ SY839 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) ) @ SY839 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_D @ SY839 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) ) @ SV225 )
| ( in @ ( ordered_pair @ ( sK32_D @ SY839 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) ) @ SY839 ) ) ) )
| ( SY839
= ( relation_rng_restriction @ SV113 @ SV225 ) ) )
| ~ ! [SY840: $i] :
( ~ ( relation @ SY840 )
| ( SY840
!= ( relation_rng_restriction @ SV113 @ SV225 ) )
| ~ ( ~ ! [SY841: $i,SY842: $i] :
( ~ ( in @ SY842 @ SV113 )
| ~ ( in @ ( ordered_pair @ SY841 @ SY842 ) @ SV225 )
| ( in @ ( ordered_pair @ SY841 @ SY842 ) @ SY840 ) )
| ~ ~ ( ~ ! [SY619: $i,SY620: $i] :
( ~ ( in @ ( ordered_pair @ SY619 @ SY620 ) @ SY840 )
| ( in @ SY620 @ SV113 ) )
| ~ ! [SY845: $i,SY846: $i] :
( ~ ( in @ ( ordered_pair @ SY845 @ SY846 ) @ SY840 )
| ( in @ ( ordered_pair @ SY845 @ SY846 ) @ SV225 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1158]) ).
thf(1365,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1159]) ).
thf(1366,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1160]) ).
thf(1367,plain,
( ( relation @ sK3_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1161]) ).
thf(1368,plain,
( ( relation_empty_yielding @ sK3_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1162]) ).
thf(1369,plain,
! [SV226: $i,SV114: $i] :
( ( ~ ! [SY847: $i,SY848: $i] :
( ~ ( in @ SV114 @ SY847 )
| ~ ( in @ SV226 @ SY848 )
| ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SY847 @ SY848 ) ) )
| ~ ~ ( ~ ! [SY849: $i] :
( ! [SY850: $i] :
~ ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SY849 @ SY850 ) )
| ( in @ SV114 @ SY849 ) )
| ~ ! [SY851: $i,SY852: $i] :
( ~ ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SY851 @ SY852 ) )
| ( in @ SV226 @ SY852 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1163]) ).
thf(1370,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK72_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK72_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1164]) ).
thf(1371,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1165]) ).
thf(1372,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK62_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK62_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK62_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK62_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1166]) ).
thf(1373,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1167]) ).
thf(1374,plain,
( ( ! [SX0: $i] :
( ( in @ ( sK61_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1168]) ).
thf(1375,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1169]) ).
thf(1376,plain,
! [SV115: $i] :
( ( ~ ! [SY630: $i] :
( ~ ( subset @ SY630 @ ( sK42_B @ SV115 ) )
| ( are_equipotent @ SY630 @ ( sK42_B @ SV115 ) )
| ( in @ SY630 @ ( sK42_B @ SV115 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1170]) ).
thf(1377,plain,
! [SV115: $i] :
( ( ~ ~ ( ~ ! [SY631: $i] :
( ~ ( ~ ! [SY632: $i] :
( ~ ( subset @ SY632 @ SY631 )
| ( in @ SY632 @ ( sK43_SY481 @ SY631 @ SV115 ) ) )
| ~ ( in @ ( sK43_SY481 @ SY631 @ SV115 ) @ ( sK42_B @ SV115 ) ) )
| ~ ( in @ SY631 @ ( sK42_B @ SV115 ) ) )
| ~ ~ ( ~ ! [SY633: $i,SY634: $i] :
( ~ ( in @ SY633 @ ( sK42_B @ SV115 ) )
| ~ ( subset @ SY634 @ SY633 )
| ( in @ SY634 @ ( sK42_B @ SV115 ) ) )
| ~ ( in @ SV115 @ ( sK42_B @ SV115 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1170]) ).
thf(1378,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1171]) ).
thf(1379,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1172]) ).
thf(1380,plain,
! [SV116: $i] :
( ( ( ~ ( function @ SV116 ) )
= $true )
| ( ( ~ ( relation @ SV116 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY635: $i] :
( ~ ( in @ SY635 @ ( relation_dom @ SV116 ) )
| ! [SY636: $i] :
( ( SY636
!= ( apply @ SV116 @ SY635 ) )
| ( in @ ( ordered_pair @ SY635 @ SY636 ) @ SV116 ) ) )
| ~ ! [SY637: $i] :
( ~ ( in @ SY637 @ ( relation_dom @ SV116 ) )
| ! [SY638: $i] :
( ~ ( in @ ( ordered_pair @ SY637 @ SY638 ) @ SV116 )
| ( SY638
= ( apply @ SV116 @ SY637 ) ) ) ) )
| ~ ~ ( ~ ! [SY639: $i] :
( ( in @ SY639 @ ( relation_dom @ SV116 ) )
| ! [SY640: $i] :
( ( SY640
!= ( apply @ SV116 @ SY639 ) )
| ( SY640 = empty_set ) ) )
| ~ ! [SY641: $i] :
( ( in @ SY641 @ ( relation_dom @ SV116 ) )
| ! [SY642: $i] :
( ( SY642 != empty_set )
| ( SY642
= ( apply @ SV116 @ SY641 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1173]) ).
thf(1381,plain,
! [SV117: $i] :
( ( ~ ! [SY643: $i,SY644: $i] :
( ~ ( ~ ( ! [SY645: $i,SY646: $i] :
( ~ ( in @ SY645 @ SV117 )
| ~ ( in @ SY646 @ SY643 )
| ( ( sK53_D @ SY644 @ SY643 @ SV117 )
!= ( ordered_pair @ SY645 @ SY646 ) ) )
| ~ ( in @ ( sK53_D @ SY644 @ SY643 @ SV117 ) @ SY644 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK54_SY491 @ SY644 @ SY643 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK55_SY493 @ SY644 @ SY643 @ SV117 ) @ SY643 ) )
| ( ( sK53_D @ SY644 @ SY643 @ SV117 )
!= ( ordered_pair @ ( sK54_SY491 @ SY644 @ SY643 @ SV117 ) @ ( sK55_SY493 @ SY644 @ SY643 @ SV117 ) ) ) )
| ( in @ ( sK53_D @ SY644 @ SY643 @ SV117 ) @ SY644 ) ) )
| ( SY644
= ( cartesian_product2 @ SV117 @ SY643 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1174]) ).
thf(1382,plain,
! [SV117: $i] :
( ( ~ ! [SY647: $i,SY648: $i] :
( ( SY648
!= ( cartesian_product2 @ SV117 @ SY647 ) )
| ~ ( ~ ! [SY649: $i] :
( ! [SY650: $i,SY651: $i] :
( ~ ( in @ SY650 @ SV117 )
| ~ ( in @ SY651 @ SY647 )
| ( SY649
!= ( ordered_pair @ SY650 @ SY651 ) ) )
| ( in @ SY649 @ SY648 ) )
| ~ ! [SY652: $i] :
( ~ ( in @ SY652 @ SY648 )
| ~ ( ~ ~ ( ~ ( in @ ( sK51_E @ SY652 @ SY648 @ SY647 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK52_SY488 @ SY652 @ SY648 @ SY647 @ SV117 ) @ SY647 ) )
| ( SY652
!= ( ordered_pair @ ( sK51_E @ SY652 @ SY648 @ SY647 @ SV117 ) @ ( sK52_SY488 @ SY652 @ SY648 @ SY647 @ SV117 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1174]) ).
thf(1383,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1175]) ).
thf(1384,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1176]) ).
thf(1385,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( ( relation_rng @ SX0 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1177]) ).
thf(1386,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( ( relation_dom @ SX0 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1178]) ).
thf(1387,plain,
( ( function @ sK10_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1179]) ).
thf(1388,plain,
( ( relation @ sK10_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1180]) ).
thf(1389,plain,
! [SV118: $i] :
( ( ~ ! [SY653: $i,SY654: $i] :
( ~ ( function @ SY654 )
| ~ ( relation @ SY654 )
| ( SY653
!= ( apply @ SY654 @ SV118 ) )
| ~ ( in @ SV118 @ ( relation_dom @ SY654 ) )
| ( in @ ( ordered_pair @ SV118 @ SY653 ) @ SY654 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1181]) ).
thf(1390,plain,
! [SV118: $i] :
( ( ~ ~ ( ~ ! [SY655: $i,SY656: $i] :
( ~ ( function @ SY656 )
| ~ ( relation @ SY656 )
| ~ ( in @ ( ordered_pair @ SV118 @ SY655 ) @ SY656 )
| ( SY655
= ( apply @ SY656 @ SV118 ) ) )
| ~ ! [SY657: $i,SY658: $i] :
( ~ ( function @ SY658 )
| ~ ( relation @ SY658 )
| ~ ( in @ ( ordered_pair @ SV118 @ SY657 ) @ SY658 )
| ( in @ SV118 @ ( relation_dom @ SY658 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1181]) ).
thf(1391,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1182]) ).
thf(1392,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1183]) ).
thf(1393,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK69_C @ SX1 @ SX0 )
!= ( sK70_SY500 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK69_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK69_C @ SX1 @ SX0 ) @ ( sK70_SY500 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK69_C @ SX1 @ SX0 )
= ( sK70_SY500 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK69_C @ SX1 @ SX0 ) @ ( sK70_SY500 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK69_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK69_C @ SX1 @ SX0 ) @ ( sK70_SY500 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1184]) ).
thf(1394,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)],[1185]) ).
thf(1395,plain,
! [SV119: $i] :
( ( ~ ( element @ ( sK5_B @ SV119 ) @ ( powerset @ SV119 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1186]) ).
thf(1396,plain,
! [SV119: $i] :
( ( ~ ( empty @ ( sK5_B @ SV119 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1186]) ).
thf(1397,plain,
! [SV120: $i] :
( ( ( relation @ SV120 )
= $false )
| ( ( ! [SY659: $i] :
( ~ ( relation @ SY659 )
| ~ ( ~ ! [SY660: $i] :
( ~ ( relation @ SY660 )
| ~ ( ~ ( ! [SY661: $i] :
( ~ ( in @ ( ordered_pair @ ( sK13_D @ SY660 @ SY659 @ SV120 ) @ SY661 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY661 @ ( sK14_SY457 @ SY660 @ SY659 @ SV120 ) ) @ SY659 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_D @ SY660 @ SY659 @ SV120 ) @ ( sK14_SY457 @ SY660 @ SY659 @ SV120 ) ) @ SY660 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_D @ SY660 @ SY659 @ SV120 ) @ ( sK15_SY461 @ SY660 @ SY659 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY461 @ SY660 @ SY659 @ SV120 ) @ ( sK14_SY457 @ SY660 @ SY659 @ SV120 ) ) @ SY659 ) )
| ( in @ ( ordered_pair @ ( sK13_D @ SY660 @ SY659 @ SV120 ) @ ( sK14_SY457 @ SY660 @ SY659 @ SV120 ) ) @ SY660 ) ) )
| ( SY660
= ( relation_composition @ SV120 @ SY659 ) ) )
| ~ ! [SY662: $i] :
( ~ ( relation @ SY662 )
| ( SY662
!= ( relation_composition @ SV120 @ SY659 ) )
| ~ ( ~ ! [SY663: $i,SY664: $i] :
( ! [SY665: $i] :
( ~ ( in @ ( ordered_pair @ SY663 @ SY665 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY665 @ SY664 ) @ SY659 ) )
| ( in @ ( ordered_pair @ SY663 @ SY664 ) @ SY662 ) )
| ~ ! [SY666: $i,SY667: $i] :
( ~ ( in @ ( ordered_pair @ SY666 @ SY667 ) @ SY662 )
| ~ ( ~ ( in @ ( ordered_pair @ SY666 @ ( sK12_F @ SY667 @ SY666 @ SY662 @ SY659 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK12_F @ SY667 @ SY666 @ SY662 @ SY659 @ SV120 ) @ SY667 ) @ SY659 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1187]) ).
thf(1398,plain,
! [SV121: $i,SV227: $i] :
( ( ( ~ ( element @ SV227 @ ( powerset @ SV121 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY853: $i] :
( ~ ( element @ SY853 @ ( powerset @ SV121 ) )
| ~ ( disjoint @ SV227 @ SY853 )
| ( subset @ SV227 @ ( subset_complement @ SV121 @ SY853 ) ) )
| ~ ! [SY854: $i] :
( ~ ( element @ SY854 @ ( powerset @ SV121 ) )
| ~ ( subset @ SV227 @ ( subset_complement @ SV121 @ SY854 ) )
| ( disjoint @ SV227 @ SY854 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1188]) ).
thf(1399,plain,
! [SV122: $i] :
( ( ~ ! [SY671: $i,SY672: $i] :
( ~ ( relation @ SY672 )
| ~ ( in @ SV122 @ SY671 )
| ~ ( in @ SV122 @ ( relation_rng @ SY672 ) )
| ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SY671 @ SY672 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1189]) ).
thf(1400,plain,
! [SV122: $i] :
( ( ~ ~ ( ~ ! [SY673: $i,SY674: $i] :
( ~ ( relation @ SY674 )
| ~ ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SY673 @ SY674 ) ) )
| ( in @ SV122 @ SY673 ) )
| ~ ! [SY675: $i,SY676: $i] :
( ~ ( relation @ SY676 )
| ~ ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SY675 @ SY676 ) ) )
| ( in @ SV122 @ ( relation_rng @ SY676 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1189]) ).
thf(1401,plain,
! [SV123: $i] :
( ( ( relation @ SV123 )
= $false )
| ( ( ~ ( ~ ! [SY677: $i,SY678: $i] :
( ~ ( relation @ SY678 )
| ~ ( ~ ( ~ ( in @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ SY677 )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ ( sK35_SY473 @ SY678 @ SY677 @ SV123 ) ) @ SV123 )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ ( sK35_SY473 @ SY678 @ SY677 @ SV123 ) ) @ SY678 ) )
| ~ ~ ( ~ ( ( in @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ SY677 )
| ( in @ ( ordered_pair @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ ( sK35_SY473 @ SY678 @ SY677 @ SV123 ) ) @ SY678 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ ( sK35_SY473 @ SY678 @ SY677 @ SV123 ) ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ ( sK35_SY473 @ SY678 @ SY677 @ SV123 ) ) @ SY678 ) ) ) )
| ( SY678
= ( relation_dom_restriction @ SV123 @ SY677 ) ) )
| ~ ! [SY679: $i,SY680: $i] :
( ~ ( relation @ SY680 )
| ( SY680
!= ( relation_dom_restriction @ SV123 @ SY679 ) )
| ~ ( ~ ! [SY681: $i,SY682: $i] :
( ~ ( in @ SY681 @ SY679 )
| ~ ( in @ ( ordered_pair @ SY681 @ SY682 ) @ SV123 )
| ( in @ ( ordered_pair @ SY681 @ SY682 ) @ SY680 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY680 )
| ( in @ SX3 @ SY679 ) )
| ~ ! [SY685: $i,SY686: $i] :
( ~ ( in @ ( ordered_pair @ SY685 @ SY686 ) @ SY680 )
| ( in @ ( ordered_pair @ SY685 @ SY686 ) @ SV123 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1190]) ).
thf(1402,plain,
! [SV124: $i] :
( ( ( relation @ SV124 )
= $false )
| ( ( ~ ( ~ ! [SY687: $i] :
( ~ ( relation @ SY687 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_C @ SY687 @ SV124 ) @ ( sK17_SY462 @ SY687 @ SV124 ) ) @ SY687 )
| ~ ( in @ ( ordered_pair @ ( sK17_SY462 @ SY687 @ SV124 ) @ ( sK16_C @ SY687 @ SV124 ) ) @ SV124 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK16_C @ SY687 @ SV124 ) @ ( sK17_SY462 @ SY687 @ SV124 ) ) @ SY687 )
| ( in @ ( ordered_pair @ ( sK17_SY462 @ SY687 @ SV124 ) @ ( sK16_C @ SY687 @ SV124 ) ) @ SV124 ) ) )
| ( SY687
= ( relation_inverse @ SV124 ) ) )
| ~ ! [SY688: $i] :
( ~ ( relation @ SY688 )
| ( SY688
!= ( relation_inverse @ SV124 ) )
| ~ ( ~ ! [SY689: $i,SY690: $i] :
( ~ ( in @ ( ordered_pair @ SY689 @ SY690 ) @ SY688 )
| ( in @ ( ordered_pair @ SY690 @ SY689 ) @ SV124 ) )
| ~ ! [SY691: $i,SY692: $i] :
( ~ ( in @ ( ordered_pair @ SY692 @ SY691 ) @ SV124 )
| ( in @ ( ordered_pair @ SY691 @ SY692 ) @ SY688 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1191]) ).
thf(1403,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1192]) ).
thf(1404,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1193]) ).
thf(1405,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1194]) ).
thf(1406,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1195]) ).
thf(1407,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1196]) ).
thf(1408,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1197]) ).
thf(1409,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK38_C @ SX1 @ SX0 ) )
!= ( sK38_C @ SX1 @ SX0 ) ) ) )
| ( ( relation_dom @ SX1 )
!= SX0 )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1198]) ).
thf(1410,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)],[1199]) ).
thf(1411,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1200]) ).
thf(1412,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1201]) ).
thf(1413,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1202]) ).
thf(1414,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1203]) ).
thf(1415,plain,
! [SV125: $i] :
( ( ( relation @ SV125 )
= $false )
| ( ( ~ ( ~ ! [SY693: $i,SY694: $i] :
( ~ ( ~ ( ! [SY695: $i] :
( ~ ( in @ ( ordered_pair @ SY695 @ ( sK30_D @ SY694 @ SY693 @ SV125 ) ) @ SV125 )
| ~ ( in @ SY695 @ SY693 ) )
| ~ ( in @ ( sK30_D @ SY694 @ SY693 @ SV125 ) @ SY694 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_SY471 @ SY694 @ SY693 @ SV125 ) @ ( sK30_D @ SY694 @ SY693 @ SV125 ) ) @ SV125 )
| ~ ( in @ ( sK31_SY471 @ SY694 @ SY693 @ SV125 ) @ SY693 ) )
| ( in @ ( sK30_D @ SY694 @ SY693 @ SV125 ) @ SY694 ) ) )
| ( SY694
= ( relation_image @ SV125 @ SY693 ) ) )
| ~ ! [SY696: $i,SY697: $i] :
( ( SY697
!= ( relation_image @ SV125 @ SY696 ) )
| ~ ( ~ ! [SY698: $i] :
( ! [SY699: $i] :
( ~ ( in @ ( ordered_pair @ SY699 @ SY698 ) @ SV125 )
| ~ ( in @ SY699 @ SY696 ) )
| ( in @ SY698 @ SY697 ) )
| ~ ! [SY700: $i] :
( ~ ( in @ SY700 @ SY697 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK29_E @ SY700 @ SY697 @ SY696 @ SV125 ) @ SY700 ) @ SV125 )
| ~ ( in @ ( sK29_E @ SY700 @ SY697 @ SY696 @ SV125 ) @ SY696 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1204]) ).
thf(1416,plain,
! [SV126: $i] :
( ( ~ ! [SY701: $i,SY702: $i] :
( ~ ( relation @ SY702 )
| ~ ( in @ ( ordered_pair @ SV126 @ SY701 ) @ SY702 )
| ( in @ SV126 @ ( relation_field @ SY702 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1205]) ).
thf(1417,plain,
! [SV126: $i] :
( ( ~ ! [SY703: $i,SY704: $i] :
( ~ ( relation @ SY704 )
| ~ ( in @ ( ordered_pair @ SV126 @ SY703 ) @ SY704 )
| ( in @ SY703 @ ( relation_field @ SY704 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1205]) ).
thf(1418,plain,
! [SV228: $i,SV127: $i] :
( ( ~ ! [SY855: $i,SY856: $i] :
( ~ ( relation @ SY856 )
| ~ ( in @ SV127 @ SY855 )
| ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ SY856 )
| ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SY855 ) @ SY856 ) ) )
| ~ ~ ( ~ ! [SY857: $i,SY858: $i] :
( ~ ( relation @ SY858 )
| ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SY857 ) @ SY858 ) )
| ( in @ SV127 @ SY857 ) )
| ~ ! [SY859: $i,SY860: $i] :
( ~ ( relation @ SY860 )
| ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SY859 ) @ SY860 ) )
| ( in @ ( ordered_pair @ SV127 @ SV228 ) @ SY860 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1206]) ).
thf(1419,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1207]) ).
thf(1420,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1208]) ).
thf(1421,plain,
! [SV128: $i] :
( ( ~ ! [SY712: $i,SY713: $i] :
( ~ ( in @ SV128 @ SY713 )
| ~ ( in @ SY712 @ SY713 )
| ( subset @ ( unordered_pair @ SV128 @ SY712 ) @ SY713 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1209]) ).
thf(1422,plain,
! [SV128: $i] :
( ( ~ ~ ( ~ ! [SY714: $i,SY715: $i] :
( ~ ( subset @ ( unordered_pair @ SV128 @ SY714 ) @ SY715 )
| ( in @ SV128 @ SY715 ) )
| ~ ! [SY716: $i,SY717: $i] :
( ~ ( subset @ ( unordered_pair @ SV128 @ SY716 ) @ SY717 )
| ( in @ SY716 @ SY717 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1209]) ).
thf(1423,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1210]) ).
thf(1424,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1211]) ).
thf(1425,plain,
( ( empty @ sK9_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1212]) ).
thf(1426,plain,
( ( relation @ sK9_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1213]) ).
thf(1427,plain,
! [SV129: $i] :
( ( ( relation @ SV129 )
= $false )
| ( ( ~ ( ~ ! [SY718: $i] :
( ~ ( ~ ( ! [SY719: $i] :
~ ( in @ ( ordered_pair @ SY719 @ ( sK19_C @ SY718 @ SV129 ) ) @ SV129 )
| ~ ( in @ ( sK19_C @ SY718 @ SV129 ) @ SY718 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_SY464 @ SY718 @ SV129 ) @ ( sK19_C @ SY718 @ SV129 ) ) @ SV129 )
| ( in @ ( sK19_C @ SY718 @ SV129 ) @ SY718 ) ) )
| ( SY718
= ( relation_rng @ SV129 ) ) )
| ~ ! [SY720: $i] :
( ( SY720
!= ( relation_rng @ SV129 ) )
| ~ ( ~ ! [SY721: $i] :
( ! [SY722: $i] :
~ ( in @ ( ordered_pair @ SY722 @ SY721 ) @ SV129 )
| ( in @ SY721 @ SY720 ) )
| ~ ! [SY723: $i] :
( ~ ( in @ SY723 @ SY720 )
| ( in @ ( ordered_pair @ ( sK18_D @ SY723 @ SY720 @ SV129 ) @ SY723 ) @ SV129 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1214]) ).
thf(1428,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1215]) ).
thf(1429,plain,
( ( relation_empty_yielding @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1216]) ).
thf(1430,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1217]) ).
thf(1431,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1218]) ).
thf(1432,plain,
( ( ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1219]) ).
thf(1433,plain,
( ( ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1220]) ).
thf(1434,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK71_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1221]) ).
thf(1435,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1222]) ).
thf(1436,plain,
! [SV130: $i,SV229: $i] :
( ( ( ~ ( ~ ( in @ ( sK73_C @ SV229 @ SV130 ) @ SV130 )
| ~ ~ ( in @ ( sK73_C @ SV229 @ SV130 ) @ SV229 ) ) )
= $true )
| ( ( element @ SV130 @ ( powerset @ SV229 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1223]) ).
thf(1437,plain,
! [SV131: $i] :
( ( ( relation @ SV131 )
= $false )
| ( ( ~ ( ~ ! [SY725: $i,SY726: $i] :
( ~ ( ~ ( ! [SY727: $i] :
( ~ ( in @ ( ordered_pair @ ( sK27_D @ SY726 @ SY725 @ SV131 ) @ SY727 ) @ SV131 )
| ~ ( in @ SY727 @ SY725 ) )
| ~ ( in @ ( sK27_D @ SY726 @ SY725 @ SV131 ) @ SY726 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK27_D @ SY726 @ SY725 @ SV131 ) @ ( sK28_SY469 @ SY726 @ SY725 @ SV131 ) ) @ SV131 )
| ~ ( in @ ( sK28_SY469 @ SY726 @ SY725 @ SV131 ) @ SY725 ) )
| ( in @ ( sK27_D @ SY726 @ SY725 @ SV131 ) @ SY726 ) ) )
| ( SY726
= ( relation_inverse_image @ SV131 @ SY725 ) ) )
| ~ ! [SY728: $i,SY729: $i] :
( ( SY729
!= ( relation_inverse_image @ SV131 @ SY728 ) )
| ~ ( ~ ! [SY730: $i] :
( ! [SY731: $i] :
( ~ ( in @ ( ordered_pair @ SY730 @ SY731 ) @ SV131 )
| ~ ( in @ SY731 @ SY728 ) )
| ( in @ SY730 @ SY729 ) )
| ~ ! [SY732: $i] :
( ~ ( in @ SY732 @ SY729 )
| ~ ( ~ ( in @ ( ordered_pair @ SY732 @ ( sK26_E @ SY732 @ SY729 @ SY728 @ SV131 ) ) @ SV131 )
| ~ ( in @ ( sK26_E @ SY732 @ SY729 @ SY728 @ SV131 ) @ SY728 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1224]) ).
thf(1438,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1225]) ).
thf(1439,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1226]) ).
thf(1440,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK68_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK68_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1227]) ).
thf(1441,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK66_C @ SX1 @ SX0 ) @ ( sK67_SY497 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1228]) ).
thf(1442,plain,
! [SV132: $i] :
( ( ~ ! [SY733: $i,SY734: $i] :
( ~ ( relation @ SY734 )
| ~ ( in @ SV132 @ SY733 )
| ~ ( in @ SV132 @ ( relation_dom @ SY734 ) )
| ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SY734 @ SY733 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1229]) ).
thf(1443,plain,
! [SV132: $i] :
( ( ~ ~ ( ~ ! [SY735: $i,SY736: $i] :
( ~ ( relation @ SY736 )
| ~ ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SY736 @ SY735 ) ) )
| ( in @ SV132 @ SY735 ) )
| ~ ! [SY737: $i,SY738: $i] :
( ~ ( relation @ SY738 )
| ~ ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SY738 @ SY737 ) ) )
| ( in @ SV132 @ ( relation_dom @ SY738 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1229]) ).
thf(1444,plain,
! [SV133: $i] :
( ( ~ ! [SY739: $i,SY740: $i] :
( ~ ( relation @ SY740 )
| ~ ( in @ ( ordered_pair @ SV133 @ SY739 ) @ SY740 )
| ( in @ SV133 @ ( relation_dom @ SY740 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1230]) ).
thf(1445,plain,
! [SV133: $i] :
( ( ~ ! [SY741: $i,SY742: $i] :
( ~ ( relation @ SY742 )
| ~ ( in @ ( ordered_pair @ SV133 @ SY741 ) @ SY742 )
| ( in @ SY741 @ ( relation_rng @ SY742 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1230]) ).
thf(1446,plain,
! [SV134: $i] :
( ( ( relation @ SV134 )
= $false )
| ( ( ~ ( ~ ! [SY743: $i] :
( ~ ( ~ ( ! [SY744: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SY743 @ SV134 ) @ SY744 ) @ SV134 )
| ~ ( in @ ( sK22_C @ SY743 @ SV134 ) @ SY743 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SY743 @ SV134 ) @ ( sK23_SY466 @ SY743 @ SV134 ) ) @ SV134 )
| ( in @ ( sK22_C @ SY743 @ SV134 ) @ SY743 ) ) )
| ( SY743
= ( relation_dom @ SV134 ) ) )
| ~ ! [SY745: $i] :
( ( SY745
!= ( relation_dom @ SV134 ) )
| ~ ( ~ ! [SY746: $i] :
( ! [SY747: $i] :
~ ( in @ ( ordered_pair @ SY746 @ SY747 ) @ SV134 )
| ( in @ SY746 @ SY745 ) )
| ~ ! [SY748: $i] :
( ~ ( in @ SY748 @ SY745 )
| ( in @ ( ordered_pair @ SY748 @ ( sK21_D @ SY748 @ SY745 @ SV134 ) ) @ SV134 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1231]) ).
thf(1447,plain,
! [SV135: $i] :
( ( ~ ! [SY749: $i,SY750: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK57_D @ SY750 @ SY749 @ SV135 ) @ SY750 )
| ( ( sK57_D @ SY750 @ SY749 @ SV135 )
!= SV135 ) )
| ~ ( ~ ( in @ ( sK57_D @ SY750 @ SY749 @ SV135 ) @ SY750 )
| ( ( sK57_D @ SY750 @ SY749 @ SV135 )
!= SY749 ) ) )
| ~ ( ( in @ ( sK57_D @ SY750 @ SY749 @ SV135 ) @ SY750 )
| ( ( sK57_D @ SY750 @ SY749 @ SV135 )
= SV135 )
| ( ( sK57_D @ SY750 @ SY749 @ SV135 )
= SY749 ) ) )
| ( SY750
= ( unordered_pair @ SV135 @ SY749 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1232]) ).
thf(1448,plain,
! [SV135: $i] :
( ( ~ ! [SY751: $i,SY752: $i] :
( ( SY752
!= ( unordered_pair @ SV135 @ SY751 ) )
| ~ ( ~ ! [SY753: $i] :
( ~ ( in @ SY753 @ SY752 )
| ( SY753 = SV135 )
| ( SY753 = SY751 ) )
| ~ ~ ( ~ ! [SY754: $i] :
( ( SY754 != SV135 )
| ( in @ SY754 @ SY752 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY751 )
| ( in @ SX3 @ SY752 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1232]) ).
thf(1449,plain,
( ( ( relation_dom @ empty_set )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1233]) ).
thf(1450,plain,
( ( ( relation_rng @ empty_set )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1234]) ).
thf(1451,plain,
! [SV136: $i] :
( ( ( relation @ SV136 )
= $false )
| ( ( ~ ( ~ ! [SY756: $i] :
( ~ ( relation @ SY756 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK58_C @ SY756 @ SV136 ) @ ( sK59_SY494 @ SY756 @ SV136 ) ) @ SV136 )
| ~ ( in @ ( ordered_pair @ ( sK58_C @ SY756 @ SV136 ) @ ( sK59_SY494 @ SY756 @ SV136 ) ) @ SY756 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_C @ SY756 @ SV136 ) @ ( sK59_SY494 @ SY756 @ SV136 ) ) @ SV136 )
| ( in @ ( ordered_pair @ ( sK58_C @ SY756 @ SV136 ) @ ( sK59_SY494 @ SY756 @ SV136 ) ) @ SY756 ) ) )
| ( SV136 = SY756 ) )
| ~ ! [SY757: $i] :
( ~ ( relation @ SY757 )
| ( SV136 != SY757 )
| ~ ( ~ ! [SY758: $i,SY759: $i] :
( ~ ( in @ ( ordered_pair @ SY758 @ SY759 ) @ SV136 )
| ( in @ ( ordered_pair @ SY758 @ SY759 ) @ SY757 ) )
| ~ ! [SY760: $i,SY761: $i] :
( ~ ( in @ ( ordered_pair @ SY760 @ SY761 ) @ SY757 )
| ( in @ ( ordered_pair @ SY760 @ SY761 ) @ SV136 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1235]) ).
thf(1452,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)],[1236]) ).
thf(1453,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)],[1237]) ).
thf(1454,plain,
! [SV137: $i,SV230: $i] :
( ( ( ~ ( function @ SV230 )
| ~ ( relation @ SV230 ) )
= $true )
| ( ( ~ ( ~ ! [SY861: $i] :
( ~ ( function @ SY861 )
| ~ ( relation @ SY861 )
| ~ ( in @ SV137 @ ( relation_dom @ SY861 ) )
| ~ ( in @ ( apply @ SY861 @ SV137 ) @ ( relation_dom @ SV230 ) )
| ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY861 @ SV230 ) ) ) )
| ~ ~ ( ~ ! [SY862: $i] :
( ~ ( function @ SY862 )
| ~ ( relation @ SY862 )
| ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY862 @ SV230 ) ) )
| ( in @ SV137 @ ( relation_dom @ SY862 ) ) )
| ~ ! [SY863: $i] :
( ~ ( function @ SY863 )
| ~ ( relation @ SY863 )
| ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY863 @ SV230 ) ) )
| ( in @ ( apply @ SY863 @ SV137 ) @ ( relation_dom @ SV230 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1238]) ).
thf(1455,plain,
! [SV138: $i] :
( ( ~ ! [SY766: $i] :
( ~ ( subset @ SY766 @ ( sK41_B @ SV138 ) )
| ( are_equipotent @ SY766 @ ( sK41_B @ SV138 ) )
| ( in @ SY766 @ ( sK41_B @ SV138 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1239]) ).
thf(1456,plain,
! [SV138: $i] :
( ( ~ ~ ( ~ ! [SY767: $i] :
( ~ ( in @ SY767 @ ( sK41_B @ SV138 ) )
| ( in @ ( powerset @ SY767 ) @ ( sK41_B @ SV138 ) ) )
| ~ ~ ( ~ ! [SY768: $i,SY769: $i] :
( ~ ( in @ SY768 @ ( sK41_B @ SV138 ) )
| ~ ( subset @ SY769 @ SY768 )
| ( in @ SY769 @ ( sK41_B @ SV138 ) ) )
| ~ ( in @ SV138 @ ( sK41_B @ SV138 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1239]) ).
thf(1457,plain,
! [SV139: $i] :
( ( ( relation @ SV139 )
= $false )
| ( ( ~ ( ~ ! [SY770: $i] :
( ~ ( relation @ SY770 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SY770 @ SV139 ) @ ( sK25_SY467 @ SY770 @ SV139 ) ) @ SV139 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SY770 @ SV139 ) @ ( sK25_SY467 @ SY770 @ SV139 ) ) @ SY770 ) )
| ( subset @ SV139 @ SY770 ) )
| ~ ! [SY771: $i] :
( ~ ( relation @ SY771 )
| ~ ( subset @ SV139 @ SY771 )
| ! [SY772: $i,SY773: $i] :
( ~ ( in @ ( ordered_pair @ SY772 @ SY773 ) @ SV139 )
| ( in @ ( ordered_pair @ SY772 @ SY773 ) @ SY771 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1240]) ).
thf(1458,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK60_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK60_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK60_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK60_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1241]) ).
thf(1459,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1242]) ).
thf(1460,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1243]) ).
thf(1461,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1244]) ).
thf(1462,plain,
! [SV140: $i] :
( ( ( relation @ SV140 )
= $false )
| ( ( ~ ( ~ ! [SY774: $i] :
( ~ ( relation @ SY774 )
| ~ ( subset @ SV140 @ SY774 )
| ( subset @ ( relation_dom @ SV140 ) @ ( relation_dom @ SY774 ) ) )
| ~ ! [SY775: $i] :
( ~ ( relation @ SY775 )
| ~ ( subset @ SV140 @ SY775 )
| ( subset @ ( relation_rng @ SV140 ) @ ( relation_rng @ SY775 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1245]) ).
thf(1463,plain,
! [SV141: $i] :
( ( ( ~ ( element @ ( sK8_B @ SV141 ) @ ( powerset @ SV141 ) )
| ~ ~ ( empty @ ( sK8_B @ SV141 ) ) )
= $false )
| ( ( empty @ SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1246]) ).
thf(1464,plain,
! [SV142: $i] :
( ( ~ ! [SY776: $i,SY777: $i] :
( ~ ( relation @ SY777 )
| ! [SY778: $i] :
( ~ ( in @ SY778 @ ( relation_rng @ SY777 ) )
| ~ ( in @ ( ordered_pair @ SV142 @ SY778 ) @ SY777 )
| ~ ( in @ SY778 @ SY776 ) )
| ( in @ SV142 @ ( relation_inverse_image @ SY777 @ SY776 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1247]) ).
thf(1465,plain,
! [SV142: $i] :
( ( ~ ! [SY779: $i,SY780: $i] :
( ~ ( relation @ SY780 )
| ~ ( in @ SV142 @ ( relation_inverse_image @ SY780 @ SY779 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK39_D @ SY780 @ SY779 @ SV142 ) @ ( relation_rng @ SY780 ) )
| ~ ( in @ ( ordered_pair @ SV142 @ ( sK39_D @ SY780 @ SY779 @ SV142 ) ) @ SY780 ) )
| ~ ( in @ ( sK39_D @ SY780 @ SY779 @ SV142 ) @ SY779 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1247]) ).
thf(1466,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK65_SY495 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK64_C @ SX1 @ SX0 ) @ ( sK65_SY495 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK64_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK64_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK64_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK63_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK63_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1248]) ).
thf(1467,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1249]) ).
thf(1468,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1250]) ).
thf(1469,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1251]) ).
thf(1470,plain,
( ( ! [SX0: $i] :
( ( relation_dom @ ( identity_relation @ SX0 ) )
= SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1252]) ).
thf(1471,plain,
( ( ! [SX0: $i] :
( ( relation_rng @ ( identity_relation @ SX0 ) )
= SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1253]) ).
thf(1472,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1254]) ).
thf(1473,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1255]) ).
thf(1474,plain,
! [SV231: $i,SV143: $i] :
( ( ~ ! [SY864: $i,SY865: $i] :
( ~ ( in @ SV143 @ SY864 )
| ~ ( in @ SV231 @ SY865 )
| ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SY864 @ SY865 ) ) )
| ~ ~ ( ~ ! [SY866: $i] :
( ! [SY867: $i] :
~ ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SY866 @ SY867 ) )
| ( in @ SV143 @ SY866 ) )
| ~ ! [SY868: $i,SY869: $i] :
( ~ ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SY868 @ SY869 ) )
| ( in @ SV231 @ SY869 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1256]) ).
thf(1475,plain,
! [SV144: $i] :
( ( ~ ! [SY788: $i,SY789: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK56_D @ SY789 @ SY788 @ SV144 ) @ SY789 )
| ~ ( in @ ( sK56_D @ SY789 @ SY788 @ SV144 ) @ SV144 ) )
| ~ ( ~ ( in @ ( sK56_D @ SY789 @ SY788 @ SV144 ) @ SY789 )
| ~ ( in @ ( sK56_D @ SY789 @ SY788 @ SV144 ) @ SY788 ) ) )
| ~ ( ( in @ ( sK56_D @ SY789 @ SY788 @ SV144 ) @ SY789 )
| ( in @ ( sK56_D @ SY789 @ SY788 @ SV144 ) @ SV144 )
| ( in @ ( sK56_D @ SY789 @ SY788 @ SV144 ) @ SY788 ) ) )
| ( SY789
= ( set_union2 @ SV144 @ SY788 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1257]) ).
thf(1476,plain,
! [SV144: $i] :
( ( ~ ! [SY790: $i,SY791: $i] :
( ( SY791
!= ( set_union2 @ SV144 @ SY790 ) )
| ~ ( ~ ! [SY792: $i] :
( ~ ( in @ SY792 @ SY791 )
| ( in @ SY792 @ SV144 )
| ( in @ SY792 @ SY790 ) )
| ~ ~ ( ~ ! [SY793: $i] :
( ~ ( in @ SY793 @ SV144 )
| ( in @ SY793 @ SY791 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY790 )
| ( in @ SX3 @ SY791 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1257]) ).
thf(1477,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1258]) ).
thf(1478,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1259]) ).
thf(1479,plain,
! [SV145: $i] :
( ( ~ ! [SY795: $i,SY796: $i] :
( ~ ( relation @ SY796 )
| ! [SY797: $i] :
( ~ ( in @ SY797 @ ( relation_dom @ SY796 ) )
| ~ ( in @ ( ordered_pair @ SY797 @ SV145 ) @ SY796 )
| ~ ( in @ SY797 @ SY795 ) )
| ( in @ SV145 @ ( relation_image @ SY796 @ SY795 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1260]) ).
thf(1480,plain,
! [SV145: $i] :
( ( ~ ! [SY798: $i,SY799: $i] :
( ~ ( relation @ SY799 )
| ~ ( in @ SV145 @ ( relation_image @ SY799 @ SY798 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK40_D @ SY799 @ SY798 @ SV145 ) @ ( relation_dom @ SY799 ) )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY799 @ SY798 @ SV145 ) @ SV145 ) @ SY799 ) )
| ~ ( in @ ( sK40_D @ SY799 @ SY798 @ SV145 ) @ SY798 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1260]) ).
thf(1481,plain,
! [SV146: $i] :
( ( ~ ! [SY800: $i] :
( ~ ( subset @ SV146 @ SY800 )
| ! [SY801: $i] : ( subset @ ( cartesian_product2 @ SV146 @ SY801 ) @ ( cartesian_product2 @ SY800 @ SY801 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1261]) ).
thf(1482,plain,
! [SV146: $i] :
( ( ~ ! [SY802: $i] :
( ~ ( subset @ SV146 @ SY802 )
| ! [SY803: $i] : ( subset @ ( cartesian_product2 @ SY803 @ SV146 ) @ ( cartesian_product2 @ SY803 @ SY802 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1261]) ).
thf(1483,plain,
! [SV147: $i,SV232: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK44_C @ SV232 @ SV147 ) @ SV147 )
| ~ ( in @ ( sK44_C @ SV232 @ SV147 ) @ SV232 ) )
| ~ ( ( in @ ( sK44_C @ SV232 @ SV147 ) @ SV147 )
| ( in @ ( sK44_C @ SV232 @ SV147 ) @ SV232 ) ) ) )
= $true )
| ( ( SV147 = SV232 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1262]) ).
thf(1484,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1263]) ).
thf(1485,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1264]) ).
thf(1486,plain,
! [SV233: $i,SV148: $i] :
( ( ~ ! [SY870: $i] :
( ! [SY871: $i] :
( ( ordered_pair @ SV148 @ SV233 )
!= ( ordered_pair @ SY870 @ SY871 ) )
| ( SV148 = SY870 ) )
| ~ ! [SY872: $i,SY873: $i] :
( ( ( ordered_pair @ SV148 @ SV233 )
!= ( ordered_pair @ SY872 @ SY873 ) )
| ( SV233 = SY873 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1265]) ).
thf(1487,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK50_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK50_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1266]) ).
thf(1488,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1267]) ).
thf(1489,plain,
( ( ~ ( empty @ sK6_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1268]) ).
thf(1490,plain,
( ( relation @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1269]) ).
thf(1491,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1270]) ).
thf(1492,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1271]) ).
thf(1493,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1272]) ).
thf(1494,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1273]) ).
thf(1495,plain,
! [SV149: $i] :
( ( ~ ! [SY810: $i,SY811: $i] :
( ~ ( ~ ( ~ ( in @ ( sK45_D @ SY811 @ SY810 @ SV149 ) @ SV149 )
| ( in @ ( sK45_D @ SY811 @ SY810 @ SV149 ) @ SY810 )
| ~ ( in @ ( sK45_D @ SY811 @ SY810 @ SV149 ) @ SY811 ) )
| ~ ~ ( ~ ( ( in @ ( sK45_D @ SY811 @ SY810 @ SV149 ) @ SV149 )
| ( in @ ( sK45_D @ SY811 @ SY810 @ SV149 ) @ SY811 ) )
| ~ ( ~ ( in @ ( sK45_D @ SY811 @ SY810 @ SV149 ) @ SY810 )
| ( in @ ( sK45_D @ SY811 @ SY810 @ SV149 ) @ SY811 ) ) ) )
| ( SY811
= ( set_difference @ SV149 @ SY810 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1274]) ).
thf(1496,plain,
! [SV149: $i] :
( ( ~ ! [SY812: $i,SY813: $i] :
( ( SY813
!= ( set_difference @ SV149 @ SY812 ) )
| ~ ( ~ ! [SY814: $i] :
( ~ ( in @ SY814 @ SV149 )
| ( in @ SY814 @ SY812 )
| ( in @ SY814 @ SY813 ) )
| ~ ~ ( ~ ! [SY815: $i] :
( ~ ( in @ SY815 @ SY813 )
| ( in @ SY815 @ SV149 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY813 )
| ~ ( in @ SX3 @ SY812 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1274]) ).
thf(1497,plain,
! [SV150: $i,SV1: $i] :
( ( ( in @ SV1 @ SV150 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV1 ) @ SV150 )
= SV150 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1275]) ).
thf(1498,plain,
! [SV151: $i,SV2: $i] :
( ( ( disjoint @ ( singleton @ SV2 ) @ SV151 )
= $false )
| ( ( ~ ( in @ SV2 @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1276]) ).
thf(1499,plain,
! [SV4: $i,SV153: $i] :
( ( ( element @ SV153 @ ( powerset @ SV4 ) )
= $false )
| ( ( ! [SY817: $i] :
( ~ ( in @ SY817 @ SV153 )
| ( in @ SY817 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1278]) ).
thf(1500,plain,
! [SV154: $i,SV5: $i] :
( ( ( in @ SV5 @ SV154 )
= $false )
| ( ( subset @ SV5 @ ( union @ SV154 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1279]) ).
thf(1501,plain,
! [SV155: $i,SV6: $i] :
( ( ( in @ SV6 @ SV155 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV6 ) @ SV155 )
= SV155 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1280]) ).
thf(1502,plain,
! [SV156: $i,SV7: $i] :
( ( ( in @ SV7 @ SV156 )
= $false )
| ( ( subset @ SV7 @ ( union @ SV156 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1281]) ).
thf(1503,plain,
! [SV157: $i,SV8: $i] :
( ( ( in @ SV8 @ SV157 )
= $false )
| ( ( ~ ( in @ SV157 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1282]) ).
thf(1504,plain,
! [SV158: $i,SV10: $i] :
( ( ( in @ SV10 @ SV158 )
= $false )
| ( ( element @ SV10 @ SV158 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1283]) ).
thf(1505,plain,
! [SV159: $i,SV11: $i] :
( ( ( element @ SV11 @ SV159 )
= $false )
| ( ( ( empty @ SV159 )
| ( in @ SV11 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1284]) ).
thf(1506,plain,
! [SV12: $i,SV234: $i,SV160: $i] :
( ( ( ~ ( element @ SV160 @ ( powerset @ SV234 ) )
| ~ ( in @ SV12 @ SV160 ) )
= $true )
| ( ( element @ SV12 @ SV234 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1285]) ).
thf(1507,plain,
! [SV13: $i,SV161: $i] :
( ( ( empty @ SV161 )
= $false )
| ( ( ~ ( in @ SV13 @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1286]) ).
thf(1508,plain,
! [SV162: $i,SV15: $i] :
( ( ( subset @ SV15 @ SV162 )
= $false )
| ( ( ! [SY819: $i] :
( ( in @ SY819 @ SV15 )
| ( subset @ SV15 @ ( set_difference @ SV162 @ ( singleton @ SY819 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1287]) ).
thf(1509,plain,
! [SV163: $i,SV235: $i,SV250: $i,SV16: $i] :
( ( ( SV16 = SV250 )
| ( SV16 = SV235 )
| ( ( unordered_pair @ SV16 @ SV163 )
!= ( unordered_pair @ SV235 @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1510,plain,
! [SV17: $i,SV164: $i] :
( ( ( relation @ SV164 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV17 @ SV164 ) ) @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1289]) ).
thf(1511,plain,
! [SV18: $i,SV165: $i] :
( ( ( relation @ SV165 )
= $false )
| ( ( subset @ ( relation_rng_restriction @ SV18 @ SV165 ) @ SV165 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1290]) ).
thf(1512,plain,
! [SV19: $i,SV166: $i] :
( ( ( relation @ SV166 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV19 @ SV166 ) ) @ ( relation_rng @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1291]) ).
thf(1513,plain,
! [SV20: $i,SV167: $i] :
( ( ( relation @ SV167 )
= $false )
| ( ( ( relation_rng @ ( relation_rng_restriction @ SV20 @ SV167 ) )
= ( set_intersection2 @ ( relation_rng @ SV167 ) @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1292]) ).
thf(1514,plain,
! [SV251: $i,SV236: $i,SV168: $i,SV21: $i] :
( ( ~ ( subset @ SV21 @ SV168 )
| ~ ( subset @ SV236 @ SV251 )
| ( subset @ ( cartesian_product2 @ SV21 @ SV236 ) @ ( cartesian_product2 @ SV168 @ SV251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1515,plain,
! [SV169: $i,SV22: $i] :
( ( ( subset @ SV22 @ SV169 )
= $false )
| ( ( ( set_union2 @ SV22 @ SV169 )
= SV169 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1294]) ).
thf(1516,plain,
! [SV23: $i,SV170: $i] :
( ( ( relation @ SV170 )
= $false )
| ( ( subset @ ( relation_image @ SV170 @ SV23 ) @ ( relation_rng @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1295]) ).
thf(1517,plain,
! [SV24: $i,SV171: $i] :
( ( ( relation @ SV171 )
= $false )
| ( ( ( relation_image @ SV171 @ SV24 )
= ( relation_image @ SV171 @ ( set_intersection2 @ ( relation_dom @ SV171 ) @ SV24 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1296]) ).
thf(1518,plain,
! [SV26: $i,SV172: $i] :
( ( ( relation @ SV172 )
= $false )
| ( ( subset @ ( relation_inverse_image @ SV172 @ SV26 ) @ ( relation_dom @ SV172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1298]) ).
thf(1519,plain,
! [SV27: $i,SV173: $i] :
( ( ( relation @ SV173 )
= $false )
| ( ( ( SV27 = empty_set )
| ~ ( subset @ SV27 @ ( relation_rng @ SV173 ) )
| ( ( relation_inverse_image @ SV173 @ SV27 )
!= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1299]) ).
thf(1520,plain,
! [SV174: $i,SV28: $i,SV237: $i] :
( ( ( ~ ( relation @ SV237 ) )
= $true )
| ( ( ~ ( subset @ SV28 @ SV174 )
| ( subset @ ( relation_inverse_image @ SV237 @ SV28 ) @ ( relation_inverse_image @ SV237 @ SV174 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1300]) ).
thf(1521,plain,
! [SV238: $i,SV176: $i,SV30: $i] :
( ( ( ~ ( subset @ SV30 @ SV176 )
| ~ ( subset @ SV30 @ SV238 ) )
= $true )
| ( ( subset @ SV30 @ ( set_intersection2 @ SV176 @ SV238 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1301]) ).
thf(1522,plain,
! [SV239: $i,SV177: $i,SV31: $i] :
( ( ( ~ ( subset @ SV31 @ SV177 )
| ~ ( subset @ SV177 @ SV239 ) )
= $true )
| ( ( subset @ SV31 @ SV239 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1302]) ).
thf(1523,plain,
! [SV33: $i,SV178: $i] :
( ( ( ~ ( function @ SV178 ) )
= $true )
| ( ( ~ ( relation @ SV178 ) )
= $true )
| ( ( ! [SY827: $i] :
( ~ ( function @ SY827 )
| ~ ( relation @ SY827 )
| ~ ( in @ SV33 @ ( relation_dom @ ( relation_composition @ SY827 @ SV178 ) ) )
| ( ( apply @ ( relation_composition @ SY827 @ SV178 ) @ SV33 )
= ( apply @ SV178 @ ( apply @ SY827 @ SV33 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1304]) ).
thf(1524,plain,
! [SV34: $i,SV179: $i] :
( ( ( ~ ( function @ SV179 ) )
= $true )
| ( ( ~ ( relation @ SV179 ) )
= $true )
| ( ( ! [SY828: $i] :
( ~ ( function @ SY828 )
| ~ ( relation @ SY828 )
| ~ ( in @ SV34 @ ( relation_dom @ SV179 ) )
| ( ( apply @ ( relation_composition @ SV179 @ SY828 ) @ SV34 )
= ( apply @ SY828 @ ( apply @ SV179 @ SV34 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1305]) ).
thf(1525,plain,
! [SV180: $i,SV35: $i] :
( ( ( subset @ SV35 @ SV180 )
= $false )
| ( ( ! [SY829: $i] : ( subset @ ( set_intersection2 @ SV35 @ SY829 ) @ ( set_intersection2 @ SV180 @ SY829 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1306]) ).
thf(1526,plain,
! [SV181: $i,SV36: $i] :
( ( ( subset @ SV36 @ SV181 )
= $false )
| ( ( ( set_intersection2 @ SV36 @ SV181 )
= SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1307]) ).
thf(1527,plain,
! [SV182: $i,SV38: $i] :
( ( ( subset @ SV38 @ SV182 )
= $false )
| ( ( ! [SY830: $i] : ( subset @ ( set_difference @ SV38 @ SY830 ) @ ( set_difference @ SV182 @ SY830 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1308]) ).
thf(1528,plain,
! [SV43: $i,SV252: $i] :
( ( ( ~ ( relation @ SV252 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV43 @ SV252 ) ) @ ( relation_dom @ SV43 ) ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1310]) ).
thf(1529,plain,
! [SV44: $i,SV253: $i] :
( ( ( ~ ( relation @ SV253 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV44 @ SV253 ) ) @ ( relation_rng @ SV253 ) ) )
= $true )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1530,plain,
! [SV186: $i,SV45: $i] :
( ( ( subset @ SV45 @ SV186 )
= $false )
| ( ( SV186
= ( set_union2 @ SV45 @ ( set_difference @ SV186 @ SV45 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1312]) ).
thf(1531,plain,
! [SV46: $i,SV254: $i] :
( ( ( ~ ( relation @ SV254 )
| ~ ( subset @ ( relation_rng @ SV46 ) @ ( relation_dom @ SV254 ) )
| ( ( relation_dom @ ( relation_composition @ SV46 @ SV254 ) )
= ( relation_dom @ SV46 ) ) )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1313]) ).
thf(1532,plain,
! [SV47: $i,SV187: $i] :
( ( ( element @ SV187 @ ( powerset @ ( powerset @ SV47 ) ) )
= $false )
| ( ( ( SV187 = empty_set )
| ( ( complements_of_subsets @ SV47 @ SV187 )
!= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1314]) ).
thf(1533,plain,
! [SV48: $i,SV255: $i] :
( ( ( ~ ( relation @ SV255 )
| ~ ( subset @ ( relation_dom @ SV48 ) @ ( relation_rng @ SV255 ) )
| ( ( relation_rng @ ( relation_composition @ SV255 @ SV48 ) )
= ( relation_rng @ SV48 ) ) )
= $true )
| ( ( relation @ SV48 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1534,plain,
! [SV50: $i,SV240: $i] :
( ( ( ~ ( element @ SV240 @ ( powerset @ SV50 ) ) )
= $true )
| ( ( ! [SY876: $i] :
( ~ ( element @ SY876 @ SV50 )
| ( in @ SY876 @ SV240 )
| ( in @ SY876 @ ( subset_complement @ SV50 @ SV240 ) ) ) )
= $true )
| ( ( SV50 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1316]) ).
thf(1535,plain,
! [SV189: $i,SV51: $i,SV241: $i] :
( ( ( ~ ( element @ SV241 @ ( powerset @ SV51 ) ) )
= $true )
| ( ( ~ ( in @ SV189 @ ( subset_complement @ SV51 @ SV241 ) )
| ~ ( in @ SV189 @ SV241 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1317]) ).
thf(1536,plain,
! [SV52: $i] :
( ( ( in @ ( ordered_pair @ ( sK36_B @ SV52 ) @ ( sK37_SY474 @ SV52 ) ) @ SV52 )
= $true )
| ( ( SV52 = empty_set )
= $true )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1318]) ).
thf(1537,plain,
! [SV53: $i,SV190: $i] :
( ( ( proper_subset @ SV190 @ SV53 )
= $false )
| ( ( ~ ( subset @ SV53 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1319]) ).
thf(1538,plain,
! [SV54: $i,SV242: $i,SV191: $i] :
( ( ( ~ ( disjoint @ SV191 @ SV242 )
| ~ ( subset @ SV54 @ SV191 ) )
= $true )
| ( ( disjoint @ SV54 @ SV242 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1320]) ).
thf(1539,plain,
! [SV192: $i,SV56: $i] :
( ( ( subset @ ( singleton @ SV56 ) @ ( singleton @ SV192 ) )
= $false )
| ( ( SV56 = SV192 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1321]) ).
thf(1540,plain,
! [SV58: $i,SV194: $i] :
( ( ( relation @ SV194 )
= $false )
| ( ( subset @ ( relation_dom_restriction @ SV194 @ SV58 ) @ SV194 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1322]) ).
thf(1541,plain,
! [SV243: $i,SV195: $i,SV59: $i] :
( ( ( ~ ( subset @ SV59 @ SV195 )
| ~ ( subset @ SV243 @ SV195 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV59 @ SV243 ) @ SV195 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1323]) ).
thf(1542,plain,
! [SV256: $i,SV196: $i,SV60: $i] :
( ( ( ( ( singleton @ SV60 )
!= ( unordered_pair @ SV196 @ SV256 ) ) )
= $true )
| ( ( SV60 = SV196 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1543,plain,
! [SV61: $i,SV197: $i] :
( ( ( relation @ SV197 )
= $false )
| ( ( ( relation_dom @ ( relation_dom_restriction @ SV197 @ SV61 ) )
= ( set_intersection2 @ ( relation_dom @ SV197 ) @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1325]) ).
thf(1544,plain,
! [SV62: $i,SV198: $i] :
( ( ( relation @ SV198 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV198 @ SV62 ) ) @ ( relation_rng @ SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1326]) ).
thf(1545,plain,
! [SV244: $i,SV199: $i,SV64: $i] :
( ( ( ( ( singleton @ SV64 )
!= ( unordered_pair @ SV199 @ SV244 ) ) )
= $true )
| ( ( SV199 = SV244 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1327]) ).
thf(1546,plain,
! [SV70: $i,SV203: $i] :
( ( ( element @ SV203 @ ( powerset @ SV70 ) )
= $false )
| ( ( ( subset_complement @ SV70 @ SV203 )
= ( set_difference @ SV70 @ SV203 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1330]) ).
thf(1547,plain,
! [SV74: $i,SV205: $i] :
( ( ( element @ SV205 @ ( powerset @ SV74 ) )
= $false )
| ( ( element @ ( subset_complement @ SV74 @ SV205 ) @ ( powerset @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1332]) ).
thf(1548,plain,
! [SV206: $i,SV76: $i] :
( ( ( ~ ( relation @ SV76 ) )
= $true )
| ( ( ~ ( relation @ SV206 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV76 @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1334]) ).
thf(1549,plain,
! [SV77: $i,SV207: $i] :
( ( ( element @ SV207 @ ( powerset @ ( powerset @ SV77 ) ) )
= $false )
| ( ( element @ ( union_of_subsets @ SV77 @ SV207 ) @ ( powerset @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1335]) ).
thf(1550,plain,
! [SV78: $i,SV208: $i] :
( ( ( element @ SV208 @ ( powerset @ ( powerset @ SV78 ) ) )
= $false )
| ( ( element @ ( meet_of_subsets @ SV78 @ SV208 ) @ ( powerset @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1336]) ).
thf(1551,plain,
! [SV245: $i,SV79: $i,SV209: $i] :
( ( ( ~ ( element @ SV209 @ ( powerset @ SV79 ) )
| ~ ( element @ SV245 @ ( powerset @ SV79 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV79 @ SV209 @ SV245 ) @ ( powerset @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1337]) ).
thf(1552,plain,
! [SV257: $i,SV80: $i] :
( ( ( relation @ ( relation_dom_restriction @ SV80 @ SV257 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1338]) ).
thf(1553,plain,
! [SV81: $i,SV210: $i] :
( ( ( element @ SV210 @ ( powerset @ ( powerset @ SV81 ) ) )
= $false )
| ( ( element @ ( complements_of_subsets @ SV81 @ SV210 ) @ ( powerset @ ( powerset @ SV81 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1339]) ).
thf(1554,plain,
! [SV82: $i,SV211: $i] :
( ( ( relation @ SV211 )
= $false )
| ( ( relation @ ( relation_rng_restriction @ SV82 @ SV211 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1340]) ).
thf(1555,plain,
! [SV212: $i,SV84: $i] :
( ( ( ~ ( relation @ SV84 ) )
= $true )
| ( ( ~ ( relation @ SV212 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV84 @ SV212 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1341]) ).
thf(1556,plain,
! [SV214: $i,SV87: $i] :
( ( ( ~ ( relation @ SV87 ) )
= $true )
| ( ( ~ ( relation @ SV214 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV87 @ SV214 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1343]) ).
thf(1557,plain,
! [SV246: $i,SV89: $i] :
( ( ( empty @ ( set_union2 @ SV89 @ SV246 ) )
= $false )
| ( ( empty @ SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1344]) ).
thf(1558,plain,
! [SV91: $i,SV247: $i] :
( ( ( empty @ ( set_union2 @ SV247 @ SV91 ) )
= $false )
| ( ( empty @ SV91 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1346]) ).
thf(1559,plain,
! [SV216: $i,SV92: $i] :
( ( ( empty @ SV92 )
= $true )
| ( ( empty @ SV216 )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV92 @ SV216 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1347]) ).
thf(1560,plain,
! [SV93: $i] :
( ( ( relation @ SV93 )
= $false )
| ( ( empty @ SV93 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV93 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1348]) ).
thf(1561,plain,
! [SV94: $i] :
( ( ( relation @ SV94 )
= $false )
| ( ( empty @ SV94 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV94 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1349]) ).
thf(1562,plain,
! [SV97: $i,SV217: $i] :
( ( ( element @ SV217 @ ( powerset @ SV97 ) )
= $false )
| ( ( ( subset_complement @ SV97 @ ( subset_complement @ SV97 @ SV217 ) )
= SV217 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1350]) ).
thf(1563,plain,
! [SV99: $i,SV218: $i] :
( ( ( element @ SV218 @ ( powerset @ ( powerset @ SV99 ) ) )
= $false )
| ( ( ( complements_of_subsets @ SV99 @ ( complements_of_subsets @ SV99 @ SV218 ) )
= SV218 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1352]) ).
thf(1564,plain,
! [SV100: $i,SV219: $i] :
( ( ( element @ SV219 @ ( powerset @ ( powerset @ SV100 ) ) )
= $false )
| ( ( ( union_of_subsets @ SV100 @ SV219 )
= ( union @ SV219 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1353]) ).
thf(1565,plain,
! [SV101: $i,SV220: $i] :
( ( ( element @ SV220 @ ( powerset @ ( powerset @ SV101 ) ) )
= $false )
| ( ( ( meet_of_subsets @ SV101 @ SV220 )
= ( set_meet @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1354]) ).
thf(1566,plain,
! [SV248: $i,SV102: $i,SV221: $i] :
( ( ( ~ ( element @ SV221 @ ( powerset @ SV102 ) )
| ~ ( element @ SV248 @ ( powerset @ SV102 ) ) )
= $true )
| ( ( ( subset_difference @ SV102 @ SV221 @ SV248 )
= ( set_difference @ SV221 @ SV248 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1355]) ).
thf(1567,plain,
! [SV222: $i,SV104: $i] :
( ( ( disjoint @ SV104 @ SV222 )
= $false )
| ( ( disjoint @ SV222 @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1356]) ).
thf(1568,plain,
! [SV109: $i,SV249: $i,SV223: $i] :
( ( ( ~ ( element @ SV223 @ ( powerset @ SV249 ) )
| ~ ( in @ SV109 @ SV223 ) )
= $true )
| ( ( ~ ( empty @ SV249 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1357]) ).
thf(1569,plain,
! [SV224: $i,SV111: $i] :
( ( ( SV111 = SV224 )
= $true )
| ( ( ~ ( empty @ SV111 ) )
= $true )
| ( ( ~ ( empty @ SV224 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1359]) ).
thf(1570,plain,
! [SV112: $i] :
( ( ! [SY607: $i,SY608: $i] :
( ~ ( ~ ( ~ ( in @ ( sK49_D @ SY608 @ SY607 @ SV112 ) @ SV112 )
| ~ ( in @ ( sK49_D @ SY608 @ SY607 @ SV112 ) @ SY607 )
| ~ ( in @ ( sK49_D @ SY608 @ SY607 @ SV112 ) @ SY608 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_D @ SY608 @ SY607 @ SV112 ) @ SV112 )
| ( in @ ( sK49_D @ SY608 @ SY607 @ SV112 ) @ SY608 ) )
| ~ ( ( in @ ( sK49_D @ SY608 @ SY607 @ SV112 ) @ SY607 )
| ( in @ ( sK49_D @ SY608 @ SY607 @ SV112 ) @ SY608 ) ) ) )
| ( SY608
= ( set_intersection2 @ SV112 @ SY607 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1360]) ).
thf(1571,plain,
! [SV112: $i] :
( ( ! [SY609: $i,SY610: $i] :
( ( SY610
!= ( set_intersection2 @ SV112 @ SY609 ) )
| ~ ( ~ ! [SY611: $i] :
( ~ ( in @ SY611 @ SV112 )
| ~ ( in @ SY611 @ SY609 )
| ( in @ SY611 @ SY610 ) )
| ~ ~ ( ~ ! [SY612: $i] :
( ~ ( in @ SY612 @ SY610 )
| ( in @ SY612 @ SV112 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY610 )
| ( in @ SX3 @ SY609 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1361]) ).
thf(1572,plain,
! [SV258: $i] :
( ( ! [SY877: $i] :
( ~ ( ~ ( ! [SY878: $i] :
( ~ ( in @ ( sK47_C @ SY877 @ SV258 ) @ SY878 )
| ~ ( in @ SY878 @ SV258 ) )
| ~ ( in @ ( sK47_C @ SY877 @ SV258 ) @ SY877 ) )
| ~ ( ~ ( ~ ( in @ ( sK47_C @ SY877 @ SV258 ) @ ( sK48_SY487 @ SY877 @ SV258 ) )
| ~ ( in @ ( sK48_SY487 @ SY877 @ SV258 ) @ SV258 ) )
| ( in @ ( sK47_C @ SY877 @ SV258 ) @ SY877 ) ) )
| ( SY877
= ( union @ SV258 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1362]) ).
thf(1573,plain,
! [SV259: $i] :
( ( ! [SY879: $i] :
( ( SY879
!= ( union @ SV259 ) )
| ~ ( ~ ! [SY880: $i] :
( ! [SY881: $i] :
( ~ ( in @ SY880 @ SY881 )
| ~ ( in @ SY881 @ SV259 ) )
| ( in @ SY880 @ SY879 ) )
| ~ ! [SY882: $i] :
( ~ ( in @ SY882 @ SY879 )
| ~ ( ~ ( in @ SY882 @ ( sK46_D @ SY882 @ SY879 @ SV259 ) )
| ~ ( in @ ( sK46_D @ SY882 @ SY879 @ SV259 ) @ SV259 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1363]) ).
thf(1574,plain,
! [SV113: $i,SV225: $i] :
( ( ( relation @ SV225 )
= $false )
| ( ( ~ ( ~ ! [SY839: $i] :
( ~ ( relation @ SY839 )
| ~ ( ~ ( ~ ( in @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) @ SV113 )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ SY839 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) ) @ SV225 )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ SY839 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) ) @ SY839 ) )
| ~ ~ ( ~ ( ( in @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) @ SV113 )
| ( in @ ( ordered_pair @ ( sK32_D @ SY839 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) ) @ SY839 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_D @ SY839 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) ) @ SV225 )
| ( in @ ( ordered_pair @ ( sK32_D @ SY839 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) ) @ SY839 ) ) ) )
| ( SY839
= ( relation_rng_restriction @ SV113 @ SV225 ) ) )
| ~ ! [SY840: $i] :
( ~ ( relation @ SY840 )
| ( SY840
!= ( relation_rng_restriction @ SV113 @ SV225 ) )
| ~ ( ~ ! [SY841: $i,SY842: $i] :
( ~ ( in @ SY842 @ SV113 )
| ~ ( in @ ( ordered_pair @ SY841 @ SY842 ) @ SV225 )
| ( in @ ( ordered_pair @ SY841 @ SY842 ) @ SY840 ) )
| ~ ~ ( ~ ! [SY619: $i,SY620: $i] :
( ~ ( in @ ( ordered_pair @ SY619 @ SY620 ) @ SY840 )
| ( in @ SY620 @ SV113 ) )
| ~ ! [SY845: $i,SY846: $i] :
( ~ ( in @ ( ordered_pair @ SY845 @ SY846 ) @ SY840 )
| ( in @ ( ordered_pair @ SY845 @ SY846 ) @ SV225 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1364]) ).
thf(1575,plain,
! [SV260: $i] :
( ( ! [SY883: $i] :
( ~ ( empty @ SV260 )
| ~ ( relation @ SY883 )
| ( empty @ ( relation_composition @ SY883 @ SV260 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1365]) ).
thf(1576,plain,
! [SV261: $i] :
( ( ! [SY884: $i] :
( ~ ( empty @ SV261 )
| ~ ( relation @ SY884 )
| ( relation @ ( relation_composition @ SY884 @ SV261 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1366]) ).
thf(1577,plain,
! [SV226: $i,SV114: $i] :
( ( ~ ! [SY847: $i,SY848: $i] :
( ~ ( in @ SV114 @ SY847 )
| ~ ( in @ SV226 @ SY848 )
| ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SY847 @ SY848 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1369]) ).
thf(1578,plain,
! [SV226: $i,SV114: $i] :
( ( ~ ~ ( ~ ! [SY849: $i] :
( ! [SY850: $i] :
~ ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SY849 @ SY850 ) )
| ( in @ SV114 @ SY849 ) )
| ~ ! [SY851: $i,SY852: $i] :
( ~ ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SY851 @ SY852 ) )
| ( in @ SV226 @ SY852 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1369]) ).
thf(1579,plain,
! [SV262: $i] :
( ( ! [SY885: $i] :
( ( disjoint @ SV262 @ SY885 )
| ~ ( ~ ( in @ ( sK72_C @ SY885 @ SV262 ) @ SV262 )
| ~ ( in @ ( sK72_C @ SY885 @ SV262 ) @ SY885 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1580,plain,
! [SV263: $i] :
( ( ! [SY886: $i] :
( ! [SY887: $i] :
( ~ ( in @ SY887 @ SV263 )
| ~ ( in @ SY887 @ SY886 ) )
| ~ ( disjoint @ SV263 @ SY886 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1371]) ).
thf(1581,plain,
! [SV264: $i] :
( ( ! [SY888: $i] :
( ~ ( ~ ( ( ( sK62_C @ SY888 @ SV264 )
!= SV264 )
| ~ ( in @ ( sK62_C @ SY888 @ SV264 ) @ SY888 ) )
| ~ ( ( ( sK62_C @ SY888 @ SV264 )
= SV264 )
| ( in @ ( sK62_C @ SY888 @ SV264 ) @ SY888 ) ) )
| ( SY888
= ( singleton @ SV264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1372]) ).
thf(1582,plain,
! [SV265: $i] :
( ( ! [SY889: $i] :
( ( SY889
!= ( singleton @ SV265 ) )
| ~ ( ~ ! [SY890: $i] :
( ( SY890 != SV265 )
| ( in @ SY890 @ SY889 ) )
| ~ ! [SY891: $i] :
( ~ ( in @ SY891 @ SY889 )
| ( SY891 = SV265 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1373]) ).
thf(1583,plain,
! [SV266: $i] :
( ( ( in @ ( sK61_B @ SV266 ) @ SV266 )
| ( SV266 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1374]) ).
thf(1584,plain,
! [SV267: $i] :
( ( ( SV267 != empty_set )
| ! [SY892: $i] :
~ ( in @ SY892 @ SV267 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1375]) ).
thf(1585,plain,
! [SV115: $i] :
( ( ! [SY630: $i] :
( ~ ( subset @ SY630 @ ( sK42_B @ SV115 ) )
| ( are_equipotent @ SY630 @ ( sK42_B @ SV115 ) )
| ( in @ SY630 @ ( sK42_B @ SV115 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1376]) ).
thf(1586,plain,
! [SV115: $i] :
( ( ~ ( ~ ! [SY631: $i] :
( ~ ( ~ ! [SY632: $i] :
( ~ ( subset @ SY632 @ SY631 )
| ( in @ SY632 @ ( sK43_SY481 @ SY631 @ SV115 ) ) )
| ~ ( in @ ( sK43_SY481 @ SY631 @ SV115 ) @ ( sK42_B @ SV115 ) ) )
| ~ ( in @ SY631 @ ( sK42_B @ SV115 ) ) )
| ~ ~ ( ~ ! [SY633: $i,SY634: $i] :
( ~ ( in @ SY633 @ ( sK42_B @ SV115 ) )
| ~ ( subset @ SY634 @ SY633 )
| ( in @ SY634 @ ( sK42_B @ SV115 ) ) )
| ~ ( in @ SV115 @ ( sK42_B @ SV115 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1377]) ).
thf(1587,plain,
! [SV268: $i] :
( ( ! [SY893: $i] :
( ~ ( subset @ SV268 @ ( singleton @ SY893 ) )
| ( SV268 = empty_set )
| ( SV268
= ( singleton @ SY893 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1378]) ).
thf(1588,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1379]) ).
thf(1589,plain,
! [SV116: $i] :
( ( ( function @ SV116 )
= $false )
| ( ( ~ ( relation @ SV116 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY635: $i] :
( ~ ( in @ SY635 @ ( relation_dom @ SV116 ) )
| ! [SY636: $i] :
( ( SY636
!= ( apply @ SV116 @ SY635 ) )
| ( in @ ( ordered_pair @ SY635 @ SY636 ) @ SV116 ) ) )
| ~ ! [SY637: $i] :
( ~ ( in @ SY637 @ ( relation_dom @ SV116 ) )
| ! [SY638: $i] :
( ~ ( in @ ( ordered_pair @ SY637 @ SY638 ) @ SV116 )
| ( SY638
= ( apply @ SV116 @ SY637 ) ) ) ) )
| ~ ~ ( ~ ! [SY639: $i] :
( ( in @ SY639 @ ( relation_dom @ SV116 ) )
| ! [SY640: $i] :
( ( SY640
!= ( apply @ SV116 @ SY639 ) )
| ( SY640 = empty_set ) ) )
| ~ ! [SY641: $i] :
( ( in @ SY641 @ ( relation_dom @ SV116 ) )
| ! [SY642: $i] :
( ( SY642 != empty_set )
| ( SY642
= ( apply @ SV116 @ SY641 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1380]) ).
thf(1590,plain,
! [SV117: $i] :
( ( ! [SY643: $i,SY644: $i] :
( ~ ( ~ ( ! [SY645: $i,SY646: $i] :
( ~ ( in @ SY645 @ SV117 )
| ~ ( in @ SY646 @ SY643 )
| ( ( sK53_D @ SY644 @ SY643 @ SV117 )
!= ( ordered_pair @ SY645 @ SY646 ) ) )
| ~ ( in @ ( sK53_D @ SY644 @ SY643 @ SV117 ) @ SY644 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK54_SY491 @ SY644 @ SY643 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK55_SY493 @ SY644 @ SY643 @ SV117 ) @ SY643 ) )
| ( ( sK53_D @ SY644 @ SY643 @ SV117 )
!= ( ordered_pair @ ( sK54_SY491 @ SY644 @ SY643 @ SV117 ) @ ( sK55_SY493 @ SY644 @ SY643 @ SV117 ) ) ) )
| ( in @ ( sK53_D @ SY644 @ SY643 @ SV117 ) @ SY644 ) ) )
| ( SY644
= ( cartesian_product2 @ SV117 @ SY643 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1381]) ).
thf(1591,plain,
! [SV117: $i] :
( ( ! [SY647: $i,SY648: $i] :
( ( SY648
!= ( cartesian_product2 @ SV117 @ SY647 ) )
| ~ ( ~ ! [SY649: $i] :
( ! [SY650: $i,SY651: $i] :
( ~ ( in @ SY650 @ SV117 )
| ~ ( in @ SY651 @ SY647 )
| ( SY649
!= ( ordered_pair @ SY650 @ SY651 ) ) )
| ( in @ SY649 @ SY648 ) )
| ~ ! [SY652: $i] :
( ~ ( in @ SY652 @ SY648 )
| ~ ( ~ ~ ( ~ ( in @ ( sK51_E @ SY652 @ SY648 @ SY647 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK52_SY488 @ SY652 @ SY648 @ SY647 @ SV117 ) @ SY647 ) )
| ( SY652
!= ( ordered_pair @ ( sK51_E @ SY652 @ SY648 @ SY647 @ SV117 ) @ ( sK52_SY488 @ SY652 @ SY648 @ SY647 @ SV117 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1382]) ).
thf(1592,plain,
! [SV269: $i] :
( ( ! [SY894: $i] :
( ( ( set_difference @ SV269 @ SY894 )
!= empty_set )
| ( subset @ SV269 @ SY894 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1383]) ).
thf(1593,plain,
! [SV270: $i] :
( ( ! [SY895: $i] :
( ~ ( subset @ SV270 @ SY895 )
| ( ( set_difference @ SV270 @ SY895 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1384]) ).
thf(1594,plain,
! [SV271: $i] :
( ( ~ ( relation @ SV271 )
| ( ( relation_dom @ SV271 )
!= empty_set )
| ( ( relation_rng @ SV271 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1385]) ).
thf(1595,plain,
! [SV272: $i] :
( ( ~ ( relation @ SV272 )
| ( ( relation_rng @ SV272 )
!= empty_set )
| ( ( relation_dom @ SV272 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1386]) ).
thf(1596,plain,
! [SV118: $i] :
( ( ! [SY653: $i,SY654: $i] :
( ~ ( function @ SY654 )
| ~ ( relation @ SY654 )
| ( SY653
!= ( apply @ SY654 @ SV118 ) )
| ~ ( in @ SV118 @ ( relation_dom @ SY654 ) )
| ( in @ ( ordered_pair @ SV118 @ SY653 ) @ SY654 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1389]) ).
thf(1597,plain,
! [SV118: $i] :
( ( ~ ( ~ ! [SY655: $i,SY656: $i] :
( ~ ( function @ SY656 )
| ~ ( relation @ SY656 )
| ~ ( in @ ( ordered_pair @ SV118 @ SY655 ) @ SY656 )
| ( SY655
= ( apply @ SY656 @ SV118 ) ) )
| ~ ! [SY657: $i,SY658: $i] :
( ~ ( function @ SY658 )
| ~ ( relation @ SY658 )
| ~ ( in @ ( ordered_pair @ SV118 @ SY657 ) @ SY658 )
| ( in @ SV118 @ ( relation_dom @ SY658 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1390]) ).
thf(1598,plain,
! [SV273: $i] :
( ( ! [SY896: $i] :
( ~ ( relation @ SY896 )
| ~ ( ~ ( ( ( sK69_C @ SY896 @ SV273 )
!= ( sK70_SY500 @ SY896 @ SV273 ) )
| ~ ( in @ ( sK69_C @ SY896 @ SV273 ) @ SV273 )
| ~ ( in @ ( ordered_pair @ ( sK69_C @ SY896 @ SV273 ) @ ( sK70_SY500 @ SY896 @ SV273 ) ) @ SY896 ) )
| ~ ~ ( ~ ( ( ( sK69_C @ SY896 @ SV273 )
= ( sK70_SY500 @ SY896 @ SV273 ) )
| ( in @ ( ordered_pair @ ( sK69_C @ SY896 @ SV273 ) @ ( sK70_SY500 @ SY896 @ SV273 ) ) @ SY896 ) )
| ~ ( ( in @ ( sK69_C @ SY896 @ SV273 ) @ SV273 )
| ( in @ ( ordered_pair @ ( sK69_C @ SY896 @ SV273 ) @ ( sK70_SY500 @ SY896 @ SV273 ) ) @ SY896 ) ) ) )
| ( SY896
= ( identity_relation @ SV273 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1393]) ).
thf(1599,plain,
! [SV274: $i] :
( ( ! [SY897: $i] :
( ~ ( relation @ SY897 )
| ( SY897
!= ( identity_relation @ SV274 ) )
| ~ ( ~ ! [SY898: $i,SY899: $i] :
( ( SY898 != SY899 )
| ~ ( in @ SY898 @ SV274 )
| ( in @ ( ordered_pair @ SY898 @ SY899 ) @ SY897 ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SY897 )
| ( SX2 = SX3 ) )
| ~ ! [SY902: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SY902 @ SX3 ) @ SY897 )
| ( in @ SY902 @ SV274 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1600,plain,
! [SV119: $i] :
( ( element @ ( sK5_B @ SV119 ) @ ( powerset @ SV119 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1395]) ).
thf(1601,plain,
! [SV119: $i] :
( ( empty @ ( sK5_B @ SV119 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1396]) ).
thf(1602,plain,
! [SV120: $i,SV275: $i] :
( ( ( ~ ( relation @ SV275 )
| ~ ( ~ ! [SY904: $i] :
( ~ ( relation @ SY904 )
| ~ ( ~ ( ! [SY905: $i] :
( ~ ( in @ ( ordered_pair @ ( sK13_D @ SY904 @ SV275 @ SV120 ) @ SY905 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY905 @ ( sK14_SY457 @ SY904 @ SV275 @ SV120 ) ) @ SV275 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_D @ SY904 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SY904 @ SV275 @ SV120 ) ) @ SY904 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_D @ SY904 @ SV275 @ SV120 ) @ ( sK15_SY461 @ SY904 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY461 @ SY904 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SY904 @ SV275 @ SV120 ) ) @ SV275 ) )
| ( in @ ( ordered_pair @ ( sK13_D @ SY904 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SY904 @ SV275 @ SV120 ) ) @ SY904 ) ) )
| ( SY904
= ( relation_composition @ SV120 @ SV275 ) ) )
| ~ ! [SY906: $i] :
( ~ ( relation @ SY906 )
| ( SY906
!= ( relation_composition @ SV120 @ SV275 ) )
| ~ ( ~ ! [SY907: $i,SY908: $i] :
( ! [SY909: $i] :
( ~ ( in @ ( ordered_pair @ SY907 @ SY909 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY909 @ SY908 ) @ SV275 ) )
| ( in @ ( ordered_pair @ SY907 @ SY908 ) @ SY906 ) )
| ~ ! [SY910: $i,SY911: $i] :
( ~ ( in @ ( ordered_pair @ SY910 @ SY911 ) @ SY906 )
| ~ ( ~ ( in @ ( ordered_pair @ SY910 @ ( sK12_F @ SY911 @ SY910 @ SY906 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK12_F @ SY911 @ SY910 @ SY906 @ SV275 @ SV120 ) @ SY911 ) @ SV275 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1397]) ).
thf(1603,plain,
! [SV121: $i,SV227: $i] :
( ( ( element @ SV227 @ ( powerset @ SV121 ) )
= $false )
| ( ( ~ ( ~ ! [SY853: $i] :
( ~ ( element @ SY853 @ ( powerset @ SV121 ) )
| ~ ( disjoint @ SV227 @ SY853 )
| ( subset @ SV227 @ ( subset_complement @ SV121 @ SY853 ) ) )
| ~ ! [SY854: $i] :
( ~ ( element @ SY854 @ ( powerset @ SV121 ) )
| ~ ( subset @ SV227 @ ( subset_complement @ SV121 @ SY854 ) )
| ( disjoint @ SV227 @ SY854 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1398]) ).
thf(1604,plain,
! [SV122: $i] :
( ( ! [SY671: $i,SY672: $i] :
( ~ ( relation @ SY672 )
| ~ ( in @ SV122 @ SY671 )
| ~ ( in @ SV122 @ ( relation_rng @ SY672 ) )
| ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SY671 @ SY672 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1399]) ).
thf(1605,plain,
! [SV122: $i] :
( ( ~ ( ~ ! [SY673: $i,SY674: $i] :
( ~ ( relation @ SY674 )
| ~ ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SY673 @ SY674 ) ) )
| ( in @ SV122 @ SY673 ) )
| ~ ! [SY675: $i,SY676: $i] :
( ~ ( relation @ SY676 )
| ~ ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SY675 @ SY676 ) ) )
| ( in @ SV122 @ ( relation_rng @ SY676 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1400]) ).
thf(1606,plain,
! [SV123: $i] :
( ( ( ~ ! [SY677: $i,SY678: $i] :
( ~ ( relation @ SY678 )
| ~ ( ~ ( ~ ( in @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ SY677 )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ ( sK35_SY473 @ SY678 @ SY677 @ SV123 ) ) @ SV123 )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ ( sK35_SY473 @ SY678 @ SY677 @ SV123 ) ) @ SY678 ) )
| ~ ~ ( ~ ( ( in @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ SY677 )
| ( in @ ( ordered_pair @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ ( sK35_SY473 @ SY678 @ SY677 @ SV123 ) ) @ SY678 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ ( sK35_SY473 @ SY678 @ SY677 @ SV123 ) ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ ( sK35_SY473 @ SY678 @ SY677 @ SV123 ) ) @ SY678 ) ) ) )
| ( SY678
= ( relation_dom_restriction @ SV123 @ SY677 ) ) )
| ~ ! [SY679: $i,SY680: $i] :
( ~ ( relation @ SY680 )
| ( SY680
!= ( relation_dom_restriction @ SV123 @ SY679 ) )
| ~ ( ~ ! [SY681: $i,SY682: $i] :
( ~ ( in @ SY681 @ SY679 )
| ~ ( in @ ( ordered_pair @ SY681 @ SY682 ) @ SV123 )
| ( in @ ( ordered_pair @ SY681 @ SY682 ) @ SY680 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY680 )
| ( in @ SX3 @ SY679 ) )
| ~ ! [SY685: $i,SY686: $i] :
( ~ ( in @ ( ordered_pair @ SY685 @ SY686 ) @ SY680 )
| ( in @ ( ordered_pair @ SY685 @ SY686 ) @ SV123 ) ) ) ) ) )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1401]) ).
thf(1607,plain,
! [SV124: $i] :
( ( ( ~ ! [SY687: $i] :
( ~ ( relation @ SY687 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_C @ SY687 @ SV124 ) @ ( sK17_SY462 @ SY687 @ SV124 ) ) @ SY687 )
| ~ ( in @ ( ordered_pair @ ( sK17_SY462 @ SY687 @ SV124 ) @ ( sK16_C @ SY687 @ SV124 ) ) @ SV124 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK16_C @ SY687 @ SV124 ) @ ( sK17_SY462 @ SY687 @ SV124 ) ) @ SY687 )
| ( in @ ( ordered_pair @ ( sK17_SY462 @ SY687 @ SV124 ) @ ( sK16_C @ SY687 @ SV124 ) ) @ SV124 ) ) )
| ( SY687
= ( relation_inverse @ SV124 ) ) )
| ~ ! [SY688: $i] :
( ~ ( relation @ SY688 )
| ( SY688
!= ( relation_inverse @ SV124 ) )
| ~ ( ~ ! [SY689: $i,SY690: $i] :
( ~ ( in @ ( ordered_pair @ SY689 @ SY690 ) @ SY688 )
| ( in @ ( ordered_pair @ SY690 @ SY689 ) @ SV124 ) )
| ~ ! [SY691: $i,SY692: $i] :
( ~ ( in @ ( ordered_pair @ SY692 @ SY691 ) @ SV124 )
| ( in @ ( ordered_pair @ SY691 @ SY692 ) @ SY688 ) ) ) ) )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1402]) ).
thf(1608,plain,
! [SV276: $i] :
( ( ! [SY912: $i] :
( ~ ( element @ SV276 @ ( powerset @ SY912 ) )
| ( subset @ SV276 @ SY912 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1403]) ).
thf(1609,plain,
! [SV277: $i] :
( ( ! [SY913: $i] :
( ~ ( subset @ SV277 @ SY913 )
| ( element @ SV277 @ ( powerset @ SY913 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1404]) ).
thf(1610,plain,
! [SV278: $i] :
( ( ! [SY914: $i] :
( ~ ( in @ SV278 @ SY914 )
| ( subset @ ( singleton @ SV278 ) @ SY914 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1405]) ).
thf(1611,plain,
! [SV279: $i] :
( ( ! [SY915: $i] :
( ~ ( subset @ ( singleton @ SV279 ) @ SY915 )
| ( in @ SV279 @ SY915 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1406]) ).
thf(1612,plain,
! [SV280: $i] :
( ( ! [SY916: $i] :
( ( ( set_intersection2 @ SV280 @ SY916 )
!= empty_set )
| ( disjoint @ SV280 @ SY916 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1407]) ).
thf(1613,plain,
! [SV281: $i] :
( ( ! [SY917: $i] :
( ~ ( disjoint @ SV281 @ SY917 )
| ( ( set_intersection2 @ SV281 @ SY917 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1408]) ).
thf(1614,plain,
! [SV282: $i] :
( ( ! [SY918: $i] :
( ~ ( function @ SY918 )
| ~ ( relation @ SY918 )
| ~ ( ~ ( in @ ( sK38_C @ SY918 @ SV282 ) @ SV282 )
| ~ ( ( ( apply @ SY918 @ ( sK38_C @ SY918 @ SV282 ) )
!= ( sK38_C @ SY918 @ SV282 ) ) ) )
| ( ( relation_dom @ SY918 )
!= SV282 )
| ( SY918
= ( identity_relation @ SV282 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1409]) ).
thf(1615,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)],[1410]) ).
thf(1616,plain,
! [SV283: $i] :
( ( ! [SY919: $i] :
( ( ( set_difference @ SV283 @ SY919 )
!= empty_set )
| ( subset @ SV283 @ SY919 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1411]) ).
thf(1617,plain,
! [SV284: $i] :
( ( ! [SY920: $i] :
( ~ ( subset @ SV284 @ SY920 )
| ( ( set_difference @ SV284 @ SY920 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1412]) ).
thf(1618,plain,
! [SV285: $i] :
( ( ! [SY921: $i] :
( ~ ( subset @ SV285 @ SY921 )
| ~ ( subset @ SY921 @ SV285 )
| ( SV285 = SY921 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1413]) ).
thf(1619,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1414]) ).
thf(1620,plain,
! [SV125: $i] :
( ( ( ~ ! [SY693: $i,SY694: $i] :
( ~ ( ~ ( ! [SY695: $i] :
( ~ ( in @ ( ordered_pair @ SY695 @ ( sK30_D @ SY694 @ SY693 @ SV125 ) ) @ SV125 )
| ~ ( in @ SY695 @ SY693 ) )
| ~ ( in @ ( sK30_D @ SY694 @ SY693 @ SV125 ) @ SY694 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_SY471 @ SY694 @ SY693 @ SV125 ) @ ( sK30_D @ SY694 @ SY693 @ SV125 ) ) @ SV125 )
| ~ ( in @ ( sK31_SY471 @ SY694 @ SY693 @ SV125 ) @ SY693 ) )
| ( in @ ( sK30_D @ SY694 @ SY693 @ SV125 ) @ SY694 ) ) )
| ( SY694
= ( relation_image @ SV125 @ SY693 ) ) )
| ~ ! [SY696: $i,SY697: $i] :
( ( SY697
!= ( relation_image @ SV125 @ SY696 ) )
| ~ ( ~ ! [SY698: $i] :
( ! [SY699: $i] :
( ~ ( in @ ( ordered_pair @ SY699 @ SY698 ) @ SV125 )
| ~ ( in @ SY699 @ SY696 ) )
| ( in @ SY698 @ SY697 ) )
| ~ ! [SY700: $i] :
( ~ ( in @ SY700 @ SY697 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK29_E @ SY700 @ SY697 @ SY696 @ SV125 ) @ SY700 ) @ SV125 )
| ~ ( in @ ( sK29_E @ SY700 @ SY697 @ SY696 @ SV125 ) @ SY696 ) ) ) ) ) )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1415]) ).
thf(1621,plain,
! [SV126: $i] :
( ( ! [SY701: $i,SY702: $i] :
( ~ ( relation @ SY702 )
| ~ ( in @ ( ordered_pair @ SV126 @ SY701 ) @ SY702 )
| ( in @ SV126 @ ( relation_field @ SY702 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1416]) ).
thf(1622,plain,
! [SV126: $i] :
( ( ! [SY703: $i,SY704: $i] :
( ~ ( relation @ SY704 )
| ~ ( in @ ( ordered_pair @ SV126 @ SY703 ) @ SY704 )
| ( in @ SY703 @ ( relation_field @ SY704 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1417]) ).
thf(1623,plain,
! [SV228: $i,SV127: $i] :
( ( ~ ! [SY855: $i,SY856: $i] :
( ~ ( relation @ SY856 )
| ~ ( in @ SV127 @ SY855 )
| ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ SY856 )
| ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SY855 ) @ SY856 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1418]) ).
thf(1624,plain,
! [SV228: $i,SV127: $i] :
( ( ~ ~ ( ~ ! [SY857: $i,SY858: $i] :
( ~ ( relation @ SY858 )
| ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SY857 ) @ SY858 ) )
| ( in @ SV127 @ SY857 ) )
| ~ ! [SY859: $i,SY860: $i] :
( ~ ( relation @ SY860 )
| ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SY859 ) @ SY860 ) )
| ( in @ ( ordered_pair @ SV127 @ SV228 ) @ SY860 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1418]) ).
thf(1625,plain,
! [SV286: $i] :
( ( ! [SY922: $i] :
( ~ ( in @ SV286 @ SY922 )
| ( subset @ ( singleton @ SV286 ) @ SY922 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1419]) ).
thf(1626,plain,
! [SV287: $i] :
( ( ! [SY923: $i] :
( ~ ( subset @ ( singleton @ SV287 ) @ SY923 )
| ( in @ SV287 @ SY923 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1420]) ).
thf(1627,plain,
! [SV128: $i] :
( ( ! [SY712: $i,SY713: $i] :
( ~ ( in @ SV128 @ SY713 )
| ~ ( in @ SY712 @ SY713 )
| ( subset @ ( unordered_pair @ SV128 @ SY712 ) @ SY713 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1421]) ).
thf(1628,plain,
! [SV128: $i] :
( ( ~ ( ~ ! [SY714: $i,SY715: $i] :
( ~ ( subset @ ( unordered_pair @ SV128 @ SY714 ) @ SY715 )
| ( in @ SV128 @ SY715 ) )
| ~ ! [SY716: $i,SY717: $i] :
( ~ ( subset @ ( unordered_pair @ SV128 @ SY716 ) @ SY717 )
| ( in @ SY716 @ SY717 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1422]) ).
thf(1629,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1423]) ).
thf(1630,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1424]) ).
thf(1631,plain,
! [SV129: $i] :
( ( ( ~ ! [SY718: $i] :
( ~ ( ~ ( ! [SY719: $i] :
~ ( in @ ( ordered_pair @ SY719 @ ( sK19_C @ SY718 @ SV129 ) ) @ SV129 )
| ~ ( in @ ( sK19_C @ SY718 @ SV129 ) @ SY718 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_SY464 @ SY718 @ SV129 ) @ ( sK19_C @ SY718 @ SV129 ) ) @ SV129 )
| ( in @ ( sK19_C @ SY718 @ SV129 ) @ SY718 ) ) )
| ( SY718
= ( relation_rng @ SV129 ) ) )
| ~ ! [SY720: $i] :
( ( SY720
!= ( relation_rng @ SV129 ) )
| ~ ( ~ ! [SY721: $i] :
( ! [SY722: $i] :
~ ( in @ ( ordered_pair @ SY722 @ SY721 ) @ SV129 )
| ( in @ SY721 @ SY720 ) )
| ~ ! [SY723: $i] :
( ~ ( in @ SY723 @ SY720 )
| ( in @ ( ordered_pair @ ( sK18_D @ SY723 @ SY720 @ SV129 ) @ SY723 ) @ SV129 ) ) ) ) )
= $false )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1427]) ).
thf(1632,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1428]) ).
thf(1633,plain,
! [SV288: $i] :
( ( ! [SY924: $i] :
( ( ( set_difference @ SV288 @ ( singleton @ SY924 ) )
!= SV288 )
| ~ ( in @ SY924 @ SV288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1430]) ).
thf(1634,plain,
! [SV289: $i] :
( ( ! [SY925: $i] :
( ( in @ SY925 @ SV289 )
| ( ( set_difference @ SV289 @ ( singleton @ SY925 ) )
= SV289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1431]) ).
thf(1635,plain,
! [SV290: $i] :
( ( function @ ( identity_relation @ SV290 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1432]) ).
thf(1636,plain,
! [SV291: $i] :
( ( relation @ ( identity_relation @ SV291 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1433]) ).
thf(1637,plain,
! [SV292: $i] :
( ( ! [SY926: $i] :
( ( disjoint @ SV292 @ SY926 )
| ( in @ ( sK71_C @ SY926 @ SV292 ) @ ( set_intersection2 @ SV292 @ SY926 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1434]) ).
thf(1638,plain,
! [SV293: $i] :
( ( ! [SY927: $i] :
( ! [SY928: $i] :
~ ( in @ SY928 @ ( set_intersection2 @ SV293 @ SY927 ) )
| ~ ( disjoint @ SV293 @ SY927 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1435]) ).
thf(1639,plain,
! [SV130: $i,SV229: $i] :
( ( ( ~ ( in @ ( sK73_C @ SV229 @ SV130 ) @ SV130 )
| ~ ~ ( in @ ( sK73_C @ SV229 @ SV130 ) @ SV229 ) )
= $false )
| ( ( element @ SV130 @ ( powerset @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1436]) ).
thf(1640,plain,
! [SV131: $i] :
( ( ( ~ ! [SY725: $i,SY726: $i] :
( ~ ( ~ ( ! [SY727: $i] :
( ~ ( in @ ( ordered_pair @ ( sK27_D @ SY726 @ SY725 @ SV131 ) @ SY727 ) @ SV131 )
| ~ ( in @ SY727 @ SY725 ) )
| ~ ( in @ ( sK27_D @ SY726 @ SY725 @ SV131 ) @ SY726 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK27_D @ SY726 @ SY725 @ SV131 ) @ ( sK28_SY469 @ SY726 @ SY725 @ SV131 ) ) @ SV131 )
| ~ ( in @ ( sK28_SY469 @ SY726 @ SY725 @ SV131 ) @ SY725 ) )
| ( in @ ( sK27_D @ SY726 @ SY725 @ SV131 ) @ SY726 ) ) )
| ( SY726
= ( relation_inverse_image @ SV131 @ SY725 ) ) )
| ~ ! [SY728: $i,SY729: $i] :
( ( SY729
!= ( relation_inverse_image @ SV131 @ SY728 ) )
| ~ ( ~ ! [SY730: $i] :
( ! [SY731: $i] :
( ~ ( in @ ( ordered_pair @ SY730 @ SY731 ) @ SV131 )
| ~ ( in @ SY731 @ SY728 ) )
| ( in @ SY730 @ SY729 ) )
| ~ ! [SY732: $i] :
( ~ ( in @ SY732 @ SY729 )
| ~ ( ~ ( in @ ( ordered_pair @ SY732 @ ( sK26_E @ SY732 @ SY729 @ SY728 @ SV131 ) ) @ SV131 )
| ~ ( in @ ( sK26_E @ SY732 @ SY729 @ SY728 @ SV131 ) @ SY728 ) ) ) ) ) )
= $false )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1437]) ).
thf(1641,plain,
! [SV294: $i] :
( ( ! [SY929: $i] :
( ( ( set_difference @ SV294 @ SY929 )
!= SV294 )
| ( disjoint @ SV294 @ SY929 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(1642,plain,
! [SV295: $i] :
( ( ! [SY930: $i] :
( ~ ( disjoint @ SV295 @ SY930 )
| ( ( set_difference @ SV295 @ SY930 )
= SV295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1439]) ).
thf(1643,plain,
! [SV296: $i] :
( ( ~ ( ~ ! [SY931: $i,SY932: $i] :
( ( sK68_B @ SV296 )
!= ( ordered_pair @ SY931 @ SY932 ) )
| ~ ( in @ ( sK68_B @ SV296 ) @ SV296 ) )
| ( relation @ SV296 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1440]) ).
thf(1644,plain,
! [SV297: $i] :
( ( ~ ( relation @ SV297 )
| ! [SY933: $i] :
( ( SY933
= ( ordered_pair @ ( sK66_C @ SY933 @ SV297 ) @ ( sK67_SY497 @ SY933 @ SV297 ) ) )
| ~ ( in @ SY933 @ SV297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1441]) ).
thf(1645,plain,
! [SV132: $i] :
( ( ! [SY733: $i,SY734: $i] :
( ~ ( relation @ SY734 )
| ~ ( in @ SV132 @ SY733 )
| ~ ( in @ SV132 @ ( relation_dom @ SY734 ) )
| ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SY734 @ SY733 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1442]) ).
thf(1646,plain,
! [SV132: $i] :
( ( ~ ( ~ ! [SY735: $i,SY736: $i] :
( ~ ( relation @ SY736 )
| ~ ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SY736 @ SY735 ) ) )
| ( in @ SV132 @ SY735 ) )
| ~ ! [SY737: $i,SY738: $i] :
( ~ ( relation @ SY738 )
| ~ ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SY738 @ SY737 ) ) )
| ( in @ SV132 @ ( relation_dom @ SY738 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1443]) ).
thf(1647,plain,
! [SV133: $i] :
( ( ! [SY739: $i,SY740: $i] :
( ~ ( relation @ SY740 )
| ~ ( in @ ( ordered_pair @ SV133 @ SY739 ) @ SY740 )
| ( in @ SV133 @ ( relation_dom @ SY740 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1444]) ).
thf(1648,plain,
! [SV133: $i] :
( ( ! [SY741: $i,SY742: $i] :
( ~ ( relation @ SY742 )
| ~ ( in @ ( ordered_pair @ SV133 @ SY741 ) @ SY742 )
| ( in @ SY741 @ ( relation_rng @ SY742 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1445]) ).
thf(1649,plain,
! [SV134: $i] :
( ( ( ~ ! [SY743: $i] :
( ~ ( ~ ( ! [SY744: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SY743 @ SV134 ) @ SY744 ) @ SV134 )
| ~ ( in @ ( sK22_C @ SY743 @ SV134 ) @ SY743 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SY743 @ SV134 ) @ ( sK23_SY466 @ SY743 @ SV134 ) ) @ SV134 )
| ( in @ ( sK22_C @ SY743 @ SV134 ) @ SY743 ) ) )
| ( SY743
= ( relation_dom @ SV134 ) ) )
| ~ ! [SY745: $i] :
( ( SY745
!= ( relation_dom @ SV134 ) )
| ~ ( ~ ! [SY746: $i] :
( ! [SY747: $i] :
~ ( in @ ( ordered_pair @ SY746 @ SY747 ) @ SV134 )
| ( in @ SY746 @ SY745 ) )
| ~ ! [SY748: $i] :
( ~ ( in @ SY748 @ SY745 )
| ( in @ ( ordered_pair @ SY748 @ ( sK21_D @ SY748 @ SY745 @ SV134 ) ) @ SV134 ) ) ) ) )
= $false )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1446]) ).
thf(1650,plain,
! [SV135: $i] :
( ( ! [SY749: $i,SY750: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK57_D @ SY750 @ SY749 @ SV135 ) @ SY750 )
| ( ( sK57_D @ SY750 @ SY749 @ SV135 )
!= SV135 ) )
| ~ ( ~ ( in @ ( sK57_D @ SY750 @ SY749 @ SV135 ) @ SY750 )
| ( ( sK57_D @ SY750 @ SY749 @ SV135 )
!= SY749 ) ) )
| ~ ( ( in @ ( sK57_D @ SY750 @ SY749 @ SV135 ) @ SY750 )
| ( ( sK57_D @ SY750 @ SY749 @ SV135 )
= SV135 )
| ( ( sK57_D @ SY750 @ SY749 @ SV135 )
= SY749 ) ) )
| ( SY750
= ( unordered_pair @ SV135 @ SY749 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1447]) ).
thf(1651,plain,
! [SV135: $i] :
( ( ! [SY751: $i,SY752: $i] :
( ( SY752
!= ( unordered_pair @ SV135 @ SY751 ) )
| ~ ( ~ ! [SY753: $i] :
( ~ ( in @ SY753 @ SY752 )
| ( SY753 = SV135 )
| ( SY753 = SY751 ) )
| ~ ~ ( ~ ! [SY754: $i] :
( ( SY754 != SV135 )
| ( in @ SY754 @ SY752 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY751 )
| ( in @ SX3 @ SY752 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1448]) ).
thf(1652,plain,
! [SV136: $i] :
( ( ( ~ ! [SY756: $i] :
( ~ ( relation @ SY756 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK58_C @ SY756 @ SV136 ) @ ( sK59_SY494 @ SY756 @ SV136 ) ) @ SV136 )
| ~ ( in @ ( ordered_pair @ ( sK58_C @ SY756 @ SV136 ) @ ( sK59_SY494 @ SY756 @ SV136 ) ) @ SY756 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_C @ SY756 @ SV136 ) @ ( sK59_SY494 @ SY756 @ SV136 ) ) @ SV136 )
| ( in @ ( ordered_pair @ ( sK58_C @ SY756 @ SV136 ) @ ( sK59_SY494 @ SY756 @ SV136 ) ) @ SY756 ) ) )
| ( SV136 = SY756 ) )
| ~ ! [SY757: $i] :
( ~ ( relation @ SY757 )
| ( SV136 != SY757 )
| ~ ( ~ ! [SY758: $i,SY759: $i] :
( ~ ( in @ ( ordered_pair @ SY758 @ SY759 ) @ SV136 )
| ( in @ ( ordered_pair @ SY758 @ SY759 ) @ SY757 ) )
| ~ ! [SY760: $i,SY761: $i] :
( ~ ( in @ ( ordered_pair @ SY760 @ SY761 ) @ SY757 )
| ( in @ ( ordered_pair @ SY760 @ SY761 ) @ SV136 ) ) ) ) )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1451]) ).
thf(1653,plain,
! [SV298: $i] :
( ( ! [SY934: $i] :
( ~ ( function @ SV298 )
| ~ ( relation @ SV298 )
| ~ ( relation @ SY934 )
| ~ ( function @ SY934 )
| ( function @ ( relation_composition @ SV298 @ SY934 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(1654,plain,
! [SV299: $i] :
( ( ! [SY935: $i] :
( ~ ( function @ SV299 )
| ~ ( relation @ SV299 )
| ~ ( relation @ SY935 )
| ~ ( function @ SY935 )
| ( relation @ ( relation_composition @ SV299 @ SY935 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(1655,plain,
! [SV137: $i,SV230: $i] :
( ( ( ~ ( function @ SV230 ) )
= $true )
| ( ( ~ ( relation @ SV230 ) )
= $true )
| ( ( ~ ( ~ ! [SY861: $i] :
( ~ ( function @ SY861 )
| ~ ( relation @ SY861 )
| ~ ( in @ SV137 @ ( relation_dom @ SY861 ) )
| ~ ( in @ ( apply @ SY861 @ SV137 ) @ ( relation_dom @ SV230 ) )
| ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY861 @ SV230 ) ) ) )
| ~ ~ ( ~ ! [SY862: $i] :
( ~ ( function @ SY862 )
| ~ ( relation @ SY862 )
| ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY862 @ SV230 ) ) )
| ( in @ SV137 @ ( relation_dom @ SY862 ) ) )
| ~ ! [SY863: $i] :
( ~ ( function @ SY863 )
| ~ ( relation @ SY863 )
| ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY863 @ SV230 ) ) )
| ( in @ ( apply @ SY863 @ SV137 ) @ ( relation_dom @ SV230 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1454]) ).
thf(1656,plain,
! [SV138: $i] :
( ( ! [SY766: $i] :
( ~ ( subset @ SY766 @ ( sK41_B @ SV138 ) )
| ( are_equipotent @ SY766 @ ( sK41_B @ SV138 ) )
| ( in @ SY766 @ ( sK41_B @ SV138 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1455]) ).
thf(1657,plain,
! [SV138: $i] :
( ( ~ ( ~ ! [SY767: $i] :
( ~ ( in @ SY767 @ ( sK41_B @ SV138 ) )
| ( in @ ( powerset @ SY767 ) @ ( sK41_B @ SV138 ) ) )
| ~ ~ ( ~ ! [SY768: $i,SY769: $i] :
( ~ ( in @ SY768 @ ( sK41_B @ SV138 ) )
| ~ ( subset @ SY769 @ SY768 )
| ( in @ SY769 @ ( sK41_B @ SV138 ) ) )
| ~ ( in @ SV138 @ ( sK41_B @ SV138 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1456]) ).
thf(1658,plain,
! [SV139: $i] :
( ( ( ~ ! [SY770: $i] :
( ~ ( relation @ SY770 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SY770 @ SV139 ) @ ( sK25_SY467 @ SY770 @ SV139 ) ) @ SV139 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SY770 @ SV139 ) @ ( sK25_SY467 @ SY770 @ SV139 ) ) @ SY770 ) )
| ( subset @ SV139 @ SY770 ) )
| ~ ! [SY771: $i] :
( ~ ( relation @ SY771 )
| ~ ( subset @ SV139 @ SY771 )
| ! [SY772: $i,SY773: $i] :
( ~ ( in @ ( ordered_pair @ SY772 @ SY773 ) @ SV139 )
| ( in @ ( ordered_pair @ SY772 @ SY773 ) @ SY771 ) ) ) )
= $false )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1457]) ).
thf(1659,plain,
! [SV300: $i] :
( ( ! [SY936: $i] :
( ~ ( ~ ( ~ ( in @ ( sK60_C @ SY936 @ SV300 ) @ SY936 )
| ~ ( subset @ ( sK60_C @ SY936 @ SV300 ) @ SV300 ) )
| ~ ( ( in @ ( sK60_C @ SY936 @ SV300 ) @ SY936 )
| ( subset @ ( sK60_C @ SY936 @ SV300 ) @ SV300 ) ) )
| ( SY936
= ( powerset @ SV300 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1458]) ).
thf(1660,plain,
! [SV301: $i] :
( ( ! [SY937: $i] :
( ( SY937
!= ( powerset @ SV301 ) )
| ~ ( ~ ! [SY938: $i] :
( ~ ( in @ SY938 @ SY937 )
| ( subset @ SY938 @ SV301 ) )
| ~ ! [SY939: $i] :
( ~ ( subset @ SY939 @ SV301 )
| ( in @ SY939 @ SY937 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(1661,plain,
! [SV302: $i] :
( ( ! [SY940: $i] :
( ~ ( empty @ SV302 )
| ~ ( relation @ SY940 )
| ( empty @ ( relation_composition @ SV302 @ SY940 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(1662,plain,
! [SV303: $i] :
( ( ! [SY941: $i] :
( ~ ( empty @ SV303 )
| ~ ( relation @ SY941 )
| ( relation @ ( relation_composition @ SV303 @ SY941 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1461]) ).
thf(1663,plain,
! [SV140: $i] :
( ( ( ~ ! [SY774: $i] :
( ~ ( relation @ SY774 )
| ~ ( subset @ SV140 @ SY774 )
| ( subset @ ( relation_dom @ SV140 ) @ ( relation_dom @ SY774 ) ) )
| ~ ! [SY775: $i] :
( ~ ( relation @ SY775 )
| ~ ( subset @ SV140 @ SY775 )
| ( subset @ ( relation_rng @ SV140 ) @ ( relation_rng @ SY775 ) ) ) )
= $false )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1462]) ).
thf(1664,plain,
! [SV141: $i] :
( ( ( ~ ( element @ ( sK8_B @ SV141 ) @ ( powerset @ SV141 ) ) )
= $false )
| ( ( empty @ SV141 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1463]) ).
thf(1665,plain,
! [SV141: $i] :
( ( ( ~ ~ ( empty @ ( sK8_B @ SV141 ) ) )
= $false )
| ( ( empty @ SV141 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1463]) ).
thf(1666,plain,
! [SV142: $i] :
( ( ! [SY776: $i,SY777: $i] :
( ~ ( relation @ SY777 )
| ! [SY778: $i] :
( ~ ( in @ SY778 @ ( relation_rng @ SY777 ) )
| ~ ( in @ ( ordered_pair @ SV142 @ SY778 ) @ SY777 )
| ~ ( in @ SY778 @ SY776 ) )
| ( in @ SV142 @ ( relation_inverse_image @ SY777 @ SY776 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1464]) ).
thf(1667,plain,
! [SV142: $i] :
( ( ! [SY779: $i,SY780: $i] :
( ~ ( relation @ SY780 )
| ~ ( in @ SV142 @ ( relation_inverse_image @ SY780 @ SY779 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK39_D @ SY780 @ SY779 @ SV142 ) @ ( relation_rng @ SY780 ) )
| ~ ( in @ ( ordered_pair @ SV142 @ ( sK39_D @ SY780 @ SY779 @ SV142 ) ) @ SY780 ) )
| ~ ( in @ ( sK39_D @ SY780 @ SY779 @ SV142 ) @ SY779 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1465]) ).
thf(1668,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK65_SY495 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK64_C @ SX1 @ SX0 ) @ ( sK65_SY495 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK64_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK64_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK64_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK63_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK63_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1466]) ).
thf(1669,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1467]) ).
thf(1670,plain,
! [SV304: $i] :
( ( ~ ( relation @ SV304 )
| ( ( relation_rng @ SV304 )
= ( relation_dom @ ( relation_inverse @ SV304 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1468]) ).
thf(1671,plain,
! [SV305: $i] :
( ( ~ ( relation @ SV305 )
| ( ( relation_dom @ SV305 )
= ( relation_rng @ ( relation_inverse @ SV305 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1469]) ).
thf(1672,plain,
! [SV306: $i] :
( ( ( relation_dom @ ( identity_relation @ SV306 ) )
= SV306 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1470]) ).
thf(1673,plain,
! [SV307: $i] :
( ( ( relation_rng @ ( identity_relation @ SV307 ) )
= SV307 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1471]) ).
thf(1674,plain,
! [SV308: $i] :
( ( ! [SY942: $i] :
( ( SV308 = SY942 )
| ~ ( subset @ SV308 @ SY942 )
| ( proper_subset @ SV308 @ SY942 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1472]) ).
thf(1675,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1473]) ).
thf(1676,plain,
! [SV231: $i,SV143: $i] :
( ( ~ ! [SY864: $i,SY865: $i] :
( ~ ( in @ SV143 @ SY864 )
| ~ ( in @ SV231 @ SY865 )
| ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SY864 @ SY865 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1474]) ).
thf(1677,plain,
! [SV231: $i,SV143: $i] :
( ( ~ ~ ( ~ ! [SY866: $i] :
( ! [SY867: $i] :
~ ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SY866 @ SY867 ) )
| ( in @ SV143 @ SY866 ) )
| ~ ! [SY868: $i,SY869: $i] :
( ~ ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SY868 @ SY869 ) )
| ( in @ SV231 @ SY869 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1474]) ).
thf(1678,plain,
! [SV144: $i] :
( ( ! [SY788: $i,SY789: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK56_D @ SY789 @ SY788 @ SV144 ) @ SY789 )
| ~ ( in @ ( sK56_D @ SY789 @ SY788 @ SV144 ) @ SV144 ) )
| ~ ( ~ ( in @ ( sK56_D @ SY789 @ SY788 @ SV144 ) @ SY789 )
| ~ ( in @ ( sK56_D @ SY789 @ SY788 @ SV144 ) @ SY788 ) ) )
| ~ ( ( in @ ( sK56_D @ SY789 @ SY788 @ SV144 ) @ SY789 )
| ( in @ ( sK56_D @ SY789 @ SY788 @ SV144 ) @ SV144 )
| ( in @ ( sK56_D @ SY789 @ SY788 @ SV144 ) @ SY788 ) ) )
| ( SY789
= ( set_union2 @ SV144 @ SY788 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1475]) ).
thf(1679,plain,
! [SV144: $i] :
( ( ! [SY790: $i,SY791: $i] :
( ( SY791
!= ( set_union2 @ SV144 @ SY790 ) )
| ~ ( ~ ! [SY792: $i] :
( ~ ( in @ SY792 @ SY791 )
| ( in @ SY792 @ SV144 )
| ( in @ SY792 @ SY790 ) )
| ~ ~ ( ~ ! [SY793: $i] :
( ~ ( in @ SY793 @ SV144 )
| ( in @ SY793 @ SY791 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY790 )
| ( in @ SX3 @ SY791 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1476]) ).
thf(1680,plain,
! [SV309: $i] :
( ( ~ ( empty @ SV309 )
| ( empty @ ( relation_dom @ SV309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1477]) ).
thf(1681,plain,
! [SV310: $i] :
( ( ~ ( empty @ SV310 )
| ( relation @ ( relation_dom @ SV310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1478]) ).
thf(1682,plain,
! [SV145: $i] :
( ( ! [SY795: $i,SY796: $i] :
( ~ ( relation @ SY796 )
| ! [SY797: $i] :
( ~ ( in @ SY797 @ ( relation_dom @ SY796 ) )
| ~ ( in @ ( ordered_pair @ SY797 @ SV145 ) @ SY796 )
| ~ ( in @ SY797 @ SY795 ) )
| ( in @ SV145 @ ( relation_image @ SY796 @ SY795 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1479]) ).
thf(1683,plain,
! [SV145: $i] :
( ( ! [SY798: $i,SY799: $i] :
( ~ ( relation @ SY799 )
| ~ ( in @ SV145 @ ( relation_image @ SY799 @ SY798 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK40_D @ SY799 @ SY798 @ SV145 ) @ ( relation_dom @ SY799 ) )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY799 @ SY798 @ SV145 ) @ SV145 ) @ SY799 ) )
| ~ ( in @ ( sK40_D @ SY799 @ SY798 @ SV145 ) @ SY798 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1480]) ).
thf(1684,plain,
! [SV146: $i] :
( ( ! [SY800: $i] :
( ~ ( subset @ SV146 @ SY800 )
| ! [SY801: $i] : ( subset @ ( cartesian_product2 @ SV146 @ SY801 ) @ ( cartesian_product2 @ SY800 @ SY801 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1481]) ).
thf(1685,plain,
! [SV146: $i] :
( ( ! [SY802: $i] :
( ~ ( subset @ SV146 @ SY802 )
| ! [SY803: $i] : ( subset @ ( cartesian_product2 @ SY803 @ SV146 ) @ ( cartesian_product2 @ SY803 @ SY802 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1482]) ).
thf(1686,plain,
! [SV147: $i,SV232: $i] :
( ( ( ~ ( ~ ( in @ ( sK44_C @ SV232 @ SV147 ) @ SV147 )
| ~ ( in @ ( sK44_C @ SV232 @ SV147 ) @ SV232 ) )
| ~ ( ( in @ ( sK44_C @ SV232 @ SV147 ) @ SV147 )
| ( in @ ( sK44_C @ SV232 @ SV147 ) @ SV232 ) ) )
= $false )
| ( ( SV147 = SV232 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1483]) ).
thf(1687,plain,
! [SV311: $i] :
( ( ! [SY943: $i] :
( ~ ( subset @ SV311 @ ( singleton @ SY943 ) )
| ( SV311 = empty_set )
| ( SV311
= ( singleton @ SY943 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1484]) ).
thf(1688,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1485]) ).
thf(1689,plain,
! [SV233: $i,SV148: $i] :
( ( ~ ! [SY870: $i] :
( ! [SY871: $i] :
( ( ordered_pair @ SV148 @ SV233 )
!= ( ordered_pair @ SY870 @ SY871 ) )
| ( SV148 = SY870 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1486]) ).
thf(1690,plain,
! [SV233: $i,SV148: $i] :
( ( ~ ! [SY872: $i,SY873: $i] :
( ( ( ordered_pair @ SV148 @ SV233 )
!= ( ordered_pair @ SY872 @ SY873 ) )
| ( SV233 = SY873 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1486]) ).
thf(1691,plain,
! [SV312: $i] :
( ( ! [SY944: $i] :
( ~ ( ~ ( in @ ( sK50_C @ SY944 @ SV312 ) @ SV312 )
| ~ ~ ( in @ ( sK50_C @ SY944 @ SV312 ) @ SY944 ) )
| ( subset @ SV312 @ SY944 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1487]) ).
thf(1692,plain,
! [SV313: $i] :
( ( ! [SY945: $i] :
( ~ ( subset @ SV313 @ SY945 )
| ! [SY946: $i] :
( ~ ( in @ SY946 @ SV313 )
| ( in @ SY946 @ SY945 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1488]) ).
thf(1693,plain,
( ( empty @ sK6_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1489]) ).
thf(1694,plain,
! [SV314: $i] :
( ( ~ ( relation @ SV314 )
| ( ( relation_dom @ SV314 )
!= empty_set )
| ( SV314 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1491]) ).
thf(1695,plain,
! [SV315: $i] :
( ( ~ ( relation @ SV315 )
| ( ( relation_rng @ SV315 )
!= empty_set )
| ( SV315 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1492]) ).
thf(1696,plain,
! [SV316: $i] :
( ( ~ ( empty @ SV316 )
| ( empty @ ( relation_rng @ SV316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(1697,plain,
! [SV317: $i] :
( ( ~ ( empty @ SV317 )
| ( relation @ ( relation_rng @ SV317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(1698,plain,
! [SV149: $i] :
( ( ! [SY810: $i,SY811: $i] :
( ~ ( ~ ( ~ ( in @ ( sK45_D @ SY811 @ SY810 @ SV149 ) @ SV149 )
| ( in @ ( sK45_D @ SY811 @ SY810 @ SV149 ) @ SY810 )
| ~ ( in @ ( sK45_D @ SY811 @ SY810 @ SV149 ) @ SY811 ) )
| ~ ~ ( ~ ( ( in @ ( sK45_D @ SY811 @ SY810 @ SV149 ) @ SV149 )
| ( in @ ( sK45_D @ SY811 @ SY810 @ SV149 ) @ SY811 ) )
| ~ ( ~ ( in @ ( sK45_D @ SY811 @ SY810 @ SV149 ) @ SY810 )
| ( in @ ( sK45_D @ SY811 @ SY810 @ SV149 ) @ SY811 ) ) ) )
| ( SY811
= ( set_difference @ SV149 @ SY810 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1495]) ).
thf(1699,plain,
! [SV149: $i] :
( ( ! [SY812: $i,SY813: $i] :
( ( SY813
!= ( set_difference @ SV149 @ SY812 ) )
| ~ ( ~ ! [SY814: $i] :
( ~ ( in @ SY814 @ SV149 )
| ( in @ SY814 @ SY812 )
| ( in @ SY814 @ SY813 ) )
| ~ ~ ( ~ ! [SY815: $i] :
( ~ ( in @ SY815 @ SY813 )
| ( in @ SY815 @ SV149 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY813 )
| ~ ( in @ SX3 @ SY812 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1496]) ).
thf(1700,plain,
! [SV151: $i,SV2: $i] :
( ( ( in @ SV2 @ SV151 )
= $false )
| ( ( disjoint @ ( singleton @ SV2 ) @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1498]) ).
thf(1701,plain,
! [SV4: $i,SV153: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV153 )
| ( in @ SV318 @ SV4 ) )
= $true )
| ( ( element @ SV153 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1499]) ).
thf(1702,plain,
! [SV8: $i,SV157: $i] :
( ( ( in @ SV157 @ SV8 )
= $false )
| ( ( in @ SV8 @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1503]) ).
thf(1703,plain,
! [SV11: $i,SV159: $i] :
( ( ( empty @ SV159 )
= $true )
| ( ( in @ SV11 @ SV159 )
= $true )
| ( ( element @ SV11 @ SV159 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1505]) ).
thf(1704,plain,
! [SV12: $i,SV234: $i,SV160: $i] :
( ( ( ~ ( element @ SV160 @ ( powerset @ SV234 ) ) )
= $true )
| ( ( ~ ( in @ SV12 @ SV160 ) )
= $true )
| ( ( element @ SV12 @ SV234 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1506]) ).
thf(1705,plain,
! [SV161: $i,SV13: $i] :
( ( ( in @ SV13 @ SV161 )
= $false )
| ( ( empty @ SV161 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1507]) ).
thf(1706,plain,
! [SV162: $i,SV15: $i,SV319: $i] :
( ( ( ( in @ SV319 @ SV15 )
| ( subset @ SV15 @ ( set_difference @ SV162 @ ( singleton @ SV319 ) ) ) )
= $true )
| ( ( subset @ SV15 @ SV162 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1508]) ).
thf(1707,plain,
! [SV163: $i,SV235: $i,SV250: $i,SV16: $i] :
( ( ( SV16 = SV250 )
= $true )
| ( ( ( SV16 = SV235 )
| ( ( unordered_pair @ SV16 @ SV163 )
!= ( unordered_pair @ SV235 @ SV250 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1509]) ).
thf(1708,plain,
! [SV251: $i,SV236: $i,SV168: $i,SV21: $i] :
( ( ( ~ ( subset @ SV21 @ SV168 )
| ~ ( subset @ SV236 @ SV251 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV21 @ SV236 ) @ ( cartesian_product2 @ SV168 @ SV251 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1514]) ).
thf(1709,plain,
! [SV173: $i,SV27: $i] :
( ( ( ( SV27 = empty_set )
| ~ ( subset @ SV27 @ ( relation_rng @ SV173 ) ) )
= $true )
| ( ( ( ( relation_inverse_image @ SV173 @ SV27 )
!= empty_set ) )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1519]) ).
thf(1710,plain,
! [SV174: $i,SV28: $i,SV237: $i] :
( ( ( relation @ SV237 )
= $false )
| ( ( ~ ( subset @ SV28 @ SV174 )
| ( subset @ ( relation_inverse_image @ SV237 @ SV28 ) @ ( relation_inverse_image @ SV237 @ SV174 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1520]) ).
thf(1711,plain,
! [SV238: $i,SV176: $i,SV30: $i] :
( ( ( ~ ( subset @ SV30 @ SV176 ) )
= $true )
| ( ( ~ ( subset @ SV30 @ SV238 ) )
= $true )
| ( ( subset @ SV30 @ ( set_intersection2 @ SV176 @ SV238 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1521]) ).
thf(1712,plain,
! [SV239: $i,SV177: $i,SV31: $i] :
( ( ( ~ ( subset @ SV31 @ SV177 ) )
= $true )
| ( ( ~ ( subset @ SV177 @ SV239 ) )
= $true )
| ( ( subset @ SV31 @ SV239 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1522]) ).
thf(1713,plain,
! [SV33: $i,SV178: $i] :
( ( ( function @ SV178 )
= $false )
| ( ( ~ ( relation @ SV178 ) )
= $true )
| ( ( ! [SY827: $i] :
( ~ ( function @ SY827 )
| ~ ( relation @ SY827 )
| ~ ( in @ SV33 @ ( relation_dom @ ( relation_composition @ SY827 @ SV178 ) ) )
| ( ( apply @ ( relation_composition @ SY827 @ SV178 ) @ SV33 )
= ( apply @ SV178 @ ( apply @ SY827 @ SV33 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1523]) ).
thf(1714,plain,
! [SV34: $i,SV179: $i] :
( ( ( function @ SV179 )
= $false )
| ( ( ~ ( relation @ SV179 ) )
= $true )
| ( ( ! [SY828: $i] :
( ~ ( function @ SY828 )
| ~ ( relation @ SY828 )
| ~ ( in @ SV34 @ ( relation_dom @ SV179 ) )
| ( ( apply @ ( relation_composition @ SV179 @ SY828 ) @ SV34 )
= ( apply @ SY828 @ ( apply @ SV179 @ SV34 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1524]) ).
thf(1715,plain,
! [SV180: $i,SV320: $i,SV35: $i] :
( ( ( subset @ ( set_intersection2 @ SV35 @ SV320 ) @ ( set_intersection2 @ SV180 @ SV320 ) )
= $true )
| ( ( subset @ SV35 @ SV180 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1525]) ).
thf(1716,plain,
! [SV182: $i,SV321: $i,SV38: $i] :
( ( ( subset @ ( set_difference @ SV38 @ SV321 ) @ ( set_difference @ SV182 @ SV321 ) )
= $true )
| ( ( subset @ SV38 @ SV182 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1527]) ).
thf(1717,plain,
! [SV43: $i,SV252: $i] :
( ( ( ~ ( relation @ SV252 ) )
= $true )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV43 @ SV252 ) ) @ ( relation_dom @ SV43 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1528]) ).
thf(1718,plain,
! [SV44: $i,SV253: $i] :
( ( ( ~ ( relation @ SV253 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV44 @ SV253 ) ) @ ( relation_rng @ SV253 ) )
= $true )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1529]) ).
thf(1719,plain,
! [SV46: $i,SV254: $i] :
( ( ( ~ ( relation @ SV254 ) )
= $true )
| ( ( ~ ( subset @ ( relation_rng @ SV46 ) @ ( relation_dom @ SV254 ) )
| ( ( relation_dom @ ( relation_composition @ SV46 @ SV254 ) )
= ( relation_dom @ SV46 ) ) )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1531]) ).
thf(1720,plain,
! [SV47: $i,SV187: $i] :
( ( ( SV187 = empty_set )
= $true )
| ( ( ( ( complements_of_subsets @ SV47 @ SV187 )
!= empty_set ) )
= $true )
| ( ( element @ SV187 @ ( powerset @ ( powerset @ SV47 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1532]) ).
thf(1721,plain,
! [SV48: $i,SV255: $i] :
( ( ( ~ ( relation @ SV255 ) )
= $true )
| ( ( ~ ( subset @ ( relation_dom @ SV48 ) @ ( relation_rng @ SV255 ) )
| ( ( relation_rng @ ( relation_composition @ SV255 @ SV48 ) )
= ( relation_rng @ SV48 ) ) )
= $true )
| ( ( relation @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1533]) ).
thf(1722,plain,
! [SV50: $i,SV240: $i] :
( ( ( element @ SV240 @ ( powerset @ SV50 ) )
= $false )
| ( ( ! [SY876: $i] :
( ~ ( element @ SY876 @ SV50 )
| ( in @ SY876 @ SV240 )
| ( in @ SY876 @ ( subset_complement @ SV50 @ SV240 ) ) ) )
= $true )
| ( ( SV50 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1534]) ).
thf(1723,plain,
! [SV189: $i,SV51: $i,SV241: $i] :
( ( ( element @ SV241 @ ( powerset @ SV51 ) )
= $false )
| ( ( ~ ( in @ SV189 @ ( subset_complement @ SV51 @ SV241 ) )
| ~ ( in @ SV189 @ SV241 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1535]) ).
thf(1724,plain,
! [SV190: $i,SV53: $i] :
( ( ( subset @ SV53 @ SV190 )
= $false )
| ( ( proper_subset @ SV190 @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1537]) ).
thf(1725,plain,
! [SV54: $i,SV242: $i,SV191: $i] :
( ( ( ~ ( disjoint @ SV191 @ SV242 ) )
= $true )
| ( ( ~ ( subset @ SV54 @ SV191 ) )
= $true )
| ( ( disjoint @ SV54 @ SV242 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1538]) ).
thf(1726,plain,
! [SV243: $i,SV195: $i,SV59: $i] :
( ( ( ~ ( subset @ SV59 @ SV195 ) )
= $true )
| ( ( ~ ( subset @ SV243 @ SV195 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV59 @ SV243 ) @ SV195 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1541]) ).
thf(1727,plain,
! [SV256: $i,SV196: $i,SV60: $i] :
( ( ( ( singleton @ SV60 )
= ( unordered_pair @ SV196 @ SV256 ) )
= $false )
| ( ( SV60 = SV196 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1542]) ).
thf(1728,plain,
! [SV244: $i,SV199: $i,SV64: $i] :
( ( ( ( singleton @ SV64 )
= ( unordered_pair @ SV199 @ SV244 ) )
= $false )
| ( ( SV199 = SV244 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1545]) ).
thf(1729,plain,
! [SV206: $i,SV76: $i] :
( ( ( relation @ SV76 )
= $false )
| ( ( ~ ( relation @ SV206 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV76 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1548]) ).
thf(1730,plain,
! [SV245: $i,SV79: $i,SV209: $i] :
( ( ( ~ ( element @ SV209 @ ( powerset @ SV79 ) ) )
= $true )
| ( ( ~ ( element @ SV245 @ ( powerset @ SV79 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV79 @ SV209 @ SV245 ) @ ( powerset @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1551]) ).
thf(1731,plain,
! [SV212: $i,SV84: $i] :
( ( ( relation @ SV84 )
= $false )
| ( ( ~ ( relation @ SV212 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV84 @ SV212 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1555]) ).
thf(1732,plain,
! [SV214: $i,SV87: $i] :
( ( ( relation @ SV87 )
= $false )
| ( ( ~ ( relation @ SV214 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV87 @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1556]) ).
thf(1733,plain,
! [SV216: $i,SV92: $i] :
( ( ( empty @ ( cartesian_product2 @ SV92 @ SV216 ) )
= $false )
| ( ( empty @ SV216 )
= $true )
| ( ( empty @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1559]) ).
thf(1734,plain,
! [SV93: $i] :
( ( ( empty @ ( relation_dom @ SV93 ) )
= $false )
| ( ( empty @ SV93 )
= $true )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1560]) ).
thf(1735,plain,
! [SV94: $i] :
( ( ( empty @ ( relation_rng @ SV94 ) )
= $false )
| ( ( empty @ SV94 )
= $true )
| ( ( relation @ SV94 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1561]) ).
thf(1736,plain,
! [SV248: $i,SV102: $i,SV221: $i] :
( ( ( ~ ( element @ SV221 @ ( powerset @ SV102 ) ) )
= $true )
| ( ( ~ ( element @ SV248 @ ( powerset @ SV102 ) ) )
= $true )
| ( ( ( subset_difference @ SV102 @ SV221 @ SV248 )
= ( set_difference @ SV221 @ SV248 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1566]) ).
thf(1737,plain,
! [SV109: $i,SV249: $i,SV223: $i] :
( ( ( ~ ( element @ SV223 @ ( powerset @ SV249 ) ) )
= $true )
| ( ( ~ ( in @ SV109 @ SV223 ) )
= $true )
| ( ( ~ ( empty @ SV249 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1568]) ).
thf(1738,plain,
! [SV224: $i,SV111: $i] :
( ( ( empty @ SV111 )
= $false )
| ( ( SV111 = SV224 )
= $true )
| ( ( ~ ( empty @ SV224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1569]) ).
thf(1739,plain,
! [SV112: $i,SV322: $i] :
( ( ! [SY947: $i] :
( ~ ( ~ ( ~ ( in @ ( sK49_D @ SY947 @ SV322 @ SV112 ) @ SV112 )
| ~ ( in @ ( sK49_D @ SY947 @ SV322 @ SV112 ) @ SV322 )
| ~ ( in @ ( sK49_D @ SY947 @ SV322 @ SV112 ) @ SY947 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_D @ SY947 @ SV322 @ SV112 ) @ SV112 )
| ( in @ ( sK49_D @ SY947 @ SV322 @ SV112 ) @ SY947 ) )
| ~ ( ( in @ ( sK49_D @ SY947 @ SV322 @ SV112 ) @ SV322 )
| ( in @ ( sK49_D @ SY947 @ SV322 @ SV112 ) @ SY947 ) ) ) )
| ( SY947
= ( set_intersection2 @ SV112 @ SV322 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1570]) ).
thf(1740,plain,
! [SV323: $i,SV112: $i] :
( ( ! [SY948: $i] :
( ( SY948
!= ( set_intersection2 @ SV112 @ SV323 ) )
| ~ ( ~ ! [SY949: $i] :
( ~ ( in @ SY949 @ SV112 )
| ~ ( in @ SY949 @ SV323 )
| ( in @ SY949 @ SY948 ) )
| ~ ~ ( ~ ! [SY612: $i] :
( ~ ( in @ SY612 @ SY948 )
| ( in @ SY612 @ SV112 ) )
| ~ ! [SY951: $i] :
( ~ ( in @ SY951 @ SY948 )
| ( in @ SY951 @ SV323 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1571]) ).
thf(1741,plain,
! [SV258: $i,SV324: $i] :
( ( ~ ( ~ ( ! [SY952: $i] :
( ~ ( in @ ( sK47_C @ SV324 @ SV258 ) @ SY952 )
| ~ ( in @ SY952 @ SV258 ) )
| ~ ( in @ ( sK47_C @ SV324 @ SV258 ) @ SV324 ) )
| ~ ( ~ ( ~ ( in @ ( sK47_C @ SV324 @ SV258 ) @ ( sK48_SY487 @ SV324 @ SV258 ) )
| ~ ( in @ ( sK48_SY487 @ SV324 @ SV258 ) @ SV258 ) )
| ( in @ ( sK47_C @ SV324 @ SV258 ) @ SV324 ) ) )
| ( SV324
= ( union @ SV258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1572]) ).
thf(1742,plain,
! [SV259: $i,SV325: $i] :
( ( ( SV325
!= ( union @ SV259 ) )
| ~ ( ~ ! [SY953: $i] :
( ! [SY881: $i] :
( ~ ( in @ SY953 @ SY881 )
| ~ ( in @ SY881 @ SV259 ) )
| ( in @ SY953 @ SV325 ) )
| ~ ! [SY955: $i] :
( ~ ( in @ SY955 @ SV325 )
| ~ ( ~ ( in @ SY955 @ ( sK46_D @ SY955 @ SV325 @ SV259 ) )
| ~ ( in @ ( sK46_D @ SY955 @ SV325 @ SV259 ) @ SV259 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1573]) ).
thf(1743,plain,
! [SV113: $i,SV225: $i] :
( ( ( ~ ! [SY839: $i] :
( ~ ( relation @ SY839 )
| ~ ( ~ ( ~ ( in @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) @ SV113 )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ SY839 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) ) @ SV225 )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ SY839 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) ) @ SY839 ) )
| ~ ~ ( ~ ( ( in @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) @ SV113 )
| ( in @ ( ordered_pair @ ( sK32_D @ SY839 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) ) @ SY839 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_D @ SY839 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) ) @ SV225 )
| ( in @ ( ordered_pair @ ( sK32_D @ SY839 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) ) @ SY839 ) ) ) )
| ( SY839
= ( relation_rng_restriction @ SV113 @ SV225 ) ) )
| ~ ! [SY840: $i] :
( ~ ( relation @ SY840 )
| ( SY840
!= ( relation_rng_restriction @ SV113 @ SV225 ) )
| ~ ( ~ ! [SY841: $i,SY842: $i] :
( ~ ( in @ SY842 @ SV113 )
| ~ ( in @ ( ordered_pair @ SY841 @ SY842 ) @ SV225 )
| ( in @ ( ordered_pair @ SY841 @ SY842 ) @ SY840 ) )
| ~ ~ ( ~ ! [SY619: $i,SY620: $i] :
( ~ ( in @ ( ordered_pair @ SY619 @ SY620 ) @ SY840 )
| ( in @ SY620 @ SV113 ) )
| ~ ! [SY845: $i,SY846: $i] :
( ~ ( in @ ( ordered_pair @ SY845 @ SY846 ) @ SY840 )
| ( in @ ( ordered_pair @ SY845 @ SY846 ) @ SV225 ) ) ) ) ) )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1574]) ).
thf(1744,plain,
! [SV326: $i,SV260: $i] :
( ( ~ ( empty @ SV260 )
| ~ ( relation @ SV326 )
| ( empty @ ( relation_composition @ SV326 @ SV260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1575]) ).
thf(1745,plain,
! [SV327: $i,SV261: $i] :
( ( ~ ( empty @ SV261 )
| ~ ( relation @ SV327 )
| ( relation @ ( relation_composition @ SV327 @ SV261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1576]) ).
thf(1746,plain,
! [SV226: $i,SV114: $i] :
( ( ! [SY847: $i,SY848: $i] :
( ~ ( in @ SV114 @ SY847 )
| ~ ( in @ SV226 @ SY848 )
| ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SY847 @ SY848 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1577]) ).
thf(1747,plain,
! [SV226: $i,SV114: $i] :
( ( ~ ( ~ ! [SY849: $i] :
( ! [SY850: $i] :
~ ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SY849 @ SY850 ) )
| ( in @ SV114 @ SY849 ) )
| ~ ! [SY851: $i,SY852: $i] :
( ~ ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SY851 @ SY852 ) )
| ( in @ SV226 @ SY852 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1578]) ).
thf(1748,plain,
! [SV328: $i,SV262: $i] :
( ( ( disjoint @ SV262 @ SV328 )
| ~ ( ~ ( in @ ( sK72_C @ SV328 @ SV262 ) @ SV262 )
| ~ ( in @ ( sK72_C @ SV328 @ SV262 ) @ SV328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1579]) ).
thf(1749,plain,
! [SV329: $i,SV263: $i] :
( ( ! [SY956: $i] :
( ~ ( in @ SY956 @ SV263 )
| ~ ( in @ SY956 @ SV329 ) )
| ~ ( disjoint @ SV263 @ SV329 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1580]) ).
thf(1750,plain,
! [SV264: $i,SV330: $i] :
( ( ~ ( ~ ( ( ( sK62_C @ SV330 @ SV264 )
!= SV264 )
| ~ ( in @ ( sK62_C @ SV330 @ SV264 ) @ SV330 ) )
| ~ ( ( ( sK62_C @ SV330 @ SV264 )
= SV264 )
| ( in @ ( sK62_C @ SV330 @ SV264 ) @ SV330 ) ) )
| ( SV330
= ( singleton @ SV264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1581]) ).
thf(1751,plain,
! [SV265: $i,SV331: $i] :
( ( ( SV331
!= ( singleton @ SV265 ) )
| ~ ( ~ ! [SY957: $i] :
( ( SY957 != SV265 )
| ( in @ SY957 @ SV331 ) )
| ~ ! [SY958: $i] :
( ~ ( in @ SY958 @ SV331 )
| ( SY958 = SV265 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1582]) ).
thf(1752,plain,
! [SV266: $i] :
( ( ( in @ ( sK61_B @ SV266 ) @ SV266 )
= $true )
| ( ( SV266 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1583]) ).
thf(1753,plain,
! [SV267: $i] :
( ( ( ( SV267 != empty_set ) )
= $true )
| ( ( ! [SY892: $i] :
~ ( in @ SY892 @ SV267 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1584]) ).
thf(1754,plain,
! [SV115: $i,SV332: $i] :
( ( ~ ( subset @ SV332 @ ( sK42_B @ SV115 ) )
| ( are_equipotent @ SV332 @ ( sK42_B @ SV115 ) )
| ( in @ SV332 @ ( sK42_B @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1585]) ).
thf(1755,plain,
! [SV115: $i] :
( ( ~ ! [SY631: $i] :
( ~ ( ~ ! [SY632: $i] :
( ~ ( subset @ SY632 @ SY631 )
| ( in @ SY632 @ ( sK43_SY481 @ SY631 @ SV115 ) ) )
| ~ ( in @ ( sK43_SY481 @ SY631 @ SV115 ) @ ( sK42_B @ SV115 ) ) )
| ~ ( in @ SY631 @ ( sK42_B @ SV115 ) ) )
| ~ ~ ( ~ ! [SY633: $i,SY634: $i] :
( ~ ( in @ SY633 @ ( sK42_B @ SV115 ) )
| ~ ( subset @ SY634 @ SY633 )
| ( in @ SY634 @ ( sK42_B @ SV115 ) ) )
| ~ ( in @ SV115 @ ( sK42_B @ SV115 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1586]) ).
thf(1756,plain,
! [SV333: $i,SV268: $i] :
( ( ~ ( subset @ SV268 @ ( singleton @ SV333 ) )
| ( SV268 = empty_set )
| ( SV268
= ( singleton @ SV333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1587]) ).
thf(1757,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1588]) ).
thf(1758,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1588]) ).
thf(1759,plain,
! [SV116: $i] :
( ( ( relation @ SV116 )
= $false )
| ( ( function @ SV116 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY635: $i] :
( ~ ( in @ SY635 @ ( relation_dom @ SV116 ) )
| ! [SY636: $i] :
( ( SY636
!= ( apply @ SV116 @ SY635 ) )
| ( in @ ( ordered_pair @ SY635 @ SY636 ) @ SV116 ) ) )
| ~ ! [SY637: $i] :
( ~ ( in @ SY637 @ ( relation_dom @ SV116 ) )
| ! [SY638: $i] :
( ~ ( in @ ( ordered_pair @ SY637 @ SY638 ) @ SV116 )
| ( SY638
= ( apply @ SV116 @ SY637 ) ) ) ) )
| ~ ~ ( ~ ! [SY639: $i] :
( ( in @ SY639 @ ( relation_dom @ SV116 ) )
| ! [SY640: $i] :
( ( SY640
!= ( apply @ SV116 @ SY639 ) )
| ( SY640 = empty_set ) ) )
| ~ ! [SY641: $i] :
( ( in @ SY641 @ ( relation_dom @ SV116 ) )
| ! [SY642: $i] :
( ( SY642 != empty_set )
| ( SY642
= ( apply @ SV116 @ SY641 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1589]) ).
thf(1760,plain,
! [SV334: $i,SV117: $i] :
( ( ! [SY959: $i] :
( ~ ( ~ ( ! [SY960: $i,SY961: $i] :
( ~ ( in @ SY960 @ SV117 )
| ~ ( in @ SY961 @ SV334 )
| ( ( sK53_D @ SY959 @ SV334 @ SV117 )
!= ( ordered_pair @ SY960 @ SY961 ) ) )
| ~ ( in @ ( sK53_D @ SY959 @ SV334 @ SV117 ) @ SY959 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK54_SY491 @ SY959 @ SV334 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK55_SY493 @ SY959 @ SV334 @ SV117 ) @ SV334 ) )
| ( ( sK53_D @ SY959 @ SV334 @ SV117 )
!= ( ordered_pair @ ( sK54_SY491 @ SY959 @ SV334 @ SV117 ) @ ( sK55_SY493 @ SY959 @ SV334 @ SV117 ) ) ) )
| ( in @ ( sK53_D @ SY959 @ SV334 @ SV117 ) @ SY959 ) ) )
| ( SY959
= ( cartesian_product2 @ SV117 @ SV334 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1590]) ).
thf(1761,plain,
! [SV335: $i,SV117: $i] :
( ( ! [SY962: $i] :
( ( SY962
!= ( cartesian_product2 @ SV117 @ SV335 ) )
| ~ ( ~ ! [SY963: $i] :
( ! [SY964: $i,SY965: $i] :
( ~ ( in @ SY964 @ SV117 )
| ~ ( in @ SY965 @ SV335 )
| ( SY963
!= ( ordered_pair @ SY964 @ SY965 ) ) )
| ( in @ SY963 @ SY962 ) )
| ~ ! [SY966: $i] :
( ~ ( in @ SY966 @ SY962 )
| ~ ( ~ ~ ( ~ ( in @ ( sK51_E @ SY966 @ SY962 @ SV335 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK52_SY488 @ SY966 @ SY962 @ SV335 @ SV117 ) @ SV335 ) )
| ( SY966
!= ( ordered_pair @ ( sK51_E @ SY966 @ SY962 @ SV335 @ SV117 ) @ ( sK52_SY488 @ SY966 @ SY962 @ SV335 @ SV117 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1591]) ).
thf(1762,plain,
! [SV336: $i,SV269: $i] :
( ( ( ( set_difference @ SV269 @ SV336 )
!= empty_set )
| ( subset @ SV269 @ SV336 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1592]) ).
thf(1763,plain,
! [SV337: $i,SV270: $i] :
( ( ~ ( subset @ SV270 @ SV337 )
| ( ( set_difference @ SV270 @ SV337 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(1764,plain,
! [SV271: $i] :
( ( ( ~ ( relation @ SV271 ) )
= $true )
| ( ( ( ( relation_dom @ SV271 )
!= empty_set )
| ( ( relation_rng @ SV271 )
= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1594]) ).
thf(1765,plain,
! [SV272: $i] :
( ( ( ~ ( relation @ SV272 ) )
= $true )
| ( ( ( ( relation_rng @ SV272 )
!= empty_set )
| ( ( relation_dom @ SV272 )
= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1595]) ).
thf(1766,plain,
! [SV118: $i,SV338: $i] :
( ( ! [SY967: $i] :
( ~ ( function @ SY967 )
| ~ ( relation @ SY967 )
| ( SV338
!= ( apply @ SY967 @ SV118 ) )
| ~ ( in @ SV118 @ ( relation_dom @ SY967 ) )
| ( in @ ( ordered_pair @ SV118 @ SV338 ) @ SY967 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1596]) ).
thf(1767,plain,
! [SV118: $i] :
( ( ~ ! [SY655: $i,SY656: $i] :
( ~ ( function @ SY656 )
| ~ ( relation @ SY656 )
| ~ ( in @ ( ordered_pair @ SV118 @ SY655 ) @ SY656 )
| ( SY655
= ( apply @ SY656 @ SV118 ) ) )
| ~ ! [SY657: $i,SY658: $i] :
( ~ ( function @ SY658 )
| ~ ( relation @ SY658 )
| ~ ( in @ ( ordered_pair @ SV118 @ SY657 ) @ SY658 )
| ( in @ SV118 @ ( relation_dom @ SY658 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1597]) ).
thf(1768,plain,
! [SV273: $i,SV339: $i] :
( ( ~ ( relation @ SV339 )
| ~ ( ~ ( ( ( sK69_C @ SV339 @ SV273 )
!= ( sK70_SY500 @ SV339 @ SV273 ) )
| ~ ( in @ ( sK69_C @ SV339 @ SV273 ) @ SV273 )
| ~ ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 ) )
| ~ ~ ( ~ ( ( ( sK69_C @ SV339 @ SV273 )
= ( sK70_SY500 @ SV339 @ SV273 ) )
| ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 ) )
| ~ ( ( in @ ( sK69_C @ SV339 @ SV273 ) @ SV273 )
| ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 ) ) ) )
| ( SV339
= ( identity_relation @ SV273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1598]) ).
thf(1769,plain,
! [SV274: $i,SV340: $i] :
( ( ~ ( relation @ SV340 )
| ( SV340
!= ( identity_relation @ SV274 ) )
| ~ ( ~ ! [SY968: $i,SY969: $i] :
( ( SY968 != SY969 )
| ~ ( in @ SY968 @ SV274 )
| ( in @ ( ordered_pair @ SY968 @ SY969 ) @ SV340 ) )
| ~ ~ ( ~ ! [SY970: $i,SY971: $i] :
( ~ ( in @ ( ordered_pair @ SY970 @ SY971 ) @ SV340 )
| ( SY970 = SY971 ) )
| ~ ! [SY972: $i] :
( ! [SY973: $i] :
~ ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV340 )
| ( in @ SY972 @ SV274 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1599]) ).
thf(1770,plain,
! [SV120: $i,SV275: $i] :
( ( ( ~ ( relation @ SV275 ) )
= $true )
| ( ( ~ ( ~ ! [SY904: $i] :
( ~ ( relation @ SY904 )
| ~ ( ~ ( ! [SY905: $i] :
( ~ ( in @ ( ordered_pair @ ( sK13_D @ SY904 @ SV275 @ SV120 ) @ SY905 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY905 @ ( sK14_SY457 @ SY904 @ SV275 @ SV120 ) ) @ SV275 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_D @ SY904 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SY904 @ SV275 @ SV120 ) ) @ SY904 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_D @ SY904 @ SV275 @ SV120 ) @ ( sK15_SY461 @ SY904 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY461 @ SY904 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SY904 @ SV275 @ SV120 ) ) @ SV275 ) )
| ( in @ ( ordered_pair @ ( sK13_D @ SY904 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SY904 @ SV275 @ SV120 ) ) @ SY904 ) ) )
| ( SY904
= ( relation_composition @ SV120 @ SV275 ) ) )
| ~ ! [SY906: $i] :
( ~ ( relation @ SY906 )
| ( SY906
!= ( relation_composition @ SV120 @ SV275 ) )
| ~ ( ~ ! [SY907: $i,SY908: $i] :
( ! [SY909: $i] :
( ~ ( in @ ( ordered_pair @ SY907 @ SY909 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY909 @ SY908 ) @ SV275 ) )
| ( in @ ( ordered_pair @ SY907 @ SY908 ) @ SY906 ) )
| ~ ! [SY910: $i,SY911: $i] :
( ~ ( in @ ( ordered_pair @ SY910 @ SY911 ) @ SY906 )
| ~ ( ~ ( in @ ( ordered_pair @ SY910 @ ( sK12_F @ SY911 @ SY910 @ SY906 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK12_F @ SY911 @ SY910 @ SY906 @ SV275 @ SV120 ) @ SY911 ) @ SV275 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1602]) ).
thf(1771,plain,
! [SV227: $i,SV121: $i] :
( ( ( ~ ! [SY853: $i] :
( ~ ( element @ SY853 @ ( powerset @ SV121 ) )
| ~ ( disjoint @ SV227 @ SY853 )
| ( subset @ SV227 @ ( subset_complement @ SV121 @ SY853 ) ) )
| ~ ! [SY854: $i] :
( ~ ( element @ SY854 @ ( powerset @ SV121 ) )
| ~ ( subset @ SV227 @ ( subset_complement @ SV121 @ SY854 ) )
| ( disjoint @ SV227 @ SY854 ) ) )
= $false )
| ( ( element @ SV227 @ ( powerset @ SV121 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1603]) ).
thf(1772,plain,
! [SV341: $i,SV122: $i] :
( ( ! [SY974: $i] :
( ~ ( relation @ SY974 )
| ~ ( in @ SV122 @ SV341 )
| ~ ( in @ SV122 @ ( relation_rng @ SY974 ) )
| ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SV341 @ SY974 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1604]) ).
thf(1773,plain,
! [SV122: $i] :
( ( ~ ! [SY673: $i,SY674: $i] :
( ~ ( relation @ SY674 )
| ~ ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SY673 @ SY674 ) ) )
| ( in @ SV122 @ SY673 ) )
| ~ ! [SY675: $i,SY676: $i] :
( ~ ( relation @ SY676 )
| ~ ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SY675 @ SY676 ) ) )
| ( in @ SV122 @ ( relation_rng @ SY676 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1605]) ).
thf(1774,plain,
! [SV123: $i] :
( ( ( ~ ! [SY677: $i,SY678: $i] :
( ~ ( relation @ SY678 )
| ~ ( ~ ( ~ ( in @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ SY677 )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ ( sK35_SY473 @ SY678 @ SY677 @ SV123 ) ) @ SV123 )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ ( sK35_SY473 @ SY678 @ SY677 @ SV123 ) ) @ SY678 ) )
| ~ ~ ( ~ ( ( in @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ SY677 )
| ( in @ ( ordered_pair @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ ( sK35_SY473 @ SY678 @ SY677 @ SV123 ) ) @ SY678 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ ( sK35_SY473 @ SY678 @ SY677 @ SV123 ) ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ ( sK35_SY473 @ SY678 @ SY677 @ SV123 ) ) @ SY678 ) ) ) )
| ( SY678
= ( relation_dom_restriction @ SV123 @ SY677 ) ) ) )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1606]) ).
thf(1775,plain,
! [SV123: $i] :
( ( ( ~ ! [SY679: $i,SY680: $i] :
( ~ ( relation @ SY680 )
| ( SY680
!= ( relation_dom_restriction @ SV123 @ SY679 ) )
| ~ ( ~ ! [SY681: $i,SY682: $i] :
( ~ ( in @ SY681 @ SY679 )
| ~ ( in @ ( ordered_pair @ SY681 @ SY682 ) @ SV123 )
| ( in @ ( ordered_pair @ SY681 @ SY682 ) @ SY680 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY680 )
| ( in @ SX3 @ SY679 ) )
| ~ ! [SY685: $i,SY686: $i] :
( ~ ( in @ ( ordered_pair @ SY685 @ SY686 ) @ SY680 )
| ( in @ ( ordered_pair @ SY685 @ SY686 ) @ SV123 ) ) ) ) ) )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1606]) ).
thf(1776,plain,
! [SV124: $i] :
( ( ( ~ ! [SY687: $i] :
( ~ ( relation @ SY687 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_C @ SY687 @ SV124 ) @ ( sK17_SY462 @ SY687 @ SV124 ) ) @ SY687 )
| ~ ( in @ ( ordered_pair @ ( sK17_SY462 @ SY687 @ SV124 ) @ ( sK16_C @ SY687 @ SV124 ) ) @ SV124 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK16_C @ SY687 @ SV124 ) @ ( sK17_SY462 @ SY687 @ SV124 ) ) @ SY687 )
| ( in @ ( ordered_pair @ ( sK17_SY462 @ SY687 @ SV124 ) @ ( sK16_C @ SY687 @ SV124 ) ) @ SV124 ) ) )
| ( SY687
= ( relation_inverse @ SV124 ) ) ) )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1607]) ).
thf(1777,plain,
! [SV124: $i] :
( ( ( ~ ! [SY688: $i] :
( ~ ( relation @ SY688 )
| ( SY688
!= ( relation_inverse @ SV124 ) )
| ~ ( ~ ! [SY689: $i,SY690: $i] :
( ~ ( in @ ( ordered_pair @ SY689 @ SY690 ) @ SY688 )
| ( in @ ( ordered_pair @ SY690 @ SY689 ) @ SV124 ) )
| ~ ! [SY691: $i,SY692: $i] :
( ~ ( in @ ( ordered_pair @ SY692 @ SY691 ) @ SV124 )
| ( in @ ( ordered_pair @ SY691 @ SY692 ) @ SY688 ) ) ) ) )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1607]) ).
thf(1778,plain,
! [SV342: $i,SV276: $i] :
( ( ~ ( element @ SV276 @ ( powerset @ SV342 ) )
| ( subset @ SV276 @ SV342 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1608]) ).
thf(1779,plain,
! [SV343: $i,SV277: $i] :
( ( ~ ( subset @ SV277 @ SV343 )
| ( element @ SV277 @ ( powerset @ SV343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1609]) ).
thf(1780,plain,
! [SV344: $i,SV278: $i] :
( ( ~ ( in @ SV278 @ SV344 )
| ( subset @ ( singleton @ SV278 ) @ SV344 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1610]) ).
thf(1781,plain,
! [SV345: $i,SV279: $i] :
( ( ~ ( subset @ ( singleton @ SV279 ) @ SV345 )
| ( in @ SV279 @ SV345 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1611]) ).
thf(1782,plain,
! [SV346: $i,SV280: $i] :
( ( ( ( set_intersection2 @ SV280 @ SV346 )
!= empty_set )
| ( disjoint @ SV280 @ SV346 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(1783,plain,
! [SV347: $i,SV281: $i] :
( ( ~ ( disjoint @ SV281 @ SV347 )
| ( ( set_intersection2 @ SV281 @ SV347 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(1784,plain,
! [SV282: $i,SV348: $i] :
( ( ~ ( function @ SV348 )
| ~ ( relation @ SV348 )
| ~ ( ~ ( in @ ( sK38_C @ SV348 @ SV282 ) @ SV282 )
| ~ ( ( ( apply @ SV348 @ ( sK38_C @ SV348 @ SV282 ) )
!= ( sK38_C @ SV348 @ SV282 ) ) ) )
| ( ( relation_dom @ SV348 )
!= SV282 )
| ( SV348
= ( identity_relation @ SV282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1614]) ).
thf(1785,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)],[1615]) ).
thf(1786,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1615]) ).
thf(1787,plain,
! [SV349: $i,SV283: $i] :
( ( ( ( set_difference @ SV283 @ SV349 )
!= empty_set )
| ( subset @ SV283 @ SV349 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1616]) ).
thf(1788,plain,
! [SV350: $i,SV284: $i] :
( ( ~ ( subset @ SV284 @ SV350 )
| ( ( set_difference @ SV284 @ SV350 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1617]) ).
thf(1789,plain,
! [SV351: $i,SV285: $i] :
( ( ~ ( subset @ SV285 @ SV351 )
| ~ ( subset @ SV351 @ SV285 )
| ( SV285 = SV351 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1618]) ).
thf(1790,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1619]) ).
thf(1791,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1619]) ).
thf(1792,plain,
! [SV125: $i] :
( ( ( ~ ! [SY693: $i,SY694: $i] :
( ~ ( ~ ( ! [SY695: $i] :
( ~ ( in @ ( ordered_pair @ SY695 @ ( sK30_D @ SY694 @ SY693 @ SV125 ) ) @ SV125 )
| ~ ( in @ SY695 @ SY693 ) )
| ~ ( in @ ( sK30_D @ SY694 @ SY693 @ SV125 ) @ SY694 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_SY471 @ SY694 @ SY693 @ SV125 ) @ ( sK30_D @ SY694 @ SY693 @ SV125 ) ) @ SV125 )
| ~ ( in @ ( sK31_SY471 @ SY694 @ SY693 @ SV125 ) @ SY693 ) )
| ( in @ ( sK30_D @ SY694 @ SY693 @ SV125 ) @ SY694 ) ) )
| ( SY694
= ( relation_image @ SV125 @ SY693 ) ) ) )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1620]) ).
thf(1793,plain,
! [SV125: $i] :
( ( ( ~ ! [SY696: $i,SY697: $i] :
( ( SY697
!= ( relation_image @ SV125 @ SY696 ) )
| ~ ( ~ ! [SY698: $i] :
( ! [SY699: $i] :
( ~ ( in @ ( ordered_pair @ SY699 @ SY698 ) @ SV125 )
| ~ ( in @ SY699 @ SY696 ) )
| ( in @ SY698 @ SY697 ) )
| ~ ! [SY700: $i] :
( ~ ( in @ SY700 @ SY697 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK29_E @ SY700 @ SY697 @ SY696 @ SV125 ) @ SY700 ) @ SV125 )
| ~ ( in @ ( sK29_E @ SY700 @ SY697 @ SY696 @ SV125 ) @ SY696 ) ) ) ) ) )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1620]) ).
thf(1794,plain,
! [SV352: $i,SV126: $i] :
( ( ! [SY975: $i] :
( ~ ( relation @ SY975 )
| ~ ( in @ ( ordered_pair @ SV126 @ SV352 ) @ SY975 )
| ( in @ SV126 @ ( relation_field @ SY975 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1621]) ).
thf(1795,plain,
! [SV353: $i,SV126: $i] :
( ( ! [SY976: $i] :
( ~ ( relation @ SY976 )
| ~ ( in @ ( ordered_pair @ SV126 @ SV353 ) @ SY976 )
| ( in @ SV353 @ ( relation_field @ SY976 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1622]) ).
thf(1796,plain,
! [SV228: $i,SV127: $i] :
( ( ! [SY855: $i,SY856: $i] :
( ~ ( relation @ SY856 )
| ~ ( in @ SV127 @ SY855 )
| ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ SY856 )
| ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SY855 ) @ SY856 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1623]) ).
thf(1797,plain,
! [SV228: $i,SV127: $i] :
( ( ~ ( ~ ! [SY857: $i,SY858: $i] :
( ~ ( relation @ SY858 )
| ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SY857 ) @ SY858 ) )
| ( in @ SV127 @ SY857 ) )
| ~ ! [SY859: $i,SY860: $i] :
( ~ ( relation @ SY860 )
| ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SY859 ) @ SY860 ) )
| ( in @ ( ordered_pair @ SV127 @ SV228 ) @ SY860 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1624]) ).
thf(1798,plain,
! [SV354: $i,SV286: $i] :
( ( ~ ( in @ SV286 @ SV354 )
| ( subset @ ( singleton @ SV286 ) @ SV354 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1625]) ).
thf(1799,plain,
! [SV355: $i,SV287: $i] :
( ( ~ ( subset @ ( singleton @ SV287 ) @ SV355 )
| ( in @ SV287 @ SV355 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1626]) ).
thf(1800,plain,
! [SV356: $i,SV128: $i] :
( ( ! [SY977: $i] :
( ~ ( in @ SV128 @ SY977 )
| ~ ( in @ SV356 @ SY977 )
| ( subset @ ( unordered_pair @ SV128 @ SV356 ) @ SY977 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1627]) ).
thf(1801,plain,
! [SV128: $i] :
( ( ~ ! [SY714: $i,SY715: $i] :
( ~ ( subset @ ( unordered_pair @ SV128 @ SY714 ) @ SY715 )
| ( in @ SV128 @ SY715 ) )
| ~ ! [SY716: $i,SY717: $i] :
( ~ ( subset @ ( unordered_pair @ SV128 @ SY716 ) @ SY717 )
| ( in @ SY716 @ SY717 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1628]) ).
thf(1802,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1629]) ).
thf(1803,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1629]) ).
thf(1804,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1630]) ).
thf(1805,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1630]) ).
thf(1806,plain,
! [SV129: $i] :
( ( ( ~ ! [SY718: $i] :
( ~ ( ~ ( ! [SY719: $i] :
~ ( in @ ( ordered_pair @ SY719 @ ( sK19_C @ SY718 @ SV129 ) ) @ SV129 )
| ~ ( in @ ( sK19_C @ SY718 @ SV129 ) @ SY718 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_SY464 @ SY718 @ SV129 ) @ ( sK19_C @ SY718 @ SV129 ) ) @ SV129 )
| ( in @ ( sK19_C @ SY718 @ SV129 ) @ SY718 ) ) )
| ( SY718
= ( relation_rng @ SV129 ) ) ) )
= $false )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1631]) ).
thf(1807,plain,
! [SV129: $i] :
( ( ( ~ ! [SY720: $i] :
( ( SY720
!= ( relation_rng @ SV129 ) )
| ~ ( ~ ! [SY721: $i] :
( ! [SY722: $i] :
~ ( in @ ( ordered_pair @ SY722 @ SY721 ) @ SV129 )
| ( in @ SY721 @ SY720 ) )
| ~ ! [SY723: $i] :
( ~ ( in @ SY723 @ SY720 )
| ( in @ ( ordered_pair @ ( sK18_D @ SY723 @ SY720 @ SV129 ) @ SY723 ) @ SV129 ) ) ) ) )
= $false )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1631]) ).
thf(1808,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1632]) ).
thf(1809,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1632]) ).
thf(1810,plain,
! [SV357: $i,SV288: $i] :
( ( ( ( set_difference @ SV288 @ ( singleton @ SV357 ) )
!= SV288 )
| ~ ( in @ SV357 @ SV288 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1633]) ).
thf(1811,plain,
! [SV289: $i,SV358: $i] :
( ( ( in @ SV358 @ SV289 )
| ( ( set_difference @ SV289 @ ( singleton @ SV358 ) )
= SV289 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(1812,plain,
! [SV359: $i,SV292: $i] :
( ( ( disjoint @ SV292 @ SV359 )
| ( in @ ( sK71_C @ SV359 @ SV292 ) @ ( set_intersection2 @ SV292 @ SV359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(1813,plain,
! [SV360: $i,SV293: $i] :
( ( ! [SY978: $i] :
~ ( in @ SY978 @ ( set_intersection2 @ SV293 @ SV360 ) )
| ~ ( disjoint @ SV293 @ SV360 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(1814,plain,
! [SV130: $i,SV229: $i] :
( ( ( ~ ( in @ ( sK73_C @ SV229 @ SV130 ) @ SV130 ) )
= $false )
| ( ( element @ SV130 @ ( powerset @ SV229 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1639]) ).
thf(1815,plain,
! [SV130: $i,SV229: $i] :
( ( ( ~ ~ ( in @ ( sK73_C @ SV229 @ SV130 ) @ SV229 ) )
= $false )
| ( ( element @ SV130 @ ( powerset @ SV229 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1639]) ).
thf(1816,plain,
! [SV131: $i] :
( ( ( ~ ! [SY725: $i,SY726: $i] :
( ~ ( ~ ( ! [SY727: $i] :
( ~ ( in @ ( ordered_pair @ ( sK27_D @ SY726 @ SY725 @ SV131 ) @ SY727 ) @ SV131 )
| ~ ( in @ SY727 @ SY725 ) )
| ~ ( in @ ( sK27_D @ SY726 @ SY725 @ SV131 ) @ SY726 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK27_D @ SY726 @ SY725 @ SV131 ) @ ( sK28_SY469 @ SY726 @ SY725 @ SV131 ) ) @ SV131 )
| ~ ( in @ ( sK28_SY469 @ SY726 @ SY725 @ SV131 ) @ SY725 ) )
| ( in @ ( sK27_D @ SY726 @ SY725 @ SV131 ) @ SY726 ) ) )
| ( SY726
= ( relation_inverse_image @ SV131 @ SY725 ) ) ) )
= $false )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1640]) ).
thf(1817,plain,
! [SV131: $i] :
( ( ( ~ ! [SY728: $i,SY729: $i] :
( ( SY729
!= ( relation_inverse_image @ SV131 @ SY728 ) )
| ~ ( ~ ! [SY730: $i] :
( ! [SY731: $i] :
( ~ ( in @ ( ordered_pair @ SY730 @ SY731 ) @ SV131 )
| ~ ( in @ SY731 @ SY728 ) )
| ( in @ SY730 @ SY729 ) )
| ~ ! [SY732: $i] :
( ~ ( in @ SY732 @ SY729 )
| ~ ( ~ ( in @ ( ordered_pair @ SY732 @ ( sK26_E @ SY732 @ SY729 @ SY728 @ SV131 ) ) @ SV131 )
| ~ ( in @ ( sK26_E @ SY732 @ SY729 @ SY728 @ SV131 ) @ SY728 ) ) ) ) ) )
= $false )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1640]) ).
thf(1818,plain,
! [SV361: $i,SV294: $i] :
( ( ( ( set_difference @ SV294 @ SV361 )
!= SV294 )
| ( disjoint @ SV294 @ SV361 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1641]) ).
thf(1819,plain,
! [SV362: $i,SV295: $i] :
( ( ~ ( disjoint @ SV295 @ SV362 )
| ( ( set_difference @ SV295 @ SV362 )
= SV295 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1642]) ).
thf(1820,plain,
! [SV296: $i] :
( ( ( ~ ( ~ ! [SY931: $i,SY932: $i] :
( ( sK68_B @ SV296 )
!= ( ordered_pair @ SY931 @ SY932 ) )
| ~ ( in @ ( sK68_B @ SV296 ) @ SV296 ) ) )
= $true )
| ( ( relation @ SV296 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1643]) ).
thf(1821,plain,
! [SV297: $i] :
( ( ( ~ ( relation @ SV297 ) )
= $true )
| ( ( ! [SY933: $i] :
( ( SY933
= ( ordered_pair @ ( sK66_C @ SY933 @ SV297 ) @ ( sK67_SY497 @ SY933 @ SV297 ) ) )
| ~ ( in @ SY933 @ SV297 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1644]) ).
thf(1822,plain,
! [SV363: $i,SV132: $i] :
( ( ! [SY979: $i] :
( ~ ( relation @ SY979 )
| ~ ( in @ SV132 @ SV363 )
| ~ ( in @ SV132 @ ( relation_dom @ SY979 ) )
| ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SY979 @ SV363 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1645]) ).
thf(1823,plain,
! [SV132: $i] :
( ( ~ ! [SY735: $i,SY736: $i] :
( ~ ( relation @ SY736 )
| ~ ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SY736 @ SY735 ) ) )
| ( in @ SV132 @ SY735 ) )
| ~ ! [SY737: $i,SY738: $i] :
( ~ ( relation @ SY738 )
| ~ ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SY738 @ SY737 ) ) )
| ( in @ SV132 @ ( relation_dom @ SY738 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1646]) ).
thf(1824,plain,
! [SV364: $i,SV133: $i] :
( ( ! [SY980: $i] :
( ~ ( relation @ SY980 )
| ~ ( in @ ( ordered_pair @ SV133 @ SV364 ) @ SY980 )
| ( in @ SV133 @ ( relation_dom @ SY980 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1647]) ).
thf(1825,plain,
! [SV365: $i,SV133: $i] :
( ( ! [SY981: $i] :
( ~ ( relation @ SY981 )
| ~ ( in @ ( ordered_pair @ SV133 @ SV365 ) @ SY981 )
| ( in @ SV365 @ ( relation_rng @ SY981 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1648]) ).
thf(1826,plain,
! [SV134: $i] :
( ( ( ~ ! [SY743: $i] :
( ~ ( ~ ( ! [SY744: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SY743 @ SV134 ) @ SY744 ) @ SV134 )
| ~ ( in @ ( sK22_C @ SY743 @ SV134 ) @ SY743 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SY743 @ SV134 ) @ ( sK23_SY466 @ SY743 @ SV134 ) ) @ SV134 )
| ( in @ ( sK22_C @ SY743 @ SV134 ) @ SY743 ) ) )
| ( SY743
= ( relation_dom @ SV134 ) ) ) )
= $false )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1649]) ).
thf(1827,plain,
! [SV134: $i] :
( ( ( ~ ! [SY745: $i] :
( ( SY745
!= ( relation_dom @ SV134 ) )
| ~ ( ~ ! [SY746: $i] :
( ! [SY747: $i] :
~ ( in @ ( ordered_pair @ SY746 @ SY747 ) @ SV134 )
| ( in @ SY746 @ SY745 ) )
| ~ ! [SY748: $i] :
( ~ ( in @ SY748 @ SY745 )
| ( in @ ( ordered_pair @ SY748 @ ( sK21_D @ SY748 @ SY745 @ SV134 ) ) @ SV134 ) ) ) ) )
= $false )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1649]) ).
thf(1828,plain,
! [SV135: $i,SV366: $i] :
( ( ! [SY982: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK57_D @ SY982 @ SV366 @ SV135 ) @ SY982 )
| ( ( sK57_D @ SY982 @ SV366 @ SV135 )
!= SV135 ) )
| ~ ( ~ ( in @ ( sK57_D @ SY982 @ SV366 @ SV135 ) @ SY982 )
| ( ( sK57_D @ SY982 @ SV366 @ SV135 )
!= SV366 ) ) )
| ~ ( ( in @ ( sK57_D @ SY982 @ SV366 @ SV135 ) @ SY982 )
| ( ( sK57_D @ SY982 @ SV366 @ SV135 )
= SV135 )
| ( ( sK57_D @ SY982 @ SV366 @ SV135 )
= SV366 ) ) )
| ( SY982
= ( unordered_pair @ SV135 @ SV366 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(1829,plain,
! [SV367: $i,SV135: $i] :
( ( ! [SY983: $i] :
( ( SY983
!= ( unordered_pair @ SV135 @ SV367 ) )
| ~ ( ~ ! [SY984: $i] :
( ~ ( in @ SY984 @ SY983 )
| ( SY984 = SV135 )
| ( SY984 = SV367 ) )
| ~ ~ ( ~ ! [SY754: $i] :
( ( SY754 != SV135 )
| ( in @ SY754 @ SY983 ) )
| ~ ! [SY986: $i] :
( ( SY986 != SV367 )
| ( in @ SY986 @ SY983 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(1830,plain,
! [SV136: $i] :
( ( ( ~ ! [SY756: $i] :
( ~ ( relation @ SY756 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK58_C @ SY756 @ SV136 ) @ ( sK59_SY494 @ SY756 @ SV136 ) ) @ SV136 )
| ~ ( in @ ( ordered_pair @ ( sK58_C @ SY756 @ SV136 ) @ ( sK59_SY494 @ SY756 @ SV136 ) ) @ SY756 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_C @ SY756 @ SV136 ) @ ( sK59_SY494 @ SY756 @ SV136 ) ) @ SV136 )
| ( in @ ( ordered_pair @ ( sK58_C @ SY756 @ SV136 ) @ ( sK59_SY494 @ SY756 @ SV136 ) ) @ SY756 ) ) )
| ( SV136 = SY756 ) ) )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1652]) ).
thf(1831,plain,
! [SV136: $i] :
( ( ( ~ ! [SY757: $i] :
( ~ ( relation @ SY757 )
| ( SV136 != SY757 )
| ~ ( ~ ! [SY758: $i,SY759: $i] :
( ~ ( in @ ( ordered_pair @ SY758 @ SY759 ) @ SV136 )
| ( in @ ( ordered_pair @ SY758 @ SY759 ) @ SY757 ) )
| ~ ! [SY760: $i,SY761: $i] :
( ~ ( in @ ( ordered_pair @ SY760 @ SY761 ) @ SY757 )
| ( in @ ( ordered_pair @ SY760 @ SY761 ) @ SV136 ) ) ) ) )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1652]) ).
thf(1832,plain,
! [SV368: $i,SV298: $i] :
( ( ~ ( function @ SV298 )
| ~ ( relation @ SV298 )
| ~ ( relation @ SV368 )
| ~ ( function @ SV368 )
| ( function @ ( relation_composition @ SV298 @ SV368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1653]) ).
thf(1833,plain,
! [SV369: $i,SV299: $i] :
( ( ~ ( function @ SV299 )
| ~ ( relation @ SV299 )
| ~ ( relation @ SV369 )
| ~ ( function @ SV369 )
| ( relation @ ( relation_composition @ SV299 @ SV369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(1834,plain,
! [SV137: $i,SV230: $i] :
( ( ( function @ SV230 )
= $false )
| ( ( ~ ( relation @ SV230 ) )
= $true )
| ( ( ~ ( ~ ! [SY861: $i] :
( ~ ( function @ SY861 )
| ~ ( relation @ SY861 )
| ~ ( in @ SV137 @ ( relation_dom @ SY861 ) )
| ~ ( in @ ( apply @ SY861 @ SV137 ) @ ( relation_dom @ SV230 ) )
| ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY861 @ SV230 ) ) ) )
| ~ ~ ( ~ ! [SY862: $i] :
( ~ ( function @ SY862 )
| ~ ( relation @ SY862 )
| ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY862 @ SV230 ) ) )
| ( in @ SV137 @ ( relation_dom @ SY862 ) ) )
| ~ ! [SY863: $i] :
( ~ ( function @ SY863 )
| ~ ( relation @ SY863 )
| ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY863 @ SV230 ) ) )
| ( in @ ( apply @ SY863 @ SV137 ) @ ( relation_dom @ SV230 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1655]) ).
thf(1835,plain,
! [SV138: $i,SV370: $i] :
( ( ~ ( subset @ SV370 @ ( sK41_B @ SV138 ) )
| ( are_equipotent @ SV370 @ ( sK41_B @ SV138 ) )
| ( in @ SV370 @ ( sK41_B @ SV138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1656]) ).
thf(1836,plain,
! [SV138: $i] :
( ( ~ ! [SY767: $i] :
( ~ ( in @ SY767 @ ( sK41_B @ SV138 ) )
| ( in @ ( powerset @ SY767 ) @ ( sK41_B @ SV138 ) ) )
| ~ ~ ( ~ ! [SY768: $i,SY769: $i] :
( ~ ( in @ SY768 @ ( sK41_B @ SV138 ) )
| ~ ( subset @ SY769 @ SY768 )
| ( in @ SY769 @ ( sK41_B @ SV138 ) ) )
| ~ ( in @ SV138 @ ( sK41_B @ SV138 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1657]) ).
thf(1837,plain,
! [SV139: $i] :
( ( ( ~ ! [SY770: $i] :
( ~ ( relation @ SY770 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SY770 @ SV139 ) @ ( sK25_SY467 @ SY770 @ SV139 ) ) @ SV139 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SY770 @ SV139 ) @ ( sK25_SY467 @ SY770 @ SV139 ) ) @ SY770 ) )
| ( subset @ SV139 @ SY770 ) ) )
= $false )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1658]) ).
thf(1838,plain,
! [SV139: $i] :
( ( ( ~ ! [SY771: $i] :
( ~ ( relation @ SY771 )
| ~ ( subset @ SV139 @ SY771 )
| ! [SY772: $i,SY773: $i] :
( ~ ( in @ ( ordered_pair @ SY772 @ SY773 ) @ SV139 )
| ( in @ ( ordered_pair @ SY772 @ SY773 ) @ SY771 ) ) ) )
= $false )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1658]) ).
thf(1839,plain,
! [SV300: $i,SV371: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK60_C @ SV371 @ SV300 ) @ SV371 )
| ~ ( subset @ ( sK60_C @ SV371 @ SV300 ) @ SV300 ) )
| ~ ( ( in @ ( sK60_C @ SV371 @ SV300 ) @ SV371 )
| ( subset @ ( sK60_C @ SV371 @ SV300 ) @ SV300 ) ) )
| ( SV371
= ( powerset @ SV300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1659]) ).
thf(1840,plain,
! [SV301: $i,SV372: $i] :
( ( ( SV372
!= ( powerset @ SV301 ) )
| ~ ( ~ ! [SY987: $i] :
( ~ ( in @ SY987 @ SV372 )
| ( subset @ SY987 @ SV301 ) )
| ~ ! [SY988: $i] :
( ~ ( subset @ SY988 @ SV301 )
| ( in @ SY988 @ SV372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1660]) ).
thf(1841,plain,
! [SV373: $i,SV302: $i] :
( ( ~ ( empty @ SV302 )
| ~ ( relation @ SV373 )
| ( empty @ ( relation_composition @ SV302 @ SV373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1661]) ).
thf(1842,plain,
! [SV374: $i,SV303: $i] :
( ( ~ ( empty @ SV303 )
| ~ ( relation @ SV374 )
| ( relation @ ( relation_composition @ SV303 @ SV374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1662]) ).
thf(1843,plain,
! [SV140: $i] :
( ( ( ~ ! [SY774: $i] :
( ~ ( relation @ SY774 )
| ~ ( subset @ SV140 @ SY774 )
| ( subset @ ( relation_dom @ SV140 ) @ ( relation_dom @ SY774 ) ) ) )
= $false )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1663]) ).
thf(1844,plain,
! [SV140: $i] :
( ( ( ~ ! [SY775: $i] :
( ~ ( relation @ SY775 )
| ~ ( subset @ SV140 @ SY775 )
| ( subset @ ( relation_rng @ SV140 ) @ ( relation_rng @ SY775 ) ) ) )
= $false )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1663]) ).
thf(1845,plain,
! [SV141: $i] :
( ( ( element @ ( sK8_B @ SV141 ) @ ( powerset @ SV141 ) )
= $true )
| ( ( empty @ SV141 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1664]) ).
thf(1846,plain,
! [SV141: $i] :
( ( ( ~ ( empty @ ( sK8_B @ SV141 ) ) )
= $true )
| ( ( empty @ SV141 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1665]) ).
thf(1847,plain,
! [SV375: $i,SV142: $i] :
( ( ! [SY989: $i] :
( ~ ( relation @ SY989 )
| ! [SY990: $i] :
( ~ ( in @ SY990 @ ( relation_rng @ SY989 ) )
| ~ ( in @ ( ordered_pair @ SV142 @ SY990 ) @ SY989 )
| ~ ( in @ SY990 @ SV375 ) )
| ( in @ SV142 @ ( relation_inverse_image @ SY989 @ SV375 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1666]) ).
thf(1848,plain,
! [SV376: $i,SV142: $i] :
( ( ! [SY991: $i] :
( ~ ( relation @ SY991 )
| ~ ( in @ SV142 @ ( relation_inverse_image @ SY991 @ SV376 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK39_D @ SY991 @ SV376 @ SV142 ) @ ( relation_rng @ SY991 ) )
| ~ ( in @ ( ordered_pair @ SV142 @ ( sK39_D @ SY991 @ SV376 @ SV142 ) ) @ SY991 ) )
| ~ ( in @ ( sK39_D @ SY991 @ SV376 @ SV142 ) @ SV376 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1667]) ).
thf(1849,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK65_SY495 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK64_C @ SX1 @ SX0 ) @ ( sK65_SY495 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK64_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK64_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK64_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1668]) ).
thf(1850,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK63_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK63_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1668]) ).
thf(1851,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1669]) ).
thf(1852,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1669]) ).
thf(1853,plain,
! [SV304: $i] :
( ( ( ~ ( relation @ SV304 ) )
= $true )
| ( ( ( relation_rng @ SV304 )
= ( relation_dom @ ( relation_inverse @ SV304 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1670]) ).
thf(1854,plain,
! [SV305: $i] :
( ( ( ~ ( relation @ SV305 ) )
= $true )
| ( ( ( relation_dom @ SV305 )
= ( relation_rng @ ( relation_inverse @ SV305 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1671]) ).
thf(1855,plain,
! [SV377: $i,SV308: $i] :
( ( ( SV308 = SV377 )
| ~ ( subset @ SV308 @ SV377 )
| ( proper_subset @ SV308 @ SV377 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1674]) ).
thf(1856,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1675]) ).
thf(1857,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1675]) ).
thf(1858,plain,
! [SV231: $i,SV143: $i] :
( ( ! [SY864: $i,SY865: $i] :
( ~ ( in @ SV143 @ SY864 )
| ~ ( in @ SV231 @ SY865 )
| ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SY864 @ SY865 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1676]) ).
thf(1859,plain,
! [SV231: $i,SV143: $i] :
( ( ~ ( ~ ! [SY866: $i] :
( ! [SY867: $i] :
~ ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SY866 @ SY867 ) )
| ( in @ SV143 @ SY866 ) )
| ~ ! [SY868: $i,SY869: $i] :
( ~ ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SY868 @ SY869 ) )
| ( in @ SV231 @ SY869 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1677]) ).
thf(1860,plain,
! [SV144: $i,SV378: $i] :
( ( ! [SY992: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK56_D @ SY992 @ SV378 @ SV144 ) @ SY992 )
| ~ ( in @ ( sK56_D @ SY992 @ SV378 @ SV144 ) @ SV144 ) )
| ~ ( ~ ( in @ ( sK56_D @ SY992 @ SV378 @ SV144 ) @ SY992 )
| ~ ( in @ ( sK56_D @ SY992 @ SV378 @ SV144 ) @ SV378 ) ) )
| ~ ( ( in @ ( sK56_D @ SY992 @ SV378 @ SV144 ) @ SY992 )
| ( in @ ( sK56_D @ SY992 @ SV378 @ SV144 ) @ SV144 )
| ( in @ ( sK56_D @ SY992 @ SV378 @ SV144 ) @ SV378 ) ) )
| ( SY992
= ( set_union2 @ SV144 @ SV378 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1678]) ).
thf(1861,plain,
! [SV379: $i,SV144: $i] :
( ( ! [SY993: $i] :
( ( SY993
!= ( set_union2 @ SV144 @ SV379 ) )
| ~ ( ~ ! [SY994: $i] :
( ~ ( in @ SY994 @ SY993 )
| ( in @ SY994 @ SV144 )
| ( in @ SY994 @ SV379 ) )
| ~ ~ ( ~ ! [SY793: $i] :
( ~ ( in @ SY793 @ SV144 )
| ( in @ SY793 @ SY993 ) )
| ~ ! [SY996: $i] :
( ~ ( in @ SY996 @ SV379 )
| ( in @ SY996 @ SY993 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1679]) ).
thf(1862,plain,
! [SV309: $i] :
( ( ( ~ ( empty @ SV309 ) )
= $true )
| ( ( empty @ ( relation_dom @ SV309 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1680]) ).
thf(1863,plain,
! [SV310: $i] :
( ( ( ~ ( empty @ SV310 ) )
= $true )
| ( ( relation @ ( relation_dom @ SV310 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1681]) ).
thf(1864,plain,
! [SV380: $i,SV145: $i] :
( ( ! [SY997: $i] :
( ~ ( relation @ SY997 )
| ! [SY998: $i] :
( ~ ( in @ SY998 @ ( relation_dom @ SY997 ) )
| ~ ( in @ ( ordered_pair @ SY998 @ SV145 ) @ SY997 )
| ~ ( in @ SY998 @ SV380 ) )
| ( in @ SV145 @ ( relation_image @ SY997 @ SV380 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1682]) ).
thf(1865,plain,
! [SV381: $i,SV145: $i] :
( ( ! [SY999: $i] :
( ~ ( relation @ SY999 )
| ~ ( in @ SV145 @ ( relation_image @ SY999 @ SV381 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK40_D @ SY999 @ SV381 @ SV145 ) @ ( relation_dom @ SY999 ) )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SY999 @ SV381 @ SV145 ) @ SV145 ) @ SY999 ) )
| ~ ( in @ ( sK40_D @ SY999 @ SV381 @ SV145 ) @ SV381 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1683]) ).
thf(1866,plain,
! [SV382: $i,SV146: $i] :
( ( ~ ( subset @ SV146 @ SV382 )
| ! [SY1000: $i] : ( subset @ ( cartesian_product2 @ SV146 @ SY1000 ) @ ( cartesian_product2 @ SV382 @ SY1000 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1684]) ).
thf(1867,plain,
! [SV383: $i,SV146: $i] :
( ( ~ ( subset @ SV146 @ SV383 )
| ! [SY1001: $i] : ( subset @ ( cartesian_product2 @ SY1001 @ SV146 ) @ ( cartesian_product2 @ SY1001 @ SV383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1685]) ).
thf(1868,plain,
! [SV147: $i,SV232: $i] :
( ( ( ~ ( ~ ( in @ ( sK44_C @ SV232 @ SV147 ) @ SV147 )
| ~ ( in @ ( sK44_C @ SV232 @ SV147 ) @ SV232 ) ) )
= $false )
| ( ( SV147 = SV232 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1686]) ).
thf(1869,plain,
! [SV147: $i,SV232: $i] :
( ( ( ~ ( ( in @ ( sK44_C @ SV232 @ SV147 ) @ SV147 )
| ( in @ ( sK44_C @ SV232 @ SV147 ) @ SV232 ) ) )
= $false )
| ( ( SV147 = SV232 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1686]) ).
thf(1870,plain,
! [SV384: $i,SV311: $i] :
( ( ~ ( subset @ SV311 @ ( singleton @ SV384 ) )
| ( SV311 = empty_set )
| ( SV311
= ( singleton @ SV384 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1687]) ).
thf(1871,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1688]) ).
thf(1872,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1688]) ).
thf(1873,plain,
! [SV233: $i,SV148: $i] :
( ( ! [SY870: $i] :
( ! [SY871: $i] :
( ( ordered_pair @ SV148 @ SV233 )
!= ( ordered_pair @ SY870 @ SY871 ) )
| ( SV148 = SY870 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1689]) ).
thf(1874,plain,
! [SV233: $i,SV148: $i] :
( ( ! [SY872: $i,SY873: $i] :
( ( ( ordered_pair @ SV148 @ SV233 )
!= ( ordered_pair @ SY872 @ SY873 ) )
| ( SV233 = SY873 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1690]) ).
thf(1875,plain,
! [SV312: $i,SV385: $i] :
( ( ~ ( ~ ( in @ ( sK50_C @ SV385 @ SV312 ) @ SV312 )
| ~ ~ ( in @ ( sK50_C @ SV385 @ SV312 ) @ SV385 ) )
| ( subset @ SV312 @ SV385 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1691]) ).
thf(1876,plain,
! [SV386: $i,SV313: $i] :
( ( ~ ( subset @ SV313 @ SV386 )
| ! [SY1002: $i] :
( ~ ( in @ SY1002 @ SV313 )
| ( in @ SY1002 @ SV386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1692]) ).
thf(1877,plain,
! [SV314: $i] :
( ( ( ~ ( relation @ SV314 ) )
= $true )
| ( ( ( ( relation_dom @ SV314 )
!= empty_set )
| ( SV314 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1694]) ).
thf(1878,plain,
! [SV315: $i] :
( ( ( ~ ( relation @ SV315 ) )
= $true )
| ( ( ( ( relation_rng @ SV315 )
!= empty_set )
| ( SV315 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1695]) ).
thf(1879,plain,
! [SV316: $i] :
( ( ( ~ ( empty @ SV316 ) )
= $true )
| ( ( empty @ ( relation_rng @ SV316 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1696]) ).
thf(1880,plain,
! [SV317: $i] :
( ( ( ~ ( empty @ SV317 ) )
= $true )
| ( ( relation @ ( relation_rng @ SV317 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1697]) ).
thf(1881,plain,
! [SV149: $i,SV387: $i] :
( ( ! [SY1003: $i] :
( ~ ( ~ ( ~ ( in @ ( sK45_D @ SY1003 @ SV387 @ SV149 ) @ SV149 )
| ( in @ ( sK45_D @ SY1003 @ SV387 @ SV149 ) @ SV387 )
| ~ ( in @ ( sK45_D @ SY1003 @ SV387 @ SV149 ) @ SY1003 ) )
| ~ ~ ( ~ ( ( in @ ( sK45_D @ SY1003 @ SV387 @ SV149 ) @ SV149 )
| ( in @ ( sK45_D @ SY1003 @ SV387 @ SV149 ) @ SY1003 ) )
| ~ ( ~ ( in @ ( sK45_D @ SY1003 @ SV387 @ SV149 ) @ SV387 )
| ( in @ ( sK45_D @ SY1003 @ SV387 @ SV149 ) @ SY1003 ) ) ) )
| ( SY1003
= ( set_difference @ SV149 @ SV387 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1698]) ).
thf(1882,plain,
! [SV388: $i,SV149: $i] :
( ( ! [SY1004: $i] :
( ( SY1004
!= ( set_difference @ SV149 @ SV388 ) )
| ~ ( ~ ! [SY1005: $i] :
( ~ ( in @ SY1005 @ SV149 )
| ( in @ SY1005 @ SV388 )
| ( in @ SY1005 @ SY1004 ) )
| ~ ~ ( ~ ! [SY815: $i] :
( ~ ( in @ SY815 @ SY1004 )
| ( in @ SY815 @ SV149 ) )
| ~ ! [SY1007: $i] :
( ~ ( in @ SY1007 @ SY1004 )
| ~ ( in @ SY1007 @ SV388 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1699]) ).
thf(1883,plain,
! [SV4: $i,SV153: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV153 ) )
= $true )
| ( ( in @ SV318 @ SV4 )
= $true )
| ( ( element @ SV153 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1701]) ).
thf(1884,plain,
! [SV12: $i,SV234: $i,SV160: $i] :
( ( ( element @ SV160 @ ( powerset @ SV234 ) )
= $false )
| ( ( ~ ( in @ SV12 @ SV160 ) )
= $true )
| ( ( element @ SV12 @ SV234 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1704]) ).
thf(1885,plain,
! [SV162: $i,SV15: $i,SV319: $i] :
( ( ( in @ SV319 @ SV15 )
= $true )
| ( ( subset @ SV15 @ ( set_difference @ SV162 @ ( singleton @ SV319 ) ) )
= $true )
| ( ( subset @ SV15 @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1706]) ).
thf(1886,plain,
! [SV250: $i,SV163: $i,SV235: $i,SV16: $i] :
( ( ( SV16 = SV235 )
= $true )
| ( ( ( ( unordered_pair @ SV16 @ SV163 )
!= ( unordered_pair @ SV235 @ SV250 ) ) )
= $true )
| ( ( SV16 = SV250 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1707]) ).
thf(1887,plain,
! [SV251: $i,SV236: $i,SV168: $i,SV21: $i] :
( ( ( ~ ( subset @ SV21 @ SV168 ) )
= $true )
| ( ( ~ ( subset @ SV236 @ SV251 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV21 @ SV236 ) @ ( cartesian_product2 @ SV168 @ SV251 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1708]) ).
thf(1888,plain,
! [SV173: $i,SV27: $i] :
( ( ( SV27 = empty_set )
= $true )
| ( ( ~ ( subset @ SV27 @ ( relation_rng @ SV173 ) ) )
= $true )
| ( ( ( ( relation_inverse_image @ SV173 @ SV27 )
!= empty_set ) )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1709]) ).
thf(1889,plain,
! [SV237: $i,SV174: $i,SV28: $i] :
( ( ( ~ ( subset @ SV28 @ SV174 ) )
= $true )
| ( ( subset @ ( relation_inverse_image @ SV237 @ SV28 ) @ ( relation_inverse_image @ SV237 @ SV174 ) )
= $true )
| ( ( relation @ SV237 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1710]) ).
thf(1890,plain,
! [SV238: $i,SV176: $i,SV30: $i] :
( ( ( subset @ SV30 @ SV176 )
= $false )
| ( ( ~ ( subset @ SV30 @ SV238 ) )
= $true )
| ( ( subset @ SV30 @ ( set_intersection2 @ SV176 @ SV238 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1711]) ).
thf(1891,plain,
! [SV239: $i,SV177: $i,SV31: $i] :
( ( ( subset @ SV31 @ SV177 )
= $false )
| ( ( ~ ( subset @ SV177 @ SV239 ) )
= $true )
| ( ( subset @ SV31 @ SV239 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1712]) ).
thf(1892,plain,
! [SV33: $i,SV178: $i] :
( ( ( relation @ SV178 )
= $false )
| ( ( function @ SV178 )
= $false )
| ( ( ! [SY827: $i] :
( ~ ( function @ SY827 )
| ~ ( relation @ SY827 )
| ~ ( in @ SV33 @ ( relation_dom @ ( relation_composition @ SY827 @ SV178 ) ) )
| ( ( apply @ ( relation_composition @ SY827 @ SV178 ) @ SV33 )
= ( apply @ SV178 @ ( apply @ SY827 @ SV33 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1713]) ).
thf(1893,plain,
! [SV34: $i,SV179: $i] :
( ( ( relation @ SV179 )
= $false )
| ( ( function @ SV179 )
= $false )
| ( ( ! [SY828: $i] :
( ~ ( function @ SY828 )
| ~ ( relation @ SY828 )
| ~ ( in @ SV34 @ ( relation_dom @ SV179 ) )
| ( ( apply @ ( relation_composition @ SV179 @ SY828 ) @ SV34 )
= ( apply @ SY828 @ ( apply @ SV179 @ SV34 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1714]) ).
thf(1894,plain,
! [SV43: $i,SV252: $i] :
( ( ( relation @ SV252 )
= $false )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV43 @ SV252 ) ) @ ( relation_dom @ SV43 ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1717]) ).
thf(1895,plain,
! [SV44: $i,SV253: $i] :
( ( ( relation @ SV253 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV44 @ SV253 ) ) @ ( relation_rng @ SV253 ) )
= $true )
| ( ( relation @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1718]) ).
thf(1896,plain,
! [SV46: $i,SV254: $i] :
( ( ( relation @ SV254 )
= $false )
| ( ( ~ ( subset @ ( relation_rng @ SV46 ) @ ( relation_dom @ SV254 ) )
| ( ( relation_dom @ ( relation_composition @ SV46 @ SV254 ) )
= ( relation_dom @ SV46 ) ) )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1719]) ).
thf(1897,plain,
! [SV187: $i,SV47: $i] :
( ( ( ( complements_of_subsets @ SV47 @ SV187 )
= empty_set )
= $false )
| ( ( SV187 = empty_set )
= $true )
| ( ( element @ SV187 @ ( powerset @ ( powerset @ SV47 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1720]) ).
thf(1898,plain,
! [SV48: $i,SV255: $i] :
( ( ( relation @ SV255 )
= $false )
| ( ( ~ ( subset @ ( relation_dom @ SV48 ) @ ( relation_rng @ SV255 ) )
| ( ( relation_rng @ ( relation_composition @ SV255 @ SV48 ) )
= ( relation_rng @ SV48 ) ) )
= $true )
| ( ( relation @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1721]) ).
thf(1899,plain,
! [SV240: $i,SV50: $i,SV389: $i] :
( ( ( ~ ( element @ SV389 @ SV50 )
| ( in @ SV389 @ SV240 )
| ( in @ SV389 @ ( subset_complement @ SV50 @ SV240 ) ) )
= $true )
| ( ( element @ SV240 @ ( powerset @ SV50 ) )
= $false )
| ( ( SV50 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1722]) ).
thf(1900,plain,
! [SV241: $i,SV51: $i,SV189: $i] :
( ( ( ~ ( in @ SV189 @ ( subset_complement @ SV51 @ SV241 ) ) )
= $true )
| ( ( ~ ( in @ SV189 @ SV241 ) )
= $true )
| ( ( element @ SV241 @ ( powerset @ SV51 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1723]) ).
thf(1901,plain,
! [SV54: $i,SV242: $i,SV191: $i] :
( ( ( disjoint @ SV191 @ SV242 )
= $false )
| ( ( ~ ( subset @ SV54 @ SV191 ) )
= $true )
| ( ( disjoint @ SV54 @ SV242 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1725]) ).
thf(1902,plain,
! [SV243: $i,SV195: $i,SV59: $i] :
( ( ( subset @ SV59 @ SV195 )
= $false )
| ( ( ~ ( subset @ SV243 @ SV195 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV59 @ SV243 ) @ SV195 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1726]) ).
thf(1903,plain,
! [SV76: $i,SV206: $i] :
( ( ( relation @ SV206 )
= $false )
| ( ( relation @ SV76 )
= $false )
| ( ( relation @ ( relation_composition @ SV76 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1729]) ).
thf(1904,plain,
! [SV245: $i,SV79: $i,SV209: $i] :
( ( ( element @ SV209 @ ( powerset @ SV79 ) )
= $false )
| ( ( ~ ( element @ SV245 @ ( powerset @ SV79 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV79 @ SV209 @ SV245 ) @ ( powerset @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1730]) ).
thf(1905,plain,
! [SV84: $i,SV212: $i] :
( ( ( relation @ SV212 )
= $false )
| ( ( relation @ SV84 )
= $false )
| ( ( relation @ ( set_intersection2 @ SV84 @ SV212 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1731]) ).
thf(1906,plain,
! [SV87: $i,SV214: $i] :
( ( ( relation @ SV214 )
= $false )
| ( ( relation @ SV87 )
= $false )
| ( ( relation @ ( set_union2 @ SV87 @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1732]) ).
thf(1907,plain,
! [SV248: $i,SV102: $i,SV221: $i] :
( ( ( element @ SV221 @ ( powerset @ SV102 ) )
= $false )
| ( ( ~ ( element @ SV248 @ ( powerset @ SV102 ) ) )
= $true )
| ( ( ( subset_difference @ SV102 @ SV221 @ SV248 )
= ( set_difference @ SV221 @ SV248 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1736]) ).
thf(1908,plain,
! [SV109: $i,SV249: $i,SV223: $i] :
( ( ( element @ SV223 @ ( powerset @ SV249 ) )
= $false )
| ( ( ~ ( in @ SV109 @ SV223 ) )
= $true )
| ( ( ~ ( empty @ SV249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1737]) ).
thf(1909,plain,
! [SV111: $i,SV224: $i] :
( ( ( empty @ SV224 )
= $false )
| ( ( SV111 = SV224 )
= $true )
| ( ( empty @ SV111 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1738]) ).
thf(1910,plain,
! [SV112: $i,SV322: $i,SV390: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV112 )
| ~ ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV322 )
| ~ ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV390 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV112 )
| ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV390 ) )
| ~ ( ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV322 )
| ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV390 ) ) ) )
| ( SV390
= ( set_intersection2 @ SV112 @ SV322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1739]) ).
thf(1911,plain,
! [SV323: $i,SV112: $i,SV391: $i] :
( ( ( SV391
!= ( set_intersection2 @ SV112 @ SV323 ) )
| ~ ( ~ ! [SY1008: $i] :
( ~ ( in @ SY1008 @ SV112 )
| ~ ( in @ SY1008 @ SV323 )
| ( in @ SY1008 @ SV391 ) )
| ~ ~ ( ~ ! [SY1009: $i] :
( ~ ( in @ SY1009 @ SV391 )
| ( in @ SY1009 @ SV112 ) )
| ~ ! [SY1010: $i] :
( ~ ( in @ SY1010 @ SV391 )
| ( in @ SY1010 @ SV323 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1740]) ).
thf(1912,plain,
! [SV258: $i,SV324: $i] :
( ( ( ~ ( ~ ( ! [SY952: $i] :
( ~ ( in @ ( sK47_C @ SV324 @ SV258 ) @ SY952 )
| ~ ( in @ SY952 @ SV258 ) )
| ~ ( in @ ( sK47_C @ SV324 @ SV258 ) @ SV324 ) )
| ~ ( ~ ( ~ ( in @ ( sK47_C @ SV324 @ SV258 ) @ ( sK48_SY487 @ SV324 @ SV258 ) )
| ~ ( in @ ( sK48_SY487 @ SV324 @ SV258 ) @ SV258 ) )
| ( in @ ( sK47_C @ SV324 @ SV258 ) @ SV324 ) ) ) )
= $true )
| ( ( SV324
= ( union @ SV258 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1741]) ).
thf(1913,plain,
! [SV259: $i,SV325: $i] :
( ( ( ( SV325
!= ( union @ SV259 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY953: $i] :
( ! [SY881: $i] :
( ~ ( in @ SY953 @ SY881 )
| ~ ( in @ SY881 @ SV259 ) )
| ( in @ SY953 @ SV325 ) )
| ~ ! [SY955: $i] :
( ~ ( in @ SY955 @ SV325 )
| ~ ( ~ ( in @ SY955 @ ( sK46_D @ SY955 @ SV325 @ SV259 ) )
| ~ ( in @ ( sK46_D @ SY955 @ SV325 @ SV259 ) @ SV259 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1742]) ).
thf(1914,plain,
! [SV113: $i,SV225: $i] :
( ( ( ~ ! [SY839: $i] :
( ~ ( relation @ SY839 )
| ~ ( ~ ( ~ ( in @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) @ SV113 )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ SY839 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) ) @ SV225 )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ SY839 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) ) @ SY839 ) )
| ~ ~ ( ~ ( ( in @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) @ SV113 )
| ( in @ ( ordered_pair @ ( sK32_D @ SY839 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) ) @ SY839 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_D @ SY839 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) ) @ SV225 )
| ( in @ ( ordered_pair @ ( sK32_D @ SY839 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) ) @ SY839 ) ) ) )
| ( SY839
= ( relation_rng_restriction @ SV113 @ SV225 ) ) ) )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1743]) ).
thf(1915,plain,
! [SV225: $i,SV113: $i] :
( ( ( ~ ! [SY840: $i] :
( ~ ( relation @ SY840 )
| ( SY840
!= ( relation_rng_restriction @ SV113 @ SV225 ) )
| ~ ( ~ ! [SY841: $i,SY842: $i] :
( ~ ( in @ SY842 @ SV113 )
| ~ ( in @ ( ordered_pair @ SY841 @ SY842 ) @ SV225 )
| ( in @ ( ordered_pair @ SY841 @ SY842 ) @ SY840 ) )
| ~ ~ ( ~ ! [SY619: $i,SY620: $i] :
( ~ ( in @ ( ordered_pair @ SY619 @ SY620 ) @ SY840 )
| ( in @ SY620 @ SV113 ) )
| ~ ! [SY845: $i,SY846: $i] :
( ~ ( in @ ( ordered_pair @ SY845 @ SY846 ) @ SY840 )
| ( in @ ( ordered_pair @ SY845 @ SY846 ) @ SV225 ) ) ) ) ) )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1743]) ).
thf(1916,plain,
! [SV326: $i,SV260: $i] :
( ( ( ~ ( empty @ SV260 )
| ~ ( relation @ SV326 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV326 @ SV260 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1744]) ).
thf(1917,plain,
! [SV327: $i,SV261: $i] :
( ( ( ~ ( empty @ SV261 )
| ~ ( relation @ SV327 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV327 @ SV261 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1745]) ).
thf(1918,plain,
! [SV226: $i,SV392: $i,SV114: $i] :
( ( ! [SY1011: $i] :
( ~ ( in @ SV114 @ SV392 )
| ~ ( in @ SV226 @ SY1011 )
| ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SV392 @ SY1011 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1746]) ).
thf(1919,plain,
! [SV226: $i,SV114: $i] :
( ( ~ ! [SY849: $i] :
( ! [SY850: $i] :
~ ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SY849 @ SY850 ) )
| ( in @ SV114 @ SY849 ) )
| ~ ! [SY851: $i,SY852: $i] :
( ~ ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SY851 @ SY852 ) )
| ( in @ SV226 @ SY852 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1747]) ).
thf(1920,plain,
! [SV328: $i,SV262: $i] :
( ( ( disjoint @ SV262 @ SV328 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK72_C @ SV328 @ SV262 ) @ SV262 )
| ~ ( in @ ( sK72_C @ SV328 @ SV262 ) @ SV328 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1748]) ).
thf(1921,plain,
! [SV329: $i,SV263: $i] :
( ( ( ! [SY956: $i] :
( ~ ( in @ SY956 @ SV263 )
| ~ ( in @ SY956 @ SV329 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV263 @ SV329 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1749]) ).
thf(1922,plain,
! [SV264: $i,SV330: $i] :
( ( ( ~ ( ~ ( ( ( sK62_C @ SV330 @ SV264 )
!= SV264 )
| ~ ( in @ ( sK62_C @ SV330 @ SV264 ) @ SV330 ) )
| ~ ( ( ( sK62_C @ SV330 @ SV264 )
= SV264 )
| ( in @ ( sK62_C @ SV330 @ SV264 ) @ SV330 ) ) ) )
= $true )
| ( ( SV330
= ( singleton @ SV264 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1750]) ).
thf(1923,plain,
! [SV265: $i,SV331: $i] :
( ( ( ( SV331
!= ( singleton @ SV265 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY957: $i] :
( ( SY957 != SV265 )
| ( in @ SY957 @ SV331 ) )
| ~ ! [SY958: $i] :
( ~ ( in @ SY958 @ SV331 )
| ( SY958 = SV265 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1751]) ).
thf(1924,plain,
! [SV267: $i] :
( ( ( SV267 = empty_set )
= $false )
| ( ( ! [SY892: $i] :
~ ( in @ SY892 @ SV267 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1753]) ).
thf(1925,plain,
! [SV115: $i,SV332: $i] :
( ( ( ~ ( subset @ SV332 @ ( sK42_B @ SV115 ) )
| ( are_equipotent @ SV332 @ ( sK42_B @ SV115 ) ) )
= $true )
| ( ( in @ SV332 @ ( sK42_B @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1754]) ).
thf(1926,plain,
! [SV115: $i] :
( ( ~ ! [SY631: $i] :
( ~ ( ~ ! [SY632: $i] :
( ~ ( subset @ SY632 @ SY631 )
| ( in @ SY632 @ ( sK43_SY481 @ SY631 @ SV115 ) ) )
| ~ ( in @ ( sK43_SY481 @ SY631 @ SV115 ) @ ( sK42_B @ SV115 ) ) )
| ~ ( in @ SY631 @ ( sK42_B @ SV115 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1755]) ).
thf(1927,plain,
! [SV115: $i] :
( ( ~ ~ ( ~ ! [SY633: $i,SY634: $i] :
( ~ ( in @ SY633 @ ( sK42_B @ SV115 ) )
| ~ ( subset @ SY634 @ SY633 )
| ( in @ SY634 @ ( sK42_B @ SV115 ) ) )
| ~ ( in @ SV115 @ ( sK42_B @ SV115 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1755]) ).
thf(1928,plain,
! [SV333: $i,SV268: $i] :
( ( ( ~ ( subset @ SV268 @ ( singleton @ SV333 ) ) )
= $true )
| ( ( ( SV268 = empty_set )
| ( SV268
= ( singleton @ SV333 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1756]) ).
thf(1929,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1757]) ).
thf(1930,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1758]) ).
thf(1931,plain,
! [SV116: $i] :
( ( ( ~ ~ ( ~ ! [SY635: $i] :
( ~ ( in @ SY635 @ ( relation_dom @ SV116 ) )
| ! [SY636: $i] :
( ( SY636
!= ( apply @ SV116 @ SY635 ) )
| ( in @ ( ordered_pair @ SY635 @ SY636 ) @ SV116 ) ) )
| ~ ! [SY637: $i] :
( ~ ( in @ SY637 @ ( relation_dom @ SV116 ) )
| ! [SY638: $i] :
( ~ ( in @ ( ordered_pair @ SY637 @ SY638 ) @ SV116 )
| ( SY638
= ( apply @ SV116 @ SY637 ) ) ) ) )
| ~ ~ ( ~ ! [SY639: $i] :
( ( in @ SY639 @ ( relation_dom @ SV116 ) )
| ! [SY640: $i] :
( ( SY640
!= ( apply @ SV116 @ SY639 ) )
| ( SY640 = empty_set ) ) )
| ~ ! [SY641: $i] :
( ( in @ SY641 @ ( relation_dom @ SV116 ) )
| ! [SY642: $i] :
( ( SY642 != empty_set )
| ( SY642
= ( apply @ SV116 @ SY641 ) ) ) ) ) )
= $false )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1759]) ).
thf(1932,plain,
! [SV393: $i,SV334: $i,SV117: $i] :
( ( ~ ( ~ ( ! [SY1012: $i,SY1013: $i] :
( ~ ( in @ SY1012 @ SV117 )
| ~ ( in @ SY1013 @ SV334 )
| ( ( sK53_D @ SV393 @ SV334 @ SV117 )
!= ( ordered_pair @ SY1012 @ SY1013 ) ) )
| ~ ( in @ ( sK53_D @ SV393 @ SV334 @ SV117 ) @ SV393 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK54_SY491 @ SV393 @ SV334 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK55_SY493 @ SV393 @ SV334 @ SV117 ) @ SV334 ) )
| ( ( sK53_D @ SV393 @ SV334 @ SV117 )
!= ( ordered_pair @ ( sK54_SY491 @ SV393 @ SV334 @ SV117 ) @ ( sK55_SY493 @ SV393 @ SV334 @ SV117 ) ) ) )
| ( in @ ( sK53_D @ SV393 @ SV334 @ SV117 ) @ SV393 ) ) )
| ( SV393
= ( cartesian_product2 @ SV117 @ SV334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1760]) ).
thf(1933,plain,
! [SV335: $i,SV117: $i,SV394: $i] :
( ( ( SV394
!= ( cartesian_product2 @ SV117 @ SV335 ) )
| ~ ( ~ ! [SY1014: $i] :
( ! [SY964: $i,SY965: $i] :
( ~ ( in @ SY964 @ SV117 )
| ~ ( in @ SY965 @ SV335 )
| ( SY1014
!= ( ordered_pair @ SY964 @ SY965 ) ) )
| ( in @ SY1014 @ SV394 ) )
| ~ ! [SY1017: $i] :
( ~ ( in @ SY1017 @ SV394 )
| ~ ( ~ ~ ( ~ ( in @ ( sK51_E @ SY1017 @ SV394 @ SV335 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK52_SY488 @ SY1017 @ SV394 @ SV335 @ SV117 ) @ SV335 ) )
| ( SY1017
!= ( ordered_pair @ ( sK51_E @ SY1017 @ SV394 @ SV335 @ SV117 ) @ ( sK52_SY488 @ SY1017 @ SV394 @ SV335 @ SV117 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1761]) ).
thf(1934,plain,
! [SV336: $i,SV269: $i] :
( ( ( ( ( set_difference @ SV269 @ SV336 )
!= empty_set ) )
= $true )
| ( ( subset @ SV269 @ SV336 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1762]) ).
thf(1935,plain,
! [SV337: $i,SV270: $i] :
( ( ( ~ ( subset @ SV270 @ SV337 ) )
= $true )
| ( ( ( set_difference @ SV270 @ SV337 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1763]) ).
thf(1936,plain,
! [SV271: $i] :
( ( ( relation @ SV271 )
= $false )
| ( ( ( ( relation_dom @ SV271 )
!= empty_set )
| ( ( relation_rng @ SV271 )
= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1764]) ).
thf(1937,plain,
! [SV272: $i] :
( ( ( relation @ SV272 )
= $false )
| ( ( ( ( relation_rng @ SV272 )
!= empty_set )
| ( ( relation_dom @ SV272 )
= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1765]) ).
thf(1938,plain,
! [SV118: $i,SV338: $i,SV395: $i] :
( ( ~ ( function @ SV395 )
| ~ ( relation @ SV395 )
| ( SV338
!= ( apply @ SV395 @ SV118 ) )
| ~ ( in @ SV118 @ ( relation_dom @ SV395 ) )
| ( in @ ( ordered_pair @ SV118 @ SV338 ) @ SV395 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1766]) ).
thf(1939,plain,
! [SV118: $i] :
( ( ~ ! [SY655: $i,SY656: $i] :
( ~ ( function @ SY656 )
| ~ ( relation @ SY656 )
| ~ ( in @ ( ordered_pair @ SV118 @ SY655 ) @ SY656 )
| ( SY655
= ( apply @ SY656 @ SV118 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1767]) ).
thf(1940,plain,
! [SV118: $i] :
( ( ~ ! [SY657: $i,SY658: $i] :
( ~ ( function @ SY658 )
| ~ ( relation @ SY658 )
| ~ ( in @ ( ordered_pair @ SV118 @ SY657 ) @ SY658 )
| ( in @ SV118 @ ( relation_dom @ SY658 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1767]) ).
thf(1941,plain,
! [SV273: $i,SV339: $i] :
( ( ( ~ ( relation @ SV339 ) )
= $true )
| ( ( ~ ( ~ ( ( ( sK69_C @ SV339 @ SV273 )
!= ( sK70_SY500 @ SV339 @ SV273 ) )
| ~ ( in @ ( sK69_C @ SV339 @ SV273 ) @ SV273 )
| ~ ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 ) )
| ~ ~ ( ~ ( ( ( sK69_C @ SV339 @ SV273 )
= ( sK70_SY500 @ SV339 @ SV273 ) )
| ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 ) )
| ~ ( ( in @ ( sK69_C @ SV339 @ SV273 ) @ SV273 )
| ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 ) ) ) )
| ( SV339
= ( identity_relation @ SV273 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1768]) ).
thf(1942,plain,
! [SV274: $i,SV340: $i] :
( ( ( ~ ( relation @ SV340 ) )
= $true )
| ( ( ( SV340
!= ( identity_relation @ SV274 ) )
| ~ ( ~ ! [SY968: $i,SY969: $i] :
( ( SY968 != SY969 )
| ~ ( in @ SY968 @ SV274 )
| ( in @ ( ordered_pair @ SY968 @ SY969 ) @ SV340 ) )
| ~ ~ ( ~ ! [SY970: $i,SY971: $i] :
( ~ ( in @ ( ordered_pair @ SY970 @ SY971 ) @ SV340 )
| ( SY970 = SY971 ) )
| ~ ! [SY972: $i] :
( ! [SY973: $i] :
~ ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV340 )
| ( in @ SY972 @ SV274 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1769]) ).
thf(1943,plain,
! [SV120: $i,SV275: $i] :
( ( ( relation @ SV275 )
= $false )
| ( ( ~ ( ~ ! [SY904: $i] :
( ~ ( relation @ SY904 )
| ~ ( ~ ( ! [SY905: $i] :
( ~ ( in @ ( ordered_pair @ ( sK13_D @ SY904 @ SV275 @ SV120 ) @ SY905 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY905 @ ( sK14_SY457 @ SY904 @ SV275 @ SV120 ) ) @ SV275 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_D @ SY904 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SY904 @ SV275 @ SV120 ) ) @ SY904 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_D @ SY904 @ SV275 @ SV120 ) @ ( sK15_SY461 @ SY904 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY461 @ SY904 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SY904 @ SV275 @ SV120 ) ) @ SV275 ) )
| ( in @ ( ordered_pair @ ( sK13_D @ SY904 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SY904 @ SV275 @ SV120 ) ) @ SY904 ) ) )
| ( SY904
= ( relation_composition @ SV120 @ SV275 ) ) )
| ~ ! [SY906: $i] :
( ~ ( relation @ SY906 )
| ( SY906
!= ( relation_composition @ SV120 @ SV275 ) )
| ~ ( ~ ! [SY907: $i,SY908: $i] :
( ! [SY909: $i] :
( ~ ( in @ ( ordered_pair @ SY907 @ SY909 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY909 @ SY908 ) @ SV275 ) )
| ( in @ ( ordered_pair @ SY907 @ SY908 ) @ SY906 ) )
| ~ ! [SY910: $i,SY911: $i] :
( ~ ( in @ ( ordered_pair @ SY910 @ SY911 ) @ SY906 )
| ~ ( ~ ( in @ ( ordered_pair @ SY910 @ ( sK12_F @ SY911 @ SY910 @ SY906 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK12_F @ SY911 @ SY910 @ SY906 @ SV275 @ SV120 ) @ SY911 ) @ SV275 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1770]) ).
thf(1944,plain,
! [SV227: $i,SV121: $i] :
( ( ( ~ ! [SY853: $i] :
( ~ ( element @ SY853 @ ( powerset @ SV121 ) )
| ~ ( disjoint @ SV227 @ SY853 )
| ( subset @ SV227 @ ( subset_complement @ SV121 @ SY853 ) ) ) )
= $false )
| ( ( element @ SV227 @ ( powerset @ SV121 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1771]) ).
thf(1945,plain,
! [SV227: $i,SV121: $i] :
( ( ( ~ ! [SY854: $i] :
( ~ ( element @ SY854 @ ( powerset @ SV121 ) )
| ~ ( subset @ SV227 @ ( subset_complement @ SV121 @ SY854 ) )
| ( disjoint @ SV227 @ SY854 ) ) )
= $false )
| ( ( element @ SV227 @ ( powerset @ SV121 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1771]) ).
thf(1946,plain,
! [SV341: $i,SV122: $i,SV396: $i] :
( ( ~ ( relation @ SV396 )
| ~ ( in @ SV122 @ SV341 )
| ~ ( in @ SV122 @ ( relation_rng @ SV396 ) )
| ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SV341 @ SV396 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1772]) ).
thf(1947,plain,
! [SV122: $i] :
( ( ~ ! [SY673: $i,SY674: $i] :
( ~ ( relation @ SY674 )
| ~ ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SY673 @ SY674 ) ) )
| ( in @ SV122 @ SY673 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1773]) ).
thf(1948,plain,
! [SV122: $i] :
( ( ~ ! [SY675: $i,SY676: $i] :
( ~ ( relation @ SY676 )
| ~ ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SY675 @ SY676 ) ) )
| ( in @ SV122 @ ( relation_rng @ SY676 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1773]) ).
thf(1949,plain,
! [SV123: $i] :
( ( ( ! [SY677: $i,SY678: $i] :
( ~ ( relation @ SY678 )
| ~ ( ~ ( ~ ( in @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ SY677 )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ ( sK35_SY473 @ SY678 @ SY677 @ SV123 ) ) @ SV123 )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ ( sK35_SY473 @ SY678 @ SY677 @ SV123 ) ) @ SY678 ) )
| ~ ~ ( ~ ( ( in @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ SY677 )
| ( in @ ( ordered_pair @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ ( sK35_SY473 @ SY678 @ SY677 @ SV123 ) ) @ SY678 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ ( sK35_SY473 @ SY678 @ SY677 @ SV123 ) ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK34_D @ SY678 @ SY677 @ SV123 ) @ ( sK35_SY473 @ SY678 @ SY677 @ SV123 ) ) @ SY678 ) ) ) )
| ( SY678
= ( relation_dom_restriction @ SV123 @ SY677 ) ) ) )
= $true )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1774]) ).
thf(1950,plain,
! [SV123: $i] :
( ( ( ! [SY679: $i,SY680: $i] :
( ~ ( relation @ SY680 )
| ( SY680
!= ( relation_dom_restriction @ SV123 @ SY679 ) )
| ~ ( ~ ! [SY681: $i,SY682: $i] :
( ~ ( in @ SY681 @ SY679 )
| ~ ( in @ ( ordered_pair @ SY681 @ SY682 ) @ SV123 )
| ( in @ ( ordered_pair @ SY681 @ SY682 ) @ SY680 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY680 )
| ( in @ SX3 @ SY679 ) )
| ~ ! [SY685: $i,SY686: $i] :
( ~ ( in @ ( ordered_pair @ SY685 @ SY686 ) @ SY680 )
| ( in @ ( ordered_pair @ SY685 @ SY686 ) @ SV123 ) ) ) ) ) )
= $true )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1775]) ).
thf(1951,plain,
! [SV124: $i] :
( ( ( ! [SY687: $i] :
( ~ ( relation @ SY687 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_C @ SY687 @ SV124 ) @ ( sK17_SY462 @ SY687 @ SV124 ) ) @ SY687 )
| ~ ( in @ ( ordered_pair @ ( sK17_SY462 @ SY687 @ SV124 ) @ ( sK16_C @ SY687 @ SV124 ) ) @ SV124 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK16_C @ SY687 @ SV124 ) @ ( sK17_SY462 @ SY687 @ SV124 ) ) @ SY687 )
| ( in @ ( ordered_pair @ ( sK17_SY462 @ SY687 @ SV124 ) @ ( sK16_C @ SY687 @ SV124 ) ) @ SV124 ) ) )
| ( SY687
= ( relation_inverse @ SV124 ) ) ) )
= $true )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1776]) ).
thf(1952,plain,
! [SV124: $i] :
( ( ( ! [SY688: $i] :
( ~ ( relation @ SY688 )
| ( SY688
!= ( relation_inverse @ SV124 ) )
| ~ ( ~ ! [SY689: $i,SY690: $i] :
( ~ ( in @ ( ordered_pair @ SY689 @ SY690 ) @ SY688 )
| ( in @ ( ordered_pair @ SY690 @ SY689 ) @ SV124 ) )
| ~ ! [SY691: $i,SY692: $i] :
( ~ ( in @ ( ordered_pair @ SY692 @ SY691 ) @ SV124 )
| ( in @ ( ordered_pair @ SY691 @ SY692 ) @ SY688 ) ) ) ) )
= $true )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1777]) ).
thf(1953,plain,
! [SV342: $i,SV276: $i] :
( ( ( ~ ( element @ SV276 @ ( powerset @ SV342 ) ) )
= $true )
| ( ( subset @ SV276 @ SV342 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1778]) ).
thf(1954,plain,
! [SV343: $i,SV277: $i] :
( ( ( ~ ( subset @ SV277 @ SV343 ) )
= $true )
| ( ( element @ SV277 @ ( powerset @ SV343 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1779]) ).
thf(1955,plain,
! [SV344: $i,SV278: $i] :
( ( ( ~ ( in @ SV278 @ SV344 ) )
= $true )
| ( ( subset @ ( singleton @ SV278 ) @ SV344 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1780]) ).
thf(1956,plain,
! [SV345: $i,SV279: $i] :
( ( ( ~ ( subset @ ( singleton @ SV279 ) @ SV345 ) )
= $true )
| ( ( in @ SV279 @ SV345 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1781]) ).
thf(1957,plain,
! [SV346: $i,SV280: $i] :
( ( ( ( ( set_intersection2 @ SV280 @ SV346 )
!= empty_set ) )
= $true )
| ( ( disjoint @ SV280 @ SV346 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1782]) ).
thf(1958,plain,
! [SV347: $i,SV281: $i] :
( ( ( ~ ( disjoint @ SV281 @ SV347 ) )
= $true )
| ( ( ( set_intersection2 @ SV281 @ SV347 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1783]) ).
thf(1959,plain,
! [SV282: $i,SV348: $i] :
( ( ( ~ ( function @ SV348 )
| ~ ( relation @ SV348 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK38_C @ SV348 @ SV282 ) @ SV282 )
| ~ ( ( ( apply @ SV348 @ ( sK38_C @ SV348 @ SV282 ) )
!= ( sK38_C @ SV348 @ SV282 ) ) ) )
| ( ( relation_dom @ SV348 )
!= SV282 )
| ( SV348
= ( identity_relation @ SV282 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1784]) ).
thf(1960,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)],[1785]) ).
thf(1961,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1786]) ).
thf(1962,plain,
! [SV349: $i,SV283: $i] :
( ( ( ( ( set_difference @ SV283 @ SV349 )
!= empty_set ) )
= $true )
| ( ( subset @ SV283 @ SV349 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1787]) ).
thf(1963,plain,
! [SV350: $i,SV284: $i] :
( ( ( ~ ( subset @ SV284 @ SV350 ) )
= $true )
| ( ( ( set_difference @ SV284 @ SV350 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1788]) ).
thf(1964,plain,
! [SV351: $i,SV285: $i] :
( ( ( ~ ( subset @ SV285 @ SV351 )
| ~ ( subset @ SV351 @ SV285 ) )
= $true )
| ( ( SV285 = SV351 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1789]) ).
thf(1965,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1790]) ).
thf(1966,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1791]) ).
thf(1967,plain,
! [SV125: $i] :
( ( ( ! [SY693: $i,SY694: $i] :
( ~ ( ~ ( ! [SY695: $i] :
( ~ ( in @ ( ordered_pair @ SY695 @ ( sK30_D @ SY694 @ SY693 @ SV125 ) ) @ SV125 )
| ~ ( in @ SY695 @ SY693 ) )
| ~ ( in @ ( sK30_D @ SY694 @ SY693 @ SV125 ) @ SY694 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_SY471 @ SY694 @ SY693 @ SV125 ) @ ( sK30_D @ SY694 @ SY693 @ SV125 ) ) @ SV125 )
| ~ ( in @ ( sK31_SY471 @ SY694 @ SY693 @ SV125 ) @ SY693 ) )
| ( in @ ( sK30_D @ SY694 @ SY693 @ SV125 ) @ SY694 ) ) )
| ( SY694
= ( relation_image @ SV125 @ SY693 ) ) ) )
= $true )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1792]) ).
thf(1968,plain,
! [SV125: $i] :
( ( ( ! [SY696: $i,SY697: $i] :
( ( SY697
!= ( relation_image @ SV125 @ SY696 ) )
| ~ ( ~ ! [SY698: $i] :
( ! [SY699: $i] :
( ~ ( in @ ( ordered_pair @ SY699 @ SY698 ) @ SV125 )
| ~ ( in @ SY699 @ SY696 ) )
| ( in @ SY698 @ SY697 ) )
| ~ ! [SY700: $i] :
( ~ ( in @ SY700 @ SY697 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK29_E @ SY700 @ SY697 @ SY696 @ SV125 ) @ SY700 ) @ SV125 )
| ~ ( in @ ( sK29_E @ SY700 @ SY697 @ SY696 @ SV125 ) @ SY696 ) ) ) ) ) )
= $true )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1793]) ).
thf(1969,plain,
! [SV352: $i,SV126: $i,SV397: $i] :
( ( ~ ( relation @ SV397 )
| ~ ( in @ ( ordered_pair @ SV126 @ SV352 ) @ SV397 )
| ( in @ SV126 @ ( relation_field @ SV397 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1794]) ).
thf(1970,plain,
! [SV353: $i,SV126: $i,SV398: $i] :
( ( ~ ( relation @ SV398 )
| ~ ( in @ ( ordered_pair @ SV126 @ SV353 ) @ SV398 )
| ( in @ SV353 @ ( relation_field @ SV398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1795]) ).
thf(1971,plain,
! [SV228: $i,SV399: $i,SV127: $i] :
( ( ! [SY1018: $i] :
( ~ ( relation @ SY1018 )
| ~ ( in @ SV127 @ SV399 )
| ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ SY1018 )
| ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SV399 ) @ SY1018 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1796]) ).
thf(1972,plain,
! [SV228: $i,SV127: $i] :
( ( ~ ! [SY857: $i,SY858: $i] :
( ~ ( relation @ SY858 )
| ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SY857 ) @ SY858 ) )
| ( in @ SV127 @ SY857 ) )
| ~ ! [SY859: $i,SY860: $i] :
( ~ ( relation @ SY860 )
| ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SY859 ) @ SY860 ) )
| ( in @ ( ordered_pair @ SV127 @ SV228 ) @ SY860 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1797]) ).
thf(1973,plain,
! [SV354: $i,SV286: $i] :
( ( ( ~ ( in @ SV286 @ SV354 ) )
= $true )
| ( ( subset @ ( singleton @ SV286 ) @ SV354 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1798]) ).
thf(1974,plain,
! [SV355: $i,SV287: $i] :
( ( ( ~ ( subset @ ( singleton @ SV287 ) @ SV355 ) )
= $true )
| ( ( in @ SV287 @ SV355 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1799]) ).
thf(1975,plain,
! [SV356: $i,SV400: $i,SV128: $i] :
( ( ~ ( in @ SV128 @ SV400 )
| ~ ( in @ SV356 @ SV400 )
| ( subset @ ( unordered_pair @ SV128 @ SV356 ) @ SV400 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1800]) ).
thf(1976,plain,
! [SV128: $i] :
( ( ~ ! [SY714: $i,SY715: $i] :
( ~ ( subset @ ( unordered_pair @ SV128 @ SY714 ) @ SY715 )
| ( in @ SV128 @ SY715 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1801]) ).
thf(1977,plain,
! [SV128: $i] :
( ( ~ ! [SY716: $i,SY717: $i] :
( ~ ( subset @ ( unordered_pair @ SV128 @ SY716 ) @ SY717 )
| ( in @ SY716 @ SY717 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1801]) ).
thf(1978,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1802]) ).
thf(1979,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1803]) ).
thf(1980,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1804]) ).
thf(1981,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1805]) ).
thf(1982,plain,
! [SV129: $i] :
( ( ( ! [SY718: $i] :
( ~ ( ~ ( ! [SY719: $i] :
~ ( in @ ( ordered_pair @ SY719 @ ( sK19_C @ SY718 @ SV129 ) ) @ SV129 )
| ~ ( in @ ( sK19_C @ SY718 @ SV129 ) @ SY718 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_SY464 @ SY718 @ SV129 ) @ ( sK19_C @ SY718 @ SV129 ) ) @ SV129 )
| ( in @ ( sK19_C @ SY718 @ SV129 ) @ SY718 ) ) )
| ( SY718
= ( relation_rng @ SV129 ) ) ) )
= $true )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1806]) ).
thf(1983,plain,
! [SV129: $i] :
( ( ( ! [SY720: $i] :
( ( SY720
!= ( relation_rng @ SV129 ) )
| ~ ( ~ ! [SY721: $i] :
( ! [SY722: $i] :
~ ( in @ ( ordered_pair @ SY722 @ SY721 ) @ SV129 )
| ( in @ SY721 @ SY720 ) )
| ~ ! [SY723: $i] :
( ~ ( in @ SY723 @ SY720 )
| ( in @ ( ordered_pair @ ( sK18_D @ SY723 @ SY720 @ SV129 ) @ SY723 ) @ SV129 ) ) ) ) )
= $true )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1807]) ).
thf(1984,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1808]) ).
thf(1985,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1809]) ).
thf(1986,plain,
! [SV357: $i,SV288: $i] :
( ( ( ( ( set_difference @ SV288 @ ( singleton @ SV357 ) )
!= SV288 ) )
= $true )
| ( ( ~ ( in @ SV357 @ SV288 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1810]) ).
thf(1987,plain,
! [SV289: $i,SV358: $i] :
( ( ( in @ SV358 @ SV289 )
= $true )
| ( ( ( set_difference @ SV289 @ ( singleton @ SV358 ) )
= SV289 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1811]) ).
thf(1988,plain,
! [SV359: $i,SV292: $i] :
( ( ( disjoint @ SV292 @ SV359 )
= $true )
| ( ( in @ ( sK71_C @ SV359 @ SV292 ) @ ( set_intersection2 @ SV292 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1812]) ).
thf(1989,plain,
! [SV360: $i,SV293: $i] :
( ( ( ! [SY978: $i] :
~ ( in @ SY978 @ ( set_intersection2 @ SV293 @ SV360 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV293 @ SV360 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1813]) ).
thf(1990,plain,
! [SV130: $i,SV229: $i] :
( ( ( in @ ( sK73_C @ SV229 @ SV130 ) @ SV130 )
= $true )
| ( ( element @ SV130 @ ( powerset @ SV229 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1814]) ).
thf(1991,plain,
! [SV130: $i,SV229: $i] :
( ( ( ~ ( in @ ( sK73_C @ SV229 @ SV130 ) @ SV229 ) )
= $true )
| ( ( element @ SV130 @ ( powerset @ SV229 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1815]) ).
thf(1992,plain,
! [SV131: $i] :
( ( ( ! [SY725: $i,SY726: $i] :
( ~ ( ~ ( ! [SY727: $i] :
( ~ ( in @ ( ordered_pair @ ( sK27_D @ SY726 @ SY725 @ SV131 ) @ SY727 ) @ SV131 )
| ~ ( in @ SY727 @ SY725 ) )
| ~ ( in @ ( sK27_D @ SY726 @ SY725 @ SV131 ) @ SY726 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK27_D @ SY726 @ SY725 @ SV131 ) @ ( sK28_SY469 @ SY726 @ SY725 @ SV131 ) ) @ SV131 )
| ~ ( in @ ( sK28_SY469 @ SY726 @ SY725 @ SV131 ) @ SY725 ) )
| ( in @ ( sK27_D @ SY726 @ SY725 @ SV131 ) @ SY726 ) ) )
| ( SY726
= ( relation_inverse_image @ SV131 @ SY725 ) ) ) )
= $true )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1816]) ).
thf(1993,plain,
! [SV131: $i] :
( ( ( ! [SY728: $i,SY729: $i] :
( ( SY729
!= ( relation_inverse_image @ SV131 @ SY728 ) )
| ~ ( ~ ! [SY730: $i] :
( ! [SY731: $i] :
( ~ ( in @ ( ordered_pair @ SY730 @ SY731 ) @ SV131 )
| ~ ( in @ SY731 @ SY728 ) )
| ( in @ SY730 @ SY729 ) )
| ~ ! [SY732: $i] :
( ~ ( in @ SY732 @ SY729 )
| ~ ( ~ ( in @ ( ordered_pair @ SY732 @ ( sK26_E @ SY732 @ SY729 @ SY728 @ SV131 ) ) @ SV131 )
| ~ ( in @ ( sK26_E @ SY732 @ SY729 @ SY728 @ SV131 ) @ SY728 ) ) ) ) ) )
= $true )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1817]) ).
thf(1994,plain,
! [SV361: $i,SV294: $i] :
( ( ( ( ( set_difference @ SV294 @ SV361 )
!= SV294 ) )
= $true )
| ( ( disjoint @ SV294 @ SV361 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1818]) ).
thf(1995,plain,
! [SV362: $i,SV295: $i] :
( ( ( ~ ( disjoint @ SV295 @ SV362 ) )
= $true )
| ( ( ( set_difference @ SV295 @ SV362 )
= SV295 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1819]) ).
thf(1996,plain,
! [SV296: $i] :
( ( ( ~ ! [SY931: $i,SY932: $i] :
( ( sK68_B @ SV296 )
!= ( ordered_pair @ SY931 @ SY932 ) )
| ~ ( in @ ( sK68_B @ SV296 ) @ SV296 ) )
= $false )
| ( ( relation @ SV296 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1820]) ).
thf(1997,plain,
! [SV297: $i] :
( ( ( relation @ SV297 )
= $false )
| ( ( ! [SY933: $i] :
( ( SY933
= ( ordered_pair @ ( sK66_C @ SY933 @ SV297 ) @ ( sK67_SY497 @ SY933 @ SV297 ) ) )
| ~ ( in @ SY933 @ SV297 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1821]) ).
thf(1998,plain,
! [SV363: $i,SV132: $i,SV401: $i] :
( ( ~ ( relation @ SV401 )
| ~ ( in @ SV132 @ SV363 )
| ~ ( in @ SV132 @ ( relation_dom @ SV401 ) )
| ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SV401 @ SV363 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1822]) ).
thf(1999,plain,
! [SV132: $i] :
( ( ~ ! [SY735: $i,SY736: $i] :
( ~ ( relation @ SY736 )
| ~ ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SY736 @ SY735 ) ) )
| ( in @ SV132 @ SY735 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1823]) ).
thf(2000,plain,
! [SV132: $i] :
( ( ~ ! [SY737: $i,SY738: $i] :
( ~ ( relation @ SY738 )
| ~ ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SY738 @ SY737 ) ) )
| ( in @ SV132 @ ( relation_dom @ SY738 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1823]) ).
thf(2001,plain,
! [SV364: $i,SV133: $i,SV402: $i] :
( ( ~ ( relation @ SV402 )
| ~ ( in @ ( ordered_pair @ SV133 @ SV364 ) @ SV402 )
| ( in @ SV133 @ ( relation_dom @ SV402 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1824]) ).
thf(2002,plain,
! [SV365: $i,SV133: $i,SV403: $i] :
( ( ~ ( relation @ SV403 )
| ~ ( in @ ( ordered_pair @ SV133 @ SV365 ) @ SV403 )
| ( in @ SV365 @ ( relation_rng @ SV403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1825]) ).
thf(2003,plain,
! [SV134: $i] :
( ( ( ! [SY743: $i] :
( ~ ( ~ ( ! [SY744: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SY743 @ SV134 ) @ SY744 ) @ SV134 )
| ~ ( in @ ( sK22_C @ SY743 @ SV134 ) @ SY743 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SY743 @ SV134 ) @ ( sK23_SY466 @ SY743 @ SV134 ) ) @ SV134 )
| ( in @ ( sK22_C @ SY743 @ SV134 ) @ SY743 ) ) )
| ( SY743
= ( relation_dom @ SV134 ) ) ) )
= $true )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1826]) ).
thf(2004,plain,
! [SV134: $i] :
( ( ( ! [SY745: $i] :
( ( SY745
!= ( relation_dom @ SV134 ) )
| ~ ( ~ ! [SY746: $i] :
( ! [SY747: $i] :
~ ( in @ ( ordered_pair @ SY746 @ SY747 ) @ SV134 )
| ( in @ SY746 @ SY745 ) )
| ~ ! [SY748: $i] :
( ~ ( in @ SY748 @ SY745 )
| ( in @ ( ordered_pair @ SY748 @ ( sK21_D @ SY748 @ SY745 @ SV134 ) ) @ SV134 ) ) ) ) )
= $true )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1827]) ).
thf(2005,plain,
! [SV135: $i,SV366: $i,SV404: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK57_D @ SV404 @ SV366 @ SV135 ) @ SV404 )
| ( ( sK57_D @ SV404 @ SV366 @ SV135 )
!= SV135 ) )
| ~ ( ~ ( in @ ( sK57_D @ SV404 @ SV366 @ SV135 ) @ SV404 )
| ( ( sK57_D @ SV404 @ SV366 @ SV135 )
!= SV366 ) ) )
| ~ ( ( in @ ( sK57_D @ SV404 @ SV366 @ SV135 ) @ SV404 )
| ( ( sK57_D @ SV404 @ SV366 @ SV135 )
= SV135 )
| ( ( sK57_D @ SV404 @ SV366 @ SV135 )
= SV366 ) ) )
| ( SV404
= ( unordered_pair @ SV135 @ SV366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1828]) ).
thf(2006,plain,
! [SV367: $i,SV135: $i,SV405: $i] :
( ( ( SV405
!= ( unordered_pair @ SV135 @ SV367 ) )
| ~ ( ~ ! [SY1019: $i] :
( ~ ( in @ SY1019 @ SV405 )
| ( SY1019 = SV135 )
| ( SY1019 = SV367 ) )
| ~ ~ ( ~ ! [SY1020: $i] :
( ( SY1020 != SV135 )
| ( in @ SY1020 @ SV405 ) )
| ~ ! [SY1021: $i] :
( ( SY1021 != SV367 )
| ( in @ SY1021 @ SV405 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(2007,plain,
! [SV136: $i] :
( ( ( ! [SY756: $i] :
( ~ ( relation @ SY756 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK58_C @ SY756 @ SV136 ) @ ( sK59_SY494 @ SY756 @ SV136 ) ) @ SV136 )
| ~ ( in @ ( ordered_pair @ ( sK58_C @ SY756 @ SV136 ) @ ( sK59_SY494 @ SY756 @ SV136 ) ) @ SY756 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_C @ SY756 @ SV136 ) @ ( sK59_SY494 @ SY756 @ SV136 ) ) @ SV136 )
| ( in @ ( ordered_pair @ ( sK58_C @ SY756 @ SV136 ) @ ( sK59_SY494 @ SY756 @ SV136 ) ) @ SY756 ) ) )
| ( SV136 = SY756 ) ) )
= $true )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1830]) ).
thf(2008,plain,
! [SV136: $i] :
( ( ( ! [SY757: $i] :
( ~ ( relation @ SY757 )
| ( SV136 != SY757 )
| ~ ( ~ ! [SY758: $i,SY759: $i] :
( ~ ( in @ ( ordered_pair @ SY758 @ SY759 ) @ SV136 )
| ( in @ ( ordered_pair @ SY758 @ SY759 ) @ SY757 ) )
| ~ ! [SY760: $i,SY761: $i] :
( ~ ( in @ ( ordered_pair @ SY760 @ SY761 ) @ SY757 )
| ( in @ ( ordered_pair @ SY760 @ SY761 ) @ SV136 ) ) ) ) )
= $true )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1831]) ).
thf(2009,plain,
! [SV368: $i,SV298: $i] :
( ( ( ~ ( function @ SV298 )
| ~ ( relation @ SV298 )
| ~ ( relation @ SV368 )
| ~ ( function @ SV368 ) )
= $true )
| ( ( function @ ( relation_composition @ SV298 @ SV368 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1832]) ).
thf(2010,plain,
! [SV369: $i,SV299: $i] :
( ( ( ~ ( function @ SV299 )
| ~ ( relation @ SV299 )
| ~ ( relation @ SV369 )
| ~ ( function @ SV369 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV299 @ SV369 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1833]) ).
thf(2011,plain,
! [SV137: $i,SV230: $i] :
( ( ( relation @ SV230 )
= $false )
| ( ( function @ SV230 )
= $false )
| ( ( ~ ( ~ ! [SY861: $i] :
( ~ ( function @ SY861 )
| ~ ( relation @ SY861 )
| ~ ( in @ SV137 @ ( relation_dom @ SY861 ) )
| ~ ( in @ ( apply @ SY861 @ SV137 ) @ ( relation_dom @ SV230 ) )
| ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY861 @ SV230 ) ) ) )
| ~ ~ ( ~ ! [SY862: $i] :
( ~ ( function @ SY862 )
| ~ ( relation @ SY862 )
| ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY862 @ SV230 ) ) )
| ( in @ SV137 @ ( relation_dom @ SY862 ) ) )
| ~ ! [SY863: $i] :
( ~ ( function @ SY863 )
| ~ ( relation @ SY863 )
| ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY863 @ SV230 ) ) )
| ( in @ ( apply @ SY863 @ SV137 ) @ ( relation_dom @ SV230 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1834]) ).
thf(2012,plain,
! [SV138: $i,SV370: $i] :
( ( ( ~ ( subset @ SV370 @ ( sK41_B @ SV138 ) )
| ( are_equipotent @ SV370 @ ( sK41_B @ SV138 ) ) )
= $true )
| ( ( in @ SV370 @ ( sK41_B @ SV138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1835]) ).
thf(2013,plain,
! [SV138: $i] :
( ( ~ ! [SY767: $i] :
( ~ ( in @ SY767 @ ( sK41_B @ SV138 ) )
| ( in @ ( powerset @ SY767 ) @ ( sK41_B @ SV138 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1836]) ).
thf(2014,plain,
! [SV138: $i] :
( ( ~ ~ ( ~ ! [SY768: $i,SY769: $i] :
( ~ ( in @ SY768 @ ( sK41_B @ SV138 ) )
| ~ ( subset @ SY769 @ SY768 )
| ( in @ SY769 @ ( sK41_B @ SV138 ) ) )
| ~ ( in @ SV138 @ ( sK41_B @ SV138 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1836]) ).
thf(2015,plain,
! [SV139: $i] :
( ( ( ! [SY770: $i] :
( ~ ( relation @ SY770 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SY770 @ SV139 ) @ ( sK25_SY467 @ SY770 @ SV139 ) ) @ SV139 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SY770 @ SV139 ) @ ( sK25_SY467 @ SY770 @ SV139 ) ) @ SY770 ) )
| ( subset @ SV139 @ SY770 ) ) )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1837]) ).
thf(2016,plain,
! [SV139: $i] :
( ( ( ! [SY771: $i] :
( ~ ( relation @ SY771 )
| ~ ( subset @ SV139 @ SY771 )
| ! [SY772: $i,SY773: $i] :
( ~ ( in @ ( ordered_pair @ SY772 @ SY773 ) @ SV139 )
| ( in @ ( ordered_pair @ SY772 @ SY773 ) @ SY771 ) ) ) )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1838]) ).
thf(2017,plain,
! [SV300: $i,SV371: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK60_C @ SV371 @ SV300 ) @ SV371 )
| ~ ( subset @ ( sK60_C @ SV371 @ SV300 ) @ SV300 ) )
| ~ ( ( in @ ( sK60_C @ SV371 @ SV300 ) @ SV371 )
| ( subset @ ( sK60_C @ SV371 @ SV300 ) @ SV300 ) ) ) )
= $true )
| ( ( SV371
= ( powerset @ SV300 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1839]) ).
thf(2018,plain,
! [SV301: $i,SV372: $i] :
( ( ( ( SV372
!= ( powerset @ SV301 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY987: $i] :
( ~ ( in @ SY987 @ SV372 )
| ( subset @ SY987 @ SV301 ) )
| ~ ! [SY988: $i] :
( ~ ( subset @ SY988 @ SV301 )
| ( in @ SY988 @ SV372 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1840]) ).
thf(2019,plain,
! [SV373: $i,SV302: $i] :
( ( ( ~ ( empty @ SV302 )
| ~ ( relation @ SV373 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV302 @ SV373 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1841]) ).
thf(2020,plain,
! [SV374: $i,SV303: $i] :
( ( ( ~ ( empty @ SV303 )
| ~ ( relation @ SV374 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV303 @ SV374 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1842]) ).
thf(2021,plain,
! [SV140: $i] :
( ( ( ! [SY774: $i] :
( ~ ( relation @ SY774 )
| ~ ( subset @ SV140 @ SY774 )
| ( subset @ ( relation_dom @ SV140 ) @ ( relation_dom @ SY774 ) ) ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1843]) ).
thf(2022,plain,
! [SV140: $i] :
( ( ( ! [SY775: $i] :
( ~ ( relation @ SY775 )
| ~ ( subset @ SV140 @ SY775 )
| ( subset @ ( relation_rng @ SV140 ) @ ( relation_rng @ SY775 ) ) ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1844]) ).
thf(2023,plain,
! [SV141: $i] :
( ( ( empty @ ( sK8_B @ SV141 ) )
= $false )
| ( ( empty @ SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1846]) ).
thf(2024,plain,
! [SV375: $i,SV142: $i,SV406: $i] :
( ( ~ ( relation @ SV406 )
| ! [SY1022: $i] :
( ~ ( in @ SY1022 @ ( relation_rng @ SV406 ) )
| ~ ( in @ ( ordered_pair @ SV142 @ SY1022 ) @ SV406 )
| ~ ( in @ SY1022 @ SV375 ) )
| ( in @ SV142 @ ( relation_inverse_image @ SV406 @ SV375 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1847]) ).
thf(2025,plain,
! [SV376: $i,SV142: $i,SV407: $i] :
( ( ~ ( relation @ SV407 )
| ~ ( in @ SV142 @ ( relation_inverse_image @ SV407 @ SV376 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK39_D @ SV407 @ SV376 @ SV142 ) @ ( relation_rng @ SV407 ) )
| ~ ( in @ ( ordered_pair @ SV142 @ ( sK39_D @ SV407 @ SV376 @ SV142 ) ) @ SV407 ) )
| ~ ( in @ ( sK39_D @ SV407 @ SV376 @ SV142 ) @ SV376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1848]) ).
thf(2026,plain,
( ( ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK65_SY495 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK64_C @ SX1 @ SX0 ) @ ( sK65_SY495 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK64_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK64_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK64_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1849]) ).
thf(2027,plain,
( ( ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK63_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK63_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1850]) ).
thf(2028,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1851]) ).
thf(2029,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1852]) ).
thf(2030,plain,
! [SV304: $i] :
( ( ( relation @ SV304 )
= $false )
| ( ( ( relation_rng @ SV304 )
= ( relation_dom @ ( relation_inverse @ SV304 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1853]) ).
thf(2031,plain,
! [SV305: $i] :
( ( ( relation @ SV305 )
= $false )
| ( ( ( relation_dom @ SV305 )
= ( relation_rng @ ( relation_inverse @ SV305 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1854]) ).
thf(2032,plain,
! [SV377: $i,SV308: $i] :
( ( ( ( SV308 = SV377 )
| ~ ( subset @ SV308 @ SV377 ) )
= $true )
| ( ( proper_subset @ SV308 @ SV377 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1855]) ).
thf(2033,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1856]) ).
thf(2034,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1857]) ).
thf(2035,plain,
! [SV231: $i,SV408: $i,SV143: $i] :
( ( ! [SY1023: $i] :
( ~ ( in @ SV143 @ SV408 )
| ~ ( in @ SV231 @ SY1023 )
| ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SV408 @ SY1023 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1858]) ).
thf(2036,plain,
! [SV231: $i,SV143: $i] :
( ( ~ ! [SY866: $i] :
( ! [SY867: $i] :
~ ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SY866 @ SY867 ) )
| ( in @ SV143 @ SY866 ) )
| ~ ! [SY868: $i,SY869: $i] :
( ~ ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SY868 @ SY869 ) )
| ( in @ SV231 @ SY869 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1859]) ).
thf(2037,plain,
! [SV144: $i,SV378: $i,SV409: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV409 )
| ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV144 ) )
| ~ ( ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV409 )
| ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV378 ) ) )
| ~ ( ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV409 )
| ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV144 )
| ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV378 ) ) )
| ( SV409
= ( set_union2 @ SV144 @ SV378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1860]) ).
thf(2038,plain,
! [SV379: $i,SV144: $i,SV410: $i] :
( ( ( SV410
!= ( set_union2 @ SV144 @ SV379 ) )
| ~ ( ~ ! [SY1024: $i] :
( ~ ( in @ SY1024 @ SV410 )
| ( in @ SY1024 @ SV144 )
| ( in @ SY1024 @ SV379 ) )
| ~ ~ ( ~ ! [SY1025: $i] :
( ~ ( in @ SY1025 @ SV144 )
| ( in @ SY1025 @ SV410 ) )
| ~ ! [SY1026: $i] :
( ~ ( in @ SY1026 @ SV379 )
| ( in @ SY1026 @ SV410 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1861]) ).
thf(2039,plain,
! [SV309: $i] :
( ( ( empty @ SV309 )
= $false )
| ( ( empty @ ( relation_dom @ SV309 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1862]) ).
thf(2040,plain,
! [SV310: $i] :
( ( ( empty @ SV310 )
= $false )
| ( ( relation @ ( relation_dom @ SV310 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1863]) ).
thf(2041,plain,
! [SV380: $i,SV145: $i,SV411: $i] :
( ( ~ ( relation @ SV411 )
| ! [SY1027: $i] :
( ~ ( in @ SY1027 @ ( relation_dom @ SV411 ) )
| ~ ( in @ ( ordered_pair @ SY1027 @ SV145 ) @ SV411 )
| ~ ( in @ SY1027 @ SV380 ) )
| ( in @ SV145 @ ( relation_image @ SV411 @ SV380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1864]) ).
thf(2042,plain,
! [SV381: $i,SV145: $i,SV412: $i] :
( ( ~ ( relation @ SV412 )
| ~ ( in @ SV145 @ ( relation_image @ SV412 @ SV381 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK40_D @ SV412 @ SV381 @ SV145 ) @ ( relation_dom @ SV412 ) )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV412 @ SV381 @ SV145 ) @ SV145 ) @ SV412 ) )
| ~ ( in @ ( sK40_D @ SV412 @ SV381 @ SV145 ) @ SV381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1865]) ).
thf(2043,plain,
! [SV382: $i,SV146: $i] :
( ( ( ~ ( subset @ SV146 @ SV382 ) )
= $true )
| ( ( ! [SY1000: $i] : ( subset @ ( cartesian_product2 @ SV146 @ SY1000 ) @ ( cartesian_product2 @ SV382 @ SY1000 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1866]) ).
thf(2044,plain,
! [SV383: $i,SV146: $i] :
( ( ( ~ ( subset @ SV146 @ SV383 ) )
= $true )
| ( ( ! [SY1001: $i] : ( subset @ ( cartesian_product2 @ SY1001 @ SV146 ) @ ( cartesian_product2 @ SY1001 @ SV383 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1867]) ).
thf(2045,plain,
! [SV147: $i,SV232: $i] :
( ( ( ~ ( in @ ( sK44_C @ SV232 @ SV147 ) @ SV147 )
| ~ ( in @ ( sK44_C @ SV232 @ SV147 ) @ SV232 ) )
= $true )
| ( ( SV147 = SV232 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1868]) ).
thf(2046,plain,
! [SV147: $i,SV232: $i] :
( ( ( ( in @ ( sK44_C @ SV232 @ SV147 ) @ SV147 )
| ( in @ ( sK44_C @ SV232 @ SV147 ) @ SV232 ) )
= $true )
| ( ( SV147 = SV232 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1869]) ).
thf(2047,plain,
! [SV384: $i,SV311: $i] :
( ( ( ~ ( subset @ SV311 @ ( singleton @ SV384 ) ) )
= $true )
| ( ( ( SV311 = empty_set )
| ( SV311
= ( singleton @ SV384 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1870]) ).
thf(2048,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1871]) ).
thf(2049,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1872]) ).
thf(2050,plain,
! [SV413: $i,SV233: $i,SV148: $i] :
( ( ! [SY1028: $i] :
( ( ordered_pair @ SV148 @ SV233 )
!= ( ordered_pair @ SV413 @ SY1028 ) )
| ( SV148 = SV413 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1873]) ).
thf(2051,plain,
! [SV414: $i,SV233: $i,SV148: $i] :
( ( ! [SY1029: $i] :
( ( ( ordered_pair @ SV148 @ SV233 )
!= ( ordered_pair @ SV414 @ SY1029 ) )
| ( SV233 = SY1029 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1874]) ).
thf(2052,plain,
! [SV312: $i,SV385: $i] :
( ( ( ~ ( ~ ( in @ ( sK50_C @ SV385 @ SV312 ) @ SV312 )
| ~ ~ ( in @ ( sK50_C @ SV385 @ SV312 ) @ SV385 ) ) )
= $true )
| ( ( subset @ SV312 @ SV385 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1875]) ).
thf(2053,plain,
! [SV386: $i,SV313: $i] :
( ( ( ~ ( subset @ SV313 @ SV386 ) )
= $true )
| ( ( ! [SY1002: $i] :
( ~ ( in @ SY1002 @ SV313 )
| ( in @ SY1002 @ SV386 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1876]) ).
thf(2054,plain,
! [SV314: $i] :
( ( ( relation @ SV314 )
= $false )
| ( ( ( ( relation_dom @ SV314 )
!= empty_set )
| ( SV314 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1877]) ).
thf(2055,plain,
! [SV315: $i] :
( ( ( relation @ SV315 )
= $false )
| ( ( ( ( relation_rng @ SV315 )
!= empty_set )
| ( SV315 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1878]) ).
thf(2056,plain,
! [SV316: $i] :
( ( ( empty @ SV316 )
= $false )
| ( ( empty @ ( relation_rng @ SV316 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1879]) ).
thf(2057,plain,
! [SV317: $i] :
( ( ( empty @ SV317 )
= $false )
| ( ( relation @ ( relation_rng @ SV317 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1880]) ).
thf(2058,plain,
! [SV149: $i,SV387: $i,SV415: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV149 )
| ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV387 )
| ~ ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV415 ) )
| ~ ~ ( ~ ( ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV149 )
| ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV415 ) )
| ~ ( ~ ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV387 )
| ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV415 ) ) ) )
| ( SV415
= ( set_difference @ SV149 @ SV387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1881]) ).
thf(2059,plain,
! [SV388: $i,SV149: $i,SV416: $i] :
( ( ( SV416
!= ( set_difference @ SV149 @ SV388 ) )
| ~ ( ~ ! [SY1030: $i] :
( ~ ( in @ SY1030 @ SV149 )
| ( in @ SY1030 @ SV388 )
| ( in @ SY1030 @ SV416 ) )
| ~ ~ ( ~ ! [SY1031: $i] :
( ~ ( in @ SY1031 @ SV416 )
| ( in @ SY1031 @ SV149 ) )
| ~ ! [SY1032: $i] :
( ~ ( in @ SY1032 @ SV416 )
| ~ ( in @ SY1032 @ SV388 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(2060,plain,
! [SV4: $i,SV153: $i,SV318: $i] :
( ( ( in @ SV318 @ SV153 )
= $false )
| ( ( in @ SV318 @ SV4 )
= $true )
| ( ( element @ SV153 @ ( powerset @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1883]) ).
thf(2061,plain,
! [SV234: $i,SV160: $i,SV12: $i] :
( ( ( in @ SV12 @ SV160 )
= $false )
| ( ( element @ SV160 @ ( powerset @ SV234 ) )
= $false )
| ( ( element @ SV12 @ SV234 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1884]) ).
thf(2062,plain,
! [SV250: $i,SV235: $i,SV163: $i,SV16: $i] :
( ( ( ( unordered_pair @ SV16 @ SV163 )
= ( unordered_pair @ SV235 @ SV250 ) )
= $false )
| ( ( SV16 = SV235 )
= $true )
| ( ( SV16 = SV250 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1886]) ).
thf(2063,plain,
! [SV251: $i,SV236: $i,SV168: $i,SV21: $i] :
( ( ( subset @ SV21 @ SV168 )
= $false )
| ( ( ~ ( subset @ SV236 @ SV251 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV21 @ SV236 ) @ ( cartesian_product2 @ SV168 @ SV251 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1887]) ).
thf(2064,plain,
! [SV173: $i,SV27: $i] :
( ( ( subset @ SV27 @ ( relation_rng @ SV173 ) )
= $false )
| ( ( SV27 = empty_set )
= $true )
| ( ( ( ( relation_inverse_image @ SV173 @ SV27 )
!= empty_set ) )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1888]) ).
thf(2065,plain,
! [SV237: $i,SV174: $i,SV28: $i] :
( ( ( subset @ SV28 @ SV174 )
= $false )
| ( ( subset @ ( relation_inverse_image @ SV237 @ SV28 ) @ ( relation_inverse_image @ SV237 @ SV174 ) )
= $true )
| ( ( relation @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1889]) ).
thf(2066,plain,
! [SV176: $i,SV238: $i,SV30: $i] :
( ( ( subset @ SV30 @ SV238 )
= $false )
| ( ( subset @ SV30 @ SV176 )
= $false )
| ( ( subset @ SV30 @ ( set_intersection2 @ SV176 @ SV238 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1890]) ).
thf(2067,plain,
! [SV31: $i,SV239: $i,SV177: $i] :
( ( ( subset @ SV177 @ SV239 )
= $false )
| ( ( subset @ SV31 @ SV177 )
= $false )
| ( ( subset @ SV31 @ SV239 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1891]) ).
thf(2068,plain,
! [SV178: $i,SV33: $i,SV417: $i] :
( ( ( ~ ( function @ SV417 )
| ~ ( relation @ SV417 )
| ~ ( in @ SV33 @ ( relation_dom @ ( relation_composition @ SV417 @ SV178 ) ) )
| ( ( apply @ ( relation_composition @ SV417 @ SV178 ) @ SV33 )
= ( apply @ SV178 @ ( apply @ SV417 @ SV33 ) ) ) )
= $true )
| ( ( function @ SV178 )
= $false )
| ( ( relation @ SV178 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1892]) ).
thf(2069,plain,
! [SV179: $i,SV34: $i,SV418: $i] :
( ( ( ~ ( function @ SV418 )
| ~ ( relation @ SV418 )
| ~ ( in @ SV34 @ ( relation_dom @ SV179 ) )
| ( ( apply @ ( relation_composition @ SV179 @ SV418 ) @ SV34 )
= ( apply @ SV418 @ ( apply @ SV179 @ SV34 ) ) ) )
= $true )
| ( ( function @ SV179 )
= $false )
| ( ( relation @ SV179 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1893]) ).
thf(2070,plain,
! [SV254: $i,SV46: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV46 ) @ ( relation_dom @ SV254 ) ) )
= $true )
| ( ( ( relation_dom @ ( relation_composition @ SV46 @ SV254 ) )
= ( relation_dom @ SV46 ) )
= $true )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1896]) ).
thf(2071,plain,
! [SV255: $i,SV48: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV48 ) @ ( relation_rng @ SV255 ) ) )
= $true )
| ( ( ( relation_rng @ ( relation_composition @ SV255 @ SV48 ) )
= ( relation_rng @ SV48 ) )
= $true )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1898]) ).
thf(2072,plain,
! [SV240: $i,SV50: $i,SV389: $i] :
( ( ( ~ ( element @ SV389 @ SV50 ) )
= $true )
| ( ( ( in @ SV389 @ SV240 )
| ( in @ SV389 @ ( subset_complement @ SV50 @ SV240 ) ) )
= $true )
| ( ( element @ SV240 @ ( powerset @ SV50 ) )
= $false )
| ( ( SV50 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1899]) ).
thf(2073,plain,
! [SV241: $i,SV51: $i,SV189: $i] :
( ( ( in @ SV189 @ ( subset_complement @ SV51 @ SV241 ) )
= $false )
| ( ( ~ ( in @ SV189 @ SV241 ) )
= $true )
| ( ( element @ SV241 @ ( powerset @ SV51 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1900]) ).
thf(2074,plain,
! [SV242: $i,SV191: $i,SV54: $i] :
( ( ( subset @ SV54 @ SV191 )
= $false )
| ( ( disjoint @ SV191 @ SV242 )
= $false )
| ( ( disjoint @ SV54 @ SV242 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1901]) ).
thf(2075,plain,
! [SV59: $i,SV195: $i,SV243: $i] :
( ( ( subset @ SV243 @ SV195 )
= $false )
| ( ( subset @ SV59 @ SV195 )
= $false )
| ( ( subset @ ( set_union2 @ SV59 @ SV243 ) @ SV195 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1902]) ).
thf(2076,plain,
! [SV209: $i,SV79: $i,SV245: $i] :
( ( ( element @ SV245 @ ( powerset @ SV79 ) )
= $false )
| ( ( element @ SV209 @ ( powerset @ SV79 ) )
= $false )
| ( ( element @ ( subset_difference @ SV79 @ SV209 @ SV245 ) @ ( powerset @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1904]) ).
thf(2077,plain,
! [SV221: $i,SV102: $i,SV248: $i] :
( ( ( element @ SV248 @ ( powerset @ SV102 ) )
= $false )
| ( ( element @ SV221 @ ( powerset @ SV102 ) )
= $false )
| ( ( ( subset_difference @ SV102 @ SV221 @ SV248 )
= ( set_difference @ SV221 @ SV248 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1907]) ).
thf(2078,plain,
! [SV249: $i,SV223: $i,SV109: $i] :
( ( ( in @ SV109 @ SV223 )
= $false )
| ( ( element @ SV223 @ ( powerset @ SV249 ) )
= $false )
| ( ( ~ ( empty @ SV249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1908]) ).
thf(2079,plain,
! [SV112: $i,SV322: $i,SV390: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV112 )
| ~ ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV322 )
| ~ ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV390 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV112 )
| ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV390 ) )
| ~ ( ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV322 )
| ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV390 ) ) ) ) )
= $true )
| ( ( SV390
= ( set_intersection2 @ SV112 @ SV322 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1910]) ).
thf(2080,plain,
! [SV323: $i,SV112: $i,SV391: $i] :
( ( ( ( SV391
!= ( set_intersection2 @ SV112 @ SV323 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1008: $i] :
( ~ ( in @ SY1008 @ SV112 )
| ~ ( in @ SY1008 @ SV323 )
| ( in @ SY1008 @ SV391 ) )
| ~ ~ ( ~ ! [SY1009: $i] :
( ~ ( in @ SY1009 @ SV391 )
| ( in @ SY1009 @ SV112 ) )
| ~ ! [SY1010: $i] :
( ~ ( in @ SY1010 @ SV391 )
| ( in @ SY1010 @ SV323 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1911]) ).
thf(2081,plain,
! [SV258: $i,SV324: $i] :
( ( ( ~ ( ! [SY952: $i] :
( ~ ( in @ ( sK47_C @ SV324 @ SV258 ) @ SY952 )
| ~ ( in @ SY952 @ SV258 ) )
| ~ ( in @ ( sK47_C @ SV324 @ SV258 ) @ SV324 ) )
| ~ ( ~ ( ~ ( in @ ( sK47_C @ SV324 @ SV258 ) @ ( sK48_SY487 @ SV324 @ SV258 ) )
| ~ ( in @ ( sK48_SY487 @ SV324 @ SV258 ) @ SV258 ) )
| ( in @ ( sK47_C @ SV324 @ SV258 ) @ SV324 ) ) )
= $false )
| ( ( SV324
= ( union @ SV258 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1912]) ).
thf(2082,plain,
! [SV259: $i,SV325: $i] :
( ( ( SV325
= ( union @ SV259 ) )
= $false )
| ( ( ~ ( ~ ! [SY953: $i] :
( ! [SY881: $i] :
( ~ ( in @ SY953 @ SY881 )
| ~ ( in @ SY881 @ SV259 ) )
| ( in @ SY953 @ SV325 ) )
| ~ ! [SY955: $i] :
( ~ ( in @ SY955 @ SV325 )
| ~ ( ~ ( in @ SY955 @ ( sK46_D @ SY955 @ SV325 @ SV259 ) )
| ~ ( in @ ( sK46_D @ SY955 @ SV325 @ SV259 ) @ SV259 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1913]) ).
thf(2083,plain,
! [SV113: $i,SV225: $i] :
( ( ( ! [SY839: $i] :
( ~ ( relation @ SY839 )
| ~ ( ~ ( ~ ( in @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) @ SV113 )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ SY839 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) ) @ SV225 )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ SY839 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) ) @ SY839 ) )
| ~ ~ ( ~ ( ( in @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) @ SV113 )
| ( in @ ( ordered_pair @ ( sK32_D @ SY839 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) ) @ SY839 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_D @ SY839 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) ) @ SV225 )
| ( in @ ( ordered_pair @ ( sK32_D @ SY839 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SY839 @ SV225 @ SV113 ) ) @ SY839 ) ) ) )
| ( SY839
= ( relation_rng_restriction @ SV113 @ SV225 ) ) ) )
= $true )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1914]) ).
thf(2084,plain,
! [SV225: $i,SV113: $i] :
( ( ( ! [SY840: $i] :
( ~ ( relation @ SY840 )
| ( SY840
!= ( relation_rng_restriction @ SV113 @ SV225 ) )
| ~ ( ~ ! [SY841: $i,SY842: $i] :
( ~ ( in @ SY842 @ SV113 )
| ~ ( in @ ( ordered_pair @ SY841 @ SY842 ) @ SV225 )
| ( in @ ( ordered_pair @ SY841 @ SY842 ) @ SY840 ) )
| ~ ~ ( ~ ! [SY619: $i,SY620: $i] :
( ~ ( in @ ( ordered_pair @ SY619 @ SY620 ) @ SY840 )
| ( in @ SY620 @ SV113 ) )
| ~ ! [SY845: $i,SY846: $i] :
( ~ ( in @ ( ordered_pair @ SY845 @ SY846 ) @ SY840 )
| ( in @ ( ordered_pair @ SY845 @ SY846 ) @ SV225 ) ) ) ) ) )
= $true )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1915]) ).
thf(2085,plain,
! [SV326: $i,SV260: $i] :
( ( ( ~ ( empty @ SV260 ) )
= $true )
| ( ( ~ ( relation @ SV326 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV326 @ SV260 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1916]) ).
thf(2086,plain,
! [SV327: $i,SV261: $i] :
( ( ( ~ ( empty @ SV261 ) )
= $true )
| ( ( ~ ( relation @ SV327 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV327 @ SV261 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1917]) ).
thf(2087,plain,
! [SV419: $i,SV226: $i,SV392: $i,SV114: $i] :
( ( ~ ( in @ SV114 @ SV392 )
| ~ ( in @ SV226 @ SV419 )
| ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SV392 @ SV419 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1918]) ).
thf(2088,plain,
! [SV226: $i,SV114: $i] :
( ( ~ ! [SY849: $i] :
( ! [SY850: $i] :
~ ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SY849 @ SY850 ) )
| ( in @ SV114 @ SY849 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1919]) ).
thf(2089,plain,
! [SV226: $i,SV114: $i] :
( ( ~ ! [SY851: $i,SY852: $i] :
( ~ ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SY851 @ SY852 ) )
| ( in @ SV226 @ SY852 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1919]) ).
thf(2090,plain,
! [SV262: $i,SV328: $i] :
( ( ( ~ ( in @ ( sK72_C @ SV328 @ SV262 ) @ SV262 )
| ~ ( in @ ( sK72_C @ SV328 @ SV262 ) @ SV328 ) )
= $false )
| ( ( disjoint @ SV262 @ SV328 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1920]) ).
thf(2091,plain,
! [SV329: $i,SV263: $i,SV420: $i] :
( ( ( ~ ( in @ SV420 @ SV263 )
| ~ ( in @ SV420 @ SV329 ) )
= $true )
| ( ( ~ ( disjoint @ SV263 @ SV329 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1921]) ).
thf(2092,plain,
! [SV264: $i,SV330: $i] :
( ( ( ~ ( ( ( sK62_C @ SV330 @ SV264 )
!= SV264 )
| ~ ( in @ ( sK62_C @ SV330 @ SV264 ) @ SV330 ) )
| ~ ( ( ( sK62_C @ SV330 @ SV264 )
= SV264 )
| ( in @ ( sK62_C @ SV330 @ SV264 ) @ SV330 ) ) )
= $false )
| ( ( SV330
= ( singleton @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1922]) ).
thf(2093,plain,
! [SV265: $i,SV331: $i] :
( ( ( SV331
= ( singleton @ SV265 ) )
= $false )
| ( ( ~ ( ~ ! [SY957: $i] :
( ( SY957 != SV265 )
| ( in @ SY957 @ SV331 ) )
| ~ ! [SY958: $i] :
( ~ ( in @ SY958 @ SV331 )
| ( SY958 = SV265 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1923]) ).
thf(2094,plain,
! [SV267: $i,SV421: $i] :
( ( ( ~ ( in @ SV421 @ SV267 ) )
= $true )
| ( ( SV267 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1924]) ).
thf(2095,plain,
! [SV115: $i,SV332: $i] :
( ( ( ~ ( subset @ SV332 @ ( sK42_B @ SV115 ) ) )
= $true )
| ( ( are_equipotent @ SV332 @ ( sK42_B @ SV115 ) )
= $true )
| ( ( in @ SV332 @ ( sK42_B @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1925]) ).
thf(2096,plain,
! [SV115: $i] :
( ( ! [SY631: $i] :
( ~ ( ~ ! [SY632: $i] :
( ~ ( subset @ SY632 @ SY631 )
| ( in @ SY632 @ ( sK43_SY481 @ SY631 @ SV115 ) ) )
| ~ ( in @ ( sK43_SY481 @ SY631 @ SV115 ) @ ( sK42_B @ SV115 ) ) )
| ~ ( in @ SY631 @ ( sK42_B @ SV115 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1926]) ).
thf(2097,plain,
! [SV115: $i] :
( ( ~ ( ~ ! [SY633: $i,SY634: $i] :
( ~ ( in @ SY633 @ ( sK42_B @ SV115 ) )
| ~ ( subset @ SY634 @ SY633 )
| ( in @ SY634 @ ( sK42_B @ SV115 ) ) )
| ~ ( in @ SV115 @ ( sK42_B @ SV115 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1927]) ).
thf(2098,plain,
! [SV333: $i,SV268: $i] :
( ( ( subset @ SV268 @ ( singleton @ SV333 ) )
= $false )
| ( ( ( SV268 = empty_set )
| ( SV268
= ( singleton @ SV333 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1928]) ).
thf(2099,plain,
! [SV422: $i] :
( ( ( SV422 != empty_set )
| ! [SY1033: $i] : ( subset @ SV422 @ ( singleton @ SY1033 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1929]) ).
thf(2100,plain,
! [SV423: $i] :
( ( ! [SY1034: $i] :
( ( SV423
!= ( singleton @ SY1034 ) )
| ( subset @ SV423 @ ( singleton @ SY1034 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1930]) ).
thf(2101,plain,
! [SV116: $i] :
( ( ( ~ ~ ( ~ ! [SY635: $i] :
( ~ ( in @ SY635 @ ( relation_dom @ SV116 ) )
| ! [SY636: $i] :
( ( SY636
!= ( apply @ SV116 @ SY635 ) )
| ( in @ ( ordered_pair @ SY635 @ SY636 ) @ SV116 ) ) )
| ~ ! [SY637: $i] :
( ~ ( in @ SY637 @ ( relation_dom @ SV116 ) )
| ! [SY638: $i] :
( ~ ( in @ ( ordered_pair @ SY637 @ SY638 ) @ SV116 )
| ( SY638
= ( apply @ SV116 @ SY637 ) ) ) ) ) )
= $false )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1931]) ).
thf(2102,plain,
! [SV116: $i] :
( ( ( ~ ~ ( ~ ! [SY639: $i] :
( ( in @ SY639 @ ( relation_dom @ SV116 ) )
| ! [SY640: $i] :
( ( SY640
!= ( apply @ SV116 @ SY639 ) )
| ( SY640 = empty_set ) ) )
| ~ ! [SY641: $i] :
( ( in @ SY641 @ ( relation_dom @ SV116 ) )
| ! [SY642: $i] :
( ( SY642 != empty_set )
| ( SY642
= ( apply @ SV116 @ SY641 ) ) ) ) ) )
= $false )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1931]) ).
thf(2103,plain,
! [SV393: $i,SV334: $i,SV117: $i] :
( ( ( ~ ( ~ ( ! [SY1012: $i,SY1013: $i] :
( ~ ( in @ SY1012 @ SV117 )
| ~ ( in @ SY1013 @ SV334 )
| ( ( sK53_D @ SV393 @ SV334 @ SV117 )
!= ( ordered_pair @ SY1012 @ SY1013 ) ) )
| ~ ( in @ ( sK53_D @ SV393 @ SV334 @ SV117 ) @ SV393 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK54_SY491 @ SV393 @ SV334 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK55_SY493 @ SV393 @ SV334 @ SV117 ) @ SV334 ) )
| ( ( sK53_D @ SV393 @ SV334 @ SV117 )
!= ( ordered_pair @ ( sK54_SY491 @ SV393 @ SV334 @ SV117 ) @ ( sK55_SY493 @ SV393 @ SV334 @ SV117 ) ) ) )
| ( in @ ( sK53_D @ SV393 @ SV334 @ SV117 ) @ SV393 ) ) ) )
= $true )
| ( ( SV393
= ( cartesian_product2 @ SV117 @ SV334 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1932]) ).
thf(2104,plain,
! [SV335: $i,SV117: $i,SV394: $i] :
( ( ( ( SV394
!= ( cartesian_product2 @ SV117 @ SV335 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1014: $i] :
( ! [SY964: $i,SY965: $i] :
( ~ ( in @ SY964 @ SV117 )
| ~ ( in @ SY965 @ SV335 )
| ( SY1014
!= ( ordered_pair @ SY964 @ SY965 ) ) )
| ( in @ SY1014 @ SV394 ) )
| ~ ! [SY1017: $i] :
( ~ ( in @ SY1017 @ SV394 )
| ~ ( ~ ~ ( ~ ( in @ ( sK51_E @ SY1017 @ SV394 @ SV335 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK52_SY488 @ SY1017 @ SV394 @ SV335 @ SV117 ) @ SV335 ) )
| ( SY1017
!= ( ordered_pair @ ( sK51_E @ SY1017 @ SV394 @ SV335 @ SV117 ) @ ( sK52_SY488 @ SY1017 @ SV394 @ SV335 @ SV117 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1933]) ).
thf(2105,plain,
! [SV336: $i,SV269: $i] :
( ( ( ( set_difference @ SV269 @ SV336 )
= empty_set )
= $false )
| ( ( subset @ SV269 @ SV336 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1934]) ).
thf(2106,plain,
! [SV337: $i,SV270: $i] :
( ( ( subset @ SV270 @ SV337 )
= $false )
| ( ( ( set_difference @ SV270 @ SV337 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1935]) ).
thf(2107,plain,
! [SV271: $i] :
( ( ( ( ( relation_dom @ SV271 )
!= empty_set ) )
= $true )
| ( ( ( relation_rng @ SV271 )
= empty_set )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1936]) ).
thf(2108,plain,
! [SV272: $i] :
( ( ( ( ( relation_rng @ SV272 )
!= empty_set ) )
= $true )
| ( ( ( relation_dom @ SV272 )
= empty_set )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1937]) ).
thf(2109,plain,
! [SV118: $i,SV338: $i,SV395: $i] :
( ( ( ~ ( function @ SV395 )
| ~ ( relation @ SV395 ) )
= $true )
| ( ( ( SV338
!= ( apply @ SV395 @ SV118 ) )
| ~ ( in @ SV118 @ ( relation_dom @ SV395 ) )
| ( in @ ( ordered_pair @ SV118 @ SV338 ) @ SV395 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1938]) ).
thf(2110,plain,
! [SV118: $i] :
( ( ! [SY655: $i,SY656: $i] :
( ~ ( function @ SY656 )
| ~ ( relation @ SY656 )
| ~ ( in @ ( ordered_pair @ SV118 @ SY655 ) @ SY656 )
| ( SY655
= ( apply @ SY656 @ SV118 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1939]) ).
thf(2111,plain,
! [SV118: $i] :
( ( ! [SY657: $i,SY658: $i] :
( ~ ( function @ SY658 )
| ~ ( relation @ SY658 )
| ~ ( in @ ( ordered_pair @ SV118 @ SY657 ) @ SY658 )
| ( in @ SV118 @ ( relation_dom @ SY658 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1940]) ).
thf(2112,plain,
! [SV273: $i,SV339: $i] :
( ( ( relation @ SV339 )
= $false )
| ( ( ~ ( ~ ( ( ( sK69_C @ SV339 @ SV273 )
!= ( sK70_SY500 @ SV339 @ SV273 ) )
| ~ ( in @ ( sK69_C @ SV339 @ SV273 ) @ SV273 )
| ~ ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 ) )
| ~ ~ ( ~ ( ( ( sK69_C @ SV339 @ SV273 )
= ( sK70_SY500 @ SV339 @ SV273 ) )
| ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 ) )
| ~ ( ( in @ ( sK69_C @ SV339 @ SV273 ) @ SV273 )
| ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 ) ) ) )
| ( SV339
= ( identity_relation @ SV273 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1941]) ).
thf(2113,plain,
! [SV274: $i,SV340: $i] :
( ( ( relation @ SV340 )
= $false )
| ( ( ( SV340
!= ( identity_relation @ SV274 ) )
| ~ ( ~ ! [SY968: $i,SY969: $i] :
( ( SY968 != SY969 )
| ~ ( in @ SY968 @ SV274 )
| ( in @ ( ordered_pair @ SY968 @ SY969 ) @ SV340 ) )
| ~ ~ ( ~ ! [SY970: $i,SY971: $i] :
( ~ ( in @ ( ordered_pair @ SY970 @ SY971 ) @ SV340 )
| ( SY970 = SY971 ) )
| ~ ! [SY972: $i] :
( ! [SY973: $i] :
~ ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV340 )
| ( in @ SY972 @ SV274 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1942]) ).
thf(2114,plain,
! [SV120: $i,SV275: $i] :
( ( ( ~ ! [SY904: $i] :
( ~ ( relation @ SY904 )
| ~ ( ~ ( ! [SY905: $i] :
( ~ ( in @ ( ordered_pair @ ( sK13_D @ SY904 @ SV275 @ SV120 ) @ SY905 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY905 @ ( sK14_SY457 @ SY904 @ SV275 @ SV120 ) ) @ SV275 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_D @ SY904 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SY904 @ SV275 @ SV120 ) ) @ SY904 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_D @ SY904 @ SV275 @ SV120 ) @ ( sK15_SY461 @ SY904 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY461 @ SY904 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SY904 @ SV275 @ SV120 ) ) @ SV275 ) )
| ( in @ ( ordered_pair @ ( sK13_D @ SY904 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SY904 @ SV275 @ SV120 ) ) @ SY904 ) ) )
| ( SY904
= ( relation_composition @ SV120 @ SV275 ) ) )
| ~ ! [SY906: $i] :
( ~ ( relation @ SY906 )
| ( SY906
!= ( relation_composition @ SV120 @ SV275 ) )
| ~ ( ~ ! [SY907: $i,SY908: $i] :
( ! [SY909: $i] :
( ~ ( in @ ( ordered_pair @ SY907 @ SY909 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY909 @ SY908 ) @ SV275 ) )
| ( in @ ( ordered_pair @ SY907 @ SY908 ) @ SY906 ) )
| ~ ! [SY910: $i,SY911: $i] :
( ~ ( in @ ( ordered_pair @ SY910 @ SY911 ) @ SY906 )
| ~ ( ~ ( in @ ( ordered_pair @ SY910 @ ( sK12_F @ SY911 @ SY910 @ SY906 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK12_F @ SY911 @ SY910 @ SY906 @ SV275 @ SV120 ) @ SY911 ) @ SV275 ) ) ) ) ) )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1943]) ).
thf(2115,plain,
! [SV227: $i,SV121: $i] :
( ( ( ! [SY853: $i] :
( ~ ( element @ SY853 @ ( powerset @ SV121 ) )
| ~ ( disjoint @ SV227 @ SY853 )
| ( subset @ SV227 @ ( subset_complement @ SV121 @ SY853 ) ) ) )
= $true )
| ( ( element @ SV227 @ ( powerset @ SV121 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1944]) ).
thf(2116,plain,
! [SV227: $i,SV121: $i] :
( ( ( ! [SY854: $i] :
( ~ ( element @ SY854 @ ( powerset @ SV121 ) )
| ~ ( subset @ SV227 @ ( subset_complement @ SV121 @ SY854 ) )
| ( disjoint @ SV227 @ SY854 ) ) )
= $true )
| ( ( element @ SV227 @ ( powerset @ SV121 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1945]) ).
thf(2117,plain,
! [SV341: $i,SV122: $i,SV396: $i] :
( ( ( ~ ( relation @ SV396 ) )
= $true )
| ( ( ~ ( in @ SV122 @ SV341 )
| ~ ( in @ SV122 @ ( relation_rng @ SV396 ) )
| ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SV341 @ SV396 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1946]) ).
thf(2118,plain,
! [SV122: $i] :
( ( ! [SY673: $i,SY674: $i] :
( ~ ( relation @ SY674 )
| ~ ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SY673 @ SY674 ) ) )
| ( in @ SV122 @ SY673 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1947]) ).
thf(2119,plain,
! [SV122: $i] :
( ( ! [SY675: $i,SY676: $i] :
( ~ ( relation @ SY676 )
| ~ ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SY675 @ SY676 ) ) )
| ( in @ SV122 @ ( relation_rng @ SY676 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1948]) ).
thf(2120,plain,
! [SV123: $i,SV424: $i] :
( ( ( ! [SY1035: $i] :
( ~ ( relation @ SY1035 )
| ~ ( ~ ( ~ ( in @ ( sK34_D @ SY1035 @ SV424 @ SV123 ) @ SV424 )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ SY1035 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SY1035 @ SV424 @ SV123 ) ) @ SV123 )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ SY1035 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SY1035 @ SV424 @ SV123 ) ) @ SY1035 ) )
| ~ ~ ( ~ ( ( in @ ( sK34_D @ SY1035 @ SV424 @ SV123 ) @ SV424 )
| ( in @ ( ordered_pair @ ( sK34_D @ SY1035 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SY1035 @ SV424 @ SV123 ) ) @ SY1035 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK34_D @ SY1035 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SY1035 @ SV424 @ SV123 ) ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK34_D @ SY1035 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SY1035 @ SV424 @ SV123 ) ) @ SY1035 ) ) ) )
| ( SY1035
= ( relation_dom_restriction @ SV123 @ SV424 ) ) ) )
= $true )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1949]) ).
thf(2121,plain,
! [SV425: $i,SV123: $i] :
( ( ( ! [SY1036: $i] :
( ~ ( relation @ SY1036 )
| ( SY1036
!= ( relation_dom_restriction @ SV123 @ SV425 ) )
| ~ ( ~ ! [SY1037: $i,SY1038: $i] :
( ~ ( in @ SY1037 @ SV425 )
| ~ ( in @ ( ordered_pair @ SY1037 @ SY1038 ) @ SV123 )
| ( in @ ( ordered_pair @ SY1037 @ SY1038 ) @ SY1036 ) )
| ~ ~ ( ~ ! [SY1039: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SY1039 @ SX4 ) @ SY1036 )
| ( in @ SY1039 @ SV425 ) )
| ~ ! [SY685: $i,SY686: $i] :
( ~ ( in @ ( ordered_pair @ SY685 @ SY686 ) @ SY1036 )
| ( in @ ( ordered_pair @ SY685 @ SY686 ) @ SV123 ) ) ) ) ) )
= $true )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1950]) ).
thf(2122,plain,
! [SV124: $i,SV426: $i] :
( ( ( ~ ( relation @ SV426 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_C @ SV426 @ SV124 ) @ ( sK17_SY462 @ SV426 @ SV124 ) ) @ SV426 )
| ~ ( in @ ( ordered_pair @ ( sK17_SY462 @ SV426 @ SV124 ) @ ( sK16_C @ SV426 @ SV124 ) ) @ SV124 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK16_C @ SV426 @ SV124 ) @ ( sK17_SY462 @ SV426 @ SV124 ) ) @ SV426 )
| ( in @ ( ordered_pair @ ( sK17_SY462 @ SV426 @ SV124 ) @ ( sK16_C @ SV426 @ SV124 ) ) @ SV124 ) ) )
| ( SV426
= ( relation_inverse @ SV124 ) ) )
= $true )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1951]) ).
thf(2123,plain,
! [SV124: $i,SV427: $i] :
( ( ( ~ ( relation @ SV427 )
| ( SV427
!= ( relation_inverse @ SV124 ) )
| ~ ( ~ ! [SY1043: $i,SY1044: $i] :
( ~ ( in @ ( ordered_pair @ SY1043 @ SY1044 ) @ SV427 )
| ( in @ ( ordered_pair @ SY1044 @ SY1043 ) @ SV124 ) )
| ~ ! [SY1045: $i,SY1046: $i] :
( ~ ( in @ ( ordered_pair @ SY1046 @ SY1045 ) @ SV124 )
| ( in @ ( ordered_pair @ SY1045 @ SY1046 ) @ SV427 ) ) ) )
= $true )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1952]) ).
thf(2124,plain,
! [SV342: $i,SV276: $i] :
( ( ( element @ SV276 @ ( powerset @ SV342 ) )
= $false )
| ( ( subset @ SV276 @ SV342 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1953]) ).
thf(2125,plain,
! [SV343: $i,SV277: $i] :
( ( ( subset @ SV277 @ SV343 )
= $false )
| ( ( element @ SV277 @ ( powerset @ SV343 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1954]) ).
thf(2126,plain,
! [SV344: $i,SV278: $i] :
( ( ( in @ SV278 @ SV344 )
= $false )
| ( ( subset @ ( singleton @ SV278 ) @ SV344 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1955]) ).
thf(2127,plain,
! [SV345: $i,SV279: $i] :
( ( ( subset @ ( singleton @ SV279 ) @ SV345 )
= $false )
| ( ( in @ SV279 @ SV345 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1956]) ).
thf(2128,plain,
! [SV346: $i,SV280: $i] :
( ( ( ( set_intersection2 @ SV280 @ SV346 )
= empty_set )
= $false )
| ( ( disjoint @ SV280 @ SV346 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1957]) ).
thf(2129,plain,
! [SV347: $i,SV281: $i] :
( ( ( disjoint @ SV281 @ SV347 )
= $false )
| ( ( ( set_intersection2 @ SV281 @ SV347 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1958]) ).
thf(2130,plain,
! [SV282: $i,SV348: $i] :
( ( ( ~ ( function @ SV348 ) )
= $true )
| ( ( ~ ( relation @ SV348 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK38_C @ SV348 @ SV282 ) @ SV282 )
| ~ ( ( ( apply @ SV348 @ ( sK38_C @ SV348 @ SV282 ) )
!= ( sK38_C @ SV348 @ SV282 ) ) ) )
| ( ( relation_dom @ SV348 )
!= SV282 )
| ( SV348
= ( identity_relation @ SV282 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1959]) ).
thf(2131,plain,
! [SV428: $i] :
( ( ! [SY1047: $i] :
( ~ ( function @ SY1047 )
| ~ ( relation @ SY1047 )
| ( SY1047
!= ( identity_relation @ SV428 ) )
| ! [SY1048: $i] :
( ~ ( in @ SY1048 @ SV428 )
| ( ( apply @ SY1047 @ SY1048 )
= SY1048 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1960]) ).
thf(2132,plain,
! [SV429: $i] :
( ( ! [SY1049: $i] :
( ~ ( function @ SY1049 )
| ~ ( relation @ SY1049 )
| ( SY1049
!= ( identity_relation @ SV429 ) )
| ( ( relation_dom @ SY1049 )
= SV429 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1961]) ).
thf(2133,plain,
! [SV349: $i,SV283: $i] :
( ( ( ( set_difference @ SV283 @ SV349 )
= empty_set )
= $false )
| ( ( subset @ SV283 @ SV349 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1962]) ).
thf(2134,plain,
! [SV350: $i,SV284: $i] :
( ( ( subset @ SV284 @ SV350 )
= $false )
| ( ( ( set_difference @ SV284 @ SV350 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1963]) ).
thf(2135,plain,
! [SV351: $i,SV285: $i] :
( ( ( ~ ( subset @ SV285 @ SV351 ) )
= $true )
| ( ( ~ ( subset @ SV351 @ SV285 ) )
= $true )
| ( ( SV285 = SV351 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1964]) ).
thf(2136,plain,
! [SV430: $i] :
( ( ! [SY1050: $i] :
( ( SV430 != SY1050 )
| ( subset @ SV430 @ SY1050 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1965]) ).
thf(2137,plain,
! [SV431: $i] :
( ( ! [SY1051: $i] :
( ( SV431 != SY1051 )
| ( subset @ SY1051 @ SV431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1966]) ).
thf(2138,plain,
! [SV125: $i,SV432: $i] :
( ( ( ! [SY1052: $i] :
( ~ ( ~ ( ! [SY1053: $i] :
( ~ ( in @ ( ordered_pair @ SY1053 @ ( sK30_D @ SY1052 @ SV432 @ SV125 ) ) @ SV125 )
| ~ ( in @ SY1053 @ SV432 ) )
| ~ ( in @ ( sK30_D @ SY1052 @ SV432 @ SV125 ) @ SY1052 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_SY471 @ SY1052 @ SV432 @ SV125 ) @ ( sK30_D @ SY1052 @ SV432 @ SV125 ) ) @ SV125 )
| ~ ( in @ ( sK31_SY471 @ SY1052 @ SV432 @ SV125 ) @ SV432 ) )
| ( in @ ( sK30_D @ SY1052 @ SV432 @ SV125 ) @ SY1052 ) ) )
| ( SY1052
= ( relation_image @ SV125 @ SV432 ) ) ) )
= $true )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2139,plain,
! [SV433: $i,SV125: $i] :
( ( ( ! [SY1054: $i] :
( ( SY1054
!= ( relation_image @ SV125 @ SV433 ) )
| ~ ( ~ ! [SY1055: $i] :
( ! [SY1056: $i] :
( ~ ( in @ ( ordered_pair @ SY1056 @ SY1055 ) @ SV125 )
| ~ ( in @ SY1056 @ SV433 ) )
| ( in @ SY1055 @ SY1054 ) )
| ~ ! [SY1057: $i] :
( ~ ( in @ SY1057 @ SY1054 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK29_E @ SY1057 @ SY1054 @ SV433 @ SV125 ) @ SY1057 ) @ SV125 )
| ~ ( in @ ( sK29_E @ SY1057 @ SY1054 @ SV433 @ SV125 ) @ SV433 ) ) ) ) ) )
= $true )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1968]) ).
thf(2140,plain,
! [SV352: $i,SV126: $i,SV397: $i] :
( ( ( ~ ( relation @ SV397 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV126 @ SV352 ) @ SV397 )
| ( in @ SV126 @ ( relation_field @ SV397 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1969]) ).
thf(2141,plain,
! [SV353: $i,SV126: $i,SV398: $i] :
( ( ( ~ ( relation @ SV398 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV126 @ SV353 ) @ SV398 )
| ( in @ SV353 @ ( relation_field @ SV398 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1970]) ).
thf(2142,plain,
! [SV228: $i,SV399: $i,SV127: $i,SV434: $i] :
( ( ~ ( relation @ SV434 )
| ~ ( in @ SV127 @ SV399 )
| ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ SV434 )
| ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SV399 ) @ SV434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1971]) ).
thf(2143,plain,
! [SV228: $i,SV127: $i] :
( ( ~ ! [SY857: $i,SY858: $i] :
( ~ ( relation @ SY858 )
| ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SY857 ) @ SY858 ) )
| ( in @ SV127 @ SY857 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1972]) ).
thf(2144,plain,
! [SV228: $i,SV127: $i] :
( ( ~ ! [SY859: $i,SY860: $i] :
( ~ ( relation @ SY860 )
| ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SY859 ) @ SY860 ) )
| ( in @ ( ordered_pair @ SV127 @ SV228 ) @ SY860 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1972]) ).
thf(2145,plain,
! [SV354: $i,SV286: $i] :
( ( ( in @ SV286 @ SV354 )
= $false )
| ( ( subset @ ( singleton @ SV286 ) @ SV354 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1973]) ).
thf(2146,plain,
! [SV355: $i,SV287: $i] :
( ( ( subset @ ( singleton @ SV287 ) @ SV355 )
= $false )
| ( ( in @ SV287 @ SV355 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1974]) ).
thf(2147,plain,
! [SV356: $i,SV400: $i,SV128: $i] :
( ( ( ~ ( in @ SV128 @ SV400 )
| ~ ( in @ SV356 @ SV400 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV128 @ SV356 ) @ SV400 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1975]) ).
thf(2148,plain,
! [SV128: $i] :
( ( ! [SY714: $i,SY715: $i] :
( ~ ( subset @ ( unordered_pair @ SV128 @ SY714 ) @ SY715 )
| ( in @ SV128 @ SY715 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1976]) ).
thf(2149,plain,
! [SV128: $i] :
( ( ! [SY716: $i,SY717: $i] :
( ~ ( subset @ ( unordered_pair @ SV128 @ SY716 ) @ SY717 )
| ( in @ SY716 @ SY717 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1977]) ).
thf(2150,plain,
! [SV435: $i] :
( ( ( empty @ SV435 )
| ! [SY1058: $i] :
( ~ ( element @ SY1058 @ SV435 )
| ( in @ SY1058 @ SV435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1978]) ).
thf(2151,plain,
! [SV436: $i] :
( ( ( empty @ SV436 )
| ! [SY1059: $i] :
( ~ ( in @ SY1059 @ SV436 )
| ( element @ SY1059 @ SV436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1979]) ).
thf(2152,plain,
! [SV437: $i] :
( ( ~ ( empty @ SV437 )
| ! [SY1060: $i] :
( ~ ( element @ SY1060 @ SV437 )
| ( empty @ SY1060 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1980]) ).
thf(2153,plain,
! [SV438: $i] :
( ( ~ ( empty @ SV438 )
| ! [SY1061: $i] :
( ~ ( empty @ SY1061 )
| ( element @ SY1061 @ SV438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1981]) ).
thf(2154,plain,
! [SV129: $i,SV439: $i] :
( ( ( ~ ( ~ ( ! [SY1062: $i] :
~ ( in @ ( ordered_pair @ SY1062 @ ( sK19_C @ SV439 @ SV129 ) ) @ SV129 )
| ~ ( in @ ( sK19_C @ SV439 @ SV129 ) @ SV439 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_SY464 @ SV439 @ SV129 ) @ ( sK19_C @ SV439 @ SV129 ) ) @ SV129 )
| ( in @ ( sK19_C @ SV439 @ SV129 ) @ SV439 ) ) )
| ( SV439
= ( relation_rng @ SV129 ) ) )
= $true )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1982]) ).
thf(2155,plain,
! [SV129: $i,SV440: $i] :
( ( ( ( SV440
!= ( relation_rng @ SV129 ) )
| ~ ( ~ ! [SY1063: $i] :
( ! [SY722: $i] :
~ ( in @ ( ordered_pair @ SY722 @ SY1063 ) @ SV129 )
| ( in @ SY1063 @ SV440 ) )
| ~ ! [SY1065: $i] :
( ~ ( in @ SY1065 @ SV440 )
| ( in @ ( ordered_pair @ ( sK18_D @ SY1065 @ SV440 @ SV129 ) @ SY1065 ) @ SV129 ) ) ) )
= $true )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2156,plain,
! [SV357: $i,SV288: $i] :
( ( ( ( set_difference @ SV288 @ ( singleton @ SV357 ) )
= SV288 )
= $false )
| ( ( ~ ( in @ SV357 @ SV288 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1986]) ).
thf(2157,plain,
! [SV360: $i,SV293: $i,SV441: $i] :
( ( ( ~ ( in @ SV441 @ ( set_intersection2 @ SV293 @ SV360 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV293 @ SV360 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1989]) ).
thf(2158,plain,
! [SV130: $i,SV229: $i] :
( ( ( in @ ( sK73_C @ SV229 @ SV130 ) @ SV229 )
= $false )
| ( ( element @ SV130 @ ( powerset @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1991]) ).
thf(2159,plain,
! [SV131: $i,SV442: $i] :
( ( ( ! [SY1066: $i] :
( ~ ( ~ ( ! [SY1067: $i] :
( ~ ( in @ ( ordered_pair @ ( sK27_D @ SY1066 @ SV442 @ SV131 ) @ SY1067 ) @ SV131 )
| ~ ( in @ SY1067 @ SV442 ) )
| ~ ( in @ ( sK27_D @ SY1066 @ SV442 @ SV131 ) @ SY1066 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK27_D @ SY1066 @ SV442 @ SV131 ) @ ( sK28_SY469 @ SY1066 @ SV442 @ SV131 ) ) @ SV131 )
| ~ ( in @ ( sK28_SY469 @ SY1066 @ SV442 @ SV131 ) @ SV442 ) )
| ( in @ ( sK27_D @ SY1066 @ SV442 @ SV131 ) @ SY1066 ) ) )
| ( SY1066
= ( relation_inverse_image @ SV131 @ SV442 ) ) ) )
= $true )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1992]) ).
thf(2160,plain,
! [SV443: $i,SV131: $i] :
( ( ( ! [SY1068: $i] :
( ( SY1068
!= ( relation_inverse_image @ SV131 @ SV443 ) )
| ~ ( ~ ! [SY1069: $i] :
( ! [SY1070: $i] :
( ~ ( in @ ( ordered_pair @ SY1069 @ SY1070 ) @ SV131 )
| ~ ( in @ SY1070 @ SV443 ) )
| ( in @ SY1069 @ SY1068 ) )
| ~ ! [SY1071: $i] :
( ~ ( in @ SY1071 @ SY1068 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1071 @ ( sK26_E @ SY1071 @ SY1068 @ SV443 @ SV131 ) ) @ SV131 )
| ~ ( in @ ( sK26_E @ SY1071 @ SY1068 @ SV443 @ SV131 ) @ SV443 ) ) ) ) ) )
= $true )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1993]) ).
thf(2161,plain,
! [SV361: $i,SV294: $i] :
( ( ( ( set_difference @ SV294 @ SV361 )
= SV294 )
= $false )
| ( ( disjoint @ SV294 @ SV361 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1994]) ).
thf(2162,plain,
! [SV362: $i,SV295: $i] :
( ( ( disjoint @ SV295 @ SV362 )
= $false )
| ( ( ( set_difference @ SV295 @ SV362 )
= SV295 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1995]) ).
thf(2163,plain,
! [SV296: $i] :
( ( ( ~ ! [SY931: $i,SY932: $i] :
( ( sK68_B @ SV296 )
!= ( ordered_pair @ SY931 @ SY932 ) ) )
= $false )
| ( ( relation @ SV296 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1996]) ).
thf(2164,plain,
! [SV296: $i] :
( ( ( ~ ( in @ ( sK68_B @ SV296 ) @ SV296 ) )
= $false )
| ( ( relation @ SV296 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1996]) ).
thf(2165,plain,
! [SV297: $i,SV444: $i] :
( ( ( ( SV444
= ( ordered_pair @ ( sK66_C @ SV444 @ SV297 ) @ ( sK67_SY497 @ SV444 @ SV297 ) ) )
| ~ ( in @ SV444 @ SV297 ) )
= $true )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1997]) ).
thf(2166,plain,
! [SV363: $i,SV132: $i,SV401: $i] :
( ( ( ~ ( relation @ SV401 ) )
= $true )
| ( ( ~ ( in @ SV132 @ SV363 )
| ~ ( in @ SV132 @ ( relation_dom @ SV401 ) )
| ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SV401 @ SV363 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1998]) ).
thf(2167,plain,
! [SV132: $i] :
( ( ! [SY735: $i,SY736: $i] :
( ~ ( relation @ SY736 )
| ~ ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SY736 @ SY735 ) ) )
| ( in @ SV132 @ SY735 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1999]) ).
thf(2168,plain,
! [SV132: $i] :
( ( ! [SY737: $i,SY738: $i] :
( ~ ( relation @ SY738 )
| ~ ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SY738 @ SY737 ) ) )
| ( in @ SV132 @ ( relation_dom @ SY738 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2000]) ).
thf(2169,plain,
! [SV364: $i,SV133: $i,SV402: $i] :
( ( ( ~ ( relation @ SV402 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV133 @ SV364 ) @ SV402 )
| ( in @ SV133 @ ( relation_dom @ SV402 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2001]) ).
thf(2170,plain,
! [SV365: $i,SV133: $i,SV403: $i] :
( ( ( ~ ( relation @ SV403 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV133 @ SV365 ) @ SV403 )
| ( in @ SV365 @ ( relation_rng @ SV403 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2002]) ).
thf(2171,plain,
! [SV134: $i,SV445: $i] :
( ( ( ~ ( ~ ( ! [SY1072: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SV445 @ SV134 ) @ SY1072 ) @ SV134 )
| ~ ( in @ ( sK22_C @ SV445 @ SV134 ) @ SV445 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SV445 @ SV134 ) @ ( sK23_SY466 @ SV445 @ SV134 ) ) @ SV134 )
| ( in @ ( sK22_C @ SV445 @ SV134 ) @ SV445 ) ) )
| ( SV445
= ( relation_dom @ SV134 ) ) )
= $true )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2003]) ).
thf(2172,plain,
! [SV134: $i,SV446: $i] :
( ( ( ( SV446
!= ( relation_dom @ SV134 ) )
| ~ ( ~ ! [SY1073: $i] :
( ! [SY747: $i] :
~ ( in @ ( ordered_pair @ SY1073 @ SY747 ) @ SV134 )
| ( in @ SY1073 @ SV446 ) )
| ~ ! [SY1075: $i] :
( ~ ( in @ SY1075 @ SV446 )
| ( in @ ( ordered_pair @ SY1075 @ ( sK21_D @ SY1075 @ SV446 @ SV134 ) ) @ SV134 ) ) ) )
= $true )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2004]) ).
thf(2173,plain,
! [SV135: $i,SV366: $i,SV404: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK57_D @ SV404 @ SV366 @ SV135 ) @ SV404 )
| ( ( sK57_D @ SV404 @ SV366 @ SV135 )
!= SV135 ) )
| ~ ( ~ ( in @ ( sK57_D @ SV404 @ SV366 @ SV135 ) @ SV404 )
| ( ( sK57_D @ SV404 @ SV366 @ SV135 )
!= SV366 ) ) )
| ~ ( ( in @ ( sK57_D @ SV404 @ SV366 @ SV135 ) @ SV404 )
| ( ( sK57_D @ SV404 @ SV366 @ SV135 )
= SV135 )
| ( ( sK57_D @ SV404 @ SV366 @ SV135 )
= SV366 ) ) ) )
= $true )
| ( ( SV404
= ( unordered_pair @ SV135 @ SV366 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2005]) ).
thf(2174,plain,
! [SV367: $i,SV135: $i,SV405: $i] :
( ( ( ( SV405
!= ( unordered_pair @ SV135 @ SV367 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1019: $i] :
( ~ ( in @ SY1019 @ SV405 )
| ( SY1019 = SV135 )
| ( SY1019 = SV367 ) )
| ~ ~ ( ~ ! [SY1020: $i] :
( ( SY1020 != SV135 )
| ( in @ SY1020 @ SV405 ) )
| ~ ! [SY1021: $i] :
( ( SY1021 != SV367 )
| ( in @ SY1021 @ SV405 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2006]) ).
thf(2175,plain,
! [SV136: $i,SV447: $i] :
( ( ( ~ ( relation @ SV447 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV136 )
| ~ ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV447 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV136 )
| ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV447 ) ) )
| ( SV136 = SV447 ) )
= $true )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2007]) ).
thf(2176,plain,
! [SV136: $i,SV448: $i] :
( ( ( ~ ( relation @ SV448 )
| ( SV136 != SV448 )
| ~ ( ~ ! [SY1076: $i,SY1077: $i] :
( ~ ( in @ ( ordered_pair @ SY1076 @ SY1077 ) @ SV136 )
| ( in @ ( ordered_pair @ SY1076 @ SY1077 ) @ SV448 ) )
| ~ ! [SY1078: $i,SY1079: $i] :
( ~ ( in @ ( ordered_pair @ SY1078 @ SY1079 ) @ SV448 )
| ( in @ ( ordered_pair @ SY1078 @ SY1079 ) @ SV136 ) ) ) )
= $true )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2008]) ).
thf(2177,plain,
! [SV368: $i,SV298: $i] :
( ( ( ~ ( function @ SV298 )
| ~ ( relation @ SV298 )
| ~ ( relation @ SV368 ) )
= $true )
| ( ( ~ ( function @ SV368 ) )
= $true )
| ( ( function @ ( relation_composition @ SV298 @ SV368 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2009]) ).
thf(2178,plain,
! [SV369: $i,SV299: $i] :
( ( ( ~ ( function @ SV299 )
| ~ ( relation @ SV299 )
| ~ ( relation @ SV369 ) )
= $true )
| ( ( ~ ( function @ SV369 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV299 @ SV369 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2010]) ).
thf(2179,plain,
! [SV230: $i,SV137: $i] :
( ( ( ~ ! [SY861: $i] :
( ~ ( function @ SY861 )
| ~ ( relation @ SY861 )
| ~ ( in @ SV137 @ ( relation_dom @ SY861 ) )
| ~ ( in @ ( apply @ SY861 @ SV137 ) @ ( relation_dom @ SV230 ) )
| ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY861 @ SV230 ) ) ) )
| ~ ~ ( ~ ! [SY862: $i] :
( ~ ( function @ SY862 )
| ~ ( relation @ SY862 )
| ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY862 @ SV230 ) ) )
| ( in @ SV137 @ ( relation_dom @ SY862 ) ) )
| ~ ! [SY863: $i] :
( ~ ( function @ SY863 )
| ~ ( relation @ SY863 )
| ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY863 @ SV230 ) ) )
| ( in @ ( apply @ SY863 @ SV137 ) @ ( relation_dom @ SV230 ) ) ) ) )
= $false )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2011]) ).
thf(2180,plain,
! [SV138: $i,SV370: $i] :
( ( ( ~ ( subset @ SV370 @ ( sK41_B @ SV138 ) ) )
= $true )
| ( ( are_equipotent @ SV370 @ ( sK41_B @ SV138 ) )
= $true )
| ( ( in @ SV370 @ ( sK41_B @ SV138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2012]) ).
thf(2181,plain,
! [SV138: $i] :
( ( ! [SY767: $i] :
( ~ ( in @ SY767 @ ( sK41_B @ SV138 ) )
| ( in @ ( powerset @ SY767 ) @ ( sK41_B @ SV138 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2013]) ).
thf(2182,plain,
! [SV138: $i] :
( ( ~ ( ~ ! [SY768: $i,SY769: $i] :
( ~ ( in @ SY768 @ ( sK41_B @ SV138 ) )
| ~ ( subset @ SY769 @ SY768 )
| ( in @ SY769 @ ( sK41_B @ SV138 ) ) )
| ~ ( in @ SV138 @ ( sK41_B @ SV138 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2014]) ).
thf(2183,plain,
! [SV139: $i,SV449: $i] :
( ( ( ~ ( relation @ SV449 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV449 @ SV139 ) @ ( sK25_SY467 @ SV449 @ SV139 ) ) @ SV139 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SV449 @ SV139 ) @ ( sK25_SY467 @ SV449 @ SV139 ) ) @ SV449 ) )
| ( subset @ SV139 @ SV449 ) )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2015]) ).
thf(2184,plain,
! [SV139: $i,SV450: $i] :
( ( ( ~ ( relation @ SV450 )
| ~ ( subset @ SV139 @ SV450 )
| ! [SY1080: $i,SY1081: $i] :
( ~ ( in @ ( ordered_pair @ SY1080 @ SY1081 ) @ SV139 )
| ( in @ ( ordered_pair @ SY1080 @ SY1081 ) @ SV450 ) ) )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2016]) ).
thf(2185,plain,
! [SV300: $i,SV371: $i] :
( ( ( ~ ( ~ ( in @ ( sK60_C @ SV371 @ SV300 ) @ SV371 )
| ~ ( subset @ ( sK60_C @ SV371 @ SV300 ) @ SV300 ) )
| ~ ( ( in @ ( sK60_C @ SV371 @ SV300 ) @ SV371 )
| ( subset @ ( sK60_C @ SV371 @ SV300 ) @ SV300 ) ) )
= $false )
| ( ( SV371
= ( powerset @ SV300 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2017]) ).
thf(2186,plain,
! [SV301: $i,SV372: $i] :
( ( ( SV372
= ( powerset @ SV301 ) )
= $false )
| ( ( ~ ( ~ ! [SY987: $i] :
( ~ ( in @ SY987 @ SV372 )
| ( subset @ SY987 @ SV301 ) )
| ~ ! [SY988: $i] :
( ~ ( subset @ SY988 @ SV301 )
| ( in @ SY988 @ SV372 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2018]) ).
thf(2187,plain,
! [SV373: $i,SV302: $i] :
( ( ( ~ ( empty @ SV302 ) )
= $true )
| ( ( ~ ( relation @ SV373 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV302 @ SV373 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2019]) ).
thf(2188,plain,
! [SV374: $i,SV303: $i] :
( ( ( ~ ( empty @ SV303 ) )
= $true )
| ( ( ~ ( relation @ SV374 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV303 @ SV374 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2020]) ).
thf(2189,plain,
! [SV140: $i,SV451: $i] :
( ( ( ~ ( relation @ SV451 )
| ~ ( subset @ SV140 @ SV451 )
| ( subset @ ( relation_dom @ SV140 ) @ ( relation_dom @ SV451 ) ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2021]) ).
thf(2190,plain,
! [SV140: $i,SV452: $i] :
( ( ( ~ ( relation @ SV452 )
| ~ ( subset @ SV140 @ SV452 )
| ( subset @ ( relation_rng @ SV140 ) @ ( relation_rng @ SV452 ) ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2022]) ).
thf(2191,plain,
! [SV375: $i,SV142: $i,SV406: $i] :
( ( ( ~ ( relation @ SV406 ) )
= $true )
| ( ( ! [SY1022: $i] :
( ~ ( in @ SY1022 @ ( relation_rng @ SV406 ) )
| ~ ( in @ ( ordered_pair @ SV142 @ SY1022 ) @ SV406 )
| ~ ( in @ SY1022 @ SV375 ) )
| ( in @ SV142 @ ( relation_inverse_image @ SV406 @ SV375 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2024]) ).
thf(2192,plain,
! [SV376: $i,SV142: $i,SV407: $i] :
( ( ( ~ ( relation @ SV407 ) )
= $true )
| ( ( ~ ( in @ SV142 @ ( relation_inverse_image @ SV407 @ SV376 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK39_D @ SV407 @ SV376 @ SV142 ) @ ( relation_rng @ SV407 ) )
| ~ ( in @ ( ordered_pair @ SV142 @ ( sK39_D @ SV407 @ SV376 @ SV142 ) ) @ SV407 ) )
| ~ ( in @ ( sK39_D @ SV407 @ SV376 @ SV142 ) @ SV376 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2025]) ).
thf(2193,plain,
! [SV453: $i] :
( ( ( SV453 = empty_set )
| ! [SY1082: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK65_SY495 @ SY1082 @ SV453 ) @ SV453 )
| ~ ~ ( in @ ( sK64_C @ SY1082 @ SV453 ) @ ( sK65_SY495 @ SY1082 @ SV453 ) ) )
| ~ ( in @ ( sK64_C @ SY1082 @ SV453 ) @ SY1082 ) )
| ~ ( ! [SY1083: $i] :
( ~ ( in @ SY1083 @ SV453 )
| ( in @ ( sK64_C @ SY1082 @ SV453 ) @ SY1083 ) )
| ( in @ ( sK64_C @ SY1082 @ SV453 ) @ SY1082 ) ) )
| ( SY1082
= ( set_meet @ SV453 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2026]) ).
thf(2194,plain,
! [SV454: $i] :
( ( ( SV454 = empty_set )
| ! [SY1084: $i] :
( ( SY1084
!= ( set_meet @ SV454 ) )
| ~ ( ~ ! [SY1085: $i] :
( ~ ( ~ ( in @ ( sK63_D @ SY1085 @ SY1084 @ SV454 ) @ SV454 )
| ~ ~ ( in @ SY1085 @ ( sK63_D @ SY1085 @ SY1084 @ SV454 ) ) )
| ( in @ SY1085 @ SY1084 ) )
| ~ ! [SY1086: $i] :
( ~ ( in @ SY1086 @ SY1084 )
| ! [SY1087: $i] :
( ~ ( in @ SY1087 @ SV454 )
| ( in @ SY1086 @ SY1087 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2027]) ).
thf(2195,plain,
! [SV455: $i] :
( ( ( SV455 != empty_set )
| ! [SY1088: $i] :
( ( SY1088
!= ( set_meet @ SV455 ) )
| ( SY1088 = empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(2196,plain,
! [SV456: $i] :
( ( ( SV456 != empty_set )
| ! [SY1089: $i] :
( ( SY1089 != empty_set )
| ( SY1089
= ( set_meet @ SV456 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(2197,plain,
! [SV377: $i,SV308: $i] :
( ( ( SV308 = SV377 )
= $true )
| ( ( ~ ( subset @ SV308 @ SV377 ) )
= $true )
| ( ( proper_subset @ SV308 @ SV377 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2032]) ).
thf(2198,plain,
! [SV457: $i] :
( ( ! [SY1090: $i] :
( ~ ( proper_subset @ SV457 @ SY1090 )
| ( SV457 != SY1090 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2033]) ).
thf(2199,plain,
! [SV458: $i] :
( ( ! [SY1091: $i] :
( ~ ( proper_subset @ SV458 @ SY1091 )
| ( subset @ SV458 @ SY1091 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2034]) ).
thf(2200,plain,
! [SV459: $i,SV231: $i,SV408: $i,SV143: $i] :
( ( ~ ( in @ SV143 @ SV408 )
| ~ ( in @ SV231 @ SV459 )
| ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SV408 @ SV459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2201,plain,
! [SV231: $i,SV143: $i] :
( ( ~ ! [SY866: $i] :
( ! [SY867: $i] :
~ ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SY866 @ SY867 ) )
| ( in @ SV143 @ SY866 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2036]) ).
thf(2202,plain,
! [SV231: $i,SV143: $i] :
( ( ~ ! [SY868: $i,SY869: $i] :
( ~ ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SY868 @ SY869 ) )
| ( in @ SV231 @ SY869 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2036]) ).
thf(2203,plain,
! [SV144: $i,SV378: $i,SV409: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV409 )
| ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV144 ) )
| ~ ( ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV409 )
| ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV378 ) ) )
| ~ ( ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV409 )
| ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV144 )
| ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV378 ) ) ) )
= $true )
| ( ( SV409
= ( set_union2 @ SV144 @ SV378 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2037]) ).
thf(2204,plain,
! [SV379: $i,SV144: $i,SV410: $i] :
( ( ( ( SV410
!= ( set_union2 @ SV144 @ SV379 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1024: $i] :
( ~ ( in @ SY1024 @ SV410 )
| ( in @ SY1024 @ SV144 )
| ( in @ SY1024 @ SV379 ) )
| ~ ~ ( ~ ! [SY1025: $i] :
( ~ ( in @ SY1025 @ SV144 )
| ( in @ SY1025 @ SV410 ) )
| ~ ! [SY1026: $i] :
( ~ ( in @ SY1026 @ SV379 )
| ( in @ SY1026 @ SV410 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2038]) ).
thf(2205,plain,
! [SV380: $i,SV145: $i,SV411: $i] :
( ( ( ~ ( relation @ SV411 ) )
= $true )
| ( ( ! [SY1027: $i] :
( ~ ( in @ SY1027 @ ( relation_dom @ SV411 ) )
| ~ ( in @ ( ordered_pair @ SY1027 @ SV145 ) @ SV411 )
| ~ ( in @ SY1027 @ SV380 ) )
| ( in @ SV145 @ ( relation_image @ SV411 @ SV380 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2041]) ).
thf(2206,plain,
! [SV381: $i,SV145: $i,SV412: $i] :
( ( ( ~ ( relation @ SV412 ) )
= $true )
| ( ( ~ ( in @ SV145 @ ( relation_image @ SV412 @ SV381 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK40_D @ SV412 @ SV381 @ SV145 ) @ ( relation_dom @ SV412 ) )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV412 @ SV381 @ SV145 ) @ SV145 ) @ SV412 ) )
| ~ ( in @ ( sK40_D @ SV412 @ SV381 @ SV145 ) @ SV381 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2042]) ).
thf(2207,plain,
! [SV382: $i,SV146: $i] :
( ( ( subset @ SV146 @ SV382 )
= $false )
| ( ( ! [SY1000: $i] : ( subset @ ( cartesian_product2 @ SV146 @ SY1000 ) @ ( cartesian_product2 @ SV382 @ SY1000 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2043]) ).
thf(2208,plain,
! [SV383: $i,SV146: $i] :
( ( ( subset @ SV146 @ SV383 )
= $false )
| ( ( ! [SY1001: $i] : ( subset @ ( cartesian_product2 @ SY1001 @ SV146 ) @ ( cartesian_product2 @ SY1001 @ SV383 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2044]) ).
thf(2209,plain,
! [SV147: $i,SV232: $i] :
( ( ( ~ ( in @ ( sK44_C @ SV232 @ SV147 ) @ SV147 ) )
= $true )
| ( ( ~ ( in @ ( sK44_C @ SV232 @ SV147 ) @ SV232 ) )
= $true )
| ( ( SV147 = SV232 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2045]) ).
thf(2210,plain,
! [SV147: $i,SV232: $i] :
( ( ( in @ ( sK44_C @ SV232 @ SV147 ) @ SV147 )
= $true )
| ( ( in @ ( sK44_C @ SV232 @ SV147 ) @ SV232 )
= $true )
| ( ( SV147 = SV232 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2046]) ).
thf(2211,plain,
! [SV384: $i,SV311: $i] :
( ( ( subset @ SV311 @ ( singleton @ SV384 ) )
= $false )
| ( ( ( SV311 = empty_set )
| ( SV311
= ( singleton @ SV384 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2047]) ).
thf(2212,plain,
! [SV460: $i] :
( ( ( SV460 != empty_set )
| ! [SY1092: $i] : ( subset @ SV460 @ ( singleton @ SY1092 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2048]) ).
thf(2213,plain,
! [SV461: $i] :
( ( ! [SY1093: $i] :
( ( SV461
!= ( singleton @ SY1093 ) )
| ( subset @ SV461 @ ( singleton @ SY1093 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2049]) ).
thf(2214,plain,
! [SV413: $i,SV233: $i,SV148: $i] :
( ( ( ! [SY1028: $i] :
( ( ordered_pair @ SV148 @ SV233 )
!= ( ordered_pair @ SV413 @ SY1028 ) ) )
= $true )
| ( ( SV148 = SV413 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2050]) ).
thf(2215,plain,
! [SV462: $i,SV414: $i,SV233: $i,SV148: $i] :
( ( ( ( ordered_pair @ SV148 @ SV233 )
!= ( ordered_pair @ SV414 @ SV462 ) )
| ( SV233 = SV462 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2051]) ).
thf(2216,plain,
! [SV312: $i,SV385: $i] :
( ( ( ~ ( in @ ( sK50_C @ SV385 @ SV312 ) @ SV312 )
| ~ ~ ( in @ ( sK50_C @ SV385 @ SV312 ) @ SV385 ) )
= $false )
| ( ( subset @ SV312 @ SV385 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2052]) ).
thf(2217,plain,
! [SV386: $i,SV313: $i] :
( ( ( subset @ SV313 @ SV386 )
= $false )
| ( ( ! [SY1002: $i] :
( ~ ( in @ SY1002 @ SV313 )
| ( in @ SY1002 @ SV386 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2053]) ).
thf(2218,plain,
! [SV314: $i] :
( ( ( ( ( relation_dom @ SV314 )
!= empty_set ) )
= $true )
| ( ( SV314 = empty_set )
= $true )
| ( ( relation @ SV314 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2054]) ).
thf(2219,plain,
! [SV315: $i] :
( ( ( ( ( relation_rng @ SV315 )
!= empty_set ) )
= $true )
| ( ( SV315 = empty_set )
= $true )
| ( ( relation @ SV315 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2055]) ).
thf(2220,plain,
! [SV149: $i,SV387: $i,SV415: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV149 )
| ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV387 )
| ~ ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV415 ) )
| ~ ~ ( ~ ( ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV149 )
| ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV415 ) )
| ~ ( ~ ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV387 )
| ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV415 ) ) ) ) )
= $true )
| ( ( SV415
= ( set_difference @ SV149 @ SV387 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2058]) ).
thf(2221,plain,
! [SV388: $i,SV149: $i,SV416: $i] :
( ( ( ( SV416
!= ( set_difference @ SV149 @ SV388 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1030: $i] :
( ~ ( in @ SY1030 @ SV149 )
| ( in @ SY1030 @ SV388 )
| ( in @ SY1030 @ SV416 ) )
| ~ ~ ( ~ ! [SY1031: $i] :
( ~ ( in @ SY1031 @ SV416 )
| ( in @ SY1031 @ SV149 ) )
| ~ ! [SY1032: $i] :
( ~ ( in @ SY1032 @ SV416 )
| ~ ( in @ SY1032 @ SV388 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2059]) ).
thf(2222,plain,
! [SV168: $i,SV21: $i,SV251: $i,SV236: $i] :
( ( ( subset @ SV236 @ SV251 )
= $false )
| ( ( subset @ SV21 @ SV168 )
= $false )
| ( ( subset @ ( cartesian_product2 @ SV21 @ SV236 ) @ ( cartesian_product2 @ SV168 @ SV251 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2063]) ).
thf(2223,plain,
! [SV27: $i,SV173: $i] :
( ( ( ( relation_inverse_image @ SV173 @ SV27 )
= empty_set )
= $false )
| ( ( SV27 = empty_set )
= $true )
| ( ( subset @ SV27 @ ( relation_rng @ SV173 ) )
= $false )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2064]) ).
thf(2224,plain,
! [SV178: $i,SV33: $i,SV417: $i] :
( ( ( ~ ( function @ SV417 )
| ~ ( relation @ SV417 ) )
= $true )
| ( ( ~ ( in @ SV33 @ ( relation_dom @ ( relation_composition @ SV417 @ SV178 ) ) )
| ( ( apply @ ( relation_composition @ SV417 @ SV178 ) @ SV33 )
= ( apply @ SV178 @ ( apply @ SV417 @ SV33 ) ) ) )
= $true )
| ( ( function @ SV178 )
= $false )
| ( ( relation @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2068]) ).
thf(2225,plain,
! [SV179: $i,SV34: $i,SV418: $i] :
( ( ( ~ ( function @ SV418 )
| ~ ( relation @ SV418 ) )
= $true )
| ( ( ~ ( in @ SV34 @ ( relation_dom @ SV179 ) )
| ( ( apply @ ( relation_composition @ SV179 @ SV418 ) @ SV34 )
= ( apply @ SV418 @ ( apply @ SV179 @ SV34 ) ) ) )
= $true )
| ( ( function @ SV179 )
= $false )
| ( ( relation @ SV179 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2069]) ).
thf(2226,plain,
! [SV254: $i,SV46: $i] :
( ( ( subset @ ( relation_rng @ SV46 ) @ ( relation_dom @ SV254 ) )
= $false )
| ( ( ( relation_dom @ ( relation_composition @ SV46 @ SV254 ) )
= ( relation_dom @ SV46 ) )
= $true )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2070]) ).
thf(2227,plain,
! [SV255: $i,SV48: $i] :
( ( ( subset @ ( relation_dom @ SV48 ) @ ( relation_rng @ SV255 ) )
= $false )
| ( ( ( relation_rng @ ( relation_composition @ SV255 @ SV48 ) )
= ( relation_rng @ SV48 ) )
= $true )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2071]) ).
thf(2228,plain,
! [SV240: $i,SV50: $i,SV389: $i] :
( ( ( element @ SV389 @ SV50 )
= $false )
| ( ( ( in @ SV389 @ SV240 )
| ( in @ SV389 @ ( subset_complement @ SV50 @ SV240 ) ) )
= $true )
| ( ( element @ SV240 @ ( powerset @ SV50 ) )
= $false )
| ( ( SV50 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2072]) ).
thf(2229,plain,
! [SV51: $i,SV241: $i,SV189: $i] :
( ( ( in @ SV189 @ SV241 )
= $false )
| ( ( in @ SV189 @ ( subset_complement @ SV51 @ SV241 ) )
= $false )
| ( ( element @ SV241 @ ( powerset @ SV51 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2073]) ).
thf(2230,plain,
! [SV109: $i,SV223: $i,SV249: $i] :
( ( ( empty @ SV249 )
= $false )
| ( ( element @ SV223 @ ( powerset @ SV249 ) )
= $false )
| ( ( in @ SV109 @ SV223 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2078]) ).
thf(2231,plain,
! [SV112: $i,SV322: $i,SV390: $i] :
( ( ( ~ ( ~ ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV112 )
| ~ ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV322 )
| ~ ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV390 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV112 )
| ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV390 ) )
| ~ ( ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV322 )
| ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV390 ) ) ) )
= $false )
| ( ( SV390
= ( set_intersection2 @ SV112 @ SV322 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2079]) ).
thf(2232,plain,
! [SV323: $i,SV112: $i,SV391: $i] :
( ( ( SV391
= ( set_intersection2 @ SV112 @ SV323 ) )
= $false )
| ( ( ~ ( ~ ! [SY1008: $i] :
( ~ ( in @ SY1008 @ SV112 )
| ~ ( in @ SY1008 @ SV323 )
| ( in @ SY1008 @ SV391 ) )
| ~ ~ ( ~ ! [SY1009: $i] :
( ~ ( in @ SY1009 @ SV391 )
| ( in @ SY1009 @ SV112 ) )
| ~ ! [SY1010: $i] :
( ~ ( in @ SY1010 @ SV391 )
| ( in @ SY1010 @ SV323 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2080]) ).
thf(2233,plain,
! [SV258: $i,SV324: $i] :
( ( ( ~ ( ! [SY952: $i] :
( ~ ( in @ ( sK47_C @ SV324 @ SV258 ) @ SY952 )
| ~ ( in @ SY952 @ SV258 ) )
| ~ ( in @ ( sK47_C @ SV324 @ SV258 ) @ SV324 ) ) )
= $false )
| ( ( SV324
= ( union @ SV258 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2081]) ).
thf(2234,plain,
! [SV258: $i,SV324: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK47_C @ SV324 @ SV258 ) @ ( sK48_SY487 @ SV324 @ SV258 ) )
| ~ ( in @ ( sK48_SY487 @ SV324 @ SV258 ) @ SV258 ) )
| ( in @ ( sK47_C @ SV324 @ SV258 ) @ SV324 ) ) )
= $false )
| ( ( SV324
= ( union @ SV258 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2081]) ).
thf(2235,plain,
! [SV325: $i,SV259: $i] :
( ( ( ~ ! [SY953: $i] :
( ! [SY881: $i] :
( ~ ( in @ SY953 @ SY881 )
| ~ ( in @ SY881 @ SV259 ) )
| ( in @ SY953 @ SV325 ) )
| ~ ! [SY955: $i] :
( ~ ( in @ SY955 @ SV325 )
| ~ ( ~ ( in @ SY955 @ ( sK46_D @ SY955 @ SV325 @ SV259 ) )
| ~ ( in @ ( sK46_D @ SY955 @ SV325 @ SV259 ) @ SV259 ) ) ) )
= $false )
| ( ( SV325
= ( union @ SV259 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2082]) ).
thf(2236,plain,
! [SV113: $i,SV225: $i,SV463: $i] :
( ( ( ~ ( relation @ SV463 )
| ~ ( ~ ( ~ ( in @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) @ SV113 )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV225 )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 ) )
| ~ ~ ( ~ ( ( in @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) @ SV113 )
| ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV225 )
| ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 ) ) ) )
| ( SV463
= ( relation_rng_restriction @ SV113 @ SV225 ) ) )
= $true )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2083]) ).
thf(2237,plain,
! [SV225: $i,SV113: $i,SV464: $i] :
( ( ( ~ ( relation @ SV464 )
| ( SV464
!= ( relation_rng_restriction @ SV113 @ SV225 ) )
| ~ ( ~ ! [SY1094: $i,SY1095: $i] :
( ~ ( in @ SY1095 @ SV113 )
| ~ ( in @ ( ordered_pair @ SY1094 @ SY1095 ) @ SV225 )
| ( in @ ( ordered_pair @ SY1094 @ SY1095 ) @ SV464 ) )
| ~ ~ ( ~ ! [SY1096: $i,SY1097: $i] :
( ~ ( in @ ( ordered_pair @ SY1096 @ SY1097 ) @ SV464 )
| ( in @ SY1097 @ SV113 ) )
| ~ ! [SY1098: $i,SY1099: $i] :
( ~ ( in @ ( ordered_pair @ SY1098 @ SY1099 ) @ SV464 )
| ( in @ ( ordered_pair @ SY1098 @ SY1099 ) @ SV225 ) ) ) ) )
= $true )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2084]) ).
thf(2238,plain,
! [SV326: $i,SV260: $i] :
( ( ( empty @ SV260 )
= $false )
| ( ( ~ ( relation @ SV326 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV326 @ SV260 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2085]) ).
thf(2239,plain,
! [SV327: $i,SV261: $i] :
( ( ( empty @ SV261 )
= $false )
| ( ( ~ ( relation @ SV327 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV327 @ SV261 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2086]) ).
thf(2240,plain,
! [SV419: $i,SV226: $i,SV392: $i,SV114: $i] :
( ( ( ~ ( in @ SV114 @ SV392 )
| ~ ( in @ SV226 @ SV419 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SV392 @ SV419 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2087]) ).
thf(2241,plain,
! [SV226: $i,SV114: $i] :
( ( ! [SY849: $i] :
( ! [SY850: $i] :
~ ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SY849 @ SY850 ) )
| ( in @ SV114 @ SY849 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2088]) ).
thf(2242,plain,
! [SV226: $i,SV114: $i] :
( ( ! [SY851: $i,SY852: $i] :
( ~ ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SY851 @ SY852 ) )
| ( in @ SV226 @ SY852 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2089]) ).
thf(2243,plain,
! [SV262: $i,SV328: $i] :
( ( ( ~ ( in @ ( sK72_C @ SV328 @ SV262 ) @ SV262 ) )
= $false )
| ( ( disjoint @ SV262 @ SV328 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2090]) ).
thf(2244,plain,
! [SV262: $i,SV328: $i] :
( ( ( ~ ( in @ ( sK72_C @ SV328 @ SV262 ) @ SV328 ) )
= $false )
| ( ( disjoint @ SV262 @ SV328 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2090]) ).
thf(2245,plain,
! [SV329: $i,SV263: $i,SV420: $i] :
( ( ( ~ ( in @ SV420 @ SV263 ) )
= $true )
| ( ( ~ ( in @ SV420 @ SV329 ) )
= $true )
| ( ( ~ ( disjoint @ SV263 @ SV329 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2091]) ).
thf(2246,plain,
! [SV264: $i,SV330: $i] :
( ( ( ~ ( ( ( sK62_C @ SV330 @ SV264 )
!= SV264 )
| ~ ( in @ ( sK62_C @ SV330 @ SV264 ) @ SV330 ) ) )
= $false )
| ( ( SV330
= ( singleton @ SV264 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2092]) ).
thf(2247,plain,
! [SV264: $i,SV330: $i] :
( ( ( ~ ( ( ( sK62_C @ SV330 @ SV264 )
= SV264 )
| ( in @ ( sK62_C @ SV330 @ SV264 ) @ SV330 ) ) )
= $false )
| ( ( SV330
= ( singleton @ SV264 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2092]) ).
thf(2248,plain,
! [SV331: $i,SV265: $i] :
( ( ( ~ ! [SY957: $i] :
( ( SY957 != SV265 )
| ( in @ SY957 @ SV331 ) )
| ~ ! [SY958: $i] :
( ~ ( in @ SY958 @ SV331 )
| ( SY958 = SV265 ) ) )
= $false )
| ( ( SV331
= ( singleton @ SV265 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2093]) ).
thf(2249,plain,
! [SV267: $i,SV421: $i] :
( ( ( in @ SV421 @ SV267 )
= $false )
| ( ( SV267 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2094]) ).
thf(2250,plain,
! [SV115: $i,SV332: $i] :
( ( ( subset @ SV332 @ ( sK42_B @ SV115 ) )
= $false )
| ( ( are_equipotent @ SV332 @ ( sK42_B @ SV115 ) )
= $true )
| ( ( in @ SV332 @ ( sK42_B @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2095]) ).
thf(2251,plain,
! [SV115: $i,SV465: $i] :
( ( ~ ( ~ ! [SY1100: $i] :
( ~ ( subset @ SY1100 @ SV465 )
| ( in @ SY1100 @ ( sK43_SY481 @ SV465 @ SV115 ) ) )
| ~ ( in @ ( sK43_SY481 @ SV465 @ SV115 ) @ ( sK42_B @ SV115 ) ) )
| ~ ( in @ SV465 @ ( sK42_B @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2096]) ).
thf(2252,plain,
! [SV115: $i] :
( ( ~ ! [SY633: $i,SY634: $i] :
( ~ ( in @ SY633 @ ( sK42_B @ SV115 ) )
| ~ ( subset @ SY634 @ SY633 )
| ( in @ SY634 @ ( sK42_B @ SV115 ) ) )
| ~ ( in @ SV115 @ ( sK42_B @ SV115 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2097]) ).
thf(2253,plain,
! [SV333: $i,SV268: $i] :
( ( ( SV268 = empty_set )
= $true )
| ( ( SV268
= ( singleton @ SV333 ) )
= $true )
| ( ( subset @ SV268 @ ( singleton @ SV333 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2098]) ).
thf(2254,plain,
! [SV422: $i] :
( ( ( ( SV422 != empty_set ) )
= $true )
| ( ( ! [SY1033: $i] : ( subset @ SV422 @ ( singleton @ SY1033 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2099]) ).
thf(2255,plain,
! [SV466: $i,SV423: $i] :
( ( ( SV423
!= ( singleton @ SV466 ) )
| ( subset @ SV423 @ ( singleton @ SV466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2100]) ).
thf(2256,plain,
! [SV116: $i] :
( ( ( ~ ( ~ ! [SY635: $i] :
( ~ ( in @ SY635 @ ( relation_dom @ SV116 ) )
| ! [SY636: $i] :
( ( SY636
!= ( apply @ SV116 @ SY635 ) )
| ( in @ ( ordered_pair @ SY635 @ SY636 ) @ SV116 ) ) )
| ~ ! [SY637: $i] :
( ~ ( in @ SY637 @ ( relation_dom @ SV116 ) )
| ! [SY638: $i] :
( ~ ( in @ ( ordered_pair @ SY637 @ SY638 ) @ SV116 )
| ( SY638
= ( apply @ SV116 @ SY637 ) ) ) ) ) )
= $true )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2101]) ).
thf(2257,plain,
! [SV116: $i] :
( ( ( ~ ( ~ ! [SY639: $i] :
( ( in @ SY639 @ ( relation_dom @ SV116 ) )
| ! [SY640: $i] :
( ( SY640
!= ( apply @ SV116 @ SY639 ) )
| ( SY640 = empty_set ) ) )
| ~ ! [SY641: $i] :
( ( in @ SY641 @ ( relation_dom @ SV116 ) )
| ! [SY642: $i] :
( ( SY642 != empty_set )
| ( SY642
= ( apply @ SV116 @ SY641 ) ) ) ) ) )
= $true )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2102]) ).
thf(2258,plain,
! [SV393: $i,SV334: $i,SV117: $i] :
( ( ( ~ ( ! [SY1012: $i,SY1013: $i] :
( ~ ( in @ SY1012 @ SV117 )
| ~ ( in @ SY1013 @ SV334 )
| ( ( sK53_D @ SV393 @ SV334 @ SV117 )
!= ( ordered_pair @ SY1012 @ SY1013 ) ) )
| ~ ( in @ ( sK53_D @ SV393 @ SV334 @ SV117 ) @ SV393 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK54_SY491 @ SV393 @ SV334 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK55_SY493 @ SV393 @ SV334 @ SV117 ) @ SV334 ) )
| ( ( sK53_D @ SV393 @ SV334 @ SV117 )
!= ( ordered_pair @ ( sK54_SY491 @ SV393 @ SV334 @ SV117 ) @ ( sK55_SY493 @ SV393 @ SV334 @ SV117 ) ) ) )
| ( in @ ( sK53_D @ SV393 @ SV334 @ SV117 ) @ SV393 ) ) )
= $false )
| ( ( SV393
= ( cartesian_product2 @ SV117 @ SV334 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2103]) ).
thf(2259,plain,
! [SV335: $i,SV117: $i,SV394: $i] :
( ( ( SV394
= ( cartesian_product2 @ SV117 @ SV335 ) )
= $false )
| ( ( ~ ( ~ ! [SY1014: $i] :
( ! [SY964: $i,SY965: $i] :
( ~ ( in @ SY964 @ SV117 )
| ~ ( in @ SY965 @ SV335 )
| ( SY1014
!= ( ordered_pair @ SY964 @ SY965 ) ) )
| ( in @ SY1014 @ SV394 ) )
| ~ ! [SY1017: $i] :
( ~ ( in @ SY1017 @ SV394 )
| ~ ( ~ ~ ( ~ ( in @ ( sK51_E @ SY1017 @ SV394 @ SV335 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK52_SY488 @ SY1017 @ SV394 @ SV335 @ SV117 ) @ SV335 ) )
| ( SY1017
!= ( ordered_pair @ ( sK51_E @ SY1017 @ SV394 @ SV335 @ SV117 ) @ ( sK52_SY488 @ SY1017 @ SV394 @ SV335 @ SV117 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2104]) ).
thf(2260,plain,
! [SV271: $i] :
( ( ( ( relation_dom @ SV271 )
= empty_set )
= $false )
| ( ( ( relation_rng @ SV271 )
= empty_set )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2107]) ).
thf(2261,plain,
! [SV272: $i] :
( ( ( ( relation_rng @ SV272 )
= empty_set )
= $false )
| ( ( ( relation_dom @ SV272 )
= empty_set )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2108]) ).
thf(2262,plain,
! [SV118: $i,SV338: $i,SV395: $i] :
( ( ( ~ ( function @ SV395 ) )
= $true )
| ( ( ~ ( relation @ SV395 ) )
= $true )
| ( ( ( SV338
!= ( apply @ SV395 @ SV118 ) )
| ~ ( in @ SV118 @ ( relation_dom @ SV395 ) )
| ( in @ ( ordered_pair @ SV118 @ SV338 ) @ SV395 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2109]) ).
thf(2263,plain,
! [SV467: $i,SV118: $i] :
( ( ! [SY1101: $i] :
( ~ ( function @ SY1101 )
| ~ ( relation @ SY1101 )
| ~ ( in @ ( ordered_pair @ SV118 @ SV467 ) @ SY1101 )
| ( SV467
= ( apply @ SY1101 @ SV118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2110]) ).
thf(2264,plain,
! [SV468: $i,SV118: $i] :
( ( ! [SY1102: $i] :
( ~ ( function @ SY1102 )
| ~ ( relation @ SY1102 )
| ~ ( in @ ( ordered_pair @ SV118 @ SV468 ) @ SY1102 )
| ( in @ SV118 @ ( relation_dom @ SY1102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2111]) ).
thf(2265,plain,
! [SV273: $i,SV339: $i] :
( ( ( ~ ( ~ ( ( ( sK69_C @ SV339 @ SV273 )
!= ( sK70_SY500 @ SV339 @ SV273 ) )
| ~ ( in @ ( sK69_C @ SV339 @ SV273 ) @ SV273 )
| ~ ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 ) )
| ~ ~ ( ~ ( ( ( sK69_C @ SV339 @ SV273 )
= ( sK70_SY500 @ SV339 @ SV273 ) )
| ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 ) )
| ~ ( ( in @ ( sK69_C @ SV339 @ SV273 ) @ SV273 )
| ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 ) ) ) ) )
= $true )
| ( ( SV339
= ( identity_relation @ SV273 ) )
= $true )
| ( ( relation @ SV339 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2112]) ).
thf(2266,plain,
! [SV274: $i,SV340: $i] :
( ( ( ( SV340
!= ( identity_relation @ SV274 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY968: $i,SY969: $i] :
( ( SY968 != SY969 )
| ~ ( in @ SY968 @ SV274 )
| ( in @ ( ordered_pair @ SY968 @ SY969 ) @ SV340 ) )
| ~ ~ ( ~ ! [SY970: $i,SY971: $i] :
( ~ ( in @ ( ordered_pair @ SY970 @ SY971 ) @ SV340 )
| ( SY970 = SY971 ) )
| ~ ! [SY972: $i] :
( ! [SY973: $i] :
~ ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV340 )
| ( in @ SY972 @ SV274 ) ) ) ) )
= $true )
| ( ( relation @ SV340 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2113]) ).
thf(2267,plain,
! [SV120: $i,SV275: $i] :
( ( ( ~ ! [SY904: $i] :
( ~ ( relation @ SY904 )
| ~ ( ~ ( ! [SY905: $i] :
( ~ ( in @ ( ordered_pair @ ( sK13_D @ SY904 @ SV275 @ SV120 ) @ SY905 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY905 @ ( sK14_SY457 @ SY904 @ SV275 @ SV120 ) ) @ SV275 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_D @ SY904 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SY904 @ SV275 @ SV120 ) ) @ SY904 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_D @ SY904 @ SV275 @ SV120 ) @ ( sK15_SY461 @ SY904 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY461 @ SY904 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SY904 @ SV275 @ SV120 ) ) @ SV275 ) )
| ( in @ ( ordered_pair @ ( sK13_D @ SY904 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SY904 @ SV275 @ SV120 ) ) @ SY904 ) ) )
| ( SY904
= ( relation_composition @ SV120 @ SV275 ) ) ) )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2114]) ).
thf(2268,plain,
! [SV275: $i,SV120: $i] :
( ( ( ~ ! [SY906: $i] :
( ~ ( relation @ SY906 )
| ( SY906
!= ( relation_composition @ SV120 @ SV275 ) )
| ~ ( ~ ! [SY907: $i,SY908: $i] :
( ! [SY909: $i] :
( ~ ( in @ ( ordered_pair @ SY907 @ SY909 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY909 @ SY908 ) @ SV275 ) )
| ( in @ ( ordered_pair @ SY907 @ SY908 ) @ SY906 ) )
| ~ ! [SY910: $i,SY911: $i] :
( ~ ( in @ ( ordered_pair @ SY910 @ SY911 ) @ SY906 )
| ~ ( ~ ( in @ ( ordered_pair @ SY910 @ ( sK12_F @ SY911 @ SY910 @ SY906 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK12_F @ SY911 @ SY910 @ SY906 @ SV275 @ SV120 ) @ SY911 ) @ SV275 ) ) ) ) ) )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2114]) ).
thf(2269,plain,
! [SV227: $i,SV121: $i,SV469: $i] :
( ( ( ~ ( element @ SV469 @ ( powerset @ SV121 ) )
| ~ ( disjoint @ SV227 @ SV469 )
| ( subset @ SV227 @ ( subset_complement @ SV121 @ SV469 ) ) )
= $true )
| ( ( element @ SV227 @ ( powerset @ SV121 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2115]) ).
thf(2270,plain,
! [SV227: $i,SV121: $i,SV470: $i] :
( ( ( ~ ( element @ SV470 @ ( powerset @ SV121 ) )
| ~ ( subset @ SV227 @ ( subset_complement @ SV121 @ SV470 ) )
| ( disjoint @ SV227 @ SV470 ) )
= $true )
| ( ( element @ SV227 @ ( powerset @ SV121 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2116]) ).
thf(2271,plain,
! [SV341: $i,SV122: $i,SV396: $i] :
( ( ( relation @ SV396 )
= $false )
| ( ( ~ ( in @ SV122 @ SV341 )
| ~ ( in @ SV122 @ ( relation_rng @ SV396 ) )
| ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SV341 @ SV396 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2117]) ).
thf(2272,plain,
! [SV471: $i,SV122: $i] :
( ( ! [SY1103: $i] :
( ~ ( relation @ SY1103 )
| ~ ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SV471 @ SY1103 ) ) )
| ( in @ SV122 @ SV471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2118]) ).
thf(2273,plain,
! [SV472: $i,SV122: $i] :
( ( ! [SY1104: $i] :
( ~ ( relation @ SY1104 )
| ~ ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SV472 @ SY1104 ) ) )
| ( in @ SV122 @ ( relation_rng @ SY1104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2119]) ).
thf(2274,plain,
! [SV123: $i,SV424: $i,SV473: $i] :
( ( ( ~ ( relation @ SV473 )
| ~ ( ~ ( ~ ( in @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ SV424 )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV123 )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 ) )
| ~ ~ ( ~ ( ( in @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ SV424 )
| ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 ) ) ) )
| ( SV473
= ( relation_dom_restriction @ SV123 @ SV424 ) ) )
= $true )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2120]) ).
thf(2275,plain,
! [SV425: $i,SV123: $i,SV474: $i] :
( ( ( ~ ( relation @ SV474 )
| ( SV474
!= ( relation_dom_restriction @ SV123 @ SV425 ) )
| ~ ( ~ ! [SY1105: $i,SY1106: $i] :
( ~ ( in @ SY1105 @ SV425 )
| ~ ( in @ ( ordered_pair @ SY1105 @ SY1106 ) @ SV123 )
| ( in @ ( ordered_pair @ SY1105 @ SY1106 ) @ SV474 ) )
| ~ ~ ( ~ ! [SY1107: $i] :
( ! [SY1108: $i] :
~ ( in @ ( ordered_pair @ SY1107 @ SY1108 ) @ SV474 )
| ( in @ SY1107 @ SV425 ) )
| ~ ! [SY1109: $i,SY1110: $i] :
( ~ ( in @ ( ordered_pair @ SY1109 @ SY1110 ) @ SV474 )
| ( in @ ( ordered_pair @ SY1109 @ SY1110 ) @ SV123 ) ) ) ) )
= $true )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2121]) ).
thf(2276,plain,
! [SV124: $i,SV426: $i] :
( ( ( ~ ( relation @ SV426 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_C @ SV426 @ SV124 ) @ ( sK17_SY462 @ SV426 @ SV124 ) ) @ SV426 )
| ~ ( in @ ( ordered_pair @ ( sK17_SY462 @ SV426 @ SV124 ) @ ( sK16_C @ SV426 @ SV124 ) ) @ SV124 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK16_C @ SV426 @ SV124 ) @ ( sK17_SY462 @ SV426 @ SV124 ) ) @ SV426 )
| ( in @ ( ordered_pair @ ( sK17_SY462 @ SV426 @ SV124 ) @ ( sK16_C @ SV426 @ SV124 ) ) @ SV124 ) ) )
| ( SV426
= ( relation_inverse @ SV124 ) ) )
= $true )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2122]) ).
thf(2277,plain,
! [SV124: $i,SV427: $i] :
( ( ( ~ ( relation @ SV427 ) )
= $true )
| ( ( ( SV427
!= ( relation_inverse @ SV124 ) )
| ~ ( ~ ! [SY1043: $i,SY1044: $i] :
( ~ ( in @ ( ordered_pair @ SY1043 @ SY1044 ) @ SV427 )
| ( in @ ( ordered_pair @ SY1044 @ SY1043 ) @ SV124 ) )
| ~ ! [SY1045: $i,SY1046: $i] :
( ~ ( in @ ( ordered_pair @ SY1046 @ SY1045 ) @ SV124 )
| ( in @ ( ordered_pair @ SY1045 @ SY1046 ) @ SV427 ) ) ) )
= $true )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2123]) ).
thf(2278,plain,
! [SV282: $i,SV348: $i] :
( ( ( function @ SV348 )
= $false )
| ( ( ~ ( relation @ SV348 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK38_C @ SV348 @ SV282 ) @ SV282 )
| ~ ( ( ( apply @ SV348 @ ( sK38_C @ SV348 @ SV282 ) )
!= ( sK38_C @ SV348 @ SV282 ) ) ) )
| ( ( relation_dom @ SV348 )
!= SV282 )
| ( SV348
= ( identity_relation @ SV282 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2130]) ).
thf(2279,plain,
! [SV428: $i,SV475: $i] :
( ( ~ ( function @ SV475 )
| ~ ( relation @ SV475 )
| ( SV475
!= ( identity_relation @ SV428 ) )
| ! [SY1111: $i] :
( ~ ( in @ SY1111 @ SV428 )
| ( ( apply @ SV475 @ SY1111 )
= SY1111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2131]) ).
thf(2280,plain,
! [SV429: $i,SV476: $i] :
( ( ~ ( function @ SV476 )
| ~ ( relation @ SV476 )
| ( SV476
!= ( identity_relation @ SV429 ) )
| ( ( relation_dom @ SV476 )
= SV429 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2132]) ).
thf(2281,plain,
! [SV351: $i,SV285: $i] :
( ( ( subset @ SV285 @ SV351 )
= $false )
| ( ( ~ ( subset @ SV351 @ SV285 ) )
= $true )
| ( ( SV285 = SV351 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2135]) ).
thf(2282,plain,
! [SV477: $i,SV430: $i] :
( ( ( SV430 != SV477 )
| ( subset @ SV430 @ SV477 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2136]) ).
thf(2283,plain,
! [SV478: $i,SV431: $i] :
( ( ( SV431 != SV478 )
| ( subset @ SV478 @ SV431 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2137]) ).
thf(2284,plain,
! [SV125: $i,SV432: $i,SV479: $i] :
( ( ( ~ ( ~ ( ! [SY1112: $i] :
( ~ ( in @ ( ordered_pair @ SY1112 @ ( sK30_D @ SV479 @ SV432 @ SV125 ) ) @ SV125 )
| ~ ( in @ SY1112 @ SV432 ) )
| ~ ( in @ ( sK30_D @ SV479 @ SV432 @ SV125 ) @ SV479 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_SY471 @ SV479 @ SV432 @ SV125 ) @ ( sK30_D @ SV479 @ SV432 @ SV125 ) ) @ SV125 )
| ~ ( in @ ( sK31_SY471 @ SV479 @ SV432 @ SV125 ) @ SV432 ) )
| ( in @ ( sK30_D @ SV479 @ SV432 @ SV125 ) @ SV479 ) ) )
| ( SV479
= ( relation_image @ SV125 @ SV432 ) ) )
= $true )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2138]) ).
thf(2285,plain,
! [SV433: $i,SV125: $i,SV480: $i] :
( ( ( ( SV480
!= ( relation_image @ SV125 @ SV433 ) )
| ~ ( ~ ! [SY1113: $i] :
( ! [SY1056: $i] :
( ~ ( in @ ( ordered_pair @ SY1056 @ SY1113 ) @ SV125 )
| ~ ( in @ SY1056 @ SV433 ) )
| ( in @ SY1113 @ SV480 ) )
| ~ ! [SY1115: $i] :
( ~ ( in @ SY1115 @ SV480 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK29_E @ SY1115 @ SV480 @ SV433 @ SV125 ) @ SY1115 ) @ SV125 )
| ~ ( in @ ( sK29_E @ SY1115 @ SV480 @ SV433 @ SV125 ) @ SV433 ) ) ) ) )
= $true )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2139]) ).
thf(2286,plain,
! [SV352: $i,SV126: $i,SV397: $i] :
( ( ( relation @ SV397 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV126 @ SV352 ) @ SV397 )
| ( in @ SV126 @ ( relation_field @ SV397 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2140]) ).
thf(2287,plain,
! [SV353: $i,SV126: $i,SV398: $i] :
( ( ( relation @ SV398 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV126 @ SV353 ) @ SV398 )
| ( in @ SV353 @ ( relation_field @ SV398 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2141]) ).
thf(2288,plain,
! [SV228: $i,SV399: $i,SV127: $i,SV434: $i] :
( ( ( ~ ( relation @ SV434 ) )
= $true )
| ( ( ~ ( in @ SV127 @ SV399 )
| ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ SV434 )
| ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SV399 ) @ SV434 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2142]) ).
thf(2289,plain,
! [SV228: $i,SV127: $i] :
( ( ! [SY857: $i,SY858: $i] :
( ~ ( relation @ SY858 )
| ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SY857 ) @ SY858 ) )
| ( in @ SV127 @ SY857 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2143]) ).
thf(2290,plain,
! [SV228: $i,SV127: $i] :
( ( ! [SY859: $i,SY860: $i] :
( ~ ( relation @ SY860 )
| ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SY859 ) @ SY860 ) )
| ( in @ ( ordered_pair @ SV127 @ SV228 ) @ SY860 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2144]) ).
thf(2291,plain,
! [SV356: $i,SV400: $i,SV128: $i] :
( ( ( ~ ( in @ SV128 @ SV400 ) )
= $true )
| ( ( ~ ( in @ SV356 @ SV400 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV128 @ SV356 ) @ SV400 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2147]) ).
thf(2292,plain,
! [SV481: $i,SV128: $i] :
( ( ! [SY1116: $i] :
( ~ ( subset @ ( unordered_pair @ SV128 @ SV481 ) @ SY1116 )
| ( in @ SV128 @ SY1116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2148]) ).
thf(2293,plain,
! [SV482: $i,SV128: $i] :
( ( ! [SY1117: $i] :
( ~ ( subset @ ( unordered_pair @ SV128 @ SV482 ) @ SY1117 )
| ( in @ SV482 @ SY1117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2149]) ).
thf(2294,plain,
! [SV435: $i] :
( ( ( empty @ SV435 )
= $true )
| ( ( ! [SY1058: $i] :
( ~ ( element @ SY1058 @ SV435 )
| ( in @ SY1058 @ SV435 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2150]) ).
thf(2295,plain,
! [SV436: $i] :
( ( ( empty @ SV436 )
= $true )
| ( ( ! [SY1059: $i] :
( ~ ( in @ SY1059 @ SV436 )
| ( element @ SY1059 @ SV436 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2151]) ).
thf(2296,plain,
! [SV437: $i] :
( ( ( ~ ( empty @ SV437 ) )
= $true )
| ( ( ! [SY1060: $i] :
( ~ ( element @ SY1060 @ SV437 )
| ( empty @ SY1060 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2152]) ).
thf(2297,plain,
! [SV438: $i] :
( ( ( ~ ( empty @ SV438 ) )
= $true )
| ( ( ! [SY1061: $i] :
( ~ ( empty @ SY1061 )
| ( element @ SY1061 @ SV438 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2153]) ).
thf(2298,plain,
! [SV129: $i,SV439: $i] :
( ( ( ~ ( ~ ( ! [SY1062: $i] :
~ ( in @ ( ordered_pair @ SY1062 @ ( sK19_C @ SV439 @ SV129 ) ) @ SV129 )
| ~ ( in @ ( sK19_C @ SV439 @ SV129 ) @ SV439 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_SY464 @ SV439 @ SV129 ) @ ( sK19_C @ SV439 @ SV129 ) ) @ SV129 )
| ( in @ ( sK19_C @ SV439 @ SV129 ) @ SV439 ) ) ) )
= $true )
| ( ( SV439
= ( relation_rng @ SV129 ) )
= $true )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2154]) ).
thf(2299,plain,
! [SV129: $i,SV440: $i] :
( ( ( ( SV440
!= ( relation_rng @ SV129 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1063: $i] :
( ! [SY722: $i] :
~ ( in @ ( ordered_pair @ SY722 @ SY1063 ) @ SV129 )
| ( in @ SY1063 @ SV440 ) )
| ~ ! [SY1065: $i] :
( ~ ( in @ SY1065 @ SV440 )
| ( in @ ( ordered_pair @ ( sK18_D @ SY1065 @ SV440 @ SV129 ) @ SY1065 ) @ SV129 ) ) ) )
= $true )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2155]) ).
thf(2300,plain,
! [SV288: $i,SV357: $i] :
( ( ( in @ SV357 @ SV288 )
= $false )
| ( ( ( set_difference @ SV288 @ ( singleton @ SV357 ) )
= SV288 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2156]) ).
thf(2301,plain,
! [SV360: $i,SV293: $i,SV441: $i] :
( ( ( in @ SV441 @ ( set_intersection2 @ SV293 @ SV360 ) )
= $false )
| ( ( ~ ( disjoint @ SV293 @ SV360 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2157]) ).
thf(2302,plain,
! [SV131: $i,SV442: $i,SV483: $i] :
( ( ( ~ ( ~ ( ! [SY1118: $i] :
( ~ ( in @ ( ordered_pair @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SY1118 ) @ SV131 )
| ~ ( in @ SY1118 @ SV442 ) )
| ~ ( in @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SV483 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ ( sK28_SY469 @ SV483 @ SV442 @ SV131 ) ) @ SV131 )
| ~ ( in @ ( sK28_SY469 @ SV483 @ SV442 @ SV131 ) @ SV442 ) )
| ( in @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SV483 ) ) )
| ( SV483
= ( relation_inverse_image @ SV131 @ SV442 ) ) )
= $true )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2159]) ).
thf(2303,plain,
! [SV443: $i,SV131: $i,SV484: $i] :
( ( ( ( SV484
!= ( relation_inverse_image @ SV131 @ SV443 ) )
| ~ ( ~ ! [SY1119: $i] :
( ! [SY1070: $i] :
( ~ ( in @ ( ordered_pair @ SY1119 @ SY1070 ) @ SV131 )
| ~ ( in @ SY1070 @ SV443 ) )
| ( in @ SY1119 @ SV484 ) )
| ~ ! [SY1121: $i] :
( ~ ( in @ SY1121 @ SV484 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1121 @ ( sK26_E @ SY1121 @ SV484 @ SV443 @ SV131 ) ) @ SV131 )
| ~ ( in @ ( sK26_E @ SY1121 @ SV484 @ SV443 @ SV131 ) @ SV443 ) ) ) ) )
= $true )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2160]) ).
thf(2304,plain,
! [SV296: $i] :
( ( ( ! [SY931: $i,SY932: $i] :
( ( sK68_B @ SV296 )
!= ( ordered_pair @ SY931 @ SY932 ) ) )
= $true )
| ( ( relation @ SV296 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2163]) ).
thf(2305,plain,
! [SV296: $i] :
( ( ( in @ ( sK68_B @ SV296 ) @ SV296 )
= $true )
| ( ( relation @ SV296 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2164]) ).
thf(2306,plain,
! [SV297: $i,SV444: $i] :
( ( ( SV444
= ( ordered_pair @ ( sK66_C @ SV444 @ SV297 ) @ ( sK67_SY497 @ SV444 @ SV297 ) ) )
= $true )
| ( ( ~ ( in @ SV444 @ SV297 ) )
= $true )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2165]) ).
thf(2307,plain,
! [SV363: $i,SV132: $i,SV401: $i] :
( ( ( relation @ SV401 )
= $false )
| ( ( ~ ( in @ SV132 @ SV363 )
| ~ ( in @ SV132 @ ( relation_dom @ SV401 ) )
| ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SV401 @ SV363 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2166]) ).
thf(2308,plain,
! [SV485: $i,SV132: $i] :
( ( ! [SY1122: $i] :
( ~ ( relation @ SY1122 )
| ~ ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SY1122 @ SV485 ) ) )
| ( in @ SV132 @ SV485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2167]) ).
thf(2309,plain,
! [SV486: $i,SV132: $i] :
( ( ! [SY1123: $i] :
( ~ ( relation @ SY1123 )
| ~ ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SY1123 @ SV486 ) ) )
| ( in @ SV132 @ ( relation_dom @ SY1123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2168]) ).
thf(2310,plain,
! [SV364: $i,SV133: $i,SV402: $i] :
( ( ( relation @ SV402 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV133 @ SV364 ) @ SV402 )
| ( in @ SV133 @ ( relation_dom @ SV402 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2169]) ).
thf(2311,plain,
! [SV365: $i,SV133: $i,SV403: $i] :
( ( ( relation @ SV403 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV133 @ SV365 ) @ SV403 )
| ( in @ SV365 @ ( relation_rng @ SV403 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2170]) ).
thf(2312,plain,
! [SV134: $i,SV445: $i] :
( ( ( ~ ( ~ ( ! [SY1072: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SV445 @ SV134 ) @ SY1072 ) @ SV134 )
| ~ ( in @ ( sK22_C @ SV445 @ SV134 ) @ SV445 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SV445 @ SV134 ) @ ( sK23_SY466 @ SV445 @ SV134 ) ) @ SV134 )
| ( in @ ( sK22_C @ SV445 @ SV134 ) @ SV445 ) ) ) )
= $true )
| ( ( SV445
= ( relation_dom @ SV134 ) )
= $true )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2171]) ).
thf(2313,plain,
! [SV134: $i,SV446: $i] :
( ( ( ( SV446
!= ( relation_dom @ SV134 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1073: $i] :
( ! [SY747: $i] :
~ ( in @ ( ordered_pair @ SY1073 @ SY747 ) @ SV134 )
| ( in @ SY1073 @ SV446 ) )
| ~ ! [SY1075: $i] :
( ~ ( in @ SY1075 @ SV446 )
| ( in @ ( ordered_pair @ SY1075 @ ( sK21_D @ SY1075 @ SV446 @ SV134 ) ) @ SV134 ) ) ) )
= $true )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2172]) ).
thf(2314,plain,
! [SV135: $i,SV366: $i,SV404: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK57_D @ SV404 @ SV366 @ SV135 ) @ SV404 )
| ( ( sK57_D @ SV404 @ SV366 @ SV135 )
!= SV135 ) )
| ~ ( ~ ( in @ ( sK57_D @ SV404 @ SV366 @ SV135 ) @ SV404 )
| ( ( sK57_D @ SV404 @ SV366 @ SV135 )
!= SV366 ) ) )
| ~ ( ( in @ ( sK57_D @ SV404 @ SV366 @ SV135 ) @ SV404 )
| ( ( sK57_D @ SV404 @ SV366 @ SV135 )
= SV135 )
| ( ( sK57_D @ SV404 @ SV366 @ SV135 )
= SV366 ) ) )
= $false )
| ( ( SV404
= ( unordered_pair @ SV135 @ SV366 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2173]) ).
thf(2315,plain,
! [SV367: $i,SV135: $i,SV405: $i] :
( ( ( SV405
= ( unordered_pair @ SV135 @ SV367 ) )
= $false )
| ( ( ~ ( ~ ! [SY1019: $i] :
( ~ ( in @ SY1019 @ SV405 )
| ( SY1019 = SV135 )
| ( SY1019 = SV367 ) )
| ~ ~ ( ~ ! [SY1020: $i] :
( ( SY1020 != SV135 )
| ( in @ SY1020 @ SV405 ) )
| ~ ! [SY1021: $i] :
( ( SY1021 != SV367 )
| ( in @ SY1021 @ SV405 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2174]) ).
thf(2316,plain,
! [SV136: $i,SV447: $i] :
( ( ( ~ ( relation @ SV447 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV136 )
| ~ ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV447 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV136 )
| ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV447 ) ) )
| ( SV136 = SV447 ) )
= $true )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2175]) ).
thf(2317,plain,
! [SV136: $i,SV448: $i] :
( ( ( ~ ( relation @ SV448 ) )
= $true )
| ( ( ( SV136 != SV448 )
| ~ ( ~ ! [SY1076: $i,SY1077: $i] :
( ~ ( in @ ( ordered_pair @ SY1076 @ SY1077 ) @ SV136 )
| ( in @ ( ordered_pair @ SY1076 @ SY1077 ) @ SV448 ) )
| ~ ! [SY1078: $i,SY1079: $i] :
( ~ ( in @ ( ordered_pair @ SY1078 @ SY1079 ) @ SV448 )
| ( in @ ( ordered_pair @ SY1078 @ SY1079 ) @ SV136 ) ) ) )
= $true )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2176]) ).
thf(2318,plain,
! [SV368: $i,SV298: $i] :
( ( ( ~ ( function @ SV298 )
| ~ ( relation @ SV298 ) )
= $true )
| ( ( ~ ( relation @ SV368 ) )
= $true )
| ( ( ~ ( function @ SV368 ) )
= $true )
| ( ( function @ ( relation_composition @ SV298 @ SV368 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2177]) ).
thf(2319,plain,
! [SV369: $i,SV299: $i] :
( ( ( ~ ( function @ SV299 )
| ~ ( relation @ SV299 ) )
= $true )
| ( ( ~ ( relation @ SV369 ) )
= $true )
| ( ( ~ ( function @ SV369 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV299 @ SV369 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2178]) ).
thf(2320,plain,
! [SV230: $i,SV137: $i] :
( ( ( ~ ! [SY861: $i] :
( ~ ( function @ SY861 )
| ~ ( relation @ SY861 )
| ~ ( in @ SV137 @ ( relation_dom @ SY861 ) )
| ~ ( in @ ( apply @ SY861 @ SV137 ) @ ( relation_dom @ SV230 ) )
| ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY861 @ SV230 ) ) ) ) )
= $false )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2179]) ).
thf(2321,plain,
! [SV230: $i,SV137: $i] :
( ( ( ~ ~ ( ~ ! [SY862: $i] :
( ~ ( function @ SY862 )
| ~ ( relation @ SY862 )
| ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY862 @ SV230 ) ) )
| ( in @ SV137 @ ( relation_dom @ SY862 ) ) )
| ~ ! [SY863: $i] :
( ~ ( function @ SY863 )
| ~ ( relation @ SY863 )
| ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY863 @ SV230 ) ) )
| ( in @ ( apply @ SY863 @ SV137 ) @ ( relation_dom @ SV230 ) ) ) ) )
= $false )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2179]) ).
thf(2322,plain,
! [SV138: $i,SV370: $i] :
( ( ( subset @ SV370 @ ( sK41_B @ SV138 ) )
= $false )
| ( ( are_equipotent @ SV370 @ ( sK41_B @ SV138 ) )
= $true )
| ( ( in @ SV370 @ ( sK41_B @ SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2180]) ).
thf(2323,plain,
! [SV138: $i,SV487: $i] :
( ( ~ ( in @ SV487 @ ( sK41_B @ SV138 ) )
| ( in @ ( powerset @ SV487 ) @ ( sK41_B @ SV138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2181]) ).
thf(2324,plain,
! [SV138: $i] :
( ( ~ ! [SY768: $i,SY769: $i] :
( ~ ( in @ SY768 @ ( sK41_B @ SV138 ) )
| ~ ( subset @ SY769 @ SY768 )
| ( in @ SY769 @ ( sK41_B @ SV138 ) ) )
| ~ ( in @ SV138 @ ( sK41_B @ SV138 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2182]) ).
thf(2325,plain,
! [SV139: $i,SV449: $i] :
( ( ( ~ ( relation @ SV449 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV449 @ SV139 ) @ ( sK25_SY467 @ SV449 @ SV139 ) ) @ SV139 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SV449 @ SV139 ) @ ( sK25_SY467 @ SV449 @ SV139 ) ) @ SV449 ) )
| ( subset @ SV139 @ SV449 ) )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2183]) ).
thf(2326,plain,
! [SV139: $i,SV450: $i] :
( ( ( ~ ( relation @ SV450 ) )
= $true )
| ( ( ~ ( subset @ SV139 @ SV450 )
| ! [SY1080: $i,SY1081: $i] :
( ~ ( in @ ( ordered_pair @ SY1080 @ SY1081 ) @ SV139 )
| ( in @ ( ordered_pair @ SY1080 @ SY1081 ) @ SV450 ) ) )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2184]) ).
thf(2327,plain,
! [SV300: $i,SV371: $i] :
( ( ( ~ ( ~ ( in @ ( sK60_C @ SV371 @ SV300 ) @ SV371 )
| ~ ( subset @ ( sK60_C @ SV371 @ SV300 ) @ SV300 ) ) )
= $false )
| ( ( SV371
= ( powerset @ SV300 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2185]) ).
thf(2328,plain,
! [SV300: $i,SV371: $i] :
( ( ( ~ ( ( in @ ( sK60_C @ SV371 @ SV300 ) @ SV371 )
| ( subset @ ( sK60_C @ SV371 @ SV300 ) @ SV300 ) ) )
= $false )
| ( ( SV371
= ( powerset @ SV300 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2185]) ).
thf(2329,plain,
! [SV301: $i,SV372: $i] :
( ( ( ~ ! [SY987: $i] :
( ~ ( in @ SY987 @ SV372 )
| ( subset @ SY987 @ SV301 ) )
| ~ ! [SY988: $i] :
( ~ ( subset @ SY988 @ SV301 )
| ( in @ SY988 @ SV372 ) ) )
= $false )
| ( ( SV372
= ( powerset @ SV301 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2186]) ).
thf(2330,plain,
! [SV373: $i,SV302: $i] :
( ( ( empty @ SV302 )
= $false )
| ( ( ~ ( relation @ SV373 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV302 @ SV373 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2187]) ).
thf(2331,plain,
! [SV374: $i,SV303: $i] :
( ( ( empty @ SV303 )
= $false )
| ( ( ~ ( relation @ SV374 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV303 @ SV374 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2188]) ).
thf(2332,plain,
! [SV140: $i,SV451: $i] :
( ( ( ~ ( relation @ SV451 ) )
= $true )
| ( ( ~ ( subset @ SV140 @ SV451 )
| ( subset @ ( relation_dom @ SV140 ) @ ( relation_dom @ SV451 ) ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2189]) ).
thf(2333,plain,
! [SV140: $i,SV452: $i] :
( ( ( ~ ( relation @ SV452 ) )
= $true )
| ( ( ~ ( subset @ SV140 @ SV452 )
| ( subset @ ( relation_rng @ SV140 ) @ ( relation_rng @ SV452 ) ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2190]) ).
thf(2334,plain,
! [SV375: $i,SV142: $i,SV406: $i] :
( ( ( relation @ SV406 )
= $false )
| ( ( ! [SY1022: $i] :
( ~ ( in @ SY1022 @ ( relation_rng @ SV406 ) )
| ~ ( in @ ( ordered_pair @ SV142 @ SY1022 ) @ SV406 )
| ~ ( in @ SY1022 @ SV375 ) )
| ( in @ SV142 @ ( relation_inverse_image @ SV406 @ SV375 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2191]) ).
thf(2335,plain,
! [SV376: $i,SV142: $i,SV407: $i] :
( ( ( relation @ SV407 )
= $false )
| ( ( ~ ( in @ SV142 @ ( relation_inverse_image @ SV407 @ SV376 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK39_D @ SV407 @ SV376 @ SV142 ) @ ( relation_rng @ SV407 ) )
| ~ ( in @ ( ordered_pair @ SV142 @ ( sK39_D @ SV407 @ SV376 @ SV142 ) ) @ SV407 ) )
| ~ ( in @ ( sK39_D @ SV407 @ SV376 @ SV142 ) @ SV376 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2192]) ).
thf(2336,plain,
! [SV453: $i] :
( ( ( SV453 = empty_set )
= $true )
| ( ( ! [SY1082: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK65_SY495 @ SY1082 @ SV453 ) @ SV453 )
| ~ ~ ( in @ ( sK64_C @ SY1082 @ SV453 ) @ ( sK65_SY495 @ SY1082 @ SV453 ) ) )
| ~ ( in @ ( sK64_C @ SY1082 @ SV453 ) @ SY1082 ) )
| ~ ( ! [SY1083: $i] :
( ~ ( in @ SY1083 @ SV453 )
| ( in @ ( sK64_C @ SY1082 @ SV453 ) @ SY1083 ) )
| ( in @ ( sK64_C @ SY1082 @ SV453 ) @ SY1082 ) ) )
| ( SY1082
= ( set_meet @ SV453 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2193]) ).
thf(2337,plain,
! [SV454: $i] :
( ( ( SV454 = empty_set )
= $true )
| ( ( ! [SY1084: $i] :
( ( SY1084
!= ( set_meet @ SV454 ) )
| ~ ( ~ ! [SY1085: $i] :
( ~ ( ~ ( in @ ( sK63_D @ SY1085 @ SY1084 @ SV454 ) @ SV454 )
| ~ ~ ( in @ SY1085 @ ( sK63_D @ SY1085 @ SY1084 @ SV454 ) ) )
| ( in @ SY1085 @ SY1084 ) )
| ~ ! [SY1086: $i] :
( ~ ( in @ SY1086 @ SY1084 )
| ! [SY1087: $i] :
( ~ ( in @ SY1087 @ SV454 )
| ( in @ SY1086 @ SY1087 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2194]) ).
thf(2338,plain,
! [SV455: $i] :
( ( ( ( SV455 != empty_set ) )
= $true )
| ( ( ! [SY1088: $i] :
( ( SY1088
!= ( set_meet @ SV455 ) )
| ( SY1088 = empty_set ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2195]) ).
thf(2339,plain,
! [SV456: $i] :
( ( ( ( SV456 != empty_set ) )
= $true )
| ( ( ! [SY1089: $i] :
( ( SY1089 != empty_set )
| ( SY1089
= ( set_meet @ SV456 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2196]) ).
thf(2340,plain,
! [SV377: $i,SV308: $i] :
( ( ( subset @ SV308 @ SV377 )
= $false )
| ( ( SV308 = SV377 )
= $true )
| ( ( proper_subset @ SV308 @ SV377 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2197]) ).
thf(2341,plain,
! [SV488: $i,SV457: $i] :
( ( ~ ( proper_subset @ SV457 @ SV488 )
| ( SV457 != SV488 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2198]) ).
thf(2342,plain,
! [SV489: $i,SV458: $i] :
( ( ~ ( proper_subset @ SV458 @ SV489 )
| ( subset @ SV458 @ SV489 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2199]) ).
thf(2343,plain,
! [SV459: $i,SV231: $i,SV408: $i,SV143: $i] :
( ( ( ~ ( in @ SV143 @ SV408 )
| ~ ( in @ SV231 @ SV459 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SV408 @ SV459 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2200]) ).
thf(2344,plain,
! [SV231: $i,SV143: $i] :
( ( ! [SY866: $i] :
( ! [SY867: $i] :
~ ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SY866 @ SY867 ) )
| ( in @ SV143 @ SY866 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2201]) ).
thf(2345,plain,
! [SV231: $i,SV143: $i] :
( ( ! [SY868: $i,SY869: $i] :
( ~ ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SY868 @ SY869 ) )
| ( in @ SV231 @ SY869 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2202]) ).
thf(2346,plain,
! [SV144: $i,SV378: $i,SV409: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV409 )
| ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV144 ) )
| ~ ( ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV409 )
| ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV378 ) ) )
| ~ ( ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV409 )
| ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV144 )
| ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV378 ) ) )
= $false )
| ( ( SV409
= ( set_union2 @ SV144 @ SV378 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2203]) ).
thf(2347,plain,
! [SV379: $i,SV144: $i,SV410: $i] :
( ( ( SV410
= ( set_union2 @ SV144 @ SV379 ) )
= $false )
| ( ( ~ ( ~ ! [SY1024: $i] :
( ~ ( in @ SY1024 @ SV410 )
| ( in @ SY1024 @ SV144 )
| ( in @ SY1024 @ SV379 ) )
| ~ ~ ( ~ ! [SY1025: $i] :
( ~ ( in @ SY1025 @ SV144 )
| ( in @ SY1025 @ SV410 ) )
| ~ ! [SY1026: $i] :
( ~ ( in @ SY1026 @ SV379 )
| ( in @ SY1026 @ SV410 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2204]) ).
thf(2348,plain,
! [SV380: $i,SV145: $i,SV411: $i] :
( ( ( relation @ SV411 )
= $false )
| ( ( ! [SY1027: $i] :
( ~ ( in @ SY1027 @ ( relation_dom @ SV411 ) )
| ~ ( in @ ( ordered_pair @ SY1027 @ SV145 ) @ SV411 )
| ~ ( in @ SY1027 @ SV380 ) )
| ( in @ SV145 @ ( relation_image @ SV411 @ SV380 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2205]) ).
thf(2349,plain,
! [SV381: $i,SV145: $i,SV412: $i] :
( ( ( relation @ SV412 )
= $false )
| ( ( ~ ( in @ SV145 @ ( relation_image @ SV412 @ SV381 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK40_D @ SV412 @ SV381 @ SV145 ) @ ( relation_dom @ SV412 ) )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV412 @ SV381 @ SV145 ) @ SV145 ) @ SV412 ) )
| ~ ( in @ ( sK40_D @ SV412 @ SV381 @ SV145 ) @ SV381 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2206]) ).
thf(2350,plain,
! [SV382: $i,SV490: $i,SV146: $i] :
( ( ( subset @ ( cartesian_product2 @ SV146 @ SV490 ) @ ( cartesian_product2 @ SV382 @ SV490 ) )
= $true )
| ( ( subset @ SV146 @ SV382 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2207]) ).
thf(2351,plain,
! [SV383: $i,SV146: $i,SV491: $i] :
( ( ( subset @ ( cartesian_product2 @ SV491 @ SV146 ) @ ( cartesian_product2 @ SV491 @ SV383 ) )
= $true )
| ( ( subset @ SV146 @ SV383 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2208]) ).
thf(2352,plain,
! [SV147: $i,SV232: $i] :
( ( ( in @ ( sK44_C @ SV232 @ SV147 ) @ SV147 )
= $false )
| ( ( ~ ( in @ ( sK44_C @ SV232 @ SV147 ) @ SV232 ) )
= $true )
| ( ( SV147 = SV232 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2209]) ).
thf(2353,plain,
! [SV384: $i,SV311: $i] :
( ( ( SV311 = empty_set )
= $true )
| ( ( SV311
= ( singleton @ SV384 ) )
= $true )
| ( ( subset @ SV311 @ ( singleton @ SV384 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2211]) ).
thf(2354,plain,
! [SV460: $i] :
( ( ( ( SV460 != empty_set ) )
= $true )
| ( ( ! [SY1092: $i] : ( subset @ SV460 @ ( singleton @ SY1092 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2212]) ).
thf(2355,plain,
! [SV492: $i,SV461: $i] :
( ( ( SV461
!= ( singleton @ SV492 ) )
| ( subset @ SV461 @ ( singleton @ SV492 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2213]) ).
thf(2356,plain,
! [SV493: $i,SV413: $i,SV233: $i,SV148: $i] :
( ( ( ( ( ordered_pair @ SV148 @ SV233 )
!= ( ordered_pair @ SV413 @ SV493 ) ) )
= $true )
| ( ( SV148 = SV413 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2214]) ).
thf(2357,plain,
! [SV462: $i,SV414: $i,SV233: $i,SV148: $i] :
( ( ( ( ( ordered_pair @ SV148 @ SV233 )
!= ( ordered_pair @ SV414 @ SV462 ) ) )
= $true )
| ( ( SV233 = SV462 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2215]) ).
thf(2358,plain,
! [SV312: $i,SV385: $i] :
( ( ( ~ ( in @ ( sK50_C @ SV385 @ SV312 ) @ SV312 ) )
= $false )
| ( ( subset @ SV312 @ SV385 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2216]) ).
thf(2359,plain,
! [SV312: $i,SV385: $i] :
( ( ( ~ ~ ( in @ ( sK50_C @ SV385 @ SV312 ) @ SV385 ) )
= $false )
| ( ( subset @ SV312 @ SV385 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2216]) ).
thf(2360,plain,
! [SV386: $i,SV313: $i,SV494: $i] :
( ( ( ~ ( in @ SV494 @ SV313 )
| ( in @ SV494 @ SV386 ) )
= $true )
| ( ( subset @ SV313 @ SV386 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2217]) ).
thf(2361,plain,
! [SV314: $i] :
( ( ( ( relation_dom @ SV314 )
= empty_set )
= $false )
| ( ( SV314 = empty_set )
= $true )
| ( ( relation @ SV314 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2218]) ).
thf(2362,plain,
! [SV315: $i] :
( ( ( ( relation_rng @ SV315 )
= empty_set )
= $false )
| ( ( SV315 = empty_set )
= $true )
| ( ( relation @ SV315 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2219]) ).
thf(2363,plain,
! [SV149: $i,SV387: $i,SV415: $i] :
( ( ( ~ ( ~ ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV149 )
| ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV387 )
| ~ ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV415 ) )
| ~ ~ ( ~ ( ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV149 )
| ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV415 ) )
| ~ ( ~ ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV387 )
| ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV415 ) ) ) )
= $false )
| ( ( SV415
= ( set_difference @ SV149 @ SV387 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2220]) ).
thf(2364,plain,
! [SV388: $i,SV149: $i,SV416: $i] :
( ( ( SV416
= ( set_difference @ SV149 @ SV388 ) )
= $false )
| ( ( ~ ( ~ ! [SY1030: $i] :
( ~ ( in @ SY1030 @ SV149 )
| ( in @ SY1030 @ SV388 )
| ( in @ SY1030 @ SV416 ) )
| ~ ~ ( ~ ! [SY1031: $i] :
( ~ ( in @ SY1031 @ SV416 )
| ( in @ SY1031 @ SV149 ) )
| ~ ! [SY1032: $i] :
( ~ ( in @ SY1032 @ SV416 )
| ~ ( in @ SY1032 @ SV388 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2221]) ).
thf(2365,plain,
! [SV178: $i,SV33: $i,SV417: $i] :
( ( ( ~ ( function @ SV417 ) )
= $true )
| ( ( ~ ( relation @ SV417 ) )
= $true )
| ( ( ~ ( in @ SV33 @ ( relation_dom @ ( relation_composition @ SV417 @ SV178 ) ) )
| ( ( apply @ ( relation_composition @ SV417 @ SV178 ) @ SV33 )
= ( apply @ SV178 @ ( apply @ SV417 @ SV33 ) ) ) )
= $true )
| ( ( function @ SV178 )
= $false )
| ( ( relation @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2224]) ).
thf(2366,plain,
! [SV179: $i,SV34: $i,SV418: $i] :
( ( ( ~ ( function @ SV418 ) )
= $true )
| ( ( ~ ( relation @ SV418 ) )
= $true )
| ( ( ~ ( in @ SV34 @ ( relation_dom @ SV179 ) )
| ( ( apply @ ( relation_composition @ SV179 @ SV418 ) @ SV34 )
= ( apply @ SV418 @ ( apply @ SV179 @ SV34 ) ) ) )
= $true )
| ( ( function @ SV179 )
= $false )
| ( ( relation @ SV179 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2225]) ).
thf(2367,plain,
! [SV50: $i,SV240: $i,SV389: $i] :
( ( ( in @ SV389 @ SV240 )
= $true )
| ( ( in @ SV389 @ ( subset_complement @ SV50 @ SV240 ) )
= $true )
| ( ( element @ SV389 @ SV50 )
= $false )
| ( ( element @ SV240 @ ( powerset @ SV50 ) )
= $false )
| ( ( SV50 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2228]) ).
thf(2368,plain,
! [SV112: $i,SV322: $i,SV390: $i] :
( ( ( ~ ( ~ ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV112 )
| ~ ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV322 )
| ~ ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV390 ) ) )
= $false )
| ( ( SV390
= ( set_intersection2 @ SV112 @ SV322 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2231]) ).
thf(2369,plain,
! [SV112: $i,SV322: $i,SV390: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV112 )
| ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV390 ) )
| ~ ( ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV322 )
| ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV390 ) ) ) )
= $false )
| ( ( SV390
= ( set_intersection2 @ SV112 @ SV322 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2231]) ).
thf(2370,plain,
! [SV391: $i,SV323: $i,SV112: $i] :
( ( ( ~ ! [SY1008: $i] :
( ~ ( in @ SY1008 @ SV112 )
| ~ ( in @ SY1008 @ SV323 )
| ( in @ SY1008 @ SV391 ) )
| ~ ~ ( ~ ! [SY1009: $i] :
( ~ ( in @ SY1009 @ SV391 )
| ( in @ SY1009 @ SV112 ) )
| ~ ! [SY1010: $i] :
( ~ ( in @ SY1010 @ SV391 )
| ( in @ SY1010 @ SV323 ) ) ) )
= $false )
| ( ( SV391
= ( set_intersection2 @ SV112 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2232]) ).
thf(2371,plain,
! [SV258: $i,SV324: $i] :
( ( ( ! [SY952: $i] :
( ~ ( in @ ( sK47_C @ SV324 @ SV258 ) @ SY952 )
| ~ ( in @ SY952 @ SV258 ) )
| ~ ( in @ ( sK47_C @ SV324 @ SV258 ) @ SV324 ) )
= $true )
| ( ( SV324
= ( union @ SV258 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2233]) ).
thf(2372,plain,
! [SV258: $i,SV324: $i] :
( ( ( ~ ( ~ ( in @ ( sK47_C @ SV324 @ SV258 ) @ ( sK48_SY487 @ SV324 @ SV258 ) )
| ~ ( in @ ( sK48_SY487 @ SV324 @ SV258 ) @ SV258 ) )
| ( in @ ( sK47_C @ SV324 @ SV258 ) @ SV324 ) )
= $true )
| ( ( SV324
= ( union @ SV258 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2234]) ).
thf(2373,plain,
! [SV325: $i,SV259: $i] :
( ( ( ~ ! [SY953: $i] :
( ! [SY881: $i] :
( ~ ( in @ SY953 @ SY881 )
| ~ ( in @ SY881 @ SV259 ) )
| ( in @ SY953 @ SV325 ) ) )
= $false )
| ( ( SV325
= ( union @ SV259 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2235]) ).
thf(2374,plain,
! [SV259: $i,SV325: $i] :
( ( ( ~ ! [SY955: $i] :
( ~ ( in @ SY955 @ SV325 )
| ~ ( ~ ( in @ SY955 @ ( sK46_D @ SY955 @ SV325 @ SV259 ) )
| ~ ( in @ ( sK46_D @ SY955 @ SV325 @ SV259 ) @ SV259 ) ) ) )
= $false )
| ( ( SV325
= ( union @ SV259 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2235]) ).
thf(2375,plain,
! [SV113: $i,SV225: $i,SV463: $i] :
( ( ( ~ ( relation @ SV463 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) @ SV113 )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV225 )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 ) )
| ~ ~ ( ~ ( ( in @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) @ SV113 )
| ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV225 )
| ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 ) ) ) )
| ( SV463
= ( relation_rng_restriction @ SV113 @ SV225 ) ) )
= $true )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2236]) ).
thf(2376,plain,
! [SV225: $i,SV113: $i,SV464: $i] :
( ( ( ~ ( relation @ SV464 ) )
= $true )
| ( ( ( SV464
!= ( relation_rng_restriction @ SV113 @ SV225 ) )
| ~ ( ~ ! [SY1094: $i,SY1095: $i] :
( ~ ( in @ SY1095 @ SV113 )
| ~ ( in @ ( ordered_pair @ SY1094 @ SY1095 ) @ SV225 )
| ( in @ ( ordered_pair @ SY1094 @ SY1095 ) @ SV464 ) )
| ~ ~ ( ~ ! [SY1096: $i,SY1097: $i] :
( ~ ( in @ ( ordered_pair @ SY1096 @ SY1097 ) @ SV464 )
| ( in @ SY1097 @ SV113 ) )
| ~ ! [SY1098: $i,SY1099: $i] :
( ~ ( in @ ( ordered_pair @ SY1098 @ SY1099 ) @ SV464 )
| ( in @ ( ordered_pair @ SY1098 @ SY1099 ) @ SV225 ) ) ) ) )
= $true )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2237]) ).
thf(2377,plain,
! [SV260: $i,SV326: $i] :
( ( ( relation @ SV326 )
= $false )
| ( ( empty @ SV260 )
= $false )
| ( ( empty @ ( relation_composition @ SV326 @ SV260 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2238]) ).
thf(2378,plain,
! [SV261: $i,SV327: $i] :
( ( ( relation @ SV327 )
= $false )
| ( ( empty @ SV261 )
= $false )
| ( ( relation @ ( relation_composition @ SV327 @ SV261 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2239]) ).
thf(2379,plain,
! [SV419: $i,SV226: $i,SV392: $i,SV114: $i] :
( ( ( ~ ( in @ SV114 @ SV392 ) )
= $true )
| ( ( ~ ( in @ SV226 @ SV419 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SV392 @ SV419 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2240]) ).
thf(2380,plain,
! [SV495: $i,SV226: $i,SV114: $i] :
( ( ! [SY1124: $i] :
~ ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SV495 @ SY1124 ) )
| ( in @ SV114 @ SV495 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2241]) ).
thf(2381,plain,
! [SV496: $i,SV226: $i,SV114: $i] :
( ( ! [SY1125: $i] :
( ~ ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SV496 @ SY1125 ) )
| ( in @ SV226 @ SY1125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2242]) ).
thf(2382,plain,
! [SV262: $i,SV328: $i] :
( ( ( in @ ( sK72_C @ SV328 @ SV262 ) @ SV262 )
= $true )
| ( ( disjoint @ SV262 @ SV328 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2243]) ).
thf(2383,plain,
! [SV262: $i,SV328: $i] :
( ( ( in @ ( sK72_C @ SV328 @ SV262 ) @ SV328 )
= $true )
| ( ( disjoint @ SV262 @ SV328 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2244]) ).
thf(2384,plain,
! [SV329: $i,SV263: $i,SV420: $i] :
( ( ( in @ SV420 @ SV263 )
= $false )
| ( ( ~ ( in @ SV420 @ SV329 ) )
= $true )
| ( ( ~ ( disjoint @ SV263 @ SV329 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2245]) ).
thf(2385,plain,
! [SV264: $i,SV330: $i] :
( ( ( ( ( sK62_C @ SV330 @ SV264 )
!= SV264 )
| ~ ( in @ ( sK62_C @ SV330 @ SV264 ) @ SV330 ) )
= $true )
| ( ( SV330
= ( singleton @ SV264 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2246]) ).
thf(2386,plain,
! [SV264: $i,SV330: $i] :
( ( ( ( ( sK62_C @ SV330 @ SV264 )
= SV264 )
| ( in @ ( sK62_C @ SV330 @ SV264 ) @ SV330 ) )
= $true )
| ( ( SV330
= ( singleton @ SV264 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2247]) ).
thf(2387,plain,
! [SV331: $i,SV265: $i] :
( ( ( ~ ! [SY957: $i] :
( ( SY957 != SV265 )
| ( in @ SY957 @ SV331 ) ) )
= $false )
| ( ( SV331
= ( singleton @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2248]) ).
thf(2388,plain,
! [SV265: $i,SV331: $i] :
( ( ( ~ ! [SY958: $i] :
( ~ ( in @ SY958 @ SV331 )
| ( SY958 = SV265 ) ) )
= $false )
| ( ( SV331
= ( singleton @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2248]) ).
thf(2389,plain,
! [SV115: $i,SV465: $i] :
( ( ( ~ ( ~ ! [SY1100: $i] :
( ~ ( subset @ SY1100 @ SV465 )
| ( in @ SY1100 @ ( sK43_SY481 @ SV465 @ SV115 ) ) )
| ~ ( in @ ( sK43_SY481 @ SV465 @ SV115 ) @ ( sK42_B @ SV115 ) ) ) )
= $true )
| ( ( ~ ( in @ SV465 @ ( sK42_B @ SV115 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2251]) ).
thf(2390,plain,
! [SV115: $i] :
( ( ~ ! [SY633: $i,SY634: $i] :
( ~ ( in @ SY633 @ ( sK42_B @ SV115 ) )
| ~ ( subset @ SY634 @ SY633 )
| ( in @ SY634 @ ( sK42_B @ SV115 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2252]) ).
thf(2391,plain,
! [SV115: $i] :
( ( ~ ( in @ SV115 @ ( sK42_B @ SV115 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2252]) ).
thf(2392,plain,
! [SV422: $i] :
( ( ( SV422 = empty_set )
= $false )
| ( ( ! [SY1033: $i] : ( subset @ SV422 @ ( singleton @ SY1033 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2254]) ).
thf(2393,plain,
! [SV466: $i,SV423: $i] :
( ( ( ( SV423
!= ( singleton @ SV466 ) ) )
= $true )
| ( ( subset @ SV423 @ ( singleton @ SV466 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2255]) ).
thf(2394,plain,
! [SV116: $i] :
( ( ( ~ ! [SY635: $i] :
( ~ ( in @ SY635 @ ( relation_dom @ SV116 ) )
| ! [SY636: $i] :
( ( SY636
!= ( apply @ SV116 @ SY635 ) )
| ( in @ ( ordered_pair @ SY635 @ SY636 ) @ SV116 ) ) )
| ~ ! [SY637: $i] :
( ~ ( in @ SY637 @ ( relation_dom @ SV116 ) )
| ! [SY638: $i] :
( ~ ( in @ ( ordered_pair @ SY637 @ SY638 ) @ SV116 )
| ( SY638
= ( apply @ SV116 @ SY637 ) ) ) ) )
= $false )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2256]) ).
thf(2395,plain,
! [SV116: $i] :
( ( ( ~ ! [SY639: $i] :
( ( in @ SY639 @ ( relation_dom @ SV116 ) )
| ! [SY640: $i] :
( ( SY640
!= ( apply @ SV116 @ SY639 ) )
| ( SY640 = empty_set ) ) )
| ~ ! [SY641: $i] :
( ( in @ SY641 @ ( relation_dom @ SV116 ) )
| ! [SY642: $i] :
( ( SY642 != empty_set )
| ( SY642
= ( apply @ SV116 @ SY641 ) ) ) ) )
= $false )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2257]) ).
thf(2396,plain,
! [SV393: $i,SV334: $i,SV117: $i] :
( ( ( ~ ( ! [SY1012: $i,SY1013: $i] :
( ~ ( in @ SY1012 @ SV117 )
| ~ ( in @ SY1013 @ SV334 )
| ( ( sK53_D @ SV393 @ SV334 @ SV117 )
!= ( ordered_pair @ SY1012 @ SY1013 ) ) )
| ~ ( in @ ( sK53_D @ SV393 @ SV334 @ SV117 ) @ SV393 ) ) )
= $false )
| ( ( SV393
= ( cartesian_product2 @ SV117 @ SV334 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2258]) ).
thf(2397,plain,
! [SV117: $i,SV334: $i,SV393: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK54_SY491 @ SV393 @ SV334 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK55_SY493 @ SV393 @ SV334 @ SV117 ) @ SV334 ) )
| ( ( sK53_D @ SV393 @ SV334 @ SV117 )
!= ( ordered_pair @ ( sK54_SY491 @ SV393 @ SV334 @ SV117 ) @ ( sK55_SY493 @ SV393 @ SV334 @ SV117 ) ) ) )
| ( in @ ( sK53_D @ SV393 @ SV334 @ SV117 ) @ SV393 ) ) )
= $false )
| ( ( SV393
= ( cartesian_product2 @ SV117 @ SV334 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2258]) ).
thf(2398,plain,
! [SV394: $i,SV335: $i,SV117: $i] :
( ( ( ~ ! [SY1014: $i] :
( ! [SY964: $i,SY965: $i] :
( ~ ( in @ SY964 @ SV117 )
| ~ ( in @ SY965 @ SV335 )
| ( SY1014
!= ( ordered_pair @ SY964 @ SY965 ) ) )
| ( in @ SY1014 @ SV394 ) )
| ~ ! [SY1017: $i] :
( ~ ( in @ SY1017 @ SV394 )
| ~ ( ~ ~ ( ~ ( in @ ( sK51_E @ SY1017 @ SV394 @ SV335 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK52_SY488 @ SY1017 @ SV394 @ SV335 @ SV117 ) @ SV335 ) )
| ( SY1017
!= ( ordered_pair @ ( sK51_E @ SY1017 @ SV394 @ SV335 @ SV117 ) @ ( sK52_SY488 @ SY1017 @ SV394 @ SV335 @ SV117 ) ) ) ) ) )
= $false )
| ( ( SV394
= ( cartesian_product2 @ SV117 @ SV335 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2259]) ).
thf(2399,plain,
! [SV118: $i,SV338: $i,SV395: $i] :
( ( ( function @ SV395 )
= $false )
| ( ( ~ ( relation @ SV395 ) )
= $true )
| ( ( ( SV338
!= ( apply @ SV395 @ SV118 ) )
| ~ ( in @ SV118 @ ( relation_dom @ SV395 ) )
| ( in @ ( ordered_pair @ SV118 @ SV338 ) @ SV395 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2262]) ).
thf(2400,plain,
! [SV467: $i,SV118: $i,SV497: $i] :
( ( ~ ( function @ SV497 )
| ~ ( relation @ SV497 )
| ~ ( in @ ( ordered_pair @ SV118 @ SV467 ) @ SV497 )
| ( SV467
= ( apply @ SV497 @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2263]) ).
thf(2401,plain,
! [SV468: $i,SV118: $i,SV498: $i] :
( ( ~ ( function @ SV498 )
| ~ ( relation @ SV498 )
| ~ ( in @ ( ordered_pair @ SV118 @ SV468 ) @ SV498 )
| ( in @ SV118 @ ( relation_dom @ SV498 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2264]) ).
thf(2402,plain,
! [SV273: $i,SV339: $i] :
( ( ( ~ ( ( ( sK69_C @ SV339 @ SV273 )
!= ( sK70_SY500 @ SV339 @ SV273 ) )
| ~ ( in @ ( sK69_C @ SV339 @ SV273 ) @ SV273 )
| ~ ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 ) )
| ~ ~ ( ~ ( ( ( sK69_C @ SV339 @ SV273 )
= ( sK70_SY500 @ SV339 @ SV273 ) )
| ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 ) )
| ~ ( ( in @ ( sK69_C @ SV339 @ SV273 ) @ SV273 )
| ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 ) ) ) )
= $false )
| ( ( SV339
= ( identity_relation @ SV273 ) )
= $true )
| ( ( relation @ SV339 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2265]) ).
thf(2403,plain,
! [SV274: $i,SV340: $i] :
( ( ( SV340
= ( identity_relation @ SV274 ) )
= $false )
| ( ( ~ ( ~ ! [SY968: $i,SY969: $i] :
( ( SY968 != SY969 )
| ~ ( in @ SY968 @ SV274 )
| ( in @ ( ordered_pair @ SY968 @ SY969 ) @ SV340 ) )
| ~ ~ ( ~ ! [SY970: $i,SY971: $i] :
( ~ ( in @ ( ordered_pair @ SY970 @ SY971 ) @ SV340 )
| ( SY970 = SY971 ) )
| ~ ! [SY972: $i] :
( ! [SY973: $i] :
~ ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV340 )
| ( in @ SY972 @ SV274 ) ) ) ) )
= $true )
| ( ( relation @ SV340 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2266]) ).
thf(2404,plain,
! [SV120: $i,SV275: $i] :
( ( ( ! [SY904: $i] :
( ~ ( relation @ SY904 )
| ~ ( ~ ( ! [SY905: $i] :
( ~ ( in @ ( ordered_pair @ ( sK13_D @ SY904 @ SV275 @ SV120 ) @ SY905 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY905 @ ( sK14_SY457 @ SY904 @ SV275 @ SV120 ) ) @ SV275 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_D @ SY904 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SY904 @ SV275 @ SV120 ) ) @ SY904 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_D @ SY904 @ SV275 @ SV120 ) @ ( sK15_SY461 @ SY904 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY461 @ SY904 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SY904 @ SV275 @ SV120 ) ) @ SV275 ) )
| ( in @ ( ordered_pair @ ( sK13_D @ SY904 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SY904 @ SV275 @ SV120 ) ) @ SY904 ) ) )
| ( SY904
= ( relation_composition @ SV120 @ SV275 ) ) ) )
= $true )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2267]) ).
thf(2405,plain,
! [SV275: $i,SV120: $i] :
( ( ( ! [SY906: $i] :
( ~ ( relation @ SY906 )
| ( SY906
!= ( relation_composition @ SV120 @ SV275 ) )
| ~ ( ~ ! [SY907: $i,SY908: $i] :
( ! [SY909: $i] :
( ~ ( in @ ( ordered_pair @ SY907 @ SY909 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY909 @ SY908 ) @ SV275 ) )
| ( in @ ( ordered_pair @ SY907 @ SY908 ) @ SY906 ) )
| ~ ! [SY910: $i,SY911: $i] :
( ~ ( in @ ( ordered_pair @ SY910 @ SY911 ) @ SY906 )
| ~ ( ~ ( in @ ( ordered_pair @ SY910 @ ( sK12_F @ SY911 @ SY910 @ SY906 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK12_F @ SY911 @ SY910 @ SY906 @ SV275 @ SV120 ) @ SY911 ) @ SV275 ) ) ) ) ) )
= $true )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2268]) ).
thf(2406,plain,
! [SV227: $i,SV121: $i,SV469: $i] :
( ( ( ~ ( element @ SV469 @ ( powerset @ SV121 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV227 @ SV469 )
| ( subset @ SV227 @ ( subset_complement @ SV121 @ SV469 ) ) )
= $true )
| ( ( element @ SV227 @ ( powerset @ SV121 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2269]) ).
thf(2407,plain,
! [SV227: $i,SV121: $i,SV470: $i] :
( ( ( ~ ( element @ SV470 @ ( powerset @ SV121 ) ) )
= $true )
| ( ( ~ ( subset @ SV227 @ ( subset_complement @ SV121 @ SV470 ) )
| ( disjoint @ SV227 @ SV470 ) )
= $true )
| ( ( element @ SV227 @ ( powerset @ SV121 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2270]) ).
thf(2408,plain,
! [SV396: $i,SV341: $i,SV122: $i] :
( ( ( ~ ( in @ SV122 @ SV341 )
| ~ ( in @ SV122 @ ( relation_rng @ SV396 ) ) )
= $true )
| ( ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SV341 @ SV396 ) ) )
= $true )
| ( ( relation @ SV396 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2271]) ).
thf(2409,plain,
! [SV471: $i,SV122: $i,SV499: $i] :
( ( ~ ( relation @ SV499 )
| ~ ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SV471 @ SV499 ) ) )
| ( in @ SV122 @ SV471 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2272]) ).
thf(2410,plain,
! [SV472: $i,SV122: $i,SV500: $i] :
( ( ~ ( relation @ SV500 )
| ~ ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SV472 @ SV500 ) ) )
| ( in @ SV122 @ ( relation_rng @ SV500 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2273]) ).
thf(2411,plain,
! [SV123: $i,SV424: $i,SV473: $i] :
( ( ( ~ ( relation @ SV473 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ SV424 )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV123 )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 ) )
| ~ ~ ( ~ ( ( in @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ SV424 )
| ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 ) ) ) )
| ( SV473
= ( relation_dom_restriction @ SV123 @ SV424 ) ) )
= $true )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2274]) ).
thf(2412,plain,
! [SV425: $i,SV123: $i,SV474: $i] :
( ( ( ~ ( relation @ SV474 ) )
= $true )
| ( ( ( SV474
!= ( relation_dom_restriction @ SV123 @ SV425 ) )
| ~ ( ~ ! [SY1105: $i,SY1106: $i] :
( ~ ( in @ SY1105 @ SV425 )
| ~ ( in @ ( ordered_pair @ SY1105 @ SY1106 ) @ SV123 )
| ( in @ ( ordered_pair @ SY1105 @ SY1106 ) @ SV474 ) )
| ~ ~ ( ~ ! [SY1107: $i] :
( ! [SY1108: $i] :
~ ( in @ ( ordered_pair @ SY1107 @ SY1108 ) @ SV474 )
| ( in @ SY1107 @ SV425 ) )
| ~ ! [SY1109: $i,SY1110: $i] :
( ~ ( in @ ( ordered_pair @ SY1109 @ SY1110 ) @ SV474 )
| ( in @ ( ordered_pair @ SY1109 @ SY1110 ) @ SV123 ) ) ) ) )
= $true )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2275]) ).
thf(2413,plain,
! [SV124: $i,SV426: $i] :
( ( ( relation @ SV426 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_C @ SV426 @ SV124 ) @ ( sK17_SY462 @ SV426 @ SV124 ) ) @ SV426 )
| ~ ( in @ ( ordered_pair @ ( sK17_SY462 @ SV426 @ SV124 ) @ ( sK16_C @ SV426 @ SV124 ) ) @ SV124 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK16_C @ SV426 @ SV124 ) @ ( sK17_SY462 @ SV426 @ SV124 ) ) @ SV426 )
| ( in @ ( ordered_pair @ ( sK17_SY462 @ SV426 @ SV124 ) @ ( sK16_C @ SV426 @ SV124 ) ) @ SV124 ) ) )
| ( SV426
= ( relation_inverse @ SV124 ) ) )
= $true )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2276]) ).
thf(2414,plain,
! [SV124: $i,SV427: $i] :
( ( ( relation @ SV427 )
= $false )
| ( ( ( SV427
!= ( relation_inverse @ SV124 ) )
| ~ ( ~ ! [SY1043: $i,SY1044: $i] :
( ~ ( in @ ( ordered_pair @ SY1043 @ SY1044 ) @ SV427 )
| ( in @ ( ordered_pair @ SY1044 @ SY1043 ) @ SV124 ) )
| ~ ! [SY1045: $i,SY1046: $i] :
( ~ ( in @ ( ordered_pair @ SY1046 @ SY1045 ) @ SV124 )
| ( in @ ( ordered_pair @ SY1045 @ SY1046 ) @ SV427 ) ) ) )
= $true )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2277]) ).
thf(2415,plain,
! [SV282: $i,SV348: $i] :
( ( ( relation @ SV348 )
= $false )
| ( ( function @ SV348 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK38_C @ SV348 @ SV282 ) @ SV282 )
| ~ ( ( ( apply @ SV348 @ ( sK38_C @ SV348 @ SV282 ) )
!= ( sK38_C @ SV348 @ SV282 ) ) ) )
| ( ( relation_dom @ SV348 )
!= SV282 )
| ( SV348
= ( identity_relation @ SV282 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2278]) ).
thf(2416,plain,
! [SV428: $i,SV475: $i] :
( ( ( ~ ( function @ SV475 )
| ~ ( relation @ SV475 ) )
= $true )
| ( ( ( SV475
!= ( identity_relation @ SV428 ) )
| ! [SY1111: $i] :
( ~ ( in @ SY1111 @ SV428 )
| ( ( apply @ SV475 @ SY1111 )
= SY1111 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2279]) ).
thf(2417,plain,
! [SV429: $i,SV476: $i] :
( ( ( ~ ( function @ SV476 )
| ~ ( relation @ SV476 ) )
= $true )
| ( ( ( SV476
!= ( identity_relation @ SV429 ) )
| ( ( relation_dom @ SV476 )
= SV429 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2280]) ).
thf(2418,plain,
! [SV285: $i,SV351: $i] :
( ( ( subset @ SV351 @ SV285 )
= $false )
| ( ( subset @ SV285 @ SV351 )
= $false )
| ( ( SV285 = SV351 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2281]) ).
thf(2419,plain,
! [SV477: $i,SV430: $i] :
( ( ( ( SV430 != SV477 ) )
= $true )
| ( ( subset @ SV430 @ SV477 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2282]) ).
thf(2420,plain,
! [SV478: $i,SV431: $i] :
( ( ( ( SV431 != SV478 ) )
= $true )
| ( ( subset @ SV478 @ SV431 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2283]) ).
thf(2421,plain,
! [SV125: $i,SV432: $i,SV479: $i] :
( ( ( ~ ( ~ ( ! [SY1112: $i] :
( ~ ( in @ ( ordered_pair @ SY1112 @ ( sK30_D @ SV479 @ SV432 @ SV125 ) ) @ SV125 )
| ~ ( in @ SY1112 @ SV432 ) )
| ~ ( in @ ( sK30_D @ SV479 @ SV432 @ SV125 ) @ SV479 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_SY471 @ SV479 @ SV432 @ SV125 ) @ ( sK30_D @ SV479 @ SV432 @ SV125 ) ) @ SV125 )
| ~ ( in @ ( sK31_SY471 @ SV479 @ SV432 @ SV125 ) @ SV432 ) )
| ( in @ ( sK30_D @ SV479 @ SV432 @ SV125 ) @ SV479 ) ) ) )
= $true )
| ( ( SV479
= ( relation_image @ SV125 @ SV432 ) )
= $true )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2284]) ).
thf(2422,plain,
! [SV433: $i,SV125: $i,SV480: $i] :
( ( ( ( SV480
!= ( relation_image @ SV125 @ SV433 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1113: $i] :
( ! [SY1056: $i] :
( ~ ( in @ ( ordered_pair @ SY1056 @ SY1113 ) @ SV125 )
| ~ ( in @ SY1056 @ SV433 ) )
| ( in @ SY1113 @ SV480 ) )
| ~ ! [SY1115: $i] :
( ~ ( in @ SY1115 @ SV480 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK29_E @ SY1115 @ SV480 @ SV433 @ SV125 ) @ SY1115 ) @ SV125 )
| ~ ( in @ ( sK29_E @ SY1115 @ SV480 @ SV433 @ SV125 ) @ SV433 ) ) ) ) )
= $true )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2285]) ).
thf(2423,plain,
! [SV397: $i,SV352: $i,SV126: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV126 @ SV352 ) @ SV397 ) )
= $true )
| ( ( in @ SV126 @ ( relation_field @ SV397 ) )
= $true )
| ( ( relation @ SV397 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2286]) ).
thf(2424,plain,
! [SV398: $i,SV353: $i,SV126: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV126 @ SV353 ) @ SV398 ) )
= $true )
| ( ( in @ SV353 @ ( relation_field @ SV398 ) )
= $true )
| ( ( relation @ SV398 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2287]) ).
thf(2425,plain,
! [SV228: $i,SV399: $i,SV127: $i,SV434: $i] :
( ( ( relation @ SV434 )
= $false )
| ( ( ~ ( in @ SV127 @ SV399 )
| ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ SV434 )
| ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SV399 ) @ SV434 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2288]) ).
thf(2426,plain,
! [SV501: $i,SV228: $i,SV127: $i] :
( ( ! [SY1126: $i] :
( ~ ( relation @ SY1126 )
| ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SV501 ) @ SY1126 ) )
| ( in @ SV127 @ SV501 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2289]) ).
thf(2427,plain,
! [SV502: $i,SV228: $i,SV127: $i] :
( ( ! [SY1127: $i] :
( ~ ( relation @ SY1127 )
| ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SV502 ) @ SY1127 ) )
| ( in @ ( ordered_pair @ SV127 @ SV228 ) @ SY1127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2290]) ).
thf(2428,plain,
! [SV356: $i,SV400: $i,SV128: $i] :
( ( ( in @ SV128 @ SV400 )
= $false )
| ( ( ~ ( in @ SV356 @ SV400 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV128 @ SV356 ) @ SV400 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2291]) ).
thf(2429,plain,
! [SV503: $i,SV481: $i,SV128: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV128 @ SV481 ) @ SV503 )
| ( in @ SV128 @ SV503 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2292]) ).
thf(2430,plain,
! [SV504: $i,SV482: $i,SV128: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV128 @ SV482 ) @ SV504 )
| ( in @ SV482 @ SV504 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2293]) ).
thf(2431,plain,
! [SV435: $i,SV505: $i] :
( ( ( ~ ( element @ SV505 @ SV435 )
| ( in @ SV505 @ SV435 ) )
= $true )
| ( ( empty @ SV435 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2294]) ).
thf(2432,plain,
! [SV436: $i,SV506: $i] :
( ( ( ~ ( in @ SV506 @ SV436 )
| ( element @ SV506 @ SV436 ) )
= $true )
| ( ( empty @ SV436 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2295]) ).
thf(2433,plain,
! [SV437: $i] :
( ( ( empty @ SV437 )
= $false )
| ( ( ! [SY1060: $i] :
( ~ ( element @ SY1060 @ SV437 )
| ( empty @ SY1060 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2296]) ).
thf(2434,plain,
! [SV438: $i] :
( ( ( empty @ SV438 )
= $false )
| ( ( ! [SY1061: $i] :
( ~ ( empty @ SY1061 )
| ( element @ SY1061 @ SV438 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2297]) ).
thf(2435,plain,
! [SV129: $i,SV439: $i] :
( ( ( ~ ( ! [SY1062: $i] :
~ ( in @ ( ordered_pair @ SY1062 @ ( sK19_C @ SV439 @ SV129 ) ) @ SV129 )
| ~ ( in @ ( sK19_C @ SV439 @ SV129 ) @ SV439 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK20_SY464 @ SV439 @ SV129 ) @ ( sK19_C @ SV439 @ SV129 ) ) @ SV129 )
| ( in @ ( sK19_C @ SV439 @ SV129 ) @ SV439 ) ) )
= $false )
| ( ( SV439
= ( relation_rng @ SV129 ) )
= $true )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2298]) ).
thf(2436,plain,
! [SV129: $i,SV440: $i] :
( ( ( SV440
= ( relation_rng @ SV129 ) )
= $false )
| ( ( ~ ( ~ ! [SY1063: $i] :
( ! [SY722: $i] :
~ ( in @ ( ordered_pair @ SY722 @ SY1063 ) @ SV129 )
| ( in @ SY1063 @ SV440 ) )
| ~ ! [SY1065: $i] :
( ~ ( in @ SY1065 @ SV440 )
| ( in @ ( ordered_pair @ ( sK18_D @ SY1065 @ SV440 @ SV129 ) @ SY1065 ) @ SV129 ) ) ) )
= $true )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2299]) ).
thf(2437,plain,
! [SV441: $i,SV360: $i,SV293: $i] :
( ( ( disjoint @ SV293 @ SV360 )
= $false )
| ( ( in @ SV441 @ ( set_intersection2 @ SV293 @ SV360 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2301]) ).
thf(2438,plain,
! [SV131: $i,SV442: $i,SV483: $i] :
( ( ( ~ ( ~ ( ! [SY1118: $i] :
( ~ ( in @ ( ordered_pair @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SY1118 ) @ SV131 )
| ~ ( in @ SY1118 @ SV442 ) )
| ~ ( in @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SV483 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ ( sK28_SY469 @ SV483 @ SV442 @ SV131 ) ) @ SV131 )
| ~ ( in @ ( sK28_SY469 @ SV483 @ SV442 @ SV131 ) @ SV442 ) )
| ( in @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SV483 ) ) ) )
= $true )
| ( ( SV483
= ( relation_inverse_image @ SV131 @ SV442 ) )
= $true )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2302]) ).
thf(2439,plain,
! [SV443: $i,SV131: $i,SV484: $i] :
( ( ( ( SV484
!= ( relation_inverse_image @ SV131 @ SV443 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1119: $i] :
( ! [SY1070: $i] :
( ~ ( in @ ( ordered_pair @ SY1119 @ SY1070 ) @ SV131 )
| ~ ( in @ SY1070 @ SV443 ) )
| ( in @ SY1119 @ SV484 ) )
| ~ ! [SY1121: $i] :
( ~ ( in @ SY1121 @ SV484 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1121 @ ( sK26_E @ SY1121 @ SV484 @ SV443 @ SV131 ) ) @ SV131 )
| ~ ( in @ ( sK26_E @ SY1121 @ SV484 @ SV443 @ SV131 ) @ SV443 ) ) ) ) )
= $true )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2303]) ).
thf(2440,plain,
! [SV507: $i,SV296: $i] :
( ( ( ! [SY1128: $i] :
( ( sK68_B @ SV296 )
!= ( ordered_pair @ SV507 @ SY1128 ) ) )
= $true )
| ( ( relation @ SV296 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2304]) ).
thf(2441,plain,
! [SV297: $i,SV444: $i] :
( ( ( in @ SV444 @ SV297 )
= $false )
| ( ( SV444
= ( ordered_pair @ ( sK66_C @ SV444 @ SV297 ) @ ( sK67_SY497 @ SV444 @ SV297 ) ) )
= $true )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2306]) ).
thf(2442,plain,
! [SV401: $i,SV363: $i,SV132: $i] :
( ( ( ~ ( in @ SV132 @ SV363 )
| ~ ( in @ SV132 @ ( relation_dom @ SV401 ) ) )
= $true )
| ( ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SV401 @ SV363 ) ) )
= $true )
| ( ( relation @ SV401 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2307]) ).
thf(2443,plain,
! [SV485: $i,SV132: $i,SV508: $i] :
( ( ~ ( relation @ SV508 )
| ~ ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SV508 @ SV485 ) ) )
| ( in @ SV132 @ SV485 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2308]) ).
thf(2444,plain,
! [SV486: $i,SV132: $i,SV509: $i] :
( ( ~ ( relation @ SV509 )
| ~ ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SV509 @ SV486 ) ) )
| ( in @ SV132 @ ( relation_dom @ SV509 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2309]) ).
thf(2445,plain,
! [SV402: $i,SV364: $i,SV133: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV133 @ SV364 ) @ SV402 ) )
= $true )
| ( ( in @ SV133 @ ( relation_dom @ SV402 ) )
= $true )
| ( ( relation @ SV402 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2310]) ).
thf(2446,plain,
! [SV403: $i,SV365: $i,SV133: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV133 @ SV365 ) @ SV403 ) )
= $true )
| ( ( in @ SV365 @ ( relation_rng @ SV403 ) )
= $true )
| ( ( relation @ SV403 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2311]) ).
thf(2447,plain,
! [SV134: $i,SV445: $i] :
( ( ( ~ ( ! [SY1072: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SV445 @ SV134 ) @ SY1072 ) @ SV134 )
| ~ ( in @ ( sK22_C @ SV445 @ SV134 ) @ SV445 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SV445 @ SV134 ) @ ( sK23_SY466 @ SV445 @ SV134 ) ) @ SV134 )
| ( in @ ( sK22_C @ SV445 @ SV134 ) @ SV445 ) ) )
= $false )
| ( ( SV445
= ( relation_dom @ SV134 ) )
= $true )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2312]) ).
thf(2448,plain,
! [SV134: $i,SV446: $i] :
( ( ( SV446
= ( relation_dom @ SV134 ) )
= $false )
| ( ( ~ ( ~ ! [SY1073: $i] :
( ! [SY747: $i] :
~ ( in @ ( ordered_pair @ SY1073 @ SY747 ) @ SV134 )
| ( in @ SY1073 @ SV446 ) )
| ~ ! [SY1075: $i] :
( ~ ( in @ SY1075 @ SV446 )
| ( in @ ( ordered_pair @ SY1075 @ ( sK21_D @ SY1075 @ SV446 @ SV134 ) ) @ SV134 ) ) ) )
= $true )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2313]) ).
thf(2449,plain,
! [SV135: $i,SV366: $i,SV404: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK57_D @ SV404 @ SV366 @ SV135 ) @ SV404 )
| ( ( sK57_D @ SV404 @ SV366 @ SV135 )
!= SV135 ) )
| ~ ( ~ ( in @ ( sK57_D @ SV404 @ SV366 @ SV135 ) @ SV404 )
| ( ( sK57_D @ SV404 @ SV366 @ SV135 )
!= SV366 ) ) ) )
= $false )
| ( ( SV404
= ( unordered_pair @ SV135 @ SV366 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2314]) ).
thf(2450,plain,
! [SV135: $i,SV366: $i,SV404: $i] :
( ( ( ~ ( ( in @ ( sK57_D @ SV404 @ SV366 @ SV135 ) @ SV404 )
| ( ( sK57_D @ SV404 @ SV366 @ SV135 )
= SV135 )
| ( ( sK57_D @ SV404 @ SV366 @ SV135 )
= SV366 ) ) )
= $false )
| ( ( SV404
= ( unordered_pair @ SV135 @ SV366 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2314]) ).
thf(2451,plain,
! [SV367: $i,SV135: $i,SV405: $i] :
( ( ( ~ ! [SY1019: $i] :
( ~ ( in @ SY1019 @ SV405 )
| ( SY1019 = SV135 )
| ( SY1019 = SV367 ) )
| ~ ~ ( ~ ! [SY1020: $i] :
( ( SY1020 != SV135 )
| ( in @ SY1020 @ SV405 ) )
| ~ ! [SY1021: $i] :
( ( SY1021 != SV367 )
| ( in @ SY1021 @ SV405 ) ) ) )
= $false )
| ( ( SV405
= ( unordered_pair @ SV135 @ SV367 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2315]) ).
thf(2452,plain,
! [SV136: $i,SV447: $i] :
( ( ( relation @ SV447 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV136 )
| ~ ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV447 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV136 )
| ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV447 ) ) )
| ( SV136 = SV447 ) )
= $true )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2316]) ).
thf(2453,plain,
! [SV136: $i,SV448: $i] :
( ( ( relation @ SV448 )
= $false )
| ( ( ( SV136 != SV448 )
| ~ ( ~ ! [SY1076: $i,SY1077: $i] :
( ~ ( in @ ( ordered_pair @ SY1076 @ SY1077 ) @ SV136 )
| ( in @ ( ordered_pair @ SY1076 @ SY1077 ) @ SV448 ) )
| ~ ! [SY1078: $i,SY1079: $i] :
( ~ ( in @ ( ordered_pair @ SY1078 @ SY1079 ) @ SV448 )
| ( in @ ( ordered_pair @ SY1078 @ SY1079 ) @ SV136 ) ) ) )
= $true )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2317]) ).
thf(2454,plain,
! [SV368: $i,SV298: $i] :
( ( ( ~ ( function @ SV298 ) )
= $true )
| ( ( ~ ( relation @ SV298 ) )
= $true )
| ( ( ~ ( relation @ SV368 ) )
= $true )
| ( ( ~ ( function @ SV368 ) )
= $true )
| ( ( function @ ( relation_composition @ SV298 @ SV368 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2318]) ).
thf(2455,plain,
! [SV369: $i,SV299: $i] :
( ( ( ~ ( function @ SV299 ) )
= $true )
| ( ( ~ ( relation @ SV299 ) )
= $true )
| ( ( ~ ( relation @ SV369 ) )
= $true )
| ( ( ~ ( function @ SV369 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV299 @ SV369 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2319]) ).
thf(2456,plain,
! [SV230: $i,SV137: $i] :
( ( ( ! [SY861: $i] :
( ~ ( function @ SY861 )
| ~ ( relation @ SY861 )
| ~ ( in @ SV137 @ ( relation_dom @ SY861 ) )
| ~ ( in @ ( apply @ SY861 @ SV137 ) @ ( relation_dom @ SV230 ) )
| ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY861 @ SV230 ) ) ) ) )
= $true )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2320]) ).
thf(2457,plain,
! [SV230: $i,SV137: $i] :
( ( ( ~ ( ~ ! [SY862: $i] :
( ~ ( function @ SY862 )
| ~ ( relation @ SY862 )
| ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY862 @ SV230 ) ) )
| ( in @ SV137 @ ( relation_dom @ SY862 ) ) )
| ~ ! [SY863: $i] :
( ~ ( function @ SY863 )
| ~ ( relation @ SY863 )
| ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY863 @ SV230 ) ) )
| ( in @ ( apply @ SY863 @ SV137 ) @ ( relation_dom @ SV230 ) ) ) ) )
= $true )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2321]) ).
thf(2458,plain,
! [SV138: $i,SV487: $i] :
( ( ( ~ ( in @ SV487 @ ( sK41_B @ SV138 ) ) )
= $true )
| ( ( in @ ( powerset @ SV487 ) @ ( sK41_B @ SV138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2323]) ).
thf(2459,plain,
! [SV138: $i] :
( ( ~ ! [SY768: $i,SY769: $i] :
( ~ ( in @ SY768 @ ( sK41_B @ SV138 ) )
| ~ ( subset @ SY769 @ SY768 )
| ( in @ SY769 @ ( sK41_B @ SV138 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2324]) ).
thf(2460,plain,
! [SV138: $i] :
( ( ~ ( in @ SV138 @ ( sK41_B @ SV138 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2324]) ).
thf(2461,plain,
! [SV139: $i,SV449: $i] :
( ( ( relation @ SV449 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV449 @ SV139 ) @ ( sK25_SY467 @ SV449 @ SV139 ) ) @ SV139 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SV449 @ SV139 ) @ ( sK25_SY467 @ SV449 @ SV139 ) ) @ SV449 ) )
| ( subset @ SV139 @ SV449 ) )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2325]) ).
thf(2462,plain,
! [SV139: $i,SV450: $i] :
( ( ( relation @ SV450 )
= $false )
| ( ( ~ ( subset @ SV139 @ SV450 )
| ! [SY1080: $i,SY1081: $i] :
( ~ ( in @ ( ordered_pair @ SY1080 @ SY1081 ) @ SV139 )
| ( in @ ( ordered_pair @ SY1080 @ SY1081 ) @ SV450 ) ) )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2326]) ).
thf(2463,plain,
! [SV300: $i,SV371: $i] :
( ( ( ~ ( in @ ( sK60_C @ SV371 @ SV300 ) @ SV371 )
| ~ ( subset @ ( sK60_C @ SV371 @ SV300 ) @ SV300 ) )
= $true )
| ( ( SV371
= ( powerset @ SV300 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2327]) ).
thf(2464,plain,
! [SV300: $i,SV371: $i] :
( ( ( ( in @ ( sK60_C @ SV371 @ SV300 ) @ SV371 )
| ( subset @ ( sK60_C @ SV371 @ SV300 ) @ SV300 ) )
= $true )
| ( ( SV371
= ( powerset @ SV300 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2328]) ).
thf(2465,plain,
! [SV301: $i,SV372: $i] :
( ( ( ~ ! [SY987: $i] :
( ~ ( in @ SY987 @ SV372 )
| ( subset @ SY987 @ SV301 ) ) )
= $false )
| ( ( SV372
= ( powerset @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2329]) ).
thf(2466,plain,
! [SV372: $i,SV301: $i] :
( ( ( ~ ! [SY988: $i] :
( ~ ( subset @ SY988 @ SV301 )
| ( in @ SY988 @ SV372 ) ) )
= $false )
| ( ( SV372
= ( powerset @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2329]) ).
thf(2467,plain,
! [SV302: $i,SV373: $i] :
( ( ( relation @ SV373 )
= $false )
| ( ( empty @ SV302 )
= $false )
| ( ( empty @ ( relation_composition @ SV302 @ SV373 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2330]) ).
thf(2468,plain,
! [SV303: $i,SV374: $i] :
( ( ( relation @ SV374 )
= $false )
| ( ( empty @ SV303 )
= $false )
| ( ( relation @ ( relation_composition @ SV303 @ SV374 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2331]) ).
thf(2469,plain,
! [SV140: $i,SV451: $i] :
( ( ( relation @ SV451 )
= $false )
| ( ( ~ ( subset @ SV140 @ SV451 )
| ( subset @ ( relation_dom @ SV140 ) @ ( relation_dom @ SV451 ) ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2332]) ).
thf(2470,plain,
! [SV140: $i,SV452: $i] :
( ( ( relation @ SV452 )
= $false )
| ( ( ~ ( subset @ SV140 @ SV452 )
| ( subset @ ( relation_rng @ SV140 ) @ ( relation_rng @ SV452 ) ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2333]) ).
thf(2471,plain,
! [SV375: $i,SV142: $i,SV406: $i] :
( ( ( ! [SY1022: $i] :
( ~ ( in @ SY1022 @ ( relation_rng @ SV406 ) )
| ~ ( in @ ( ordered_pair @ SV142 @ SY1022 ) @ SV406 )
| ~ ( in @ SY1022 @ SV375 ) ) )
= $true )
| ( ( in @ SV142 @ ( relation_inverse_image @ SV406 @ SV375 ) )
= $true )
| ( ( relation @ SV406 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2334]) ).
thf(2472,plain,
! [SV376: $i,SV407: $i,SV142: $i] :
( ( ( ~ ( in @ SV142 @ ( relation_inverse_image @ SV407 @ SV376 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK39_D @ SV407 @ SV376 @ SV142 ) @ ( relation_rng @ SV407 ) )
| ~ ( in @ ( ordered_pair @ SV142 @ ( sK39_D @ SV407 @ SV376 @ SV142 ) ) @ SV407 ) )
| ~ ( in @ ( sK39_D @ SV407 @ SV376 @ SV142 ) @ SV376 ) ) )
= $true )
| ( ( relation @ SV407 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2335]) ).
thf(2473,plain,
! [SV453: $i,SV510: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( in @ ( sK65_SY495 @ SV510 @ SV453 ) @ SV453 )
| ~ ~ ( in @ ( sK64_C @ SV510 @ SV453 ) @ ( sK65_SY495 @ SV510 @ SV453 ) ) )
| ~ ( in @ ( sK64_C @ SV510 @ SV453 ) @ SV510 ) )
| ~ ( ! [SY1129: $i] :
( ~ ( in @ SY1129 @ SV453 )
| ( in @ ( sK64_C @ SV510 @ SV453 ) @ SY1129 ) )
| ( in @ ( sK64_C @ SV510 @ SV453 ) @ SV510 ) ) )
| ( SV510
= ( set_meet @ SV453 ) ) )
= $true )
| ( ( SV453 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2336]) ).
thf(2474,plain,
! [SV454: $i,SV511: $i] :
( ( ( ( SV511
!= ( set_meet @ SV454 ) )
| ~ ( ~ ! [SY1130: $i] :
( ~ ( ~ ( in @ ( sK63_D @ SY1130 @ SV511 @ SV454 ) @ SV454 )
| ~ ~ ( in @ SY1130 @ ( sK63_D @ SY1130 @ SV511 @ SV454 ) ) )
| ( in @ SY1130 @ SV511 ) )
| ~ ! [SY1131: $i] :
( ~ ( in @ SY1131 @ SV511 )
| ! [SY1087: $i] :
( ~ ( in @ SY1087 @ SV454 )
| ( in @ SY1131 @ SY1087 ) ) ) ) )
= $true )
| ( ( SV454 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2337]) ).
thf(2475,plain,
! [SV455: $i] :
( ( ( SV455 = empty_set )
= $false )
| ( ( ! [SY1088: $i] :
( ( SY1088
!= ( set_meet @ SV455 ) )
| ( SY1088 = empty_set ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2338]) ).
thf(2476,plain,
! [SV456: $i] :
( ( ( SV456 = empty_set )
= $false )
| ( ( ! [SY1089: $i] :
( ( SY1089 != empty_set )
| ( SY1089
= ( set_meet @ SV456 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2339]) ).
thf(2477,plain,
! [SV488: $i,SV457: $i] :
( ( ( ~ ( proper_subset @ SV457 @ SV488 ) )
= $true )
| ( ( ( SV457 != SV488 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2341]) ).
thf(2478,plain,
! [SV489: $i,SV458: $i] :
( ( ( ~ ( proper_subset @ SV458 @ SV489 ) )
= $true )
| ( ( subset @ SV458 @ SV489 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2342]) ).
thf(2479,plain,
! [SV459: $i,SV231: $i,SV408: $i,SV143: $i] :
( ( ( ~ ( in @ SV143 @ SV408 ) )
= $true )
| ( ( ~ ( in @ SV231 @ SV459 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SV408 @ SV459 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2343]) ).
thf(2480,plain,
! [SV512: $i,SV231: $i,SV143: $i] :
( ( ! [SY1133: $i] :
~ ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SV512 @ SY1133 ) )
| ( in @ SV143 @ SV512 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2344]) ).
thf(2481,plain,
! [SV513: $i,SV231: $i,SV143: $i] :
( ( ! [SY1134: $i] :
( ~ ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SV513 @ SY1134 ) )
| ( in @ SV231 @ SY1134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2345]) ).
thf(2482,plain,
! [SV144: $i,SV378: $i,SV409: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV409 )
| ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV144 ) )
| ~ ( ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV409 )
| ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV378 ) ) ) )
= $false )
| ( ( SV409
= ( set_union2 @ SV144 @ SV378 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2346]) ).
thf(2483,plain,
! [SV144: $i,SV378: $i,SV409: $i] :
( ( ( ~ ( ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV409 )
| ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV144 )
| ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV378 ) ) )
= $false )
| ( ( SV409
= ( set_union2 @ SV144 @ SV378 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2346]) ).
thf(2484,plain,
! [SV379: $i,SV144: $i,SV410: $i] :
( ( ( ~ ! [SY1024: $i] :
( ~ ( in @ SY1024 @ SV410 )
| ( in @ SY1024 @ SV144 )
| ( in @ SY1024 @ SV379 ) )
| ~ ~ ( ~ ! [SY1025: $i] :
( ~ ( in @ SY1025 @ SV144 )
| ( in @ SY1025 @ SV410 ) )
| ~ ! [SY1026: $i] :
( ~ ( in @ SY1026 @ SV379 )
| ( in @ SY1026 @ SV410 ) ) ) )
= $false )
| ( ( SV410
= ( set_union2 @ SV144 @ SV379 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2347]) ).
thf(2485,plain,
! [SV380: $i,SV145: $i,SV411: $i] :
( ( ( ! [SY1027: $i] :
( ~ ( in @ SY1027 @ ( relation_dom @ SV411 ) )
| ~ ( in @ ( ordered_pair @ SY1027 @ SV145 ) @ SV411 )
| ~ ( in @ SY1027 @ SV380 ) ) )
= $true )
| ( ( in @ SV145 @ ( relation_image @ SV411 @ SV380 ) )
= $true )
| ( ( relation @ SV411 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2348]) ).
thf(2486,plain,
! [SV381: $i,SV412: $i,SV145: $i] :
( ( ( ~ ( in @ SV145 @ ( relation_image @ SV412 @ SV381 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK40_D @ SV412 @ SV381 @ SV145 ) @ ( relation_dom @ SV412 ) )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV412 @ SV381 @ SV145 ) @ SV145 ) @ SV412 ) )
| ~ ( in @ ( sK40_D @ SV412 @ SV381 @ SV145 ) @ SV381 ) ) )
= $true )
| ( ( relation @ SV412 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2349]) ).
thf(2487,plain,
! [SV147: $i,SV232: $i] :
( ( ( in @ ( sK44_C @ SV232 @ SV147 ) @ SV232 )
= $false )
| ( ( in @ ( sK44_C @ SV232 @ SV147 ) @ SV147 )
= $false )
| ( ( SV147 = SV232 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2352]) ).
thf(2488,plain,
! [SV460: $i] :
( ( ( SV460 = empty_set )
= $false )
| ( ( ! [SY1092: $i] : ( subset @ SV460 @ ( singleton @ SY1092 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2354]) ).
thf(2489,plain,
! [SV492: $i,SV461: $i] :
( ( ( ( SV461
!= ( singleton @ SV492 ) ) )
= $true )
| ( ( subset @ SV461 @ ( singleton @ SV492 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2355]) ).
thf(2490,plain,
! [SV493: $i,SV413: $i,SV233: $i,SV148: $i] :
( ( ( ( ordered_pair @ SV148 @ SV233 )
= ( ordered_pair @ SV413 @ SV493 ) )
= $false )
| ( ( SV148 = SV413 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2356]) ).
thf(2491,plain,
! [SV462: $i,SV414: $i,SV233: $i,SV148: $i] :
( ( ( ( ordered_pair @ SV148 @ SV233 )
= ( ordered_pair @ SV414 @ SV462 ) )
= $false )
| ( ( SV233 = SV462 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2357]) ).
thf(2492,plain,
! [SV312: $i,SV385: $i] :
( ( ( in @ ( sK50_C @ SV385 @ SV312 ) @ SV312 )
= $true )
| ( ( subset @ SV312 @ SV385 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2358]) ).
thf(2493,plain,
! [SV312: $i,SV385: $i] :
( ( ( ~ ( in @ ( sK50_C @ SV385 @ SV312 ) @ SV385 ) )
= $true )
| ( ( subset @ SV312 @ SV385 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2359]) ).
thf(2494,plain,
! [SV386: $i,SV313: $i,SV494: $i] :
( ( ( ~ ( in @ SV494 @ SV313 ) )
= $true )
| ( ( in @ SV494 @ SV386 )
= $true )
| ( ( subset @ SV313 @ SV386 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2360]) ).
thf(2495,plain,
! [SV149: $i,SV387: $i,SV415: $i] :
( ( ( ~ ( ~ ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV149 )
| ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV387 )
| ~ ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV415 ) ) )
= $false )
| ( ( SV415
= ( set_difference @ SV149 @ SV387 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2363]) ).
thf(2496,plain,
! [SV149: $i,SV387: $i,SV415: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV149 )
| ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV415 ) )
| ~ ( ~ ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV387 )
| ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV415 ) ) ) )
= $false )
| ( ( SV415
= ( set_difference @ SV149 @ SV387 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2363]) ).
thf(2497,plain,
! [SV416: $i,SV388: $i,SV149: $i] :
( ( ( ~ ! [SY1030: $i] :
( ~ ( in @ SY1030 @ SV149 )
| ( in @ SY1030 @ SV388 )
| ( in @ SY1030 @ SV416 ) )
| ~ ~ ( ~ ! [SY1031: $i] :
( ~ ( in @ SY1031 @ SV416 )
| ( in @ SY1031 @ SV149 ) )
| ~ ! [SY1032: $i] :
( ~ ( in @ SY1032 @ SV416 )
| ~ ( in @ SY1032 @ SV388 ) ) ) )
= $false )
| ( ( SV416
= ( set_difference @ SV149 @ SV388 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2364]) ).
thf(2498,plain,
! [SV178: $i,SV33: $i,SV417: $i] :
( ( ( function @ SV417 )
= $false )
| ( ( ~ ( relation @ SV417 ) )
= $true )
| ( ( ~ ( in @ SV33 @ ( relation_dom @ ( relation_composition @ SV417 @ SV178 ) ) )
| ( ( apply @ ( relation_composition @ SV417 @ SV178 ) @ SV33 )
= ( apply @ SV178 @ ( apply @ SV417 @ SV33 ) ) ) )
= $true )
| ( ( function @ SV178 )
= $false )
| ( ( relation @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2365]) ).
thf(2499,plain,
! [SV179: $i,SV34: $i,SV418: $i] :
( ( ( function @ SV418 )
= $false )
| ( ( ~ ( relation @ SV418 ) )
= $true )
| ( ( ~ ( in @ SV34 @ ( relation_dom @ SV179 ) )
| ( ( apply @ ( relation_composition @ SV179 @ SV418 ) @ SV34 )
= ( apply @ SV418 @ ( apply @ SV179 @ SV34 ) ) ) )
= $true )
| ( ( function @ SV179 )
= $false )
| ( ( relation @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2366]) ).
thf(2500,plain,
! [SV112: $i,SV322: $i,SV390: $i] :
( ( ( ~ ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV112 )
| ~ ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV322 )
| ~ ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV390 ) )
= $true )
| ( ( SV390
= ( set_intersection2 @ SV112 @ SV322 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2368]) ).
thf(2501,plain,
! [SV112: $i,SV322: $i,SV390: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV112 )
| ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV390 ) )
| ~ ( ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV322 )
| ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV390 ) ) ) )
= $true )
| ( ( SV390
= ( set_intersection2 @ SV112 @ SV322 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2369]) ).
thf(2502,plain,
! [SV391: $i,SV323: $i,SV112: $i] :
( ( ( ~ ! [SY1008: $i] :
( ~ ( in @ SY1008 @ SV112 )
| ~ ( in @ SY1008 @ SV323 )
| ( in @ SY1008 @ SV391 ) ) )
= $false )
| ( ( SV391
= ( set_intersection2 @ SV112 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2370]) ).
thf(2503,plain,
! [SV323: $i,SV112: $i,SV391: $i] :
( ( ( ~ ~ ( ~ ! [SY1009: $i] :
( ~ ( in @ SY1009 @ SV391 )
| ( in @ SY1009 @ SV112 ) )
| ~ ! [SY1010: $i] :
( ~ ( in @ SY1010 @ SV391 )
| ( in @ SY1010 @ SV323 ) ) ) )
= $false )
| ( ( SV391
= ( set_intersection2 @ SV112 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2370]) ).
thf(2504,plain,
! [SV258: $i,SV324: $i] :
( ( ( ! [SY952: $i] :
( ~ ( in @ ( sK47_C @ SV324 @ SV258 ) @ SY952 )
| ~ ( in @ SY952 @ SV258 ) ) )
= $true )
| ( ( ~ ( in @ ( sK47_C @ SV324 @ SV258 ) @ SV324 ) )
= $true )
| ( ( SV324
= ( union @ SV258 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2371]) ).
thf(2505,plain,
! [SV258: $i,SV324: $i] :
( ( ( ~ ( ~ ( in @ ( sK47_C @ SV324 @ SV258 ) @ ( sK48_SY487 @ SV324 @ SV258 ) )
| ~ ( in @ ( sK48_SY487 @ SV324 @ SV258 ) @ SV258 ) ) )
= $true )
| ( ( in @ ( sK47_C @ SV324 @ SV258 ) @ SV324 )
= $true )
| ( ( SV324
= ( union @ SV258 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2372]) ).
thf(2506,plain,
! [SV325: $i,SV259: $i] :
( ( ( ! [SY953: $i] :
( ! [SY881: $i] :
( ~ ( in @ SY953 @ SY881 )
| ~ ( in @ SY881 @ SV259 ) )
| ( in @ SY953 @ SV325 ) ) )
= $true )
| ( ( SV325
= ( union @ SV259 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2373]) ).
thf(2507,plain,
! [SV259: $i,SV325: $i] :
( ( ( ! [SY955: $i] :
( ~ ( in @ SY955 @ SV325 )
| ~ ( ~ ( in @ SY955 @ ( sK46_D @ SY955 @ SV325 @ SV259 ) )
| ~ ( in @ ( sK46_D @ SY955 @ SV325 @ SV259 ) @ SV259 ) ) ) )
= $true )
| ( ( SV325
= ( union @ SV259 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2374]) ).
thf(2508,plain,
! [SV113: $i,SV225: $i,SV463: $i] :
( ( ( relation @ SV463 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) @ SV113 )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV225 )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 ) )
| ~ ~ ( ~ ( ( in @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) @ SV113 )
| ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV225 )
| ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 ) ) ) )
| ( SV463
= ( relation_rng_restriction @ SV113 @ SV225 ) ) )
= $true )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2375]) ).
thf(2509,plain,
! [SV225: $i,SV113: $i,SV464: $i] :
( ( ( relation @ SV464 )
= $false )
| ( ( ( SV464
!= ( relation_rng_restriction @ SV113 @ SV225 ) )
| ~ ( ~ ! [SY1094: $i,SY1095: $i] :
( ~ ( in @ SY1095 @ SV113 )
| ~ ( in @ ( ordered_pair @ SY1094 @ SY1095 ) @ SV225 )
| ( in @ ( ordered_pair @ SY1094 @ SY1095 ) @ SV464 ) )
| ~ ~ ( ~ ! [SY1096: $i,SY1097: $i] :
( ~ ( in @ ( ordered_pair @ SY1096 @ SY1097 ) @ SV464 )
| ( in @ SY1097 @ SV113 ) )
| ~ ! [SY1098: $i,SY1099: $i] :
( ~ ( in @ ( ordered_pair @ SY1098 @ SY1099 ) @ SV464 )
| ( in @ ( ordered_pair @ SY1098 @ SY1099 ) @ SV225 ) ) ) ) )
= $true )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2376]) ).
thf(2510,plain,
! [SV419: $i,SV226: $i,SV392: $i,SV114: $i] :
( ( ( in @ SV114 @ SV392 )
= $false )
| ( ( ~ ( in @ SV226 @ SV419 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SV392 @ SV419 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2379]) ).
thf(2511,plain,
! [SV495: $i,SV226: $i,SV114: $i] :
( ( ( ! [SY1124: $i] :
~ ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SV495 @ SY1124 ) ) )
= $true )
| ( ( in @ SV114 @ SV495 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2380]) ).
thf(2512,plain,
! [SV514: $i,SV496: $i,SV226: $i,SV114: $i] :
( ( ~ ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SV496 @ SV514 ) )
| ( in @ SV226 @ SV514 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2381]) ).
thf(2513,plain,
! [SV263: $i,SV329: $i,SV420: $i] :
( ( ( in @ SV420 @ SV329 )
= $false )
| ( ( in @ SV420 @ SV263 )
= $false )
| ( ( ~ ( disjoint @ SV263 @ SV329 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2384]) ).
thf(2514,plain,
! [SV264: $i,SV330: $i] :
( ( ( ( ( sK62_C @ SV330 @ SV264 )
!= SV264 ) )
= $true )
| ( ( ~ ( in @ ( sK62_C @ SV330 @ SV264 ) @ SV330 ) )
= $true )
| ( ( SV330
= ( singleton @ SV264 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2385]) ).
thf(2515,plain,
! [SV264: $i,SV330: $i] :
( ( ( ( sK62_C @ SV330 @ SV264 )
= SV264 )
= $true )
| ( ( in @ ( sK62_C @ SV330 @ SV264 ) @ SV330 )
= $true )
| ( ( SV330
= ( singleton @ SV264 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2386]) ).
thf(2516,plain,
! [SV331: $i,SV265: $i] :
( ( ( ! [SY957: $i] :
( ( SY957 != SV265 )
| ( in @ SY957 @ SV331 ) ) )
= $true )
| ( ( SV331
= ( singleton @ SV265 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2387]) ).
thf(2517,plain,
! [SV265: $i,SV331: $i] :
( ( ( ! [SY958: $i] :
( ~ ( in @ SY958 @ SV331 )
| ( SY958 = SV265 ) ) )
= $true )
| ( ( SV331
= ( singleton @ SV265 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2388]) ).
thf(2518,plain,
! [SV115: $i,SV465: $i] :
( ( ( ~ ! [SY1100: $i] :
( ~ ( subset @ SY1100 @ SV465 )
| ( in @ SY1100 @ ( sK43_SY481 @ SV465 @ SV115 ) ) )
| ~ ( in @ ( sK43_SY481 @ SV465 @ SV115 ) @ ( sK42_B @ SV115 ) ) )
= $false )
| ( ( ~ ( in @ SV465 @ ( sK42_B @ SV115 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2389]) ).
thf(2519,plain,
! [SV115: $i] :
( ( ! [SY633: $i,SY634: $i] :
( ~ ( in @ SY633 @ ( sK42_B @ SV115 ) )
| ~ ( subset @ SY634 @ SY633 )
| ( in @ SY634 @ ( sK42_B @ SV115 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2390]) ).
thf(2520,plain,
! [SV115: $i] :
( ( in @ SV115 @ ( sK42_B @ SV115 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2391]) ).
thf(2521,plain,
! [SV515: $i,SV422: $i] :
( ( ( subset @ SV422 @ ( singleton @ SV515 ) )
= $true )
| ( ( SV422 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2392]) ).
thf(2522,plain,
! [SV466: $i,SV423: $i] :
( ( ( SV423
= ( singleton @ SV466 ) )
= $false )
| ( ( subset @ SV423 @ ( singleton @ SV466 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2393]) ).
thf(2523,plain,
! [SV116: $i] :
( ( ( ~ ! [SY635: $i] :
( ~ ( in @ SY635 @ ( relation_dom @ SV116 ) )
| ! [SY636: $i] :
( ( SY636
!= ( apply @ SV116 @ SY635 ) )
| ( in @ ( ordered_pair @ SY635 @ SY636 ) @ SV116 ) ) ) )
= $false )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2394]) ).
thf(2524,plain,
! [SV116: $i] :
( ( ( ~ ! [SY637: $i] :
( ~ ( in @ SY637 @ ( relation_dom @ SV116 ) )
| ! [SY638: $i] :
( ~ ( in @ ( ordered_pair @ SY637 @ SY638 ) @ SV116 )
| ( SY638
= ( apply @ SV116 @ SY637 ) ) ) ) )
= $false )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2394]) ).
thf(2525,plain,
! [SV116: $i] :
( ( ( ~ ! [SY639: $i] :
( ( in @ SY639 @ ( relation_dom @ SV116 ) )
| ! [SY640: $i] :
( ( SY640
!= ( apply @ SV116 @ SY639 ) )
| ( SY640 = empty_set ) ) ) )
= $false )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2395]) ).
thf(2526,plain,
! [SV116: $i] :
( ( ( ~ ! [SY641: $i] :
( ( in @ SY641 @ ( relation_dom @ SV116 ) )
| ! [SY642: $i] :
( ( SY642 != empty_set )
| ( SY642
= ( apply @ SV116 @ SY641 ) ) ) ) )
= $false )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2395]) ).
thf(2527,plain,
! [SV393: $i,SV334: $i,SV117: $i] :
( ( ( ! [SY1012: $i,SY1013: $i] :
( ~ ( in @ SY1012 @ SV117 )
| ~ ( in @ SY1013 @ SV334 )
| ( ( sK53_D @ SV393 @ SV334 @ SV117 )
!= ( ordered_pair @ SY1012 @ SY1013 ) ) )
| ~ ( in @ ( sK53_D @ SV393 @ SV334 @ SV117 ) @ SV393 ) )
= $true )
| ( ( SV393
= ( cartesian_product2 @ SV117 @ SV334 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2396]) ).
thf(2528,plain,
! [SV117: $i,SV334: $i,SV393: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK54_SY491 @ SV393 @ SV334 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK55_SY493 @ SV393 @ SV334 @ SV117 ) @ SV334 ) )
| ( ( sK53_D @ SV393 @ SV334 @ SV117 )
!= ( ordered_pair @ ( sK54_SY491 @ SV393 @ SV334 @ SV117 ) @ ( sK55_SY493 @ SV393 @ SV334 @ SV117 ) ) ) )
| ( in @ ( sK53_D @ SV393 @ SV334 @ SV117 ) @ SV393 ) )
= $true )
| ( ( SV393
= ( cartesian_product2 @ SV117 @ SV334 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2397]) ).
thf(2529,plain,
! [SV394: $i,SV335: $i,SV117: $i] :
( ( ( ~ ! [SY1014: $i] :
( ! [SY964: $i,SY965: $i] :
( ~ ( in @ SY964 @ SV117 )
| ~ ( in @ SY965 @ SV335 )
| ( SY1014
!= ( ordered_pair @ SY964 @ SY965 ) ) )
| ( in @ SY1014 @ SV394 ) ) )
= $false )
| ( ( SV394
= ( cartesian_product2 @ SV117 @ SV335 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2398]) ).
thf(2530,plain,
! [SV117: $i,SV335: $i,SV394: $i] :
( ( ( ~ ! [SY1017: $i] :
( ~ ( in @ SY1017 @ SV394 )
| ~ ( ~ ~ ( ~ ( in @ ( sK51_E @ SY1017 @ SV394 @ SV335 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK52_SY488 @ SY1017 @ SV394 @ SV335 @ SV117 ) @ SV335 ) )
| ( SY1017
!= ( ordered_pair @ ( sK51_E @ SY1017 @ SV394 @ SV335 @ SV117 ) @ ( sK52_SY488 @ SY1017 @ SV394 @ SV335 @ SV117 ) ) ) ) ) )
= $false )
| ( ( SV394
= ( cartesian_product2 @ SV117 @ SV335 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2398]) ).
thf(2531,plain,
! [SV118: $i,SV338: $i,SV395: $i] :
( ( ( relation @ SV395 )
= $false )
| ( ( function @ SV395 )
= $false )
| ( ( ( SV338
!= ( apply @ SV395 @ SV118 ) )
| ~ ( in @ SV118 @ ( relation_dom @ SV395 ) )
| ( in @ ( ordered_pair @ SV118 @ SV338 ) @ SV395 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2399]) ).
thf(2532,plain,
! [SV467: $i,SV118: $i,SV497: $i] :
( ( ( ~ ( function @ SV497 )
| ~ ( relation @ SV497 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV118 @ SV467 ) @ SV497 )
| ( SV467
= ( apply @ SV497 @ SV118 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2400]) ).
thf(2533,plain,
! [SV468: $i,SV118: $i,SV498: $i] :
( ( ( ~ ( function @ SV498 )
| ~ ( relation @ SV498 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV118 @ SV468 ) @ SV498 )
| ( in @ SV118 @ ( relation_dom @ SV498 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2401]) ).
thf(2534,plain,
! [SV273: $i,SV339: $i] :
( ( ( ~ ( ( ( sK69_C @ SV339 @ SV273 )
!= ( sK70_SY500 @ SV339 @ SV273 ) )
| ~ ( in @ ( sK69_C @ SV339 @ SV273 ) @ SV273 )
| ~ ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 ) ) )
= $false )
| ( ( SV339
= ( identity_relation @ SV273 ) )
= $true )
| ( ( relation @ SV339 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2402]) ).
thf(2535,plain,
! [SV273: $i,SV339: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK69_C @ SV339 @ SV273 )
= ( sK70_SY500 @ SV339 @ SV273 ) )
| ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 ) )
| ~ ( ( in @ ( sK69_C @ SV339 @ SV273 ) @ SV273 )
| ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 ) ) ) )
= $false )
| ( ( SV339
= ( identity_relation @ SV273 ) )
= $true )
| ( ( relation @ SV339 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2402]) ).
thf(2536,plain,
! [SV340: $i,SV274: $i] :
( ( ( ~ ! [SY968: $i,SY969: $i] :
( ( SY968 != SY969 )
| ~ ( in @ SY968 @ SV274 )
| ( in @ ( ordered_pair @ SY968 @ SY969 ) @ SV340 ) )
| ~ ~ ( ~ ! [SY970: $i,SY971: $i] :
( ~ ( in @ ( ordered_pair @ SY970 @ SY971 ) @ SV340 )
| ( SY970 = SY971 ) )
| ~ ! [SY972: $i] :
( ! [SY973: $i] :
~ ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV340 )
| ( in @ SY972 @ SV274 ) ) ) )
= $false )
| ( ( SV340
= ( identity_relation @ SV274 ) )
= $false )
| ( ( relation @ SV340 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2403]) ).
thf(2537,plain,
! [SV120: $i,SV275: $i,SV516: $i] :
( ( ( ~ ( relation @ SV516 )
| ~ ( ~ ( ! [SY1135: $i] :
( ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ SY1135 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY1135 @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV275 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV516 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK15_SY461 @ SV516 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY461 @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV275 ) )
| ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV516 ) ) )
| ( SV516
= ( relation_composition @ SV120 @ SV275 ) ) )
= $true )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2404]) ).
thf(2538,plain,
! [SV275: $i,SV120: $i,SV517: $i] :
( ( ( ~ ( relation @ SV517 )
| ( SV517
!= ( relation_composition @ SV120 @ SV275 ) )
| ~ ( ~ ! [SY1136: $i,SY1137: $i] :
( ! [SY909: $i] :
( ~ ( in @ ( ordered_pair @ SY1136 @ SY909 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY909 @ SY1137 ) @ SV275 ) )
| ( in @ ( ordered_pair @ SY1136 @ SY1137 ) @ SV517 ) )
| ~ ! [SY1139: $i,SY1140: $i] :
( ~ ( in @ ( ordered_pair @ SY1139 @ SY1140 ) @ SV517 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1139 @ ( sK12_F @ SY1140 @ SY1139 @ SV517 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK12_F @ SY1140 @ SY1139 @ SV517 @ SV275 @ SV120 ) @ SY1140 ) @ SV275 ) ) ) ) )
= $true )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2405]) ).
thf(2539,plain,
! [SV227: $i,SV121: $i,SV469: $i] :
( ( ( element @ SV469 @ ( powerset @ SV121 ) )
= $false )
| ( ( ~ ( disjoint @ SV227 @ SV469 )
| ( subset @ SV227 @ ( subset_complement @ SV121 @ SV469 ) ) )
= $true )
| ( ( element @ SV227 @ ( powerset @ SV121 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2406]) ).
thf(2540,plain,
! [SV227: $i,SV121: $i,SV470: $i] :
( ( ( element @ SV470 @ ( powerset @ SV121 ) )
= $false )
| ( ( ~ ( subset @ SV227 @ ( subset_complement @ SV121 @ SV470 ) )
| ( disjoint @ SV227 @ SV470 ) )
= $true )
| ( ( element @ SV227 @ ( powerset @ SV121 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2407]) ).
thf(2541,plain,
! [SV396: $i,SV341: $i,SV122: $i] :
( ( ( ~ ( in @ SV122 @ SV341 ) )
= $true )
| ( ( ~ ( in @ SV122 @ ( relation_rng @ SV396 ) ) )
= $true )
| ( ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SV341 @ SV396 ) ) )
= $true )
| ( ( relation @ SV396 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2408]) ).
thf(2542,plain,
! [SV471: $i,SV122: $i,SV499: $i] :
( ( ( ~ ( relation @ SV499 ) )
= $true )
| ( ( ~ ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SV471 @ SV499 ) ) )
| ( in @ SV122 @ SV471 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2409]) ).
thf(2543,plain,
! [SV472: $i,SV122: $i,SV500: $i] :
( ( ( ~ ( relation @ SV500 ) )
= $true )
| ( ( ~ ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SV472 @ SV500 ) ) )
| ( in @ SV122 @ ( relation_rng @ SV500 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2410]) ).
thf(2544,plain,
! [SV123: $i,SV424: $i,SV473: $i] :
( ( ( relation @ SV473 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ SV424 )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV123 )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 ) )
| ~ ~ ( ~ ( ( in @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ SV424 )
| ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 ) ) ) )
| ( SV473
= ( relation_dom_restriction @ SV123 @ SV424 ) ) )
= $true )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2411]) ).
thf(2545,plain,
! [SV425: $i,SV123: $i,SV474: $i] :
( ( ( relation @ SV474 )
= $false )
| ( ( ( SV474
!= ( relation_dom_restriction @ SV123 @ SV425 ) )
| ~ ( ~ ! [SY1105: $i,SY1106: $i] :
( ~ ( in @ SY1105 @ SV425 )
| ~ ( in @ ( ordered_pair @ SY1105 @ SY1106 ) @ SV123 )
| ( in @ ( ordered_pair @ SY1105 @ SY1106 ) @ SV474 ) )
| ~ ~ ( ~ ! [SY1107: $i] :
( ! [SY1108: $i] :
~ ( in @ ( ordered_pair @ SY1107 @ SY1108 ) @ SV474 )
| ( in @ SY1107 @ SV425 ) )
| ~ ! [SY1109: $i,SY1110: $i] :
( ~ ( in @ ( ordered_pair @ SY1109 @ SY1110 ) @ SV474 )
| ( in @ ( ordered_pair @ SY1109 @ SY1110 ) @ SV123 ) ) ) ) )
= $true )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2412]) ).
thf(2546,plain,
! [SV124: $i,SV426: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_C @ SV426 @ SV124 ) @ ( sK17_SY462 @ SV426 @ SV124 ) ) @ SV426 )
| ~ ( in @ ( ordered_pair @ ( sK17_SY462 @ SV426 @ SV124 ) @ ( sK16_C @ SV426 @ SV124 ) ) @ SV124 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK16_C @ SV426 @ SV124 ) @ ( sK17_SY462 @ SV426 @ SV124 ) ) @ SV426 )
| ( in @ ( ordered_pair @ ( sK17_SY462 @ SV426 @ SV124 ) @ ( sK16_C @ SV426 @ SV124 ) ) @ SV124 ) ) ) )
= $true )
| ( ( SV426
= ( relation_inverse @ SV124 ) )
= $true )
| ( ( relation @ SV426 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2413]) ).
thf(2547,plain,
! [SV124: $i,SV427: $i] :
( ( ( ( SV427
!= ( relation_inverse @ SV124 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1043: $i,SY1044: $i] :
( ~ ( in @ ( ordered_pair @ SY1043 @ SY1044 ) @ SV427 )
| ( in @ ( ordered_pair @ SY1044 @ SY1043 ) @ SV124 ) )
| ~ ! [SY1045: $i,SY1046: $i] :
( ~ ( in @ ( ordered_pair @ SY1046 @ SY1045 ) @ SV124 )
| ( in @ ( ordered_pair @ SY1045 @ SY1046 ) @ SV427 ) ) ) )
= $true )
| ( ( relation @ SV427 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2414]) ).
thf(2548,plain,
! [SV282: $i,SV348: $i] :
( ( ( ~ ( ~ ( in @ ( sK38_C @ SV348 @ SV282 ) @ SV282 )
| ~ ( ( ( apply @ SV348 @ ( sK38_C @ SV348 @ SV282 ) )
!= ( sK38_C @ SV348 @ SV282 ) ) ) )
| ( ( relation_dom @ SV348 )
!= SV282 ) )
= $true )
| ( ( SV348
= ( identity_relation @ SV282 ) )
= $true )
| ( ( function @ SV348 )
= $false )
| ( ( relation @ SV348 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2415]) ).
thf(2549,plain,
! [SV428: $i,SV475: $i] :
( ( ( ~ ( function @ SV475 ) )
= $true )
| ( ( ~ ( relation @ SV475 ) )
= $true )
| ( ( ( SV475
!= ( identity_relation @ SV428 ) )
| ! [SY1111: $i] :
( ~ ( in @ SY1111 @ SV428 )
| ( ( apply @ SV475 @ SY1111 )
= SY1111 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2416]) ).
thf(2550,plain,
! [SV429: $i,SV476: $i] :
( ( ( ~ ( function @ SV476 ) )
= $true )
| ( ( ~ ( relation @ SV476 ) )
= $true )
| ( ( ( SV476
!= ( identity_relation @ SV429 ) )
| ( ( relation_dom @ SV476 )
= SV429 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2417]) ).
thf(2551,plain,
! [SV477: $i,SV430: $i] :
( ( ( SV430 = SV477 )
= $false )
| ( ( subset @ SV430 @ SV477 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2419]) ).
thf(2552,plain,
! [SV478: $i,SV431: $i] :
( ( ( SV431 = SV478 )
= $false )
| ( ( subset @ SV478 @ SV431 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2420]) ).
thf(2553,plain,
! [SV125: $i,SV432: $i,SV479: $i] :
( ( ( ~ ( ! [SY1112: $i] :
( ~ ( in @ ( ordered_pair @ SY1112 @ ( sK30_D @ SV479 @ SV432 @ SV125 ) ) @ SV125 )
| ~ ( in @ SY1112 @ SV432 ) )
| ~ ( in @ ( sK30_D @ SV479 @ SV432 @ SV125 ) @ SV479 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_SY471 @ SV479 @ SV432 @ SV125 ) @ ( sK30_D @ SV479 @ SV432 @ SV125 ) ) @ SV125 )
| ~ ( in @ ( sK31_SY471 @ SV479 @ SV432 @ SV125 ) @ SV432 ) )
| ( in @ ( sK30_D @ SV479 @ SV432 @ SV125 ) @ SV479 ) ) )
= $false )
| ( ( SV479
= ( relation_image @ SV125 @ SV432 ) )
= $true )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2421]) ).
thf(2554,plain,
! [SV433: $i,SV125: $i,SV480: $i] :
( ( ( SV480
= ( relation_image @ SV125 @ SV433 ) )
= $false )
| ( ( ~ ( ~ ! [SY1113: $i] :
( ! [SY1056: $i] :
( ~ ( in @ ( ordered_pair @ SY1056 @ SY1113 ) @ SV125 )
| ~ ( in @ SY1056 @ SV433 ) )
| ( in @ SY1113 @ SV480 ) )
| ~ ! [SY1115: $i] :
( ~ ( in @ SY1115 @ SV480 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK29_E @ SY1115 @ SV480 @ SV433 @ SV125 ) @ SY1115 ) @ SV125 )
| ~ ( in @ ( sK29_E @ SY1115 @ SV480 @ SV433 @ SV125 ) @ SV433 ) ) ) ) )
= $true )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2422]) ).
thf(2555,plain,
! [SV397: $i,SV352: $i,SV126: $i] :
( ( ( in @ ( ordered_pair @ SV126 @ SV352 ) @ SV397 )
= $false )
| ( ( in @ SV126 @ ( relation_field @ SV397 ) )
= $true )
| ( ( relation @ SV397 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2423]) ).
thf(2556,plain,
! [SV398: $i,SV353: $i,SV126: $i] :
( ( ( in @ ( ordered_pair @ SV126 @ SV353 ) @ SV398 )
= $false )
| ( ( in @ SV353 @ ( relation_field @ SV398 ) )
= $true )
| ( ( relation @ SV398 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2424]) ).
thf(2557,plain,
! [SV434: $i,SV228: $i,SV399: $i,SV127: $i] :
( ( ( ~ ( in @ SV127 @ SV399 )
| ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ SV434 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SV399 ) @ SV434 ) )
= $true )
| ( ( relation @ SV434 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2425]) ).
thf(2558,plain,
! [SV501: $i,SV228: $i,SV127: $i,SV518: $i] :
( ( ~ ( relation @ SV518 )
| ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SV501 ) @ SV518 ) )
| ( in @ SV127 @ SV501 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2426]) ).
thf(2559,plain,
! [SV502: $i,SV228: $i,SV127: $i,SV519: $i] :
( ( ~ ( relation @ SV519 )
| ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SV502 ) @ SV519 ) )
| ( in @ ( ordered_pair @ SV127 @ SV228 ) @ SV519 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2427]) ).
thf(2560,plain,
! [SV128: $i,SV400: $i,SV356: $i] :
( ( ( in @ SV356 @ SV400 )
= $false )
| ( ( in @ SV128 @ SV400 )
= $false )
| ( ( subset @ ( unordered_pair @ SV128 @ SV356 ) @ SV400 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2428]) ).
thf(2561,plain,
! [SV503: $i,SV481: $i,SV128: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV128 @ SV481 ) @ SV503 ) )
= $true )
| ( ( in @ SV128 @ SV503 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2429]) ).
thf(2562,plain,
! [SV504: $i,SV482: $i,SV128: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV128 @ SV482 ) @ SV504 ) )
= $true )
| ( ( in @ SV482 @ SV504 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2430]) ).
thf(2563,plain,
! [SV435: $i,SV505: $i] :
( ( ( ~ ( element @ SV505 @ SV435 ) )
= $true )
| ( ( in @ SV505 @ SV435 )
= $true )
| ( ( empty @ SV435 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2431]) ).
thf(2564,plain,
! [SV436: $i,SV506: $i] :
( ( ( ~ ( in @ SV506 @ SV436 ) )
= $true )
| ( ( element @ SV506 @ SV436 )
= $true )
| ( ( empty @ SV436 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2432]) ).
thf(2565,plain,
! [SV437: $i,SV520: $i] :
( ( ( ~ ( element @ SV520 @ SV437 )
| ( empty @ SV520 ) )
= $true )
| ( ( empty @ SV437 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2433]) ).
thf(2566,plain,
! [SV438: $i,SV521: $i] :
( ( ( ~ ( empty @ SV521 )
| ( element @ SV521 @ SV438 ) )
= $true )
| ( ( empty @ SV438 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2434]) ).
thf(2567,plain,
! [SV129: $i,SV439: $i] :
( ( ( ~ ( ! [SY1062: $i] :
~ ( in @ ( ordered_pair @ SY1062 @ ( sK19_C @ SV439 @ SV129 ) ) @ SV129 )
| ~ ( in @ ( sK19_C @ SV439 @ SV129 ) @ SV439 ) ) )
= $false )
| ( ( SV439
= ( relation_rng @ SV129 ) )
= $true )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2435]) ).
thf(2568,plain,
! [SV129: $i,SV439: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK20_SY464 @ SV439 @ SV129 ) @ ( sK19_C @ SV439 @ SV129 ) ) @ SV129 )
| ( in @ ( sK19_C @ SV439 @ SV129 ) @ SV439 ) ) )
= $false )
| ( ( SV439
= ( relation_rng @ SV129 ) )
= $true )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2435]) ).
thf(2569,plain,
! [SV440: $i,SV129: $i] :
( ( ( ~ ! [SY1063: $i] :
( ! [SY722: $i] :
~ ( in @ ( ordered_pair @ SY722 @ SY1063 ) @ SV129 )
| ( in @ SY1063 @ SV440 ) )
| ~ ! [SY1065: $i] :
( ~ ( in @ SY1065 @ SV440 )
| ( in @ ( ordered_pair @ ( sK18_D @ SY1065 @ SV440 @ SV129 ) @ SY1065 ) @ SV129 ) ) )
= $false )
| ( ( SV440
= ( relation_rng @ SV129 ) )
= $false )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2436]) ).
thf(2570,plain,
! [SV131: $i,SV442: $i,SV483: $i] :
( ( ( ~ ( ! [SY1118: $i] :
( ~ ( in @ ( ordered_pair @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SY1118 ) @ SV131 )
| ~ ( in @ SY1118 @ SV442 ) )
| ~ ( in @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SV483 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ ( sK28_SY469 @ SV483 @ SV442 @ SV131 ) ) @ SV131 )
| ~ ( in @ ( sK28_SY469 @ SV483 @ SV442 @ SV131 ) @ SV442 ) )
| ( in @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SV483 ) ) )
= $false )
| ( ( SV483
= ( relation_inverse_image @ SV131 @ SV442 ) )
= $true )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2438]) ).
thf(2571,plain,
! [SV443: $i,SV131: $i,SV484: $i] :
( ( ( SV484
= ( relation_inverse_image @ SV131 @ SV443 ) )
= $false )
| ( ( ~ ( ~ ! [SY1119: $i] :
( ! [SY1070: $i] :
( ~ ( in @ ( ordered_pair @ SY1119 @ SY1070 ) @ SV131 )
| ~ ( in @ SY1070 @ SV443 ) )
| ( in @ SY1119 @ SV484 ) )
| ~ ! [SY1121: $i] :
( ~ ( in @ SY1121 @ SV484 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1121 @ ( sK26_E @ SY1121 @ SV484 @ SV443 @ SV131 ) ) @ SV131 )
| ~ ( in @ ( sK26_E @ SY1121 @ SV484 @ SV443 @ SV131 ) @ SV443 ) ) ) ) )
= $true )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2439]) ).
thf(2572,plain,
! [SV522: $i,SV507: $i,SV296: $i] :
( ( ( ( ( sK68_B @ SV296 )
!= ( ordered_pair @ SV507 @ SV522 ) ) )
= $true )
| ( ( relation @ SV296 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2440]) ).
thf(2573,plain,
! [SV401: $i,SV363: $i,SV132: $i] :
( ( ( ~ ( in @ SV132 @ SV363 ) )
= $true )
| ( ( ~ ( in @ SV132 @ ( relation_dom @ SV401 ) ) )
= $true )
| ( ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SV401 @ SV363 ) ) )
= $true )
| ( ( relation @ SV401 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2442]) ).
thf(2574,plain,
! [SV485: $i,SV132: $i,SV508: $i] :
( ( ( ~ ( relation @ SV508 ) )
= $true )
| ( ( ~ ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SV508 @ SV485 ) ) )
| ( in @ SV132 @ SV485 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2443]) ).
thf(2575,plain,
! [SV486: $i,SV132: $i,SV509: $i] :
( ( ( ~ ( relation @ SV509 ) )
= $true )
| ( ( ~ ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SV509 @ SV486 ) ) )
| ( in @ SV132 @ ( relation_dom @ SV509 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2444]) ).
thf(2576,plain,
! [SV402: $i,SV364: $i,SV133: $i] :
( ( ( in @ ( ordered_pair @ SV133 @ SV364 ) @ SV402 )
= $false )
| ( ( in @ SV133 @ ( relation_dom @ SV402 ) )
= $true )
| ( ( relation @ SV402 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2445]) ).
thf(2577,plain,
! [SV403: $i,SV365: $i,SV133: $i] :
( ( ( in @ ( ordered_pair @ SV133 @ SV365 ) @ SV403 )
= $false )
| ( ( in @ SV365 @ ( relation_rng @ SV403 ) )
= $true )
| ( ( relation @ SV403 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2446]) ).
thf(2578,plain,
! [SV134: $i,SV445: $i] :
( ( ( ~ ( ! [SY1072: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SV445 @ SV134 ) @ SY1072 ) @ SV134 )
| ~ ( in @ ( sK22_C @ SV445 @ SV134 ) @ SV445 ) ) )
= $false )
| ( ( SV445
= ( relation_dom @ SV134 ) )
= $true )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2447]) ).
thf(2579,plain,
! [SV134: $i,SV445: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SV445 @ SV134 ) @ ( sK23_SY466 @ SV445 @ SV134 ) ) @ SV134 )
| ( in @ ( sK22_C @ SV445 @ SV134 ) @ SV445 ) ) )
= $false )
| ( ( SV445
= ( relation_dom @ SV134 ) )
= $true )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2447]) ).
thf(2580,plain,
! [SV446: $i,SV134: $i] :
( ( ( ~ ! [SY1073: $i] :
( ! [SY747: $i] :
~ ( in @ ( ordered_pair @ SY1073 @ SY747 ) @ SV134 )
| ( in @ SY1073 @ SV446 ) )
| ~ ! [SY1075: $i] :
( ~ ( in @ SY1075 @ SV446 )
| ( in @ ( ordered_pair @ SY1075 @ ( sK21_D @ SY1075 @ SV446 @ SV134 ) ) @ SV134 ) ) )
= $false )
| ( ( SV446
= ( relation_dom @ SV134 ) )
= $false )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2448]) ).
thf(2581,plain,
! [SV135: $i,SV366: $i,SV404: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK57_D @ SV404 @ SV366 @ SV135 ) @ SV404 )
| ( ( sK57_D @ SV404 @ SV366 @ SV135 )
!= SV135 ) )
| ~ ( ~ ( in @ ( sK57_D @ SV404 @ SV366 @ SV135 ) @ SV404 )
| ( ( sK57_D @ SV404 @ SV366 @ SV135 )
!= SV366 ) ) ) )
= $true )
| ( ( SV404
= ( unordered_pair @ SV135 @ SV366 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2449]) ).
thf(2582,plain,
! [SV135: $i,SV366: $i,SV404: $i] :
( ( ( ( in @ ( sK57_D @ SV404 @ SV366 @ SV135 ) @ SV404 )
| ( ( sK57_D @ SV404 @ SV366 @ SV135 )
= SV135 )
| ( ( sK57_D @ SV404 @ SV366 @ SV135 )
= SV366 ) )
= $true )
| ( ( SV404
= ( unordered_pair @ SV135 @ SV366 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2450]) ).
thf(2583,plain,
! [SV367: $i,SV135: $i,SV405: $i] :
( ( ( ~ ! [SY1019: $i] :
( ~ ( in @ SY1019 @ SV405 )
| ( SY1019 = SV135 )
| ( SY1019 = SV367 ) ) )
= $false )
| ( ( SV405
= ( unordered_pair @ SV135 @ SV367 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2451]) ).
thf(2584,plain,
! [SV367: $i,SV405: $i,SV135: $i] :
( ( ( ~ ~ ( ~ ! [SY1020: $i] :
( ( SY1020 != SV135 )
| ( in @ SY1020 @ SV405 ) )
| ~ ! [SY1021: $i] :
( ( SY1021 != SV367 )
| ( in @ SY1021 @ SV405 ) ) ) )
= $false )
| ( ( SV405
= ( unordered_pair @ SV135 @ SV367 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2451]) ).
thf(2585,plain,
! [SV136: $i,SV447: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV136 )
| ~ ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV447 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV136 )
| ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV447 ) ) ) )
= $true )
| ( ( SV136 = SV447 )
= $true )
| ( ( relation @ SV447 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2452]) ).
thf(2586,plain,
! [SV448: $i,SV136: $i] :
( ( ( ( SV136 != SV448 ) )
= $true )
| ( ( ~ ( ~ ! [SY1076: $i,SY1077: $i] :
( ~ ( in @ ( ordered_pair @ SY1076 @ SY1077 ) @ SV136 )
| ( in @ ( ordered_pair @ SY1076 @ SY1077 ) @ SV448 ) )
| ~ ! [SY1078: $i,SY1079: $i] :
( ~ ( in @ ( ordered_pair @ SY1078 @ SY1079 ) @ SV448 )
| ( in @ ( ordered_pair @ SY1078 @ SY1079 ) @ SV136 ) ) ) )
= $true )
| ( ( relation @ SV448 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2453]) ).
thf(2587,plain,
! [SV368: $i,SV298: $i] :
( ( ( function @ SV298 )
= $false )
| ( ( ~ ( relation @ SV298 ) )
= $true )
| ( ( ~ ( relation @ SV368 ) )
= $true )
| ( ( ~ ( function @ SV368 ) )
= $true )
| ( ( function @ ( relation_composition @ SV298 @ SV368 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2454]) ).
thf(2588,plain,
! [SV369: $i,SV299: $i] :
( ( ( function @ SV299 )
= $false )
| ( ( ~ ( relation @ SV299 ) )
= $true )
| ( ( ~ ( relation @ SV369 ) )
= $true )
| ( ( ~ ( function @ SV369 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV299 @ SV369 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2455]) ).
thf(2589,plain,
! [SV230: $i,SV137: $i,SV523: $i] :
( ( ( ~ ( function @ SV523 )
| ~ ( relation @ SV523 )
| ~ ( in @ SV137 @ ( relation_dom @ SV523 ) )
| ~ ( in @ ( apply @ SV523 @ SV137 ) @ ( relation_dom @ SV230 ) )
| ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SV523 @ SV230 ) ) ) )
= $true )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2456]) ).
thf(2590,plain,
! [SV230: $i,SV137: $i] :
( ( ( ~ ! [SY862: $i] :
( ~ ( function @ SY862 )
| ~ ( relation @ SY862 )
| ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY862 @ SV230 ) ) )
| ( in @ SV137 @ ( relation_dom @ SY862 ) ) )
| ~ ! [SY863: $i] :
( ~ ( function @ SY863 )
| ~ ( relation @ SY863 )
| ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY863 @ SV230 ) ) )
| ( in @ ( apply @ SY863 @ SV137 ) @ ( relation_dom @ SV230 ) ) ) )
= $false )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2457]) ).
thf(2591,plain,
! [SV138: $i,SV487: $i] :
( ( ( in @ SV487 @ ( sK41_B @ SV138 ) )
= $false )
| ( ( in @ ( powerset @ SV487 ) @ ( sK41_B @ SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2458]) ).
thf(2592,plain,
! [SV138: $i] :
( ( ! [SY768: $i,SY769: $i] :
( ~ ( in @ SY768 @ ( sK41_B @ SV138 ) )
| ~ ( subset @ SY769 @ SY768 )
| ( in @ SY769 @ ( sK41_B @ SV138 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2459]) ).
thf(2593,plain,
! [SV138: $i] :
( ( in @ SV138 @ ( sK41_B @ SV138 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2460]) ).
thf(2594,plain,
! [SV139: $i,SV449: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV449 @ SV139 ) @ ( sK25_SY467 @ SV449 @ SV139 ) ) @ SV139 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SV449 @ SV139 ) @ ( sK25_SY467 @ SV449 @ SV139 ) ) @ SV449 ) ) )
= $true )
| ( ( subset @ SV139 @ SV449 )
= $true )
| ( ( relation @ SV449 )
= $false )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2461]) ).
thf(2595,plain,
! [SV450: $i,SV139: $i] :
( ( ( ~ ( subset @ SV139 @ SV450 ) )
= $true )
| ( ( ! [SY1080: $i,SY1081: $i] :
( ~ ( in @ ( ordered_pair @ SY1080 @ SY1081 ) @ SV139 )
| ( in @ ( ordered_pair @ SY1080 @ SY1081 ) @ SV450 ) ) )
= $true )
| ( ( relation @ SV450 )
= $false )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2462]) ).
thf(2596,plain,
! [SV300: $i,SV371: $i] :
( ( ( ~ ( in @ ( sK60_C @ SV371 @ SV300 ) @ SV371 ) )
= $true )
| ( ( ~ ( subset @ ( sK60_C @ SV371 @ SV300 ) @ SV300 ) )
= $true )
| ( ( SV371
= ( powerset @ SV300 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2463]) ).
thf(2597,plain,
! [SV300: $i,SV371: $i] :
( ( ( in @ ( sK60_C @ SV371 @ SV300 ) @ SV371 )
= $true )
| ( ( subset @ ( sK60_C @ SV371 @ SV300 ) @ SV300 )
= $true )
| ( ( SV371
= ( powerset @ SV300 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2464]) ).
thf(2598,plain,
! [SV301: $i,SV372: $i] :
( ( ( ! [SY987: $i] :
( ~ ( in @ SY987 @ SV372 )
| ( subset @ SY987 @ SV301 ) ) )
= $true )
| ( ( SV372
= ( powerset @ SV301 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2465]) ).
thf(2599,plain,
! [SV372: $i,SV301: $i] :
( ( ( ! [SY988: $i] :
( ~ ( subset @ SY988 @ SV301 )
| ( in @ SY988 @ SV372 ) ) )
= $true )
| ( ( SV372
= ( powerset @ SV301 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2466]) ).
thf(2600,plain,
! [SV451: $i,SV140: $i] :
( ( ( ~ ( subset @ SV140 @ SV451 ) )
= $true )
| ( ( subset @ ( relation_dom @ SV140 ) @ ( relation_dom @ SV451 ) )
= $true )
| ( ( relation @ SV451 )
= $false )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2469]) ).
thf(2601,plain,
! [SV452: $i,SV140: $i] :
( ( ( ~ ( subset @ SV140 @ SV452 ) )
= $true )
| ( ( subset @ ( relation_rng @ SV140 ) @ ( relation_rng @ SV452 ) )
= $true )
| ( ( relation @ SV452 )
= $false )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2470]) ).
thf(2602,plain,
! [SV375: $i,SV142: $i,SV406: $i,SV524: $i] :
( ( ( ~ ( in @ SV524 @ ( relation_rng @ SV406 ) )
| ~ ( in @ ( ordered_pair @ SV142 @ SV524 ) @ SV406 )
| ~ ( in @ SV524 @ SV375 ) )
= $true )
| ( ( in @ SV142 @ ( relation_inverse_image @ SV406 @ SV375 ) )
= $true )
| ( ( relation @ SV406 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2471]) ).
thf(2603,plain,
! [SV376: $i,SV407: $i,SV142: $i] :
( ( ( in @ SV142 @ ( relation_inverse_image @ SV407 @ SV376 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK39_D @ SV407 @ SV376 @ SV142 ) @ ( relation_rng @ SV407 ) )
| ~ ( in @ ( ordered_pair @ SV142 @ ( sK39_D @ SV407 @ SV376 @ SV142 ) ) @ SV407 ) )
| ~ ( in @ ( sK39_D @ SV407 @ SV376 @ SV142 ) @ SV376 ) ) )
= $true )
| ( ( relation @ SV407 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2472]) ).
thf(2604,plain,
! [SV453: $i,SV510: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( in @ ( sK65_SY495 @ SV510 @ SV453 ) @ SV453 )
| ~ ~ ( in @ ( sK64_C @ SV510 @ SV453 ) @ ( sK65_SY495 @ SV510 @ SV453 ) ) )
| ~ ( in @ ( sK64_C @ SV510 @ SV453 ) @ SV510 ) )
| ~ ( ! [SY1129: $i] :
( ~ ( in @ SY1129 @ SV453 )
| ( in @ ( sK64_C @ SV510 @ SV453 ) @ SY1129 ) )
| ( in @ ( sK64_C @ SV510 @ SV453 ) @ SV510 ) ) ) )
= $true )
| ( ( SV510
= ( set_meet @ SV453 ) )
= $true )
| ( ( SV453 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2473]) ).
thf(2605,plain,
! [SV454: $i,SV511: $i] :
( ( ( ( SV511
!= ( set_meet @ SV454 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1130: $i] :
( ~ ( ~ ( in @ ( sK63_D @ SY1130 @ SV511 @ SV454 ) @ SV454 )
| ~ ~ ( in @ SY1130 @ ( sK63_D @ SY1130 @ SV511 @ SV454 ) ) )
| ( in @ SY1130 @ SV511 ) )
| ~ ! [SY1131: $i] :
( ~ ( in @ SY1131 @ SV511 )
| ! [SY1087: $i] :
( ~ ( in @ SY1087 @ SV454 )
| ( in @ SY1131 @ SY1087 ) ) ) ) )
= $true )
| ( ( SV454 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2474]) ).
thf(2606,plain,
! [SV455: $i,SV525: $i] :
( ( ( ( SV525
!= ( set_meet @ SV455 ) )
| ( SV525 = empty_set ) )
= $true )
| ( ( SV455 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2475]) ).
thf(2607,plain,
! [SV456: $i,SV526: $i] :
( ( ( ( SV526 != empty_set )
| ( SV526
= ( set_meet @ SV456 ) ) )
= $true )
| ( ( SV456 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2476]) ).
thf(2608,plain,
! [SV488: $i,SV457: $i] :
( ( ( proper_subset @ SV457 @ SV488 )
= $false )
| ( ( ( SV457 != SV488 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2477]) ).
thf(2609,plain,
! [SV489: $i,SV458: $i] :
( ( ( proper_subset @ SV458 @ SV489 )
= $false )
| ( ( subset @ SV458 @ SV489 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2478]) ).
thf(2610,plain,
! [SV459: $i,SV231: $i,SV408: $i,SV143: $i] :
( ( ( in @ SV143 @ SV408 )
= $false )
| ( ( ~ ( in @ SV231 @ SV459 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SV408 @ SV459 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2479]) ).
thf(2611,plain,
! [SV512: $i,SV231: $i,SV143: $i] :
( ( ( ! [SY1133: $i] :
~ ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SV512 @ SY1133 ) ) )
= $true )
| ( ( in @ SV143 @ SV512 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2480]) ).
thf(2612,plain,
! [SV527: $i,SV513: $i,SV231: $i,SV143: $i] :
( ( ~ ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SV513 @ SV527 ) )
| ( in @ SV231 @ SV527 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2481]) ).
thf(2613,plain,
! [SV144: $i,SV378: $i,SV409: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV409 )
| ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV144 ) )
| ~ ( ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV409 )
| ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV378 ) ) ) )
= $true )
| ( ( SV409
= ( set_union2 @ SV144 @ SV378 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2482]) ).
thf(2614,plain,
! [SV144: $i,SV378: $i,SV409: $i] :
( ( ( ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV409 )
| ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV144 )
| ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV378 ) )
= $true )
| ( ( SV409
= ( set_union2 @ SV144 @ SV378 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2483]) ).
thf(2615,plain,
! [SV379: $i,SV144: $i,SV410: $i] :
( ( ( ~ ! [SY1024: $i] :
( ~ ( in @ SY1024 @ SV410 )
| ( in @ SY1024 @ SV144 )
| ( in @ SY1024 @ SV379 ) ) )
= $false )
| ( ( SV410
= ( set_union2 @ SV144 @ SV379 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2484]) ).
thf(2616,plain,
! [SV379: $i,SV410: $i,SV144: $i] :
( ( ( ~ ~ ( ~ ! [SY1025: $i] :
( ~ ( in @ SY1025 @ SV144 )
| ( in @ SY1025 @ SV410 ) )
| ~ ! [SY1026: $i] :
( ~ ( in @ SY1026 @ SV379 )
| ( in @ SY1026 @ SV410 ) ) ) )
= $false )
| ( ( SV410
= ( set_union2 @ SV144 @ SV379 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2484]) ).
thf(2617,plain,
! [SV380: $i,SV145: $i,SV411: $i,SV528: $i] :
( ( ( ~ ( in @ SV528 @ ( relation_dom @ SV411 ) )
| ~ ( in @ ( ordered_pair @ SV528 @ SV145 ) @ SV411 )
| ~ ( in @ SV528 @ SV380 ) )
= $true )
| ( ( in @ SV145 @ ( relation_image @ SV411 @ SV380 ) )
= $true )
| ( ( relation @ SV411 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2485]) ).
thf(2618,plain,
! [SV381: $i,SV412: $i,SV145: $i] :
( ( ( in @ SV145 @ ( relation_image @ SV412 @ SV381 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK40_D @ SV412 @ SV381 @ SV145 ) @ ( relation_dom @ SV412 ) )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV412 @ SV381 @ SV145 ) @ SV145 ) @ SV412 ) )
| ~ ( in @ ( sK40_D @ SV412 @ SV381 @ SV145 ) @ SV381 ) ) )
= $true )
| ( ( relation @ SV412 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2486]) ).
thf(2619,plain,
! [SV529: $i,SV460: $i] :
( ( ( subset @ SV460 @ ( singleton @ SV529 ) )
= $true )
| ( ( SV460 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2488]) ).
thf(2620,plain,
! [SV492: $i,SV461: $i] :
( ( ( SV461
= ( singleton @ SV492 ) )
= $false )
| ( ( subset @ SV461 @ ( singleton @ SV492 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2489]) ).
thf(2621,plain,
! [SV312: $i,SV385: $i] :
( ( ( in @ ( sK50_C @ SV385 @ SV312 ) @ SV385 )
= $false )
| ( ( subset @ SV312 @ SV385 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2493]) ).
thf(2622,plain,
! [SV386: $i,SV313: $i,SV494: $i] :
( ( ( in @ SV494 @ SV313 )
= $false )
| ( ( in @ SV494 @ SV386 )
= $true )
| ( ( subset @ SV313 @ SV386 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2494]) ).
thf(2623,plain,
! [SV149: $i,SV387: $i,SV415: $i] :
( ( ( ~ ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV149 )
| ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV387 )
| ~ ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV415 ) )
= $true )
| ( ( SV415
= ( set_difference @ SV149 @ SV387 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2495]) ).
thf(2624,plain,
! [SV149: $i,SV387: $i,SV415: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV149 )
| ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV415 ) )
| ~ ( ~ ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV387 )
| ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV415 ) ) ) )
= $true )
| ( ( SV415
= ( set_difference @ SV149 @ SV387 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2496]) ).
thf(2625,plain,
! [SV416: $i,SV388: $i,SV149: $i] :
( ( ( ~ ! [SY1030: $i] :
( ~ ( in @ SY1030 @ SV149 )
| ( in @ SY1030 @ SV388 )
| ( in @ SY1030 @ SV416 ) ) )
= $false )
| ( ( SV416
= ( set_difference @ SV149 @ SV388 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2497]) ).
thf(2626,plain,
! [SV388: $i,SV149: $i,SV416: $i] :
( ( ( ~ ~ ( ~ ! [SY1031: $i] :
( ~ ( in @ SY1031 @ SV416 )
| ( in @ SY1031 @ SV149 ) )
| ~ ! [SY1032: $i] :
( ~ ( in @ SY1032 @ SV416 )
| ~ ( in @ SY1032 @ SV388 ) ) ) )
= $false )
| ( ( SV416
= ( set_difference @ SV149 @ SV388 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2497]) ).
thf(2627,plain,
! [SV178: $i,SV33: $i,SV417: $i] :
( ( ( relation @ SV417 )
= $false )
| ( ( function @ SV417 )
= $false )
| ( ( ~ ( in @ SV33 @ ( relation_dom @ ( relation_composition @ SV417 @ SV178 ) ) )
| ( ( apply @ ( relation_composition @ SV417 @ SV178 ) @ SV33 )
= ( apply @ SV178 @ ( apply @ SV417 @ SV33 ) ) ) )
= $true )
| ( ( function @ SV178 )
= $false )
| ( ( relation @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2498]) ).
thf(2628,plain,
! [SV179: $i,SV34: $i,SV418: $i] :
( ( ( relation @ SV418 )
= $false )
| ( ( function @ SV418 )
= $false )
| ( ( ~ ( in @ SV34 @ ( relation_dom @ SV179 ) )
| ( ( apply @ ( relation_composition @ SV179 @ SV418 ) @ SV34 )
= ( apply @ SV418 @ ( apply @ SV179 @ SV34 ) ) ) )
= $true )
| ( ( function @ SV179 )
= $false )
| ( ( relation @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2499]) ).
thf(2629,plain,
! [SV112: $i,SV322: $i,SV390: $i] :
( ( ( ~ ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV112 )
| ~ ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV322 ) )
= $true )
| ( ( ~ ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV390 ) )
= $true )
| ( ( SV390
= ( set_intersection2 @ SV112 @ SV322 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2500]) ).
thf(2630,plain,
! [SV112: $i,SV322: $i,SV390: $i] :
( ( ( ~ ( ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV112 )
| ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV390 ) )
| ~ ( ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV322 )
| ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV390 ) ) )
= $false )
| ( ( SV390
= ( set_intersection2 @ SV112 @ SV322 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2501]) ).
thf(2631,plain,
! [SV391: $i,SV323: $i,SV112: $i] :
( ( ( ! [SY1008: $i] :
( ~ ( in @ SY1008 @ SV112 )
| ~ ( in @ SY1008 @ SV323 )
| ( in @ SY1008 @ SV391 ) ) )
= $true )
| ( ( SV391
= ( set_intersection2 @ SV112 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2502]) ).
thf(2632,plain,
! [SV323: $i,SV112: $i,SV391: $i] :
( ( ( ~ ( ~ ! [SY1009: $i] :
( ~ ( in @ SY1009 @ SV391 )
| ( in @ SY1009 @ SV112 ) )
| ~ ! [SY1010: $i] :
( ~ ( in @ SY1010 @ SV391 )
| ( in @ SY1010 @ SV323 ) ) ) )
= $true )
| ( ( SV391
= ( set_intersection2 @ SV112 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2503]) ).
thf(2633,plain,
! [SV530: $i,SV258: $i,SV324: $i] :
( ( ( ~ ( in @ ( sK47_C @ SV324 @ SV258 ) @ SV530 )
| ~ ( in @ SV530 @ SV258 ) )
= $true )
| ( ( ~ ( in @ ( sK47_C @ SV324 @ SV258 ) @ SV324 ) )
= $true )
| ( ( SV324
= ( union @ SV258 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2504]) ).
thf(2634,plain,
! [SV258: $i,SV324: $i] :
( ( ( ~ ( in @ ( sK47_C @ SV324 @ SV258 ) @ ( sK48_SY487 @ SV324 @ SV258 ) )
| ~ ( in @ ( sK48_SY487 @ SV324 @ SV258 ) @ SV258 ) )
= $false )
| ( ( in @ ( sK47_C @ SV324 @ SV258 ) @ SV324 )
= $true )
| ( ( SV324
= ( union @ SV258 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2505]) ).
thf(2635,plain,
! [SV325: $i,SV259: $i,SV531: $i] :
( ( ( ! [SY1141: $i] :
( ~ ( in @ SV531 @ SY1141 )
| ~ ( in @ SY1141 @ SV259 ) )
| ( in @ SV531 @ SV325 ) )
= $true )
| ( ( SV325
= ( union @ SV259 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2506]) ).
thf(2636,plain,
! [SV259: $i,SV325: $i,SV532: $i] :
( ( ( ~ ( in @ SV532 @ SV325 )
| ~ ( ~ ( in @ SV532 @ ( sK46_D @ SV532 @ SV325 @ SV259 ) )
| ~ ( in @ ( sK46_D @ SV532 @ SV325 @ SV259 ) @ SV259 ) ) )
= $true )
| ( ( SV325
= ( union @ SV259 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2507]) ).
thf(2637,plain,
! [SV113: $i,SV225: $i,SV463: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) @ SV113 )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV225 )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 ) )
| ~ ~ ( ~ ( ( in @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) @ SV113 )
| ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV225 )
| ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 ) ) ) ) )
= $true )
| ( ( SV463
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $true )
| ( ( relation @ SV463 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2508]) ).
thf(2638,plain,
! [SV225: $i,SV113: $i,SV464: $i] :
( ( ( ( SV464
!= ( relation_rng_restriction @ SV113 @ SV225 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1094: $i,SY1095: $i] :
( ~ ( in @ SY1095 @ SV113 )
| ~ ( in @ ( ordered_pair @ SY1094 @ SY1095 ) @ SV225 )
| ( in @ ( ordered_pair @ SY1094 @ SY1095 ) @ SV464 ) )
| ~ ~ ( ~ ! [SY1096: $i,SY1097: $i] :
( ~ ( in @ ( ordered_pair @ SY1096 @ SY1097 ) @ SV464 )
| ( in @ SY1097 @ SV113 ) )
| ~ ! [SY1098: $i,SY1099: $i] :
( ~ ( in @ ( ordered_pair @ SY1098 @ SY1099 ) @ SV464 )
| ( in @ ( ordered_pair @ SY1098 @ SY1099 ) @ SV225 ) ) ) ) )
= $true )
| ( ( relation @ SV464 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2509]) ).
thf(2639,plain,
! [SV392: $i,SV114: $i,SV419: $i,SV226: $i] :
( ( ( in @ SV226 @ SV419 )
= $false )
| ( ( in @ SV114 @ SV392 )
= $false )
| ( ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SV392 @ SV419 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2510]) ).
thf(2640,plain,
! [SV533: $i,SV495: $i,SV226: $i,SV114: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SV495 @ SV533 ) ) )
= $true )
| ( ( in @ SV114 @ SV495 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2511]) ).
thf(2641,plain,
! [SV514: $i,SV496: $i,SV226: $i,SV114: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SV496 @ SV514 ) ) )
= $true )
| ( ( in @ SV226 @ SV514 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2512]) ).
thf(2642,plain,
! [SV420: $i,SV329: $i,SV263: $i] :
( ( ( disjoint @ SV263 @ SV329 )
= $false )
| ( ( in @ SV420 @ SV263 )
= $false )
| ( ( in @ SV420 @ SV329 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2513]) ).
thf(2643,plain,
! [SV264: $i,SV330: $i] :
( ( ( ( sK62_C @ SV330 @ SV264 )
= SV264 )
= $false )
| ( ( ~ ( in @ ( sK62_C @ SV330 @ SV264 ) @ SV330 ) )
= $true )
| ( ( SV330
= ( singleton @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2514]) ).
thf(2644,plain,
! [SV331: $i,SV265: $i,SV534: $i] :
( ( ( ( SV534 != SV265 )
| ( in @ SV534 @ SV331 ) )
= $true )
| ( ( SV331
= ( singleton @ SV265 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2516]) ).
thf(2645,plain,
! [SV265: $i,SV331: $i,SV535: $i] :
( ( ( ~ ( in @ SV535 @ SV331 )
| ( SV535 = SV265 ) )
= $true )
| ( ( SV331
= ( singleton @ SV265 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2517]) ).
thf(2646,plain,
! [SV115: $i,SV465: $i] :
( ( ( ~ ! [SY1100: $i] :
( ~ ( subset @ SY1100 @ SV465 )
| ( in @ SY1100 @ ( sK43_SY481 @ SV465 @ SV115 ) ) ) )
= $false )
| ( ( ~ ( in @ SV465 @ ( sK42_B @ SV115 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2518]) ).
thf(2647,plain,
! [SV115: $i,SV465: $i] :
( ( ( ~ ( in @ ( sK43_SY481 @ SV465 @ SV115 ) @ ( sK42_B @ SV115 ) ) )
= $false )
| ( ( ~ ( in @ SV465 @ ( sK42_B @ SV115 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2518]) ).
thf(2648,plain,
! [SV115: $i,SV536: $i] :
( ( ! [SY1142: $i] :
( ~ ( in @ SV536 @ ( sK42_B @ SV115 ) )
| ~ ( subset @ SY1142 @ SV536 )
| ( in @ SY1142 @ ( sK42_B @ SV115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2519]) ).
thf(2649,plain,
! [SV116: $i] :
( ( ( ! [SY635: $i] :
( ~ ( in @ SY635 @ ( relation_dom @ SV116 ) )
| ! [SY636: $i] :
( ( SY636
!= ( apply @ SV116 @ SY635 ) )
| ( in @ ( ordered_pair @ SY635 @ SY636 ) @ SV116 ) ) ) )
= $true )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2523]) ).
thf(2650,plain,
! [SV116: $i] :
( ( ( ! [SY637: $i] :
( ~ ( in @ SY637 @ ( relation_dom @ SV116 ) )
| ! [SY638: $i] :
( ~ ( in @ ( ordered_pair @ SY637 @ SY638 ) @ SV116 )
| ( SY638
= ( apply @ SV116 @ SY637 ) ) ) ) )
= $true )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2524]) ).
thf(2651,plain,
! [SV116: $i] :
( ( ( ! [SY639: $i] :
( ( in @ SY639 @ ( relation_dom @ SV116 ) )
| ! [SY640: $i] :
( ( SY640
!= ( apply @ SV116 @ SY639 ) )
| ( SY640 = empty_set ) ) ) )
= $true )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2525]) ).
thf(2652,plain,
! [SV116: $i] :
( ( ( ! [SY641: $i] :
( ( in @ SY641 @ ( relation_dom @ SV116 ) )
| ! [SY642: $i] :
( ( SY642 != empty_set )
| ( SY642
= ( apply @ SV116 @ SY641 ) ) ) ) )
= $true )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2526]) ).
thf(2653,plain,
! [SV393: $i,SV334: $i,SV117: $i] :
( ( ( ! [SY1012: $i,SY1013: $i] :
( ~ ( in @ SY1012 @ SV117 )
| ~ ( in @ SY1013 @ SV334 )
| ( ( sK53_D @ SV393 @ SV334 @ SV117 )
!= ( ordered_pair @ SY1012 @ SY1013 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK53_D @ SV393 @ SV334 @ SV117 ) @ SV393 ) )
= $true )
| ( ( SV393
= ( cartesian_product2 @ SV117 @ SV334 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2527]) ).
thf(2654,plain,
! [SV117: $i,SV334: $i,SV393: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK54_SY491 @ SV393 @ SV334 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK55_SY493 @ SV393 @ SV334 @ SV117 ) @ SV334 ) )
| ( ( sK53_D @ SV393 @ SV334 @ SV117 )
!= ( ordered_pair @ ( sK54_SY491 @ SV393 @ SV334 @ SV117 ) @ ( sK55_SY493 @ SV393 @ SV334 @ SV117 ) ) ) ) )
= $true )
| ( ( in @ ( sK53_D @ SV393 @ SV334 @ SV117 ) @ SV393 )
= $true )
| ( ( SV393
= ( cartesian_product2 @ SV117 @ SV334 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2528]) ).
thf(2655,plain,
! [SV394: $i,SV335: $i,SV117: $i] :
( ( ( ! [SY1014: $i] :
( ! [SY964: $i,SY965: $i] :
( ~ ( in @ SY964 @ SV117 )
| ~ ( in @ SY965 @ SV335 )
| ( SY1014
!= ( ordered_pair @ SY964 @ SY965 ) ) )
| ( in @ SY1014 @ SV394 ) ) )
= $true )
| ( ( SV394
= ( cartesian_product2 @ SV117 @ SV335 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2529]) ).
thf(2656,plain,
! [SV117: $i,SV335: $i,SV394: $i] :
( ( ( ! [SY1017: $i] :
( ~ ( in @ SY1017 @ SV394 )
| ~ ( ~ ~ ( ~ ( in @ ( sK51_E @ SY1017 @ SV394 @ SV335 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK52_SY488 @ SY1017 @ SV394 @ SV335 @ SV117 ) @ SV335 ) )
| ( SY1017
!= ( ordered_pair @ ( sK51_E @ SY1017 @ SV394 @ SV335 @ SV117 ) @ ( sK52_SY488 @ SY1017 @ SV394 @ SV335 @ SV117 ) ) ) ) ) )
= $true )
| ( ( SV394
= ( cartesian_product2 @ SV117 @ SV335 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2530]) ).
thf(2657,plain,
! [SV118: $i,SV395: $i,SV338: $i] :
( ( ( ( SV338
!= ( apply @ SV395 @ SV118 ) )
| ~ ( in @ SV118 @ ( relation_dom @ SV395 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV118 @ SV338 ) @ SV395 )
= $true )
| ( ( function @ SV395 )
= $false )
| ( ( relation @ SV395 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2531]) ).
thf(2658,plain,
! [SV467: $i,SV118: $i,SV497: $i] :
( ( ( ~ ( function @ SV497 ) )
= $true )
| ( ( ~ ( relation @ SV497 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV118 @ SV467 ) @ SV497 )
| ( SV467
= ( apply @ SV497 @ SV118 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2532]) ).
thf(2659,plain,
! [SV468: $i,SV118: $i,SV498: $i] :
( ( ( ~ ( function @ SV498 ) )
= $true )
| ( ( ~ ( relation @ SV498 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV118 @ SV468 ) @ SV498 )
| ( in @ SV118 @ ( relation_dom @ SV498 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2533]) ).
thf(2660,plain,
! [SV273: $i,SV339: $i] :
( ( ( ( ( sK69_C @ SV339 @ SV273 )
!= ( sK70_SY500 @ SV339 @ SV273 ) )
| ~ ( in @ ( sK69_C @ SV339 @ SV273 ) @ SV273 )
| ~ ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 ) )
= $true )
| ( ( SV339
= ( identity_relation @ SV273 ) )
= $true )
| ( ( relation @ SV339 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2534]) ).
thf(2661,plain,
! [SV273: $i,SV339: $i] :
( ( ( ~ ( ~ ( ( ( sK69_C @ SV339 @ SV273 )
= ( sK70_SY500 @ SV339 @ SV273 ) )
| ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 ) )
| ~ ( ( in @ ( sK69_C @ SV339 @ SV273 ) @ SV273 )
| ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 ) ) ) )
= $true )
| ( ( SV339
= ( identity_relation @ SV273 ) )
= $true )
| ( ( relation @ SV339 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2535]) ).
thf(2662,plain,
! [SV340: $i,SV274: $i] :
( ( ( ~ ! [SY968: $i,SY969: $i] :
( ( SY968 != SY969 )
| ~ ( in @ SY968 @ SV274 )
| ( in @ ( ordered_pair @ SY968 @ SY969 ) @ SV340 ) ) )
= $false )
| ( ( SV340
= ( identity_relation @ SV274 ) )
= $false )
| ( ( relation @ SV340 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2536]) ).
thf(2663,plain,
! [SV274: $i,SV340: $i] :
( ( ( ~ ~ ( ~ ! [SY970: $i,SY971: $i] :
( ~ ( in @ ( ordered_pair @ SY970 @ SY971 ) @ SV340 )
| ( SY970 = SY971 ) )
| ~ ! [SY972: $i] :
( ! [SY973: $i] :
~ ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV340 )
| ( in @ SY972 @ SV274 ) ) ) )
= $false )
| ( ( SV340
= ( identity_relation @ SV274 ) )
= $false )
| ( ( relation @ SV340 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2536]) ).
thf(2664,plain,
! [SV120: $i,SV275: $i,SV516: $i] :
( ( ( ~ ( relation @ SV516 ) )
= $true )
| ( ( ~ ( ~ ( ! [SY1135: $i] :
( ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ SY1135 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY1135 @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV275 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV516 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK15_SY461 @ SV516 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY461 @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV275 ) )
| ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV516 ) ) )
| ( SV516
= ( relation_composition @ SV120 @ SV275 ) ) )
= $true )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2537]) ).
thf(2665,plain,
! [SV275: $i,SV120: $i,SV517: $i] :
( ( ( ~ ( relation @ SV517 ) )
= $true )
| ( ( ( SV517
!= ( relation_composition @ SV120 @ SV275 ) )
| ~ ( ~ ! [SY1136: $i,SY1137: $i] :
( ! [SY909: $i] :
( ~ ( in @ ( ordered_pair @ SY1136 @ SY909 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY909 @ SY1137 ) @ SV275 ) )
| ( in @ ( ordered_pair @ SY1136 @ SY1137 ) @ SV517 ) )
| ~ ! [SY1139: $i,SY1140: $i] :
( ~ ( in @ ( ordered_pair @ SY1139 @ SY1140 ) @ SV517 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1139 @ ( sK12_F @ SY1140 @ SY1139 @ SV517 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK12_F @ SY1140 @ SY1139 @ SV517 @ SV275 @ SV120 ) @ SY1140 ) @ SV275 ) ) ) ) )
= $true )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2538]) ).
thf(2666,plain,
! [SV121: $i,SV469: $i,SV227: $i] :
( ( ( ~ ( disjoint @ SV227 @ SV469 ) )
= $true )
| ( ( subset @ SV227 @ ( subset_complement @ SV121 @ SV469 ) )
= $true )
| ( ( element @ SV469 @ ( powerset @ SV121 ) )
= $false )
| ( ( element @ SV227 @ ( powerset @ SV121 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2539]) ).
thf(2667,plain,
! [SV470: $i,SV121: $i,SV227: $i] :
( ( ( ~ ( subset @ SV227 @ ( subset_complement @ SV121 @ SV470 ) ) )
= $true )
| ( ( disjoint @ SV227 @ SV470 )
= $true )
| ( ( element @ SV470 @ ( powerset @ SV121 ) )
= $false )
| ( ( element @ SV227 @ ( powerset @ SV121 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2540]) ).
thf(2668,plain,
! [SV396: $i,SV341: $i,SV122: $i] :
( ( ( in @ SV122 @ SV341 )
= $false )
| ( ( ~ ( in @ SV122 @ ( relation_rng @ SV396 ) ) )
= $true )
| ( ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SV341 @ SV396 ) ) )
= $true )
| ( ( relation @ SV396 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2541]) ).
thf(2669,plain,
! [SV471: $i,SV122: $i,SV499: $i] :
( ( ( relation @ SV499 )
= $false )
| ( ( ~ ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SV471 @ SV499 ) ) )
| ( in @ SV122 @ SV471 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2542]) ).
thf(2670,plain,
! [SV472: $i,SV122: $i,SV500: $i] :
( ( ( relation @ SV500 )
= $false )
| ( ( ~ ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SV472 @ SV500 ) ) )
| ( in @ SV122 @ ( relation_rng @ SV500 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2543]) ).
thf(2671,plain,
! [SV123: $i,SV424: $i,SV473: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ SV424 )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV123 )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 ) )
| ~ ~ ( ~ ( ( in @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ SV424 )
| ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 ) ) ) ) )
= $true )
| ( ( SV473
= ( relation_dom_restriction @ SV123 @ SV424 ) )
= $true )
| ( ( relation @ SV473 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2544]) ).
thf(2672,plain,
! [SV425: $i,SV123: $i,SV474: $i] :
( ( ( ( SV474
!= ( relation_dom_restriction @ SV123 @ SV425 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1105: $i,SY1106: $i] :
( ~ ( in @ SY1105 @ SV425 )
| ~ ( in @ ( ordered_pair @ SY1105 @ SY1106 ) @ SV123 )
| ( in @ ( ordered_pair @ SY1105 @ SY1106 ) @ SV474 ) )
| ~ ~ ( ~ ! [SY1107: $i] :
( ! [SY1108: $i] :
~ ( in @ ( ordered_pair @ SY1107 @ SY1108 ) @ SV474 )
| ( in @ SY1107 @ SV425 ) )
| ~ ! [SY1109: $i,SY1110: $i] :
( ~ ( in @ ( ordered_pair @ SY1109 @ SY1110 ) @ SV474 )
| ( in @ ( ordered_pair @ SY1109 @ SY1110 ) @ SV123 ) ) ) ) )
= $true )
| ( ( relation @ SV474 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2545]) ).
thf(2673,plain,
! [SV124: $i,SV426: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_C @ SV426 @ SV124 ) @ ( sK17_SY462 @ SV426 @ SV124 ) ) @ SV426 )
| ~ ( in @ ( ordered_pair @ ( sK17_SY462 @ SV426 @ SV124 ) @ ( sK16_C @ SV426 @ SV124 ) ) @ SV124 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK16_C @ SV426 @ SV124 ) @ ( sK17_SY462 @ SV426 @ SV124 ) ) @ SV426 )
| ( in @ ( ordered_pair @ ( sK17_SY462 @ SV426 @ SV124 ) @ ( sK16_C @ SV426 @ SV124 ) ) @ SV124 ) ) )
= $false )
| ( ( SV426
= ( relation_inverse @ SV124 ) )
= $true )
| ( ( relation @ SV426 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2546]) ).
thf(2674,plain,
! [SV124: $i,SV427: $i] :
( ( ( SV427
= ( relation_inverse @ SV124 ) )
= $false )
| ( ( ~ ( ~ ! [SY1043: $i,SY1044: $i] :
( ~ ( in @ ( ordered_pair @ SY1043 @ SY1044 ) @ SV427 )
| ( in @ ( ordered_pair @ SY1044 @ SY1043 ) @ SV124 ) )
| ~ ! [SY1045: $i,SY1046: $i] :
( ~ ( in @ ( ordered_pair @ SY1046 @ SY1045 ) @ SV124 )
| ( in @ ( ordered_pair @ SY1045 @ SY1046 ) @ SV427 ) ) ) )
= $true )
| ( ( relation @ SV427 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2547]) ).
thf(2675,plain,
! [SV282: $i,SV348: $i] :
( ( ( ~ ( ~ ( in @ ( sK38_C @ SV348 @ SV282 ) @ SV282 )
| ~ ( ( ( apply @ SV348 @ ( sK38_C @ SV348 @ SV282 ) )
!= ( sK38_C @ SV348 @ SV282 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV348 )
!= SV282 ) )
= $true )
| ( ( SV348
= ( identity_relation @ SV282 ) )
= $true )
| ( ( function @ SV348 )
= $false )
| ( ( relation @ SV348 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2548]) ).
thf(2676,plain,
! [SV428: $i,SV475: $i] :
( ( ( function @ SV475 )
= $false )
| ( ( ~ ( relation @ SV475 ) )
= $true )
| ( ( ( SV475
!= ( identity_relation @ SV428 ) )
| ! [SY1111: $i] :
( ~ ( in @ SY1111 @ SV428 )
| ( ( apply @ SV475 @ SY1111 )
= SY1111 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2549]) ).
thf(2677,plain,
! [SV429: $i,SV476: $i] :
( ( ( function @ SV476 )
= $false )
| ( ( ~ ( relation @ SV476 ) )
= $true )
| ( ( ( SV476
!= ( identity_relation @ SV429 ) )
| ( ( relation_dom @ SV476 )
= SV429 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2550]) ).
thf(2678,plain,
! [SV125: $i,SV432: $i,SV479: $i] :
( ( ( ~ ( ! [SY1112: $i] :
( ~ ( in @ ( ordered_pair @ SY1112 @ ( sK30_D @ SV479 @ SV432 @ SV125 ) ) @ SV125 )
| ~ ( in @ SY1112 @ SV432 ) )
| ~ ( in @ ( sK30_D @ SV479 @ SV432 @ SV125 ) @ SV479 ) ) )
= $false )
| ( ( SV479
= ( relation_image @ SV125 @ SV432 ) )
= $true )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2553]) ).
thf(2679,plain,
! [SV125: $i,SV432: $i,SV479: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_SY471 @ SV479 @ SV432 @ SV125 ) @ ( sK30_D @ SV479 @ SV432 @ SV125 ) ) @ SV125 )
| ~ ( in @ ( sK31_SY471 @ SV479 @ SV432 @ SV125 ) @ SV432 ) )
| ( in @ ( sK30_D @ SV479 @ SV432 @ SV125 ) @ SV479 ) ) )
= $false )
| ( ( SV479
= ( relation_image @ SV125 @ SV432 ) )
= $true )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2553]) ).
thf(2680,plain,
! [SV480: $i,SV433: $i,SV125: $i] :
( ( ( ~ ! [SY1113: $i] :
( ! [SY1056: $i] :
( ~ ( in @ ( ordered_pair @ SY1056 @ SY1113 ) @ SV125 )
| ~ ( in @ SY1056 @ SV433 ) )
| ( in @ SY1113 @ SV480 ) )
| ~ ! [SY1115: $i] :
( ~ ( in @ SY1115 @ SV480 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK29_E @ SY1115 @ SV480 @ SV433 @ SV125 ) @ SY1115 ) @ SV125 )
| ~ ( in @ ( sK29_E @ SY1115 @ SV480 @ SV433 @ SV125 ) @ SV433 ) ) ) )
= $false )
| ( ( SV480
= ( relation_image @ SV125 @ SV433 ) )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2554]) ).
thf(2681,plain,
! [SV434: $i,SV228: $i,SV399: $i,SV127: $i] :
( ( ( ~ ( in @ SV127 @ SV399 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ SV434 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SV399 ) @ SV434 ) )
= $true )
| ( ( relation @ SV434 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2557]) ).
thf(2682,plain,
! [SV501: $i,SV228: $i,SV127: $i,SV518: $i] :
( ( ( ~ ( relation @ SV518 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SV501 ) @ SV518 ) )
| ( in @ SV127 @ SV501 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2558]) ).
thf(2683,plain,
! [SV502: $i,SV228: $i,SV127: $i,SV519: $i] :
( ( ( ~ ( relation @ SV519 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SV502 ) @ SV519 ) )
| ( in @ ( ordered_pair @ SV127 @ SV228 ) @ SV519 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2559]) ).
thf(2684,plain,
! [SV503: $i,SV481: $i,SV128: $i] :
( ( ( subset @ ( unordered_pair @ SV128 @ SV481 ) @ SV503 )
= $false )
| ( ( in @ SV128 @ SV503 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2561]) ).
thf(2685,plain,
! [SV504: $i,SV482: $i,SV128: $i] :
( ( ( subset @ ( unordered_pair @ SV128 @ SV482 ) @ SV504 )
= $false )
| ( ( in @ SV482 @ SV504 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2562]) ).
thf(2686,plain,
! [SV435: $i,SV505: $i] :
( ( ( element @ SV505 @ SV435 )
= $false )
| ( ( in @ SV505 @ SV435 )
= $true )
| ( ( empty @ SV435 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2563]) ).
thf(2687,plain,
! [SV436: $i,SV506: $i] :
( ( ( in @ SV506 @ SV436 )
= $false )
| ( ( element @ SV506 @ SV436 )
= $true )
| ( ( empty @ SV436 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2564]) ).
thf(2688,plain,
! [SV437: $i,SV520: $i] :
( ( ( ~ ( element @ SV520 @ SV437 ) )
= $true )
| ( ( empty @ SV520 )
= $true )
| ( ( empty @ SV437 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2565]) ).
thf(2689,plain,
! [SV438: $i,SV521: $i] :
( ( ( ~ ( empty @ SV521 ) )
= $true )
| ( ( element @ SV521 @ SV438 )
= $true )
| ( ( empty @ SV438 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2566]) ).
thf(2690,plain,
! [SV129: $i,SV439: $i] :
( ( ( ! [SY1062: $i] :
~ ( in @ ( ordered_pair @ SY1062 @ ( sK19_C @ SV439 @ SV129 ) ) @ SV129 )
| ~ ( in @ ( sK19_C @ SV439 @ SV129 ) @ SV439 ) )
= $true )
| ( ( SV439
= ( relation_rng @ SV129 ) )
= $true )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2567]) ).
thf(2691,plain,
! [SV129: $i,SV439: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK20_SY464 @ SV439 @ SV129 ) @ ( sK19_C @ SV439 @ SV129 ) ) @ SV129 )
| ( in @ ( sK19_C @ SV439 @ SV129 ) @ SV439 ) )
= $true )
| ( ( SV439
= ( relation_rng @ SV129 ) )
= $true )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2568]) ).
thf(2692,plain,
! [SV440: $i,SV129: $i] :
( ( ( ~ ! [SY1063: $i] :
( ! [SY722: $i] :
~ ( in @ ( ordered_pair @ SY722 @ SY1063 ) @ SV129 )
| ( in @ SY1063 @ SV440 ) ) )
= $false )
| ( ( SV440
= ( relation_rng @ SV129 ) )
= $false )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2569]) ).
thf(2693,plain,
! [SV129: $i,SV440: $i] :
( ( ( ~ ! [SY1065: $i] :
( ~ ( in @ SY1065 @ SV440 )
| ( in @ ( ordered_pair @ ( sK18_D @ SY1065 @ SV440 @ SV129 ) @ SY1065 ) @ SV129 ) ) )
= $false )
| ( ( SV440
= ( relation_rng @ SV129 ) )
= $false )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2569]) ).
thf(2694,plain,
! [SV131: $i,SV442: $i,SV483: $i] :
( ( ( ~ ( ! [SY1118: $i] :
( ~ ( in @ ( ordered_pair @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SY1118 ) @ SV131 )
| ~ ( in @ SY1118 @ SV442 ) )
| ~ ( in @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SV483 ) ) )
= $false )
| ( ( SV483
= ( relation_inverse_image @ SV131 @ SV442 ) )
= $true )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2570]) ).
thf(2695,plain,
! [SV131: $i,SV442: $i,SV483: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ ( sK28_SY469 @ SV483 @ SV442 @ SV131 ) ) @ SV131 )
| ~ ( in @ ( sK28_SY469 @ SV483 @ SV442 @ SV131 ) @ SV442 ) )
| ( in @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SV483 ) ) )
= $false )
| ( ( SV483
= ( relation_inverse_image @ SV131 @ SV442 ) )
= $true )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2570]) ).
thf(2696,plain,
! [SV484: $i,SV443: $i,SV131: $i] :
( ( ( ~ ! [SY1119: $i] :
( ! [SY1070: $i] :
( ~ ( in @ ( ordered_pair @ SY1119 @ SY1070 ) @ SV131 )
| ~ ( in @ SY1070 @ SV443 ) )
| ( in @ SY1119 @ SV484 ) )
| ~ ! [SY1121: $i] :
( ~ ( in @ SY1121 @ SV484 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1121 @ ( sK26_E @ SY1121 @ SV484 @ SV443 @ SV131 ) ) @ SV131 )
| ~ ( in @ ( sK26_E @ SY1121 @ SV484 @ SV443 @ SV131 ) @ SV443 ) ) ) )
= $false )
| ( ( SV484
= ( relation_inverse_image @ SV131 @ SV443 ) )
= $false )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2571]) ).
thf(2697,plain,
! [SV522: $i,SV507: $i,SV296: $i] :
( ( ( ( sK68_B @ SV296 )
= ( ordered_pair @ SV507 @ SV522 ) )
= $false )
| ( ( relation @ SV296 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2572]) ).
thf(2698,plain,
! [SV401: $i,SV363: $i,SV132: $i] :
( ( ( in @ SV132 @ SV363 )
= $false )
| ( ( ~ ( in @ SV132 @ ( relation_dom @ SV401 ) ) )
= $true )
| ( ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SV401 @ SV363 ) ) )
= $true )
| ( ( relation @ SV401 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2573]) ).
thf(2699,plain,
! [SV485: $i,SV132: $i,SV508: $i] :
( ( ( relation @ SV508 )
= $false )
| ( ( ~ ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SV508 @ SV485 ) ) )
| ( in @ SV132 @ SV485 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2574]) ).
thf(2700,plain,
! [SV486: $i,SV132: $i,SV509: $i] :
( ( ( relation @ SV509 )
= $false )
| ( ( ~ ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SV509 @ SV486 ) ) )
| ( in @ SV132 @ ( relation_dom @ SV509 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2575]) ).
thf(2701,plain,
! [SV134: $i,SV445: $i] :
( ( ( ! [SY1072: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SV445 @ SV134 ) @ SY1072 ) @ SV134 )
| ~ ( in @ ( sK22_C @ SV445 @ SV134 ) @ SV445 ) )
= $true )
| ( ( SV445
= ( relation_dom @ SV134 ) )
= $true )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2578]) ).
thf(2702,plain,
! [SV134: $i,SV445: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK22_C @ SV445 @ SV134 ) @ ( sK23_SY466 @ SV445 @ SV134 ) ) @ SV134 )
| ( in @ ( sK22_C @ SV445 @ SV134 ) @ SV445 ) )
= $true )
| ( ( SV445
= ( relation_dom @ SV134 ) )
= $true )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2579]) ).
thf(2703,plain,
! [SV446: $i,SV134: $i] :
( ( ( ~ ! [SY1073: $i] :
( ! [SY747: $i] :
~ ( in @ ( ordered_pair @ SY1073 @ SY747 ) @ SV134 )
| ( in @ SY1073 @ SV446 ) ) )
= $false )
| ( ( SV446
= ( relation_dom @ SV134 ) )
= $false )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2580]) ).
thf(2704,plain,
! [SV134: $i,SV446: $i] :
( ( ( ~ ! [SY1075: $i] :
( ~ ( in @ SY1075 @ SV446 )
| ( in @ ( ordered_pair @ SY1075 @ ( sK21_D @ SY1075 @ SV446 @ SV134 ) ) @ SV134 ) ) )
= $false )
| ( ( SV446
= ( relation_dom @ SV134 ) )
= $false )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2580]) ).
thf(2705,plain,
! [SV135: $i,SV366: $i,SV404: $i] :
( ( ( ~ ( ~ ( in @ ( sK57_D @ SV404 @ SV366 @ SV135 ) @ SV404 )
| ( ( sK57_D @ SV404 @ SV366 @ SV135 )
!= SV135 ) )
| ~ ( ~ ( in @ ( sK57_D @ SV404 @ SV366 @ SV135 ) @ SV404 )
| ( ( sK57_D @ SV404 @ SV366 @ SV135 )
!= SV366 ) ) )
= $false )
| ( ( SV404
= ( unordered_pair @ SV135 @ SV366 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2581]) ).
thf(2706,plain,
! [SV135: $i,SV366: $i,SV404: $i] :
( ( ( in @ ( sK57_D @ SV404 @ SV366 @ SV135 ) @ SV404 )
= $true )
| ( ( ( ( sK57_D @ SV404 @ SV366 @ SV135 )
= SV135 )
| ( ( sK57_D @ SV404 @ SV366 @ SV135 )
= SV366 ) )
= $true )
| ( ( SV404
= ( unordered_pair @ SV135 @ SV366 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2582]) ).
thf(2707,plain,
! [SV367: $i,SV135: $i,SV405: $i] :
( ( ( ! [SY1019: $i] :
( ~ ( in @ SY1019 @ SV405 )
| ( SY1019 = SV135 )
| ( SY1019 = SV367 ) ) )
= $true )
| ( ( SV405
= ( unordered_pair @ SV135 @ SV367 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2583]) ).
thf(2708,plain,
! [SV367: $i,SV405: $i,SV135: $i] :
( ( ( ~ ( ~ ! [SY1020: $i] :
( ( SY1020 != SV135 )
| ( in @ SY1020 @ SV405 ) )
| ~ ! [SY1021: $i] :
( ( SY1021 != SV367 )
| ( in @ SY1021 @ SV405 ) ) ) )
= $true )
| ( ( SV405
= ( unordered_pair @ SV135 @ SV367 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2584]) ).
thf(2709,plain,
! [SV136: $i,SV447: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV136 )
| ~ ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV447 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV136 )
| ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV447 ) ) )
= $false )
| ( ( SV136 = SV447 )
= $true )
| ( ( relation @ SV447 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2585]) ).
thf(2710,plain,
! [SV448: $i,SV136: $i] :
( ( ( SV136 = SV448 )
= $false )
| ( ( ~ ( ~ ! [SY1076: $i,SY1077: $i] :
( ~ ( in @ ( ordered_pair @ SY1076 @ SY1077 ) @ SV136 )
| ( in @ ( ordered_pair @ SY1076 @ SY1077 ) @ SV448 ) )
| ~ ! [SY1078: $i,SY1079: $i] :
( ~ ( in @ ( ordered_pair @ SY1078 @ SY1079 ) @ SV448 )
| ( in @ ( ordered_pair @ SY1078 @ SY1079 ) @ SV136 ) ) ) )
= $true )
| ( ( relation @ SV448 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2586]) ).
thf(2711,plain,
! [SV368: $i,SV298: $i] :
( ( ( relation @ SV298 )
= $false )
| ( ( function @ SV298 )
= $false )
| ( ( ~ ( relation @ SV368 ) )
= $true )
| ( ( ~ ( function @ SV368 ) )
= $true )
| ( ( function @ ( relation_composition @ SV298 @ SV368 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2587]) ).
thf(2712,plain,
! [SV369: $i,SV299: $i] :
( ( ( relation @ SV299 )
= $false )
| ( ( function @ SV299 )
= $false )
| ( ( ~ ( relation @ SV369 ) )
= $true )
| ( ( ~ ( function @ SV369 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV299 @ SV369 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2588]) ).
thf(2713,plain,
! [SV230: $i,SV137: $i,SV523: $i] :
( ( ( ~ ( function @ SV523 )
| ~ ( relation @ SV523 ) )
= $true )
| ( ( ~ ( in @ SV137 @ ( relation_dom @ SV523 ) )
| ~ ( in @ ( apply @ SV523 @ SV137 ) @ ( relation_dom @ SV230 ) )
| ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SV523 @ SV230 ) ) ) )
= $true )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2589]) ).
thf(2714,plain,
! [SV230: $i,SV137: $i] :
( ( ( ~ ! [SY862: $i] :
( ~ ( function @ SY862 )
| ~ ( relation @ SY862 )
| ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY862 @ SV230 ) ) )
| ( in @ SV137 @ ( relation_dom @ SY862 ) ) ) )
= $false )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2590]) ).
thf(2715,plain,
! [SV230: $i,SV137: $i] :
( ( ( ~ ! [SY863: $i] :
( ~ ( function @ SY863 )
| ~ ( relation @ SY863 )
| ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY863 @ SV230 ) ) )
| ( in @ ( apply @ SY863 @ SV137 ) @ ( relation_dom @ SV230 ) ) ) )
= $false )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2590]) ).
thf(2716,plain,
! [SV138: $i,SV537: $i] :
( ( ! [SY1143: $i] :
( ~ ( in @ SV537 @ ( sK41_B @ SV138 ) )
| ~ ( subset @ SY1143 @ SV537 )
| ( in @ SY1143 @ ( sK41_B @ SV138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2592]) ).
thf(2717,plain,
! [SV139: $i,SV449: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV449 @ SV139 ) @ ( sK25_SY467 @ SV449 @ SV139 ) ) @ SV139 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SV449 @ SV139 ) @ ( sK25_SY467 @ SV449 @ SV139 ) ) @ SV449 ) )
= $false )
| ( ( subset @ SV139 @ SV449 )
= $true )
| ( ( relation @ SV449 )
= $false )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2594]) ).
thf(2718,plain,
! [SV450: $i,SV139: $i] :
( ( ( subset @ SV139 @ SV450 )
= $false )
| ( ( ! [SY1080: $i,SY1081: $i] :
( ~ ( in @ ( ordered_pair @ SY1080 @ SY1081 ) @ SV139 )
| ( in @ ( ordered_pair @ SY1080 @ SY1081 ) @ SV450 ) ) )
= $true )
| ( ( relation @ SV450 )
= $false )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2595]) ).
thf(2719,plain,
! [SV300: $i,SV371: $i] :
( ( ( in @ ( sK60_C @ SV371 @ SV300 ) @ SV371 )
= $false )
| ( ( ~ ( subset @ ( sK60_C @ SV371 @ SV300 ) @ SV300 ) )
= $true )
| ( ( SV371
= ( powerset @ SV300 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2596]) ).
thf(2720,plain,
! [SV301: $i,SV372: $i,SV538: $i] :
( ( ( ~ ( in @ SV538 @ SV372 )
| ( subset @ SV538 @ SV301 ) )
= $true )
| ( ( SV372
= ( powerset @ SV301 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2598]) ).
thf(2721,plain,
! [SV372: $i,SV301: $i,SV539: $i] :
( ( ( ~ ( subset @ SV539 @ SV301 )
| ( in @ SV539 @ SV372 ) )
= $true )
| ( ( SV372
= ( powerset @ SV301 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2599]) ).
thf(2722,plain,
! [SV451: $i,SV140: $i] :
( ( ( subset @ SV140 @ SV451 )
= $false )
| ( ( subset @ ( relation_dom @ SV140 ) @ ( relation_dom @ SV451 ) )
= $true )
| ( ( relation @ SV451 )
= $false )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2600]) ).
thf(2723,plain,
! [SV452: $i,SV140: $i] :
( ( ( subset @ SV140 @ SV452 )
= $false )
| ( ( subset @ ( relation_rng @ SV140 ) @ ( relation_rng @ SV452 ) )
= $true )
| ( ( relation @ SV452 )
= $false )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2601]) ).
thf(2724,plain,
! [SV375: $i,SV142: $i,SV406: $i,SV524: $i] :
( ( ( ~ ( in @ SV524 @ ( relation_rng @ SV406 ) )
| ~ ( in @ ( ordered_pair @ SV142 @ SV524 ) @ SV406 ) )
= $true )
| ( ( ~ ( in @ SV524 @ SV375 ) )
= $true )
| ( ( in @ SV142 @ ( relation_inverse_image @ SV406 @ SV375 ) )
= $true )
| ( ( relation @ SV406 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2602]) ).
thf(2725,plain,
! [SV142: $i,SV376: $i,SV407: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK39_D @ SV407 @ SV376 @ SV142 ) @ ( relation_rng @ SV407 ) )
| ~ ( in @ ( ordered_pair @ SV142 @ ( sK39_D @ SV407 @ SV376 @ SV142 ) ) @ SV407 ) )
| ~ ( in @ ( sK39_D @ SV407 @ SV376 @ SV142 ) @ SV376 ) )
= $false )
| ( ( in @ SV142 @ ( relation_inverse_image @ SV407 @ SV376 ) )
= $false )
| ( ( relation @ SV407 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2603]) ).
thf(2726,plain,
! [SV453: $i,SV510: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK65_SY495 @ SV510 @ SV453 ) @ SV453 )
| ~ ~ ( in @ ( sK64_C @ SV510 @ SV453 ) @ ( sK65_SY495 @ SV510 @ SV453 ) ) )
| ~ ( in @ ( sK64_C @ SV510 @ SV453 ) @ SV510 ) )
| ~ ( ! [SY1129: $i] :
( ~ ( in @ SY1129 @ SV453 )
| ( in @ ( sK64_C @ SV510 @ SV453 ) @ SY1129 ) )
| ( in @ ( sK64_C @ SV510 @ SV453 ) @ SV510 ) ) )
= $false )
| ( ( SV510
= ( set_meet @ SV453 ) )
= $true )
| ( ( SV453 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2604]) ).
thf(2727,plain,
! [SV454: $i,SV511: $i] :
( ( ( SV511
= ( set_meet @ SV454 ) )
= $false )
| ( ( ~ ( ~ ! [SY1130: $i] :
( ~ ( ~ ( in @ ( sK63_D @ SY1130 @ SV511 @ SV454 ) @ SV454 )
| ~ ~ ( in @ SY1130 @ ( sK63_D @ SY1130 @ SV511 @ SV454 ) ) )
| ( in @ SY1130 @ SV511 ) )
| ~ ! [SY1131: $i] :
( ~ ( in @ SY1131 @ SV511 )
| ! [SY1087: $i] :
( ~ ( in @ SY1087 @ SV454 )
| ( in @ SY1131 @ SY1087 ) ) ) ) )
= $true )
| ( ( SV454 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2605]) ).
thf(2728,plain,
! [SV455: $i,SV525: $i] :
( ( ( ( SV525
!= ( set_meet @ SV455 ) ) )
= $true )
| ( ( SV525 = empty_set )
= $true )
| ( ( SV455 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2606]) ).
thf(2729,plain,
! [SV456: $i,SV526: $i] :
( ( ( ( SV526 != empty_set ) )
= $true )
| ( ( SV526
= ( set_meet @ SV456 ) )
= $true )
| ( ( SV456 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2607]) ).
thf(2730,plain,
! [SV488: $i,SV457: $i] :
( ( ( SV457 = SV488 )
= $false )
| ( ( proper_subset @ SV457 @ SV488 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2608]) ).
thf(2731,plain,
! [SV408: $i,SV143: $i,SV459: $i,SV231: $i] :
( ( ( in @ SV231 @ SV459 )
= $false )
| ( ( in @ SV143 @ SV408 )
= $false )
| ( ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SV408 @ SV459 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2610]) ).
thf(2732,plain,
! [SV540: $i,SV512: $i,SV231: $i,SV143: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SV512 @ SV540 ) ) )
= $true )
| ( ( in @ SV143 @ SV512 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2611]) ).
thf(2733,plain,
! [SV527: $i,SV513: $i,SV231: $i,SV143: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SV513 @ SV527 ) ) )
= $true )
| ( ( in @ SV231 @ SV527 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2612]) ).
thf(2734,plain,
! [SV144: $i,SV378: $i,SV409: $i] :
( ( ( ~ ( ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV409 )
| ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV144 ) )
| ~ ( ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV409 )
| ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV378 ) ) )
= $false )
| ( ( SV409
= ( set_union2 @ SV144 @ SV378 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2613]) ).
thf(2735,plain,
! [SV144: $i,SV378: $i,SV409: $i] :
( ( ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV409 )
= $true )
| ( ( ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV144 )
| ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV378 ) )
= $true )
| ( ( SV409
= ( set_union2 @ SV144 @ SV378 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2614]) ).
thf(2736,plain,
! [SV379: $i,SV144: $i,SV410: $i] :
( ( ( ! [SY1024: $i] :
( ~ ( in @ SY1024 @ SV410 )
| ( in @ SY1024 @ SV144 )
| ( in @ SY1024 @ SV379 ) ) )
= $true )
| ( ( SV410
= ( set_union2 @ SV144 @ SV379 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2615]) ).
thf(2737,plain,
! [SV379: $i,SV410: $i,SV144: $i] :
( ( ( ~ ( ~ ! [SY1025: $i] :
( ~ ( in @ SY1025 @ SV144 )
| ( in @ SY1025 @ SV410 ) )
| ~ ! [SY1026: $i] :
( ~ ( in @ SY1026 @ SV379 )
| ( in @ SY1026 @ SV410 ) ) ) )
= $true )
| ( ( SV410
= ( set_union2 @ SV144 @ SV379 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2616]) ).
thf(2738,plain,
! [SV380: $i,SV145: $i,SV411: $i,SV528: $i] :
( ( ( ~ ( in @ SV528 @ ( relation_dom @ SV411 ) )
| ~ ( in @ ( ordered_pair @ SV528 @ SV145 ) @ SV411 ) )
= $true )
| ( ( ~ ( in @ SV528 @ SV380 ) )
= $true )
| ( ( in @ SV145 @ ( relation_image @ SV411 @ SV380 ) )
= $true )
| ( ( relation @ SV411 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2617]) ).
thf(2739,plain,
! [SV145: $i,SV381: $i,SV412: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK40_D @ SV412 @ SV381 @ SV145 ) @ ( relation_dom @ SV412 ) )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV412 @ SV381 @ SV145 ) @ SV145 ) @ SV412 ) )
| ~ ( in @ ( sK40_D @ SV412 @ SV381 @ SV145 ) @ SV381 ) )
= $false )
| ( ( in @ SV145 @ ( relation_image @ SV412 @ SV381 ) )
= $false )
| ( ( relation @ SV412 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2618]) ).
thf(2740,plain,
! [SV149: $i,SV387: $i,SV415: $i] :
( ( ( ~ ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV149 )
| ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV387 ) )
= $true )
| ( ( ~ ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV415 ) )
= $true )
| ( ( SV415
= ( set_difference @ SV149 @ SV387 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2623]) ).
thf(2741,plain,
! [SV149: $i,SV387: $i,SV415: $i] :
( ( ( ~ ( ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV149 )
| ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV415 ) )
| ~ ( ~ ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV387 )
| ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV415 ) ) )
= $false )
| ( ( SV415
= ( set_difference @ SV149 @ SV387 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2624]) ).
thf(2742,plain,
! [SV416: $i,SV388: $i,SV149: $i] :
( ( ( ! [SY1030: $i] :
( ~ ( in @ SY1030 @ SV149 )
| ( in @ SY1030 @ SV388 )
| ( in @ SY1030 @ SV416 ) ) )
= $true )
| ( ( SV416
= ( set_difference @ SV149 @ SV388 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2625]) ).
thf(2743,plain,
! [SV388: $i,SV149: $i,SV416: $i] :
( ( ( ~ ( ~ ! [SY1031: $i] :
( ~ ( in @ SY1031 @ SV416 )
| ( in @ SY1031 @ SV149 ) )
| ~ ! [SY1032: $i] :
( ~ ( in @ SY1032 @ SV416 )
| ~ ( in @ SY1032 @ SV388 ) ) ) )
= $true )
| ( ( SV416
= ( set_difference @ SV149 @ SV388 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2626]) ).
thf(2744,plain,
! [SV178: $i,SV417: $i,SV33: $i] :
( ( ( ~ ( in @ SV33 @ ( relation_dom @ ( relation_composition @ SV417 @ SV178 ) ) ) )
= $true )
| ( ( ( apply @ ( relation_composition @ SV417 @ SV178 ) @ SV33 )
= ( apply @ SV178 @ ( apply @ SV417 @ SV33 ) ) )
= $true )
| ( ( function @ SV417 )
= $false )
| ( ( relation @ SV417 )
= $false )
| ( ( function @ SV178 )
= $false )
| ( ( relation @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2627]) ).
thf(2745,plain,
! [SV418: $i,SV179: $i,SV34: $i] :
( ( ( ~ ( in @ SV34 @ ( relation_dom @ SV179 ) ) )
= $true )
| ( ( ( apply @ ( relation_composition @ SV179 @ SV418 ) @ SV34 )
= ( apply @ SV418 @ ( apply @ SV179 @ SV34 ) ) )
= $true )
| ( ( function @ SV418 )
= $false )
| ( ( relation @ SV418 )
= $false )
| ( ( function @ SV179 )
= $false )
| ( ( relation @ SV179 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2628]) ).
thf(2746,plain,
! [SV112: $i,SV322: $i,SV390: $i] :
( ( ( ~ ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV112 ) )
= $true )
| ( ( ~ ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV322 ) )
= $true )
| ( ( ~ ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV390 ) )
= $true )
| ( ( SV390
= ( set_intersection2 @ SV112 @ SV322 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2629]) ).
thf(2747,plain,
! [SV112: $i,SV322: $i,SV390: $i] :
( ( ( ~ ( ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV112 )
| ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV390 ) ) )
= $false )
| ( ( SV390
= ( set_intersection2 @ SV112 @ SV322 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2630]) ).
thf(2748,plain,
! [SV112: $i,SV322: $i,SV390: $i] :
( ( ( ~ ( ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV322 )
| ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV390 ) ) )
= $false )
| ( ( SV390
= ( set_intersection2 @ SV112 @ SV322 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2630]) ).
thf(2749,plain,
! [SV391: $i,SV323: $i,SV112: $i,SV541: $i] :
( ( ( ~ ( in @ SV541 @ SV112 )
| ~ ( in @ SV541 @ SV323 )
| ( in @ SV541 @ SV391 ) )
= $true )
| ( ( SV391
= ( set_intersection2 @ SV112 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2631]) ).
thf(2750,plain,
! [SV323: $i,SV112: $i,SV391: $i] :
( ( ( ~ ! [SY1009: $i] :
( ~ ( in @ SY1009 @ SV391 )
| ( in @ SY1009 @ SV112 ) )
| ~ ! [SY1010: $i] :
( ~ ( in @ SY1010 @ SV391 )
| ( in @ SY1010 @ SV323 ) ) )
= $false )
| ( ( SV391
= ( set_intersection2 @ SV112 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2632]) ).
thf(2751,plain,
! [SV530: $i,SV258: $i,SV324: $i] :
( ( ( ~ ( in @ ( sK47_C @ SV324 @ SV258 ) @ SV530 ) )
= $true )
| ( ( ~ ( in @ SV530 @ SV258 ) )
= $true )
| ( ( ~ ( in @ ( sK47_C @ SV324 @ SV258 ) @ SV324 ) )
= $true )
| ( ( SV324
= ( union @ SV258 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2633]) ).
thf(2752,plain,
! [SV258: $i,SV324: $i] :
( ( ( ~ ( in @ ( sK47_C @ SV324 @ SV258 ) @ ( sK48_SY487 @ SV324 @ SV258 ) ) )
= $false )
| ( ( in @ ( sK47_C @ SV324 @ SV258 ) @ SV324 )
= $true )
| ( ( SV324
= ( union @ SV258 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2634]) ).
thf(2753,plain,
! [SV258: $i,SV324: $i] :
( ( ( ~ ( in @ ( sK48_SY487 @ SV324 @ SV258 ) @ SV258 ) )
= $false )
| ( ( in @ ( sK47_C @ SV324 @ SV258 ) @ SV324 )
= $true )
| ( ( SV324
= ( union @ SV258 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2634]) ).
thf(2754,plain,
! [SV325: $i,SV259: $i,SV531: $i] :
( ( ( ! [SY1141: $i] :
( ~ ( in @ SV531 @ SY1141 )
| ~ ( in @ SY1141 @ SV259 ) ) )
= $true )
| ( ( in @ SV531 @ SV325 )
= $true )
| ( ( SV325
= ( union @ SV259 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2635]) ).
thf(2755,plain,
! [SV259: $i,SV325: $i,SV532: $i] :
( ( ( ~ ( in @ SV532 @ SV325 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV532 @ ( sK46_D @ SV532 @ SV325 @ SV259 ) )
| ~ ( in @ ( sK46_D @ SV532 @ SV325 @ SV259 ) @ SV259 ) ) )
= $true )
| ( ( SV325
= ( union @ SV259 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2636]) ).
thf(2756,plain,
! [SV113: $i,SV225: $i,SV463: $i] :
( ( ( ~ ( ~ ( in @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) @ SV113 )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV225 )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 ) )
| ~ ~ ( ~ ( ( in @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) @ SV113 )
| ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV225 )
| ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 ) ) ) )
= $false )
| ( ( SV463
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $true )
| ( ( relation @ SV463 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2637]) ).
thf(2757,plain,
! [SV225: $i,SV113: $i,SV464: $i] :
( ( ( SV464
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $false )
| ( ( ~ ( ~ ! [SY1094: $i,SY1095: $i] :
( ~ ( in @ SY1095 @ SV113 )
| ~ ( in @ ( ordered_pair @ SY1094 @ SY1095 ) @ SV225 )
| ( in @ ( ordered_pair @ SY1094 @ SY1095 ) @ SV464 ) )
| ~ ~ ( ~ ! [SY1096: $i,SY1097: $i] :
( ~ ( in @ ( ordered_pair @ SY1096 @ SY1097 ) @ SV464 )
| ( in @ SY1097 @ SV113 ) )
| ~ ! [SY1098: $i,SY1099: $i] :
( ~ ( in @ ( ordered_pair @ SY1098 @ SY1099 ) @ SV464 )
| ( in @ ( ordered_pair @ SY1098 @ SY1099 ) @ SV225 ) ) ) ) )
= $true )
| ( ( relation @ SV464 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2638]) ).
thf(2758,plain,
! [SV533: $i,SV495: $i,SV226: $i,SV114: $i] :
( ( ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SV495 @ SV533 ) )
= $false )
| ( ( in @ SV114 @ SV495 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2640]) ).
thf(2759,plain,
! [SV514: $i,SV496: $i,SV226: $i,SV114: $i] :
( ( ( in @ ( ordered_pair @ SV114 @ SV226 ) @ ( cartesian_product2 @ SV496 @ SV514 ) )
= $false )
| ( ( in @ SV226 @ SV514 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2641]) ).
thf(2760,plain,
! [SV264: $i,SV330: $i] :
( ( ( in @ ( sK62_C @ SV330 @ SV264 ) @ SV330 )
= $false )
| ( ( ( sK62_C @ SV330 @ SV264 )
= SV264 )
= $false )
| ( ( SV330
= ( singleton @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2643]) ).
thf(2761,plain,
! [SV331: $i,SV265: $i,SV534: $i] :
( ( ( ( SV534 != SV265 ) )
= $true )
| ( ( in @ SV534 @ SV331 )
= $true )
| ( ( SV331
= ( singleton @ SV265 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2644]) ).
thf(2762,plain,
! [SV265: $i,SV331: $i,SV535: $i] :
( ( ( ~ ( in @ SV535 @ SV331 ) )
= $true )
| ( ( SV535 = SV265 )
= $true )
| ( ( SV331
= ( singleton @ SV265 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2645]) ).
thf(2763,plain,
! [SV115: $i,SV465: $i] :
( ( ( ! [SY1100: $i] :
( ~ ( subset @ SY1100 @ SV465 )
| ( in @ SY1100 @ ( sK43_SY481 @ SV465 @ SV115 ) ) ) )
= $true )
| ( ( ~ ( in @ SV465 @ ( sK42_B @ SV115 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2646]) ).
thf(2764,plain,
! [SV115: $i,SV465: $i] :
( ( ( in @ ( sK43_SY481 @ SV465 @ SV115 ) @ ( sK42_B @ SV115 ) )
= $true )
| ( ( ~ ( in @ SV465 @ ( sK42_B @ SV115 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2647]) ).
thf(2765,plain,
! [SV542: $i,SV115: $i,SV536: $i] :
( ( ~ ( in @ SV536 @ ( sK42_B @ SV115 ) )
| ~ ( subset @ SV542 @ SV536 )
| ( in @ SV542 @ ( sK42_B @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2648]) ).
thf(2766,plain,
! [SV116: $i,SV543: $i] :
( ( ( ~ ( in @ SV543 @ ( relation_dom @ SV116 ) )
| ! [SY1144: $i] :
( ( SY1144
!= ( apply @ SV116 @ SV543 ) )
| ( in @ ( ordered_pair @ SV543 @ SY1144 ) @ SV116 ) ) )
= $true )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2649]) ).
thf(2767,plain,
! [SV116: $i,SV544: $i] :
( ( ( ~ ( in @ SV544 @ ( relation_dom @ SV116 ) )
| ! [SY1145: $i] :
( ~ ( in @ ( ordered_pair @ SV544 @ SY1145 ) @ SV116 )
| ( SY1145
= ( apply @ SV116 @ SV544 ) ) ) )
= $true )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2650]) ).
thf(2768,plain,
! [SV116: $i,SV545: $i] :
( ( ( ( in @ SV545 @ ( relation_dom @ SV116 ) )
| ! [SY1146: $i] :
( ( SY1146
!= ( apply @ SV116 @ SV545 ) )
| ( SY1146 = empty_set ) ) )
= $true )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2651]) ).
thf(2769,plain,
! [SV116: $i,SV546: $i] :
( ( ( ( in @ SV546 @ ( relation_dom @ SV116 ) )
| ! [SY1147: $i] :
( ( SY1147 != empty_set )
| ( SY1147
= ( apply @ SV116 @ SV546 ) ) ) )
= $true )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2652]) ).
thf(2770,plain,
! [SV393: $i,SV334: $i,SV117: $i,SV547: $i] :
( ( ( ! [SY1148: $i] :
( ~ ( in @ SV547 @ SV117 )
| ~ ( in @ SY1148 @ SV334 )
| ( ( sK53_D @ SV393 @ SV334 @ SV117 )
!= ( ordered_pair @ SV547 @ SY1148 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK53_D @ SV393 @ SV334 @ SV117 ) @ SV393 ) )
= $true )
| ( ( SV393
= ( cartesian_product2 @ SV117 @ SV334 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2653]) ).
thf(2771,plain,
! [SV117: $i,SV334: $i,SV393: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK54_SY491 @ SV393 @ SV334 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK55_SY493 @ SV393 @ SV334 @ SV117 ) @ SV334 ) )
| ( ( sK53_D @ SV393 @ SV334 @ SV117 )
!= ( ordered_pair @ ( sK54_SY491 @ SV393 @ SV334 @ SV117 ) @ ( sK55_SY493 @ SV393 @ SV334 @ SV117 ) ) ) )
= $false )
| ( ( in @ ( sK53_D @ SV393 @ SV334 @ SV117 ) @ SV393 )
= $true )
| ( ( SV393
= ( cartesian_product2 @ SV117 @ SV334 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2654]) ).
thf(2772,plain,
! [SV394: $i,SV548: $i,SV335: $i,SV117: $i] :
( ( ( ! [SY1149: $i,SY1150: $i] :
( ~ ( in @ SY1149 @ SV117 )
| ~ ( in @ SY1150 @ SV335 )
| ( SV548
!= ( ordered_pair @ SY1149 @ SY1150 ) ) )
| ( in @ SV548 @ SV394 ) )
= $true )
| ( ( SV394
= ( cartesian_product2 @ SV117 @ SV335 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2655]) ).
thf(2773,plain,
! [SV117: $i,SV335: $i,SV394: $i,SV549: $i] :
( ( ( ~ ( in @ SV549 @ SV394 )
| ~ ( ~ ~ ( ~ ( in @ ( sK51_E @ SV549 @ SV394 @ SV335 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK52_SY488 @ SV549 @ SV394 @ SV335 @ SV117 ) @ SV335 ) )
| ( SV549
!= ( ordered_pair @ ( sK51_E @ SV549 @ SV394 @ SV335 @ SV117 ) @ ( sK52_SY488 @ SV549 @ SV394 @ SV335 @ SV117 ) ) ) ) )
= $true )
| ( ( SV394
= ( cartesian_product2 @ SV117 @ SV335 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2656]) ).
thf(2774,plain,
! [SV118: $i,SV395: $i,SV338: $i] :
( ( ( ( SV338
!= ( apply @ SV395 @ SV118 ) ) )
= $true )
| ( ( ~ ( in @ SV118 @ ( relation_dom @ SV395 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV118 @ SV338 ) @ SV395 )
= $true )
| ( ( function @ SV395 )
= $false )
| ( ( relation @ SV395 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2657]) ).
thf(2775,plain,
! [SV467: $i,SV118: $i,SV497: $i] :
( ( ( function @ SV497 )
= $false )
| ( ( ~ ( relation @ SV497 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV118 @ SV467 ) @ SV497 )
| ( SV467
= ( apply @ SV497 @ SV118 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2658]) ).
thf(2776,plain,
! [SV468: $i,SV118: $i,SV498: $i] :
( ( ( function @ SV498 )
= $false )
| ( ( ~ ( relation @ SV498 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV118 @ SV468 ) @ SV498 )
| ( in @ SV118 @ ( relation_dom @ SV498 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2659]) ).
thf(2777,plain,
! [SV273: $i,SV339: $i] :
( ( ( ( ( sK69_C @ SV339 @ SV273 )
!= ( sK70_SY500 @ SV339 @ SV273 ) )
| ~ ( in @ ( sK69_C @ SV339 @ SV273 ) @ SV273 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 ) )
= $true )
| ( ( SV339
= ( identity_relation @ SV273 ) )
= $true )
| ( ( relation @ SV339 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2660]) ).
thf(2778,plain,
! [SV273: $i,SV339: $i] :
( ( ( ~ ( ( ( sK69_C @ SV339 @ SV273 )
= ( sK70_SY500 @ SV339 @ SV273 ) )
| ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 ) )
| ~ ( ( in @ ( sK69_C @ SV339 @ SV273 ) @ SV273 )
| ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 ) ) )
= $false )
| ( ( SV339
= ( identity_relation @ SV273 ) )
= $true )
| ( ( relation @ SV339 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2661]) ).
thf(2779,plain,
! [SV340: $i,SV274: $i] :
( ( ( ! [SY968: $i,SY969: $i] :
( ( SY968 != SY969 )
| ~ ( in @ SY968 @ SV274 )
| ( in @ ( ordered_pair @ SY968 @ SY969 ) @ SV340 ) ) )
= $true )
| ( ( SV340
= ( identity_relation @ SV274 ) )
= $false )
| ( ( relation @ SV340 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2662]) ).
thf(2780,plain,
! [SV274: $i,SV340: $i] :
( ( ( ~ ( ~ ! [SY970: $i,SY971: $i] :
( ~ ( in @ ( ordered_pair @ SY970 @ SY971 ) @ SV340 )
| ( SY970 = SY971 ) )
| ~ ! [SY972: $i] :
( ! [SY973: $i] :
~ ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV340 )
| ( in @ SY972 @ SV274 ) ) ) )
= $true )
| ( ( SV340
= ( identity_relation @ SV274 ) )
= $false )
| ( ( relation @ SV340 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2663]) ).
thf(2781,plain,
! [SV120: $i,SV275: $i,SV516: $i] :
( ( ( relation @ SV516 )
= $false )
| ( ( ~ ( ~ ( ! [SY1135: $i] :
( ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ SY1135 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY1135 @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV275 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV516 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK15_SY461 @ SV516 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY461 @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV275 ) )
| ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV516 ) ) )
| ( SV516
= ( relation_composition @ SV120 @ SV275 ) ) )
= $true )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2664]) ).
thf(2782,plain,
! [SV275: $i,SV120: $i,SV517: $i] :
( ( ( relation @ SV517 )
= $false )
| ( ( ( SV517
!= ( relation_composition @ SV120 @ SV275 ) )
| ~ ( ~ ! [SY1136: $i,SY1137: $i] :
( ! [SY909: $i] :
( ~ ( in @ ( ordered_pair @ SY1136 @ SY909 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY909 @ SY1137 ) @ SV275 ) )
| ( in @ ( ordered_pair @ SY1136 @ SY1137 ) @ SV517 ) )
| ~ ! [SY1139: $i,SY1140: $i] :
( ~ ( in @ ( ordered_pair @ SY1139 @ SY1140 ) @ SV517 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1139 @ ( sK12_F @ SY1140 @ SY1139 @ SV517 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK12_F @ SY1140 @ SY1139 @ SV517 @ SV275 @ SV120 ) @ SY1140 ) @ SV275 ) ) ) ) )
= $true )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2665]) ).
thf(2783,plain,
! [SV121: $i,SV469: $i,SV227: $i] :
( ( ( disjoint @ SV227 @ SV469 )
= $false )
| ( ( subset @ SV227 @ ( subset_complement @ SV121 @ SV469 ) )
= $true )
| ( ( element @ SV469 @ ( powerset @ SV121 ) )
= $false )
| ( ( element @ SV227 @ ( powerset @ SV121 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2666]) ).
thf(2784,plain,
! [SV470: $i,SV121: $i,SV227: $i] :
( ( ( subset @ SV227 @ ( subset_complement @ SV121 @ SV470 ) )
= $false )
| ( ( disjoint @ SV227 @ SV470 )
= $true )
| ( ( element @ SV470 @ ( powerset @ SV121 ) )
= $false )
| ( ( element @ SV227 @ ( powerset @ SV121 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2667]) ).
thf(2785,plain,
! [SV341: $i,SV396: $i,SV122: $i] :
( ( ( in @ SV122 @ ( relation_rng @ SV396 ) )
= $false )
| ( ( in @ SV122 @ SV341 )
= $false )
| ( ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SV341 @ SV396 ) ) )
= $true )
| ( ( relation @ SV396 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2668]) ).
thf(2786,plain,
! [SV499: $i,SV471: $i,SV122: $i] :
( ( ( ~ ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SV471 @ SV499 ) ) ) )
= $true )
| ( ( in @ SV122 @ SV471 )
= $true )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2669]) ).
thf(2787,plain,
! [SV500: $i,SV472: $i,SV122: $i] :
( ( ( ~ ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SV472 @ SV500 ) ) ) )
= $true )
| ( ( in @ SV122 @ ( relation_rng @ SV500 ) )
= $true )
| ( ( relation @ SV500 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2670]) ).
thf(2788,plain,
! [SV123: $i,SV424: $i,SV473: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ SV424 )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV123 )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 ) )
| ~ ~ ( ~ ( ( in @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ SV424 )
| ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 ) ) ) )
= $false )
| ( ( SV473
= ( relation_dom_restriction @ SV123 @ SV424 ) )
= $true )
| ( ( relation @ SV473 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2671]) ).
thf(2789,plain,
! [SV425: $i,SV123: $i,SV474: $i] :
( ( ( SV474
= ( relation_dom_restriction @ SV123 @ SV425 ) )
= $false )
| ( ( ~ ( ~ ! [SY1105: $i,SY1106: $i] :
( ~ ( in @ SY1105 @ SV425 )
| ~ ( in @ ( ordered_pair @ SY1105 @ SY1106 ) @ SV123 )
| ( in @ ( ordered_pair @ SY1105 @ SY1106 ) @ SV474 ) )
| ~ ~ ( ~ ! [SY1107: $i] :
( ! [SY1108: $i] :
~ ( in @ ( ordered_pair @ SY1107 @ SY1108 ) @ SV474 )
| ( in @ SY1107 @ SV425 ) )
| ~ ! [SY1109: $i,SY1110: $i] :
( ~ ( in @ ( ordered_pair @ SY1109 @ SY1110 ) @ SV474 )
| ( in @ ( ordered_pair @ SY1109 @ SY1110 ) @ SV123 ) ) ) ) )
= $true )
| ( ( relation @ SV474 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2672]) ).
thf(2790,plain,
! [SV124: $i,SV426: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_C @ SV426 @ SV124 ) @ ( sK17_SY462 @ SV426 @ SV124 ) ) @ SV426 )
| ~ ( in @ ( ordered_pair @ ( sK17_SY462 @ SV426 @ SV124 ) @ ( sK16_C @ SV426 @ SV124 ) ) @ SV124 ) ) )
= $false )
| ( ( SV426
= ( relation_inverse @ SV124 ) )
= $true )
| ( ( relation @ SV426 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2673]) ).
thf(2791,plain,
! [SV124: $i,SV426: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK16_C @ SV426 @ SV124 ) @ ( sK17_SY462 @ SV426 @ SV124 ) ) @ SV426 )
| ( in @ ( ordered_pair @ ( sK17_SY462 @ SV426 @ SV124 ) @ ( sK16_C @ SV426 @ SV124 ) ) @ SV124 ) ) )
= $false )
| ( ( SV426
= ( relation_inverse @ SV124 ) )
= $true )
| ( ( relation @ SV426 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2673]) ).
thf(2792,plain,
! [SV124: $i,SV427: $i] :
( ( ( ~ ! [SY1043: $i,SY1044: $i] :
( ~ ( in @ ( ordered_pair @ SY1043 @ SY1044 ) @ SV427 )
| ( in @ ( ordered_pair @ SY1044 @ SY1043 ) @ SV124 ) )
| ~ ! [SY1045: $i,SY1046: $i] :
( ~ ( in @ ( ordered_pair @ SY1046 @ SY1045 ) @ SV124 )
| ( in @ ( ordered_pair @ SY1045 @ SY1046 ) @ SV427 ) ) )
= $false )
| ( ( SV427
= ( relation_inverse @ SV124 ) )
= $false )
| ( ( relation @ SV427 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2674]) ).
thf(2793,plain,
! [SV282: $i,SV348: $i] :
( ( ( ~ ( in @ ( sK38_C @ SV348 @ SV282 ) @ SV282 )
| ~ ( ( ( apply @ SV348 @ ( sK38_C @ SV348 @ SV282 ) )
!= ( sK38_C @ SV348 @ SV282 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV348 )
!= SV282 ) )
= $true )
| ( ( SV348
= ( identity_relation @ SV282 ) )
= $true )
| ( ( function @ SV348 )
= $false )
| ( ( relation @ SV348 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2675]) ).
thf(2794,plain,
! [SV428: $i,SV475: $i] :
( ( ( relation @ SV475 )
= $false )
| ( ( function @ SV475 )
= $false )
| ( ( ( SV475
!= ( identity_relation @ SV428 ) )
| ! [SY1111: $i] :
( ~ ( in @ SY1111 @ SV428 )
| ( ( apply @ SV475 @ SY1111 )
= SY1111 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2676]) ).
thf(2795,plain,
! [SV429: $i,SV476: $i] :
( ( ( relation @ SV476 )
= $false )
| ( ( function @ SV476 )
= $false )
| ( ( ( SV476
!= ( identity_relation @ SV429 ) )
| ( ( relation_dom @ SV476 )
= SV429 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2677]) ).
thf(2796,plain,
! [SV125: $i,SV432: $i,SV479: $i] :
( ( ( ! [SY1112: $i] :
( ~ ( in @ ( ordered_pair @ SY1112 @ ( sK30_D @ SV479 @ SV432 @ SV125 ) ) @ SV125 )
| ~ ( in @ SY1112 @ SV432 ) )
| ~ ( in @ ( sK30_D @ SV479 @ SV432 @ SV125 ) @ SV479 ) )
= $true )
| ( ( SV479
= ( relation_image @ SV125 @ SV432 ) )
= $true )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2678]) ).
thf(2797,plain,
! [SV125: $i,SV432: $i,SV479: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_SY471 @ SV479 @ SV432 @ SV125 ) @ ( sK30_D @ SV479 @ SV432 @ SV125 ) ) @ SV125 )
| ~ ( in @ ( sK31_SY471 @ SV479 @ SV432 @ SV125 ) @ SV432 ) )
| ( in @ ( sK30_D @ SV479 @ SV432 @ SV125 ) @ SV479 ) )
= $true )
| ( ( SV479
= ( relation_image @ SV125 @ SV432 ) )
= $true )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2679]) ).
thf(2798,plain,
! [SV480: $i,SV433: $i,SV125: $i] :
( ( ( ~ ! [SY1113: $i] :
( ! [SY1056: $i] :
( ~ ( in @ ( ordered_pair @ SY1056 @ SY1113 ) @ SV125 )
| ~ ( in @ SY1056 @ SV433 ) )
| ( in @ SY1113 @ SV480 ) ) )
= $false )
| ( ( SV480
= ( relation_image @ SV125 @ SV433 ) )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2680]) ).
thf(2799,plain,
! [SV125: $i,SV433: $i,SV480: $i] :
( ( ( ~ ! [SY1115: $i] :
( ~ ( in @ SY1115 @ SV480 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK29_E @ SY1115 @ SV480 @ SV433 @ SV125 ) @ SY1115 ) @ SV125 )
| ~ ( in @ ( sK29_E @ SY1115 @ SV480 @ SV433 @ SV125 ) @ SV433 ) ) ) )
= $false )
| ( ( SV480
= ( relation_image @ SV125 @ SV433 ) )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2680]) ).
thf(2800,plain,
! [SV434: $i,SV228: $i,SV399: $i,SV127: $i] :
( ( ( in @ SV127 @ SV399 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ SV434 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SV399 ) @ SV434 ) )
= $true )
| ( ( relation @ SV434 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2681]) ).
thf(2801,plain,
! [SV501: $i,SV228: $i,SV127: $i,SV518: $i] :
( ( ( relation @ SV518 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SV501 ) @ SV518 ) )
| ( in @ SV127 @ SV501 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2682]) ).
thf(2802,plain,
! [SV502: $i,SV228: $i,SV127: $i,SV519: $i] :
( ( ( relation @ SV519 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SV502 ) @ SV519 ) )
| ( in @ ( ordered_pair @ SV127 @ SV228 ) @ SV519 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2683]) ).
thf(2803,plain,
! [SV437: $i,SV520: $i] :
( ( ( element @ SV520 @ SV437 )
= $false )
| ( ( empty @ SV520 )
= $true )
| ( ( empty @ SV437 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2688]) ).
thf(2804,plain,
! [SV438: $i,SV521: $i] :
( ( ( empty @ SV521 )
= $false )
| ( ( element @ SV521 @ SV438 )
= $true )
| ( ( empty @ SV438 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2689]) ).
thf(2805,plain,
! [SV129: $i,SV439: $i] :
( ( ( ! [SY1062: $i] :
~ ( in @ ( ordered_pair @ SY1062 @ ( sK19_C @ SV439 @ SV129 ) ) @ SV129 ) )
= $true )
| ( ( ~ ( in @ ( sK19_C @ SV439 @ SV129 ) @ SV439 ) )
= $true )
| ( ( SV439
= ( relation_rng @ SV129 ) )
= $true )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2690]) ).
thf(2806,plain,
! [SV129: $i,SV439: $i] :
( ( ( in @ ( ordered_pair @ ( sK20_SY464 @ SV439 @ SV129 ) @ ( sK19_C @ SV439 @ SV129 ) ) @ SV129 )
= $true )
| ( ( in @ ( sK19_C @ SV439 @ SV129 ) @ SV439 )
= $true )
| ( ( SV439
= ( relation_rng @ SV129 ) )
= $true )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2691]) ).
thf(2807,plain,
! [SV440: $i,SV129: $i] :
( ( ( ! [SY1063: $i] :
( ! [SY722: $i] :
~ ( in @ ( ordered_pair @ SY722 @ SY1063 ) @ SV129 )
| ( in @ SY1063 @ SV440 ) ) )
= $true )
| ( ( SV440
= ( relation_rng @ SV129 ) )
= $false )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2692]) ).
thf(2808,plain,
! [SV129: $i,SV440: $i] :
( ( ( ! [SY1065: $i] :
( ~ ( in @ SY1065 @ SV440 )
| ( in @ ( ordered_pair @ ( sK18_D @ SY1065 @ SV440 @ SV129 ) @ SY1065 ) @ SV129 ) ) )
= $true )
| ( ( SV440
= ( relation_rng @ SV129 ) )
= $false )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2693]) ).
thf(2809,plain,
! [SV131: $i,SV442: $i,SV483: $i] :
( ( ( ! [SY1118: $i] :
( ~ ( in @ ( ordered_pair @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SY1118 ) @ SV131 )
| ~ ( in @ SY1118 @ SV442 ) )
| ~ ( in @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SV483 ) )
= $true )
| ( ( SV483
= ( relation_inverse_image @ SV131 @ SV442 ) )
= $true )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2694]) ).
thf(2810,plain,
! [SV131: $i,SV442: $i,SV483: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ ( sK28_SY469 @ SV483 @ SV442 @ SV131 ) ) @ SV131 )
| ~ ( in @ ( sK28_SY469 @ SV483 @ SV442 @ SV131 ) @ SV442 ) )
| ( in @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SV483 ) )
= $true )
| ( ( SV483
= ( relation_inverse_image @ SV131 @ SV442 ) )
= $true )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2695]) ).
thf(2811,plain,
! [SV484: $i,SV443: $i,SV131: $i] :
( ( ( ~ ! [SY1119: $i] :
( ! [SY1070: $i] :
( ~ ( in @ ( ordered_pair @ SY1119 @ SY1070 ) @ SV131 )
| ~ ( in @ SY1070 @ SV443 ) )
| ( in @ SY1119 @ SV484 ) ) )
= $false )
| ( ( SV484
= ( relation_inverse_image @ SV131 @ SV443 ) )
= $false )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2696]) ).
thf(2812,plain,
! [SV131: $i,SV443: $i,SV484: $i] :
( ( ( ~ ! [SY1121: $i] :
( ~ ( in @ SY1121 @ SV484 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1121 @ ( sK26_E @ SY1121 @ SV484 @ SV443 @ SV131 ) ) @ SV131 )
| ~ ( in @ ( sK26_E @ SY1121 @ SV484 @ SV443 @ SV131 ) @ SV443 ) ) ) )
= $false )
| ( ( SV484
= ( relation_inverse_image @ SV131 @ SV443 ) )
= $false )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2696]) ).
thf(2813,plain,
! [SV363: $i,SV401: $i,SV132: $i] :
( ( ( in @ SV132 @ ( relation_dom @ SV401 ) )
= $false )
| ( ( in @ SV132 @ SV363 )
= $false )
| ( ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SV401 @ SV363 ) ) )
= $true )
| ( ( relation @ SV401 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2698]) ).
thf(2814,plain,
! [SV485: $i,SV508: $i,SV132: $i] :
( ( ( ~ ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SV508 @ SV485 ) ) ) )
= $true )
| ( ( in @ SV132 @ SV485 )
= $true )
| ( ( relation @ SV508 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2699]) ).
thf(2815,plain,
! [SV486: $i,SV509: $i,SV132: $i] :
( ( ( ~ ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SV509 @ SV486 ) ) ) )
= $true )
| ( ( in @ SV132 @ ( relation_dom @ SV509 ) )
= $true )
| ( ( relation @ SV509 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2700]) ).
thf(2816,plain,
! [SV134: $i,SV445: $i] :
( ( ( ! [SY1072: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SV445 @ SV134 ) @ SY1072 ) @ SV134 ) )
= $true )
| ( ( ~ ( in @ ( sK22_C @ SV445 @ SV134 ) @ SV445 ) )
= $true )
| ( ( SV445
= ( relation_dom @ SV134 ) )
= $true )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2701]) ).
thf(2817,plain,
! [SV134: $i,SV445: $i] :
( ( ( in @ ( ordered_pair @ ( sK22_C @ SV445 @ SV134 ) @ ( sK23_SY466 @ SV445 @ SV134 ) ) @ SV134 )
= $true )
| ( ( in @ ( sK22_C @ SV445 @ SV134 ) @ SV445 )
= $true )
| ( ( SV445
= ( relation_dom @ SV134 ) )
= $true )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2702]) ).
thf(2818,plain,
! [SV446: $i,SV134: $i] :
( ( ( ! [SY1073: $i] :
( ! [SY747: $i] :
~ ( in @ ( ordered_pair @ SY1073 @ SY747 ) @ SV134 )
| ( in @ SY1073 @ SV446 ) ) )
= $true )
| ( ( SV446
= ( relation_dom @ SV134 ) )
= $false )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2703]) ).
thf(2819,plain,
! [SV134: $i,SV446: $i] :
( ( ( ! [SY1075: $i] :
( ~ ( in @ SY1075 @ SV446 )
| ( in @ ( ordered_pair @ SY1075 @ ( sK21_D @ SY1075 @ SV446 @ SV134 ) ) @ SV134 ) ) )
= $true )
| ( ( SV446
= ( relation_dom @ SV134 ) )
= $false )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2704]) ).
thf(2820,plain,
! [SV135: $i,SV366: $i,SV404: $i] :
( ( ( ~ ( ~ ( in @ ( sK57_D @ SV404 @ SV366 @ SV135 ) @ SV404 )
| ( ( sK57_D @ SV404 @ SV366 @ SV135 )
!= SV135 ) ) )
= $false )
| ( ( SV404
= ( unordered_pair @ SV135 @ SV366 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2705]) ).
thf(2821,plain,
! [SV135: $i,SV366: $i,SV404: $i] :
( ( ( ~ ( ~ ( in @ ( sK57_D @ SV404 @ SV366 @ SV135 ) @ SV404 )
| ( ( sK57_D @ SV404 @ SV366 @ SV135 )
!= SV366 ) ) )
= $false )
| ( ( SV404
= ( unordered_pair @ SV135 @ SV366 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2705]) ).
thf(2822,plain,
! [SV135: $i,SV366: $i,SV404: $i] :
( ( ( ( sK57_D @ SV404 @ SV366 @ SV135 )
= SV135 )
= $true )
| ( ( ( sK57_D @ SV404 @ SV366 @ SV135 )
= SV366 )
= $true )
| ( ( in @ ( sK57_D @ SV404 @ SV366 @ SV135 ) @ SV404 )
= $true )
| ( ( SV404
= ( unordered_pair @ SV135 @ SV366 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2706]) ).
thf(2823,plain,
! [SV367: $i,SV135: $i,SV405: $i,SV550: $i] :
( ( ( ~ ( in @ SV550 @ SV405 )
| ( SV550 = SV135 )
| ( SV550 = SV367 ) )
= $true )
| ( ( SV405
= ( unordered_pair @ SV135 @ SV367 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2707]) ).
thf(2824,plain,
! [SV367: $i,SV405: $i,SV135: $i] :
( ( ( ~ ! [SY1020: $i] :
( ( SY1020 != SV135 )
| ( in @ SY1020 @ SV405 ) )
| ~ ! [SY1021: $i] :
( ( SY1021 != SV367 )
| ( in @ SY1021 @ SV405 ) ) )
= $false )
| ( ( SV405
= ( unordered_pair @ SV135 @ SV367 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2708]) ).
thf(2825,plain,
! [SV136: $i,SV447: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV136 )
| ~ ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV447 ) ) )
= $false )
| ( ( SV136 = SV447 )
= $true )
| ( ( relation @ SV447 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2709]) ).
thf(2826,plain,
! [SV136: $i,SV447: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV136 )
| ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV447 ) ) )
= $false )
| ( ( SV136 = SV447 )
= $true )
| ( ( relation @ SV447 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2709]) ).
thf(2827,plain,
! [SV448: $i,SV136: $i] :
( ( ( ~ ! [SY1076: $i,SY1077: $i] :
( ~ ( in @ ( ordered_pair @ SY1076 @ SY1077 ) @ SV136 )
| ( in @ ( ordered_pair @ SY1076 @ SY1077 ) @ SV448 ) )
| ~ ! [SY1078: $i,SY1079: $i] :
( ~ ( in @ ( ordered_pair @ SY1078 @ SY1079 ) @ SV448 )
| ( in @ ( ordered_pair @ SY1078 @ SY1079 ) @ SV136 ) ) )
= $false )
| ( ( SV136 = SV448 )
= $false )
| ( ( relation @ SV448 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2710]) ).
thf(2828,plain,
! [SV298: $i,SV368: $i] :
( ( ( relation @ SV368 )
= $false )
| ( ( function @ SV298 )
= $false )
| ( ( relation @ SV298 )
= $false )
| ( ( ~ ( function @ SV368 ) )
= $true )
| ( ( function @ ( relation_composition @ SV298 @ SV368 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2711]) ).
thf(2829,plain,
! [SV299: $i,SV369: $i] :
( ( ( relation @ SV369 )
= $false )
| ( ( function @ SV299 )
= $false )
| ( ( relation @ SV299 )
= $false )
| ( ( ~ ( function @ SV369 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV299 @ SV369 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2712]) ).
thf(2830,plain,
! [SV230: $i,SV137: $i,SV523: $i] :
( ( ( ~ ( function @ SV523 ) )
= $true )
| ( ( ~ ( relation @ SV523 ) )
= $true )
| ( ( ~ ( in @ SV137 @ ( relation_dom @ SV523 ) )
| ~ ( in @ ( apply @ SV523 @ SV137 ) @ ( relation_dom @ SV230 ) )
| ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SV523 @ SV230 ) ) ) )
= $true )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2713]) ).
thf(2831,plain,
! [SV230: $i,SV137: $i] :
( ( ( ! [SY862: $i] :
( ~ ( function @ SY862 )
| ~ ( relation @ SY862 )
| ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY862 @ SV230 ) ) )
| ( in @ SV137 @ ( relation_dom @ SY862 ) ) ) )
= $true )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2714]) ).
thf(2832,plain,
! [SV230: $i,SV137: $i] :
( ( ( ! [SY863: $i] :
( ~ ( function @ SY863 )
| ~ ( relation @ SY863 )
| ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SY863 @ SV230 ) ) )
| ( in @ ( apply @ SY863 @ SV137 ) @ ( relation_dom @ SV230 ) ) ) )
= $true )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2715]) ).
thf(2833,plain,
! [SV551: $i,SV138: $i,SV537: $i] :
( ( ~ ( in @ SV537 @ ( sK41_B @ SV138 ) )
| ~ ( subset @ SV551 @ SV537 )
| ( in @ SV551 @ ( sK41_B @ SV138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2716]) ).
thf(2834,plain,
! [SV139: $i,SV449: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV449 @ SV139 ) @ ( sK25_SY467 @ SV449 @ SV139 ) ) @ SV139 ) )
= $false )
| ( ( subset @ SV139 @ SV449 )
= $true )
| ( ( relation @ SV449 )
= $false )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2717]) ).
thf(2835,plain,
! [SV139: $i,SV449: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SV449 @ SV139 ) @ ( sK25_SY467 @ SV449 @ SV139 ) ) @ SV449 ) )
= $false )
| ( ( subset @ SV139 @ SV449 )
= $true )
| ( ( relation @ SV449 )
= $false )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2717]) ).
thf(2836,plain,
! [SV450: $i,SV139: $i,SV552: $i] :
( ( ( ! [SY1151: $i] :
( ~ ( in @ ( ordered_pair @ SV552 @ SY1151 ) @ SV139 )
| ( in @ ( ordered_pair @ SV552 @ SY1151 ) @ SV450 ) ) )
= $true )
| ( ( subset @ SV139 @ SV450 )
= $false )
| ( ( relation @ SV450 )
= $false )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2718]) ).
thf(2837,plain,
! [SV300: $i,SV371: $i] :
( ( ( subset @ ( sK60_C @ SV371 @ SV300 ) @ SV300 )
= $false )
| ( ( in @ ( sK60_C @ SV371 @ SV300 ) @ SV371 )
= $false )
| ( ( SV371
= ( powerset @ SV300 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2719]) ).
thf(2838,plain,
! [SV301: $i,SV372: $i,SV538: $i] :
( ( ( ~ ( in @ SV538 @ SV372 ) )
= $true )
| ( ( subset @ SV538 @ SV301 )
= $true )
| ( ( SV372
= ( powerset @ SV301 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2720]) ).
thf(2839,plain,
! [SV372: $i,SV301: $i,SV539: $i] :
( ( ( ~ ( subset @ SV539 @ SV301 ) )
= $true )
| ( ( in @ SV539 @ SV372 )
= $true )
| ( ( SV372
= ( powerset @ SV301 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2721]) ).
thf(2840,plain,
! [SV375: $i,SV142: $i,SV406: $i,SV524: $i] :
( ( ( ~ ( in @ SV524 @ ( relation_rng @ SV406 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV142 @ SV524 ) @ SV406 ) )
= $true )
| ( ( ~ ( in @ SV524 @ SV375 ) )
= $true )
| ( ( in @ SV142 @ ( relation_inverse_image @ SV406 @ SV375 ) )
= $true )
| ( ( relation @ SV406 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2724]) ).
thf(2841,plain,
! [SV142: $i,SV376: $i,SV407: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK39_D @ SV407 @ SV376 @ SV142 ) @ ( relation_rng @ SV407 ) )
| ~ ( in @ ( ordered_pair @ SV142 @ ( sK39_D @ SV407 @ SV376 @ SV142 ) ) @ SV407 ) ) )
= $false )
| ( ( in @ SV142 @ ( relation_inverse_image @ SV407 @ SV376 ) )
= $false )
| ( ( relation @ SV407 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2725]) ).
thf(2842,plain,
! [SV142: $i,SV376: $i,SV407: $i] :
( ( ( ~ ( in @ ( sK39_D @ SV407 @ SV376 @ SV142 ) @ SV376 ) )
= $false )
| ( ( in @ SV142 @ ( relation_inverse_image @ SV407 @ SV376 ) )
= $false )
| ( ( relation @ SV407 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2725]) ).
thf(2843,plain,
! [SV453: $i,SV510: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK65_SY495 @ SV510 @ SV453 ) @ SV453 )
| ~ ~ ( in @ ( sK64_C @ SV510 @ SV453 ) @ ( sK65_SY495 @ SV510 @ SV453 ) ) )
| ~ ( in @ ( sK64_C @ SV510 @ SV453 ) @ SV510 ) ) )
= $false )
| ( ( SV510
= ( set_meet @ SV453 ) )
= $true )
| ( ( SV453 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2726]) ).
thf(2844,plain,
! [SV510: $i,SV453: $i] :
( ( ( ~ ( ! [SY1129: $i] :
( ~ ( in @ SY1129 @ SV453 )
| ( in @ ( sK64_C @ SV510 @ SV453 ) @ SY1129 ) )
| ( in @ ( sK64_C @ SV510 @ SV453 ) @ SV510 ) ) )
= $false )
| ( ( SV510
= ( set_meet @ SV453 ) )
= $true )
| ( ( SV453 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2726]) ).
thf(2845,plain,
! [SV454: $i,SV511: $i] :
( ( ( ~ ! [SY1130: $i] :
( ~ ( ~ ( in @ ( sK63_D @ SY1130 @ SV511 @ SV454 ) @ SV454 )
| ~ ~ ( in @ SY1130 @ ( sK63_D @ SY1130 @ SV511 @ SV454 ) ) )
| ( in @ SY1130 @ SV511 ) )
| ~ ! [SY1131: $i] :
( ~ ( in @ SY1131 @ SV511 )
| ! [SY1087: $i] :
( ~ ( in @ SY1087 @ SV454 )
| ( in @ SY1131 @ SY1087 ) ) ) )
= $false )
| ( ( SV511
= ( set_meet @ SV454 ) )
= $false )
| ( ( SV454 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2727]) ).
thf(2846,plain,
! [SV455: $i,SV525: $i] :
( ( ( SV525
= ( set_meet @ SV455 ) )
= $false )
| ( ( SV525 = empty_set )
= $true )
| ( ( SV455 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2728]) ).
thf(2847,plain,
! [SV456: $i,SV526: $i] :
( ( ( SV526 = empty_set )
= $false )
| ( ( SV526
= ( set_meet @ SV456 ) )
= $true )
| ( ( SV456 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2729]) ).
thf(2848,plain,
! [SV540: $i,SV512: $i,SV231: $i,SV143: $i] :
( ( ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SV512 @ SV540 ) )
= $false )
| ( ( in @ SV143 @ SV512 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2732]) ).
thf(2849,plain,
! [SV527: $i,SV513: $i,SV231: $i,SV143: $i] :
( ( ( in @ ( ordered_pair @ SV143 @ SV231 ) @ ( cartesian_product2 @ SV513 @ SV527 ) )
= $false )
| ( ( in @ SV231 @ SV527 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2733]) ).
thf(2850,plain,
! [SV144: $i,SV378: $i,SV409: $i] :
( ( ( ~ ( ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV409 )
| ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV144 ) ) )
= $false )
| ( ( SV409
= ( set_union2 @ SV144 @ SV378 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2734]) ).
thf(2851,plain,
! [SV144: $i,SV378: $i,SV409: $i] :
( ( ( ~ ( ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV409 )
| ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV378 ) ) )
= $false )
| ( ( SV409
= ( set_union2 @ SV144 @ SV378 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2734]) ).
thf(2852,plain,
! [SV144: $i,SV378: $i,SV409: $i] :
( ( ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV144 )
= $true )
| ( ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV378 )
= $true )
| ( ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV409 )
= $true )
| ( ( SV409
= ( set_union2 @ SV144 @ SV378 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2735]) ).
thf(2853,plain,
! [SV379: $i,SV144: $i,SV410: $i,SV553: $i] :
( ( ( ~ ( in @ SV553 @ SV410 )
| ( in @ SV553 @ SV144 )
| ( in @ SV553 @ SV379 ) )
= $true )
| ( ( SV410
= ( set_union2 @ SV144 @ SV379 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2736]) ).
thf(2854,plain,
! [SV379: $i,SV410: $i,SV144: $i] :
( ( ( ~ ! [SY1025: $i] :
( ~ ( in @ SY1025 @ SV144 )
| ( in @ SY1025 @ SV410 ) )
| ~ ! [SY1026: $i] :
( ~ ( in @ SY1026 @ SV379 )
| ( in @ SY1026 @ SV410 ) ) )
= $false )
| ( ( SV410
= ( set_union2 @ SV144 @ SV379 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2737]) ).
thf(2855,plain,
! [SV380: $i,SV145: $i,SV411: $i,SV528: $i] :
( ( ( ~ ( in @ SV528 @ ( relation_dom @ SV411 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV528 @ SV145 ) @ SV411 ) )
= $true )
| ( ( ~ ( in @ SV528 @ SV380 ) )
= $true )
| ( ( in @ SV145 @ ( relation_image @ SV411 @ SV380 ) )
= $true )
| ( ( relation @ SV411 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2738]) ).
thf(2856,plain,
! [SV145: $i,SV381: $i,SV412: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK40_D @ SV412 @ SV381 @ SV145 ) @ ( relation_dom @ SV412 ) )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV412 @ SV381 @ SV145 ) @ SV145 ) @ SV412 ) ) )
= $false )
| ( ( in @ SV145 @ ( relation_image @ SV412 @ SV381 ) )
= $false )
| ( ( relation @ SV412 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2739]) ).
thf(2857,plain,
! [SV145: $i,SV381: $i,SV412: $i] :
( ( ( ~ ( in @ ( sK40_D @ SV412 @ SV381 @ SV145 ) @ SV381 ) )
= $false )
| ( ( in @ SV145 @ ( relation_image @ SV412 @ SV381 ) )
= $false )
| ( ( relation @ SV412 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2739]) ).
thf(2858,plain,
! [SV149: $i,SV387: $i,SV415: $i] :
( ( ( ~ ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV149 ) )
= $true )
| ( ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV387 )
= $true )
| ( ( ~ ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV415 ) )
= $true )
| ( ( SV415
= ( set_difference @ SV149 @ SV387 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2740]) ).
thf(2859,plain,
! [SV149: $i,SV387: $i,SV415: $i] :
( ( ( ~ ( ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV149 )
| ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV415 ) ) )
= $false )
| ( ( SV415
= ( set_difference @ SV149 @ SV387 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2741]) ).
thf(2860,plain,
! [SV149: $i,SV387: $i,SV415: $i] :
( ( ( ~ ( ~ ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV387 )
| ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV415 ) ) )
= $false )
| ( ( SV415
= ( set_difference @ SV149 @ SV387 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2741]) ).
thf(2861,plain,
! [SV416: $i,SV388: $i,SV149: $i,SV554: $i] :
( ( ( ~ ( in @ SV554 @ SV149 )
| ( in @ SV554 @ SV388 )
| ( in @ SV554 @ SV416 ) )
= $true )
| ( ( SV416
= ( set_difference @ SV149 @ SV388 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2742]) ).
thf(2862,plain,
! [SV388: $i,SV149: $i,SV416: $i] :
( ( ( ~ ! [SY1031: $i] :
( ~ ( in @ SY1031 @ SV416 )
| ( in @ SY1031 @ SV149 ) )
| ~ ! [SY1032: $i] :
( ~ ( in @ SY1032 @ SV416 )
| ~ ( in @ SY1032 @ SV388 ) ) )
= $false )
| ( ( SV416
= ( set_difference @ SV149 @ SV388 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2743]) ).
thf(2863,plain,
! [SV178: $i,SV417: $i,SV33: $i] :
( ( ( in @ SV33 @ ( relation_dom @ ( relation_composition @ SV417 @ SV178 ) ) )
= $false )
| ( ( ( apply @ ( relation_composition @ SV417 @ SV178 ) @ SV33 )
= ( apply @ SV178 @ ( apply @ SV417 @ SV33 ) ) )
= $true )
| ( ( function @ SV417 )
= $false )
| ( ( relation @ SV417 )
= $false )
| ( ( function @ SV178 )
= $false )
| ( ( relation @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2744]) ).
thf(2864,plain,
! [SV418: $i,SV179: $i,SV34: $i] :
( ( ( in @ SV34 @ ( relation_dom @ SV179 ) )
= $false )
| ( ( ( apply @ ( relation_composition @ SV179 @ SV418 ) @ SV34 )
= ( apply @ SV418 @ ( apply @ SV179 @ SV34 ) ) )
= $true )
| ( ( function @ SV418 )
= $false )
| ( ( relation @ SV418 )
= $false )
| ( ( function @ SV179 )
= $false )
| ( ( relation @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2745]) ).
thf(2865,plain,
! [SV112: $i,SV322: $i,SV390: $i] :
( ( ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV112 )
= $false )
| ( ( ~ ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV322 ) )
= $true )
| ( ( ~ ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV390 ) )
= $true )
| ( ( SV390
= ( set_intersection2 @ SV112 @ SV322 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2746]) ).
thf(2866,plain,
! [SV112: $i,SV322: $i,SV390: $i] :
( ( ( ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV112 )
| ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV390 ) )
= $true )
| ( ( SV390
= ( set_intersection2 @ SV112 @ SV322 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2747]) ).
thf(2867,plain,
! [SV112: $i,SV322: $i,SV390: $i] :
( ( ( ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV322 )
| ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV390 ) )
= $true )
| ( ( SV390
= ( set_intersection2 @ SV112 @ SV322 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2748]) ).
thf(2868,plain,
! [SV391: $i,SV323: $i,SV112: $i,SV541: $i] :
( ( ( ~ ( in @ SV541 @ SV112 )
| ~ ( in @ SV541 @ SV323 ) )
= $true )
| ( ( in @ SV541 @ SV391 )
= $true )
| ( ( SV391
= ( set_intersection2 @ SV112 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2749]) ).
thf(2869,plain,
! [SV323: $i,SV112: $i,SV391: $i] :
( ( ( ~ ! [SY1009: $i] :
( ~ ( in @ SY1009 @ SV391 )
| ( in @ SY1009 @ SV112 ) ) )
= $false )
| ( ( SV391
= ( set_intersection2 @ SV112 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2750]) ).
thf(2870,plain,
! [SV112: $i,SV323: $i,SV391: $i] :
( ( ( ~ ! [SY1010: $i] :
( ~ ( in @ SY1010 @ SV391 )
| ( in @ SY1010 @ SV323 ) ) )
= $false )
| ( ( SV391
= ( set_intersection2 @ SV112 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2750]) ).
thf(2871,plain,
! [SV530: $i,SV258: $i,SV324: $i] :
( ( ( in @ ( sK47_C @ SV324 @ SV258 ) @ SV530 )
= $false )
| ( ( ~ ( in @ SV530 @ SV258 ) )
= $true )
| ( ( ~ ( in @ ( sK47_C @ SV324 @ SV258 ) @ SV324 ) )
= $true )
| ( ( SV324
= ( union @ SV258 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2751]) ).
thf(2872,plain,
! [SV258: $i,SV324: $i] :
( ( ( in @ ( sK47_C @ SV324 @ SV258 ) @ ( sK48_SY487 @ SV324 @ SV258 ) )
= $true )
| ( ( in @ ( sK47_C @ SV324 @ SV258 ) @ SV324 )
= $true )
| ( ( SV324
= ( union @ SV258 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2752]) ).
thf(2873,plain,
! [SV258: $i,SV324: $i] :
( ( ( in @ ( sK48_SY487 @ SV324 @ SV258 ) @ SV258 )
= $true )
| ( ( in @ ( sK47_C @ SV324 @ SV258 ) @ SV324 )
= $true )
| ( ( SV324
= ( union @ SV258 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2753]) ).
thf(2874,plain,
! [SV325: $i,SV259: $i,SV555: $i,SV531: $i] :
( ( ( ~ ( in @ SV531 @ SV555 )
| ~ ( in @ SV555 @ SV259 ) )
= $true )
| ( ( in @ SV531 @ SV325 )
= $true )
| ( ( SV325
= ( union @ SV259 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2754]) ).
thf(2875,plain,
! [SV259: $i,SV325: $i,SV532: $i] :
( ( ( in @ SV532 @ SV325 )
= $false )
| ( ( ~ ( ~ ( in @ SV532 @ ( sK46_D @ SV532 @ SV325 @ SV259 ) )
| ~ ( in @ ( sK46_D @ SV532 @ SV325 @ SV259 ) @ SV259 ) ) )
= $true )
| ( ( SV325
= ( union @ SV259 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2755]) ).
thf(2876,plain,
! [SV113: $i,SV225: $i,SV463: $i] :
( ( ( ~ ( ~ ( in @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) @ SV113 )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV225 )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 ) ) )
= $false )
| ( ( SV463
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $true )
| ( ( relation @ SV463 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2756]) ).
thf(2877,plain,
! [SV113: $i,SV225: $i,SV463: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) @ SV113 )
| ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV225 )
| ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 ) ) ) )
= $false )
| ( ( SV463
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $true )
| ( ( relation @ SV463 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2756]) ).
thf(2878,plain,
! [SV464: $i,SV225: $i,SV113: $i] :
( ( ( ~ ! [SY1094: $i,SY1095: $i] :
( ~ ( in @ SY1095 @ SV113 )
| ~ ( in @ ( ordered_pair @ SY1094 @ SY1095 ) @ SV225 )
| ( in @ ( ordered_pair @ SY1094 @ SY1095 ) @ SV464 ) )
| ~ ~ ( ~ ! [SY1096: $i,SY1097: $i] :
( ~ ( in @ ( ordered_pair @ SY1096 @ SY1097 ) @ SV464 )
| ( in @ SY1097 @ SV113 ) )
| ~ ! [SY1098: $i,SY1099: $i] :
( ~ ( in @ ( ordered_pair @ SY1098 @ SY1099 ) @ SV464 )
| ( in @ ( ordered_pair @ SY1098 @ SY1099 ) @ SV225 ) ) ) )
= $false )
| ( ( SV464
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $false )
| ( ( relation @ SV464 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2757]) ).
thf(2879,plain,
! [SV331: $i,SV265: $i,SV534: $i] :
( ( ( SV534 = SV265 )
= $false )
| ( ( in @ SV534 @ SV331 )
= $true )
| ( ( SV331
= ( singleton @ SV265 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2761]) ).
thf(2880,plain,
! [SV265: $i,SV331: $i,SV535: $i] :
( ( ( in @ SV535 @ SV331 )
= $false )
| ( ( SV535 = SV265 )
= $true )
| ( ( SV331
= ( singleton @ SV265 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2762]) ).
thf(2881,plain,
! [SV115: $i,SV465: $i,SV556: $i] :
( ( ( ~ ( subset @ SV556 @ SV465 )
| ( in @ SV556 @ ( sK43_SY481 @ SV465 @ SV115 ) ) )
= $true )
| ( ( ~ ( in @ SV465 @ ( sK42_B @ SV115 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2763]) ).
thf(2882,plain,
! [SV115: $i,SV465: $i] :
( ( ( in @ SV465 @ ( sK42_B @ SV115 ) )
= $false )
| ( ( in @ ( sK43_SY481 @ SV465 @ SV115 ) @ ( sK42_B @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2764]) ).
thf(2883,plain,
! [SV542: $i,SV115: $i,SV536: $i] :
( ( ( ~ ( in @ SV536 @ ( sK42_B @ SV115 ) )
| ~ ( subset @ SV542 @ SV536 ) )
= $true )
| ( ( in @ SV542 @ ( sK42_B @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2765]) ).
thf(2884,plain,
! [SV116: $i,SV543: $i] :
( ( ( ~ ( in @ SV543 @ ( relation_dom @ SV116 ) ) )
= $true )
| ( ( ! [SY1144: $i] :
( ( SY1144
!= ( apply @ SV116 @ SV543 ) )
| ( in @ ( ordered_pair @ SV543 @ SY1144 ) @ SV116 ) ) )
= $true )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2766]) ).
thf(2885,plain,
! [SV116: $i,SV544: $i] :
( ( ( ~ ( in @ SV544 @ ( relation_dom @ SV116 ) ) )
= $true )
| ( ( ! [SY1145: $i] :
( ~ ( in @ ( ordered_pair @ SV544 @ SY1145 ) @ SV116 )
| ( SY1145
= ( apply @ SV116 @ SV544 ) ) ) )
= $true )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2767]) ).
thf(2886,plain,
! [SV116: $i,SV545: $i] :
( ( ( in @ SV545 @ ( relation_dom @ SV116 ) )
= $true )
| ( ( ! [SY1146: $i] :
( ( SY1146
!= ( apply @ SV116 @ SV545 ) )
| ( SY1146 = empty_set ) ) )
= $true )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2768]) ).
thf(2887,plain,
! [SV116: $i,SV546: $i] :
( ( ( in @ SV546 @ ( relation_dom @ SV116 ) )
= $true )
| ( ( ! [SY1147: $i] :
( ( SY1147 != empty_set )
| ( SY1147
= ( apply @ SV116 @ SV546 ) ) ) )
= $true )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2769]) ).
thf(2888,plain,
! [SV393: $i,SV334: $i,SV557: $i,SV117: $i,SV547: $i] :
( ( ( ~ ( in @ SV547 @ SV117 )
| ~ ( in @ SV557 @ SV334 )
| ( ( sK53_D @ SV393 @ SV334 @ SV117 )
!= ( ordered_pair @ SV547 @ SV557 ) ) )
= $true )
| ( ( ~ ( in @ ( sK53_D @ SV393 @ SV334 @ SV117 ) @ SV393 ) )
= $true )
| ( ( SV393
= ( cartesian_product2 @ SV117 @ SV334 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2770]) ).
thf(2889,plain,
! [SV117: $i,SV334: $i,SV393: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK54_SY491 @ SV393 @ SV334 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK55_SY493 @ SV393 @ SV334 @ SV117 ) @ SV334 ) ) )
= $false )
| ( ( in @ ( sK53_D @ SV393 @ SV334 @ SV117 ) @ SV393 )
= $true )
| ( ( SV393
= ( cartesian_product2 @ SV117 @ SV334 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2771]) ).
thf(2890,plain,
! [SV117: $i,SV334: $i,SV393: $i] :
( ( ( ( ( sK53_D @ SV393 @ SV334 @ SV117 )
!= ( ordered_pair @ ( sK54_SY491 @ SV393 @ SV334 @ SV117 ) @ ( sK55_SY493 @ SV393 @ SV334 @ SV117 ) ) ) )
= $false )
| ( ( in @ ( sK53_D @ SV393 @ SV334 @ SV117 ) @ SV393 )
= $true )
| ( ( SV393
= ( cartesian_product2 @ SV117 @ SV334 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2771]) ).
thf(2891,plain,
! [SV394: $i,SV548: $i,SV335: $i,SV117: $i] :
( ( ( ! [SY1149: $i,SY1150: $i] :
( ~ ( in @ SY1149 @ SV117 )
| ~ ( in @ SY1150 @ SV335 )
| ( SV548
!= ( ordered_pair @ SY1149 @ SY1150 ) ) ) )
= $true )
| ( ( in @ SV548 @ SV394 )
= $true )
| ( ( SV394
= ( cartesian_product2 @ SV117 @ SV335 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2772]) ).
thf(2892,plain,
! [SV117: $i,SV335: $i,SV394: $i,SV549: $i] :
( ( ( ~ ( in @ SV549 @ SV394 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK51_E @ SV549 @ SV394 @ SV335 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK52_SY488 @ SV549 @ SV394 @ SV335 @ SV117 ) @ SV335 ) )
| ( SV549
!= ( ordered_pair @ ( sK51_E @ SV549 @ SV394 @ SV335 @ SV117 ) @ ( sK52_SY488 @ SV549 @ SV394 @ SV335 @ SV117 ) ) ) ) )
= $true )
| ( ( SV394
= ( cartesian_product2 @ SV117 @ SV335 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2773]) ).
thf(2893,plain,
! [SV118: $i,SV395: $i,SV338: $i] :
( ( ( SV338
= ( apply @ SV395 @ SV118 ) )
= $false )
| ( ( ~ ( in @ SV118 @ ( relation_dom @ SV395 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV118 @ SV338 ) @ SV395 )
= $true )
| ( ( function @ SV395 )
= $false )
| ( ( relation @ SV395 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2774]) ).
thf(2894,plain,
! [SV467: $i,SV118: $i,SV497: $i] :
( ( ( relation @ SV497 )
= $false )
| ( ( function @ SV497 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV118 @ SV467 ) @ SV497 )
| ( SV467
= ( apply @ SV497 @ SV118 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2775]) ).
thf(2895,plain,
! [SV468: $i,SV118: $i,SV498: $i] :
( ( ( relation @ SV498 )
= $false )
| ( ( function @ SV498 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV118 @ SV468 ) @ SV498 )
| ( in @ SV118 @ ( relation_dom @ SV498 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2776]) ).
thf(2896,plain,
! [SV273: $i,SV339: $i] :
( ( ( ( ( sK69_C @ SV339 @ SV273 )
!= ( sK70_SY500 @ SV339 @ SV273 ) ) )
= $true )
| ( ( ~ ( in @ ( sK69_C @ SV339 @ SV273 ) @ SV273 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 ) )
= $true )
| ( ( SV339
= ( identity_relation @ SV273 ) )
= $true )
| ( ( relation @ SV339 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2777]) ).
thf(2897,plain,
! [SV273: $i,SV339: $i] :
( ( ( ~ ( ( ( sK69_C @ SV339 @ SV273 )
= ( sK70_SY500 @ SV339 @ SV273 ) )
| ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 ) ) )
= $false )
| ( ( SV339
= ( identity_relation @ SV273 ) )
= $true )
| ( ( relation @ SV339 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2778]) ).
thf(2898,plain,
! [SV273: $i,SV339: $i] :
( ( ( ~ ( ( in @ ( sK69_C @ SV339 @ SV273 ) @ SV273 )
| ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 ) ) )
= $false )
| ( ( SV339
= ( identity_relation @ SV273 ) )
= $true )
| ( ( relation @ SV339 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2778]) ).
thf(2899,plain,
! [SV340: $i,SV274: $i,SV558: $i] :
( ( ( ! [SY1152: $i] :
( ( SV558 != SY1152 )
| ~ ( in @ SV558 @ SV274 )
| ( in @ ( ordered_pair @ SV558 @ SY1152 ) @ SV340 ) ) )
= $true )
| ( ( SV340
= ( identity_relation @ SV274 ) )
= $false )
| ( ( relation @ SV340 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2779]) ).
thf(2900,plain,
! [SV274: $i,SV340: $i] :
( ( ( ~ ! [SY970: $i,SY971: $i] :
( ~ ( in @ ( ordered_pair @ SY970 @ SY971 ) @ SV340 )
| ( SY970 = SY971 ) )
| ~ ! [SY972: $i] :
( ! [SY973: $i] :
~ ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV340 )
| ( in @ SY972 @ SV274 ) ) )
= $false )
| ( ( SV340
= ( identity_relation @ SV274 ) )
= $false )
| ( ( relation @ SV340 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2780]) ).
thf(2901,plain,
! [SV120: $i,SV275: $i,SV516: $i] :
( ( ( ~ ( ~ ( ! [SY1135: $i] :
( ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ SY1135 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY1135 @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV275 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV516 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK15_SY461 @ SV516 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY461 @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV275 ) )
| ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV516 ) ) ) )
= $true )
| ( ( SV516
= ( relation_composition @ SV120 @ SV275 ) )
= $true )
| ( ( relation @ SV516 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2781]) ).
thf(2902,plain,
! [SV275: $i,SV120: $i,SV517: $i] :
( ( ( ( SV517
!= ( relation_composition @ SV120 @ SV275 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1136: $i,SY1137: $i] :
( ! [SY909: $i] :
( ~ ( in @ ( ordered_pair @ SY1136 @ SY909 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY909 @ SY1137 ) @ SV275 ) )
| ( in @ ( ordered_pair @ SY1136 @ SY1137 ) @ SV517 ) )
| ~ ! [SY1139: $i,SY1140: $i] :
( ~ ( in @ ( ordered_pair @ SY1139 @ SY1140 ) @ SV517 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1139 @ ( sK12_F @ SY1140 @ SY1139 @ SV517 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK12_F @ SY1140 @ SY1139 @ SV517 @ SV275 @ SV120 ) @ SY1140 ) @ SV275 ) ) ) ) )
= $true )
| ( ( relation @ SV517 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2782]) ).
thf(2903,plain,
! [SV499: $i,SV471: $i,SV122: $i] :
( ( ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SV471 @ SV499 ) ) )
= $false )
| ( ( in @ SV122 @ SV471 )
= $true )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2786]) ).
thf(2904,plain,
! [SV500: $i,SV472: $i,SV122: $i] :
( ( ( in @ SV122 @ ( relation_rng @ ( relation_rng_restriction @ SV472 @ SV500 ) ) )
= $false )
| ( ( in @ SV122 @ ( relation_rng @ SV500 ) )
= $true )
| ( ( relation @ SV500 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2787]) ).
thf(2905,plain,
! [SV123: $i,SV424: $i,SV473: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ SV424 )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV123 )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 ) ) )
= $false )
| ( ( SV473
= ( relation_dom_restriction @ SV123 @ SV424 ) )
= $true )
| ( ( relation @ SV473 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2788]) ).
thf(2906,plain,
! [SV123: $i,SV424: $i,SV473: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ SV424 )
| ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 ) ) ) )
= $false )
| ( ( SV473
= ( relation_dom_restriction @ SV123 @ SV424 ) )
= $true )
| ( ( relation @ SV473 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2788]) ).
thf(2907,plain,
! [SV474: $i,SV123: $i,SV425: $i] :
( ( ( ~ ! [SY1105: $i,SY1106: $i] :
( ~ ( in @ SY1105 @ SV425 )
| ~ ( in @ ( ordered_pair @ SY1105 @ SY1106 ) @ SV123 )
| ( in @ ( ordered_pair @ SY1105 @ SY1106 ) @ SV474 ) )
| ~ ~ ( ~ ! [SY1107: $i] :
( ! [SY1108: $i] :
~ ( in @ ( ordered_pair @ SY1107 @ SY1108 ) @ SV474 )
| ( in @ SY1107 @ SV425 ) )
| ~ ! [SY1109: $i,SY1110: $i] :
( ~ ( in @ ( ordered_pair @ SY1109 @ SY1110 ) @ SV474 )
| ( in @ ( ordered_pair @ SY1109 @ SY1110 ) @ SV123 ) ) ) )
= $false )
| ( ( SV474
= ( relation_dom_restriction @ SV123 @ SV425 ) )
= $false )
| ( ( relation @ SV474 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2789]) ).
thf(2908,plain,
! [SV124: $i,SV426: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK16_C @ SV426 @ SV124 ) @ ( sK17_SY462 @ SV426 @ SV124 ) ) @ SV426 )
| ~ ( in @ ( ordered_pair @ ( sK17_SY462 @ SV426 @ SV124 ) @ ( sK16_C @ SV426 @ SV124 ) ) @ SV124 ) )
= $true )
| ( ( SV426
= ( relation_inverse @ SV124 ) )
= $true )
| ( ( relation @ SV426 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2790]) ).
thf(2909,plain,
! [SV124: $i,SV426: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK16_C @ SV426 @ SV124 ) @ ( sK17_SY462 @ SV426 @ SV124 ) ) @ SV426 )
| ( in @ ( ordered_pair @ ( sK17_SY462 @ SV426 @ SV124 ) @ ( sK16_C @ SV426 @ SV124 ) ) @ SV124 ) )
= $true )
| ( ( SV426
= ( relation_inverse @ SV124 ) )
= $true )
| ( ( relation @ SV426 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2791]) ).
thf(2910,plain,
! [SV124: $i,SV427: $i] :
( ( ( ~ ! [SY1043: $i,SY1044: $i] :
( ~ ( in @ ( ordered_pair @ SY1043 @ SY1044 ) @ SV427 )
| ( in @ ( ordered_pair @ SY1044 @ SY1043 ) @ SV124 ) ) )
= $false )
| ( ( SV427
= ( relation_inverse @ SV124 ) )
= $false )
| ( ( relation @ SV427 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2792]) ).
thf(2911,plain,
! [SV427: $i,SV124: $i] :
( ( ( ~ ! [SY1045: $i,SY1046: $i] :
( ~ ( in @ ( ordered_pair @ SY1046 @ SY1045 ) @ SV124 )
| ( in @ ( ordered_pair @ SY1045 @ SY1046 ) @ SV427 ) ) )
= $false )
| ( ( SV427
= ( relation_inverse @ SV124 ) )
= $false )
| ( ( relation @ SV427 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2792]) ).
thf(2912,plain,
! [SV282: $i,SV348: $i] :
( ( ( ~ ( in @ ( sK38_C @ SV348 @ SV282 ) @ SV282 ) )
= $false )
| ( ( ( ( relation_dom @ SV348 )
!= SV282 ) )
= $true )
| ( ( SV348
= ( identity_relation @ SV282 ) )
= $true )
| ( ( function @ SV348 )
= $false )
| ( ( relation @ SV348 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2793]) ).
thf(2913,plain,
! [SV282: $i,SV348: $i] :
( ( ( ~ ( ( ( apply @ SV348 @ ( sK38_C @ SV348 @ SV282 ) )
!= ( sK38_C @ SV348 @ SV282 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV348 )
!= SV282 ) )
= $true )
| ( ( SV348
= ( identity_relation @ SV282 ) )
= $true )
| ( ( function @ SV348 )
= $false )
| ( ( relation @ SV348 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2793]) ).
thf(2914,plain,
! [SV428: $i,SV475: $i] :
( ( ( ( SV475
!= ( identity_relation @ SV428 ) ) )
= $true )
| ( ( ! [SY1111: $i] :
( ~ ( in @ SY1111 @ SV428 )
| ( ( apply @ SV475 @ SY1111 )
= SY1111 ) ) )
= $true )
| ( ( function @ SV475 )
= $false )
| ( ( relation @ SV475 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2794]) ).
thf(2915,plain,
! [SV429: $i,SV476: $i] :
( ( ( ( SV476
!= ( identity_relation @ SV429 ) ) )
= $true )
| ( ( ( relation_dom @ SV476 )
= SV429 )
= $true )
| ( ( function @ SV476 )
= $false )
| ( ( relation @ SV476 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2795]) ).
thf(2916,plain,
! [SV125: $i,SV432: $i,SV479: $i] :
( ( ( ! [SY1112: $i] :
( ~ ( in @ ( ordered_pair @ SY1112 @ ( sK30_D @ SV479 @ SV432 @ SV125 ) ) @ SV125 )
| ~ ( in @ SY1112 @ SV432 ) ) )
= $true )
| ( ( ~ ( in @ ( sK30_D @ SV479 @ SV432 @ SV125 ) @ SV479 ) )
= $true )
| ( ( SV479
= ( relation_image @ SV125 @ SV432 ) )
= $true )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2796]) ).
thf(2917,plain,
! [SV125: $i,SV432: $i,SV479: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_SY471 @ SV479 @ SV432 @ SV125 ) @ ( sK30_D @ SV479 @ SV432 @ SV125 ) ) @ SV125 )
| ~ ( in @ ( sK31_SY471 @ SV479 @ SV432 @ SV125 ) @ SV432 ) ) )
= $true )
| ( ( in @ ( sK30_D @ SV479 @ SV432 @ SV125 ) @ SV479 )
= $true )
| ( ( SV479
= ( relation_image @ SV125 @ SV432 ) )
= $true )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2797]) ).
thf(2918,plain,
! [SV480: $i,SV433: $i,SV125: $i] :
( ( ( ! [SY1113: $i] :
( ! [SY1056: $i] :
( ~ ( in @ ( ordered_pair @ SY1056 @ SY1113 ) @ SV125 )
| ~ ( in @ SY1056 @ SV433 ) )
| ( in @ SY1113 @ SV480 ) ) )
= $true )
| ( ( SV480
= ( relation_image @ SV125 @ SV433 ) )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2798]) ).
thf(2919,plain,
! [SV125: $i,SV433: $i,SV480: $i] :
( ( ( ! [SY1115: $i] :
( ~ ( in @ SY1115 @ SV480 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK29_E @ SY1115 @ SV480 @ SV433 @ SV125 ) @ SY1115 ) @ SV125 )
| ~ ( in @ ( sK29_E @ SY1115 @ SV480 @ SV433 @ SV125 ) @ SV433 ) ) ) )
= $true )
| ( ( SV480
= ( relation_image @ SV125 @ SV433 ) )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2799]) ).
thf(2920,plain,
! [SV399: $i,SV434: $i,SV228: $i,SV127: $i] :
( ( ( in @ ( ordered_pair @ SV127 @ SV228 ) @ SV434 )
= $false )
| ( ( in @ SV127 @ SV399 )
= $false )
| ( ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SV399 ) @ SV434 ) )
= $true )
| ( ( relation @ SV434 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2800]) ).
thf(2921,plain,
! [SV518: $i,SV501: $i,SV228: $i,SV127: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SV501 ) @ SV518 ) ) )
= $true )
| ( ( in @ SV127 @ SV501 )
= $true )
| ( ( relation @ SV518 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2801]) ).
thf(2922,plain,
! [SV519: $i,SV502: $i,SV228: $i,SV127: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SV502 ) @ SV519 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV127 @ SV228 ) @ SV519 )
= $true )
| ( ( relation @ SV519 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2802]) ).
thf(2923,plain,
! [SV129: $i,SV439: $i,SV559: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV559 @ ( sK19_C @ SV439 @ SV129 ) ) @ SV129 ) )
= $true )
| ( ( ~ ( in @ ( sK19_C @ SV439 @ SV129 ) @ SV439 ) )
= $true )
| ( ( SV439
= ( relation_rng @ SV129 ) )
= $true )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2805]) ).
thf(2924,plain,
! [SV440: $i,SV129: $i,SV560: $i] :
( ( ( ! [SY1153: $i] :
~ ( in @ ( ordered_pair @ SY1153 @ SV560 ) @ SV129 )
| ( in @ SV560 @ SV440 ) )
= $true )
| ( ( SV440
= ( relation_rng @ SV129 ) )
= $false )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2807]) ).
thf(2925,plain,
! [SV129: $i,SV440: $i,SV561: $i] :
( ( ( ~ ( in @ SV561 @ SV440 )
| ( in @ ( ordered_pair @ ( sK18_D @ SV561 @ SV440 @ SV129 ) @ SV561 ) @ SV129 ) )
= $true )
| ( ( SV440
= ( relation_rng @ SV129 ) )
= $false )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2808]) ).
thf(2926,plain,
! [SV131: $i,SV442: $i,SV483: $i] :
( ( ( ! [SY1118: $i] :
( ~ ( in @ ( ordered_pair @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SY1118 ) @ SV131 )
| ~ ( in @ SY1118 @ SV442 ) ) )
= $true )
| ( ( ~ ( in @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SV483 ) )
= $true )
| ( ( SV483
= ( relation_inverse_image @ SV131 @ SV442 ) )
= $true )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2809]) ).
thf(2927,plain,
! [SV131: $i,SV442: $i,SV483: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ ( sK28_SY469 @ SV483 @ SV442 @ SV131 ) ) @ SV131 )
| ~ ( in @ ( sK28_SY469 @ SV483 @ SV442 @ SV131 ) @ SV442 ) ) )
= $true )
| ( ( in @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SV483 )
= $true )
| ( ( SV483
= ( relation_inverse_image @ SV131 @ SV442 ) )
= $true )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2810]) ).
thf(2928,plain,
! [SV484: $i,SV443: $i,SV131: $i] :
( ( ( ! [SY1119: $i] :
( ! [SY1070: $i] :
( ~ ( in @ ( ordered_pair @ SY1119 @ SY1070 ) @ SV131 )
| ~ ( in @ SY1070 @ SV443 ) )
| ( in @ SY1119 @ SV484 ) ) )
= $true )
| ( ( SV484
= ( relation_inverse_image @ SV131 @ SV443 ) )
= $false )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2811]) ).
thf(2929,plain,
! [SV131: $i,SV443: $i,SV484: $i] :
( ( ( ! [SY1121: $i] :
( ~ ( in @ SY1121 @ SV484 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1121 @ ( sK26_E @ SY1121 @ SV484 @ SV443 @ SV131 ) ) @ SV131 )
| ~ ( in @ ( sK26_E @ SY1121 @ SV484 @ SV443 @ SV131 ) @ SV443 ) ) ) )
= $true )
| ( ( SV484
= ( relation_inverse_image @ SV131 @ SV443 ) )
= $false )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2812]) ).
thf(2930,plain,
! [SV485: $i,SV508: $i,SV132: $i] :
( ( ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SV508 @ SV485 ) ) )
= $false )
| ( ( in @ SV132 @ SV485 )
= $true )
| ( ( relation @ SV508 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2814]) ).
thf(2931,plain,
! [SV486: $i,SV509: $i,SV132: $i] :
( ( ( in @ SV132 @ ( relation_dom @ ( relation_dom_restriction @ SV509 @ SV486 ) ) )
= $false )
| ( ( in @ SV132 @ ( relation_dom @ SV509 ) )
= $true )
| ( ( relation @ SV509 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2815]) ).
thf(2932,plain,
! [SV562: $i,SV134: $i,SV445: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SV445 @ SV134 ) @ SV562 ) @ SV134 ) )
= $true )
| ( ( ~ ( in @ ( sK22_C @ SV445 @ SV134 ) @ SV445 ) )
= $true )
| ( ( SV445
= ( relation_dom @ SV134 ) )
= $true )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2816]) ).
thf(2933,plain,
! [SV446: $i,SV134: $i,SV563: $i] :
( ( ( ! [SY1154: $i] :
~ ( in @ ( ordered_pair @ SV563 @ SY1154 ) @ SV134 )
| ( in @ SV563 @ SV446 ) )
= $true )
| ( ( SV446
= ( relation_dom @ SV134 ) )
= $false )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2818]) ).
thf(2934,plain,
! [SV134: $i,SV446: $i,SV564: $i] :
( ( ( ~ ( in @ SV564 @ SV446 )
| ( in @ ( ordered_pair @ SV564 @ ( sK21_D @ SV564 @ SV446 @ SV134 ) ) @ SV134 ) )
= $true )
| ( ( SV446
= ( relation_dom @ SV134 ) )
= $false )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2819]) ).
thf(2935,plain,
! [SV135: $i,SV366: $i,SV404: $i] :
( ( ( ~ ( in @ ( sK57_D @ SV404 @ SV366 @ SV135 ) @ SV404 )
| ( ( sK57_D @ SV404 @ SV366 @ SV135 )
!= SV135 ) )
= $true )
| ( ( SV404
= ( unordered_pair @ SV135 @ SV366 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2820]) ).
thf(2936,plain,
! [SV135: $i,SV366: $i,SV404: $i] :
( ( ( ~ ( in @ ( sK57_D @ SV404 @ SV366 @ SV135 ) @ SV404 )
| ( ( sK57_D @ SV404 @ SV366 @ SV135 )
!= SV366 ) )
= $true )
| ( ( SV404
= ( unordered_pair @ SV135 @ SV366 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2821]) ).
thf(2937,plain,
! [SV367: $i,SV135: $i,SV405: $i,SV550: $i] :
( ( ( ~ ( in @ SV550 @ SV405 ) )
= $true )
| ( ( ( SV550 = SV135 )
| ( SV550 = SV367 ) )
= $true )
| ( ( SV405
= ( unordered_pair @ SV135 @ SV367 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2823]) ).
thf(2938,plain,
! [SV367: $i,SV405: $i,SV135: $i] :
( ( ( ~ ! [SY1020: $i] :
( ( SY1020 != SV135 )
| ( in @ SY1020 @ SV405 ) ) )
= $false )
| ( ( SV405
= ( unordered_pair @ SV135 @ SV367 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2824]) ).
thf(2939,plain,
! [SV135: $i,SV405: $i,SV367: $i] :
( ( ( ~ ! [SY1021: $i] :
( ( SY1021 != SV367 )
| ( in @ SY1021 @ SV405 ) ) )
= $false )
| ( ( SV405
= ( unordered_pair @ SV135 @ SV367 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2824]) ).
thf(2940,plain,
! [SV136: $i,SV447: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV136 )
| ~ ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV447 ) )
= $true )
| ( ( SV136 = SV447 )
= $true )
| ( ( relation @ SV447 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2825]) ).
thf(2941,plain,
! [SV136: $i,SV447: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV136 )
| ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV447 ) )
= $true )
| ( ( SV136 = SV447 )
= $true )
| ( ( relation @ SV447 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2826]) ).
thf(2942,plain,
! [SV448: $i,SV136: $i] :
( ( ( ~ ! [SY1076: $i,SY1077: $i] :
( ~ ( in @ ( ordered_pair @ SY1076 @ SY1077 ) @ SV136 )
| ( in @ ( ordered_pair @ SY1076 @ SY1077 ) @ SV448 ) ) )
= $false )
| ( ( SV136 = SV448 )
= $false )
| ( ( relation @ SV448 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2827]) ).
thf(2943,plain,
! [SV136: $i,SV448: $i] :
( ( ( ~ ! [SY1078: $i,SY1079: $i] :
( ~ ( in @ ( ordered_pair @ SY1078 @ SY1079 ) @ SV448 )
| ( in @ ( ordered_pair @ SY1078 @ SY1079 ) @ SV136 ) ) )
= $false )
| ( ( SV136 = SV448 )
= $false )
| ( ( relation @ SV448 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2827]) ).
thf(2944,plain,
! [SV298: $i,SV368: $i] :
( ( ( function @ SV368 )
= $false )
| ( ( relation @ SV298 )
= $false )
| ( ( function @ SV298 )
= $false )
| ( ( relation @ SV368 )
= $false )
| ( ( function @ ( relation_composition @ SV298 @ SV368 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2828]) ).
thf(2945,plain,
! [SV299: $i,SV369: $i] :
( ( ( function @ SV369 )
= $false )
| ( ( relation @ SV299 )
= $false )
| ( ( function @ SV299 )
= $false )
| ( ( relation @ SV369 )
= $false )
| ( ( relation @ ( relation_composition @ SV299 @ SV369 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2829]) ).
thf(2946,plain,
! [SV230: $i,SV137: $i,SV523: $i] :
( ( ( function @ SV523 )
= $false )
| ( ( ~ ( relation @ SV523 ) )
= $true )
| ( ( ~ ( in @ SV137 @ ( relation_dom @ SV523 ) )
| ~ ( in @ ( apply @ SV523 @ SV137 ) @ ( relation_dom @ SV230 ) )
| ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SV523 @ SV230 ) ) ) )
= $true )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2830]) ).
thf(2947,plain,
! [SV230: $i,SV137: $i,SV565: $i] :
( ( ( ~ ( function @ SV565 )
| ~ ( relation @ SV565 )
| ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SV565 @ SV230 ) ) )
| ( in @ SV137 @ ( relation_dom @ SV565 ) ) )
= $true )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2831]) ).
thf(2948,plain,
! [SV230: $i,SV137: $i,SV566: $i] :
( ( ( ~ ( function @ SV566 )
| ~ ( relation @ SV566 )
| ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SV566 @ SV230 ) ) )
| ( in @ ( apply @ SV566 @ SV137 ) @ ( relation_dom @ SV230 ) ) )
= $true )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2832]) ).
thf(2949,plain,
! [SV551: $i,SV138: $i,SV537: $i] :
( ( ( ~ ( in @ SV537 @ ( sK41_B @ SV138 ) )
| ~ ( subset @ SV551 @ SV537 ) )
= $true )
| ( ( in @ SV551 @ ( sK41_B @ SV138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2833]) ).
thf(2950,plain,
! [SV139: $i,SV449: $i] :
( ( ( in @ ( ordered_pair @ ( sK24_C @ SV449 @ SV139 ) @ ( sK25_SY467 @ SV449 @ SV139 ) ) @ SV139 )
= $true )
| ( ( subset @ SV139 @ SV449 )
= $true )
| ( ( relation @ SV449 )
= $false )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2834]) ).
thf(2951,plain,
! [SV139: $i,SV449: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV449 @ SV139 ) @ ( sK25_SY467 @ SV449 @ SV139 ) ) @ SV449 ) )
= $true )
| ( ( subset @ SV139 @ SV449 )
= $true )
| ( ( relation @ SV449 )
= $false )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2835]) ).
thf(2952,plain,
! [SV450: $i,SV139: $i,SV567: $i,SV552: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV552 @ SV567 ) @ SV139 )
| ( in @ ( ordered_pair @ SV552 @ SV567 ) @ SV450 ) )
= $true )
| ( ( subset @ SV139 @ SV450 )
= $false )
| ( ( relation @ SV450 )
= $false )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2836]) ).
thf(2953,plain,
! [SV301: $i,SV372: $i,SV538: $i] :
( ( ( in @ SV538 @ SV372 )
= $false )
| ( ( subset @ SV538 @ SV301 )
= $true )
| ( ( SV372
= ( powerset @ SV301 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2838]) ).
thf(2954,plain,
! [SV372: $i,SV301: $i,SV539: $i] :
( ( ( subset @ SV539 @ SV301 )
= $false )
| ( ( in @ SV539 @ SV372 )
= $true )
| ( ( SV372
= ( powerset @ SV301 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2839]) ).
thf(2955,plain,
! [SV375: $i,SV142: $i,SV406: $i,SV524: $i] :
( ( ( in @ SV524 @ ( relation_rng @ SV406 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV142 @ SV524 ) @ SV406 ) )
= $true )
| ( ( ~ ( in @ SV524 @ SV375 ) )
= $true )
| ( ( in @ SV142 @ ( relation_inverse_image @ SV406 @ SV375 ) )
= $true )
| ( ( relation @ SV406 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2840]) ).
thf(2956,plain,
! [SV142: $i,SV376: $i,SV407: $i] :
( ( ( ~ ( ~ ( in @ ( sK39_D @ SV407 @ SV376 @ SV142 ) @ ( relation_rng @ SV407 ) )
| ~ ( in @ ( ordered_pair @ SV142 @ ( sK39_D @ SV407 @ SV376 @ SV142 ) ) @ SV407 ) ) )
= $true )
| ( ( in @ SV142 @ ( relation_inverse_image @ SV407 @ SV376 ) )
= $false )
| ( ( relation @ SV407 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2841]) ).
thf(2957,plain,
! [SV142: $i,SV376: $i,SV407: $i] :
( ( ( in @ ( sK39_D @ SV407 @ SV376 @ SV142 ) @ SV376 )
= $true )
| ( ( in @ SV142 @ ( relation_inverse_image @ SV407 @ SV376 ) )
= $false )
| ( ( relation @ SV407 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2842]) ).
thf(2958,plain,
! [SV453: $i,SV510: $i] :
( ( ( ~ ( ~ ( in @ ( sK65_SY495 @ SV510 @ SV453 ) @ SV453 )
| ~ ~ ( in @ ( sK64_C @ SV510 @ SV453 ) @ ( sK65_SY495 @ SV510 @ SV453 ) ) )
| ~ ( in @ ( sK64_C @ SV510 @ SV453 ) @ SV510 ) )
= $true )
| ( ( SV510
= ( set_meet @ SV453 ) )
= $true )
| ( ( SV453 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2843]) ).
thf(2959,plain,
! [SV510: $i,SV453: $i] :
( ( ( ! [SY1129: $i] :
( ~ ( in @ SY1129 @ SV453 )
| ( in @ ( sK64_C @ SV510 @ SV453 ) @ SY1129 ) )
| ( in @ ( sK64_C @ SV510 @ SV453 ) @ SV510 ) )
= $true )
| ( ( SV510
= ( set_meet @ SV453 ) )
= $true )
| ( ( SV453 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2844]) ).
thf(2960,plain,
! [SV454: $i,SV511: $i] :
( ( ( ~ ! [SY1130: $i] :
( ~ ( ~ ( in @ ( sK63_D @ SY1130 @ SV511 @ SV454 ) @ SV454 )
| ~ ~ ( in @ SY1130 @ ( sK63_D @ SY1130 @ SV511 @ SV454 ) ) )
| ( in @ SY1130 @ SV511 ) ) )
= $false )
| ( ( SV511
= ( set_meet @ SV454 ) )
= $false )
| ( ( SV454 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2845]) ).
thf(2961,plain,
! [SV454: $i,SV511: $i] :
( ( ( ~ ! [SY1131: $i] :
( ~ ( in @ SY1131 @ SV511 )
| ! [SY1087: $i] :
( ~ ( in @ SY1087 @ SV454 )
| ( in @ SY1131 @ SY1087 ) ) ) )
= $false )
| ( ( SV511
= ( set_meet @ SV454 ) )
= $false )
| ( ( SV454 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2845]) ).
thf(2962,plain,
! [SV144: $i,SV378: $i,SV409: $i] :
( ( ( ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV409 )
| ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV144 ) )
= $true )
| ( ( SV409
= ( set_union2 @ SV144 @ SV378 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2850]) ).
thf(2963,plain,
! [SV144: $i,SV378: $i,SV409: $i] :
( ( ( ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV409 )
| ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV378 ) )
= $true )
| ( ( SV409
= ( set_union2 @ SV144 @ SV378 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2851]) ).
thf(2964,plain,
! [SV379: $i,SV144: $i,SV410: $i,SV553: $i] :
( ( ( ~ ( in @ SV553 @ SV410 ) )
= $true )
| ( ( ( in @ SV553 @ SV144 )
| ( in @ SV553 @ SV379 ) )
= $true )
| ( ( SV410
= ( set_union2 @ SV144 @ SV379 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2853]) ).
thf(2965,plain,
! [SV379: $i,SV410: $i,SV144: $i] :
( ( ( ~ ! [SY1025: $i] :
( ~ ( in @ SY1025 @ SV144 )
| ( in @ SY1025 @ SV410 ) ) )
= $false )
| ( ( SV410
= ( set_union2 @ SV144 @ SV379 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2854]) ).
thf(2966,plain,
! [SV144: $i,SV410: $i,SV379: $i] :
( ( ( ~ ! [SY1026: $i] :
( ~ ( in @ SY1026 @ SV379 )
| ( in @ SY1026 @ SV410 ) ) )
= $false )
| ( ( SV410
= ( set_union2 @ SV144 @ SV379 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2854]) ).
thf(2967,plain,
! [SV380: $i,SV145: $i,SV411: $i,SV528: $i] :
( ( ( in @ SV528 @ ( relation_dom @ SV411 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV528 @ SV145 ) @ SV411 ) )
= $true )
| ( ( ~ ( in @ SV528 @ SV380 ) )
= $true )
| ( ( in @ SV145 @ ( relation_image @ SV411 @ SV380 ) )
= $true )
| ( ( relation @ SV411 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2855]) ).
thf(2968,plain,
! [SV145: $i,SV381: $i,SV412: $i] :
( ( ( ~ ( ~ ( in @ ( sK40_D @ SV412 @ SV381 @ SV145 ) @ ( relation_dom @ SV412 ) )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV412 @ SV381 @ SV145 ) @ SV145 ) @ SV412 ) ) )
= $true )
| ( ( in @ SV145 @ ( relation_image @ SV412 @ SV381 ) )
= $false )
| ( ( relation @ SV412 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2856]) ).
thf(2969,plain,
! [SV145: $i,SV381: $i,SV412: $i] :
( ( ( in @ ( sK40_D @ SV412 @ SV381 @ SV145 ) @ SV381 )
= $true )
| ( ( in @ SV145 @ ( relation_image @ SV412 @ SV381 ) )
= $false )
| ( ( relation @ SV412 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2857]) ).
thf(2970,plain,
! [SV149: $i,SV387: $i,SV415: $i] :
( ( ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV149 )
= $false )
| ( ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV387 )
= $true )
| ( ( ~ ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV415 ) )
= $true )
| ( ( SV415
= ( set_difference @ SV149 @ SV387 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2858]) ).
thf(2971,plain,
! [SV149: $i,SV387: $i,SV415: $i] :
( ( ( ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV149 )
| ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV415 ) )
= $true )
| ( ( SV415
= ( set_difference @ SV149 @ SV387 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2859]) ).
thf(2972,plain,
! [SV149: $i,SV387: $i,SV415: $i] :
( ( ( ~ ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV387 )
| ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV415 ) )
= $true )
| ( ( SV415
= ( set_difference @ SV149 @ SV387 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2860]) ).
thf(2973,plain,
! [SV416: $i,SV388: $i,SV149: $i,SV554: $i] :
( ( ( ~ ( in @ SV554 @ SV149 )
| ( in @ SV554 @ SV388 ) )
= $true )
| ( ( in @ SV554 @ SV416 )
= $true )
| ( ( SV416
= ( set_difference @ SV149 @ SV388 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2861]) ).
thf(2974,plain,
! [SV388: $i,SV149: $i,SV416: $i] :
( ( ( ~ ! [SY1031: $i] :
( ~ ( in @ SY1031 @ SV416 )
| ( in @ SY1031 @ SV149 ) ) )
= $false )
| ( ( SV416
= ( set_difference @ SV149 @ SV388 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2862]) ).
thf(2975,plain,
! [SV149: $i,SV388: $i,SV416: $i] :
( ( ( ~ ! [SY1032: $i] :
( ~ ( in @ SY1032 @ SV416 )
| ~ ( in @ SY1032 @ SV388 ) ) )
= $false )
| ( ( SV416
= ( set_difference @ SV149 @ SV388 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2862]) ).
thf(2976,plain,
! [SV112: $i,SV322: $i,SV390: $i] :
( ( ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV322 )
= $false )
| ( ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV112 )
= $false )
| ( ( ~ ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV390 ) )
= $true )
| ( ( SV390
= ( set_intersection2 @ SV112 @ SV322 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2865]) ).
thf(2977,plain,
! [SV112: $i,SV322: $i,SV390: $i] :
( ( ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV112 )
= $true )
| ( ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV390 )
= $true )
| ( ( SV390
= ( set_intersection2 @ SV112 @ SV322 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2866]) ).
thf(2978,plain,
! [SV112: $i,SV322: $i,SV390: $i] :
( ( ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV322 )
= $true )
| ( ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV390 )
= $true )
| ( ( SV390
= ( set_intersection2 @ SV112 @ SV322 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2867]) ).
thf(2979,plain,
! [SV391: $i,SV323: $i,SV112: $i,SV541: $i] :
( ( ( ~ ( in @ SV541 @ SV112 ) )
= $true )
| ( ( ~ ( in @ SV541 @ SV323 ) )
= $true )
| ( ( in @ SV541 @ SV391 )
= $true )
| ( ( SV391
= ( set_intersection2 @ SV112 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2868]) ).
thf(2980,plain,
! [SV323: $i,SV112: $i,SV391: $i] :
( ( ( ! [SY1009: $i] :
( ~ ( in @ SY1009 @ SV391 )
| ( in @ SY1009 @ SV112 ) ) )
= $true )
| ( ( SV391
= ( set_intersection2 @ SV112 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2869]) ).
thf(2981,plain,
! [SV112: $i,SV323: $i,SV391: $i] :
( ( ( ! [SY1010: $i] :
( ~ ( in @ SY1010 @ SV391 )
| ( in @ SY1010 @ SV323 ) ) )
= $true )
| ( ( SV391
= ( set_intersection2 @ SV112 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2870]) ).
thf(2982,plain,
! [SV324: $i,SV258: $i,SV530: $i] :
( ( ( in @ SV530 @ SV258 )
= $false )
| ( ( in @ ( sK47_C @ SV324 @ SV258 ) @ SV530 )
= $false )
| ( ( ~ ( in @ ( sK47_C @ SV324 @ SV258 ) @ SV324 ) )
= $true )
| ( ( SV324
= ( union @ SV258 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2871]) ).
thf(2983,plain,
! [SV325: $i,SV259: $i,SV555: $i,SV531: $i] :
( ( ( ~ ( in @ SV531 @ SV555 ) )
= $true )
| ( ( ~ ( in @ SV555 @ SV259 ) )
= $true )
| ( ( in @ SV531 @ SV325 )
= $true )
| ( ( SV325
= ( union @ SV259 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2874]) ).
thf(2984,plain,
! [SV259: $i,SV325: $i,SV532: $i] :
( ( ( ~ ( in @ SV532 @ ( sK46_D @ SV532 @ SV325 @ SV259 ) )
| ~ ( in @ ( sK46_D @ SV532 @ SV325 @ SV259 ) @ SV259 ) )
= $false )
| ( ( in @ SV532 @ SV325 )
= $false )
| ( ( SV325
= ( union @ SV259 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2875]) ).
thf(2985,plain,
! [SV113: $i,SV225: $i,SV463: $i] :
( ( ( ~ ( in @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) @ SV113 )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV225 )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 ) )
= $true )
| ( ( SV463
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $true )
| ( ( relation @ SV463 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2876]) ).
thf(2986,plain,
! [SV113: $i,SV225: $i,SV463: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) @ SV113 )
| ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV225 )
| ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 ) ) ) )
= $true )
| ( ( SV463
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $true )
| ( ( relation @ SV463 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2877]) ).
thf(2987,plain,
! [SV464: $i,SV225: $i,SV113: $i] :
( ( ( ~ ! [SY1094: $i,SY1095: $i] :
( ~ ( in @ SY1095 @ SV113 )
| ~ ( in @ ( ordered_pair @ SY1094 @ SY1095 ) @ SV225 )
| ( in @ ( ordered_pair @ SY1094 @ SY1095 ) @ SV464 ) ) )
= $false )
| ( ( SV464
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $false )
| ( ( relation @ SV464 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2878]) ).
thf(2988,plain,
! [SV225: $i,SV113: $i,SV464: $i] :
( ( ( ~ ~ ( ~ ! [SY1096: $i,SY1097: $i] :
( ~ ( in @ ( ordered_pair @ SY1096 @ SY1097 ) @ SV464 )
| ( in @ SY1097 @ SV113 ) )
| ~ ! [SY1098: $i,SY1099: $i] :
( ~ ( in @ ( ordered_pair @ SY1098 @ SY1099 ) @ SV464 )
| ( in @ ( ordered_pair @ SY1098 @ SY1099 ) @ SV225 ) ) ) )
= $false )
| ( ( SV464
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $false )
| ( ( relation @ SV464 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2878]) ).
thf(2989,plain,
! [SV115: $i,SV465: $i,SV556: $i] :
( ( ( ~ ( subset @ SV556 @ SV465 ) )
= $true )
| ( ( in @ SV556 @ ( sK43_SY481 @ SV465 @ SV115 ) )
= $true )
| ( ( ~ ( in @ SV465 @ ( sK42_B @ SV115 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2881]) ).
thf(2990,plain,
! [SV542: $i,SV115: $i,SV536: $i] :
( ( ( ~ ( in @ SV536 @ ( sK42_B @ SV115 ) ) )
= $true )
| ( ( ~ ( subset @ SV542 @ SV536 ) )
= $true )
| ( ( in @ SV542 @ ( sK42_B @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2883]) ).
thf(2991,plain,
! [SV116: $i,SV543: $i] :
( ( ( in @ SV543 @ ( relation_dom @ SV116 ) )
= $false )
| ( ( ! [SY1144: $i] :
( ( SY1144
!= ( apply @ SV116 @ SV543 ) )
| ( in @ ( ordered_pair @ SV543 @ SY1144 ) @ SV116 ) ) )
= $true )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2884]) ).
thf(2992,plain,
! [SV116: $i,SV544: $i] :
( ( ( in @ SV544 @ ( relation_dom @ SV116 ) )
= $false )
| ( ( ! [SY1145: $i] :
( ~ ( in @ ( ordered_pair @ SV544 @ SY1145 ) @ SV116 )
| ( SY1145
= ( apply @ SV116 @ SV544 ) ) ) )
= $true )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2885]) ).
thf(2993,plain,
! [SV545: $i,SV116: $i,SV568: $i] :
( ( ( ( SV568
!= ( apply @ SV116 @ SV545 ) )
| ( SV568 = empty_set ) )
= $true )
| ( ( in @ SV545 @ ( relation_dom @ SV116 ) )
= $true )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2886]) ).
thf(2994,plain,
! [SV546: $i,SV116: $i,SV569: $i] :
( ( ( ( SV569 != empty_set )
| ( SV569
= ( apply @ SV116 @ SV546 ) ) )
= $true )
| ( ( in @ SV546 @ ( relation_dom @ SV116 ) )
= $true )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2887]) ).
thf(2995,plain,
! [SV393: $i,SV334: $i,SV557: $i,SV117: $i,SV547: $i] :
( ( ( ~ ( in @ SV547 @ SV117 )
| ~ ( in @ SV557 @ SV334 ) )
= $true )
| ( ( ( ( sK53_D @ SV393 @ SV334 @ SV117 )
!= ( ordered_pair @ SV547 @ SV557 ) ) )
= $true )
| ( ( ~ ( in @ ( sK53_D @ SV393 @ SV334 @ SV117 ) @ SV393 ) )
= $true )
| ( ( SV393
= ( cartesian_product2 @ SV117 @ SV334 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2888]) ).
thf(2996,plain,
! [SV117: $i,SV334: $i,SV393: $i] :
( ( ( ~ ( ~ ( in @ ( sK54_SY491 @ SV393 @ SV334 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK55_SY493 @ SV393 @ SV334 @ SV117 ) @ SV334 ) ) )
= $true )
| ( ( in @ ( sK53_D @ SV393 @ SV334 @ SV117 ) @ SV393 )
= $true )
| ( ( SV393
= ( cartesian_product2 @ SV117 @ SV334 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2889]) ).
thf(2997,plain,
! [SV117: $i,SV334: $i,SV393: $i] :
( ( ( ( sK53_D @ SV393 @ SV334 @ SV117 )
= ( ordered_pair @ ( sK54_SY491 @ SV393 @ SV334 @ SV117 ) @ ( sK55_SY493 @ SV393 @ SV334 @ SV117 ) ) )
= $true )
| ( ( in @ ( sK53_D @ SV393 @ SV334 @ SV117 ) @ SV393 )
= $true )
| ( ( SV393
= ( cartesian_product2 @ SV117 @ SV334 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2890]) ).
thf(2998,plain,
! [SV394: $i,SV548: $i,SV335: $i,SV117: $i,SV570: $i] :
( ( ( ! [SY1155: $i] :
( ~ ( in @ SV570 @ SV117 )
| ~ ( in @ SY1155 @ SV335 )
| ( SV548
!= ( ordered_pair @ SV570 @ SY1155 ) ) ) )
= $true )
| ( ( in @ SV548 @ SV394 )
= $true )
| ( ( SV394
= ( cartesian_product2 @ SV117 @ SV335 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2891]) ).
thf(2999,plain,
! [SV117: $i,SV335: $i,SV394: $i,SV549: $i] :
( ( ( in @ SV549 @ SV394 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK51_E @ SV549 @ SV394 @ SV335 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK52_SY488 @ SV549 @ SV394 @ SV335 @ SV117 ) @ SV335 ) )
| ( SV549
!= ( ordered_pair @ ( sK51_E @ SV549 @ SV394 @ SV335 @ SV117 ) @ ( sK52_SY488 @ SV549 @ SV394 @ SV335 @ SV117 ) ) ) ) )
= $true )
| ( ( SV394
= ( cartesian_product2 @ SV117 @ SV335 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2892]) ).
thf(3000,plain,
! [SV338: $i,SV395: $i,SV118: $i] :
( ( ( in @ SV118 @ ( relation_dom @ SV395 ) )
= $false )
| ( ( SV338
= ( apply @ SV395 @ SV118 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV118 @ SV338 ) @ SV395 )
= $true )
| ( ( function @ SV395 )
= $false )
| ( ( relation @ SV395 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2893]) ).
thf(3001,plain,
! [SV497: $i,SV467: $i,SV118: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV118 @ SV467 ) @ SV497 ) )
= $true )
| ( ( SV467
= ( apply @ SV497 @ SV118 ) )
= $true )
| ( ( function @ SV497 )
= $false )
| ( ( relation @ SV497 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2894]) ).
thf(3002,plain,
! [SV498: $i,SV468: $i,SV118: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV118 @ SV468 ) @ SV498 ) )
= $true )
| ( ( in @ SV118 @ ( relation_dom @ SV498 ) )
= $true )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2895]) ).
thf(3003,plain,
! [SV273: $i,SV339: $i] :
( ( ( ( sK69_C @ SV339 @ SV273 )
= ( sK70_SY500 @ SV339 @ SV273 ) )
= $false )
| ( ( ~ ( in @ ( sK69_C @ SV339 @ SV273 ) @ SV273 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 ) )
= $true )
| ( ( SV339
= ( identity_relation @ SV273 ) )
= $true )
| ( ( relation @ SV339 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2896]) ).
thf(3004,plain,
! [SV273: $i,SV339: $i] :
( ( ( ( ( sK69_C @ SV339 @ SV273 )
= ( sK70_SY500 @ SV339 @ SV273 ) )
| ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 ) )
= $true )
| ( ( SV339
= ( identity_relation @ SV273 ) )
= $true )
| ( ( relation @ SV339 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2897]) ).
thf(3005,plain,
! [SV273: $i,SV339: $i] :
( ( ( ( in @ ( sK69_C @ SV339 @ SV273 ) @ SV273 )
| ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 ) )
= $true )
| ( ( SV339
= ( identity_relation @ SV273 ) )
= $true )
| ( ( relation @ SV339 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2898]) ).
thf(3006,plain,
! [SV340: $i,SV274: $i,SV571: $i,SV558: $i] :
( ( ( ( SV558 != SV571 )
| ~ ( in @ SV558 @ SV274 )
| ( in @ ( ordered_pair @ SV558 @ SV571 ) @ SV340 ) )
= $true )
| ( ( SV340
= ( identity_relation @ SV274 ) )
= $false )
| ( ( relation @ SV340 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2899]) ).
thf(3007,plain,
! [SV274: $i,SV340: $i] :
( ( ( ~ ! [SY970: $i,SY971: $i] :
( ~ ( in @ ( ordered_pair @ SY970 @ SY971 ) @ SV340 )
| ( SY970 = SY971 ) ) )
= $false )
| ( ( SV340
= ( identity_relation @ SV274 ) )
= $false )
| ( ( relation @ SV340 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2900]) ).
thf(3008,plain,
! [SV274: $i,SV340: $i] :
( ( ( ~ ! [SY972: $i] :
( ! [SY973: $i] :
~ ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV340 )
| ( in @ SY972 @ SV274 ) ) )
= $false )
| ( ( SV340
= ( identity_relation @ SV274 ) )
= $false )
| ( ( relation @ SV340 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2900]) ).
thf(3009,plain,
! [SV120: $i,SV275: $i,SV516: $i] :
( ( ( ~ ( ! [SY1135: $i] :
( ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ SY1135 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY1135 @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV275 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV516 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK15_SY461 @ SV516 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY461 @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV275 ) )
| ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV516 ) ) )
= $false )
| ( ( SV516
= ( relation_composition @ SV120 @ SV275 ) )
= $true )
| ( ( relation @ SV516 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2901]) ).
thf(3010,plain,
! [SV275: $i,SV120: $i,SV517: $i] :
( ( ( SV517
= ( relation_composition @ SV120 @ SV275 ) )
= $false )
| ( ( ~ ( ~ ! [SY1136: $i,SY1137: $i] :
( ! [SY909: $i] :
( ~ ( in @ ( ordered_pair @ SY1136 @ SY909 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY909 @ SY1137 ) @ SV275 ) )
| ( in @ ( ordered_pair @ SY1136 @ SY1137 ) @ SV517 ) )
| ~ ! [SY1139: $i,SY1140: $i] :
( ~ ( in @ ( ordered_pair @ SY1139 @ SY1140 ) @ SV517 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1139 @ ( sK12_F @ SY1140 @ SY1139 @ SV517 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK12_F @ SY1140 @ SY1139 @ SV517 @ SV275 @ SV120 ) @ SY1140 ) @ SV275 ) ) ) ) )
= $true )
| ( ( relation @ SV517 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2902]) ).
thf(3011,plain,
! [SV123: $i,SV424: $i,SV473: $i] :
( ( ( ~ ( in @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ SV424 )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV123 )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 ) )
= $true )
| ( ( SV473
= ( relation_dom_restriction @ SV123 @ SV424 ) )
= $true )
| ( ( relation @ SV473 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2905]) ).
thf(3012,plain,
! [SV123: $i,SV424: $i,SV473: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ SV424 )
| ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 ) ) ) )
= $true )
| ( ( SV473
= ( relation_dom_restriction @ SV123 @ SV424 ) )
= $true )
| ( ( relation @ SV473 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2906]) ).
thf(3013,plain,
! [SV474: $i,SV123: $i,SV425: $i] :
( ( ( ~ ! [SY1105: $i,SY1106: $i] :
( ~ ( in @ SY1105 @ SV425 )
| ~ ( in @ ( ordered_pair @ SY1105 @ SY1106 ) @ SV123 )
| ( in @ ( ordered_pair @ SY1105 @ SY1106 ) @ SV474 ) ) )
= $false )
| ( ( SV474
= ( relation_dom_restriction @ SV123 @ SV425 ) )
= $false )
| ( ( relation @ SV474 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2907]) ).
thf(3014,plain,
! [SV123: $i,SV425: $i,SV474: $i] :
( ( ( ~ ~ ( ~ ! [SY1107: $i] :
( ! [SY1108: $i] :
~ ( in @ ( ordered_pair @ SY1107 @ SY1108 ) @ SV474 )
| ( in @ SY1107 @ SV425 ) )
| ~ ! [SY1109: $i,SY1110: $i] :
( ~ ( in @ ( ordered_pair @ SY1109 @ SY1110 ) @ SV474 )
| ( in @ ( ordered_pair @ SY1109 @ SY1110 ) @ SV123 ) ) ) )
= $false )
| ( ( SV474
= ( relation_dom_restriction @ SV123 @ SV425 ) )
= $false )
| ( ( relation @ SV474 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2907]) ).
thf(3015,plain,
! [SV124: $i,SV426: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK16_C @ SV426 @ SV124 ) @ ( sK17_SY462 @ SV426 @ SV124 ) ) @ SV426 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK17_SY462 @ SV426 @ SV124 ) @ ( sK16_C @ SV426 @ SV124 ) ) @ SV124 ) )
= $true )
| ( ( SV426
= ( relation_inverse @ SV124 ) )
= $true )
| ( ( relation @ SV426 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2908]) ).
thf(3016,plain,
! [SV124: $i,SV426: $i] :
( ( ( in @ ( ordered_pair @ ( sK16_C @ SV426 @ SV124 ) @ ( sK17_SY462 @ SV426 @ SV124 ) ) @ SV426 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK17_SY462 @ SV426 @ SV124 ) @ ( sK16_C @ SV426 @ SV124 ) ) @ SV124 )
= $true )
| ( ( SV426
= ( relation_inverse @ SV124 ) )
= $true )
| ( ( relation @ SV426 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2909]) ).
thf(3017,plain,
! [SV124: $i,SV427: $i] :
( ( ( ! [SY1043: $i,SY1044: $i] :
( ~ ( in @ ( ordered_pair @ SY1043 @ SY1044 ) @ SV427 )
| ( in @ ( ordered_pair @ SY1044 @ SY1043 ) @ SV124 ) ) )
= $true )
| ( ( SV427
= ( relation_inverse @ SV124 ) )
= $false )
| ( ( relation @ SV427 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2910]) ).
thf(3018,plain,
! [SV427: $i,SV124: $i] :
( ( ( ! [SY1045: $i,SY1046: $i] :
( ~ ( in @ ( ordered_pair @ SY1046 @ SY1045 ) @ SV124 )
| ( in @ ( ordered_pair @ SY1045 @ SY1046 ) @ SV427 ) ) )
= $true )
| ( ( SV427
= ( relation_inverse @ SV124 ) )
= $false )
| ( ( relation @ SV427 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2911]) ).
thf(3019,plain,
! [SV282: $i,SV348: $i] :
( ( ( in @ ( sK38_C @ SV348 @ SV282 ) @ SV282 )
= $true )
| ( ( ( ( relation_dom @ SV348 )
!= SV282 ) )
= $true )
| ( ( SV348
= ( identity_relation @ SV282 ) )
= $true )
| ( ( function @ SV348 )
= $false )
| ( ( relation @ SV348 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2912]) ).
thf(3020,plain,
! [SV282: $i,SV348: $i] :
( ( ( ( ( apply @ SV348 @ ( sK38_C @ SV348 @ SV282 ) )
!= ( sK38_C @ SV348 @ SV282 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV348 )
!= SV282 ) )
= $true )
| ( ( SV348
= ( identity_relation @ SV282 ) )
= $true )
| ( ( function @ SV348 )
= $false )
| ( ( relation @ SV348 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2913]) ).
thf(3021,plain,
! [SV428: $i,SV475: $i] :
( ( ( SV475
= ( identity_relation @ SV428 ) )
= $false )
| ( ( ! [SY1111: $i] :
( ~ ( in @ SY1111 @ SV428 )
| ( ( apply @ SV475 @ SY1111 )
= SY1111 ) ) )
= $true )
| ( ( function @ SV475 )
= $false )
| ( ( relation @ SV475 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2914]) ).
thf(3022,plain,
! [SV429: $i,SV476: $i] :
( ( ( SV476
= ( identity_relation @ SV429 ) )
= $false )
| ( ( ( relation_dom @ SV476 )
= SV429 )
= $true )
| ( ( function @ SV476 )
= $false )
| ( ( relation @ SV476 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2915]) ).
thf(3023,plain,
! [SV125: $i,SV432: $i,SV479: $i,SV572: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV572 @ ( sK30_D @ SV479 @ SV432 @ SV125 ) ) @ SV125 )
| ~ ( in @ SV572 @ SV432 ) )
= $true )
| ( ( ~ ( in @ ( sK30_D @ SV479 @ SV432 @ SV125 ) @ SV479 ) )
= $true )
| ( ( SV479
= ( relation_image @ SV125 @ SV432 ) )
= $true )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2916]) ).
thf(3024,plain,
! [SV125: $i,SV432: $i,SV479: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK31_SY471 @ SV479 @ SV432 @ SV125 ) @ ( sK30_D @ SV479 @ SV432 @ SV125 ) ) @ SV125 )
| ~ ( in @ ( sK31_SY471 @ SV479 @ SV432 @ SV125 ) @ SV432 ) )
= $false )
| ( ( in @ ( sK30_D @ SV479 @ SV432 @ SV125 ) @ SV479 )
= $true )
| ( ( SV479
= ( relation_image @ SV125 @ SV432 ) )
= $true )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2917]) ).
thf(3025,plain,
! [SV480: $i,SV433: $i,SV125: $i,SV573: $i] :
( ( ( ! [SY1156: $i] :
( ~ ( in @ ( ordered_pair @ SY1156 @ SV573 ) @ SV125 )
| ~ ( in @ SY1156 @ SV433 ) )
| ( in @ SV573 @ SV480 ) )
= $true )
| ( ( SV480
= ( relation_image @ SV125 @ SV433 ) )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2918]) ).
thf(3026,plain,
! [SV125: $i,SV433: $i,SV480: $i,SV574: $i] :
( ( ( ~ ( in @ SV574 @ SV480 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK29_E @ SV574 @ SV480 @ SV433 @ SV125 ) @ SV574 ) @ SV125 )
| ~ ( in @ ( sK29_E @ SV574 @ SV480 @ SV433 @ SV125 ) @ SV433 ) ) )
= $true )
| ( ( SV480
= ( relation_image @ SV125 @ SV433 ) )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2919]) ).
thf(3027,plain,
! [SV518: $i,SV501: $i,SV228: $i,SV127: $i] :
( ( ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SV501 ) @ SV518 ) )
= $false )
| ( ( in @ SV127 @ SV501 )
= $true )
| ( ( relation @ SV518 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2921]) ).
thf(3028,plain,
! [SV519: $i,SV502: $i,SV228: $i,SV127: $i] :
( ( ( in @ ( ordered_pair @ SV127 @ SV228 ) @ ( relation_composition @ ( identity_relation @ SV502 ) @ SV519 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV127 @ SV228 ) @ SV519 )
= $true )
| ( ( relation @ SV519 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2922]) ).
thf(3029,plain,
! [SV129: $i,SV439: $i,SV559: $i] :
( ( ( in @ ( ordered_pair @ SV559 @ ( sK19_C @ SV439 @ SV129 ) ) @ SV129 )
= $false )
| ( ( ~ ( in @ ( sK19_C @ SV439 @ SV129 ) @ SV439 ) )
= $true )
| ( ( SV439
= ( relation_rng @ SV129 ) )
= $true )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2923]) ).
thf(3030,plain,
! [SV440: $i,SV129: $i,SV560: $i] :
( ( ( ! [SY1153: $i] :
~ ( in @ ( ordered_pair @ SY1153 @ SV560 ) @ SV129 ) )
= $true )
| ( ( in @ SV560 @ SV440 )
= $true )
| ( ( SV440
= ( relation_rng @ SV129 ) )
= $false )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2924]) ).
thf(3031,plain,
! [SV129: $i,SV440: $i,SV561: $i] :
( ( ( ~ ( in @ SV561 @ SV440 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK18_D @ SV561 @ SV440 @ SV129 ) @ SV561 ) @ SV129 )
= $true )
| ( ( SV440
= ( relation_rng @ SV129 ) )
= $false )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2925]) ).
thf(3032,plain,
! [SV575: $i,SV131: $i,SV442: $i,SV483: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SV575 ) @ SV131 )
| ~ ( in @ SV575 @ SV442 ) )
= $true )
| ( ( ~ ( in @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SV483 ) )
= $true )
| ( ( SV483
= ( relation_inverse_image @ SV131 @ SV442 ) )
= $true )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2926]) ).
thf(3033,plain,
! [SV131: $i,SV442: $i,SV483: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ ( sK28_SY469 @ SV483 @ SV442 @ SV131 ) ) @ SV131 )
| ~ ( in @ ( sK28_SY469 @ SV483 @ SV442 @ SV131 ) @ SV442 ) )
= $false )
| ( ( in @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SV483 )
= $true )
| ( ( SV483
= ( relation_inverse_image @ SV131 @ SV442 ) )
= $true )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2927]) ).
thf(3034,plain,
! [SV484: $i,SV443: $i,SV131: $i,SV576: $i] :
( ( ( ! [SY1157: $i] :
( ~ ( in @ ( ordered_pair @ SV576 @ SY1157 ) @ SV131 )
| ~ ( in @ SY1157 @ SV443 ) )
| ( in @ SV576 @ SV484 ) )
= $true )
| ( ( SV484
= ( relation_inverse_image @ SV131 @ SV443 ) )
= $false )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2928]) ).
thf(3035,plain,
! [SV131: $i,SV443: $i,SV484: $i,SV577: $i] :
( ( ( ~ ( in @ SV577 @ SV484 )
| ~ ( ~ ( in @ ( ordered_pair @ SV577 @ ( sK26_E @ SV577 @ SV484 @ SV443 @ SV131 ) ) @ SV131 )
| ~ ( in @ ( sK26_E @ SV577 @ SV484 @ SV443 @ SV131 ) @ SV443 ) ) )
= $true )
| ( ( SV484
= ( relation_inverse_image @ SV131 @ SV443 ) )
= $false )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2929]) ).
thf(3036,plain,
! [SV562: $i,SV134: $i,SV445: $i] :
( ( ( in @ ( ordered_pair @ ( sK22_C @ SV445 @ SV134 ) @ SV562 ) @ SV134 )
= $false )
| ( ( ~ ( in @ ( sK22_C @ SV445 @ SV134 ) @ SV445 ) )
= $true )
| ( ( SV445
= ( relation_dom @ SV134 ) )
= $true )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2932]) ).
thf(3037,plain,
! [SV446: $i,SV134: $i,SV563: $i] :
( ( ( ! [SY1154: $i] :
~ ( in @ ( ordered_pair @ SV563 @ SY1154 ) @ SV134 ) )
= $true )
| ( ( in @ SV563 @ SV446 )
= $true )
| ( ( SV446
= ( relation_dom @ SV134 ) )
= $false )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2933]) ).
thf(3038,plain,
! [SV134: $i,SV446: $i,SV564: $i] :
( ( ( ~ ( in @ SV564 @ SV446 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV564 @ ( sK21_D @ SV564 @ SV446 @ SV134 ) ) @ SV134 )
= $true )
| ( ( SV446
= ( relation_dom @ SV134 ) )
= $false )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2934]) ).
thf(3039,plain,
! [SV135: $i,SV366: $i,SV404: $i] :
( ( ( ~ ( in @ ( sK57_D @ SV404 @ SV366 @ SV135 ) @ SV404 ) )
= $true )
| ( ( ( ( sK57_D @ SV404 @ SV366 @ SV135 )
!= SV135 ) )
= $true )
| ( ( SV404
= ( unordered_pair @ SV135 @ SV366 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2935]) ).
thf(3040,plain,
! [SV135: $i,SV366: $i,SV404: $i] :
( ( ( ~ ( in @ ( sK57_D @ SV404 @ SV366 @ SV135 ) @ SV404 ) )
= $true )
| ( ( ( ( sK57_D @ SV404 @ SV366 @ SV135 )
!= SV366 ) )
= $true )
| ( ( SV404
= ( unordered_pair @ SV135 @ SV366 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2936]) ).
thf(3041,plain,
! [SV367: $i,SV135: $i,SV405: $i,SV550: $i] :
( ( ( in @ SV550 @ SV405 )
= $false )
| ( ( ( SV550 = SV135 )
| ( SV550 = SV367 ) )
= $true )
| ( ( SV405
= ( unordered_pair @ SV135 @ SV367 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2937]) ).
thf(3042,plain,
! [SV367: $i,SV405: $i,SV135: $i] :
( ( ( ! [SY1020: $i] :
( ( SY1020 != SV135 )
| ( in @ SY1020 @ SV405 ) ) )
= $true )
| ( ( SV405
= ( unordered_pair @ SV135 @ SV367 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2938]) ).
thf(3043,plain,
! [SV135: $i,SV405: $i,SV367: $i] :
( ( ( ! [SY1021: $i] :
( ( SY1021 != SV367 )
| ( in @ SY1021 @ SV405 ) ) )
= $true )
| ( ( SV405
= ( unordered_pair @ SV135 @ SV367 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2939]) ).
thf(3044,plain,
! [SV136: $i,SV447: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV136 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV447 ) )
= $true )
| ( ( SV136 = SV447 )
= $true )
| ( ( relation @ SV447 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2940]) ).
thf(3045,plain,
! [SV136: $i,SV447: $i] :
( ( ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV136 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV447 )
= $true )
| ( ( SV136 = SV447 )
= $true )
| ( ( relation @ SV447 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2941]) ).
thf(3046,plain,
! [SV448: $i,SV136: $i] :
( ( ( ! [SY1076: $i,SY1077: $i] :
( ~ ( in @ ( ordered_pair @ SY1076 @ SY1077 ) @ SV136 )
| ( in @ ( ordered_pair @ SY1076 @ SY1077 ) @ SV448 ) ) )
= $true )
| ( ( SV136 = SV448 )
= $false )
| ( ( relation @ SV448 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2942]) ).
thf(3047,plain,
! [SV136: $i,SV448: $i] :
( ( ( ! [SY1078: $i,SY1079: $i] :
( ~ ( in @ ( ordered_pair @ SY1078 @ SY1079 ) @ SV448 )
| ( in @ ( ordered_pair @ SY1078 @ SY1079 ) @ SV136 ) ) )
= $true )
| ( ( SV136 = SV448 )
= $false )
| ( ( relation @ SV448 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2943]) ).
thf(3048,plain,
! [SV230: $i,SV137: $i,SV523: $i] :
( ( ( relation @ SV523 )
= $false )
| ( ( function @ SV523 )
= $false )
| ( ( ~ ( in @ SV137 @ ( relation_dom @ SV523 ) )
| ~ ( in @ ( apply @ SV523 @ SV137 ) @ ( relation_dom @ SV230 ) )
| ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SV523 @ SV230 ) ) ) )
= $true )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2946]) ).
thf(3049,plain,
! [SV230: $i,SV137: $i,SV565: $i] :
( ( ( ~ ( function @ SV565 )
| ~ ( relation @ SV565 ) )
= $true )
| ( ( ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SV565 @ SV230 ) ) )
| ( in @ SV137 @ ( relation_dom @ SV565 ) ) )
= $true )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2947]) ).
thf(3050,plain,
! [SV230: $i,SV137: $i,SV566: $i] :
( ( ( ~ ( function @ SV566 )
| ~ ( relation @ SV566 ) )
= $true )
| ( ( ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SV566 @ SV230 ) ) )
| ( in @ ( apply @ SV566 @ SV137 ) @ ( relation_dom @ SV230 ) ) )
= $true )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2948]) ).
thf(3051,plain,
! [SV551: $i,SV138: $i,SV537: $i] :
( ( ( ~ ( in @ SV537 @ ( sK41_B @ SV138 ) ) )
= $true )
| ( ( ~ ( subset @ SV551 @ SV537 ) )
= $true )
| ( ( in @ SV551 @ ( sK41_B @ SV138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2949]) ).
thf(3052,plain,
! [SV139: $i,SV449: $i] :
( ( ( in @ ( ordered_pair @ ( sK24_C @ SV449 @ SV139 ) @ ( sK25_SY467 @ SV449 @ SV139 ) ) @ SV449 )
= $false )
| ( ( subset @ SV139 @ SV449 )
= $true )
| ( ( relation @ SV449 )
= $false )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2951]) ).
thf(3053,plain,
! [SV450: $i,SV139: $i,SV567: $i,SV552: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV552 @ SV567 ) @ SV139 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV552 @ SV567 ) @ SV450 )
= $true )
| ( ( subset @ SV139 @ SV450 )
= $false )
| ( ( relation @ SV450 )
= $false )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2952]) ).
thf(3054,plain,
! [SV375: $i,SV406: $i,SV524: $i,SV142: $i] :
( ( ( in @ ( ordered_pair @ SV142 @ SV524 ) @ SV406 )
= $false )
| ( ( in @ SV524 @ ( relation_rng @ SV406 ) )
= $false )
| ( ( ~ ( in @ SV524 @ SV375 ) )
= $true )
| ( ( in @ SV142 @ ( relation_inverse_image @ SV406 @ SV375 ) )
= $true )
| ( ( relation @ SV406 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2955]) ).
thf(3055,plain,
! [SV142: $i,SV376: $i,SV407: $i] :
( ( ( ~ ( in @ ( sK39_D @ SV407 @ SV376 @ SV142 ) @ ( relation_rng @ SV407 ) )
| ~ ( in @ ( ordered_pair @ SV142 @ ( sK39_D @ SV407 @ SV376 @ SV142 ) ) @ SV407 ) )
= $false )
| ( ( in @ SV142 @ ( relation_inverse_image @ SV407 @ SV376 ) )
= $false )
| ( ( relation @ SV407 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2956]) ).
thf(3056,plain,
! [SV453: $i,SV510: $i] :
( ( ( ~ ( ~ ( in @ ( sK65_SY495 @ SV510 @ SV453 ) @ SV453 )
| ~ ~ ( in @ ( sK64_C @ SV510 @ SV453 ) @ ( sK65_SY495 @ SV510 @ SV453 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK64_C @ SV510 @ SV453 ) @ SV510 ) )
= $true )
| ( ( SV510
= ( set_meet @ SV453 ) )
= $true )
| ( ( SV453 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2958]) ).
thf(3057,plain,
! [SV510: $i,SV453: $i] :
( ( ( ! [SY1129: $i] :
( ~ ( in @ SY1129 @ SV453 )
| ( in @ ( sK64_C @ SV510 @ SV453 ) @ SY1129 ) ) )
= $true )
| ( ( in @ ( sK64_C @ SV510 @ SV453 ) @ SV510 )
= $true )
| ( ( SV510
= ( set_meet @ SV453 ) )
= $true )
| ( ( SV453 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2959]) ).
thf(3058,plain,
! [SV454: $i,SV511: $i] :
( ( ( ! [SY1130: $i] :
( ~ ( ~ ( in @ ( sK63_D @ SY1130 @ SV511 @ SV454 ) @ SV454 )
| ~ ~ ( in @ SY1130 @ ( sK63_D @ SY1130 @ SV511 @ SV454 ) ) )
| ( in @ SY1130 @ SV511 ) ) )
= $true )
| ( ( SV511
= ( set_meet @ SV454 ) )
= $false )
| ( ( SV454 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2960]) ).
thf(3059,plain,
! [SV454: $i,SV511: $i] :
( ( ( ! [SY1131: $i] :
( ~ ( in @ SY1131 @ SV511 )
| ! [SY1087: $i] :
( ~ ( in @ SY1087 @ SV454 )
| ( in @ SY1131 @ SY1087 ) ) ) )
= $true )
| ( ( SV511
= ( set_meet @ SV454 ) )
= $false )
| ( ( SV454 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2961]) ).
thf(3060,plain,
! [SV144: $i,SV378: $i,SV409: $i] :
( ( ( ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV409 ) )
= $true )
| ( ( ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV144 ) )
= $true )
| ( ( SV409
= ( set_union2 @ SV144 @ SV378 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2962]) ).
thf(3061,plain,
! [SV144: $i,SV378: $i,SV409: $i] :
( ( ( ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV409 ) )
= $true )
| ( ( ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV378 ) )
= $true )
| ( ( SV409
= ( set_union2 @ SV144 @ SV378 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2963]) ).
thf(3062,plain,
! [SV379: $i,SV144: $i,SV410: $i,SV553: $i] :
( ( ( in @ SV553 @ SV410 )
= $false )
| ( ( ( in @ SV553 @ SV144 )
| ( in @ SV553 @ SV379 ) )
= $true )
| ( ( SV410
= ( set_union2 @ SV144 @ SV379 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2964]) ).
thf(3063,plain,
! [SV379: $i,SV410: $i,SV144: $i] :
( ( ( ! [SY1025: $i] :
( ~ ( in @ SY1025 @ SV144 )
| ( in @ SY1025 @ SV410 ) ) )
= $true )
| ( ( SV410
= ( set_union2 @ SV144 @ SV379 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2965]) ).
thf(3064,plain,
! [SV144: $i,SV410: $i,SV379: $i] :
( ( ( ! [SY1026: $i] :
( ~ ( in @ SY1026 @ SV379 )
| ( in @ SY1026 @ SV410 ) ) )
= $true )
| ( ( SV410
= ( set_union2 @ SV144 @ SV379 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2966]) ).
thf(3065,plain,
! [SV380: $i,SV411: $i,SV145: $i,SV528: $i] :
( ( ( in @ ( ordered_pair @ SV528 @ SV145 ) @ SV411 )
= $false )
| ( ( in @ SV528 @ ( relation_dom @ SV411 ) )
= $false )
| ( ( ~ ( in @ SV528 @ SV380 ) )
= $true )
| ( ( in @ SV145 @ ( relation_image @ SV411 @ SV380 ) )
= $true )
| ( ( relation @ SV411 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2967]) ).
thf(3066,plain,
! [SV145: $i,SV381: $i,SV412: $i] :
( ( ( ~ ( in @ ( sK40_D @ SV412 @ SV381 @ SV145 ) @ ( relation_dom @ SV412 ) )
| ~ ( in @ ( ordered_pair @ ( sK40_D @ SV412 @ SV381 @ SV145 ) @ SV145 ) @ SV412 ) )
= $false )
| ( ( in @ SV145 @ ( relation_image @ SV412 @ SV381 ) )
= $false )
| ( ( relation @ SV412 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2968]) ).
thf(3067,plain,
! [SV149: $i,SV387: $i,SV415: $i] :
( ( ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV415 )
= $false )
| ( ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV387 )
= $true )
| ( ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV149 )
= $false )
| ( ( SV415
= ( set_difference @ SV149 @ SV387 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2970]) ).
thf(3068,plain,
! [SV149: $i,SV387: $i,SV415: $i] :
( ( ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV149 )
= $true )
| ( ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV415 )
= $true )
| ( ( SV415
= ( set_difference @ SV149 @ SV387 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2971]) ).
thf(3069,plain,
! [SV149: $i,SV387: $i,SV415: $i] :
( ( ( ~ ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV387 ) )
= $true )
| ( ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV415 )
= $true )
| ( ( SV415
= ( set_difference @ SV149 @ SV387 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2972]) ).
thf(3070,plain,
! [SV416: $i,SV388: $i,SV149: $i,SV554: $i] :
( ( ( ~ ( in @ SV554 @ SV149 ) )
= $true )
| ( ( in @ SV554 @ SV388 )
= $true )
| ( ( in @ SV554 @ SV416 )
= $true )
| ( ( SV416
= ( set_difference @ SV149 @ SV388 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2973]) ).
thf(3071,plain,
! [SV388: $i,SV149: $i,SV416: $i] :
( ( ( ! [SY1031: $i] :
( ~ ( in @ SY1031 @ SV416 )
| ( in @ SY1031 @ SV149 ) ) )
= $true )
| ( ( SV416
= ( set_difference @ SV149 @ SV388 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2974]) ).
thf(3072,plain,
! [SV149: $i,SV388: $i,SV416: $i] :
( ( ( ! [SY1032: $i] :
( ~ ( in @ SY1032 @ SV416 )
| ~ ( in @ SY1032 @ SV388 ) ) )
= $true )
| ( ( SV416
= ( set_difference @ SV149 @ SV388 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2975]) ).
thf(3073,plain,
! [SV112: $i,SV322: $i,SV390: $i] :
( ( ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV390 )
= $false )
| ( ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV112 )
= $false )
| ( ( in @ ( sK49_D @ SV390 @ SV322 @ SV112 ) @ SV322 )
= $false )
| ( ( SV390
= ( set_intersection2 @ SV112 @ SV322 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2976]) ).
thf(3074,plain,
! [SV391: $i,SV323: $i,SV112: $i,SV541: $i] :
( ( ( in @ SV541 @ SV112 )
= $false )
| ( ( ~ ( in @ SV541 @ SV323 ) )
= $true )
| ( ( in @ SV541 @ SV391 )
= $true )
| ( ( SV391
= ( set_intersection2 @ SV112 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2979]) ).
thf(3075,plain,
! [SV323: $i,SV112: $i,SV391: $i,SV578: $i] :
( ( ( ~ ( in @ SV578 @ SV391 )
| ( in @ SV578 @ SV112 ) )
= $true )
| ( ( SV391
= ( set_intersection2 @ SV112 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2980]) ).
thf(3076,plain,
! [SV112: $i,SV323: $i,SV391: $i,SV579: $i] :
( ( ( ~ ( in @ SV579 @ SV391 )
| ( in @ SV579 @ SV323 ) )
= $true )
| ( ( SV391
= ( set_intersection2 @ SV112 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2981]) ).
thf(3077,plain,
! [SV530: $i,SV258: $i,SV324: $i] :
( ( ( in @ ( sK47_C @ SV324 @ SV258 ) @ SV324 )
= $false )
| ( ( in @ ( sK47_C @ SV324 @ SV258 ) @ SV530 )
= $false )
| ( ( in @ SV530 @ SV258 )
= $false )
| ( ( SV324
= ( union @ SV258 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2982]) ).
thf(3078,plain,
! [SV325: $i,SV259: $i,SV555: $i,SV531: $i] :
( ( ( in @ SV531 @ SV555 )
= $false )
| ( ( ~ ( in @ SV555 @ SV259 ) )
= $true )
| ( ( in @ SV531 @ SV325 )
= $true )
| ( ( SV325
= ( union @ SV259 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2983]) ).
thf(3079,plain,
! [SV259: $i,SV325: $i,SV532: $i] :
( ( ( ~ ( in @ SV532 @ ( sK46_D @ SV532 @ SV325 @ SV259 ) ) )
= $false )
| ( ( in @ SV532 @ SV325 )
= $false )
| ( ( SV325
= ( union @ SV259 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2984]) ).
thf(3080,plain,
! [SV259: $i,SV325: $i,SV532: $i] :
( ( ( ~ ( in @ ( sK46_D @ SV532 @ SV325 @ SV259 ) @ SV259 ) )
= $false )
| ( ( in @ SV532 @ SV325 )
= $false )
| ( ( SV325
= ( union @ SV259 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2984]) ).
thf(3081,plain,
! [SV113: $i,SV225: $i,SV463: $i] :
( ( ( ~ ( in @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) @ SV113 )
| ~ ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV225 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 ) )
= $true )
| ( ( SV463
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $true )
| ( ( relation @ SV463 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2985]) ).
thf(3082,plain,
! [SV113: $i,SV225: $i,SV463: $i] :
( ( ( ~ ( ( in @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) @ SV113 )
| ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV225 )
| ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 ) ) )
= $false )
| ( ( SV463
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $true )
| ( ( relation @ SV463 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2986]) ).
thf(3083,plain,
! [SV464: $i,SV225: $i,SV113: $i] :
( ( ( ! [SY1094: $i,SY1095: $i] :
( ~ ( in @ SY1095 @ SV113 )
| ~ ( in @ ( ordered_pair @ SY1094 @ SY1095 ) @ SV225 )
| ( in @ ( ordered_pair @ SY1094 @ SY1095 ) @ SV464 ) ) )
= $true )
| ( ( SV464
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $false )
| ( ( relation @ SV464 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2987]) ).
thf(3084,plain,
! [SV225: $i,SV113: $i,SV464: $i] :
( ( ( ~ ( ~ ! [SY1096: $i,SY1097: $i] :
( ~ ( in @ ( ordered_pair @ SY1096 @ SY1097 ) @ SV464 )
| ( in @ SY1097 @ SV113 ) )
| ~ ! [SY1098: $i,SY1099: $i] :
( ~ ( in @ ( ordered_pair @ SY1098 @ SY1099 ) @ SV464 )
| ( in @ ( ordered_pair @ SY1098 @ SY1099 ) @ SV225 ) ) ) )
= $true )
| ( ( SV464
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $false )
| ( ( relation @ SV464 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2988]) ).
thf(3085,plain,
! [SV115: $i,SV465: $i,SV556: $i] :
( ( ( subset @ SV556 @ SV465 )
= $false )
| ( ( in @ SV556 @ ( sK43_SY481 @ SV465 @ SV115 ) )
= $true )
| ( ( ~ ( in @ SV465 @ ( sK42_B @ SV115 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2989]) ).
thf(3086,plain,
! [SV542: $i,SV115: $i,SV536: $i] :
( ( ( in @ SV536 @ ( sK42_B @ SV115 ) )
= $false )
| ( ( ~ ( subset @ SV542 @ SV536 ) )
= $true )
| ( ( in @ SV542 @ ( sK42_B @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2990]) ).
thf(3087,plain,
! [SV543: $i,SV116: $i,SV580: $i] :
( ( ( ( SV580
!= ( apply @ SV116 @ SV543 ) )
| ( in @ ( ordered_pair @ SV543 @ SV580 ) @ SV116 ) )
= $true )
| ( ( in @ SV543 @ ( relation_dom @ SV116 ) )
= $false )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2991]) ).
thf(3088,plain,
! [SV116: $i,SV581: $i,SV544: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV544 @ SV581 ) @ SV116 )
| ( SV581
= ( apply @ SV116 @ SV544 ) ) )
= $true )
| ( ( in @ SV544 @ ( relation_dom @ SV116 ) )
= $false )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2992]) ).
thf(3089,plain,
! [SV545: $i,SV116: $i,SV568: $i] :
( ( ( ( SV568
!= ( apply @ SV116 @ SV545 ) ) )
= $true )
| ( ( SV568 = empty_set )
= $true )
| ( ( in @ SV545 @ ( relation_dom @ SV116 ) )
= $true )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2993]) ).
thf(3090,plain,
! [SV546: $i,SV116: $i,SV569: $i] :
( ( ( ( SV569 != empty_set ) )
= $true )
| ( ( SV569
= ( apply @ SV116 @ SV546 ) )
= $true )
| ( ( in @ SV546 @ ( relation_dom @ SV116 ) )
= $true )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2994]) ).
thf(3091,plain,
! [SV393: $i,SV334: $i,SV557: $i,SV117: $i,SV547: $i] :
( ( ( ~ ( in @ SV547 @ SV117 ) )
= $true )
| ( ( ~ ( in @ SV557 @ SV334 ) )
= $true )
| ( ( ( ( sK53_D @ SV393 @ SV334 @ SV117 )
!= ( ordered_pair @ SV547 @ SV557 ) ) )
= $true )
| ( ( ~ ( in @ ( sK53_D @ SV393 @ SV334 @ SV117 ) @ SV393 ) )
= $true )
| ( ( SV393
= ( cartesian_product2 @ SV117 @ SV334 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2995]) ).
thf(3092,plain,
! [SV117: $i,SV334: $i,SV393: $i] :
( ( ( ~ ( in @ ( sK54_SY491 @ SV393 @ SV334 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK55_SY493 @ SV393 @ SV334 @ SV117 ) @ SV334 ) )
= $false )
| ( ( in @ ( sK53_D @ SV393 @ SV334 @ SV117 ) @ SV393 )
= $true )
| ( ( SV393
= ( cartesian_product2 @ SV117 @ SV334 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2996]) ).
thf(3093,plain,
! [SV394: $i,SV548: $i,SV335: $i,SV582: $i,SV117: $i,SV570: $i] :
( ( ( ~ ( in @ SV570 @ SV117 )
| ~ ( in @ SV582 @ SV335 )
| ( SV548
!= ( ordered_pair @ SV570 @ SV582 ) ) )
= $true )
| ( ( in @ SV548 @ SV394 )
= $true )
| ( ( SV394
= ( cartesian_product2 @ SV117 @ SV335 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2998]) ).
thf(3094,plain,
! [SV117: $i,SV335: $i,SV394: $i,SV549: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK51_E @ SV549 @ SV394 @ SV335 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK52_SY488 @ SV549 @ SV394 @ SV335 @ SV117 ) @ SV335 ) )
| ( SV549
!= ( ordered_pair @ ( sK51_E @ SV549 @ SV394 @ SV335 @ SV117 ) @ ( sK52_SY488 @ SV549 @ SV394 @ SV335 @ SV117 ) ) ) )
= $false )
| ( ( in @ SV549 @ SV394 )
= $false )
| ( ( SV394
= ( cartesian_product2 @ SV117 @ SV335 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2999]) ).
thf(3095,plain,
! [SV497: $i,SV467: $i,SV118: $i] :
( ( ( in @ ( ordered_pair @ SV118 @ SV467 ) @ SV497 )
= $false )
| ( ( SV467
= ( apply @ SV497 @ SV118 ) )
= $true )
| ( ( function @ SV497 )
= $false )
| ( ( relation @ SV497 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3001]) ).
thf(3096,plain,
! [SV498: $i,SV468: $i,SV118: $i] :
( ( ( in @ ( ordered_pair @ SV118 @ SV468 ) @ SV498 )
= $false )
| ( ( in @ SV118 @ ( relation_dom @ SV498 ) )
= $true )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3002]) ).
thf(3097,plain,
! [SV273: $i,SV339: $i] :
( ( ( in @ ( sK69_C @ SV339 @ SV273 ) @ SV273 )
= $false )
| ( ( ( sK69_C @ SV339 @ SV273 )
= ( sK70_SY500 @ SV339 @ SV273 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 ) )
= $true )
| ( ( SV339
= ( identity_relation @ SV273 ) )
= $true )
| ( ( relation @ SV339 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3003]) ).
thf(3098,plain,
! [SV273: $i,SV339: $i] :
( ( ( ( sK69_C @ SV339 @ SV273 )
= ( sK70_SY500 @ SV339 @ SV273 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 )
= $true )
| ( ( SV339
= ( identity_relation @ SV273 ) )
= $true )
| ( ( relation @ SV339 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3004]) ).
thf(3099,plain,
! [SV273: $i,SV339: $i] :
( ( ( in @ ( sK69_C @ SV339 @ SV273 ) @ SV273 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 )
= $true )
| ( ( SV339
= ( identity_relation @ SV273 ) )
= $true )
| ( ( relation @ SV339 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3005]) ).
thf(3100,plain,
! [SV340: $i,SV274: $i,SV571: $i,SV558: $i] :
( ( ( ( SV558 != SV571 )
| ~ ( in @ SV558 @ SV274 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV558 @ SV571 ) @ SV340 )
= $true )
| ( ( SV340
= ( identity_relation @ SV274 ) )
= $false )
| ( ( relation @ SV340 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3006]) ).
thf(3101,plain,
! [SV274: $i,SV340: $i] :
( ( ( ! [SY970: $i,SY971: $i] :
( ~ ( in @ ( ordered_pair @ SY970 @ SY971 ) @ SV340 )
| ( SY970 = SY971 ) ) )
= $true )
| ( ( SV340
= ( identity_relation @ SV274 ) )
= $false )
| ( ( relation @ SV340 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3007]) ).
thf(3102,plain,
! [SV274: $i,SV340: $i] :
( ( ( ! [SY972: $i] :
( ! [SY973: $i] :
~ ( in @ ( ordered_pair @ SY972 @ SY973 ) @ SV340 )
| ( in @ SY972 @ SV274 ) ) )
= $true )
| ( ( SV340
= ( identity_relation @ SV274 ) )
= $false )
| ( ( relation @ SV340 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3008]) ).
thf(3103,plain,
! [SV120: $i,SV275: $i,SV516: $i] :
( ( ( ~ ( ! [SY1135: $i] :
( ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ SY1135 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY1135 @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV275 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV516 ) ) )
= $false )
| ( ( SV516
= ( relation_composition @ SV120 @ SV275 ) )
= $true )
| ( ( relation @ SV516 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3009]) ).
thf(3104,plain,
! [SV120: $i,SV275: $i,SV516: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK15_SY461 @ SV516 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY461 @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV275 ) )
| ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV516 ) ) )
= $false )
| ( ( SV516
= ( relation_composition @ SV120 @ SV275 ) )
= $true )
| ( ( relation @ SV516 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3009]) ).
thf(3105,plain,
! [SV517: $i,SV275: $i,SV120: $i] :
( ( ( ~ ! [SY1136: $i,SY1137: $i] :
( ! [SY909: $i] :
( ~ ( in @ ( ordered_pair @ SY1136 @ SY909 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY909 @ SY1137 ) @ SV275 ) )
| ( in @ ( ordered_pair @ SY1136 @ SY1137 ) @ SV517 ) )
| ~ ! [SY1139: $i,SY1140: $i] :
( ~ ( in @ ( ordered_pair @ SY1139 @ SY1140 ) @ SV517 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1139 @ ( sK12_F @ SY1140 @ SY1139 @ SV517 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK12_F @ SY1140 @ SY1139 @ SV517 @ SV275 @ SV120 ) @ SY1140 ) @ SV275 ) ) ) )
= $false )
| ( ( SV517
= ( relation_composition @ SV120 @ SV275 ) )
= $false )
| ( ( relation @ SV517 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3010]) ).
thf(3106,plain,
! [SV123: $i,SV424: $i,SV473: $i] :
( ( ( ~ ( in @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ SV424 )
| ~ ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV123 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 ) )
= $true )
| ( ( SV473
= ( relation_dom_restriction @ SV123 @ SV424 ) )
= $true )
| ( ( relation @ SV473 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3011]) ).
thf(3107,plain,
! [SV123: $i,SV424: $i,SV473: $i] :
( ( ( ~ ( ( in @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ SV424 )
| ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 ) ) )
= $false )
| ( ( SV473
= ( relation_dom_restriction @ SV123 @ SV424 ) )
= $true )
| ( ( relation @ SV473 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3012]) ).
thf(3108,plain,
! [SV474: $i,SV123: $i,SV425: $i] :
( ( ( ! [SY1105: $i,SY1106: $i] :
( ~ ( in @ SY1105 @ SV425 )
| ~ ( in @ ( ordered_pair @ SY1105 @ SY1106 ) @ SV123 )
| ( in @ ( ordered_pair @ SY1105 @ SY1106 ) @ SV474 ) ) )
= $true )
| ( ( SV474
= ( relation_dom_restriction @ SV123 @ SV425 ) )
= $false )
| ( ( relation @ SV474 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3013]) ).
thf(3109,plain,
! [SV123: $i,SV425: $i,SV474: $i] :
( ( ( ~ ( ~ ! [SY1107: $i] :
( ! [SY1108: $i] :
~ ( in @ ( ordered_pair @ SY1107 @ SY1108 ) @ SV474 )
| ( in @ SY1107 @ SV425 ) )
| ~ ! [SY1109: $i,SY1110: $i] :
( ~ ( in @ ( ordered_pair @ SY1109 @ SY1110 ) @ SV474 )
| ( in @ ( ordered_pair @ SY1109 @ SY1110 ) @ SV123 ) ) ) )
= $true )
| ( ( SV474
= ( relation_dom_restriction @ SV123 @ SV425 ) )
= $false )
| ( ( relation @ SV474 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3014]) ).
thf(3110,plain,
! [SV124: $i,SV426: $i] :
( ( ( in @ ( ordered_pair @ ( sK16_C @ SV426 @ SV124 ) @ ( sK17_SY462 @ SV426 @ SV124 ) ) @ SV426 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK17_SY462 @ SV426 @ SV124 ) @ ( sK16_C @ SV426 @ SV124 ) ) @ SV124 ) )
= $true )
| ( ( SV426
= ( relation_inverse @ SV124 ) )
= $true )
| ( ( relation @ SV426 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3015]) ).
thf(3111,plain,
! [SV124: $i,SV427: $i,SV583: $i] :
( ( ( ! [SY1158: $i] :
( ~ ( in @ ( ordered_pair @ SV583 @ SY1158 ) @ SV427 )
| ( in @ ( ordered_pair @ SY1158 @ SV583 ) @ SV124 ) ) )
= $true )
| ( ( SV427
= ( relation_inverse @ SV124 ) )
= $false )
| ( ( relation @ SV427 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3017]) ).
thf(3112,plain,
! [SV427: $i,SV124: $i,SV584: $i] :
( ( ( ! [SY1159: $i] :
( ~ ( in @ ( ordered_pair @ SY1159 @ SV584 ) @ SV124 )
| ( in @ ( ordered_pair @ SV584 @ SY1159 ) @ SV427 ) ) )
= $true )
| ( ( SV427
= ( relation_inverse @ SV124 ) )
= $false )
| ( ( relation @ SV427 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3018]) ).
thf(3113,plain,
! [SV282: $i,SV348: $i] :
( ( ( ( relation_dom @ SV348 )
= SV282 )
= $false )
| ( ( in @ ( sK38_C @ SV348 @ SV282 ) @ SV282 )
= $true )
| ( ( SV348
= ( identity_relation @ SV282 ) )
= $true )
| ( ( function @ SV348 )
= $false )
| ( ( relation @ SV348 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3019]) ).
thf(3114,plain,
! [SV282: $i,SV348: $i] :
( ( ( ( apply @ SV348 @ ( sK38_C @ SV348 @ SV282 ) )
= ( sK38_C @ SV348 @ SV282 ) )
= $false )
| ( ( ( ( relation_dom @ SV348 )
!= SV282 ) )
= $true )
| ( ( SV348
= ( identity_relation @ SV282 ) )
= $true )
| ( ( function @ SV348 )
= $false )
| ( ( relation @ SV348 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3020]) ).
thf(3115,plain,
! [SV475: $i,SV428: $i,SV585: $i] :
( ( ( ~ ( in @ SV585 @ SV428 )
| ( ( apply @ SV475 @ SV585 )
= SV585 ) )
= $true )
| ( ( SV475
= ( identity_relation @ SV428 ) )
= $false )
| ( ( function @ SV475 )
= $false )
| ( ( relation @ SV475 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3021]) ).
thf(3116,plain,
! [SV125: $i,SV432: $i,SV479: $i,SV572: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV572 @ ( sK30_D @ SV479 @ SV432 @ SV125 ) ) @ SV125 ) )
= $true )
| ( ( ~ ( in @ SV572 @ SV432 ) )
= $true )
| ( ( ~ ( in @ ( sK30_D @ SV479 @ SV432 @ SV125 ) @ SV479 ) )
= $true )
| ( ( SV479
= ( relation_image @ SV125 @ SV432 ) )
= $true )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3023]) ).
thf(3117,plain,
! [SV125: $i,SV432: $i,SV479: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK31_SY471 @ SV479 @ SV432 @ SV125 ) @ ( sK30_D @ SV479 @ SV432 @ SV125 ) ) @ SV125 ) )
= $false )
| ( ( in @ ( sK30_D @ SV479 @ SV432 @ SV125 ) @ SV479 )
= $true )
| ( ( SV479
= ( relation_image @ SV125 @ SV432 ) )
= $true )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3024]) ).
thf(3118,plain,
! [SV125: $i,SV432: $i,SV479: $i] :
( ( ( ~ ( in @ ( sK31_SY471 @ SV479 @ SV432 @ SV125 ) @ SV432 ) )
= $false )
| ( ( in @ ( sK30_D @ SV479 @ SV432 @ SV125 ) @ SV479 )
= $true )
| ( ( SV479
= ( relation_image @ SV125 @ SV432 ) )
= $true )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3024]) ).
thf(3119,plain,
! [SV480: $i,SV433: $i,SV125: $i,SV573: $i] :
( ( ( ! [SY1156: $i] :
( ~ ( in @ ( ordered_pair @ SY1156 @ SV573 ) @ SV125 )
| ~ ( in @ SY1156 @ SV433 ) ) )
= $true )
| ( ( in @ SV573 @ SV480 )
= $true )
| ( ( SV480
= ( relation_image @ SV125 @ SV433 ) )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3025]) ).
thf(3120,plain,
! [SV125: $i,SV433: $i,SV480: $i,SV574: $i] :
( ( ( ~ ( in @ SV574 @ SV480 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK29_E @ SV574 @ SV480 @ SV433 @ SV125 ) @ SV574 ) @ SV125 )
| ~ ( in @ ( sK29_E @ SV574 @ SV480 @ SV433 @ SV125 ) @ SV433 ) ) )
= $true )
| ( ( SV480
= ( relation_image @ SV125 @ SV433 ) )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3026]) ).
thf(3121,plain,
! [SV559: $i,SV129: $i,SV439: $i] :
( ( ( in @ ( sK19_C @ SV439 @ SV129 ) @ SV439 )
= $false )
| ( ( in @ ( ordered_pair @ SV559 @ ( sK19_C @ SV439 @ SV129 ) ) @ SV129 )
= $false )
| ( ( SV439
= ( relation_rng @ SV129 ) )
= $true )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3029]) ).
thf(3122,plain,
! [SV440: $i,SV129: $i,SV560: $i,SV586: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV586 @ SV560 ) @ SV129 ) )
= $true )
| ( ( in @ SV560 @ SV440 )
= $true )
| ( ( SV440
= ( relation_rng @ SV129 ) )
= $false )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3030]) ).
thf(3123,plain,
! [SV129: $i,SV440: $i,SV561: $i] :
( ( ( in @ SV561 @ SV440 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK18_D @ SV561 @ SV440 @ SV129 ) @ SV561 ) @ SV129 )
= $true )
| ( ( SV440
= ( relation_rng @ SV129 ) )
= $false )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3031]) ).
thf(3124,plain,
! [SV575: $i,SV131: $i,SV442: $i,SV483: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SV575 ) @ SV131 ) )
= $true )
| ( ( ~ ( in @ SV575 @ SV442 ) )
= $true )
| ( ( ~ ( in @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SV483 ) )
= $true )
| ( ( SV483
= ( relation_inverse_image @ SV131 @ SV442 ) )
= $true )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3032]) ).
thf(3125,plain,
! [SV131: $i,SV442: $i,SV483: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ ( sK28_SY469 @ SV483 @ SV442 @ SV131 ) ) @ SV131 ) )
= $false )
| ( ( in @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SV483 )
= $true )
| ( ( SV483
= ( relation_inverse_image @ SV131 @ SV442 ) )
= $true )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3033]) ).
thf(3126,plain,
! [SV131: $i,SV442: $i,SV483: $i] :
( ( ( ~ ( in @ ( sK28_SY469 @ SV483 @ SV442 @ SV131 ) @ SV442 ) )
= $false )
| ( ( in @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SV483 )
= $true )
| ( ( SV483
= ( relation_inverse_image @ SV131 @ SV442 ) )
= $true )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3033]) ).
thf(3127,plain,
! [SV484: $i,SV443: $i,SV131: $i,SV576: $i] :
( ( ( ! [SY1157: $i] :
( ~ ( in @ ( ordered_pair @ SV576 @ SY1157 ) @ SV131 )
| ~ ( in @ SY1157 @ SV443 ) ) )
= $true )
| ( ( in @ SV576 @ SV484 )
= $true )
| ( ( SV484
= ( relation_inverse_image @ SV131 @ SV443 ) )
= $false )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3034]) ).
thf(3128,plain,
! [SV131: $i,SV443: $i,SV484: $i,SV577: $i] :
( ( ( ~ ( in @ SV577 @ SV484 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV577 @ ( sK26_E @ SV577 @ SV484 @ SV443 @ SV131 ) ) @ SV131 )
| ~ ( in @ ( sK26_E @ SV577 @ SV484 @ SV443 @ SV131 ) @ SV443 ) ) )
= $true )
| ( ( SV484
= ( relation_inverse_image @ SV131 @ SV443 ) )
= $false )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3035]) ).
thf(3129,plain,
! [SV562: $i,SV134: $i,SV445: $i] :
( ( ( in @ ( sK22_C @ SV445 @ SV134 ) @ SV445 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK22_C @ SV445 @ SV134 ) @ SV562 ) @ SV134 )
= $false )
| ( ( SV445
= ( relation_dom @ SV134 ) )
= $true )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3036]) ).
thf(3130,plain,
! [SV446: $i,SV134: $i,SV587: $i,SV563: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV563 @ SV587 ) @ SV134 ) )
= $true )
| ( ( in @ SV563 @ SV446 )
= $true )
| ( ( SV446
= ( relation_dom @ SV134 ) )
= $false )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3037]) ).
thf(3131,plain,
! [SV134: $i,SV446: $i,SV564: $i] :
( ( ( in @ SV564 @ SV446 )
= $false )
| ( ( in @ ( ordered_pair @ SV564 @ ( sK21_D @ SV564 @ SV446 @ SV134 ) ) @ SV134 )
= $true )
| ( ( SV446
= ( relation_dom @ SV134 ) )
= $false )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3038]) ).
thf(3132,plain,
! [SV135: $i,SV366: $i,SV404: $i] :
( ( ( in @ ( sK57_D @ SV404 @ SV366 @ SV135 ) @ SV404 )
= $false )
| ( ( ( ( sK57_D @ SV404 @ SV366 @ SV135 )
!= SV135 ) )
= $true )
| ( ( SV404
= ( unordered_pair @ SV135 @ SV366 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3039]) ).
thf(3133,plain,
! [SV135: $i,SV366: $i,SV404: $i] :
( ( ( in @ ( sK57_D @ SV404 @ SV366 @ SV135 ) @ SV404 )
= $false )
| ( ( ( ( sK57_D @ SV404 @ SV366 @ SV135 )
!= SV366 ) )
= $true )
| ( ( SV404
= ( unordered_pair @ SV135 @ SV366 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3040]) ).
thf(3134,plain,
! [SV405: $i,SV367: $i,SV135: $i,SV550: $i] :
( ( ( SV550 = SV135 )
= $true )
| ( ( SV550 = SV367 )
= $true )
| ( ( in @ SV550 @ SV405 )
= $false )
| ( ( SV405
= ( unordered_pair @ SV135 @ SV367 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3041]) ).
thf(3135,plain,
! [SV367: $i,SV405: $i,SV135: $i,SV588: $i] :
( ( ( ( SV588 != SV135 )
| ( in @ SV588 @ SV405 ) )
= $true )
| ( ( SV405
= ( unordered_pair @ SV135 @ SV367 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3042]) ).
thf(3136,plain,
! [SV135: $i,SV405: $i,SV367: $i,SV589: $i] :
( ( ( ( SV589 != SV367 )
| ( in @ SV589 @ SV405 ) )
= $true )
| ( ( SV405
= ( unordered_pair @ SV135 @ SV367 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3043]) ).
thf(3137,plain,
! [SV136: $i,SV447: $i] :
( ( ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV136 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV447 ) )
= $true )
| ( ( SV136 = SV447 )
= $true )
| ( ( relation @ SV447 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3044]) ).
thf(3138,plain,
! [SV448: $i,SV136: $i,SV590: $i] :
( ( ( ! [SY1160: $i] :
( ~ ( in @ ( ordered_pair @ SV590 @ SY1160 ) @ SV136 )
| ( in @ ( ordered_pair @ SV590 @ SY1160 ) @ SV448 ) ) )
= $true )
| ( ( SV136 = SV448 )
= $false )
| ( ( relation @ SV448 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3046]) ).
thf(3139,plain,
! [SV136: $i,SV448: $i,SV591: $i] :
( ( ( ! [SY1161: $i] :
( ~ ( in @ ( ordered_pair @ SV591 @ SY1161 ) @ SV448 )
| ( in @ ( ordered_pair @ SV591 @ SY1161 ) @ SV136 ) ) )
= $true )
| ( ( SV136 = SV448 )
= $false )
| ( ( relation @ SV448 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3047]) ).
thf(3140,plain,
! [SV230: $i,SV523: $i,SV137: $i] :
( ( ( ~ ( in @ SV137 @ ( relation_dom @ SV523 ) )
| ~ ( in @ ( apply @ SV523 @ SV137 ) @ ( relation_dom @ SV230 ) ) )
= $true )
| ( ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SV523 @ SV230 ) ) )
= $true )
| ( ( function @ SV523 )
= $false )
| ( ( relation @ SV523 )
= $false )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3048]) ).
thf(3141,plain,
! [SV230: $i,SV137: $i,SV565: $i] :
( ( ( ~ ( function @ SV565 ) )
= $true )
| ( ( ~ ( relation @ SV565 ) )
= $true )
| ( ( ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SV565 @ SV230 ) ) )
| ( in @ SV137 @ ( relation_dom @ SV565 ) ) )
= $true )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3049]) ).
thf(3142,plain,
! [SV230: $i,SV137: $i,SV566: $i] :
( ( ( ~ ( function @ SV566 ) )
= $true )
| ( ( ~ ( relation @ SV566 ) )
= $true )
| ( ( ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SV566 @ SV230 ) ) )
| ( in @ ( apply @ SV566 @ SV137 ) @ ( relation_dom @ SV230 ) ) )
= $true )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3050]) ).
thf(3143,plain,
! [SV551: $i,SV138: $i,SV537: $i] :
( ( ( in @ SV537 @ ( sK41_B @ SV138 ) )
= $false )
| ( ( ~ ( subset @ SV551 @ SV537 ) )
= $true )
| ( ( in @ SV551 @ ( sK41_B @ SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3051]) ).
thf(3144,plain,
! [SV450: $i,SV139: $i,SV567: $i,SV552: $i] :
( ( ( in @ ( ordered_pair @ SV552 @ SV567 ) @ SV139 )
= $false )
| ( ( in @ ( ordered_pair @ SV552 @ SV567 ) @ SV450 )
= $true )
| ( ( subset @ SV139 @ SV450 )
= $false )
| ( ( relation @ SV450 )
= $false )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3053]) ).
thf(3145,plain,
! [SV142: $i,SV406: $i,SV375: $i,SV524: $i] :
( ( ( in @ SV524 @ SV375 )
= $false )
| ( ( in @ SV524 @ ( relation_rng @ SV406 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV142 @ SV524 ) @ SV406 )
= $false )
| ( ( in @ SV142 @ ( relation_inverse_image @ SV406 @ SV375 ) )
= $true )
| ( ( relation @ SV406 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3054]) ).
thf(3146,plain,
! [SV142: $i,SV376: $i,SV407: $i] :
( ( ( ~ ( in @ ( sK39_D @ SV407 @ SV376 @ SV142 ) @ ( relation_rng @ SV407 ) ) )
= $false )
| ( ( in @ SV142 @ ( relation_inverse_image @ SV407 @ SV376 ) )
= $false )
| ( ( relation @ SV407 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3055]) ).
thf(3147,plain,
! [SV376: $i,SV407: $i,SV142: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV142 @ ( sK39_D @ SV407 @ SV376 @ SV142 ) ) @ SV407 ) )
= $false )
| ( ( in @ SV142 @ ( relation_inverse_image @ SV407 @ SV376 ) )
= $false )
| ( ( relation @ SV407 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3055]) ).
thf(3148,plain,
! [SV453: $i,SV510: $i] :
( ( ( ~ ( in @ ( sK65_SY495 @ SV510 @ SV453 ) @ SV453 )
| ~ ~ ( in @ ( sK64_C @ SV510 @ SV453 ) @ ( sK65_SY495 @ SV510 @ SV453 ) ) )
= $false )
| ( ( ~ ( in @ ( sK64_C @ SV510 @ SV453 ) @ SV510 ) )
= $true )
| ( ( SV510
= ( set_meet @ SV453 ) )
= $true )
| ( ( SV453 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3056]) ).
thf(3149,plain,
! [SV510: $i,SV453: $i,SV592: $i] :
( ( ( ~ ( in @ SV592 @ SV453 )
| ( in @ ( sK64_C @ SV510 @ SV453 ) @ SV592 ) )
= $true )
| ( ( in @ ( sK64_C @ SV510 @ SV453 ) @ SV510 )
= $true )
| ( ( SV510
= ( set_meet @ SV453 ) )
= $true )
| ( ( SV453 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3057]) ).
thf(3150,plain,
! [SV454: $i,SV511: $i,SV593: $i] :
( ( ( ~ ( ~ ( in @ ( sK63_D @ SV593 @ SV511 @ SV454 ) @ SV454 )
| ~ ~ ( in @ SV593 @ ( sK63_D @ SV593 @ SV511 @ SV454 ) ) )
| ( in @ SV593 @ SV511 ) )
= $true )
| ( ( SV511
= ( set_meet @ SV454 ) )
= $false )
| ( ( SV454 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3058]) ).
thf(3151,plain,
! [SV454: $i,SV511: $i,SV594: $i] :
( ( ( ~ ( in @ SV594 @ SV511 )
| ! [SY1162: $i] :
( ~ ( in @ SY1162 @ SV454 )
| ( in @ SV594 @ SY1162 ) ) )
= $true )
| ( ( SV511
= ( set_meet @ SV454 ) )
= $false )
| ( ( SV454 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3059]) ).
thf(3152,plain,
! [SV144: $i,SV378: $i,SV409: $i] :
( ( ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV409 )
= $false )
| ( ( ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV144 ) )
= $true )
| ( ( SV409
= ( set_union2 @ SV144 @ SV378 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3060]) ).
thf(3153,plain,
! [SV144: $i,SV378: $i,SV409: $i] :
( ( ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV409 )
= $false )
| ( ( ~ ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV378 ) )
= $true )
| ( ( SV409
= ( set_union2 @ SV144 @ SV378 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3061]) ).
thf(3154,plain,
! [SV410: $i,SV379: $i,SV144: $i,SV553: $i] :
( ( ( in @ SV553 @ SV144 )
= $true )
| ( ( in @ SV553 @ SV379 )
= $true )
| ( ( in @ SV553 @ SV410 )
= $false )
| ( ( SV410
= ( set_union2 @ SV144 @ SV379 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3062]) ).
thf(3155,plain,
! [SV379: $i,SV410: $i,SV144: $i,SV595: $i] :
( ( ( ~ ( in @ SV595 @ SV144 )
| ( in @ SV595 @ SV410 ) )
= $true )
| ( ( SV410
= ( set_union2 @ SV144 @ SV379 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3063]) ).
thf(3156,plain,
! [SV144: $i,SV410: $i,SV379: $i,SV596: $i] :
( ( ( ~ ( in @ SV596 @ SV379 )
| ( in @ SV596 @ SV410 ) )
= $true )
| ( ( SV410
= ( set_union2 @ SV144 @ SV379 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3064]) ).
thf(3157,plain,
! [SV145: $i,SV411: $i,SV380: $i,SV528: $i] :
( ( ( in @ SV528 @ SV380 )
= $false )
| ( ( in @ SV528 @ ( relation_dom @ SV411 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV528 @ SV145 ) @ SV411 )
= $false )
| ( ( in @ SV145 @ ( relation_image @ SV411 @ SV380 ) )
= $true )
| ( ( relation @ SV411 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3065]) ).
thf(3158,plain,
! [SV145: $i,SV381: $i,SV412: $i] :
( ( ( ~ ( in @ ( sK40_D @ SV412 @ SV381 @ SV145 ) @ ( relation_dom @ SV412 ) ) )
= $false )
| ( ( in @ SV145 @ ( relation_image @ SV412 @ SV381 ) )
= $false )
| ( ( relation @ SV412 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3066]) ).
thf(3159,plain,
! [SV145: $i,SV381: $i,SV412: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK40_D @ SV412 @ SV381 @ SV145 ) @ SV145 ) @ SV412 ) )
= $false )
| ( ( in @ SV145 @ ( relation_image @ SV412 @ SV381 ) )
= $false )
| ( ( relation @ SV412 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3066]) ).
thf(3160,plain,
! [SV149: $i,SV387: $i,SV415: $i] :
( ( ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV387 )
= $false )
| ( ( in @ ( sK45_D @ SV415 @ SV387 @ SV149 ) @ SV415 )
= $true )
| ( ( SV415
= ( set_difference @ SV149 @ SV387 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3069]) ).
thf(3161,plain,
! [SV416: $i,SV388: $i,SV149: $i,SV554: $i] :
( ( ( in @ SV554 @ SV149 )
= $false )
| ( ( in @ SV554 @ SV388 )
= $true )
| ( ( in @ SV554 @ SV416 )
= $true )
| ( ( SV416
= ( set_difference @ SV149 @ SV388 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3070]) ).
thf(3162,plain,
! [SV388: $i,SV149: $i,SV416: $i,SV597: $i] :
( ( ( ~ ( in @ SV597 @ SV416 )
| ( in @ SV597 @ SV149 ) )
= $true )
| ( ( SV416
= ( set_difference @ SV149 @ SV388 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3071]) ).
thf(3163,plain,
! [SV149: $i,SV388: $i,SV416: $i,SV598: $i] :
( ( ( ~ ( in @ SV598 @ SV416 )
| ~ ( in @ SV598 @ SV388 ) )
= $true )
| ( ( SV416
= ( set_difference @ SV149 @ SV388 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3072]) ).
thf(3164,plain,
! [SV391: $i,SV112: $i,SV323: $i,SV541: $i] :
( ( ( in @ SV541 @ SV323 )
= $false )
| ( ( in @ SV541 @ SV112 )
= $false )
| ( ( in @ SV541 @ SV391 )
= $true )
| ( ( SV391
= ( set_intersection2 @ SV112 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3074]) ).
thf(3165,plain,
! [SV323: $i,SV112: $i,SV391: $i,SV578: $i] :
( ( ( ~ ( in @ SV578 @ SV391 ) )
= $true )
| ( ( in @ SV578 @ SV112 )
= $true )
| ( ( SV391
= ( set_intersection2 @ SV112 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3075]) ).
thf(3166,plain,
! [SV112: $i,SV323: $i,SV391: $i,SV579: $i] :
( ( ( ~ ( in @ SV579 @ SV391 ) )
= $true )
| ( ( in @ SV579 @ SV323 )
= $true )
| ( ( SV391
= ( set_intersection2 @ SV112 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3076]) ).
thf(3167,plain,
! [SV325: $i,SV531: $i,SV259: $i,SV555: $i] :
( ( ( in @ SV555 @ SV259 )
= $false )
| ( ( in @ SV531 @ SV555 )
= $false )
| ( ( in @ SV531 @ SV325 )
= $true )
| ( ( SV325
= ( union @ SV259 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3078]) ).
thf(3168,plain,
! [SV259: $i,SV325: $i,SV532: $i] :
( ( ( in @ SV532 @ ( sK46_D @ SV532 @ SV325 @ SV259 ) )
= $true )
| ( ( in @ SV532 @ SV325 )
= $false )
| ( ( SV325
= ( union @ SV259 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3079]) ).
thf(3169,plain,
! [SV259: $i,SV325: $i,SV532: $i] :
( ( ( in @ ( sK46_D @ SV532 @ SV325 @ SV259 ) @ SV259 )
= $true )
| ( ( in @ SV532 @ SV325 )
= $false )
| ( ( SV325
= ( union @ SV259 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3080]) ).
thf(3170,plain,
! [SV113: $i,SV225: $i,SV463: $i] :
( ( ( ~ ( in @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) @ SV113 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV225 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 ) )
= $true )
| ( ( SV463
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $true )
| ( ( relation @ SV463 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3081]) ).
thf(3171,plain,
! [SV113: $i,SV225: $i,SV463: $i] :
( ( ( ~ ( ( in @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) @ SV113 )
| ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 ) ) )
= $false )
| ( ( SV463
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $true )
| ( ( relation @ SV463 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3082]) ).
thf(3172,plain,
! [SV113: $i,SV225: $i,SV463: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV225 )
| ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 ) ) )
= $false )
| ( ( SV463
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $true )
| ( ( relation @ SV463 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3082]) ).
thf(3173,plain,
! [SV464: $i,SV225: $i,SV599: $i,SV113: $i] :
( ( ( ! [SY1163: $i] :
( ~ ( in @ SY1163 @ SV113 )
| ~ ( in @ ( ordered_pair @ SV599 @ SY1163 ) @ SV225 )
| ( in @ ( ordered_pair @ SV599 @ SY1163 ) @ SV464 ) ) )
= $true )
| ( ( SV464
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $false )
| ( ( relation @ SV464 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3083]) ).
thf(3174,plain,
! [SV225: $i,SV113: $i,SV464: $i] :
( ( ( ~ ! [SY1096: $i,SY1097: $i] :
( ~ ( in @ ( ordered_pair @ SY1096 @ SY1097 ) @ SV464 )
| ( in @ SY1097 @ SV113 ) )
| ~ ! [SY1098: $i,SY1099: $i] :
( ~ ( in @ ( ordered_pair @ SY1098 @ SY1099 ) @ SV464 )
| ( in @ ( ordered_pair @ SY1098 @ SY1099 ) @ SV225 ) ) )
= $false )
| ( ( SV464
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $false )
| ( ( relation @ SV464 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3084]) ).
thf(3175,plain,
! [SV556: $i,SV115: $i,SV465: $i] :
( ( ( in @ SV465 @ ( sK42_B @ SV115 ) )
= $false )
| ( ( in @ SV556 @ ( sK43_SY481 @ SV465 @ SV115 ) )
= $true )
| ( ( subset @ SV556 @ SV465 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3085]) ).
thf(3176,plain,
! [SV115: $i,SV536: $i,SV542: $i] :
( ( ( subset @ SV542 @ SV536 )
= $false )
| ( ( in @ SV536 @ ( sK42_B @ SV115 ) )
= $false )
| ( ( in @ SV542 @ ( sK42_B @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3086]) ).
thf(3177,plain,
! [SV543: $i,SV116: $i,SV580: $i] :
( ( ( ( SV580
!= ( apply @ SV116 @ SV543 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV543 @ SV580 ) @ SV116 )
= $true )
| ( ( in @ SV543 @ ( relation_dom @ SV116 ) )
= $false )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3087]) ).
thf(3178,plain,
! [SV116: $i,SV581: $i,SV544: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV544 @ SV581 ) @ SV116 ) )
= $true )
| ( ( SV581
= ( apply @ SV116 @ SV544 ) )
= $true )
| ( ( in @ SV544 @ ( relation_dom @ SV116 ) )
= $false )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3088]) ).
thf(3179,plain,
! [SV545: $i,SV116: $i,SV568: $i] :
( ( ( SV568
= ( apply @ SV116 @ SV545 ) )
= $false )
| ( ( SV568 = empty_set )
= $true )
| ( ( in @ SV545 @ ( relation_dom @ SV116 ) )
= $true )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3089]) ).
thf(3180,plain,
! [SV546: $i,SV116: $i,SV569: $i] :
( ( ( SV569 = empty_set )
= $false )
| ( ( SV569
= ( apply @ SV116 @ SV546 ) )
= $true )
| ( ( in @ SV546 @ ( relation_dom @ SV116 ) )
= $true )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3090]) ).
thf(3181,plain,
! [SV393: $i,SV334: $i,SV557: $i,SV117: $i,SV547: $i] :
( ( ( in @ SV547 @ SV117 )
= $false )
| ( ( ~ ( in @ SV557 @ SV334 ) )
= $true )
| ( ( ( ( sK53_D @ SV393 @ SV334 @ SV117 )
!= ( ordered_pair @ SV547 @ SV557 ) ) )
= $true )
| ( ( ~ ( in @ ( sK53_D @ SV393 @ SV334 @ SV117 ) @ SV393 ) )
= $true )
| ( ( SV393
= ( cartesian_product2 @ SV117 @ SV334 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3091]) ).
thf(3182,plain,
! [SV117: $i,SV334: $i,SV393: $i] :
( ( ( ~ ( in @ ( sK54_SY491 @ SV393 @ SV334 @ SV117 ) @ SV117 ) )
= $false )
| ( ( in @ ( sK53_D @ SV393 @ SV334 @ SV117 ) @ SV393 )
= $true )
| ( ( SV393
= ( cartesian_product2 @ SV117 @ SV334 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3092]) ).
thf(3183,plain,
! [SV117: $i,SV334: $i,SV393: $i] :
( ( ( ~ ( in @ ( sK55_SY493 @ SV393 @ SV334 @ SV117 ) @ SV334 ) )
= $false )
| ( ( in @ ( sK53_D @ SV393 @ SV334 @ SV117 ) @ SV393 )
= $true )
| ( ( SV393
= ( cartesian_product2 @ SV117 @ SV334 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3092]) ).
thf(3184,plain,
! [SV394: $i,SV548: $i,SV335: $i,SV582: $i,SV117: $i,SV570: $i] :
( ( ( ~ ( in @ SV570 @ SV117 )
| ~ ( in @ SV582 @ SV335 ) )
= $true )
| ( ( ( SV548
!= ( ordered_pair @ SV570 @ SV582 ) ) )
= $true )
| ( ( in @ SV548 @ SV394 )
= $true )
| ( ( SV394
= ( cartesian_product2 @ SV117 @ SV335 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3093]) ).
thf(3185,plain,
! [SV117: $i,SV335: $i,SV394: $i,SV549: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK51_E @ SV549 @ SV394 @ SV335 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK52_SY488 @ SV549 @ SV394 @ SV335 @ SV117 ) @ SV335 ) ) )
= $false )
| ( ( in @ SV549 @ SV394 )
= $false )
| ( ( SV394
= ( cartesian_product2 @ SV117 @ SV335 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3094]) ).
thf(3186,plain,
! [SV117: $i,SV335: $i,SV394: $i,SV549: $i] :
( ( ( ( SV549
!= ( ordered_pair @ ( sK51_E @ SV549 @ SV394 @ SV335 @ SV117 ) @ ( sK52_SY488 @ SV549 @ SV394 @ SV335 @ SV117 ) ) ) )
= $false )
| ( ( in @ SV549 @ SV394 )
= $false )
| ( ( SV394
= ( cartesian_product2 @ SV117 @ SV335 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3094]) ).
thf(3187,plain,
! [SV273: $i,SV339: $i] :
( ( ( in @ ( ordered_pair @ ( sK69_C @ SV339 @ SV273 ) @ ( sK70_SY500 @ SV339 @ SV273 ) ) @ SV339 )
= $false )
| ( ( ( sK69_C @ SV339 @ SV273 )
= ( sK70_SY500 @ SV339 @ SV273 ) )
= $false )
| ( ( in @ ( sK69_C @ SV339 @ SV273 ) @ SV273 )
= $false )
| ( ( SV339
= ( identity_relation @ SV273 ) )
= $true )
| ( ( relation @ SV339 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3097]) ).
thf(3188,plain,
! [SV340: $i,SV274: $i,SV571: $i,SV558: $i] :
( ( ( ( SV558 != SV571 ) )
= $true )
| ( ( ~ ( in @ SV558 @ SV274 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV558 @ SV571 ) @ SV340 )
= $true )
| ( ( SV340
= ( identity_relation @ SV274 ) )
= $false )
| ( ( relation @ SV340 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3100]) ).
thf(3189,plain,
! [SV274: $i,SV340: $i,SV600: $i] :
( ( ( ! [SY1164: $i] :
( ~ ( in @ ( ordered_pair @ SV600 @ SY1164 ) @ SV340 )
| ( SV600 = SY1164 ) ) )
= $true )
| ( ( SV340
= ( identity_relation @ SV274 ) )
= $false )
| ( ( relation @ SV340 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3101]) ).
thf(3190,plain,
! [SV274: $i,SV340: $i,SV601: $i] :
( ( ( ! [SY1165: $i] :
~ ( in @ ( ordered_pair @ SV601 @ SY1165 ) @ SV340 )
| ( in @ SV601 @ SV274 ) )
= $true )
| ( ( SV340
= ( identity_relation @ SV274 ) )
= $false )
| ( ( relation @ SV340 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3102]) ).
thf(3191,plain,
! [SV120: $i,SV275: $i,SV516: $i] :
( ( ( ! [SY1135: $i] :
( ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ SY1135 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY1135 @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV275 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV516 ) )
= $true )
| ( ( SV516
= ( relation_composition @ SV120 @ SV275 ) )
= $true )
| ( ( relation @ SV516 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3103]) ).
thf(3192,plain,
! [SV120: $i,SV275: $i,SV516: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK15_SY461 @ SV516 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY461 @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV275 ) )
| ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV516 ) )
= $true )
| ( ( SV516
= ( relation_composition @ SV120 @ SV275 ) )
= $true )
| ( ( relation @ SV516 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3104]) ).
thf(3193,plain,
! [SV517: $i,SV275: $i,SV120: $i] :
( ( ( ~ ! [SY1136: $i,SY1137: $i] :
( ! [SY909: $i] :
( ~ ( in @ ( ordered_pair @ SY1136 @ SY909 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY909 @ SY1137 ) @ SV275 ) )
| ( in @ ( ordered_pair @ SY1136 @ SY1137 ) @ SV517 ) ) )
= $false )
| ( ( SV517
= ( relation_composition @ SV120 @ SV275 ) )
= $false )
| ( ( relation @ SV517 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3105]) ).
thf(3194,plain,
! [SV120: $i,SV275: $i,SV517: $i] :
( ( ( ~ ! [SY1139: $i,SY1140: $i] :
( ~ ( in @ ( ordered_pair @ SY1139 @ SY1140 ) @ SV517 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1139 @ ( sK12_F @ SY1140 @ SY1139 @ SV517 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK12_F @ SY1140 @ SY1139 @ SV517 @ SV275 @ SV120 ) @ SY1140 ) @ SV275 ) ) ) )
= $false )
| ( ( SV517
= ( relation_composition @ SV120 @ SV275 ) )
= $false )
| ( ( relation @ SV517 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3105]) ).
thf(3195,plain,
! [SV123: $i,SV424: $i,SV473: $i] :
( ( ( ~ ( in @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ SV424 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV123 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 ) )
= $true )
| ( ( SV473
= ( relation_dom_restriction @ SV123 @ SV424 ) )
= $true )
| ( ( relation @ SV473 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3106]) ).
thf(3196,plain,
! [SV123: $i,SV424: $i,SV473: $i] :
( ( ( ~ ( ( in @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ SV424 )
| ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 ) ) )
= $false )
| ( ( SV473
= ( relation_dom_restriction @ SV123 @ SV424 ) )
= $true )
| ( ( relation @ SV473 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3107]) ).
thf(3197,plain,
! [SV123: $i,SV424: $i,SV473: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 ) ) )
= $false )
| ( ( SV473
= ( relation_dom_restriction @ SV123 @ SV424 ) )
= $true )
| ( ( relation @ SV473 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3107]) ).
thf(3198,plain,
! [SV474: $i,SV123: $i,SV425: $i,SV602: $i] :
( ( ( ! [SY1166: $i] :
( ~ ( in @ SV602 @ SV425 )
| ~ ( in @ ( ordered_pair @ SV602 @ SY1166 ) @ SV123 )
| ( in @ ( ordered_pair @ SV602 @ SY1166 ) @ SV474 ) ) )
= $true )
| ( ( SV474
= ( relation_dom_restriction @ SV123 @ SV425 ) )
= $false )
| ( ( relation @ SV474 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3108]) ).
thf(3199,plain,
! [SV123: $i,SV425: $i,SV474: $i] :
( ( ( ~ ! [SY1107: $i] :
( ! [SY1108: $i] :
~ ( in @ ( ordered_pair @ SY1107 @ SY1108 ) @ SV474 )
| ( in @ SY1107 @ SV425 ) )
| ~ ! [SY1109: $i,SY1110: $i] :
( ~ ( in @ ( ordered_pair @ SY1109 @ SY1110 ) @ SV474 )
| ( in @ ( ordered_pair @ SY1109 @ SY1110 ) @ SV123 ) ) )
= $false )
| ( ( SV474
= ( relation_dom_restriction @ SV123 @ SV425 ) )
= $false )
| ( ( relation @ SV474 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3109]) ).
thf(3200,plain,
! [SV124: $i,SV426: $i] :
( ( ( in @ ( ordered_pair @ ( sK17_SY462 @ SV426 @ SV124 ) @ ( sK16_C @ SV426 @ SV124 ) ) @ SV124 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK16_C @ SV426 @ SV124 ) @ ( sK17_SY462 @ SV426 @ SV124 ) ) @ SV426 )
= $false )
| ( ( SV426
= ( relation_inverse @ SV124 ) )
= $true )
| ( ( relation @ SV426 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3110]) ).
thf(3201,plain,
! [SV124: $i,SV427: $i,SV603: $i,SV583: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV583 @ SV603 ) @ SV427 )
| ( in @ ( ordered_pair @ SV603 @ SV583 ) @ SV124 ) )
= $true )
| ( ( SV427
= ( relation_inverse @ SV124 ) )
= $false )
| ( ( relation @ SV427 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3111]) ).
thf(3202,plain,
! [SV427: $i,SV124: $i,SV584: $i,SV604: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV604 @ SV584 ) @ SV124 )
| ( in @ ( ordered_pair @ SV584 @ SV604 ) @ SV427 ) )
= $true )
| ( ( SV427
= ( relation_inverse @ SV124 ) )
= $false )
| ( ( relation @ SV427 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3112]) ).
thf(3203,plain,
! [SV282: $i,SV348: $i] :
( ( ( ( relation_dom @ SV348 )
= SV282 )
= $false )
| ( ( ( apply @ SV348 @ ( sK38_C @ SV348 @ SV282 ) )
= ( sK38_C @ SV348 @ SV282 ) )
= $false )
| ( ( SV348
= ( identity_relation @ SV282 ) )
= $true )
| ( ( function @ SV348 )
= $false )
| ( ( relation @ SV348 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3114]) ).
thf(3204,plain,
! [SV475: $i,SV428: $i,SV585: $i] :
( ( ( ~ ( in @ SV585 @ SV428 ) )
= $true )
| ( ( ( apply @ SV475 @ SV585 )
= SV585 )
= $true )
| ( ( SV475
= ( identity_relation @ SV428 ) )
= $false )
| ( ( function @ SV475 )
= $false )
| ( ( relation @ SV475 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3115]) ).
thf(3205,plain,
! [SV125: $i,SV432: $i,SV479: $i,SV572: $i] :
( ( ( in @ ( ordered_pair @ SV572 @ ( sK30_D @ SV479 @ SV432 @ SV125 ) ) @ SV125 )
= $false )
| ( ( ~ ( in @ SV572 @ SV432 ) )
= $true )
| ( ( ~ ( in @ ( sK30_D @ SV479 @ SV432 @ SV125 ) @ SV479 ) )
= $true )
| ( ( SV479
= ( relation_image @ SV125 @ SV432 ) )
= $true )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3116]) ).
thf(3206,plain,
! [SV125: $i,SV432: $i,SV479: $i] :
( ( ( in @ ( ordered_pair @ ( sK31_SY471 @ SV479 @ SV432 @ SV125 ) @ ( sK30_D @ SV479 @ SV432 @ SV125 ) ) @ SV125 )
= $true )
| ( ( in @ ( sK30_D @ SV479 @ SV432 @ SV125 ) @ SV479 )
= $true )
| ( ( SV479
= ( relation_image @ SV125 @ SV432 ) )
= $true )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3117]) ).
thf(3207,plain,
! [SV125: $i,SV432: $i,SV479: $i] :
( ( ( in @ ( sK31_SY471 @ SV479 @ SV432 @ SV125 ) @ SV432 )
= $true )
| ( ( in @ ( sK30_D @ SV479 @ SV432 @ SV125 ) @ SV479 )
= $true )
| ( ( SV479
= ( relation_image @ SV125 @ SV432 ) )
= $true )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3118]) ).
thf(3208,plain,
! [SV480: $i,SV433: $i,SV125: $i,SV573: $i,SV605: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV605 @ SV573 ) @ SV125 )
| ~ ( in @ SV605 @ SV433 ) )
= $true )
| ( ( in @ SV573 @ SV480 )
= $true )
| ( ( SV480
= ( relation_image @ SV125 @ SV433 ) )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3119]) ).
thf(3209,plain,
! [SV125: $i,SV433: $i,SV480: $i,SV574: $i] :
( ( ( in @ SV574 @ SV480 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK29_E @ SV574 @ SV480 @ SV433 @ SV125 ) @ SV574 ) @ SV125 )
| ~ ( in @ ( sK29_E @ SV574 @ SV480 @ SV433 @ SV125 ) @ SV433 ) ) )
= $true )
| ( ( SV480
= ( relation_image @ SV125 @ SV433 ) )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3120]) ).
thf(3210,plain,
! [SV440: $i,SV129: $i,SV560: $i,SV586: $i] :
( ( ( in @ ( ordered_pair @ SV586 @ SV560 ) @ SV129 )
= $false )
| ( ( in @ SV560 @ SV440 )
= $true )
| ( ( SV440
= ( relation_rng @ SV129 ) )
= $false )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3122]) ).
thf(3211,plain,
! [SV575: $i,SV131: $i,SV442: $i,SV483: $i] :
( ( ( in @ ( ordered_pair @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SV575 ) @ SV131 )
= $false )
| ( ( ~ ( in @ SV575 @ SV442 ) )
= $true )
| ( ( ~ ( in @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SV483 ) )
= $true )
| ( ( SV483
= ( relation_inverse_image @ SV131 @ SV442 ) )
= $true )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3124]) ).
thf(3212,plain,
! [SV131: $i,SV442: $i,SV483: $i] :
( ( ( in @ ( ordered_pair @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ ( sK28_SY469 @ SV483 @ SV442 @ SV131 ) ) @ SV131 )
= $true )
| ( ( in @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SV483 )
= $true )
| ( ( SV483
= ( relation_inverse_image @ SV131 @ SV442 ) )
= $true )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3125]) ).
thf(3213,plain,
! [SV131: $i,SV442: $i,SV483: $i] :
( ( ( in @ ( sK28_SY469 @ SV483 @ SV442 @ SV131 ) @ SV442 )
= $true )
| ( ( in @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SV483 )
= $true )
| ( ( SV483
= ( relation_inverse_image @ SV131 @ SV442 ) )
= $true )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3126]) ).
thf(3214,plain,
! [SV484: $i,SV443: $i,SV131: $i,SV606: $i,SV576: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV576 @ SV606 ) @ SV131 )
| ~ ( in @ SV606 @ SV443 ) )
= $true )
| ( ( in @ SV576 @ SV484 )
= $true )
| ( ( SV484
= ( relation_inverse_image @ SV131 @ SV443 ) )
= $false )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3127]) ).
thf(3215,plain,
! [SV131: $i,SV443: $i,SV484: $i,SV577: $i] :
( ( ( in @ SV577 @ SV484 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV577 @ ( sK26_E @ SV577 @ SV484 @ SV443 @ SV131 ) ) @ SV131 )
| ~ ( in @ ( sK26_E @ SV577 @ SV484 @ SV443 @ SV131 ) @ SV443 ) ) )
= $true )
| ( ( SV484
= ( relation_inverse_image @ SV131 @ SV443 ) )
= $false )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3128]) ).
thf(3216,plain,
! [SV446: $i,SV134: $i,SV587: $i,SV563: $i] :
( ( ( in @ ( ordered_pair @ SV563 @ SV587 ) @ SV134 )
= $false )
| ( ( in @ SV563 @ SV446 )
= $true )
| ( ( SV446
= ( relation_dom @ SV134 ) )
= $false )
| ( ( relation @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3130]) ).
thf(3217,plain,
! [SV135: $i,SV366: $i,SV404: $i] :
( ( ( ( sK57_D @ SV404 @ SV366 @ SV135 )
= SV135 )
= $false )
| ( ( in @ ( sK57_D @ SV404 @ SV366 @ SV135 ) @ SV404 )
= $false )
| ( ( SV404
= ( unordered_pair @ SV135 @ SV366 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3132]) ).
thf(3218,plain,
! [SV135: $i,SV366: $i,SV404: $i] :
( ( ( ( sK57_D @ SV404 @ SV366 @ SV135 )
= SV366 )
= $false )
| ( ( in @ ( sK57_D @ SV404 @ SV366 @ SV135 ) @ SV404 )
= $false )
| ( ( SV404
= ( unordered_pair @ SV135 @ SV366 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3133]) ).
thf(3219,plain,
! [SV367: $i,SV405: $i,SV135: $i,SV588: $i] :
( ( ( ( SV588 != SV135 ) )
= $true )
| ( ( in @ SV588 @ SV405 )
= $true )
| ( ( SV405
= ( unordered_pair @ SV135 @ SV367 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3135]) ).
thf(3220,plain,
! [SV135: $i,SV405: $i,SV367: $i,SV589: $i] :
( ( ( ( SV589 != SV367 ) )
= $true )
| ( ( in @ SV589 @ SV405 )
= $true )
| ( ( SV405
= ( unordered_pair @ SV135 @ SV367 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3136]) ).
thf(3221,plain,
! [SV136: $i,SV447: $i] :
( ( ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV447 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK58_C @ SV447 @ SV136 ) @ ( sK59_SY494 @ SV447 @ SV136 ) ) @ SV136 )
= $false )
| ( ( SV136 = SV447 )
= $true )
| ( ( relation @ SV447 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3137]) ).
thf(3222,plain,
! [SV448: $i,SV136: $i,SV607: $i,SV590: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV590 @ SV607 ) @ SV136 )
| ( in @ ( ordered_pair @ SV590 @ SV607 ) @ SV448 ) )
= $true )
| ( ( SV136 = SV448 )
= $false )
| ( ( relation @ SV448 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3138]) ).
thf(3223,plain,
! [SV136: $i,SV448: $i,SV608: $i,SV591: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV591 @ SV608 ) @ SV448 )
| ( in @ ( ordered_pair @ SV591 @ SV608 ) @ SV136 ) )
= $true )
| ( ( SV136 = SV448 )
= $false )
| ( ( relation @ SV448 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3139]) ).
thf(3224,plain,
! [SV230: $i,SV523: $i,SV137: $i] :
( ( ( ~ ( in @ SV137 @ ( relation_dom @ SV523 ) ) )
= $true )
| ( ( ~ ( in @ ( apply @ SV523 @ SV137 ) @ ( relation_dom @ SV230 ) ) )
= $true )
| ( ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SV523 @ SV230 ) ) )
= $true )
| ( ( function @ SV523 )
= $false )
| ( ( relation @ SV523 )
= $false )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3140]) ).
thf(3225,plain,
! [SV230: $i,SV137: $i,SV565: $i] :
( ( ( function @ SV565 )
= $false )
| ( ( ~ ( relation @ SV565 ) )
= $true )
| ( ( ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SV565 @ SV230 ) ) )
| ( in @ SV137 @ ( relation_dom @ SV565 ) ) )
= $true )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3141]) ).
thf(3226,plain,
! [SV230: $i,SV137: $i,SV566: $i] :
( ( ( function @ SV566 )
= $false )
| ( ( ~ ( relation @ SV566 ) )
= $true )
| ( ( ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SV566 @ SV230 ) ) )
| ( in @ ( apply @ SV566 @ SV137 ) @ ( relation_dom @ SV230 ) ) )
= $true )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3142]) ).
thf(3227,plain,
! [SV138: $i,SV537: $i,SV551: $i] :
( ( ( subset @ SV551 @ SV537 )
= $false )
| ( ( in @ SV537 @ ( sK41_B @ SV138 ) )
= $false )
| ( ( in @ SV551 @ ( sK41_B @ SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3143]) ).
thf(3228,plain,
! [SV142: $i,SV376: $i,SV407: $i] :
( ( ( in @ ( sK39_D @ SV407 @ SV376 @ SV142 ) @ ( relation_rng @ SV407 ) )
= $true )
| ( ( in @ SV142 @ ( relation_inverse_image @ SV407 @ SV376 ) )
= $false )
| ( ( relation @ SV407 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3146]) ).
thf(3229,plain,
! [SV376: $i,SV407: $i,SV142: $i] :
( ( ( in @ ( ordered_pair @ SV142 @ ( sK39_D @ SV407 @ SV376 @ SV142 ) ) @ SV407 )
= $true )
| ( ( in @ SV142 @ ( relation_inverse_image @ SV407 @ SV376 ) )
= $false )
| ( ( relation @ SV407 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3147]) ).
thf(3230,plain,
! [SV453: $i,SV510: $i] :
( ( ( ~ ( in @ ( sK65_SY495 @ SV510 @ SV453 ) @ SV453 ) )
= $false )
| ( ( ~ ( in @ ( sK64_C @ SV510 @ SV453 ) @ SV510 ) )
= $true )
| ( ( SV510
= ( set_meet @ SV453 ) )
= $true )
| ( ( SV453 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3148]) ).
thf(3231,plain,
! [SV453: $i,SV510: $i] :
( ( ( ~ ~ ( in @ ( sK64_C @ SV510 @ SV453 ) @ ( sK65_SY495 @ SV510 @ SV453 ) ) )
= $false )
| ( ( ~ ( in @ ( sK64_C @ SV510 @ SV453 ) @ SV510 ) )
= $true )
| ( ( SV510
= ( set_meet @ SV453 ) )
= $true )
| ( ( SV453 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3148]) ).
thf(3232,plain,
! [SV510: $i,SV453: $i,SV592: $i] :
( ( ( ~ ( in @ SV592 @ SV453 ) )
= $true )
| ( ( in @ ( sK64_C @ SV510 @ SV453 ) @ SV592 )
= $true )
| ( ( in @ ( sK64_C @ SV510 @ SV453 ) @ SV510 )
= $true )
| ( ( SV510
= ( set_meet @ SV453 ) )
= $true )
| ( ( SV453 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3149]) ).
thf(3233,plain,
! [SV454: $i,SV511: $i,SV593: $i] :
( ( ( ~ ( ~ ( in @ ( sK63_D @ SV593 @ SV511 @ SV454 ) @ SV454 )
| ~ ~ ( in @ SV593 @ ( sK63_D @ SV593 @ SV511 @ SV454 ) ) ) )
= $true )
| ( ( in @ SV593 @ SV511 )
= $true )
| ( ( SV511
= ( set_meet @ SV454 ) )
= $false )
| ( ( SV454 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3150]) ).
thf(3234,plain,
! [SV454: $i,SV511: $i,SV594: $i] :
( ( ( ~ ( in @ SV594 @ SV511 ) )
= $true )
| ( ( ! [SY1162: $i] :
( ~ ( in @ SY1162 @ SV454 )
| ( in @ SV594 @ SY1162 ) ) )
= $true )
| ( ( SV511
= ( set_meet @ SV454 ) )
= $false )
| ( ( SV454 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3151]) ).
thf(3235,plain,
! [SV144: $i,SV378: $i,SV409: $i] :
( ( ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV144 )
= $false )
| ( ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV409 )
= $false )
| ( ( SV409
= ( set_union2 @ SV144 @ SV378 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3152]) ).
thf(3236,plain,
! [SV144: $i,SV378: $i,SV409: $i] :
( ( ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV378 )
= $false )
| ( ( in @ ( sK56_D @ SV409 @ SV378 @ SV144 ) @ SV409 )
= $false )
| ( ( SV409
= ( set_union2 @ SV144 @ SV378 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3153]) ).
thf(3237,plain,
! [SV379: $i,SV410: $i,SV144: $i,SV595: $i] :
( ( ( ~ ( in @ SV595 @ SV144 ) )
= $true )
| ( ( in @ SV595 @ SV410 )
= $true )
| ( ( SV410
= ( set_union2 @ SV144 @ SV379 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3155]) ).
thf(3238,plain,
! [SV144: $i,SV410: $i,SV379: $i,SV596: $i] :
( ( ( ~ ( in @ SV596 @ SV379 ) )
= $true )
| ( ( in @ SV596 @ SV410 )
= $true )
| ( ( SV410
= ( set_union2 @ SV144 @ SV379 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3156]) ).
thf(3239,plain,
! [SV145: $i,SV381: $i,SV412: $i] :
( ( ( in @ ( sK40_D @ SV412 @ SV381 @ SV145 ) @ ( relation_dom @ SV412 ) )
= $true )
| ( ( in @ SV145 @ ( relation_image @ SV412 @ SV381 ) )
= $false )
| ( ( relation @ SV412 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3158]) ).
thf(3240,plain,
! [SV145: $i,SV381: $i,SV412: $i] :
( ( ( in @ ( ordered_pair @ ( sK40_D @ SV412 @ SV381 @ SV145 ) @ SV145 ) @ SV412 )
= $true )
| ( ( in @ SV145 @ ( relation_image @ SV412 @ SV381 ) )
= $false )
| ( ( relation @ SV412 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3159]) ).
thf(3241,plain,
! [SV388: $i,SV149: $i,SV416: $i,SV597: $i] :
( ( ( ~ ( in @ SV597 @ SV416 ) )
= $true )
| ( ( in @ SV597 @ SV149 )
= $true )
| ( ( SV416
= ( set_difference @ SV149 @ SV388 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3162]) ).
thf(3242,plain,
! [SV149: $i,SV388: $i,SV416: $i,SV598: $i] :
( ( ( ~ ( in @ SV598 @ SV416 ) )
= $true )
| ( ( ~ ( in @ SV598 @ SV388 ) )
= $true )
| ( ( SV416
= ( set_difference @ SV149 @ SV388 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3163]) ).
thf(3243,plain,
! [SV323: $i,SV112: $i,SV391: $i,SV578: $i] :
( ( ( in @ SV578 @ SV391 )
= $false )
| ( ( in @ SV578 @ SV112 )
= $true )
| ( ( SV391
= ( set_intersection2 @ SV112 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3165]) ).
thf(3244,plain,
! [SV112: $i,SV323: $i,SV391: $i,SV579: $i] :
( ( ( in @ SV579 @ SV391 )
= $false )
| ( ( in @ SV579 @ SV323 )
= $true )
| ( ( SV391
= ( set_intersection2 @ SV112 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3166]) ).
thf(3245,plain,
! [SV113: $i,SV225: $i,SV463: $i] :
( ( ( in @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) @ SV113 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV225 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 ) )
= $true )
| ( ( SV463
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $true )
| ( ( relation @ SV463 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3170]) ).
thf(3246,plain,
! [SV113: $i,SV225: $i,SV463: $i] :
( ( ( ( in @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) @ SV113 )
| ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 ) )
= $true )
| ( ( SV463
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $true )
| ( ( relation @ SV463 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3171]) ).
thf(3247,plain,
! [SV113: $i,SV225: $i,SV463: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV225 )
| ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 ) )
= $true )
| ( ( SV463
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $true )
| ( ( relation @ SV463 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3172]) ).
thf(3248,plain,
! [SV464: $i,SV225: $i,SV599: $i,SV113: $i,SV609: $i] :
( ( ( ~ ( in @ SV609 @ SV113 )
| ~ ( in @ ( ordered_pair @ SV599 @ SV609 ) @ SV225 )
| ( in @ ( ordered_pair @ SV599 @ SV609 ) @ SV464 ) )
= $true )
| ( ( SV464
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $false )
| ( ( relation @ SV464 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3173]) ).
thf(3249,plain,
! [SV225: $i,SV113: $i,SV464: $i] :
( ( ( ~ ! [SY1096: $i,SY1097: $i] :
( ~ ( in @ ( ordered_pair @ SY1096 @ SY1097 ) @ SV464 )
| ( in @ SY1097 @ SV113 ) ) )
= $false )
| ( ( SV464
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $false )
| ( ( relation @ SV464 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3174]) ).
thf(3250,plain,
! [SV113: $i,SV225: $i,SV464: $i] :
( ( ( ~ ! [SY1098: $i,SY1099: $i] :
( ~ ( in @ ( ordered_pair @ SY1098 @ SY1099 ) @ SV464 )
| ( in @ ( ordered_pair @ SY1098 @ SY1099 ) @ SV225 ) ) )
= $false )
| ( ( SV464
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $false )
| ( ( relation @ SV464 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3174]) ).
thf(3251,plain,
! [SV543: $i,SV116: $i,SV580: $i] :
( ( ( SV580
= ( apply @ SV116 @ SV543 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV543 @ SV580 ) @ SV116 )
= $true )
| ( ( in @ SV543 @ ( relation_dom @ SV116 ) )
= $false )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3177]) ).
thf(3252,plain,
! [SV116: $i,SV581: $i,SV544: $i] :
( ( ( in @ ( ordered_pair @ SV544 @ SV581 ) @ SV116 )
= $false )
| ( ( SV581
= ( apply @ SV116 @ SV544 ) )
= $true )
| ( ( in @ SV544 @ ( relation_dom @ SV116 ) )
= $false )
| ( ( function @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3178]) ).
thf(3253,plain,
! [SV393: $i,SV117: $i,SV547: $i,SV334: $i,SV557: $i] :
( ( ( in @ SV557 @ SV334 )
= $false )
| ( ( in @ SV547 @ SV117 )
= $false )
| ( ( ( ( sK53_D @ SV393 @ SV334 @ SV117 )
!= ( ordered_pair @ SV547 @ SV557 ) ) )
= $true )
| ( ( ~ ( in @ ( sK53_D @ SV393 @ SV334 @ SV117 ) @ SV393 ) )
= $true )
| ( ( SV393
= ( cartesian_product2 @ SV117 @ SV334 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3181]) ).
thf(3254,plain,
! [SV117: $i,SV334: $i,SV393: $i] :
( ( ( in @ ( sK54_SY491 @ SV393 @ SV334 @ SV117 ) @ SV117 )
= $true )
| ( ( in @ ( sK53_D @ SV393 @ SV334 @ SV117 ) @ SV393 )
= $true )
| ( ( SV393
= ( cartesian_product2 @ SV117 @ SV334 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3182]) ).
thf(3255,plain,
! [SV117: $i,SV334: $i,SV393: $i] :
( ( ( in @ ( sK55_SY493 @ SV393 @ SV334 @ SV117 ) @ SV334 )
= $true )
| ( ( in @ ( sK53_D @ SV393 @ SV334 @ SV117 ) @ SV393 )
= $true )
| ( ( SV393
= ( cartesian_product2 @ SV117 @ SV334 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3183]) ).
thf(3256,plain,
! [SV394: $i,SV548: $i,SV335: $i,SV582: $i,SV117: $i,SV570: $i] :
( ( ( ~ ( in @ SV570 @ SV117 ) )
= $true )
| ( ( ~ ( in @ SV582 @ SV335 ) )
= $true )
| ( ( ( SV548
!= ( ordered_pair @ SV570 @ SV582 ) ) )
= $true )
| ( ( in @ SV548 @ SV394 )
= $true )
| ( ( SV394
= ( cartesian_product2 @ SV117 @ SV335 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3184]) ).
thf(3257,plain,
! [SV117: $i,SV335: $i,SV394: $i,SV549: $i] :
( ( ( ~ ( ~ ( in @ ( sK51_E @ SV549 @ SV394 @ SV335 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK52_SY488 @ SV549 @ SV394 @ SV335 @ SV117 ) @ SV335 ) ) )
= $true )
| ( ( in @ SV549 @ SV394 )
= $false )
| ( ( SV394
= ( cartesian_product2 @ SV117 @ SV335 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3185]) ).
thf(3258,plain,
! [SV117: $i,SV335: $i,SV394: $i,SV549: $i] :
( ( ( SV549
= ( ordered_pair @ ( sK51_E @ SV549 @ SV394 @ SV335 @ SV117 ) @ ( sK52_SY488 @ SV549 @ SV394 @ SV335 @ SV117 ) ) )
= $true )
| ( ( in @ SV549 @ SV394 )
= $false )
| ( ( SV394
= ( cartesian_product2 @ SV117 @ SV335 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3186]) ).
thf(3259,plain,
! [SV340: $i,SV274: $i,SV571: $i,SV558: $i] :
( ( ( SV558 = SV571 )
= $false )
| ( ( ~ ( in @ SV558 @ SV274 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV558 @ SV571 ) @ SV340 )
= $true )
| ( ( SV340
= ( identity_relation @ SV274 ) )
= $false )
| ( ( relation @ SV340 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3188]) ).
thf(3260,plain,
! [SV274: $i,SV340: $i,SV610: $i,SV600: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV600 @ SV610 ) @ SV340 )
| ( SV600 = SV610 ) )
= $true )
| ( ( SV340
= ( identity_relation @ SV274 ) )
= $false )
| ( ( relation @ SV340 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3189]) ).
thf(3261,plain,
! [SV274: $i,SV340: $i,SV601: $i] :
( ( ( ! [SY1165: $i] :
~ ( in @ ( ordered_pair @ SV601 @ SY1165 ) @ SV340 ) )
= $true )
| ( ( in @ SV601 @ SV274 )
= $true )
| ( ( SV340
= ( identity_relation @ SV274 ) )
= $false )
| ( ( relation @ SV340 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3190]) ).
thf(3262,plain,
! [SV120: $i,SV275: $i,SV516: $i] :
( ( ( ! [SY1135: $i] :
( ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ SY1135 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY1135 @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV275 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV516 ) )
= $true )
| ( ( SV516
= ( relation_composition @ SV120 @ SV275 ) )
= $true )
| ( ( relation @ SV516 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3191]) ).
thf(3263,plain,
! [SV120: $i,SV275: $i,SV516: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK15_SY461 @ SV516 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY461 @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV275 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV516 )
= $true )
| ( ( SV516
= ( relation_composition @ SV120 @ SV275 ) )
= $true )
| ( ( relation @ SV516 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3192]) ).
thf(3264,plain,
! [SV517: $i,SV275: $i,SV120: $i] :
( ( ( ! [SY1136: $i,SY1137: $i] :
( ! [SY909: $i] :
( ~ ( in @ ( ordered_pair @ SY1136 @ SY909 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY909 @ SY1137 ) @ SV275 ) )
| ( in @ ( ordered_pair @ SY1136 @ SY1137 ) @ SV517 ) ) )
= $true )
| ( ( SV517
= ( relation_composition @ SV120 @ SV275 ) )
= $false )
| ( ( relation @ SV517 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3193]) ).
thf(3265,plain,
! [SV120: $i,SV275: $i,SV517: $i] :
( ( ( ! [SY1139: $i,SY1140: $i] :
( ~ ( in @ ( ordered_pair @ SY1139 @ SY1140 ) @ SV517 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1139 @ ( sK12_F @ SY1140 @ SY1139 @ SV517 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK12_F @ SY1140 @ SY1139 @ SV517 @ SV275 @ SV120 ) @ SY1140 ) @ SV275 ) ) ) )
= $true )
| ( ( SV517
= ( relation_composition @ SV120 @ SV275 ) )
= $false )
| ( ( relation @ SV517 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3194]) ).
thf(3266,plain,
! [SV123: $i,SV424: $i,SV473: $i] :
( ( ( in @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ SV424 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV123 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 ) )
= $true )
| ( ( SV473
= ( relation_dom_restriction @ SV123 @ SV424 ) )
= $true )
| ( ( relation @ SV473 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3195]) ).
thf(3267,plain,
! [SV123: $i,SV424: $i,SV473: $i] :
( ( ( ( in @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ SV424 )
| ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 ) )
= $true )
| ( ( SV473
= ( relation_dom_restriction @ SV123 @ SV424 ) )
= $true )
| ( ( relation @ SV473 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3196]) ).
thf(3268,plain,
! [SV123: $i,SV424: $i,SV473: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV123 )
| ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 ) )
= $true )
| ( ( SV473
= ( relation_dom_restriction @ SV123 @ SV424 ) )
= $true )
| ( ( relation @ SV473 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3197]) ).
thf(3269,plain,
! [SV474: $i,SV123: $i,SV611: $i,SV425: $i,SV602: $i] :
( ( ( ~ ( in @ SV602 @ SV425 )
| ~ ( in @ ( ordered_pair @ SV602 @ SV611 ) @ SV123 )
| ( in @ ( ordered_pair @ SV602 @ SV611 ) @ SV474 ) )
= $true )
| ( ( SV474
= ( relation_dom_restriction @ SV123 @ SV425 ) )
= $false )
| ( ( relation @ SV474 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3198]) ).
thf(3270,plain,
! [SV123: $i,SV425: $i,SV474: $i] :
( ( ( ~ ! [SY1107: $i] :
( ! [SY1108: $i] :
~ ( in @ ( ordered_pair @ SY1107 @ SY1108 ) @ SV474 )
| ( in @ SY1107 @ SV425 ) ) )
= $false )
| ( ( SV474
= ( relation_dom_restriction @ SV123 @ SV425 ) )
= $false )
| ( ( relation @ SV474 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3199]) ).
thf(3271,plain,
! [SV425: $i,SV123: $i,SV474: $i] :
( ( ( ~ ! [SY1109: $i,SY1110: $i] :
( ~ ( in @ ( ordered_pair @ SY1109 @ SY1110 ) @ SV474 )
| ( in @ ( ordered_pair @ SY1109 @ SY1110 ) @ SV123 ) ) )
= $false )
| ( ( SV474
= ( relation_dom_restriction @ SV123 @ SV425 ) )
= $false )
| ( ( relation @ SV474 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3199]) ).
thf(3272,plain,
! [SV124: $i,SV427: $i,SV603: $i,SV583: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV583 @ SV603 ) @ SV427 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV603 @ SV583 ) @ SV124 )
= $true )
| ( ( SV427
= ( relation_inverse @ SV124 ) )
= $false )
| ( ( relation @ SV427 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3201]) ).
thf(3273,plain,
! [SV427: $i,SV124: $i,SV584: $i,SV604: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV604 @ SV584 ) @ SV124 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV584 @ SV604 ) @ SV427 )
= $true )
| ( ( SV427
= ( relation_inverse @ SV124 ) )
= $false )
| ( ( relation @ SV427 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3202]) ).
thf(3274,plain,
! [SV475: $i,SV428: $i,SV585: $i] :
( ( ( in @ SV585 @ SV428 )
= $false )
| ( ( ( apply @ SV475 @ SV585 )
= SV585 )
= $true )
| ( ( SV475
= ( identity_relation @ SV428 ) )
= $false )
| ( ( function @ SV475 )
= $false )
| ( ( relation @ SV475 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3204]) ).
thf(3275,plain,
! [SV125: $i,SV479: $i,SV432: $i,SV572: $i] :
( ( ( in @ SV572 @ SV432 )
= $false )
| ( ( in @ ( ordered_pair @ SV572 @ ( sK30_D @ SV479 @ SV432 @ SV125 ) ) @ SV125 )
= $false )
| ( ( ~ ( in @ ( sK30_D @ SV479 @ SV432 @ SV125 ) @ SV479 ) )
= $true )
| ( ( SV479
= ( relation_image @ SV125 @ SV432 ) )
= $true )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3205]) ).
thf(3276,plain,
! [SV480: $i,SV433: $i,SV125: $i,SV573: $i,SV605: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV605 @ SV573 ) @ SV125 ) )
= $true )
| ( ( ~ ( in @ SV605 @ SV433 ) )
= $true )
| ( ( in @ SV573 @ SV480 )
= $true )
| ( ( SV480
= ( relation_image @ SV125 @ SV433 ) )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3208]) ).
thf(3277,plain,
! [SV125: $i,SV433: $i,SV480: $i,SV574: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK29_E @ SV574 @ SV480 @ SV433 @ SV125 ) @ SV574 ) @ SV125 )
| ~ ( in @ ( sK29_E @ SV574 @ SV480 @ SV433 @ SV125 ) @ SV433 ) )
= $false )
| ( ( in @ SV574 @ SV480 )
= $false )
| ( ( SV480
= ( relation_image @ SV125 @ SV433 ) )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3209]) ).
thf(3278,plain,
! [SV131: $i,SV483: $i,SV442: $i,SV575: $i] :
( ( ( in @ SV575 @ SV442 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SV575 ) @ SV131 )
= $false )
| ( ( ~ ( in @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SV483 ) )
= $true )
| ( ( SV483
= ( relation_inverse_image @ SV131 @ SV442 ) )
= $true )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3211]) ).
thf(3279,plain,
! [SV484: $i,SV443: $i,SV131: $i,SV606: $i,SV576: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV576 @ SV606 ) @ SV131 ) )
= $true )
| ( ( ~ ( in @ SV606 @ SV443 ) )
= $true )
| ( ( in @ SV576 @ SV484 )
= $true )
| ( ( SV484
= ( relation_inverse_image @ SV131 @ SV443 ) )
= $false )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3214]) ).
thf(3280,plain,
! [SV131: $i,SV443: $i,SV484: $i,SV577: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV577 @ ( sK26_E @ SV577 @ SV484 @ SV443 @ SV131 ) ) @ SV131 )
| ~ ( in @ ( sK26_E @ SV577 @ SV484 @ SV443 @ SV131 ) @ SV443 ) )
= $false )
| ( ( in @ SV577 @ SV484 )
= $false )
| ( ( SV484
= ( relation_inverse_image @ SV131 @ SV443 ) )
= $false )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3215]) ).
thf(3281,plain,
! [SV367: $i,SV405: $i,SV135: $i,SV588: $i] :
( ( ( SV588 = SV135 )
= $false )
| ( ( in @ SV588 @ SV405 )
= $true )
| ( ( SV405
= ( unordered_pair @ SV135 @ SV367 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3219]) ).
thf(3282,plain,
! [SV135: $i,SV405: $i,SV367: $i,SV589: $i] :
( ( ( SV589 = SV367 )
= $false )
| ( ( in @ SV589 @ SV405 )
= $true )
| ( ( SV405
= ( unordered_pair @ SV135 @ SV367 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3220]) ).
thf(3283,plain,
! [SV448: $i,SV136: $i,SV607: $i,SV590: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV590 @ SV607 ) @ SV136 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV590 @ SV607 ) @ SV448 )
= $true )
| ( ( SV136 = SV448 )
= $false )
| ( ( relation @ SV448 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3222]) ).
thf(3284,plain,
! [SV136: $i,SV448: $i,SV608: $i,SV591: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV591 @ SV608 ) @ SV448 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV591 @ SV608 ) @ SV136 )
= $true )
| ( ( SV136 = SV448 )
= $false )
| ( ( relation @ SV448 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3223]) ).
thf(3285,plain,
! [SV230: $i,SV523: $i,SV137: $i] :
( ( ( in @ SV137 @ ( relation_dom @ SV523 ) )
= $false )
| ( ( ~ ( in @ ( apply @ SV523 @ SV137 ) @ ( relation_dom @ SV230 ) ) )
= $true )
| ( ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SV523 @ SV230 ) ) )
= $true )
| ( ( function @ SV523 )
= $false )
| ( ( relation @ SV523 )
= $false )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3224]) ).
thf(3286,plain,
! [SV230: $i,SV137: $i,SV565: $i] :
( ( ( relation @ SV565 )
= $false )
| ( ( function @ SV565 )
= $false )
| ( ( ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SV565 @ SV230 ) ) )
| ( in @ SV137 @ ( relation_dom @ SV565 ) ) )
= $true )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3225]) ).
thf(3287,plain,
! [SV230: $i,SV137: $i,SV566: $i] :
( ( ( relation @ SV566 )
= $false )
| ( ( function @ SV566 )
= $false )
| ( ( ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SV566 @ SV230 ) ) )
| ( in @ ( apply @ SV566 @ SV137 ) @ ( relation_dom @ SV230 ) ) )
= $true )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3226]) ).
thf(3288,plain,
! [SV453: $i,SV510: $i] :
( ( ( in @ ( sK65_SY495 @ SV510 @ SV453 ) @ SV453 )
= $true )
| ( ( ~ ( in @ ( sK64_C @ SV510 @ SV453 ) @ SV510 ) )
= $true )
| ( ( SV510
= ( set_meet @ SV453 ) )
= $true )
| ( ( SV453 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3230]) ).
thf(3289,plain,
! [SV453: $i,SV510: $i] :
( ( ( ~ ( in @ ( sK64_C @ SV510 @ SV453 ) @ ( sK65_SY495 @ SV510 @ SV453 ) ) )
= $true )
| ( ( ~ ( in @ ( sK64_C @ SV510 @ SV453 ) @ SV510 ) )
= $true )
| ( ( SV510
= ( set_meet @ SV453 ) )
= $true )
| ( ( SV453 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3231]) ).
thf(3290,plain,
! [SV510: $i,SV453: $i,SV592: $i] :
( ( ( in @ SV592 @ SV453 )
= $false )
| ( ( in @ ( sK64_C @ SV510 @ SV453 ) @ SV592 )
= $true )
| ( ( in @ ( sK64_C @ SV510 @ SV453 ) @ SV510 )
= $true )
| ( ( SV510
= ( set_meet @ SV453 ) )
= $true )
| ( ( SV453 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3232]) ).
thf(3291,plain,
! [SV454: $i,SV511: $i,SV593: $i] :
( ( ( ~ ( in @ ( sK63_D @ SV593 @ SV511 @ SV454 ) @ SV454 )
| ~ ~ ( in @ SV593 @ ( sK63_D @ SV593 @ SV511 @ SV454 ) ) )
= $false )
| ( ( in @ SV593 @ SV511 )
= $true )
| ( ( SV511
= ( set_meet @ SV454 ) )
= $false )
| ( ( SV454 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3233]) ).
thf(3292,plain,
! [SV454: $i,SV511: $i,SV594: $i] :
( ( ( in @ SV594 @ SV511 )
= $false )
| ( ( ! [SY1162: $i] :
( ~ ( in @ SY1162 @ SV454 )
| ( in @ SV594 @ SY1162 ) ) )
= $true )
| ( ( SV511
= ( set_meet @ SV454 ) )
= $false )
| ( ( SV454 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3234]) ).
thf(3293,plain,
! [SV379: $i,SV410: $i,SV144: $i,SV595: $i] :
( ( ( in @ SV595 @ SV144 )
= $false )
| ( ( in @ SV595 @ SV410 )
= $true )
| ( ( SV410
= ( set_union2 @ SV144 @ SV379 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3237]) ).
thf(3294,plain,
! [SV144: $i,SV410: $i,SV379: $i,SV596: $i] :
( ( ( in @ SV596 @ SV379 )
= $false )
| ( ( in @ SV596 @ SV410 )
= $true )
| ( ( SV410
= ( set_union2 @ SV144 @ SV379 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3238]) ).
thf(3295,plain,
! [SV388: $i,SV149: $i,SV416: $i,SV597: $i] :
( ( ( in @ SV597 @ SV416 )
= $false )
| ( ( in @ SV597 @ SV149 )
= $true )
| ( ( SV416
= ( set_difference @ SV149 @ SV388 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3241]) ).
thf(3296,plain,
! [SV149: $i,SV388: $i,SV416: $i,SV598: $i] :
( ( ( in @ SV598 @ SV416 )
= $false )
| ( ( ~ ( in @ SV598 @ SV388 ) )
= $true )
| ( ( SV416
= ( set_difference @ SV149 @ SV388 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3242]) ).
thf(3297,plain,
! [SV113: $i,SV225: $i,SV463: $i] :
( ( ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV225 )
= $false )
| ( ( in @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) @ SV113 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 ) )
= $true )
| ( ( SV463
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $true )
| ( ( relation @ SV463 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3245]) ).
thf(3298,plain,
! [SV113: $i,SV225: $i,SV463: $i] :
( ( ( in @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) @ SV113 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 )
= $true )
| ( ( SV463
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $true )
| ( ( relation @ SV463 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3246]) ).
thf(3299,plain,
! [SV113: $i,SV225: $i,SV463: $i] :
( ( ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV225 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 )
= $true )
| ( ( SV463
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $true )
| ( ( relation @ SV463 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3247]) ).
thf(3300,plain,
! [SV464: $i,SV225: $i,SV599: $i,SV113: $i,SV609: $i] :
( ( ( ~ ( in @ SV609 @ SV113 )
| ~ ( in @ ( ordered_pair @ SV599 @ SV609 ) @ SV225 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV599 @ SV609 ) @ SV464 )
= $true )
| ( ( SV464
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $false )
| ( ( relation @ SV464 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3248]) ).
thf(3301,plain,
! [SV225: $i,SV113: $i,SV464: $i] :
( ( ( ! [SY1096: $i,SY1097: $i] :
( ~ ( in @ ( ordered_pair @ SY1096 @ SY1097 ) @ SV464 )
| ( in @ SY1097 @ SV113 ) ) )
= $true )
| ( ( SV464
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $false )
| ( ( relation @ SV464 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3249]) ).
thf(3302,plain,
! [SV113: $i,SV225: $i,SV464: $i] :
( ( ( ! [SY1098: $i,SY1099: $i] :
( ~ ( in @ ( ordered_pair @ SY1098 @ SY1099 ) @ SV464 )
| ( in @ ( ordered_pair @ SY1098 @ SY1099 ) @ SV225 ) ) )
= $true )
| ( ( SV464
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $false )
| ( ( relation @ SV464 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3250]) ).
thf(3303,plain,
! [SV557: $i,SV547: $i,SV117: $i,SV334: $i,SV393: $i] :
( ( ( ( sK53_D @ SV393 @ SV334 @ SV117 )
= ( ordered_pair @ SV547 @ SV557 ) )
= $false )
| ( ( in @ SV547 @ SV117 )
= $false )
| ( ( in @ SV557 @ SV334 )
= $false )
| ( ( ~ ( in @ ( sK53_D @ SV393 @ SV334 @ SV117 ) @ SV393 ) )
= $true )
| ( ( SV393
= ( cartesian_product2 @ SV117 @ SV334 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3253]) ).
thf(3304,plain,
! [SV394: $i,SV548: $i,SV335: $i,SV582: $i,SV117: $i,SV570: $i] :
( ( ( in @ SV570 @ SV117 )
= $false )
| ( ( ~ ( in @ SV582 @ SV335 ) )
= $true )
| ( ( ( SV548
!= ( ordered_pair @ SV570 @ SV582 ) ) )
= $true )
| ( ( in @ SV548 @ SV394 )
= $true )
| ( ( SV394
= ( cartesian_product2 @ SV117 @ SV335 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3256]) ).
thf(3305,plain,
! [SV117: $i,SV335: $i,SV394: $i,SV549: $i] :
( ( ( ~ ( in @ ( sK51_E @ SV549 @ SV394 @ SV335 @ SV117 ) @ SV117 )
| ~ ( in @ ( sK52_SY488 @ SV549 @ SV394 @ SV335 @ SV117 ) @ SV335 ) )
= $false )
| ( ( in @ SV549 @ SV394 )
= $false )
| ( ( SV394
= ( cartesian_product2 @ SV117 @ SV335 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3257]) ).
thf(3306,plain,
! [SV340: $i,SV571: $i,SV274: $i,SV558: $i] :
( ( ( in @ SV558 @ SV274 )
= $false )
| ( ( SV558 = SV571 )
= $false )
| ( ( in @ ( ordered_pair @ SV558 @ SV571 ) @ SV340 )
= $true )
| ( ( SV340
= ( identity_relation @ SV274 ) )
= $false )
| ( ( relation @ SV340 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3259]) ).
thf(3307,plain,
! [SV274: $i,SV340: $i,SV610: $i,SV600: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV600 @ SV610 ) @ SV340 ) )
= $true )
| ( ( SV600 = SV610 )
= $true )
| ( ( SV340
= ( identity_relation @ SV274 ) )
= $false )
| ( ( relation @ SV340 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3260]) ).
thf(3308,plain,
! [SV274: $i,SV340: $i,SV612: $i,SV601: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV601 @ SV612 ) @ SV340 ) )
= $true )
| ( ( in @ SV601 @ SV274 )
= $true )
| ( ( SV340
= ( identity_relation @ SV274 ) )
= $false )
| ( ( relation @ SV340 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3261]) ).
thf(3309,plain,
! [SV613: $i,SV120: $i,SV275: $i,SV516: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ SV613 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SV613 @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV275 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV516 ) )
= $true )
| ( ( SV516
= ( relation_composition @ SV120 @ SV275 ) )
= $true )
| ( ( relation @ SV516 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3262]) ).
thf(3310,plain,
! [SV120: $i,SV275: $i,SV516: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK15_SY461 @ SV516 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK15_SY461 @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV275 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV516 )
= $true )
| ( ( SV516
= ( relation_composition @ SV120 @ SV275 ) )
= $true )
| ( ( relation @ SV516 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3263]) ).
thf(3311,plain,
! [SV517: $i,SV275: $i,SV120: $i,SV614: $i] :
( ( ( ! [SY1167: $i] :
( ! [SY1168: $i] :
( ~ ( in @ ( ordered_pair @ SV614 @ SY1168 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY1168 @ SY1167 ) @ SV275 ) )
| ( in @ ( ordered_pair @ SV614 @ SY1167 ) @ SV517 ) ) )
= $true )
| ( ( SV517
= ( relation_composition @ SV120 @ SV275 ) )
= $false )
| ( ( relation @ SV517 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3264]) ).
thf(3312,plain,
! [SV120: $i,SV275: $i,SV517: $i,SV615: $i] :
( ( ( ! [SY1169: $i] :
( ~ ( in @ ( ordered_pair @ SV615 @ SY1169 ) @ SV517 )
| ~ ( ~ ( in @ ( ordered_pair @ SV615 @ ( sK12_F @ SY1169 @ SV615 @ SV517 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK12_F @ SY1169 @ SV615 @ SV517 @ SV275 @ SV120 ) @ SY1169 ) @ SV275 ) ) ) )
= $true )
| ( ( SV517
= ( relation_composition @ SV120 @ SV275 ) )
= $false )
| ( ( relation @ SV517 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3265]) ).
thf(3313,plain,
! [SV123: $i,SV424: $i,SV473: $i] :
( ( ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV123 )
= $false )
| ( ( in @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ SV424 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 ) )
= $true )
| ( ( SV473
= ( relation_dom_restriction @ SV123 @ SV424 ) )
= $true )
| ( ( relation @ SV473 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3266]) ).
thf(3314,plain,
! [SV123: $i,SV424: $i,SV473: $i] :
( ( ( in @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ SV424 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 )
= $true )
| ( ( SV473
= ( relation_dom_restriction @ SV123 @ SV424 ) )
= $true )
| ( ( relation @ SV473 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3267]) ).
thf(3315,plain,
! [SV123: $i,SV424: $i,SV473: $i] :
( ( ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV123 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 )
= $true )
| ( ( SV473
= ( relation_dom_restriction @ SV123 @ SV424 ) )
= $true )
| ( ( relation @ SV473 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3268]) ).
thf(3316,plain,
! [SV474: $i,SV123: $i,SV611: $i,SV425: $i,SV602: $i] :
( ( ( ~ ( in @ SV602 @ SV425 )
| ~ ( in @ ( ordered_pair @ SV602 @ SV611 ) @ SV123 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV602 @ SV611 ) @ SV474 )
= $true )
| ( ( SV474
= ( relation_dom_restriction @ SV123 @ SV425 ) )
= $false )
| ( ( relation @ SV474 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3269]) ).
thf(3317,plain,
! [SV123: $i,SV425: $i,SV474: $i] :
( ( ( ! [SY1107: $i] :
( ! [SY1108: $i] :
~ ( in @ ( ordered_pair @ SY1107 @ SY1108 ) @ SV474 )
| ( in @ SY1107 @ SV425 ) ) )
= $true )
| ( ( SV474
= ( relation_dom_restriction @ SV123 @ SV425 ) )
= $false )
| ( ( relation @ SV474 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3270]) ).
thf(3318,plain,
! [SV425: $i,SV123: $i,SV474: $i] :
( ( ( ! [SY1109: $i,SY1110: $i] :
( ~ ( in @ ( ordered_pair @ SY1109 @ SY1110 ) @ SV474 )
| ( in @ ( ordered_pair @ SY1109 @ SY1110 ) @ SV123 ) ) )
= $true )
| ( ( SV474
= ( relation_dom_restriction @ SV123 @ SV425 ) )
= $false )
| ( ( relation @ SV474 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3271]) ).
thf(3319,plain,
! [SV124: $i,SV427: $i,SV603: $i,SV583: $i] :
( ( ( in @ ( ordered_pair @ SV583 @ SV603 ) @ SV427 )
= $false )
| ( ( in @ ( ordered_pair @ SV603 @ SV583 ) @ SV124 )
= $true )
| ( ( SV427
= ( relation_inverse @ SV124 ) )
= $false )
| ( ( relation @ SV427 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3272]) ).
thf(3320,plain,
! [SV427: $i,SV124: $i,SV584: $i,SV604: $i] :
( ( ( in @ ( ordered_pair @ SV604 @ SV584 ) @ SV124 )
= $false )
| ( ( in @ ( ordered_pair @ SV584 @ SV604 ) @ SV427 )
= $true )
| ( ( SV427
= ( relation_inverse @ SV124 ) )
= $false )
| ( ( relation @ SV427 )
= $false )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3273]) ).
thf(3321,plain,
! [SV572: $i,SV125: $i,SV432: $i,SV479: $i] :
( ( ( in @ ( sK30_D @ SV479 @ SV432 @ SV125 ) @ SV479 )
= $false )
| ( ( in @ ( ordered_pair @ SV572 @ ( sK30_D @ SV479 @ SV432 @ SV125 ) ) @ SV125 )
= $false )
| ( ( in @ SV572 @ SV432 )
= $false )
| ( ( SV479
= ( relation_image @ SV125 @ SV432 ) )
= $true )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3275]) ).
thf(3322,plain,
! [SV480: $i,SV433: $i,SV125: $i,SV573: $i,SV605: $i] :
( ( ( in @ ( ordered_pair @ SV605 @ SV573 ) @ SV125 )
= $false )
| ( ( ~ ( in @ SV605 @ SV433 ) )
= $true )
| ( ( in @ SV573 @ SV480 )
= $true )
| ( ( SV480
= ( relation_image @ SV125 @ SV433 ) )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3276]) ).
thf(3323,plain,
! [SV125: $i,SV433: $i,SV480: $i,SV574: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK29_E @ SV574 @ SV480 @ SV433 @ SV125 ) @ SV574 ) @ SV125 ) )
= $false )
| ( ( in @ SV574 @ SV480 )
= $false )
| ( ( SV480
= ( relation_image @ SV125 @ SV433 ) )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3277]) ).
thf(3324,plain,
! [SV125: $i,SV433: $i,SV480: $i,SV574: $i] :
( ( ( ~ ( in @ ( sK29_E @ SV574 @ SV480 @ SV433 @ SV125 ) @ SV433 ) )
= $false )
| ( ( in @ SV574 @ SV480 )
= $false )
| ( ( SV480
= ( relation_image @ SV125 @ SV433 ) )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3277]) ).
thf(3325,plain,
! [SV575: $i,SV131: $i,SV442: $i,SV483: $i] :
( ( ( in @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SV483 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK27_D @ SV483 @ SV442 @ SV131 ) @ SV575 ) @ SV131 )
= $false )
| ( ( in @ SV575 @ SV442 )
= $false )
| ( ( SV483
= ( relation_inverse_image @ SV131 @ SV442 ) )
= $true )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3278]) ).
thf(3326,plain,
! [SV484: $i,SV443: $i,SV131: $i,SV606: $i,SV576: $i] :
( ( ( in @ ( ordered_pair @ SV576 @ SV606 ) @ SV131 )
= $false )
| ( ( ~ ( in @ SV606 @ SV443 ) )
= $true )
| ( ( in @ SV576 @ SV484 )
= $true )
| ( ( SV484
= ( relation_inverse_image @ SV131 @ SV443 ) )
= $false )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3279]) ).
thf(3327,plain,
! [SV131: $i,SV443: $i,SV484: $i,SV577: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV577 @ ( sK26_E @ SV577 @ SV484 @ SV443 @ SV131 ) ) @ SV131 ) )
= $false )
| ( ( in @ SV577 @ SV484 )
= $false )
| ( ( SV484
= ( relation_inverse_image @ SV131 @ SV443 ) )
= $false )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3280]) ).
thf(3328,plain,
! [SV131: $i,SV443: $i,SV484: $i,SV577: $i] :
( ( ( ~ ( in @ ( sK26_E @ SV577 @ SV484 @ SV443 @ SV131 ) @ SV443 ) )
= $false )
| ( ( in @ SV577 @ SV484 )
= $false )
| ( ( SV484
= ( relation_inverse_image @ SV131 @ SV443 ) )
= $false )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3280]) ).
thf(3329,plain,
! [SV448: $i,SV136: $i,SV607: $i,SV590: $i] :
( ( ( in @ ( ordered_pair @ SV590 @ SV607 ) @ SV136 )
= $false )
| ( ( in @ ( ordered_pair @ SV590 @ SV607 ) @ SV448 )
= $true )
| ( ( SV136 = SV448 )
= $false )
| ( ( relation @ SV448 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3283]) ).
thf(3330,plain,
! [SV136: $i,SV448: $i,SV608: $i,SV591: $i] :
( ( ( in @ ( ordered_pair @ SV591 @ SV608 ) @ SV448 )
= $false )
| ( ( in @ ( ordered_pair @ SV591 @ SV608 ) @ SV136 )
= $true )
| ( ( SV136 = SV448 )
= $false )
| ( ( relation @ SV448 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3284]) ).
thf(3331,plain,
! [SV230: $i,SV137: $i,SV523: $i] :
( ( ( in @ ( apply @ SV523 @ SV137 ) @ ( relation_dom @ SV230 ) )
= $false )
| ( ( in @ SV137 @ ( relation_dom @ SV523 ) )
= $false )
| ( ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SV523 @ SV230 ) ) )
= $true )
| ( ( function @ SV523 )
= $false )
| ( ( relation @ SV523 )
= $false )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3285]) ).
thf(3332,plain,
! [SV230: $i,SV565: $i,SV137: $i] :
( ( ( ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SV565 @ SV230 ) ) ) )
= $true )
| ( ( in @ SV137 @ ( relation_dom @ SV565 ) )
= $true )
| ( ( function @ SV565 )
= $false )
| ( ( relation @ SV565 )
= $false )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3286]) ).
thf(3333,plain,
! [SV230: $i,SV566: $i,SV137: $i] :
( ( ( ~ ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SV566 @ SV230 ) ) ) )
= $true )
| ( ( in @ ( apply @ SV566 @ SV137 ) @ ( relation_dom @ SV230 ) )
= $true )
| ( ( function @ SV566 )
= $false )
| ( ( relation @ SV566 )
= $false )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3287]) ).
thf(3334,plain,
! [SV453: $i,SV510: $i] :
( ( ( in @ ( sK64_C @ SV510 @ SV453 ) @ SV510 )
= $false )
| ( ( in @ ( sK65_SY495 @ SV510 @ SV453 ) @ SV453 )
= $true )
| ( ( SV510
= ( set_meet @ SV453 ) )
= $true )
| ( ( SV453 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3288]) ).
thf(3335,plain,
! [SV453: $i,SV510: $i] :
( ( ( in @ ( sK64_C @ SV510 @ SV453 ) @ ( sK65_SY495 @ SV510 @ SV453 ) )
= $false )
| ( ( ~ ( in @ ( sK64_C @ SV510 @ SV453 ) @ SV510 ) )
= $true )
| ( ( SV510
= ( set_meet @ SV453 ) )
= $true )
| ( ( SV453 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3289]) ).
thf(3336,plain,
! [SV454: $i,SV511: $i,SV593: $i] :
( ( ( ~ ( in @ ( sK63_D @ SV593 @ SV511 @ SV454 ) @ SV454 ) )
= $false )
| ( ( in @ SV593 @ SV511 )
= $true )
| ( ( SV511
= ( set_meet @ SV454 ) )
= $false )
| ( ( SV454 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3291]) ).
thf(3337,plain,
! [SV454: $i,SV511: $i,SV593: $i] :
( ( ( ~ ~ ( in @ SV593 @ ( sK63_D @ SV593 @ SV511 @ SV454 ) ) )
= $false )
| ( ( in @ SV593 @ SV511 )
= $true )
| ( ( SV511
= ( set_meet @ SV454 ) )
= $false )
| ( ( SV454 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3291]) ).
thf(3338,plain,
! [SV511: $i,SV594: $i,SV454: $i,SV616: $i] :
( ( ( ~ ( in @ SV616 @ SV454 )
| ( in @ SV594 @ SV616 ) )
= $true )
| ( ( in @ SV594 @ SV511 )
= $false )
| ( ( SV511
= ( set_meet @ SV454 ) )
= $false )
| ( ( SV454 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3292]) ).
thf(3339,plain,
! [SV149: $i,SV416: $i,SV388: $i,SV598: $i] :
( ( ( in @ SV598 @ SV388 )
= $false )
| ( ( in @ SV598 @ SV416 )
= $false )
| ( ( SV416
= ( set_difference @ SV149 @ SV388 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3296]) ).
thf(3340,plain,
! [SV113: $i,SV225: $i,SV463: $i] :
( ( ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV463 )
= $false )
| ( ( in @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) @ SV113 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK32_D @ SV463 @ SV225 @ SV113 ) @ ( sK33_SY472 @ SV463 @ SV225 @ SV113 ) ) @ SV225 )
= $false )
| ( ( SV463
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $true )
| ( ( relation @ SV463 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3297]) ).
thf(3341,plain,
! [SV464: $i,SV225: $i,SV599: $i,SV113: $i,SV609: $i] :
( ( ( ~ ( in @ SV609 @ SV113 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV599 @ SV609 ) @ SV225 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV599 @ SV609 ) @ SV464 )
= $true )
| ( ( SV464
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $false )
| ( ( relation @ SV464 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3300]) ).
thf(3342,plain,
! [SV225: $i,SV113: $i,SV464: $i,SV617: $i] :
( ( ( ! [SY1170: $i] :
( ~ ( in @ ( ordered_pair @ SV617 @ SY1170 ) @ SV464 )
| ( in @ SY1170 @ SV113 ) ) )
= $true )
| ( ( SV464
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $false )
| ( ( relation @ SV464 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3301]) ).
thf(3343,plain,
! [SV113: $i,SV225: $i,SV464: $i,SV618: $i] :
( ( ( ! [SY1171: $i] :
( ~ ( in @ ( ordered_pair @ SV618 @ SY1171 ) @ SV464 )
| ( in @ ( ordered_pair @ SV618 @ SY1171 ) @ SV225 ) ) )
= $true )
| ( ( SV464
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $false )
| ( ( relation @ SV464 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3302]) ).
thf(3344,plain,
! [SV547: $i,SV557: $i,SV117: $i,SV334: $i,SV393: $i] :
( ( ( in @ ( sK53_D @ SV393 @ SV334 @ SV117 ) @ SV393 )
= $false )
| ( ( in @ SV557 @ SV334 )
= $false )
| ( ( in @ SV547 @ SV117 )
= $false )
| ( ( ( sK53_D @ SV393 @ SV334 @ SV117 )
= ( ordered_pair @ SV547 @ SV557 ) )
= $false )
| ( ( SV393
= ( cartesian_product2 @ SV117 @ SV334 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3303]) ).
thf(3345,plain,
! [SV394: $i,SV548: $i,SV117: $i,SV570: $i,SV335: $i,SV582: $i] :
( ( ( in @ SV582 @ SV335 )
= $false )
| ( ( in @ SV570 @ SV117 )
= $false )
| ( ( ( SV548
!= ( ordered_pair @ SV570 @ SV582 ) ) )
= $true )
| ( ( in @ SV548 @ SV394 )
= $true )
| ( ( SV394
= ( cartesian_product2 @ SV117 @ SV335 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3304]) ).
thf(3346,plain,
! [SV117: $i,SV335: $i,SV394: $i,SV549: $i] :
( ( ( ~ ( in @ ( sK51_E @ SV549 @ SV394 @ SV335 @ SV117 ) @ SV117 ) )
= $false )
| ( ( in @ SV549 @ SV394 )
= $false )
| ( ( SV394
= ( cartesian_product2 @ SV117 @ SV335 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3305]) ).
thf(3347,plain,
! [SV117: $i,SV335: $i,SV394: $i,SV549: $i] :
( ( ( ~ ( in @ ( sK52_SY488 @ SV549 @ SV394 @ SV335 @ SV117 ) @ SV335 ) )
= $false )
| ( ( in @ SV549 @ SV394 )
= $false )
| ( ( SV394
= ( cartesian_product2 @ SV117 @ SV335 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3305]) ).
thf(3348,plain,
! [SV274: $i,SV340: $i,SV610: $i,SV600: $i] :
( ( ( in @ ( ordered_pair @ SV600 @ SV610 ) @ SV340 )
= $false )
| ( ( SV600 = SV610 )
= $true )
| ( ( SV340
= ( identity_relation @ SV274 ) )
= $false )
| ( ( relation @ SV340 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3307]) ).
thf(3349,plain,
! [SV274: $i,SV340: $i,SV612: $i,SV601: $i] :
( ( ( in @ ( ordered_pair @ SV601 @ SV612 ) @ SV340 )
= $false )
| ( ( in @ SV601 @ SV274 )
= $true )
| ( ( SV340
= ( identity_relation @ SV274 ) )
= $false )
| ( ( relation @ SV340 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3308]) ).
thf(3350,plain,
! [SV613: $i,SV120: $i,SV275: $i,SV516: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ SV613 ) @ SV120 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV613 @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV275 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV516 ) )
= $true )
| ( ( SV516
= ( relation_composition @ SV120 @ SV275 ) )
= $true )
| ( ( relation @ SV516 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3309]) ).
thf(3351,plain,
! [SV120: $i,SV275: $i,SV516: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK15_SY461 @ SV516 @ SV275 @ SV120 ) ) @ SV120 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV516 )
= $true )
| ( ( SV516
= ( relation_composition @ SV120 @ SV275 ) )
= $true )
| ( ( relation @ SV516 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3310]) ).
thf(3352,plain,
! [SV120: $i,SV275: $i,SV516: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK15_SY461 @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV275 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV516 )
= $true )
| ( ( SV516
= ( relation_composition @ SV120 @ SV275 ) )
= $true )
| ( ( relation @ SV516 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3310]) ).
thf(3353,plain,
! [SV517: $i,SV275: $i,SV619: $i,SV120: $i,SV614: $i] :
( ( ( ! [SY1172: $i] :
( ~ ( in @ ( ordered_pair @ SV614 @ SY1172 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY1172 @ SV619 ) @ SV275 ) )
| ( in @ ( ordered_pair @ SV614 @ SV619 ) @ SV517 ) )
= $true )
| ( ( SV517
= ( relation_composition @ SV120 @ SV275 ) )
= $false )
| ( ( relation @ SV517 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3311]) ).
thf(3354,plain,
! [SV120: $i,SV275: $i,SV517: $i,SV620: $i,SV615: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV615 @ SV620 ) @ SV517 )
| ~ ( ~ ( in @ ( ordered_pair @ SV615 @ ( sK12_F @ SV620 @ SV615 @ SV517 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK12_F @ SV620 @ SV615 @ SV517 @ SV275 @ SV120 ) @ SV620 ) @ SV275 ) ) )
= $true )
| ( ( SV517
= ( relation_composition @ SV120 @ SV275 ) )
= $false )
| ( ( relation @ SV517 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3312]) ).
thf(3355,plain,
! [SV123: $i,SV424: $i,SV473: $i] :
( ( ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV473 )
= $false )
| ( ( in @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ SV424 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK34_D @ SV473 @ SV424 @ SV123 ) @ ( sK35_SY473 @ SV473 @ SV424 @ SV123 ) ) @ SV123 )
= $false )
| ( ( SV473
= ( relation_dom_restriction @ SV123 @ SV424 ) )
= $true )
| ( ( relation @ SV473 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3313]) ).
thf(3356,plain,
! [SV474: $i,SV123: $i,SV611: $i,SV425: $i,SV602: $i] :
( ( ( ~ ( in @ SV602 @ SV425 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV602 @ SV611 ) @ SV123 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV602 @ SV611 ) @ SV474 )
= $true )
| ( ( SV474
= ( relation_dom_restriction @ SV123 @ SV425 ) )
= $false )
| ( ( relation @ SV474 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3316]) ).
thf(3357,plain,
! [SV123: $i,SV425: $i,SV474: $i,SV621: $i] :
( ( ( ! [SY1173: $i] :
~ ( in @ ( ordered_pair @ SV621 @ SY1173 ) @ SV474 )
| ( in @ SV621 @ SV425 ) )
= $true )
| ( ( SV474
= ( relation_dom_restriction @ SV123 @ SV425 ) )
= $false )
| ( ( relation @ SV474 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3317]) ).
thf(3358,plain,
! [SV425: $i,SV123: $i,SV474: $i,SV622: $i] :
( ( ( ! [SY1174: $i] :
( ~ ( in @ ( ordered_pair @ SV622 @ SY1174 ) @ SV474 )
| ( in @ ( ordered_pair @ SV622 @ SY1174 ) @ SV123 ) ) )
= $true )
| ( ( SV474
= ( relation_dom_restriction @ SV123 @ SV425 ) )
= $false )
| ( ( relation @ SV474 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3318]) ).
thf(3359,plain,
! [SV480: $i,SV125: $i,SV573: $i,SV433: $i,SV605: $i] :
( ( ( in @ SV605 @ SV433 )
= $false )
| ( ( in @ ( ordered_pair @ SV605 @ SV573 ) @ SV125 )
= $false )
| ( ( in @ SV573 @ SV480 )
= $true )
| ( ( SV480
= ( relation_image @ SV125 @ SV433 ) )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3322]) ).
thf(3360,plain,
! [SV125: $i,SV433: $i,SV480: $i,SV574: $i] :
( ( ( in @ ( ordered_pair @ ( sK29_E @ SV574 @ SV480 @ SV433 @ SV125 ) @ SV574 ) @ SV125 )
= $true )
| ( ( in @ SV574 @ SV480 )
= $false )
| ( ( SV480
= ( relation_image @ SV125 @ SV433 ) )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3323]) ).
thf(3361,plain,
! [SV125: $i,SV433: $i,SV480: $i,SV574: $i] :
( ( ( in @ ( sK29_E @ SV574 @ SV480 @ SV433 @ SV125 ) @ SV433 )
= $true )
| ( ( in @ SV574 @ SV480 )
= $false )
| ( ( SV480
= ( relation_image @ SV125 @ SV433 ) )
= $false )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3324]) ).
thf(3362,plain,
! [SV484: $i,SV131: $i,SV576: $i,SV443: $i,SV606: $i] :
( ( ( in @ SV606 @ SV443 )
= $false )
| ( ( in @ ( ordered_pair @ SV576 @ SV606 ) @ SV131 )
= $false )
| ( ( in @ SV576 @ SV484 )
= $true )
| ( ( SV484
= ( relation_inverse_image @ SV131 @ SV443 ) )
= $false )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3326]) ).
thf(3363,plain,
! [SV131: $i,SV443: $i,SV484: $i,SV577: $i] :
( ( ( in @ ( ordered_pair @ SV577 @ ( sK26_E @ SV577 @ SV484 @ SV443 @ SV131 ) ) @ SV131 )
= $true )
| ( ( in @ SV577 @ SV484 )
= $false )
| ( ( SV484
= ( relation_inverse_image @ SV131 @ SV443 ) )
= $false )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3327]) ).
thf(3364,plain,
! [SV131: $i,SV443: $i,SV484: $i,SV577: $i] :
( ( ( in @ ( sK26_E @ SV577 @ SV484 @ SV443 @ SV131 ) @ SV443 )
= $true )
| ( ( in @ SV577 @ SV484 )
= $false )
| ( ( SV484
= ( relation_inverse_image @ SV131 @ SV443 ) )
= $false )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3328]) ).
thf(3365,plain,
! [SV230: $i,SV565: $i,SV137: $i] :
( ( ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SV565 @ SV230 ) ) )
= $false )
| ( ( in @ SV137 @ ( relation_dom @ SV565 ) )
= $true )
| ( ( function @ SV565 )
= $false )
| ( ( relation @ SV565 )
= $false )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3332]) ).
thf(3366,plain,
! [SV230: $i,SV566: $i,SV137: $i] :
( ( ( in @ SV137 @ ( relation_dom @ ( relation_composition @ SV566 @ SV230 ) ) )
= $false )
| ( ( in @ ( apply @ SV566 @ SV137 ) @ ( relation_dom @ SV230 ) )
= $true )
| ( ( function @ SV566 )
= $false )
| ( ( relation @ SV566 )
= $false )
| ( ( function @ SV230 )
= $false )
| ( ( relation @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3333]) ).
thf(3367,plain,
! [SV453: $i,SV510: $i] :
( ( ( in @ ( sK64_C @ SV510 @ SV453 ) @ SV510 )
= $false )
| ( ( in @ ( sK64_C @ SV510 @ SV453 ) @ ( sK65_SY495 @ SV510 @ SV453 ) )
= $false )
| ( ( SV510
= ( set_meet @ SV453 ) )
= $true )
| ( ( SV453 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3335]) ).
thf(3368,plain,
! [SV454: $i,SV511: $i,SV593: $i] :
( ( ( in @ ( sK63_D @ SV593 @ SV511 @ SV454 ) @ SV454 )
= $true )
| ( ( in @ SV593 @ SV511 )
= $true )
| ( ( SV511
= ( set_meet @ SV454 ) )
= $false )
| ( ( SV454 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3336]) ).
thf(3369,plain,
! [SV454: $i,SV511: $i,SV593: $i] :
( ( ( ~ ( in @ SV593 @ ( sK63_D @ SV593 @ SV511 @ SV454 ) ) )
= $true )
| ( ( in @ SV593 @ SV511 )
= $true )
| ( ( SV511
= ( set_meet @ SV454 ) )
= $false )
| ( ( SV454 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3337]) ).
thf(3370,plain,
! [SV511: $i,SV594: $i,SV454: $i,SV616: $i] :
( ( ( ~ ( in @ SV616 @ SV454 ) )
= $true )
| ( ( in @ SV594 @ SV616 )
= $true )
| ( ( in @ SV594 @ SV511 )
= $false )
| ( ( SV511
= ( set_meet @ SV454 ) )
= $false )
| ( ( SV454 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3338]) ).
thf(3371,plain,
! [SV464: $i,SV225: $i,SV599: $i,SV113: $i,SV609: $i] :
( ( ( in @ SV609 @ SV113 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV599 @ SV609 ) @ SV225 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV599 @ SV609 ) @ SV464 )
= $true )
| ( ( SV464
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $false )
| ( ( relation @ SV464 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3341]) ).
thf(3372,plain,
! [SV225: $i,SV113: $i,SV464: $i,SV623: $i,SV617: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV617 @ SV623 ) @ SV464 )
| ( in @ SV623 @ SV113 ) )
= $true )
| ( ( SV464
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $false )
| ( ( relation @ SV464 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3342]) ).
thf(3373,plain,
! [SV113: $i,SV225: $i,SV464: $i,SV624: $i,SV618: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV618 @ SV624 ) @ SV464 )
| ( in @ ( ordered_pair @ SV618 @ SV624 ) @ SV225 ) )
= $true )
| ( ( SV464
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $false )
| ( ( relation @ SV464 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3343]) ).
thf(3374,plain,
! [SV394: $i,SV335: $i,SV117: $i,SV582: $i,SV570: $i,SV548: $i] :
( ( ( SV548
= ( ordered_pair @ SV570 @ SV582 ) )
= $false )
| ( ( in @ SV570 @ SV117 )
= $false )
| ( ( in @ SV582 @ SV335 )
= $false )
| ( ( in @ SV548 @ SV394 )
= $true )
| ( ( SV394
= ( cartesian_product2 @ SV117 @ SV335 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3345]) ).
thf(3375,plain,
! [SV117: $i,SV335: $i,SV394: $i,SV549: $i] :
( ( ( in @ ( sK51_E @ SV549 @ SV394 @ SV335 @ SV117 ) @ SV117 )
= $true )
| ( ( in @ SV549 @ SV394 )
= $false )
| ( ( SV394
= ( cartesian_product2 @ SV117 @ SV335 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3346]) ).
thf(3376,plain,
! [SV117: $i,SV335: $i,SV394: $i,SV549: $i] :
( ( ( in @ ( sK52_SY488 @ SV549 @ SV394 @ SV335 @ SV117 ) @ SV335 )
= $true )
| ( ( in @ SV549 @ SV394 )
= $false )
| ( ( SV394
= ( cartesian_product2 @ SV117 @ SV335 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3347]) ).
thf(3377,plain,
! [SV613: $i,SV120: $i,SV275: $i,SV516: $i] :
( ( ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ SV613 ) @ SV120 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV613 @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV275 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV516 ) )
= $true )
| ( ( SV516
= ( relation_composition @ SV120 @ SV275 ) )
= $true )
| ( ( relation @ SV516 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3350]) ).
thf(3378,plain,
! [SV120: $i,SV275: $i,SV516: $i] :
( ( ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK15_SY461 @ SV516 @ SV275 @ SV120 ) ) @ SV120 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV516 )
= $true )
| ( ( SV516
= ( relation_composition @ SV120 @ SV275 ) )
= $true )
| ( ( relation @ SV516 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3351]) ).
thf(3379,plain,
! [SV120: $i,SV275: $i,SV516: $i] :
( ( ( in @ ( ordered_pair @ ( sK15_SY461 @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV275 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV516 )
= $true )
| ( ( SV516
= ( relation_composition @ SV120 @ SV275 ) )
= $true )
| ( ( relation @ SV516 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3352]) ).
thf(3380,plain,
! [SV517: $i,SV275: $i,SV619: $i,SV120: $i,SV614: $i] :
( ( ( ! [SY1172: $i] :
( ~ ( in @ ( ordered_pair @ SV614 @ SY1172 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SY1172 @ SV619 ) @ SV275 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV614 @ SV619 ) @ SV517 )
= $true )
| ( ( SV517
= ( relation_composition @ SV120 @ SV275 ) )
= $false )
| ( ( relation @ SV517 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3353]) ).
thf(3381,plain,
! [SV120: $i,SV275: $i,SV517: $i,SV620: $i,SV615: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV615 @ SV620 ) @ SV517 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV615 @ ( sK12_F @ SV620 @ SV615 @ SV517 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK12_F @ SV620 @ SV615 @ SV517 @ SV275 @ SV120 ) @ SV620 ) @ SV275 ) ) )
= $true )
| ( ( SV517
= ( relation_composition @ SV120 @ SV275 ) )
= $false )
| ( ( relation @ SV517 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3354]) ).
thf(3382,plain,
! [SV474: $i,SV123: $i,SV611: $i,SV425: $i,SV602: $i] :
( ( ( in @ SV602 @ SV425 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV602 @ SV611 ) @ SV123 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV602 @ SV611 ) @ SV474 )
= $true )
| ( ( SV474
= ( relation_dom_restriction @ SV123 @ SV425 ) )
= $false )
| ( ( relation @ SV474 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3356]) ).
thf(3383,plain,
! [SV123: $i,SV425: $i,SV474: $i,SV621: $i] :
( ( ( ! [SY1173: $i] :
~ ( in @ ( ordered_pair @ SV621 @ SY1173 ) @ SV474 ) )
= $true )
| ( ( in @ SV621 @ SV425 )
= $true )
| ( ( SV474
= ( relation_dom_restriction @ SV123 @ SV425 ) )
= $false )
| ( ( relation @ SV474 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3357]) ).
thf(3384,plain,
! [SV425: $i,SV123: $i,SV474: $i,SV625: $i,SV622: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV622 @ SV625 ) @ SV474 )
| ( in @ ( ordered_pair @ SV622 @ SV625 ) @ SV123 ) )
= $true )
| ( ( SV474
= ( relation_dom_restriction @ SV123 @ SV425 ) )
= $false )
| ( ( relation @ SV474 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3358]) ).
thf(3385,plain,
! [SV454: $i,SV511: $i,SV593: $i] :
( ( ( in @ SV593 @ ( sK63_D @ SV593 @ SV511 @ SV454 ) )
= $false )
| ( ( in @ SV593 @ SV511 )
= $true )
| ( ( SV511
= ( set_meet @ SV454 ) )
= $false )
| ( ( SV454 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3369]) ).
thf(3386,plain,
! [SV511: $i,SV594: $i,SV454: $i,SV616: $i] :
( ( ( in @ SV616 @ SV454 )
= $false )
| ( ( in @ SV594 @ SV616 )
= $true )
| ( ( in @ SV594 @ SV511 )
= $false )
| ( ( SV511
= ( set_meet @ SV454 ) )
= $false )
| ( ( SV454 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3370]) ).
thf(3387,plain,
! [SV464: $i,SV113: $i,SV225: $i,SV609: $i,SV599: $i] :
( ( ( in @ ( ordered_pair @ SV599 @ SV609 ) @ SV225 )
= $false )
| ( ( in @ SV609 @ SV113 )
= $false )
| ( ( in @ ( ordered_pair @ SV599 @ SV609 ) @ SV464 )
= $true )
| ( ( SV464
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $false )
| ( ( relation @ SV464 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3371]) ).
thf(3388,plain,
! [SV225: $i,SV113: $i,SV464: $i,SV623: $i,SV617: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV617 @ SV623 ) @ SV464 ) )
= $true )
| ( ( in @ SV623 @ SV113 )
= $true )
| ( ( SV464
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $false )
| ( ( relation @ SV464 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3372]) ).
thf(3389,plain,
! [SV113: $i,SV225: $i,SV464: $i,SV624: $i,SV618: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV618 @ SV624 ) @ SV464 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV618 @ SV624 ) @ SV225 )
= $true )
| ( ( SV464
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $false )
| ( ( relation @ SV464 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3373]) ).
thf(3390,plain,
! [SV120: $i,SV275: $i,SV516: $i,SV613: $i] :
( ( ( in @ ( ordered_pair @ SV613 @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV275 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ SV613 ) @ SV120 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV516 ) )
= $true )
| ( ( SV516
= ( relation_composition @ SV120 @ SV275 ) )
= $true )
| ( ( relation @ SV516 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3377]) ).
thf(3391,plain,
! [SV517: $i,SV275: $i,SV619: $i,SV120: $i,SV626: $i,SV614: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV614 @ SV626 ) @ SV120 )
| ~ ( in @ ( ordered_pair @ SV626 @ SV619 ) @ SV275 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV614 @ SV619 ) @ SV517 )
= $true )
| ( ( SV517
= ( relation_composition @ SV120 @ SV275 ) )
= $false )
| ( ( relation @ SV517 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3380]) ).
thf(3392,plain,
! [SV120: $i,SV275: $i,SV517: $i,SV620: $i,SV615: $i] :
( ( ( in @ ( ordered_pair @ SV615 @ SV620 ) @ SV517 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV615 @ ( sK12_F @ SV620 @ SV615 @ SV517 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK12_F @ SV620 @ SV615 @ SV517 @ SV275 @ SV120 ) @ SV620 ) @ SV275 ) ) )
= $true )
| ( ( SV517
= ( relation_composition @ SV120 @ SV275 ) )
= $false )
| ( ( relation @ SV517 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3381]) ).
thf(3393,plain,
! [SV474: $i,SV425: $i,SV123: $i,SV611: $i,SV602: $i] :
( ( ( in @ ( ordered_pair @ SV602 @ SV611 ) @ SV123 )
= $false )
| ( ( in @ SV602 @ SV425 )
= $false )
| ( ( in @ ( ordered_pair @ SV602 @ SV611 ) @ SV474 )
= $true )
| ( ( SV474
= ( relation_dom_restriction @ SV123 @ SV425 ) )
= $false )
| ( ( relation @ SV474 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3382]) ).
thf(3394,plain,
! [SV123: $i,SV425: $i,SV474: $i,SV627: $i,SV621: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV621 @ SV627 ) @ SV474 ) )
= $true )
| ( ( in @ SV621 @ SV425 )
= $true )
| ( ( SV474
= ( relation_dom_restriction @ SV123 @ SV425 ) )
= $false )
| ( ( relation @ SV474 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3383]) ).
thf(3395,plain,
! [SV425: $i,SV123: $i,SV474: $i,SV625: $i,SV622: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV622 @ SV625 ) @ SV474 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV622 @ SV625 ) @ SV123 )
= $true )
| ( ( SV474
= ( relation_dom_restriction @ SV123 @ SV425 ) )
= $false )
| ( ( relation @ SV474 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3384]) ).
thf(3396,plain,
! [SV225: $i,SV113: $i,SV464: $i,SV623: $i,SV617: $i] :
( ( ( in @ ( ordered_pair @ SV617 @ SV623 ) @ SV464 )
= $false )
| ( ( in @ SV623 @ SV113 )
= $true )
| ( ( SV464
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $false )
| ( ( relation @ SV464 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3388]) ).
thf(3397,plain,
! [SV113: $i,SV225: $i,SV464: $i,SV624: $i,SV618: $i] :
( ( ( in @ ( ordered_pair @ SV618 @ SV624 ) @ SV464 )
= $false )
| ( ( in @ ( ordered_pair @ SV618 @ SV624 ) @ SV225 )
= $true )
| ( ( SV464
= ( relation_rng_restriction @ SV113 @ SV225 ) )
= $false )
| ( ( relation @ SV464 )
= $false )
| ( ( relation @ SV225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3389]) ).
thf(3398,plain,
! [SV613: $i,SV120: $i,SV275: $i,SV516: $i] :
( ( ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV516 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK13_D @ SV516 @ SV275 @ SV120 ) @ SV613 ) @ SV120 )
= $false )
| ( ( in @ ( ordered_pair @ SV613 @ ( sK14_SY457 @ SV516 @ SV275 @ SV120 ) ) @ SV275 )
= $false )
| ( ( SV516
= ( relation_composition @ SV120 @ SV275 ) )
= $true )
| ( ( relation @ SV516 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3390]) ).
thf(3399,plain,
! [SV517: $i,SV275: $i,SV619: $i,SV120: $i,SV626: $i,SV614: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV614 @ SV626 ) @ SV120 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV626 @ SV619 ) @ SV275 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV614 @ SV619 ) @ SV517 )
= $true )
| ( ( SV517
= ( relation_composition @ SV120 @ SV275 ) )
= $false )
| ( ( relation @ SV517 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3391]) ).
thf(3400,plain,
! [SV120: $i,SV275: $i,SV517: $i,SV620: $i,SV615: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV615 @ ( sK12_F @ SV620 @ SV615 @ SV517 @ SV275 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK12_F @ SV620 @ SV615 @ SV517 @ SV275 @ SV120 ) @ SV620 ) @ SV275 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV615 @ SV620 ) @ SV517 )
= $false )
| ( ( SV517
= ( relation_composition @ SV120 @ SV275 ) )
= $false )
| ( ( relation @ SV517 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3392]) ).
thf(3401,plain,
! [SV123: $i,SV425: $i,SV474: $i,SV627: $i,SV621: $i] :
( ( ( in @ ( ordered_pair @ SV621 @ SV627 ) @ SV474 )
= $false )
| ( ( in @ SV621 @ SV425 )
= $true )
| ( ( SV474
= ( relation_dom_restriction @ SV123 @ SV425 ) )
= $false )
| ( ( relation @ SV474 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3394]) ).
thf(3402,plain,
! [SV425: $i,SV123: $i,SV474: $i,SV625: $i,SV622: $i] :
( ( ( in @ ( ordered_pair @ SV622 @ SV625 ) @ SV474 )
= $false )
| ( ( in @ ( ordered_pair @ SV622 @ SV625 ) @ SV123 )
= $true )
| ( ( SV474
= ( relation_dom_restriction @ SV123 @ SV425 ) )
= $false )
| ( ( relation @ SV474 )
= $false )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3395]) ).
thf(3403,plain,
! [SV517: $i,SV275: $i,SV619: $i,SV120: $i,SV626: $i,SV614: $i] :
( ( ( in @ ( ordered_pair @ SV614 @ SV626 ) @ SV120 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV626 @ SV619 ) @ SV275 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV614 @ SV619 ) @ SV517 )
= $true )
| ( ( SV517
= ( relation_composition @ SV120 @ SV275 ) )
= $false )
| ( ( relation @ SV517 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3399]) ).
thf(3404,plain,
! [SV120: $i,SV275: $i,SV517: $i,SV620: $i,SV615: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV615 @ ( sK12_F @ SV620 @ SV615 @ SV517 @ SV275 @ SV120 ) ) @ SV120 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV615 @ SV620 ) @ SV517 )
= $false )
| ( ( SV517
= ( relation_composition @ SV120 @ SV275 ) )
= $false )
| ( ( relation @ SV517 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3400]) ).
thf(3405,plain,
! [SV120: $i,SV275: $i,SV517: $i,SV615: $i,SV620: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK12_F @ SV620 @ SV615 @ SV517 @ SV275 @ SV120 ) @ SV620 ) @ SV275 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV615 @ SV620 ) @ SV517 )
= $false )
| ( ( SV517
= ( relation_composition @ SV120 @ SV275 ) )
= $false )
| ( ( relation @ SV517 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3400]) ).
thf(3406,plain,
! [SV517: $i,SV120: $i,SV614: $i,SV275: $i,SV619: $i,SV626: $i] :
( ( ( in @ ( ordered_pair @ SV626 @ SV619 ) @ SV275 )
= $false )
| ( ( in @ ( ordered_pair @ SV614 @ SV626 ) @ SV120 )
= $false )
| ( ( in @ ( ordered_pair @ SV614 @ SV619 ) @ SV517 )
= $true )
| ( ( SV517
= ( relation_composition @ SV120 @ SV275 ) )
= $false )
| ( ( relation @ SV517 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3403]) ).
thf(3407,plain,
! [SV120: $i,SV275: $i,SV517: $i,SV620: $i,SV615: $i] :
( ( ( in @ ( ordered_pair @ SV615 @ ( sK12_F @ SV620 @ SV615 @ SV517 @ SV275 @ SV120 ) ) @ SV120 )
= $true )
| ( ( in @ ( ordered_pair @ SV615 @ SV620 ) @ SV517 )
= $false )
| ( ( SV517
= ( relation_composition @ SV120 @ SV275 ) )
= $false )
| ( ( relation @ SV517 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3404]) ).
thf(3408,plain,
! [SV120: $i,SV275: $i,SV517: $i,SV615: $i,SV620: $i] :
( ( ( in @ ( ordered_pair @ ( sK12_F @ SV620 @ SV615 @ SV517 @ SV275 @ SV120 ) @ SV620 ) @ SV275 )
= $true )
| ( ( in @ ( ordered_pair @ SV615 @ SV620 ) @ SV517 )
= $false )
| ( ( SV517
= ( relation_composition @ SV120 @ SV275 ) )
= $false )
| ( ( relation @ SV517 )
= $false )
| ( ( relation @ SV275 )
= $false )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3405]) ).
thf(3409,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[656,3408,3407,3406,3402,3401,3398,3397,3396,3393,3387,3386,3385,3379,3378,3376,3375,3374,3368,3367,3366,3365,3364,3363,3362,3361,3360,3359,3355,3349,3348,3344,3340,3339,3334,3331,3330,3329,3325,3321,3320,3319,3315,3314,3306,3299,3298,3295,3294,3293,3290,3282,3281,3274,3258,3255,3254,3252,3251,3244,3243,3240,3239,3236,3235,3229,3228,3227,3221,3218,3217,3216,3213,3212,3210,3207,3206,3203,3200,3187,3180,3179,3176,3175,3169,3168,3167,3164,3161,3160,3157,3154,3145,3144,3134,3131,3129,3123,3121,3113,3099,3098,3096,3095,3077,3073,3068,3067,3052,3045,3028,3027,3022,3016,3000,2997,2978,2977,2969,2957,2954,2953,2950,2945,2944,2931,2930,2920,2904,2903,2882,2880,2879,2873,2872,2864,2863,2852,2849,2848,2847,2846,2837,2822,2817,2813,2806,2804,2803,2785,2784,2783,2760,2759,2758,2731,2730,2723,2722,2697,2687,2686,2685,2684,2642,2639,2622,2621,2620,2619,2609,2597,2593,2591,2577,2576,2560,2556,2555,2552,2551,2522,2521,2520,2515,2492,2491,2490,2487,2468,2467,2441,2437,2418,2383,2382,2378,2377,2367,2362,2361,2353,2351,2350,2340,2322,2305,2300,2261,2260,2253,2250,2249,2230,2229,2227,2226,2223,2222,2210,2162,2161,2158,2146,2145,2134,2133,2129,2128,2127,2126,2125,2124,2106,2105,2077,2076,2075,2074,2067,2066,2065,2062,2061,2060,2057,2056,2040,2039,2031,2030,2023,1990,1988,1987,1985,1984,1909,1906,1905,1903,1897,1895,1894,1885,1845,1752,1735,1734,1733,1728,1727,1724,1716,1715,1705,1703,1702,1700,1693,1673,1672,1636,1635,1601,1600,1567,1565,1564,1563,1562,1558,1557,1554,1553,1552,1550,1549,1547,1546,1544,1543,1540,1539,1536,1530,1526,1518,1517,1516,1515,1513,1512,1511,1510,1504,1502,1501,1500,1497,1490,1450,1449,1429,1426,1425,1392,1391,1388,1387,1368,1367,1358,1351,1345,1342,1333,1331,1329,1328,1309,1303,1297,1277,1138,1135,1123,1121,1120,1119,1110,1103,1096,1094,1093,1084,1069,977,973,972,971,970,968,964,960,959,947,937,927,919,901,873,784,766,744]) ).
thf(3410,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[3409]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU217+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n026.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 00:15:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.39 ......
% 0.20/0.45
% 0.20/0.45 No.of.Axioms: 221
% 0.20/0.45
% 0.20/0.45 Length.of.Defs: 0
% 0.20/0.45
% 0.20/0.45 Contains.Choice.Funs: false
% 0.20/0.50 ..............
% 0.20/0.57 (rf:2,axioms:194,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:223,loop_count:0,foatp_calls:0,translation:fof_full)...................................................................................................................................................................................................................................................................
% 13.36/13.55
% 13.36/13.55 ********************************
% 13.36/13.55 * All subproblems solved! *
% 13.36/13.55 ********************************
% 13.36/13.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:2,axioms:195,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:73,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:3409,loop_count:0,foatp_calls:1,translation:fof_full)
% 16.63/16.80
% 16.63/16.80 %**** Beginning of derivation protocol ****
% 16.63/16.80 % SZS output start CNFRefutation
% See solution above
% 16.63/16.82
% 16.63/16.82 %**** End of derivation protocol ****
% 16.63/16.82 %**** no. of clauses in derivation: 3383 ****
% 16.63/16.82 %**** clause counter: 3409 ****
% 16.63/16.82
% 16.63/16.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:2,axioms:195,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:73,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:3409,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------